Construction of Chained True Score Equipercentile Equatings under the Kernel Equating (KE) Framework and Their Relationship to Levine True Score Equating. Research Report. ETS RR-09-24

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2009-01-01

In this paper, we develop a new chained equipercentile equating procedure for the nonequivalent groups with anchor test (NEAT) design under the assumptions of the classical test theory model. This new equating is named chained true score equipercentile equating. We also apply the kernel equating framework to this equating design, resulting in a…

Empirical models for use in designing decompression procedures for space operations

NASA Technical Reports Server (NTRS)

Conkin, Johnny; Edwards, Benjamin F.; Waligora, James M.; Horrigan, David J., Jr.

1987-01-01

Empirical models for predicting the incidence of Type 1 altitude decompression sickness (DCS) and venous gas emboli (VGE) during space extravehicular activity (EVA), and for use in designing safe denitrogenation decompression procedures are developed. The models are parameterized using DCS and VGE incidence data from NASA and USAF manned altitude chamber decompression tests using 607 male and female subject tests. These models, and procedures for their use, consist of: (1) an exponential relaxation model and procedure for computing tissue nitrogen partial pressure resulting from a specified prebreathing and stepped decompression sequence; (2) a formula for calculating Tissue Ratio (TR), a tissue decompression stress index; (3) linear and Hill equation models for predicting the total incidence of VGE and DCS attendant with a particular TR; (4) graphs of cumulative DCS and VGE incidence (risk) versus EVA exposure time at any specified TR; and (5) two equations for calculating the average delay period for the initial detection of VGE or indication of Type 1 DCS in a group after a specific denitrogenation decompression procedure. Several examples of realistic EVA preparations are provided.

Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?

ERIC Educational Resources Information Center

Oud, Johan H. L.; Folmer, Henk

2011-01-01

This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…

Analysis of eccentric annular incompressible seals. II - Effects of eccentricity on rotordynamic coefficients

NASA Technical Reports Server (NTRS)

Nelson, C. C.; Nguyen, D. T.

1987-01-01

A new analysis procedure has been presented which solves for the flow variables of an annular pressure seal in which the rotor has a large static displacement (eccentricity) from the centered position. The present paper incorporates the solutions to investigate the effect of eccentricity on the rotordynamic coefficients. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody's friction factor equation. Perturbations of the flow variables yields a set of zeroth- and first-order equations. After integration of the zeroth-order equations, the resulting zeroth-order flow variables are used as input in the solution of the first-order equations. Further integration of the first order pressures yields the eccentric rotordynamic coefficients. The results from this procedure compare well with available experimental and theoretical data, with accuracy just as good or slightly better than the predictions based on a finite-element model.

Model Specification Searches Using Ant Colony Optimization Algorithms

ERIC Educational Resources Information Center

Marcoulides, George A.; Drezner, Zvi

2003-01-01

Ant colony optimization is a recently proposed heuristic procedure inspired by the behavior of real ants. This article applies the procedure to model specification searches in structural equation modeling and reports the results. The results demonstrate the capabilities of ant colony optimization algorithms for conducting automated searches.

Investigation of supersonic jet plumes using an improved two-equation turbulence model

NASA Technical Reports Server (NTRS)

Lakshmanan, B.; Abdol-Hamid, Khaled S.

1994-01-01

Supersonic jet plumes were studied using a two-equation turbulence model employing corrections for compressible dissipation and pressure-dilatation. A space-marching procedure based on an upwind numerical scheme was used to solve the governing equations and turbulence transport equations. The computed results indicate that two-equation models employing corrections for compressible dissipation and pressure-dilatation yield improved agreement with the experimental data. In addition, the numerical study demonstrates that the computed results are sensitive to the effect of grid refinement and insensitive to the type of velocity profiles used at the inflow boundary for the cases considered in the present study.

Calculation of three-dimensional compressible laminar and turbulent boundary layers. An implicit finite-difference procedure for solving the three-dimensional compressible laminar, transitional, and turbulent boundary-layer equations

NASA Technical Reports Server (NTRS)

Harris, J. E.

1975-01-01

An implicit finite-difference procedure is presented for solving the compressible three-dimensional boundary-layer equations. The method is second-order accurate, unconditionally stable (conditional stability for reverse cross flow), and efficient from the viewpoint of computer storage and processing time. The Reynolds stress terms are modeled by (1) a single-layer mixing length model and (2) a two-layer eddy viscosity model. These models, although simple in concept, accurately predicted the equilibrium turbulent flow for the conditions considered. Numerical results are compared with experimental wall and profile data for a cone at an angle of attack larger than the cone semiapex angle. These comparisons clearly indicate that the numerical procedure and turbulence models accurately predict the experimental data with as few as 21 nodal points in the plane normal to the wall boundary.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 1 is the Analysis Description, and describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Homogenization of Large-Scale Movement Models in Ecology

USGS Publications Warehouse

Garlick, M.J.; Powell, J.A.; Hooten, M.B.; McFarlane, L.R.

2011-01-01

A difficulty in using diffusion models to predict large scale animal population dispersal is that individuals move differently based on local information (as opposed to gradients) in differing habitat types. This can be accommodated by using ecological diffusion. However, real environments are often spatially complex, limiting application of a direct approach. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion and apply it to a simple model for chronic wasting disease in mule deer. Homogenization allows us to determine the impact of small scale (10-100 m) habitat variability on large scale (10-100 km) movement. The procedure generates asymptotic equations for solutions on the large scale with parameters defined by small-scale variation. The simplicity of this homogenization procedure is striking when compared to the multi-dimensional homogenization procedure for Fickian diffusion,and the method will be equally straightforward for more complex models. ?? 2010 Society for Mathematical Biology.

Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1993-01-01

Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

Case-Deletion Diagnostics for Nonlinear Structural Equation Models

ERIC Educational Resources Information Center

Lee, Sik-Yum; Lu, Bin

2003-01-01

In this article, a case-deletion procedure is proposed to detect influential observations in a nonlinear structural equation model. The key idea is to develop the diagnostic measures based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. An one-step pseudo approximation is proposed to reduce the…

A Review of Structural Equation Modeling Applications in Turkish Educational Science Literature, 2010-2015

ERIC Educational Resources Information Center

Karakaya-Ozyer, Kubra; Aksu-Dunya, Beyza

2018-01-01

Structural equation modeling (SEM) is one of the most popular multivariate statistical techniques in Turkish educational research. This study elaborates the SEM procedures employed by 75 educational research articles which were published from 2010 to 2015 in Turkey. After documenting and coding 75 academic papers, categorical frequencies and…

An Extension of IRT-Based Equating to the Dichotomous Testlet Response Theory Model

ERIC Educational Resources Information Center

Tao, Wei; Cao, Yi

2016-01-01

Current procedures for equating number-correct scores using traditional item response theory (IRT) methods assume local independence. However, when tests are constructed using testlets, one concern is the violation of the local item independence assumption. The testlet response theory (TRT) model is one way to accommodate local item dependence.…

Fitting Meta-Analytic Structural Equation Models with Complex Datasets

ERIC Educational Resources Information Center

Wilson, Sandra Jo; Polanin, Joshua R.; Lipsey, Mark W.

2016-01-01

A modification of the first stage of the standard procedure for two-stage meta-analytic structural equation modeling for use with large complex datasets is presented. This modification addresses two common problems that arise in such meta-analyses: (a) primary studies that provide multiple measures of the same construct and (b) the correlation…

Multilevel Structural Equation Models for the Analysis of Comparative Data on Educational Performance

ERIC Educational Resources Information Center

Goldstein, Harvey; Bonnet, Gerard; Rocher, Thierry

2007-01-01

The Programme for International Student Assessment comparative study of reading performance among 15-year-olds is reanalyzed using statistical procedures that allow the full complexity of the data structures to be explored. The article extends existing multilevel factor analysis and structural equation models and shows how this can extract richer…

A two-phase micromorphic model for compressible granular materials

NASA Astrophysics Data System (ADS)

Paolucci, Samuel; Li, Weiming; Powers, Joseph

2009-11-01

We introduce a new two-phase continuum model for compressible granular material based on micromorphic theory and treat it as a two-phase mixture with inner structure. By taking an appropriate number of moments of the local micro scale balance equations, the average phase balance equations result from a systematic averaging procedure. In addition to equations for mass, momentum and energy, the balance equations also include evolution equations for microinertia and microspin tensors. The latter equations combine to yield a general form of a compaction equation when the material is assumed to be isotropic. When non-linear and inertial effects are neglected, the generalized compaction equation reduces to that originally proposed by Bear and Nunziato. We use the generalized compaction equation to numerically model a mixture of granular high explosive and interstitial gas. One-dimensional shock tube and piston-driven solutions are presented and compared with experimental results and other known solutions.

Quantum integrability and functional equations

NASA Astrophysics Data System (ADS)

Volin, Dmytro

2010-03-01

In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.

Reconstruction of the modified discrete Langevin equation from persistent time series

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

Czechowski, Zbigniew

The discrete Langevin-type equation, which can describe persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data, with short and long-tail distributions, generated by different Langevin equations. Corrections due to the finite sampling rates were derived. For an exemplary meteorological time series, an appropriate Langevin equation, which constitutes a stochastic macroscopic model of the phenomenon, was reconstructed.

Semiconductor spintronics: The full matrix approach

NASA Astrophysics Data System (ADS)

Rossani, A.

2015-12-01

A new model, based on an asymptotic procedure for solving the spinor kinetic equations of electrons and phonons is proposed, which gives naturally the displaced Fermi-Dirac distribution function at the leading order. The balance equations for the electron number, energy density and momentum, plus the Poisson’s equation, constitute now a system of six equations. Moreover, two equations for the evolution of the spin densities are added, which account for a general dispersion relation.

Diagnostic Procedures for Detecting Nonlinear Relationships between Latent Variables

ERIC Educational Resources Information Center

Bauer, Daniel J.; Baldasaro, Ruth E.; Gottfredson, Nisha C.

2012-01-01

Structural equation models are commonly used to estimate relationships between latent variables. Almost universally, the fitted models specify that these relationships are linear in form. This assumption is rarely checked empirically, largely for lack of appropriate diagnostic techniques. This article presents and evaluates two procedures that can…

An asymptotic model in acoustics: acoustic drift equations.

PubMed

Vladimirov, Vladimir A; Ilin, Konstantin

2013-11-01

A rigorous asymptotic procedure with the Mach number as a small parameter is used to derive the equations of mean flows which coexist and are affected by the background acoustic waves in the limit of very high Reynolds number.

Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow

NASA Technical Reports Server (NTRS)

Harris, J. E.; Blanchard, D. K.

1982-01-01

A numerical algorithm and computer program are presented for solving the laminar, transitional, or turbulent two dimensional or axisymmetric compressible boundary-layer equations for perfect-gas flows. The governing equations are solved by an iterative three-point implicit finite-difference procedure. The software, program VGBLP, is a modification of the approach presented in NASA TR R-368 and NASA TM X-2458, respectively. The major modifications are: (1) replacement of the fourth-order Runge-Kutta integration technique with a finite-difference procedure for numerically solving the equations required to initiate the parabolic marching procedure; (2) introduction of the Blottner variable-grid scheme; (3) implementation of an iteration scheme allowing the coupled system of equations to be converged to a specified accuracy level; and (4) inclusion of an iteration scheme for variable-entropy calculations. These modifications to the approach presented in NASA TR R-368 and NASA TM X-2458 yield a software package with high computational efficiency and flexibility. Turbulence-closure options include either two-layer eddy-viscosity or mixing-length models. Eddy conductivity is modeled as a function of eddy viscosity through a static turbulent Prandtl number formulation. Several options are provided for specifying the static turbulent Prandtl number. The transitional boundary layer is treated through a streamwise intermittency function which modifies the turbulence-closure model. This model is based on the probability distribution of turbulent spots and ranges from zero to unity for laminar and turbulent flow, respectively. Several test cases are presented as guides for potential users of the software.

A new dimension of organizational justice: procedural voice.

PubMed

Jepsen, Denise; Rodwell, John

2009-10-01

Dimensionality of the Colquitt justice measures was investigated across a wide range of service occupations. Structural equation modeling of data from 410 survey respondents found support for the 4-factor model of justice (procedural, distributive, interpersonal, and informational), although significant improvement of model fit was obtained by including a new latent variable, "procedural voice," which taps employees' desire to express their views and feelings and influence results. The model was confirmed in a second sample (N = 505) in the same organization six months later.

Implicit marching solution of compressible viscous subsonic flow in planar and axisymmetric ducts. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Towne, C. E.; Hoffman, J. D.

1982-01-01

A new streamwise marching procedure was developed and coded for compressible viscous subsonic flow in planar or axisymmetric ducts with or without centerbodies. The continuity, streamwise momentum, cross-flow momentum, and energy equations are written in generalized orthogonal curvilinear coordinates. To allow the use of a marching procedure, second derivatives in the streamwise momentum equation are written as the sum of a known two dimensional imposed pressure field and an unknown one dimensional viscous correction. For turbulent flow, the Reynolds stress and heat flux terms are modeled using two-layer eddy viscosity turbulence models.

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

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-03-01

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

Use of Item Parceling in Structural Equation Modeling with Missing Data

ERIC Educational Resources Information Center

Orcan, Fatih

2013-01-01

Parceling is referred to as a procedure for computing sums or average scores across multiple items. Parcels instead of individual items are then used as indicators of latent factors in the structural equation modeling analysis (Bandalos 2002, 2008; Little et al., 2002; Yang, Nay, & Hoyle, 2010). Item parceling may be applied to alleviate some…

Influences of Family-Systems Intervention Practices on Parent-Child Interactions and Child Development

ERIC Educational Resources Information Center

Trivette, Carol M.; Dunst, Carl J.; Hamby, Deborah W.

2010-01-01

The extent to which the influences of family-systems intervention practices could be traced to variations in parent-child interactions and child development was investigated by meta-analytic structural equation modeling (MASEM). MASEM is a procedure for producing a weighted pooled correlation matrix and fitting a structural equation model to the…

Equating Multidimensional Tests under a Random Groups Design: A Comparison of Various Equating Procedures

ERIC Educational Resources Information Center

Lee, Eunjung

2013-01-01

The purpose of this research was to compare the equating performance of various equating procedures for the multidimensional tests. To examine the various equating procedures, simulated data sets were used that were generated based on a multidimensional item response theory (MIRT) framework. Various equating procedures were examined, including…

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

Burge, S.W.

This report describes the theory and structure of the FORCE2 flow program. The manual describes the governing model equations, solution procedure and their implementation in the computer program. FORCE2 is an extension of an existing B&V multidimensional, two-phase flow program. FORCE2 was developed for application to fluid beds by flow implementing a gas-solids modeling technology derived, in part, during a joint government -- industry research program, ``Erosion of FBC Heat Transfer Tubes,`` coordinated by Argonne National Laboratory. The development of FORCE2 was sponsored by ASEA-Babcock, an industry participant in this program. This manual is the principal documentation for the programmore » theory and organization. Program usage and post-processing of code predictions with the FORCE2 post-processor are described in a companion report, FORCE2 -- A Multidimensional Flow Program for Fluid Beds, User`s Guide. This manual is segmented into sections to facilitate its usage. In section 2.0, the mass and momentum conservation principles, the basis for the code, are presented. In section 3.0, the constitutive relations used in modeling gas-solids hydrodynamics are given. The finite-difference model equations are derived in section 4.0 and the solution procedures described in sections 5.0 and 6.0. Finally, the implementation of the model equations and solution procedure in FORCE2 is described in section 7.0.« less

Four-Dimensional Data Assimilation Using the Adjoint Method

NASA Astrophysics Data System (ADS)

Bao, Jian-Wen

The calculus of variations is used to confirm that variational four-dimensional data assimilation (FDDA) using the adjoint method can be implemented when the numerical model equations have a finite number of first-order discontinuous points. These points represent the on/off switches associated with physical processes, for which the Jacobian matrix of the model equation does not exist. Numerical evidence suggests that, in some situations when the adjoint method is used for FDDA, the temperature field retrieved using horizontal wind data is numerically not unique. A physical interpretation of this type of non-uniqueness of the retrieval is proposed in terms of energetics. The adjoint equations of a numerical model can also be used for model-parameter estimation. A general computational procedure is developed to determine the size and distribution of any internal model parameter. The procedure is then applied to a one-dimensional shallow -fluid model in the context of analysis-nudging FDDA: the weighting coefficients used by the Newtonian nudging technique are determined. The sensitivity of these nudging coefficients to the optimal objectives and constraints is investigated. Experiments of FDDA using the adjoint method are conducted using the dry version of the hydrostatic Penn State/NCAR mesoscale model (MM4) and its adjoint. The minimization procedure converges and the initialization experiment is successful. Temperature-retrieval experiments involving an assimilation of the horizontal wind are also carried out using the adjoint of MM4.

A deterministic model of electron transport for electron probe microanalysis

NASA Astrophysics Data System (ADS)

Bünger, J.; Richter, S.; Torrilhon, M.

2018-01-01

Within the last decades significant improvements in the spatial resolution of electron probe microanalysis (EPMA) were obtained by instrumental enhancements. In contrast, the quantification procedures essentially remained unchanged. As the classical procedures assume either homogeneity or a multi-layered structure of the material, they limit the spatial resolution of EPMA. The possibilities of improving the spatial resolution through more sophisticated quantification procedures are therefore almost untouched. We investigate a new analytical model (M 1-model) for the quantification procedure based on fast and accurate modelling of electron-X-ray-matter interactions in complex materials using a deterministic approach to solve the electron transport equations. We outline the derivation of the model from the Boltzmann equation for electron transport using the method of moments with a minimum entropy closure and present first numerical results for three different test cases (homogeneous, thin film and interface). Taking Monte Carlo as a reference, the results for the three test cases show that the M 1-model is able to reproduce the electron dynamics in EPMA applications very well. Compared to classical analytical models like XPP and PAP, the M 1-model is more accurate and far more flexible, which indicates the potential of deterministic models of electron transport to further increase the spatial resolution of EPMA.

Three-dimensional modeling, estimation, and fault diagnosis of spacecraft air contaminants.

PubMed

Narayan, A P; Ramirez, W F

1998-01-01

A description is given of the design and implementation of a method to track the presence of air contaminants aboard a spacecraft using an accurate physical model and of a procedure that would raise alarms when certain tolerance levels are exceeded. Because our objective is to monitor the contaminants in real time, we make use of a state estimation procedure that filters measurements from a sensor system and arrives at an optimal estimate of the state of the system. The model essentially consists of a convection-diffusion equation in three dimensions, solved implicitly using the principle of operator splitting, and uses a flowfield obtained by the solution of the Navier-Stokes equations for the cabin geometry, assuming steady-state conditions. A novel implicit Kalman filter has been used for fault detection, a procedure that is an efficient way to track the state of the system and that uses the sparse nature of the state transition matrices.

PDF approach for compressible turbulent reacting flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Tsai, Y.-L. P.; Raju, M. S.

1993-01-01

The objective of the present work is to develop a probability density function (pdf) turbulence model for compressible reacting flows for use with a CFD flow solver. The probability density function of the species mass fraction and enthalpy are obtained by solving a pdf evolution equation using a Monte Carlo scheme. The pdf solution procedure is coupled with a compressible CFD flow solver which provides the velocity and pressure fields. A modeled pdf equation for compressible flows, capable of capturing shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed, and an averaging procedure is developed to provide smooth Monte-Carlo solutions to ensure convergence. Two supersonic diffusion flames are studied using the proposed pdf model and the results are compared with experimental data; marked improvements over CFD solutions without pdf are observed. Preliminary applications of pdf to 3D flows are also reported.

Exact finite difference schemes for the non-linear unidirectional wave equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

Aircraft Airframe Cost Estimation Using a Random Coefficients Model

DTIC Science & Technology

1979-12-01

approach will also be used here. 2 Model Formulation Several different types of equations could be used for the basic form of the CER, such as linear ...5) Marcotte developed several CER’s for fighter aircraft airframes using the log- linear model . A plot of the residuals from the CER for recurring...of the natural logarithm. Ordinary Least Squares The ordinary least squares procedure starts with the equation for the general linear model . The

A coupled chemo-thermo-hygro-mechanical model of concrete at high temperature and failure analysis

NASA Astrophysics Data System (ADS)

Li, Xikui; Li, Rongtao; Schrefler, B. A.

2006-06-01

A hierarchical mathematical model for analyses of coupled chemo-thermo-hygro-mechanical behaviour in concretes at high temperature is presented. The concretes are modelled as unsaturated deforming reactive porous media filled with two immiscible pore fluids, i.e. the gas mixture and the liquid mixture, in immiscible-miscible levels. The thermo-induced desalination process is particularly integrated into the model. The chemical effects of both the desalination and the dehydration processes on the material damage and the degradation of the material strength are taken into account. The mathematical model consists of a set of coupled, partial differential equations governing the mass balance of the dry air, the mass balance of the water species, the mass balance of the matrix components dissolved in the liquid phases, the enthalpy (energy) balance and momentum balance of the whole medium mixture. The governing equations, the state equations for the model and the constitutive laws used in the model are given. A mixed weak form for the finite element solution procedure is formulated for the numerical simulation of chemo-thermo-hygro-mechanical behaviours. Special considerations are given to spatial discretization of hyperbolic equation with non-self-adjoint operator nature. Numerical results demonstrate the performance and the effectiveness of the proposed model and its numerical procedure in reproducing coupled chemo-thermo-hygro-mechanical behaviour in concretes subjected to fire and thermal radiation.

Models for nearly every occasion: Part III - One box decreasing emission models.

PubMed

Hewett, Paul; Ganser, Gary H

2017-11-01

New one box "well-mixed room" decreasing emission (DE) models are introduced that allow for local exhaust or local exhaust with filtered return, as well the recirculation of a filtered (or cleaned) portion of the general room ventilation. For each control device scenario, a steady state and transient model is presented. The transient equations predict the concentration at any time t after the application of a known mass of a volatile substance to a surface, and can be used to predict the task exposure profile, the average task exposure, as well as peak and short-term exposures. The steady state equations can be used to predict the "average concentration per application" that is reached whenever the substance is repeatedly applied. Whenever the beginning and end concentrations are expected to be zero (or near zero) the steady state equations can also be used to predict the average concentration for a single task with multiple applications during the task, or even a series of such tasks. The transient equations should be used whenever these criteria cannot be met. A structured calibration procedure is proposed that utilizes a mass balance approach. Depending upon the DE model selected, one or more calibration measurements are collected. Using rearranged versions of the steady state equations, estimates of the model variables-e.g., the mass of the substance applied during each application, local exhaust capture efficiency, and the various cleaning or filtration efficiencies-can be calculated. A new procedure is proposed for estimating the emission rate constant.

Generalized heat-transport equations: parabolic and hyperbolic models

NASA Astrophysics Data System (ADS)

Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio

2018-03-01

We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

PubMed

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

HIFU procedures at moderate intensities--effect of large blood vessels.

PubMed

Hariharan, P; Myers, M R; Banerjee, R K

2007-06-21

A three-dimensional computational model is presented for studying the efficacy of high-intensity focused ultrasound (HIFU) procedures targeted near large blood vessels. The analysis applies to procedures performed at intensities below the threshold for cavitation, boiling and highly nonlinear propagation, but high enough to increase tissue temperature a few degrees per second. The model is based upon the linearized KZK equation and the bioheat equation in tissue. In the blood vessel the momentum and energy equations are satisfied. The model is first validated in a tissue phantom, to verify the absence of bubble formation and nonlinear effects. Temperature rise and lesion-volume calculations are then shown for different beam locations and orientations relative to a large vessel. Both single and multiple ablations are considered. Results show that when the vessel is located within about a beam width (few mm) of the ultrasound beam, significant reduction in lesion volume is observed due to blood flow. However, for gaps larger than a beam width, blood flow has no major effect on the lesion formation. Under the clinically representative conditions considered, the lesion volume is reduced about 40% (relative to the no-flow case) when the beam is parallel to the blood vessel, compared to about 20% for a perpendicular orientation. Procedures involving multiple ablation sites are affected less by blood flow than single ablations. The model also suggests that optimally focused transducers can generate lesions that are significantly larger (>2 times) than the ones produced by highly focused beams.

HIFU procedures at moderate intensities—effect of large blood vessels

NASA Astrophysics Data System (ADS)

Hariharan, P.; Myers, M. R.; Banerjee, R. K.

2007-07-01

A three-dimensional computational model is presented for studying the efficacy of high-intensity focused ultrasound (HIFU) procedures targeted near large blood vessels. The analysis applies to procedures performed at intensities below the threshold for cavitation, boiling and highly nonlinear propagation, but high enough to increase tissue temperature a few degrees per second. The model is based upon the linearized KZK equation and the bioheat equation in tissue. In the blood vessel the momentum and energy equations are satisfied. The model is first validated in a tissue phantom, to verify the absence of bubble formation and nonlinear effects. Temperature rise and lesion-volume calculations are then shown for different beam locations and orientations relative to a large vessel. Both single and multiple ablations are considered. Results show that when the vessel is located within about a beam width (few mm) of the ultrasound beam, significant reduction in lesion volume is observed due to blood flow. However, for gaps larger than a beam width, blood flow has no major effect on the lesion formation. Under the clinically representative conditions considered, the lesion volume is reduced about 40% (relative to the no-flow case) when the beam is parallel to the blood vessel, compared to about 20% for a perpendicular orientation. Procedures involving multiple ablation sites are affected less by blood flow than single ablations. The model also suggests that optimally focused transducers can generate lesions that are significantly larger (>2 times) than the ones produced by highly focused beams.

A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models

NASA Technical Reports Server (NTRS)

Luo, Li-Shi

1998-01-01

A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.

Modeling rainfall infiltration on hillslopes using Flux-concentration relation and time compression approximation

NASA Astrophysics Data System (ADS)

Wang, Jie; Chen, Li; Yu, Zhongbo

2018-02-01

Rainfall infiltration on hillslopes is an important issue in hydrology, which is related to many environmental problems, such as flood, soil erosion, and nutrient and contaminant transport. This study aimed to improve the quantification of infiltration on hillslopes under both steady and unsteady rainfalls. Starting from Darcy's law, an analytical integral infiltrability equation was derived for hillslope infiltration by use of the flux-concentration relation. Based on this equation, a simple scaling relation linking the infiltration times on hillslopes and horizontal planes was obtained which is applicable for both small and large times and can be used to simplify the solution procedure of hillslope infiltration. The infiltrability equation also improved the estimation of ponding time for infiltration under rainfall conditions. For infiltration after ponding, the time compression approximation (TCA) was applied together with the infiltrability equation. To improve the computational efficiency, the analytical integral infiltrability equation was approximated with a two-term power-like function by nonlinear regression. Procedures of applying this approach to both steady and unsteady rainfall conditions were proposed. To evaluate the performance of the new approach, it was compared with the Green-Ampt model for sloping surfaces by Chen and Young (2006) and Richards' equation. The proposed model outperformed the sloping Green-Ampt, and both ponding time and infiltration predictions agreed well with the solutions of Richards' equation for various soil textures, slope angles, initial water contents, and rainfall intensities for both steady and unsteady rainfalls.

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

Metric versus observable operator representation, higher spin models

NASA Astrophysics Data System (ADS)

Fring, Andreas; Frith, Thomas

2018-02-01

We elaborate further on the metric representation that is obtained by transferring the time-dependence from a Hermitian Hamiltonian to the metric operator in a related non-Hermitian system. We provide further insight into the procedure on how to employ the time-dependent Dyson relation and the quasi-Hermiticity relation to solve time-dependent Hermitian Hamiltonian systems. By solving both equations separately we argue here that it is in general easier to solve the former. We solve the mutually related time-dependent Schrödinger equation for a Hermitian and non-Hermitian spin 1/2, 1 and 3/2 model with time-independent and time-dependent metric, respectively. In all models the overdetermined coupled system of equations for the Dyson map can be decoupled algebraic manipulations and reduces to simple linear differential equations and an equation that can be converted into the non-linear Ermakov-Pinney equation.

A numerical method for computing unsteady 2-D boundary layer flows

NASA Technical Reports Server (NTRS)

Krainer, Andreas

1988-01-01

A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results.

Numerical Simulations of STOVL Hot Gas Ingestion in Ground Proximity Using a Multigrid Solution Procedure

NASA Technical Reports Server (NTRS)

Wang, Gang

2003-01-01

A multi grid solution procedure for the numerical simulation of turbulent flows in complex geometries has been developed. A Full Multigrid-Full Approximation Scheme (FMG-FAS) is incorporated into the continuity and momentum equations, while the scalars are decoupled from the multi grid V-cycle. A standard kappa-Epsilon turbulence model with wall functions has been used to close the governing equations. The numerical solution is accomplished by solving for the Cartesian velocity components either with a traditional grid staggering arrangement or with a multiple velocity grid staggering arrangement. The two solution methodologies are evaluated for relative computational efficiency. The solution procedure with traditional staggering arrangement is subsequently applied to calculate the flow and temperature fields around a model Short Take-off and Vertical Landing (STOVL) aircraft hovering in ground proximity.

The structure of shock wave in a gas consisting of ideally elastic, rigid spherical molecules

NASA Technical Reports Server (NTRS)

Cheremisin, F. G.

1972-01-01

Principal approaches are examined to the theoretical study of the shock layer structure. The choice of a molecular model is discussed and three procedures are formulated. These include a numerical calculation method, solution of the kinetic relaxation equation, and solution of the Boltzmann equation.

A soil moisture accounting-procedure with a Richards' equation-based soil texture-dependent parameterization

USDA-ARS?s Scientific Manuscript database

Given a time series of potential evapotranspiration and rainfall data, there are at least two approaches for estimating vertical percolation rates. One approach involves solving Richards' equation (RE) with a plant uptake model. An alternative approach involves applying a simple soil moisture accoun...

Turbulence kinetic energy equation for dilute suspensions

NASA Technical Reports Server (NTRS)

Abou-Arab, T. W.; Roco, M. C.

1989-01-01

A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

Artificial Intelligence Procedures for Tree Taper Estimation within a Complex Vegetation Mosaic in Brazil

PubMed Central

Nunes, Matheus Henrique

2016-01-01

Tree stem form in native tropical forests is very irregular, posing a challenge to establishing taper equations that can accurately predict the diameter at any height along the stem and subsequently merchantable volume. Artificial intelligence approaches can be useful techniques in minimizing estimation errors within complex variations of vegetation. We evaluated the performance of Random Forest® regression tree and Artificial Neural Network procedures in modelling stem taper. Diameters and volume outside bark were compared to a traditional taper-based equation across a tropical Brazilian savanna, a seasonal semi-deciduous forest and a rainforest. Neural network models were found to be more accurate than the traditional taper equation. Random forest showed trends in the residuals from the diameter prediction and provided the least precise and accurate estimations for all forest types. This study provides insights into the superiority of a neural network, which provided advantages regarding the handling of local effects. PMID:27187074

Artificial Intelligence Procedures for Tree Taper Estimation within a Complex Vegetation Mosaic in Brazil.

PubMed

Nunes, Matheus Henrique; Görgens, Eric Bastos

2016-01-01

Tree stem form in native tropical forests is very irregular, posing a challenge to establishing taper equations that can accurately predict the diameter at any height along the stem and subsequently merchantable volume. Artificial intelligence approaches can be useful techniques in minimizing estimation errors within complex variations of vegetation. We evaluated the performance of Random Forest® regression tree and Artificial Neural Network procedures in modelling stem taper. Diameters and volume outside bark were compared to a traditional taper-based equation across a tropical Brazilian savanna, a seasonal semi-deciduous forest and a rainforest. Neural network models were found to be more accurate than the traditional taper equation. Random forest showed trends in the residuals from the diameter prediction and provided the least precise and accurate estimations for all forest types. This study provides insights into the superiority of a neural network, which provided advantages regarding the handling of local effects.

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

Control of Stochastic Master Equation Models of Genetic Regulatory Networks by Approximating Their Average Behavior

NASA Astrophysics Data System (ADS)

Umut Caglar, Mehmet; Pal, Ranadip

2010-10-01

The central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid.'' However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of data in the cellular level and probabilistic nature of interactions. Probabilistic models like Stochastic Master Equation (SME) or deterministic models like differential equations (DE) can be used to analyze these types of interactions. SME models based on chemical master equation (CME) can provide detailed representation of genetic regulatory system, but their use is restricted by the large data requirements and computational costs of calculations. The differential equations models on the other hand, have low calculation costs and much more adequate to generate control procedures on the system; but they are not adequate to investigate the probabilistic nature of interactions. In this work the success of the mapping between SME and DE is analyzed, and the success of a control policy generated by DE model with respect to SME model is examined. Index Terms--- Stochastic Master Equation models, Differential Equation Models, Control Policy Design, Systems biology

The use of the logistic model in space motion sickness prediction

NASA Technical Reports Server (NTRS)

Lin, Karl K.; Reschke, Millard F.

1987-01-01

The one-equation and the two-equation logistic models were used to predict subjects' susceptibility to motion sickness in KC-135 parabolic flights using data from other ground-based motion sickness tests. The results show that the logistic models correctly predicted substantially more cases (an average of 13 percent) in the data subset used for model building. Overall, the logistic models ranged from 53 to 65 percent predictions of the three endpoint parameters, whereas the Bayes linear discriminant procedure ranged from 48 to 65 percent correct for the cross validation sample.

Finite Element Modeling of Coupled Flexible Multibody Dynamics and Liquid Sloshing

DTIC Science & Technology

2006-09-01

tanks is presented. The semi-discrete combined solid and fluid equations of motions are integrated using a time- accurate parallel explicit solver...Incompressible fluid flow in a moving/deforming container including accurate modeling of the free-surface, turbulence, and viscous effects ...paper, a single computational code which uses a time- accurate explicit solution procedure is used to solve both the solid and fluid equations of

The computation of standard solar models

NASA Technical Reports Server (NTRS)

Ulrich, Roger K.; Cox, Arthur N.

1991-01-01

Procedures for calculating standard solar models with the usual simplifying approximations of spherical symmetry, no mixing except in the surface convection zone, no mass loss or gain during the solar lifetime, and no separation of elements by diffusion are described. The standard network of nuclear reactions among the light elements is discussed including rates, energy production and abundance changes. Several of the equation of state and opacity formulations required for the basic equations of mass, momentum and energy conservation are presented. The usual mixing-length convection theory is used for these results. Numerical procedures for calculating the solar evolution, and current evolution and oscillation frequency results for the present sun by some recent authors are given.

Finite difference model for aquifer simulation in two dimensions with results of numerical experiments

USGS Publications Warehouse

Trescott, Peter C.; Pinder, George Francis; Larson, S.P.

1976-01-01

The model will simulate ground-water flow in an artesian aquifer, a water-table aquifer, or a combined artesian and water-table aquifer. The aquifer may be heterogeneous and anisotropic and have irregular boundaries. The source term in the flow equation may include well discharge, constant recharge, leakage from confining beds in which the effects of storage are considered, and evapotranspiration as a linear function of depth to water. The theoretical development includes presentation of the appropriate flow equations and derivation of the finite-difference approximations (written for a variable grid). The documentation emphasizes the numerical techniques that can be used for solving the simultaneous equations and describes the results of numerical experiments using these techniques. Of the three numerical techniques available in the model, the strongly implicit procedure, in general, requires less computer time and has fewer numerical difficulties than do the iterative alternating direction implicit procedure and line successive overrelaxation (which includes a two-dimensional correction procedure to accelerate convergence). The documentation includes a flow chart, program listing, an example simulation, and sections on designing an aquifer model and requirements for data input. It illustrates how model results can be presented on the line printer and pen plotters with a program that utilizes the graphical display software available from the Geological Survey Computer Center Division. In addition the model includes options for reading input data from a disk and writing intermediate results on a disk.

Dimensions of Employee Compensation: Practical and Theoretical Implications for Superintendents.

ERIC Educational Resources Information Center

Young, I. Phillip

1997-01-01

Explores compensation practices fundamental to the school board/employee exchange relationship, using a sample of 615 midwestern superintendents. Employs an organizational justice model, focusing on its procedural and distributive dimensions. Explores procedural justice via market-rate earnings equations and distributive justice by examining…

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Direct computation of stochastic flow in reservoirs with uncertain parameters

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

Dainton, M.P.; Nichols, N.K.; Goldwater, M.H.

1997-01-15

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point andmore » to the field convariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data. 14 refs., 14 figs., 3 tabs.« less

Calculation of turbulence-driven secondary motion in ducts with arbitrary cross section

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

Calculation methods for turbulent duct flows are generalized for ducts with arbitrary cross-sections. The irregular physical geometry is transformed into a regular one in computational space, and the flow equations are solved with a finite-volume numerical procedure. The turbulent stresses are calculated with an algebraic stress model derived by simplifying model transport equations for the individual Reynolds stresses. Two variants of such a model are considered. These procedures enable the prediction of both the turbulence-driven secondary flow and the anisotropy of the Reynolds stresses, in contrast to some of the earlier calculation methods. Model predictions are compared to experimental data for developed flow in triangular duct, trapezoidal duct and a rod-bundle geometry. The correct trends are predicted, and the quantitative agreement is mostly fair. The simpler variant of the algebraic stress model procured better agreement with the measured data.

Probability density function approach for compressible turbulent reacting flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Tsai, Y.-L. P.; Raju, M. S.

1994-01-01

The objective of the present work is to extend the probability density function (PDF) tubulence model to compressible reacting flows. The proability density function of the species mass fractions and enthalpy are obtained by solving a PDF evolution equation using a Monte Carlo scheme. The PDF solution procedure is coupled with a compression finite-volume flow solver which provides the velocity and pressure fields. A modeled PDF equation for compressible flows, capable of treating flows with shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed. Two super sonic diffusion flames are studied using the proposed PDF model and the results are compared with experimental data; marked improvements over solutions without PDF are observed.

Generating Nonnormal Multivariate Data Using Copulas: Applications to SEM.

PubMed

Mair, Patrick; Satorra, Albert; Bentler, Peter M

2012-07-01

This article develops a procedure based on copulas to simulate multivariate nonnormal data that satisfy a prespecified variance-covariance matrix. The covariance matrix used can comply with a specific moment structure form (e.g., a factor analysis or a general structural equation model). Thus, the method is particularly useful for Monte Carlo evaluation of structural equation models within the context of nonnormal data. The new procedure for nonnormal data simulation is theoretically described and also implemented in the widely used R environment. The quality of the method is assessed by Monte Carlo simulations. A 1-sample test on the observed covariance matrix based on the copula methodology is proposed. This new test for evaluating the quality of a simulation is defined through a particular structural model specification and is robust against normality violations.

Modeling of flow systems for implementation under KATE

NASA Technical Reports Server (NTRS)

Whitlow, Jonathan E.

1990-01-01

The modeling of flow systems is a task currently being investigated at Kennedy Space Center in parallel with the development of the KATE artificial intelligence system used for monitoring diagnosis and control. Various aspects of the modeling issues are focussed on with particular emphasis on a water system scheduled for demonstration within the KATE environment in September of this year. LISP procedures were written to solve the continuity equations for three internal pressure nodes using Newton's method for simultaneous nonlinear equations.

Is the Wheeler-DeWitt equation more fundamental than the Schrödinger equation?

NASA Astrophysics Data System (ADS)

Shestakova, Tatyana P.

The Wheeler-DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the literature, the opinion that the Wheeler-DeWitt equation is even more fundamental than the basic equation of quantum theory, the Schrödinger equation. We still should remember that we are in the situation when no observational data can confirm or reject the fundamental status of the Wheeler-DeWitt equation, so we can give just indirect arguments in favor of or against it, grounded on mathematical consistency and physical relevance. I shall present the analysis of the situation and comparison of the standard Wheeler-DeWitt approach with the extended phase space approach to quantization of gravity. In my analysis, I suppose, first, that a future quantum theory of gravity must be applicable to all phenomena from the early universe to quantum effects in strong gravitational fields, in the latter case, the state of the observer (the choice of a reference frame) may appear to be significant. Second, I suppose that the equation for the wave function of the universe must not be postulated but derived by means of a mathematically consistent procedure, which exists in path integral quantization. When applying this procedure to any gravitating system, one should take into account features of gravity, namely, nontrivial spacetime topology and possible absence of asymptotic states. The Schrödinger equation has been derived early for cosmological models with a finite number of degrees of freedom, and just recently it has been found for the spherically symmetric model which is a simplest model with an infinite number of degrees of freedom. The structure of the Schrödinger equation and its general solution appears to be very similar in these cases. The obtained results give grounds to say that the Schrödinger equation retains its fundamental meaning in constructing quantum theory of gravity.

Logistic Achievement Test Scaling and Equating with Fixed versus Estimated Lower Asymptotes.

ERIC Educational Resources Information Center

Phillips, S. E.

This study compared the lower asymptotes estimated by the maximum likelihood procedures of the LOGIST computer program with those obtained via application of the Norton methodology. The study also compared the equating results from the three-parameter logistic model with those obtained from the equipercentile, Rasch, and conditional…

Enthalpy measurement of coal-derived liquids. Final report, April 1981-September 1983. [517 to 10342 kPa; 340 to 664 K

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

Kidnay, A.J.; Yesavage, V.F.

This report summarizes the results of experimental measurements of enthalpies for quinoline using a freon boil-off flow calorimeter, and an investigation of the applicability of cubic equations of state to correlating the enthalpy of coal-liquids. In Part A the compound quinoline is discussed. Process flow in the flow calorimeter, operational problems, and equipment modifications are described. Procedural modifications, including a new sample purification procedure, are described. Part B discusses the correlational effort. This includes a discussion of past correlational work and the difficulties associated with a general correlation for coal liquid enthalpy. In addition experimental data and computer generated predictionsmore » are presented. Three equations of state were used to predict vapor pressures and enthalpies for ten pure component systems previously studied in the lab. In general, the results were encouraging. All three equations were found to be effective in predicting both enthalpies and vapor pressures. In addition, the equations worked well when fit to mixture enthalpies. The Modified SRK equation was found to be superior to the other equations and modeled all properties for both associating and nonassociating systems well. The Modified SRK equation did have a drawback in that it was not readily generalized since it required two parameters which must be fit to data for best results. In sum, it was shown that a four parameter equation of state could be used successfully to correlate the enthalpy of coal-liquid model compounds.« less

Ensemble Averaged Probability Density Function (APDF) for Compressible Turbulent Reacting Flows

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2012-01-01

In this paper, we present a concept of the averaged probability density function (APDF) for studying compressible turbulent reacting flows. The APDF is defined as an ensemble average of the fine grained probability density function (FG-PDF) with a mass density weighting. It can be used to exactly deduce the mass density weighted, ensemble averaged turbulent mean variables. The transport equation for APDF can be derived in two ways. One is the traditional way that starts from the transport equation of FG-PDF, in which the compressible Navier- Stokes equations are embedded. The resulting transport equation of APDF is then in a traditional form that contains conditional means of all terms from the right hand side of the Navier-Stokes equations except for the chemical reaction term. These conditional means are new unknown quantities that need to be modeled. Another way of deriving the transport equation of APDF is to start directly from the ensemble averaged Navier-Stokes equations. The resulting transport equation of APDF derived from this approach appears in a closed form without any need for additional modeling. The methodology of ensemble averaging presented in this paper can be extended to other averaging procedures: for example, the Reynolds time averaging for statistically steady flow and the Reynolds spatial averaging for statistically homogeneous flow. It can also be extended to a time or spatial filtering procedure to construct the filtered density function (FDF) for the large eddy simulation (LES) of compressible turbulent reacting flows.

Automated smoother for the numerical decoupling of dynamics models.

PubMed

Vilela, Marco; Borges, Carlos C H; Vinga, Susana; Vasconcelos, Ana Tereza R; Santos, Helena; Voit, Eberhard O; Almeida, Jonas S

2007-08-21

Structure identification of dynamic models for complex biological systems is the cornerstone of their reverse engineering. Biochemical Systems Theory (BST) offers a particularly convenient solution because its parameters are kinetic-order coefficients which directly identify the topology of the underlying network of processes. We have previously proposed a numerical decoupling procedure that allows the identification of multivariate dynamic models of complex biological processes. While described here within the context of BST, this procedure has a general applicability to signal extraction. Our original implementation relied on artificial neural networks (ANN), which caused slight, undesirable bias during the smoothing of the time courses. As an alternative, we propose here an adaptation of the Whittaker's smoother and demonstrate its role within a robust, fully automated structure identification procedure. In this report we propose a robust, fully automated solution for signal extraction from time series, which is the prerequisite for the efficient reverse engineering of biological systems models. The Whittaker's smoother is reformulated within the context of information theory and extended by the development of adaptive signal segmentation to account for heterogeneous noise structures. The resulting procedure can be used on arbitrary time series with a nonstationary noise process; it is illustrated here with metabolic profiles obtained from in-vivo NMR experiments. The smoothed solution that is free of parametric bias permits differentiation, which is crucial for the numerical decoupling of systems of differential equations. The method is applicable in signal extraction from time series with nonstationary noise structure and can be applied in the numerical decoupling of system of differential equations into algebraic equations, and thus constitutes a rather general tool for the reverse engineering of mechanistic model descriptions from multivariate experimental time series.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Computation of high Reynolds number internal/external flows

NASA Technical Reports Server (NTRS)

Cline, M. C.; Wilmoth, R. G.

1981-01-01

A general, user oriented computer program, called VNAP2, has been developed to calculate high Reynolds number, internal/external flows. VNAP2 solves the two-dimensional, time-dependent Navier-Stokes equations. The turbulence is modeled with either a mixing-length, a one transport equation, or a two transport equation model. Interior grid points are computed using the explicit MacCormack scheme with special procedures to speed up the calculation in the fine grid. All boundary conditions are calculated using a reference plane characteristic scheme with the viscous terms treated as source terms. Several internal, and internal/external flow calculations are presented.

Computation of high Reynolds number internal/external flows

NASA Technical Reports Server (NTRS)

Cline, M. C.; Wilmoth, R. G.

1981-01-01

A general, user oriented computer program, called VNAP2, was developed to calculate high Reynolds number, internal/ external flows. The VNAP2 program solves the two dimensional, time dependent Navier-Stokes equations. The turbulence is modeled with either a mixing-length, a one transport equation, or a two transport equation model. Interior grid points are computed using the explicit MacCormack Scheme with special procedures to speed up the calculation in the fine grid. All boundary conditions are calculated using a reference plane characteristic scheme with the viscous terms treated as source terms. Several internal, external, and internal/external flow calculations are presented.

Computation of high Reynolds number internal/external flows

NASA Technical Reports Server (NTRS)

Cline, M. C.; Wilmoth, R. G.

1981-01-01

A general, user oriented computer program, called VNAF2, developed to calculate high Reynolds number internal/external flows is described. The program solves the two dimensional, time dependent Navier-Stokes equations. Turbulence is modeled with either a mixing length, a one transport equation, or a two transport equation model. Interior grid points are computed using the explicit MacCormack scheme with special procedures to speed up the calculation in the fine grid. All boundary conditions are calculated using a reference plane characteristic scheme with the viscous terms treated as source terms. Several internal, external, and internal/external flow calculations are presented.

Recursive Newton-Euler formulation of manipulator dynamics

NASA Technical Reports Server (NTRS)

Nasser, M. G.

1989-01-01

A recursive Newton-Euler procedure is presented for the formulation and solution of manipulator dynamical equations. The procedure includes rotational and translational joints and a topological tree. This model was verified analytically using a planar two-link manipulator. Also, the model was tested numerically against the Walker-Orin model using the Shuttle Remote Manipulator System data. The hinge accelerations obtained from both models were identical. The computational requirements of the model vary linearly with the number of joints. The computational efficiency of this method exceeds that of Walker-Orin methods. This procedure may be viewed as a considerable generalization of Armstrong's method. A six-by-six formulation is adopted which enhances both the computational efficiency and simplicity of the model.

Liouvillian propagators, Riccati equation and differential Galois theory

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo; Suazo, Erwin

2013-11-01

In this paper a Galoisian approach to building propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schrödinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation. As the main application of this approach we solve Ince’s differential equation through the Hamiltonian algebrization procedure and the Kovacic algorithm to find the propagator for a generalized harmonic oscillator. This propagator has applications which describe the process of degenerate parametric amplification in quantum optics and light propagation in a nonlinear anisotropic waveguide. Toy models of propagators inspired by integrable Riccati equations and integrable characteristic equations are also presented.

General phase spaces: from discrete variables to rotor and continuum limits

NASA Astrophysics Data System (ADS)

Albert, Victor V.; Pascazio, Saverio; Devoret, Michel H.

2017-12-01

We provide a basic introduction to discrete-variable, rotor, and continuous-variable quantum phase spaces, explaining how the latter two can be understood as limiting cases of the first. We extend the limit-taking procedures used to travel between phase spaces to a general class of Hamiltonians (including many local stabilizer codes) and provide six examples: the Harper equation, the Baxter parafermionic spin chain, the Rabi model, the Kitaev toric code, the Haah cubic code (which we generalize to qudits), and the Kitaev honeycomb model. We obtain continuous-variable generalizations of all models, some of which are novel. The Baxter model is mapped to a chain of coupled oscillators and the Rabi model to the optomechanical radiation pressure Hamiltonian. The procedures also yield rotor versions of all models, five of which are novel many-body extensions of the almost Mathieu equation. The toric and cubic codes are mapped to lattice models of rotors, with the toric code case related to U(1) lattice gauge theory.

Spatial averaging of a dissipative particle dynamics model for active suspensions

NASA Astrophysics Data System (ADS)

Panchenko, Alexander; Hinz, Denis F.; Fried, Eliot

2018-03-01

Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving-Kirkwood-Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.

A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

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

Chatterjee, Kausik, E-mail: kausik.chatterjee@aggiemail.usu.edu; Center for Atmospheric and Space Sciences, Utah State University, Logan, UT 84322; Roadcap, John R., E-mail: john.roadcap@us.af.mil

The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals ofmore » the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.« less

A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson-Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

NASA Astrophysics Data System (ADS)

Chatterjee, Kausik; Roadcap, John R.; Singh, Surendra

2014-11-01

The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson-Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.

Atmospheric model development in support of SEASAT. Volume 1: Summary of findings

NASA Technical Reports Server (NTRS)

Kesel, P. G.

1977-01-01

Atmospheric analysis and prediction models of varying (grid) resolution were developed. The models were tested using real observational data for the purpose of assessing the impact of grid resolution on short range numerical weather prediction. The discretionary model procedures were examined so that the computational viability of SEASAT data might be enhanced during the conduct of (future) sensitivity tests. The analysis effort covers: (1) examining the procedures for allowing data to influence the analysis; (2) examining the effects of varying the weights in the analysis procedure; (3) testing and implementing procedures for solving the minimization equation in an optimal way; (4) describing the impact of grid resolution on analysis; and (5) devising and implementing numerous practical solutions to analysis problems, generally.

The development of flux-split algorithms for flows with non-equilibrium thermodynamics and chemical reactions

NASA Technical Reports Server (NTRS)

Grossman, B.; Cinella, P.

1988-01-01

A finite-volume method for the numerical computation of flows with nonequilibrium thermodynamics and chemistry is presented. A thermodynamic model is described which simplifies the coupling between the chemistry and thermodynamics and also results in the retention of the homogeneity property of the Euler equations (including all the species continuity and vibrational energy conservation equations). Flux-splitting procedures are developed for the fully coupled equations involving fluid dynamics, chemical production and thermodynamic relaxation processes. New forms of flux-vector split and flux-difference split algorithms are embodied in a fully coupled, implicit, large-block structure, including all the species conservation and energy production equations. Several numerical examples are presented, including high-temperature shock tube and nozzle flows. The methodology is compared to other existing techniques, including spectral and central-differenced procedures, and favorable comparisons are shown regarding accuracy, shock-capturing and convergence rates.

A general equation to obtain multiple cut-off scores on a test from multinomial logistic regression.

PubMed

Bersabé, Rosa; Rivas, Teresa

2010-05-01

The authors derive a general equation to compute multiple cut-offs on a total test score in order to classify individuals into more than two ordinal categories. The equation is derived from the multinomial logistic regression (MLR) model, which is an extension of the binary logistic regression (BLR) model to accommodate polytomous outcome variables. From this analytical procedure, cut-off scores are established at the test score (the predictor variable) at which an individual is as likely to be in category j as in category j+1 of an ordinal outcome variable. The application of the complete procedure is illustrated by an example with data from an actual study on eating disorders. In this example, two cut-off scores on the Eating Attitudes Test (EAT-26) scores are obtained in order to classify individuals into three ordinal categories: asymptomatic, symptomatic and eating disorder. Diagnoses were made from the responses to a self-report (Q-EDD) that operationalises DSM-IV criteria for eating disorders. Alternatives to the MLR model to set multiple cut-off scores are discussed.

Turbulence Model Selection for Low Reynolds Number Flows

PubMed Central

2016-01-01

One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil’s surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Reθ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail. PMID:27104354

Turbulence Model Selection for Low Reynolds Number Flows.

PubMed

Aftab, S M A; Mohd Rafie, A S; Razak, N A; Ahmad, K A

2016-01-01

One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil's surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Reθ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail.

A Departmental Cost-Effectiveness Model.

ERIC Educational Resources Information Center

Holleman, Thomas, Jr.

In establishing a departmental cost-effectiveness model, the traditional cost-effectiveness model was discussed and equipped with a distant and deflation equation for both benefits and costs. Next, the economics of costing was examined and program costing procedures developed. Then, the model construct was described as it was structured around the…

A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method

PubMed Central

Kojic, Milos; Filipovic, Nenad; Tsuda, Akira

2012-01-01

A multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study. We call this procedure the mesoscopic bridging scale (MBS) method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models [G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249–274]. We derive the governing equations of the MBS method and show that the differential equations of motion of the mesoscale discrete particle model and finite element (FE) model are only coupled through the force terms. Based on this coupling, we express the finite element equations which rely on the Navier–Stokes and continuity equations, in a way that the internal nodal FE forces are evaluated using viscous stresses from the mesoscale model. The dissipative particle dynamics (DPD) method for the discrete particle mesoscale model is employed. The entire fluid domain is divided into a local domain and a global domain. Fluid flow in the local domain is modeled with both DPD and FE method, while fluid flow in the global domain is modeled by the FE method only. The MBS method is suitable for modeling complex (colloidal) fluid flows, where continuum methods are sufficiently accurate only in the large fluid domain, while small, local regions of particular interest require detailed modeling by mesoscopic discrete particles. Solved examples – simple Poiseuille and driven cavity flows illustrate the applicability of the proposed MBS method. PMID:23814322

One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes

DOE PAGES

Gabitto, Jorge; Tsouris, Costas

2018-01-19

Energy storage in porous capacitor materials, capacitive deionization (CDI) for water desalination, capacitive energy generation, geophysical applications, and removal of heavy ions from wastewater streams are some examples of processes where understanding of ionic transport processes in charged porous media is very important. In this work, one- and two-equation models are derived to simulate ionic transport processes in heterogeneous porous media comprising two different pore sizes. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A two-step volume averaging technique is used to derive the averaged transportmore » equations for multi-ionic systems without any further assumptions, such as thin electrical double layers or Donnan equilibrium. A comparison between both models is presented. The effective transport parameters for isotropic porous media are calculated by solving the corresponding closure problems. An approximate analytical procedure is proposed to solve the closure problems. Numerical and theoretical calculations show that the approximate analytical procedure yields adequate solutions. Lastly, a theoretical analysis shows that the value of interphase pseudo-transport coefficients determines which model to use.« less

One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes

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

Gabitto, Jorge; Tsouris, Costas

Energy storage in porous capacitor materials, capacitive deionization (CDI) for water desalination, capacitive energy generation, geophysical applications, and removal of heavy ions from wastewater streams are some examples of processes where understanding of ionic transport processes in charged porous media is very important. In this work, one- and two-equation models are derived to simulate ionic transport processes in heterogeneous porous media comprising two different pore sizes. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A two-step volume averaging technique is used to derive the averaged transportmore » equations for multi-ionic systems without any further assumptions, such as thin electrical double layers or Donnan equilibrium. A comparison between both models is presented. The effective transport parameters for isotropic porous media are calculated by solving the corresponding closure problems. An approximate analytical procedure is proposed to solve the closure problems. Numerical and theoretical calculations show that the approximate analytical procedure yields adequate solutions. Lastly, a theoretical analysis shows that the value of interphase pseudo-transport coefficients determines which model to use.« less

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the User's Guide, and describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Representing Sudden Shifts in Intensive Dyadic Interaction Data Using Differential Equation Models with Regime Switching.

PubMed

Chow, Sy-Miin; Ou, Lu; Ciptadi, Arridhana; Prince, Emily B; You, Dongjun; Hunter, Michael D; Rehg, James M; Rozga, Agata; Messinger, Daniel S

2018-06-01

A growing number of social scientists have turned to differential equations as a tool for capturing the dynamic interdependence among a system of variables. Current tools for fitting differential equation models do not provide a straightforward mechanism for diagnosing evidence for qualitative shifts in dynamics, nor do they provide ways of identifying the timing and possible determinants of such shifts. In this paper, we discuss regime-switching differential equation models, a novel modeling framework for representing abrupt changes in a system of differential equation models. Estimation was performed by combining the Kim filter (Kim and Nelson State-space models with regime switching: classical and Gibbs-sampling approaches with applications, MIT Press, Cambridge, 1999) and a numerical differential equation solver that can handle both ordinary and stochastic differential equations. The proposed approach was motivated by the need to represent discrete shifts in the movement dynamics of [Formula: see text] mother-infant dyads during the Strange Situation Procedure (SSP), a behavioral assessment where the infant is separated from and reunited with the mother twice. We illustrate the utility of a novel regime-switching differential equation model in representing children's tendency to exhibit shifts between the goal of staying close to their mothers and intermittent interest in moving away from their mothers to explore the room during the SSP. Results from empirical model fitting were supplemented with a Monte Carlo simulation study to evaluate the use of information criterion measures to diagnose sudden shifts in dynamics.

Modeling the behaviour of shape memory materials under large deformations

NASA Astrophysics Data System (ADS)

Rogovoy, A. A.; Stolbova, O. S.

2017-06-01

In this study, the models describing the behavior of shape memory alloys, ferromagnetic materials and polymers have been constructed, using a formalized approach to develop the constitutive equations for complex media under large deformations. The kinematic and constitutive equations, satisfying the principles of thermodynamics and objectivity, have been derived. The application of the Galerkin procedure to the systems of equations of solid mechanics allowed us to obtain the Lagrange variational equation and variational formulation of the magnetostatics problems. These relations have been tested in the context of the problems of finite deformation in shape memory alloys and ferromagnetic materials during forward and reverse martensitic transformations and in shape memory polymers during forward and reverse relaxation transitions from a highly elastic to a glassy state.

Computer code for off-design performance analysis of radial-inflow turbines with rotor blade sweep

NASA Technical Reports Server (NTRS)

Meitner, P. L.; Glassman, A. J.

1983-01-01

The analysis procedure of an existing computer program was extended to include rotor blade sweep, to model the flow more accurately at the rotor exit, and to provide more detail to the loss model. The modeling changes are described and all analysis equations and procedures are presented. Program input and output are described and are illustrated by an example problem. Results obtained from this program and from a previous program are compared with experimental data.

Probabilistic wind/tornado/missile analyses for hazard and fragility evaluations

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

Park, Y.J.; Reich, M.

Detailed analysis procedures and examples are presented for the probabilistic evaluation of hazard and fragility against high wind, tornado, and tornado-generated missiles. In the tornado hazard analysis, existing risk models are modified to incorporate various uncertainties including modeling errors. A significant feature of this paper is the detailed description of the Monte-Carlo simulation analyses of tornado-generated missiles. A simulation procedure, which includes the wind field modeling, missile injection, solution of flight equations, and missile impact analysis, is described with application examples.

The Effects of Representations, Constructivist Approaches, and Engagement on Middle School Students' Algebraic Procedure and Conceptual Understanding

ERIC Educational Resources Information Center

Ross, Amanda; Willson, Victor

2012-01-01

This study examined the effects of types of representations, constructivist teaching approaches, and student engagement on middle school algebra students' procedural knowledge and conceptual understanding. Data gathered from 16 video lessons and algebra pretest/posttests were used to run three multilevel structural equation models. Symbolic…

Approximate Single-Diode Photovoltaic Model for Efficient I-V Characteristics Estimation

PubMed Central

Ting, T. O.; Zhang, Nan; Guan, Sheng-Uei; Wong, Prudence W. H.

2013-01-01

Precise photovoltaic (PV) behavior models are normally described by nonlinear analytical equations. To solve such equations, it is necessary to use iterative procedures. Aiming to make the computation easier, this paper proposes an approximate single-diode PV model that enables high-speed predictions for the electrical characteristics of commercial PV modules. Based on the experimental data, statistical analysis is conducted to validate the approximate model. Simulation results show that the calculated current-voltage (I-V) characteristics fit the measured data with high accuracy. Furthermore, compared with the existing modeling methods, the proposed model reduces the simulation time by approximately 30% in this work. PMID:24298205

Automation of reliability evaluation procedures through CARE - The computer-aided reliability estimation program.

NASA Technical Reports Server (NTRS)

Mathur, F. P.

1972-01-01

Description of an on-line interactive computer program called CARE (Computer-Aided Reliability Estimation) which can model self-repair and fault-tolerant organizations and perform certain other functions. Essentially CARE consists of a repository of mathematical equations defining the various basic redundancy schemes. These equations, under program control, are then interrelated to generate the desired mathematical model to fit the architecture of the system under evaluation. The mathematical model is then supplied with ground instances of its variables and is then evaluated to generate values for the reliability-theoretic functions applied to the model.

Computer model of two-dimensional solute transport and dispersion in ground water

USGS Publications Warehouse

Konikow, Leonard F.; Bredehoeft, J.D.

1978-01-01

This report presents a model that simulates solute transport in flowing ground water. The model is both general and flexible in that it can be applied to a wide range of problem types. It is applicable to one- or two-dimensional problems involving steady-state or transient flow. The model computes changes in concentration over time caused by the processes of convective transport, hydrodynamic dispersion, and mixing (or dilution) from fluid sources. The model assumes that the solute is non-reactive and that gradients of fluid density, viscosity, and temperature do not affect the velocity distribution. However, the aquifer may be heterogeneous and (or) anisotropic. The model couples the ground-water flow equation with the solute-transport equation. The digital computer program uses an alternating-direction implicit procedure to solve a finite-difference approximation to the ground-water flow equation, and it uses the method of characteristics to solve the solute-transport equation. The latter uses a particle- tracking procedure to represent convective transport and a two-step explicit procedure to solve a finite-difference equation that describes the effects of hydrodynamic dispersion, fluid sources and sinks, and divergence of velocity. This explicit procedure has several stability criteria, but the consequent time-step limitations are automatically determined by the program. The report includes a listing of the computer program, which is written in FORTRAN IV and contains about 2,000 lines. The model is based on a rectangular, block-centered, finite difference grid. It allows the specification of any number of injection or withdrawal wells and of spatially varying diffuse recharge or discharge, saturated thickness, transmissivity, boundary conditions, and initial heads and concentrations. The program also permits the designation of up to five nodes as observation points, for which a summary table of head and concentration versus time is printed at the end of the calculations. The data input formats for the model require three data cards and from seven to nine data sets to describe the aquifer properties, boundaries, and stresses. The accuracy of the model was evaluated for two idealized problems for which analytical solutions could be obtained. In the case of one-dimensional flow the agreement was nearly exact, but in the case of plane radial flow a small amount of numerical dispersion occurred. An analysis of several test problems indicates that the error in the mass balance will be generally less than 10 percent. The test problems demonstrated that the accuracy and precision of the numerical solution is sensitive to the initial number of particles placed in each cell and to the size of the time increment, as determined by the stability criteria. Mass balance errors are commonly the greatest during the first several time increments, but tend to decrease and stabilize with time.

Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics

NASA Astrophysics Data System (ADS)

Ahmad, Iftikhar; Ahmad, Sufyan; Awais, Muhammad; Ul Islam Ahmad, Siraj; Asif Zahoor Raja, Muhammad

2018-05-01

The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.

HYDRA-II: A hydrothermal analysis computer code: Volume 3, Verification/validation assessments

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

McCann, R.A.; Lowery, P.S.

1987-10-01

HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite difference solution in cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equationsmore » for conservation of momentum are enhanced by the incorporation of directional porosities and permeabilities that aid in modeling solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits modeling of orthotropic physical properties and film resistances. Several automated procedures are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. Volume I - Equations and Numerics describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. Volume II - User's Manual contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a model problem. This volume, Volume III - Verification/Validation Assessments, provides a comparison between the analytical solution and the numerical simulation for problems with a known solution. This volume also documents comparisons between the results of simulations of single- and multiassembly storage systems and actual experimental data. 11 refs., 55 figs., 13 tabs.« less

Numerical analysis and FORTRAN program for the computation of the turbulent wakes of turbomachinery rotor blades, isolated airfoils and cascade of airfoils. Final Report - Ph.D. Thesis Mar. 1980

NASA Technical Reports Server (NTRS)

Hah, C.; Lakshminarayana, B.

1982-01-01

Turbulent wakes of turbomachinery rotor blades, isolated airfoils, and a cascade of airfoils were investigated both numerically and experimentally. Low subsonic and incompressible wake flows were examined. A finite difference procedure was employed in the numerical analysis utilizing the continuity, momentum, and turbulence closure equations in the rotating, curvilinear, and nonorthogonal coordinate system. A nonorthogonal curvilinear coordinate system was developed to improve the accuracy and efficiency of the numerical calculation. Three turbulence models were employed to obtain closure of the governing equations. The first model was comprised to transport equations for the turbulent kinetic energy and the rate of energy dissipation, and the second and third models were comprised of equations for the rate of turbulent kinetic energy dissipation and Reynolds stresses, respectively. The second model handles the convection and diffusion terms in the Reynolds stress transport equation collectively, while the third model handles them individually. The numerical results demonstrate that the second and third models provide accurate predictions, but the computer time and memory storage can be considerably saved with the second model.

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

NASA Technical Reports Server (NTRS)

Steger, J. L.; Caradonna, F. X.

1980-01-01

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

Neighboring extremal optimal control design including model mismatch errors

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

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

1994-11-01

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

Transfer function modeling of damping mechanisms in viscoelastic plates

NASA Technical Reports Server (NTRS)

Slater, J. C.; Inman, D. J.

1991-01-01

This work formulates a method for the modeling of material damping characteristics in plates. The Sophie German equation of classical plate theory is modified to incorporate hysteresis effects represented by complex stiffness using the transfer function approach proposed by Golla and Hughes, (1985). However, this procedure is not limited to this representation. The governing characteristic equation is decoupled through separation of variables, yielding a solution similar to that of undamped classical plate theory, allowing solution of the steady state as well as the transient response problem.

Solution of the classical Yang-Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model

NASA Astrophysics Data System (ADS)

Links, Jon

2017-03-01

Solutions of the classical Yang-Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang-Baxter equation, from which commuting transfer matrices may be constructed. This procedure is reviewed, specifically for solutions without skew-symmetry. A particular solution with an exotic symmetry is identified, which is not obtained as a limiting expansion of the usual Yang-Baxter equation. This solution facilitates the construction of commuting transfer matrices which will be used to establish the integrability of a multi-species boson tunnelling model. The model generalises the well-known two-site Bose-Hubbard model, to which it reduces in the one-species limit. Due to the lack of an apparent reference state, application of the algebraic Bethe Ansatz to solve the model is prohibitive. Instead, the Bethe Ansatz solution is obtained by the use of operator identities and tensor product decompositions.

A Comparison of Methods of Vertical Equating.

ERIC Educational Resources Information Center

Loyd, Brenda H.; Hoover, H. D.

Rasch model vertical equating procedures were applied to three mathematics computation tests for grades six, seven, and eight. Each level of the test was composed of 45 items in three sets of 15 items, arranged in such a way that tests for adjacent grades had two sets (30 items) in common, and the sixth and eighth grades had 15 items in common. In…

Solvable two-dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime

NASA Astrophysics Data System (ADS)

Fring, Andreas; Frith, Thomas

2018-06-01

We provide exact analytical solutions for a two-dimensional explicitly time-dependent non-Hermitian quantum system. While the time-independent variant of the model studied is in the broken PT-symmetric phase for the entire range of the model parameters, and has therefore a partially complex energy eigenspectrum, its time-dependent version has real energy expectation values at all times. In our solution procedure we compare the two equivalent approaches of directly solving the time-dependent Dyson equation with one employing the Lewis–Riesenfeld method of invariants. We conclude that the latter approach simplifies the solution procedure due to the fact that the invariants of the non-Hermitian and Hermitian system are related to each other in a pseudo-Hermitian fashion, which in turn does not hold for their corresponding time-dependent Hamiltonians. Thus constructing invariants and subsequently using the pseudo-Hermiticity relation between them allows to compute the Dyson map and to solve the Dyson equation indirectly. In this way one can bypass to solve nonlinear differential equations, such as the dissipative Ermakov–Pinney equation emerging in our and many other systems.

A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model

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

Samet Y. Kadioglu; Robert Nourgaliev; Nam Dinh

2011-10-01

We introduce a novel approach for the hyperbolization of the well-known two-phase six equation flow model. The six-equation model has been frequently used in many two-phase flow applications such as bubbly fluid flows in nuclear reactors. One major drawback of this model is that it can be arbitrarily non-hyperbolic resulting in difficulties such as numerical instability issues. Non-hyperbolic behavior can be associated with complex eigenvalues that correspond to characteristic matrix of the system. Complex eigenvalues are often due to certain flow parameter choices such as the definition of inter-facial pressure terms. In our method, we prevent the characteristic matrix receivingmore » complex eigenvalues by fine tuning the inter-facial pressure terms with an iterative procedure. In this way, the characteristic matrix possesses all real eigenvalues meaning that the characteristic wave speeds are all real therefore the overall two-phase flowmodel becomes hyperbolic. The main advantage of this is that one can apply less diffusive highly accurate high resolution numerical schemes that often rely on explicit calculations of real eigenvalues. We note that existing non-hyperbolic models are discretized mainly based on low order highly dissipative numerical techniques in order to avoid stability issues.« less

Annotated bibliography of structural equation modelling: technical work.

PubMed

Austin, J T; Wolfle, L M

1991-05-01

Researchers must be familiar with a variety of source literature to facilitate the informed use of structural equation modelling. Knowledge can be acquired through the study of an expanding literature found in a diverse set of publishing forums. We propose that structural equation modelling publications can be roughly classified into two groups: (a) technical and (b) substantive applications. Technical materials focus on the procedures rather than substantive conclusions derived from applications. The focus of this article is the former category; included are foundational/major contributions, minor contributions, critical and evaluative reviews, integrations, simulations and computer applications, precursor and historical material, and pedagogical textbooks. After a brief introduction, we annotate 294 articles in the technical category dating back to Sewall Wright (1921).

Numerical solutions of the Navier-Stokes equations for transonic afterbody flows

NASA Technical Reports Server (NTRS)

Swanson, R. C., Jr.

1980-01-01

The time dependent Navier-Stokes equations in mass averaged variables are solved for transonic flow over axisymmetric boattail plume simulator configurations. Numerical solution of these equations is accomplished with the unsplit explict finite difference algorithm of MacCormack. A grid subcycling procedure and computer code vectorization are used to improve computational efficiency. The two layer algebraic turbulence models of Cebeci-Smith and Baldwin-Lomax are employed for investigating turbulence closure. Two relaxation models based on these baseline models are also considered. Results in the form of surface pressure distribution for three different circular arc boattails at two free stream Mach numbers are compared with experimental data. The pressures in the recirculating flow region for all separated cases are poorly predicted with the baseline turbulence models. Significant improvements in the predictions are usually obtained by using the relaxation models.

Empirical solution of Green-Ampt equation using soil conservation service - curve number values

NASA Astrophysics Data System (ADS)

Grimaldi, S.; Petroselli, A.; Romano, N.

2012-09-01

The Soil Conservation Service - Curve Number (SCS-CN) method is a popular widely used rainfall-runoff model for quantifying the total stream-flow volume generated by storm rainfall, but its application is not appropriate for sub-daily resolutions. In order to overcome this drawback, the Green-Ampt (GA) infiltration equation is considered and an empirical solution is proposed and evaluated. The procedure, named CN4GA (Curve Number for Green-Ampt), aims to calibrate the Green-Ampt model parameters distributing in time the global information provided by the SCS-CN method. The proposed procedure is evaluated by analysing observed rainfall-runoff events; results show that CN4GA seems to provide better agreement with the observed hydrographs respect to the classic SCS-CN method.

Occupational/Career Decision-Making Thought Processes of Adolescents of High Intellectual Ability

ERIC Educational Resources Information Center

Jung, Jae Yup

2017-01-01

Three competing models of the career decision-making thought processes of adolescents of high intellectual ability were tested in this study. Survey data were collected from 664 intellectually gifted Australian adolescents and analyzed using structural equation modeling procedures. The finally accepted, optimal model suggested that, regardless of…

Mediation in dyadic data at the level of the dyads: a Structural Equation Modeling approach.

PubMed

Ledermann, Thomas; Macho, Siegfried

2009-10-01

An extended version of the Common Fate Model (CFM) is presented to estimate and test mediation in dyadic data. The model can be used for distinguishable dyad members (e.g., heterosexual couples) or indistinguishable dyad members (e.g., homosexual couples) if (a) the variables measure characteristics of the dyadic relationship or shared external influences that affect both partners; if (b) the causal associations between the variables should be analyzed at the dyadic level; and if (c) the measured variables are reliable indicators of the latent variables. To assess mediation using Structural Equation Modeling, a general three-step procedure is suggested. The first is a selection of a good fitting model, the second a test of the direct effects, and the third a test of the mediating effect by means of bootstrapping. The application of the model along with the procedure for assessing mediation is illustrated using data from 184 couples on marital problems, communication, and marital quality. Differences with the Actor-Partner Interdependence Model and the analysis of longitudinal mediation by using the CFM are discussed.

Standard Errors of Equating for the Percentile Rank-Based Equipercentile Equating with Log-Linear Presmoothing

ERIC Educational Resources Information Center

Wang, Tianyou

2009-01-01

Holland and colleagues derived a formula for analytical standard error of equating using the delta-method for the kernel equating method. Extending their derivation, this article derives an analytical standard error of equating procedure for the conventional percentile rank-based equipercentile equating with log-linear smoothing. This procedure is…

Toroidal gyrofluid equations for simulations of tokamak turbulence

NASA Astrophysics Data System (ADS)

Beer, M. A.; Hammett, G. W.

1996-11-01

A set of nonlinear gyrofluid equations for simulations of tokamak turbulence are derived by taking moments of the nonlinear toroidal gyrokinetic equation. The moment hierarchy is closed with approximations that model the kinetic effects of parallel Landau damping, toroidal drift resonances, and finite Larmor radius effects. These equations generalize the work of Dorland and Hammett [Phys. Fluids B 5, 812 (1993)] to toroidal geometry by including essential toroidal effects. The closures for phase mixing from toroidal ∇B and curvature drifts take the basic form presented in Waltz et al. [Phys. Fluids B 4, 3138 (1992)], but here a more rigorous procedure is used, including an extension to higher moments, which provides significantly improved accuracy. In addition, trapped ion effects and collisions are incorporated. This reduced set of nonlinear equations accurately models most of the physics considered important for ion dynamics in core tokamak turbulence, and is simple enough to be used in high resolution direct numerical simulations.

Contact Stress Analysis of Spiral Bevel Gears Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Kumar, A; Reddy, S.; Handschuh, R.

1995-01-01

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

A Mechanobiological model for damage-induced growth in arterial tissue with application to in-stent restenosis

NASA Astrophysics Data System (ADS)

Fereidoonnezhad, B.; Naghdabadi, R.; Sohrabpour, S.; Holzapfel, G. A.

In-stent restenosis (ISR) is one of the main drawbacks of stent implementation which limits the long-term success of the procedure. Morphological changes occurring within the arterial wall due to stent-induced mechanical injury are a major cause for activation of vascular smooth muscle cells (VSMCs), and the subsequent development of ISR. Considering the theory of volumetric mass growth and adopting a multiplicative decomposition of the deformation gradient into an elastic part and a growth part, we present a mechanobiological model for ISR. An evolution equation is developed for mass growth of the neointima, in which the activation of VSMCs due to stent-induced damage (injury) and the proliferation rate of the activated cells are considered. By introducing the mass evolution into the mass balance equation, we obtain the evolution of the growth tensor over time. The model is implemented in a finite element code and the procedure of angioplasty is simulated, whereby the features of the proposed growth model are illustrated.

On the dynamics of chain systems. [applications in manipulator and human body models

NASA Technical Reports Server (NTRS)

Huston, R. L.; Passerello, C. E.

1974-01-01

A computer-oriented method for obtaining dynamical equations of motion for chain systems is presented. A chain system is defined as an arbitrarily assembled set of rigid bodies such that adjoining bodies have at least one common point and such that closed loops are not formed. The equations of motion are developed through the use of Lagrange's form of d'Alembert's principle. The method and procedure is illustrated with an elementary study of a tripod space manipulator. The method is designed for application with systems such as human body models, chains and cables, and dynamic finite-segment models.

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

2007-01-01

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

A shallow water model for the propagation of tsunami via Lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Zergani, Sara; Aziz, Z. A.; Viswanathan, K. K.

2015-01-01

An efficient implementation of the lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g. tsunami), based on the nonlinear shallow water (NSW) wave equation is presented. The LBM is an alternative numerical procedure for the description of incompressible hydrodynamics and has the potential to serve as an efficient solver for incompressible flows in complex geometries. This work proposes the NSW equations for the irrotational surface waves in the case of complex bottom elevation. In recent time, equation involving shallow water is the current norm in modelling tsunami operations which include the propagation zone estimation. Several test-cases are presented to verify our model. Some implications to tsunami wave modelling are also discussed. Numerical results are found to be in excellent agreement with theory.

Viscoelastic tides: models for use in Celestial Mechanics

NASA Astrophysics Data System (ADS)

Ragazzo, C.; Ruiz, L. S.

2017-05-01

This paper contains equations for the motion of linear viscoelastic bodies interacting under gravity. The equations are fully three dimensional and allow for the integration of the spin, the orbit, and the deformation of each body. The goal is to present good models for the tidal forces that take into account the possibly different rheology of each body. The equations are obtained within a finite dimension Lagrangian framework with dissipation function. The main contribution is a procedure to associate to each spring-dashpot model, which defines the rheology of a body, a potential and a dissipation function for the body deformation variables. The theory is applied to the Earth (solid part plus oceans) and a comparison between model and observation of the following quantities is made: norm of the Love numbers, rate of tidal energy dissipation, Chandler period, and Earth-Moon distance increase.

A quantitative approach to aquifer vulnerability mapping

NASA Astrophysics Data System (ADS)

Connell, L. D.; Daele, Gerd van den

2003-05-01

This paper presents a procedure for calculating the transport to groundwater of surface-released contaminants. The approach is derived from a series of analytical and semi-analytical solutions to the advection-dispersion equation that include root zone and unsaturated water movement effects on the transport process. The steady-state form of these equations provides an efficient means of calculating the maximum concentration at the watertable and therefore has potential for use in vulnerability mapping. A two-layer approach is used in the solutions to represent the unsaturated profile, with the root zone corresponding to the upper layer where evapotranspiration can occur and transport properties can be in contrast to the rest of the profile. A novel transformation is applied to the advection-dispersion equation that considerably simplifies the way in which water movement is represented. To provide a combined flow and transport model an approximate procedure for water movement, using averages of the infiltration and transpiration rates with a novel, simple, quasi-steady state solution, is presented that can be used in conjunction with the solutions to the advection-dispersion equation. This quasi-steady state approximation for water movement allows for layering in the soil profile and root water uptake. Results from the combined quasi-steady state water movement and semi-analytical solute transport procedure compare well with numerical solutions to the coupled unsaturated flow and solute transport equations in a series of hypothetical simulations.

Numerical Modeling of Unsteady Thermofluid Dynamics in Cryogenic Systems

NASA Technical Reports Server (NTRS)

Majumdar, Alok

2003-01-01

A finite volume based network analysis procedure has been applied to model unsteady flow without and with heat transfer. Liquid has been modeled as compressible fluid where the compressibility factor is computed from the equation of state for a real fluid. The modeling approach recognizes that the pressure oscillation is linked with the variation of the compressibility factor; therefore, the speed of sound does not explicitly appear in the governing equations. The numerical results of chilldown process also suggest that the flow and heat transfer are strongly coupled. This is evident by observing that the mass flow rate during 90-second chilldown process increases by factor of ten.

Modeling of transient heat pipe operation

NASA Technical Reports Server (NTRS)

Colwell, G. T.; Hartley, J. G.

1986-01-01

Mathematical models and associated solution procedures which can be used to design heat pipe cooled structures for use on hypersonic vehicles are being developed. The models should also have the capability to predict off-design performance for a variety of operating conditions. It is expected that the resulting models can be used to predict startup behavior of liquid metal heat pipes to be used in reentry vehicles, hypersonic aircraft, and space nuclear reactors. Work to date related to numerical solutions of governing differential equations for the outer shell and the combination capillary structure and working fluid is summarized. Finite element numerical equations using both implicit, explicit, and combination methods were examined.

Effect of liquid droplets on turbulence in a round gaseous jet

NASA Technical Reports Server (NTRS)

Mostafa, A. A.; Elghobashi, S. E.

1986-01-01

The main objective of this investigation is to develop a two-equation turbulence model for dilute vaporizing sprays or in general for dispersed two-phase flows including the effects of phase changes. The model that accounts for the interaction between the two phases is based on rigorously derived equations for turbulence kinetic energy (K) and its dissipation rate epsilon of the carrier phase using the momentum equation of that phase. Closure is achieved by modeling the turbulent correlations, up to third order, in the equations of the mean motion, concentration of the vapor in the carrier phase, and the kinetic energy of turbulence and its dissipation rate for the carrier phase. The governing equations are presented in both the exact and the modeled formes. The governing equations are solved numerically using a finite-difference procedure to test the presented model for the flow of a turbulent axisymmetric gaseous jet laden with either evaporating liquid droplets or solid particles. The predictions include the distribution of the mean velocity, volume fractions of the different phases, concentration of the evaporated material in the carrier phase, turbulence intensity and shear stress of the carrier phase, droplet diameter distribution, and the jet spreading rate. The predictions are in good agreement with the experimental data.

Combination of Alternative Models by Mutual Data Assimilation: Supermodeling With A Suite of Primitive Equation Models

NASA Astrophysics Data System (ADS)

Duane, G. S.; Selten, F.

2016-12-01

Different models of climate and weather commonly give projections/predictions that differ widely in their details. While averaging of model outputs almost always improves results, nonlinearity implies that further improvement can be obtained from model interaction in run time, as has already been demonstrated with toy systems of ODEs and idealized quasigeostrophic models. In the supermodeling scheme, models effectively assimilate data from one another and partially synchronize with one another. Spread among models is manifest as a spread in possible inter-model connection coefficients, so that the models effectively "agree to disagree". Here, we construct a supermodel formed from variants of the SPEEDO model, a primitive-equation atmospheric model (SPEEDY) coupled to ocean and land. A suite of atmospheric models, coupled to the same ocean and land, is chosen to represent typical differences among climate models by varying model parameters. Connections are introduced between all pairs of corresponding independent variables at synoptic-scale intervals. Strengths of the inter-atmospheric connections can be considered to represent inverse inter-model observation error. Connection strengths are adapted based on an established procedure that extends the dynamical equations of a pair of synchronizing systems to synchronize parameters as well. The procedure is applied to synchronize the suite of SPEEDO models with another SPEEDO model regarded as "truth", adapting the inter-model connections along the way. The supermodel with trained connections gives marginally lower error in all fields than any weighted combination of the separate model outputs when used in "weather-prediction mode", i.e. with constant nudging to truth. Stronger results are obtained if a supermodel is used to predict the formation of coherent structures or the frequency of such. Partially synchronized SPEEDO models give a better representation of the blocked-zonal index cycle than does a weighted average of the constituent model outputs. We have thus shown that supermodeling and the synchronization-based procedure to adapt inter-model connections give results superior to output averaging not only with highly nonlinear toy systems, but with smaller nonlinearities as occur in climate models.

Turbulence modeling

NASA Technical Reports Server (NTRS)

Bardina, Jorge E.

1995-01-01

The objective of this work is to develop, verify, and incorporate the baseline two-equation turbulence models which account for the effects of compressibility into the three-dimensional Reynolds averaged Navier-Stokes (RANS) code and to provide documented descriptions of the models and their numerical procedures so that they can be implemented into 3-D CFD codes for engineering applications.

A parameter study of the two-fluid solar wind

NASA Technical Reports Server (NTRS)

Sandbaek, Ornulf; Leer, Egil; Holzer, Thomas E.

1992-01-01

A two-fluid model of the solar wind was introduced by Sturrock and Hartle (1966) and Hartle and Sturrock (1968). In these studies the proton energy equation was integrated neglecting the heat conductive term. Later several authors solved the equations for the two-fluid solar wind model keeping the proton heat conductive term. Methods where the equations are integrated simultaneously outward and inward from the critical point were used. The equations were also integrated inward from a large heliocentric distance. These methods have been applied to cases with low coronal base electron densities and high base temperatures. In this paper we present a method of integrating the two-fluid solar wind equations using an iteration procedure where the equations are integrated separately and the proton flux is kept constant during the integrations. The technique is applicable for a wide range of coronal base densities and temperatures. The method is used to carry out a parameter study of the two-fluid solar wind.

DEAN: A program for dynamic engine analysis

NASA Technical Reports Server (NTRS)

Sadler, G. G.; Melcher, K. J.

1985-01-01

The Dynamic Engine Analysis program, DEAN, is a FORTRAN code implemented on the IBM/370 mainframe at NASA Lewis Research Center for digital simulation of turbofan engine dynamics. DEAN is an interactive program which allows the user to simulate engine subsystems as well as a full engine systems with relative ease. The nonlinear first order ordinary differential equations which define the engine model may be solved by one of four integration schemes, a second order Runge-Kutta, a fourth order Runge-Kutta, an Adams Predictor-Corrector, or Gear's method for still systems. The numerical data generated by the model equations are displayed at specified intervals between which the user may choose to modify various parameters affecting the model equations and transient execution. Following the transient run, versatile graphics capabilities allow close examination of the data. DEAN's modeling procedure and capabilities are demonstrated by generating a model of simple compressor rig.

Smoothed particle hydrodynamics method from a large eddy simulation perspective

NASA Astrophysics Data System (ADS)

Di Mascio, A.; Antuono, M.; Colagrossi, A.; Marrone, S.

2017-03-01

The Smoothed Particle Hydrodynamics (SPH) method, often used for the modelling of the Navier-Stokes equations by a meshless Lagrangian approach, is revisited from the point of view of Large Eddy Simulation (LES). To this aim, the LES filtering procedure is recast in a Lagrangian framework by defining a filter that moves with the positions of the fluid particles at the filtered velocity. It is shown that the SPH smoothing procedure can be reinterpreted as a sort of LES Lagrangian filtering, and that, besides the terms coming from the LES convolution, additional contributions (never accounted for in the SPH literature) appear in the equations when formulated in a filtered fashion. Appropriate closure formulas are derived for the additional terms and a preliminary numerical test is provided to show the main features of the proposed LES-SPH model.

A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.

PubMed

DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

2016-12-01

Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions. Copyright © 2016 Elsevier Inc. All rights reserved.

On the Development of an Efficient Parallel Hybrid Solver with Application to Acoustically Treated Aero-Engine Nacelles

NASA Technical Reports Server (NTRS)

Watson, Willie R.; Nark, Douglas M.; Nguyen, Duc T.; Tungkahotara, Siroj

2006-01-01

A finite element solution to the convected Helmholtz equation in a nonuniform flow is used to model the noise field within 3-D acoustically treated aero-engine nacelles. Options to select linear or cubic Hermite polynomial basis functions and isoparametric elements are included. However, the key feature of the method is a domain decomposition procedure that is based upon the inter-mixing of an iterative and a direct solve strategy for solving the discrete finite element equations. This procedure is optimized to take full advantage of sparsity and exploit the increased memory and parallel processing capability of modern computer architectures. Example computations are presented for the Langley Flow Impedance Test facility and a rectangular mapping of a full scale, generic aero-engine nacelle. The accuracy and parallel performance of this new solver are tested on both model problems using a supercomputer that contains hundreds of central processing units. Results show that the method gives extremely accurate attenuation predictions, achieves super-linear speedup over hundreds of CPUs, and solves upward of 25 million complex equations in a quarter of an hour.

SEM with Missing Data and Unknown Population Distributions Using Two-Stage ML: Theory and Its Application

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Lu, Laura

2008-01-01

This article provides the theory and application of the 2-stage maximum likelihood (ML) procedure for structural equation modeling (SEM) with missing data. The validity of this procedure does not require the assumption of a normally distributed population. When the population is normally distributed and all missing data are missing at random…

A Simple Classroom Simulation of Heat Energy Diffusing through a Metal Bar

ERIC Educational Resources Information Center

Kinsler, Mark; Kinzel, Evelyn

2007-01-01

We present an iterative procedure that does not rely on calculus to model heat flow through a uniform bar of metal and thus avoids the use of the partial differential equation typically needed to describe heat diffusion. The procedure is based on first principles and can be done with students at the blackboard. It results in a plot that…

External validation of a forest inventory and analysis volume equation and comparisons with estimates from multiple stem-profile models

Treesearch

Christopher M. Oswalt; Adam M. Saunders

2009-01-01

Sound estimation procedures are desideratum for generating credible population estimates to evaluate the status and trends in resource conditions. As such, volume estimation is an integral component of the U.S. Department of Agriculture, Forest Service, Forest Inventory and Analysis (FIA) program's reporting. In effect, reliable volume estimation procedures are...

Simulation of Two-Fluid Flows by the Least-Squares Finite Element Method Using a Continuum Surface Tension Model

NASA Technical Reports Server (NTRS)

Wu, Jie; Yu, Sheng-Tao; Jiang, Bo-nan

1996-01-01

In this paper a numerical procedure for simulating two-fluid flows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols and the continuum surface force (CSF) model developed by Brackbill, et al. In the VOF method fluids of different properties are identified through the use of a continuous field variable (color function). The color function assigns a unique constant (color) to each fluid. The interfaces between different fluids are distinct due to sharp gradients of the color function. The evolution of the interfaces is captured by solving the convective equation of the color function. The CSF model is used as a means to treat surface tension effect at the interfaces. Here a modified version of the CSF model, proposed by Jacqmin, is used to calculate the tension force. In the modified version, the force term is obtained by calculating the divergence of a stress tensor defined by the gradient of the color function. In its analytical form, this stress formulation is equivalent to the original CSF model. Numerically, however, the use of the stress formulation has some advantages over the original CSF model, as it bypasses the difficulty in approximating the curvatures of the interfaces. The least-squares finite element method (LSFEM) is used to discretize the governing equation systems. The LSFEM has proven to be effective in solving incompressible Navier-Stokes equations and pure convection equations, making it an ideal candidate for the present applications. The LSFEM handles all the equations in a unified manner without any additional special treatment such as upwinding or artificial dissipation. Various bench mark tests have been carried out for both two dimensional planar and axisymmetric flows, including a dam breaking, oscillating and stationary bubbles and a conical liquid sheet in a pressure swirl atomizer.

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Kumar, A.; Reddy, S.; Handschuh, R.

1993-01-01

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1976-01-01

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Investigation of Low-Reynolds-Number Rocket Nozzle Design Using PNS-Based Optimization Procedure

NASA Technical Reports Server (NTRS)

Hussaini, M. Moin; Korte, John J.

1996-01-01

An optimization approach to rocket nozzle design, based on computational fluid dynamics (CFD) methodology, is investigated for low-Reynolds-number cases. This study is undertaken to determine the benefits of this approach over those of classical design processes such as Rao's method. A CFD-based optimization procedure, using the parabolized Navier-Stokes (PNS) equations, is used to design conical and contoured axisymmetric nozzles. The advantage of this procedure is that it accounts for viscosity during the design process; other processes make an approximated boundary-layer correction after an inviscid design is created. Results showed significant improvement in the nozzle thrust coefficient over that of the baseline case; however, the unusual nozzle design necessitates further investigation of the accuracy of the PNS equations for modeling expanding flows with thick laminar boundary layers.

Simplified multiple scattering model for radiative transfer in turbid water

NASA Technical Reports Server (NTRS)

Ghovanlou, A. H.; Gupta, G. N.

1978-01-01

Quantitative analytical procedures for relating selected water quality parameters to the characteristics of the backscattered signals, measured by remote sensors, require the solution of the radiative transport equation in turbid media. Presented is an approximate closed form solution of this equation and based on this solution, the remote sensing of sediments is discussed. The results are compared with other standard closed form solutions such as quasi-single scattering approximations.

Representing general theoretical concepts in structural equation models: The role of composite variables

USGS Publications Warehouse

Grace, J.B.; Bollen, K.A.

2008-01-01

Structural equation modeling (SEM) holds the promise of providing natural scientists the capacity to evaluate complex multivariate hypotheses about ecological systems. Building on its predecessors, path analysis and factor analysis, SEM allows for the incorporation of both observed and unobserved (latent) variables into theoretically-based probabilistic models. In this paper we discuss the interface between theory and data in SEM and the use of an additional variable type, the composite. In simple terms, composite variables specify the influences of collections of other variables and can be helpful in modeling heterogeneous concepts of the sort commonly of interest to ecologists. While long recognized as a potentially important element of SEM, composite variables have received very limited use, in part because of a lack of theoretical consideration, but also because of difficulties that arise in parameter estimation when using conventional solution procedures. In this paper we present a framework for discussing composites and demonstrate how the use of partially-reduced-form models can help to overcome some of the parameter estimation and evaluation problems associated with models containing composites. Diagnostic procedures for evaluating the most appropriate and effective use of composites are illustrated with an example from the ecological literature. It is argued that an ability to incorporate composite variables into structural equation models may be particularly valuable in the study of natural systems, where concepts are frequently multifaceted and the influence of suites of variables are often of interest. ?? Springer Science+Business Media, LLC 2007.

The Interface Between Theory and Data in Structural Equation Models

USGS Publications Warehouse

Grace, James B.; Bollen, Kenneth A.

2006-01-01

Structural equation modeling (SEM) holds the promise of providing natural scientists the capacity to evaluate complex multivariate hypotheses about ecological systems. Building on its predecessors, path analysis and factor analysis, SEM allows for the incorporation of both observed and unobserved (latent) variables into theoretically based probabilistic models. In this paper we discuss the interface between theory and data in SEM and the use of an additional variable type, the composite, for representing general concepts. In simple terms, composite variables specify the influences of collections of other variables and can be helpful in modeling general relationships of the sort commonly of interest to ecologists. While long recognized as a potentially important element of SEM, composite variables have received very limited use, in part because of a lack of theoretical consideration, but also because of difficulties that arise in parameter estimation when using conventional solution procedures. In this paper we present a framework for discussing composites and demonstrate how the use of partially reduced form models can help to overcome some of the parameter estimation and evaluation problems associated with models containing composites. Diagnostic procedures for evaluating the most appropriate and effective use of composites are illustrated with an example from the ecological literature. It is argued that an ability to incorporate composite variables into structural equation models may be particularly valuable in the study of natural systems, where concepts are frequently multifaceted and the influences of suites of variables are often of interest.

Accuracy in parameter estimation for targeted effects in structural equation modeling: sample size planning for narrow confidence intervals.

PubMed

Lai, Keke; Kelley, Ken

2011-06-01

In addition to evaluating a structural equation model (SEM) as a whole, often the model parameters are of interest and confidence intervals for those parameters are formed. Given a model with a good overall fit, it is entirely possible for the targeted effects of interest to have very wide confidence intervals, thus giving little information about the magnitude of the population targeted effects. With the goal of obtaining sufficiently narrow confidence intervals for the model parameters of interest, sample size planning methods for SEM are developed from the accuracy in parameter estimation approach. One method plans for the sample size so that the expected confidence interval width is sufficiently narrow. An extended procedure ensures that the obtained confidence interval will be no wider than desired, with some specified degree of assurance. A Monte Carlo simulation study was conducted that verified the effectiveness of the procedures in realistic situations. The methods developed have been implemented in the MBESS package in R so that they can be easily applied by researchers. © 2011 American Psychological Association

Kullback-Leibler information function and the sequential selection of experiments to discriminate among several linear models. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Sidik, S. M.

1972-01-01

A sequential adaptive experimental design procedure for a related problem is studied. It is assumed that a finite set of potential linear models relating certain controlled variables to an observed variable is postulated, and that exactly one of these models is correct. The problem is to sequentially design most informative experiments so that the correct model equation can be determined with as little experimentation as possible. Discussion includes: structure of the linear models; prerequisite distribution theory; entropy functions and the Kullback-Leibler information function; the sequential decision procedure; and computer simulation results. An example of application is given.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

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

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Multi criteria evaluation for universal soil loss equation based on geographic information system

NASA Astrophysics Data System (ADS)

Purwaamijaya, I. M.

2018-05-01

The purpose of this research were to produce(l) a conceptual, functional model designed and implementation for universal soil loss equation (usle), (2) standard operational procedure for multi criteria evaluation of universal soil loss equation (usle) using geographic information system, (3) overlay land cover, slope, soil and rain fall layers to gain universal soil loss equation (usle) using multi criteria evaluation, (4) thematic map of universal soil loss equation (usle) in watershed, (5) attribute table of universal soil loss equation (usle) in watershed. Descriptive and formal correlation methods are used for this research. Cikapundung Watershed, Bandung, West Java, Indonesia was study location. This research was conducted on January 2016 to May 2016. A spatial analysis is used to superimposed land cover, slope, soil and rain layers become universal soil loss equation (usle). Multi criteria evaluation for universal soil loss equation (usle) using geographic information system could be used for conservation program.

A New Unsteady Model for Dense Cloud Cavitation in Cryogenic Fluids

NASA Technical Reports Server (NTRS)

Hosangadi, Ashvin; Ahuja, Vineet

2005-01-01

Contents include the following: Background on thermal effects in cavitation. Physical properties of hydrogen. Multi-phase cavitation with thermal effect. Solution procedure. Cavitation model overview. Cavitation source terms. New cavitation model. Source term for bubble growth. One equation les model. Unsteady ogive simulations: liquid nitrogen. Unsteady incompressible flow in a pipe. Time averaged cavity length for NACA15 flowfield.

Alternative Models for Small Samples in Psychological Research: Applying Linear Mixed Effects Models and Generalized Estimating Equations to Repeated Measures Data

ERIC Educational Resources Information Center

Muth, Chelsea; Bales, Karen L.; Hinde, Katie; Maninger, Nicole; Mendoza, Sally P.; Ferrer, Emilio

2016-01-01

Unavoidable sample size issues beset psychological research that involves scarce populations or costly laboratory procedures. When incorporating longitudinal designs these samples are further reduced by traditional modeling techniques, which perform listwise deletion for any instance of missing data. Moreover, these techniques are limited in their…

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models. [separated turbulent boundary layer flow problems

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Maccormack, R. W.; Deiwert, G. S.

1975-01-01

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

A boundary integral approach in primitive variables for free surface flows

NASA Astrophysics Data System (ADS)

Casciola, C.; Piva, R.

The boundary integral formulation, very efficient for free surface potential flows, was considered for its possible extension to rotational flows either inviscid or viscous. We first analyze a general formulation for unsteady Navier-Stokes equations in primitive variables, which reduces to a representation for the Euler equations in the limiting case of Reynolds infinity. A first simplified model for rotational flows, obtained by decoupling kinematics and dynamics, reduces the integral equations to a known kinematical form whose mathematical and numerical properties have been studied. The dynamics equations to complete the model are obtained for the free surface and the wake. A simple and efficient scheme for the study of the non linear evolution of the wave system and its interaction with the body wake is presented. A steady state version for the calculation of the wave resistance is also reported. A second model was proposed for the simulation of rotational separated regions, by coupling the integral equations in velocity with an integral equation for the vorticity at the body boundary. The same procedure may be extended to include the diffusion of the vorticity in the flowfield. The vortex shedding from a cylindrical body in unsteady motion is discussed, as a first application of the model.

The role of spurious correlation in the development of a komatiite alteration model

NASA Astrophysics Data System (ADS)

Butler, John C.

1986-11-01

Procedures for detecting alterations in komatiites are described. The research of Pearson (1897) on spurious correlation and of Chayes (1949, 1971) on ratio correlation is reviewed. The equations for the ratio correlation procedure are provided. The ratio correlation procedure is applied to the komatiites from Gorgona Island and the Barberton suite. Plots of the molecular proportion ratios of (FeO + MgO)/TiO2 versus SiO2/TiO2, and correlation coefficients for the komatiites are presented and analyzed.

Numerical Simulations of Homogeneous Turbulence Using Lagrangian-Averaged Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Mohseni, Kamran; Shkoller, Steve; Kosovic, Branko; Marsden, Jerrold E.; Carati, Daniele; Wray, Alan; Rogallo, Robert

2000-01-01

The Lagrangian-averaged Navier-Stokes (LANS) equations are numerically evaluated as a turbulence closure. They are derived from a novel Lagrangian averaging procedure on the space of all volume-preserving maps and can be viewed as a numerical algorithm which removes the energy content from the small scales (smaller than some a priori fixed spatial scale alpha) using a dispersive rather than dissipative mechanism, thus maintaining the crucial features of the large scale flow. We examine the modeling capabilities of the LANS equations for decaying homogeneous turbulence, ascertain their ability to track the energy spectrum of fully resolved direct numerical simulations (DNS), compare the relative energy decay rates, and compare LANS with well-accepted large eddy simulation (LES) models.

Three-Loop Automatic of Control System the Landfill of Household Solid Waste

NASA Astrophysics Data System (ADS)

Sereda, T. G.; Kostarev, S. N.

2017-05-01

The analysis of models of governance ground municipal solid waste (MSW). Considered a distributed circuit (spatio-temporal) ground control model. Developed a dynamic model of multicontour control landfill. Adjustable parameters are defined (the ratio of CH4 CO2 emission/fluxes, concentrations of heavy metals ions) and control (purging array, irrigation, adding reagents). Based on laboratory studies carried out with the analysis of equity flows and procedures developed by the transferring matrix that takes into account the relationship control loops. A system of differential equations in the frequency and time domains. Given the numerical approaches solving systems of differential equations in finite differential form.

Numerical simulations of post-surgical flow and thrombosis in basilar artery aneurysms

NASA Astrophysics Data System (ADS)

Seshadhri, Santhosh; Lawton, Michael; Boussel, Loic; Saloner, David; Rayz, Vitaliy

2015-11-01

Surgical treatment of basilar artery aneurysms presents a major challenge since it is crucial to preserve the flow to the vital brainstem perforators branching of the basilar artery. In some cases, basilar aneurysms can be treated by clipping vessels in order to induce flow reduction and aneurysm thrombosis. Patient-specific CFD models can provide guidance to clinicians by simulating postoperative flows resulting from alternative surgeries. Several surgical options were evaluated for four basilar aneurysm patients. Patient-specific models were generated from preoperative MR angiography and MR velocimetry data and modified to simulate different procedures. The Navier-Stokes equations were solved with a finite-volume solver Fluent. Virtual contrast injections were simulated by solving the advection-diffusion equation in order to estimate the flow residence time and determine thrombus-prone regions. The results indicated on procedures that reduce intra-aneurysmal velocities and flow regions which are likely to become thrombosed. Thus CFD modeling can help improve the outcome of surgeries altering the flow in basilar aneurysms.

Super Configuration Accounting Equation of State for WDM and HED plasma

NASA Astrophysics Data System (ADS)

Lee, T. G.; Busquet, M.; Gilles, D.; Klapisch, M.

2017-10-01

Rad-Hydro numerical codes require Equation of State (EOS) and opacities. We describe a procedure to obtain an EOS compatible with our STA opacity model. We use our relativistic super-configuration code - STA-2.5 to compute the average 〈 Z 〉 and excitation-ionization internal energy U and chemical potential _. These and other data will serve as basic inputs into a Yukawa Monte-Carlo improved version of quotidian EOS, known as YMCQ. The screening in the Yukawa potential describing the ion-ion interaction is modified by the data from STA. This integrated procedure yields the excess internal energy due to the non-ideal behavior of the EOS concordant with our opacity model and allows us to have an EOS model applicable from solid matter to very tenuous plasmas as found in laser fusion, astrophysics, or tokamaks. We shall present its application to Carbon, Aluminum and Iron. This work is made possible by a financial support from DOE/NNSA.

A two-scale model of radio-frequency electrosurgical tissue ablation

NASA Astrophysics Data System (ADS)

Karaki, Wafaa; Rahul; Lopez, Carlos A.; Borca-Tasciuc, Diana-Andra; De, Suvranu

2017-12-01

Radio-frequency electrosurgical procedures are widely used to simultaneously dissect and coagulate tissue. Experiments suggest that evaporation of cellular and intra-cellular water plays a significant role in the evolution of the temperature field at the tissue level, which is not adequately captured in a single scale energy balance equation. Here, we propose a two-scale model to study the effects of microscale phase change and heat dissipation in response to radiofrequency heating on the tissue level in electrosurgical ablation procedures. At the microscale, the conservation of mass along with thermodynamic and mechanical equilibrium is applied to obtain an equation-of-state relating vapor mass fraction to temperature and pressure. The evaporation losses are incorporated in the macro-level energy conservation and results are validated with mean experimental temperature distributions measured from electrosurgical ablation testing on ex vivo porcine liver at different power settings of the electrosurgical instrument. Model prediction of water loss and its effect on the temperature along with the effect of the mechanical properties on results are evaluated and discussed.

Hybrid-dual-fourier tomographic algorithm for a fast three-dimensionial optical image reconstruction in turbid media

NASA Technical Reports Server (NTRS)

Alfano, Robert R. (Inventor); Cai, Wei (Inventor)

2007-01-01

A reconstruction technique for reducing computation burden in the 3D image processes, wherein the reconstruction procedure comprises an inverse and a forward model. The inverse model uses a hybrid dual Fourier algorithm that combines a 2D Fourier inversion with a 1D matrix inversion to thereby provide high-speed inverse computations. The inverse algorithm uses a hybrid transfer to provide fast Fourier inversion for data of multiple sources and multiple detectors. The forward model is based on an analytical cumulant solution of a radiative transfer equation. The accurate analytical form of the solution to the radiative transfer equation provides an efficient formalism for fast computation of the forward model.

A computational procedure for multibody systems including flexible beam dynamics

NASA Technical Reports Server (NTRS)

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

1990-01-01

A computational procedure suitable for the solution of equations of motions for flexible multibody systems has been developed. The flexible beams are modeled using a fully nonlinear theory which accounts for both finite rotations and large deformations. The present formulation incorporates physical measures of conjugate Cauchy stress and covariant strain increments. As a consequence, the beam model can easily be interfaced with real-time strain measurements and feedback control systems. A distinct feature of the present work is the computational preservation of total energy for undamped systems; this is obtained via an objective strain increment/stress update procedure combined with an energy-conserving time integration algorithm which contains an accurate update of angular orientations. The procedure is demonstrated via several example problems.

Rule-based simulation models

NASA Technical Reports Server (NTRS)

Nieten, Joseph L.; Seraphine, Kathleen M.

1991-01-01

Procedural modeling systems, rule based modeling systems, and a method for converting a procedural model to a rule based model are described. Simulation models are used to represent real time engineering systems. A real time system can be represented by a set of equations or functions connected so that they perform in the same manner as the actual system. Most modeling system languages are based on FORTRAN or some other procedural language. Therefore, they must be enhanced with a reaction capability. Rule based systems are reactive by definition. Once the engineering system has been decomposed into a set of calculations using only basic algebraic unary operations, a knowledge network of calculations and functions can be constructed. The knowledge network required by a rule based system can be generated by a knowledge acquisition tool or a source level compiler. The compiler would take an existing model source file, a syntax template, and a symbol table and generate the knowledge network. Thus, existing procedural models can be translated and executed by a rule based system. Neural models can be provide the high capacity data manipulation required by the most complex real time models.

From the Boltzmann to the Lattice-Boltzmann Equation:. Beyond BGK Collision Models

NASA Astrophysics Data System (ADS)

Philippi, Paulo Cesar; Hegele, Luiz Adolfo; Surmas, Rodrigo; Siebert, Diogo Nardelli; Dos Santos, Luís Orlando Emerich

In this work, we present a derivation for the lattice-Boltzmann equation directly from the linearized Boltzmann equation, combining the following main features: multiple relaxation times and thermodynamic consistency in the description of non isothermal compressible flows. The method presented here is based on the discretization of increasingly order kinetic models of the Boltzmann equation. Following a Gross-Jackson procedure, the linearized collision term is developed in Hermite polynomial tensors and the resulting infinite series is diagonalized after a chosen integer N, establishing the order of approximation of the collision term. The velocity space is discretized, in accordance with a quadrature method based on prescribed abscissas (Philippi et al., Phys. Rev E 73, 056702, 2006). The problem of describing the energy transfer is discussed, in relation with the order of approximation of a two relaxation-times lattice Boltzmann model. The velocity-step, temperature-step and the shock tube problems are investigated, adopting lattices with 37, 53 and 81 velocities.

Evolution of the concentration PDF in random environments modeled by global random walk

NASA Astrophysics Data System (ADS)

Suciu, Nicolae; Vamos, Calin; Attinger, Sabine; Knabner, Peter

2013-04-01

The evolution of the probability density function (PDF) of concentrations of chemical species transported in random environments is often modeled by ensembles of notional particles. The particles move in physical space along stochastic-Lagrangian trajectories governed by Ito equations, with drift coefficients given by the local values of the resolved velocity field and diffusion coefficients obtained by stochastic or space-filtering upscaling procedures. A general model for the sub-grid mixing also can be formulated as a system of Ito equations solving for trajectories in the composition space. The PDF is finally estimated by the number of particles in space-concentration control volumes. In spite of their efficiency, Lagrangian approaches suffer from two severe limitations. Since the particle trajectories are constructed sequentially, the demanded computing resources increase linearly with the number of particles. Moreover, the need to gather particles at the center of computational cells to perform the mixing step and to estimate statistical parameters, as well as the interpolation of various terms to particle positions, inevitably produce numerical diffusion in either particle-mesh or grid-free particle methods. To overcome these limitations, we introduce a global random walk method to solve the system of Ito equations in physical and composition spaces, which models the evolution of the random concentration's PDF. The algorithm consists of a superposition on a regular lattice of many weak Euler schemes for the set of Ito equations. Since all particles starting from a site of the space-concentration lattice are spread in a single numerical procedure, one obtains PDF estimates at the lattice sites at computational costs comparable with those for solving the system of Ito equations associated to a single particle. The new method avoids the limitations concerning the number of particles in Lagrangian approaches, completely removes the numerical diffusion, and speeds up the computation by orders of magnitude. The approach is illustrated for the transport of passive scalars in heterogeneous aquifers, with hydraulic conductivity modeled as a random field.

Optimization of Equation of State and Burn Model Parameters for Explosives

NASA Astrophysics Data System (ADS)

Bergh, Magnus; Wedberg, Rasmus; Lundgren, Jonas

2017-06-01

A reactive burn model implemented in a multi-dimensional hydrocode can be a powerful tool for predicting non-ideal effects as well as initiation phenomena in explosives. Calibration against experiment is, however, critical and non-trivial. Here, a procedure is presented for calibrating the Ignition and Growth Model utilizing hydrocode simulation in conjunction with the optimization program LS-OPT. The model is applied to the explosive PBXN-109. First, a cylinder expansion test is presented together with a new automatic routine for product equation of state calibration. Secondly, rate stick tests and instrumented gap tests are presented. Data from these experiments are used to calibrate burn model parameters. Finally, we discuss the applicability and development of this optimization routine.

A Simple, Analytical Model of Collisionless Magnetic Reconnection in a Pair Plasma

NASA Technical Reports Server (NTRS)

Hesse, Michael; Zenitani, Seiji; Kuznetova, Masha; Klimas, Alex

2011-01-01

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region, and to impart thermal energy to the plasma by means of quasi-viscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative, procedure. The solutions show expected features such as dominance of enthalpy flux in the reconnection outflow, as well as combination of adiabatic and quasi-viscous heating. Furthermore, the model predicts a maximum reconnection electric field of E(sup *)=0.4, normalized to the parameters at the inflow edge of the diffusion region.

A simple, analytical model of collisionless magnetic reconnection in a pair plasma

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

Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha

2009-10-15

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region and to impart thermal energy to the plasma by means of quasiviscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative procedure. The solutions show expected features such as dominance of enthalpymore » flux in the reconnection outflow, as well as combination of adiabatic and quasiviscous heating. Furthermore, the model predicts a maximum reconnection electric field of E{sup *}=0.4, normalized to the parameters at the inflow edge of the diffusion region.« less

Structural equation modeling for observational studies

USGS Publications Warehouse

Grace, J.B.

2008-01-01

Structural equation modeling (SEM) represents a framework for developing and evaluating complex hypotheses about systems. This method of data analysis differs from conventional univariate and multivariate approaches familiar to most biologists in several ways. First, SEMs are multiequational and capable of representing a wide array of complex hypotheses about how system components interrelate. Second, models are typically developed based on theoretical knowledge and designed to represent competing hypotheses about the processes responsible for data structure. Third, SEM is conceptually based on the analysis of covariance relations. Most commonly, solutions are obtained using maximum-likelihood solution procedures, although a variety of solution procedures are used, including Bayesian estimation. Numerous extensions give SEM a very high degree of flexibility in dealing with nonnormal data, categorical responses, latent variables, hierarchical structure, multigroup comparisons, nonlinearities, and other complicating factors. Structural equation modeling allows researchers to address a variety of questions about systems, such as how different processes work in concert, how the influences of perturbations cascade through systems, and about the relative importance of different influences. I present 2 example applications of SEM, one involving interactions among lynx (Lynx pardinus), mongooses (Herpestes ichneumon), and rabbits (Oryctolagus cuniculus), and the second involving anuran species richness. Many wildlife ecologists may find SEM useful for understanding how populations function within their environments. Along with the capability of the methodology comes a need for care in the proper application of SEM.

Interaction of gliding motion of bacteria with rheological properties of the slime.

PubMed

Asghar, Z; Ali, N; Sajid, M

2017-08-01

Bacteria which do not have organelles of motility, such as flagella, adopt gliding as a mode of locomotion. In gliding motility bacterium moves under its own power by secreting a layer of slime on the substrate. The exact mechanism by which a glider achieves motility is yet in controversy but there are evidences which support the wave-like undulation on the surface of the organism, as a possible mechanism of motility. Based on this observation, a model of undulating sheet over a layer of slime is examined as a possible model of the gliding motion of a bacterium. Three different non-Newtonian constitutive equations namely, finite extendable nonlinear elastic-peterline (FENE-P), Simplified Phan-Thien-Tanner (SPTT) and Rabinowitsch equations are used to capture the rheological properties of the slime. It is found that the governing equation describing the fluid mechanics of the model under lubrication approximation is same for all the considered three constitutive equations. In fact, it involves a single non-Newtonian parameter which assumes different values for each of the considered constitutive relations. This differential equation is solved using both perturbation and semi-analytic procedure. The perturbation solution is exploited to get an estimate of the speed of the glider for different values of the non-Newtonian parameter. The solution obtained via semi-analytic procedure is used to investigate the important features of the flow field in the layer of the slime beneath the glider when the glider is held fixed. The expression of forces generated by the organism and power required for propulsion are also derived based on the perturbation analysis. Copyright © 2017 Elsevier Inc. All rights reserved.

Development of a numerical model for vehicle-bridge interaction analysis of railway bridges

NASA Astrophysics Data System (ADS)

Kim, Hee Ju; Cho, Eun Sang; Ham, Jun Su; Park, Ki Tae; Kim, Tae Heon

2016-04-01

In the field of civil engineering, analyzing dynamic response was main concern for a long time. These analysis methods can be divided into moving load analysis method and moving mass analysis method, and formulating each an equation of motion has recently been studied after dividing vehicles and bridges. In this study, the numerical method is presented, which can consider the various train types and can solve the equations of motion for a vehicle-bridge interaction analysis by non-iteration procedure through formulating the coupled equations for motion. Also, 3 dimensional accurate numerical models was developed by KTX-vehicle in order to analyze dynamic response characteristics. The equations of motion for the conventional trains are derived, and the numerical models of the conventional trains are idealized by a set of linear springs and dashpots with 18 degrees of freedom. The bridge models are simplified by the 3 dimensional space frame element which is based on the Euler-Bernoulli theory. The rail irregularities of vertical and lateral directions are generated by PSD functions of the Federal Railroad Administration (FRA).

The influence of dynamic inflow and torsional flexibility on rotor damping in forward flight from symbolically generated equations

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Warmbrodt, W.

1985-01-01

The combined effects of blade torsion and dynamic inflow on the aeroelastic stability of an elastic rotor blade in forward flight are studied. The governing sets of equations of motion (fully nonlinear, linearized, and multiblade equations) used in this study are derived symbolically using a program written in FORTRAN. Stability results are presented for different structural models with and without dynamic inflow. A combination of symbolic and numerical programs at the proper stage in the derivation process makes the obtainment of final stability results an efficient and straightforward procedure.

Investigations Regarding Anesthesia during Hypovolemic Conditions.

DTIC Science & Technology

1982-09-25

i / b ,- 18 For each level of hemoglobin, the equation was "normalized" to a pH of 7.400 for a BE of zero and a PCO of 40.0 torr, Orr et al. (171...the shifted BE values. Curve nomogram. Using the equations resulting from the above curve- fitting procedure, we calculated the relationship between pH...model for a given BE (i.e., pH = m i log PCO 2 + bi). Solve the following set of equations for pHind and log dX - 0 d(PHind) where X = (pHl - pHind) 2

Mathematical modeling of impact of two metal plates using two-fluid approach

NASA Astrophysics Data System (ADS)

Utkin, P. S.; Fortova, S. V.

2018-01-01

The paper is devoted to the development of the two-fluid mathematical model and the computational algorithm for the modeling of two metal plates impact. In one-dimensional case the governing system of equations comprises seven equations: three conservation laws for each fluid and transfer equation for the volume fraction of one of the fluids. Both fluids are considered to be compressible and equilibrium on velocities. Pressures equilibrium is used as fluids interface condition. The system has hyperbolic type but could not be written in the conservative form because of nozzling terms in the right-hand side of the equations. The algorithm is based on the Harten-Lax-van Leer numerical flux function. The robust computation in the presence of the interface boundary is carried out due to the special pressure relaxation procedure. The problem is solved using stiffened gas equations of state for each fluid. The parameters in the equations of state are calibrated using the results of computations using wide-range equations of state for the metals. In simulations of metal plates impact we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7%) to the data from the wide-range equations of states computations.

Classifying Correlation Matrices into Relatively Homogeneous Subgroups: A Cluster Analytic Approach

ERIC Educational Resources Information Center

Cheung, Mike W.-L.; Chan, Wai

2005-01-01

Researchers are becoming interested in combining meta-analytic techniques and structural equation modeling to test theoretical models from a pool of studies. Most existing procedures are based on the assumption that all correlation matrices are homogeneous. Few studies have addressed what the next step should be when studies being analyzed are…

f( R, L m ) gravity

NASA Astrophysics Data System (ADS)

Harko, Tiberiu; Lobo, Francisco S. N.

2010-11-01

We generalize the f( R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert-Einstein Lagrange density are also derived.

Numerical simulation of evolutionary erodible bedforms using the particle finite element method

NASA Astrophysics Data System (ADS)

Bravo, Rafael; Becker, Pablo; Ortiz, Pablo

2017-07-01

This paper presents a numerical strategy for the simulation of flows with evolutionary erodible boundaries. The fluid equations are fully resolved in 3D, while the sediment transport is modelled using the Exner equation and solved with an explicit Lagrangian procedure based on a fixed 2D mesh. Flow and sediment are coupled in geometry by deforming the fluid mesh in the vertical direction and in velocities with the experimental sediment flux computed using the Meyer Peter Müller model. A comparison with real experiments on channels is performed, giving good agreement.

Analysis of swimming motions.

NASA Technical Reports Server (NTRS)

Gallenstein, J.; Huston, R. L.

1973-01-01

This paper presents an analysis of swimming motion with specific attention given to the flutter kick, the breast-stroke kick, and the breast stroke. The analysis is completely theoretical. It employs a mathematical model of the human body consisting of frustrums of elliptical cones. Dynamical equations are written for this model including both viscous and inertia forces. These equations are then applied with approximated swimming strokes and solved numerically using a digital computer. The procedure is to specify the input of the swimming motion. The computer solution then provides the output displacement, velocity, and rotation or body roll of the swimmer.

Turbulence modeling for hypersonic flight

NASA Technical Reports Server (NTRS)

Bardina, Jorge E.

1993-01-01

The objective of the proposed work is to continue to develop, verify, and incorporate the baseline two-equation turbulence models, which account for the effects of compressibility at high speeds, into a three-dimensional Reynolds averaged Navier-Stokes (RANS) code. Additionally, we plan to provide documented descriptions of the models and their numerical procedures so that they can be implemented into the NASP CFD codes.

Large-eddy Simulation of Stratocumulus-topped Atmospheric Boundary Layers with Dynamic Subgrid-scale Models

NASA Technical Reports Server (NTRS)

Senocak, Inane

2003-01-01

The objective of the present study is to evaluate the dynamic procedure in LES of stratocumulus topped atmospheric boundary layer and assess the relative importance of subgrid-scale modeling, cloud microphysics and radiation modeling on the predictions. The simulations will also be used to gain insight into the processes leading to cloud top entrainment instability and cloud breakup. In this report we document the governing equations, numerical schemes and physical models that are employed in the Goddard Cumulus Ensemble model (GCEM3D). We also present the subgrid-scale dynamic procedures that have been implemented in the GCEM3D code for the purpose of the present study.

Linear network representation of multistate models of transport.

PubMed Central

Sandblom, J; Ring, A; Eisenman, G

1982-01-01

By introducing external driving forces in rate-theory models of transport we show how the Eyring rate equations can be transformed into Ohm's law with potentials that obey Kirchhoff's second law. From such a formalism the state diagram of a multioccupancy multicomponent system can be directly converted into linear network with resistors connecting nodal (branch) points and with capacitances connecting each nodal point with a reference point. The external forces appear as emf or current generators in the network. This theory allows the algebraic methods of linear network theory to be used in solving the flux equations for multistate models and is particularly useful for making proper simplifying approximation in models of complex membrane structure. Some general properties of linear network representation are also deduced. It is shown, for instance, that Maxwell's reciprocity relationships of linear networks lead directly to Onsager's relationships in the near equilibrium region. Finally, as an example of the procedure, the equivalent circuit method is used to solve the equations for a few transport models. PMID:7093425

A dynamic regularized gradient model of the subgrid-scale stress tensor for large-eddy simulation

NASA Astrophysics Data System (ADS)

Vollant, A.; Balarac, G.; Corre, C.

2016-02-01

Large-eddy simulation (LES) solves only the large scales part of turbulent flows by using a scales separation based on a filtering operation. The solution of the filtered Navier-Stokes equations requires then to model the subgrid-scale (SGS) stress tensor to take into account the effect of scales smaller than the filter size. In this work, a new model is proposed for the SGS stress model. The model formulation is based on a regularization procedure of the gradient model to correct its unstable behavior. The model is developed based on a priori tests to improve the accuracy of the modeling for both structural and functional performances, i.e., the model ability to locally approximate the SGS unknown term and to reproduce enough global SGS dissipation, respectively. LES is then performed for a posteriori validation. This work is an extension to the SGS stress tensor of the regularization procedure proposed by Balarac et al. ["A dynamic regularized gradient model of the subgrid-scale scalar flux for large eddy simulations," Phys. Fluids 25(7), 075107 (2013)] to model the SGS scalar flux. A set of dynamic regularized gradient (DRG) models is thus made available for both the momentum and the scalar equations. The second objective of this work is to compare this new set of DRG models with direct numerical simulations (DNS), filtered DNS in the case of classic flows simulated with a pseudo-spectral solver and with the standard set of models based on the dynamic Smagorinsky model. Various flow configurations are considered: decaying homogeneous isotropic turbulence, turbulent plane jet, and turbulent channel flows. These tests demonstrate the stable behavior provided by the regularization procedure, along with substantial improvement for velocity and scalar statistics predictions.

A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

NASA Technical Reports Server (NTRS)

Kandil, Osama A.

1998-01-01

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

Test Operations Procedure (TOP) 1-1-062 Environmental Effects Data Collection

DTIC Science & Technology

2008-09-12

this procedure. 11. ESTIMATION DESCRIPTION The prime example of an empirically based model is the Universal Soil Loss Equation ( USLE ) developed...impacts to human health and welfare and to the natural environment. The type of data collected might include noise levels, soil erosion, and...uptake relevant to flora/fauna and the soil erosion effects of proposed testing. c. Plan to identify any modifications/alternatives implemented

Spatial disaggregation of POWER-NASA air temperatures and effects on grass reference evapotranspiration in Sicily, Italy

NASA Astrophysics Data System (ADS)

Negm, Amro; Minacapilli, Mario; Provenzano, Giuseppe

2017-04-01

The accurate estimation of grass reference evapotranspiration (ET0) is important for many fields, including hydrology and irrigation water management. Being direct measure of ET0 difficult, expensive and time consuming, application of simplified approaches and web-based meteorological information are often preferred. The Prediction of Worldwide Energy Resource project developed by the American National Aeronautics and Space Administration (POWER-NASA) provides meteorological observations and surface energy fluxes on 1° latitude by 1° longitude grid, with a continuous daily coverage and for the entire globe. However, the broad spatial resolution of these data represents a limiting factor, for example when they have to be used for local estimations of reference ET0. In this work, a procedure for the spatial disaggregation of POWER-NASA daily average air temperature was proposed. In particular, a daily scaling factor was initially defined as the ratio between disaggregated average air temperature and the corresponding native value. This ratio was then modeled with a cosine function, characterized by three parameters depending on elevation, so to account for seasonal and regional variability. The proposed model was calibrated with three years of ground measurements (2006-2008) and then validated over six years (2009-2014). The suitability of the procedure was finally assessed by applying two simplified empirical models to estimate ET0 (Turc, 1961; Hargreaves, 1975). When compared to ET0 values obtained with FAO-56 PM equation, both simplified equations associated to downscaled meteorological observations, were characterized by RMSE ranging between 0.44 and 1.08 mm (average of 0.72-0.74 mm), and average MBE of -0.06 (Turc equation) and 0.13 mm (Hargreaves equation). These results indicated the strength of the proposed procedure to estimate ET0, even for regions characterized by the lack of detailed meteorological information.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 2 is the User's Guide, and describes the program's general features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Global Asymptotic Behavior of Iterative Implicit Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1994-01-01

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm

NASA Technical Reports Server (NTRS)

Pelaez, Juan; Mavriplis, Dimitri J.; Kandil, Osama

2001-01-01

An implicit method for the computation of unsteady flows on unstructured grids is presented. The resulting nonlinear system of equations is solved at each time step using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the code using a one-equation turbulence model is performed for the well-known case of flow over a cylinder. A Detached Eddy Simulation model is also implemented and its performance compared to the one equation Spalart-Allmaras Reynolds Averaged Navier-Stokes (RANS) turbulence model. Validation cases using DES and RANS include flow over a sphere and flow over a NACA 0012 wing including massive stall regimes. The project was driven by the ultimate goal of computing separated flows of aerodynamic interest, such as massive stall or flows over complex non-streamlined geometries.

The terminal area simulation system. Volume 1: Theoretical formulation

NASA Technical Reports Server (NTRS)

Proctor, F. H.

1987-01-01

A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Number

NASA Technical Reports Server (NTRS)

Xiao, X.; Edwards, J. R.; Hassan, H. A.

2004-01-01

Present simulation of turbulent flows involving shock wave/boundary layer interaction invariably overestimates heat flux by almost a factor of two. One possible reason for such a performance is a result of the fact that the turbulence models employed make use of Morkovin's hypothesis. This hypothesis is valid for non-hypersonic Mach numbers and moderate rates of heat transfer. At hypersonic Mach numbers, high rates of heat transfer exist in regions where shock wave/boundary layer interactions are important. As a result, one should not expect traditional turbulence models to yield accurate results. The goal of this investigation is to explore the role of a variable Prandtl number formulation in predicting heat flux in flows dominated by strong shock wave/boundary layer interactions. The intended applications involve external flows in the absence of combustion such as those encountered in supersonic inlets. This can be achieved by adding equations for the temperature variance and its dissipation rate. Such equations can be derived from the exact Navier-Stokes equations. Traditionally, modeled equations are based on the low speed energy equation where the pressure gradient term and the term responsible for energy dissipation are ignored. It is clear that such assumptions are not valid for hypersonic flows. The approach used here is based on the procedure used in deriving the k-zeta model, in which the exact equations that governed k, the variance of velocity, and zeta, the variance of vorticity, were derived and modeled. For the variable turbulent Prandtl number, the exact equations that govern the temperature variance and its dissipation rate are derived and modeled term by term. The resulting set of equations are free of damping and wall functions and are coordinate-system independent. Moreover, modeled correlations are tensorially consistent and invariant under Galilean transformation. The final set of equations will be given in the paper.

Calibration of semi-stochastic procedure for simulating high-frequency ground motions

USGS Publications Warehouse

Seyhan, Emel; Stewart, Jonathan P.; Graves, Robert

2013-01-01

Broadband ground motion simulation procedures typically utilize physics-based modeling at low frequencies, coupled with semi-stochastic procedures at high frequencies. The high-frequency procedure considered here combines deterministic Fourier amplitude spectra (dependent on source, path, and site models) with random phase. Previous work showed that high-frequency intensity measures from this simulation methodology attenuate faster with distance and have lower intra-event dispersion than in empirical equations. We address these issues by increasing crustal damping (Q) to reduce distance attenuation bias and by introducing random site-to-site variations to Fourier amplitudes using a lognormal standard deviation ranging from 0.45 for Mw < 7 to zero for Mw 8. Ground motions simulated with the updated parameterization exhibit significantly reduced distance attenuation bias and revised dispersion terms are more compatible with those from empirical models but remain lower at large distances (e.g., > 100 km).

Are traditional body fat equations and anthropometry valid to estimate body fat in children and adolescents living with HIV?

PubMed

Lima, Luiz Rodrigo Augustemak de; Martins, Priscila Custódio; Junior, Carlos Alencar Souza Alves; Castro, João Antônio Chula de; Silva, Diego Augusto Santos; Petroski, Edio Luiz

The aim of this study was to assess the validity of traditional anthropometric equations and to develop predictive equations of total body and trunk fat for children and adolescents living with HIV based on anthropometric measurements. Forty-eight children and adolescents of both sexes (24 boys) aged 7-17 years, living in Santa Catarina, Brazil, participated in the study. Dual-energy X-ray absorptiometry was used as the reference method to evaluate total body and trunk fat. Height, body weight, circumferences and triceps, subscapular, abdominal and calf skinfolds were measured. The traditional equations of Lohman and Slaughter were used to estimate body fat. Multiple regression models were fitted to predict total body fat (Model 1) and trunk fat (Model 2) using a backward selection procedure. Model 1 had an R 2 =0.85 and a standard error of the estimate of 1.43. Model 2 had an R 2 =0.80 and standard error of the estimate=0.49. The traditional equations of Lohman and Slaughter showed poor performance in estimating body fat in children and adolescents living with HIV. The prediction models using anthropometry provided reliable estimates and can be used by clinicians and healthcare professionals to monitor total body and trunk fat in children and adolescents living with HIV. Copyright © 2017 Sociedade Brasileira de Infectologia. Published by Elsevier Editora Ltda. All rights reserved.

Filtered Mass Density Function for Design Simulation of High Speed Airbreathing Propulsion Systems

NASA Technical Reports Server (NTRS)

Drozda, T. G.; Sheikhi, R. M.; Givi, Peyman

2001-01-01

The objective of this research is to develop and implement new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. We have just completed two (2) years of Phase I of this research. This annual report provides a brief and up-to-date summary of our activities during the period: September 1, 2000 through August 31, 2001. In the work within the past year, a methodology termed "velocity-scalar filtered density function" (VSFDF) is developed and implemented for large eddy simulation (LES) of turbulent flows. In this methodology the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function (PDF) of all of the components of the velocity and scalar vectors. An exact transport equation is derived for the VSFDF in which the effects of the unresolved SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source terms appear in closed form. The remaining unclosed terms in this equation are modeled. A system of stochastic differential equations (SDEs) which yields statistically equivalent results to the modeled VSFDF transport equation is constructed. These SDEs are solved numerically by a Lagrangian Monte Carlo procedure. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed by comparison with results obtained by an Eulerian LES procedure in which the corresponding transport equations for the first two SGS moments are solved. The unclosed SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source in the Eulerian LES are replaced by corresponding terms from VSFDF equation. The consistency of the results is then analyzed for a case of two dimensional mixing layer.

Generation of three-dimensional body-fitted grids by solving hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, an extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Generation of three-dimensional body-fitted grids by solving hyperbolic and parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Optimal control of CPR procedure using hemodynamic circulation model

DOEpatents

Lenhart, Suzanne M.; Protopopescu, Vladimir A.; Jung, Eunok

2007-12-25

A method for determining a chest pressure profile for cardiopulmonary resuscitation (CPR) includes the steps of representing a hemodynamic circulation model based on a plurality of difference equations for a patient, applying an optimal control (OC) algorithm to the circulation model, and determining a chest pressure profile. The chest pressure profile defines a timing pattern of externally applied pressure to a chest of the patient to maximize blood flow through the patient. A CPR device includes a chest compressor, a controller communicably connected to the chest compressor, and a computer communicably connected to the controller. The computer determines the chest pressure profile by applying an OC algorithm to a hemodynamic circulation model based on the plurality of difference equations.

Minimum-complexity helicopter simulation math model

NASA Technical Reports Server (NTRS)

Heffley, Robert K.; Mnich, Marc A.

1988-01-01

An example of a minimal complexity simulation helicopter math model is presented. Motivating factors are the computational delays, cost, and inflexibility of the very sophisticated math models now in common use. A helicopter model form is given which addresses each of these factors and provides better engineering understanding of the specific handling qualities features which are apparent to the simulator pilot. The technical approach begins with specification of features which are to be modeled, followed by a build up of individual vehicle components and definition of equations. Model matching and estimation procedures are given which enable the modeling of specific helicopters from basic data sources such as flight manuals. Checkout procedures are given which provide for total model validation. A number of possible model extensions and refinement are discussed. Math model computer programs are defined and listed.

A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere. I - Theory. II - Application

NASA Technical Reports Server (NTRS)

Weng, Fuzhong

1992-01-01

A theory is developed for discretizing the vector integro-differential radiative transfer equation including both solar and thermal radiation. A complete solution and boundary equations are obtained using the discrete-ordinate method. An efficient numerical procedure is presented for calculating the phase matrix and achieving computational stability. With natural light used as a beam source, the Stokes parameters from the model proposed here are compared with the analytical solutions of Chandrasekhar (1960) for a Rayleigh scattering atmosphere. The model is then applied to microwave frequencies with a thermal source, and the brightness temperatures are compared with those from Stamnes'(1988) radiative transfer model.

Mathematical model with autoregressive process for electrocardiogram signals

NASA Astrophysics Data System (ADS)

Evaristo, Ronaldo M.; Batista, Antonio M.; Viana, Ricardo L.; Iarosz, Kelly C.; Szezech, José D., Jr.; Godoy, Moacir F. de

2018-04-01

The cardiovascular system is composed of the heart, blood and blood vessels. Regarding the heart, cardiac conditions are determined by the electrocardiogram, that is a noninvasive medical procedure. In this work, we propose autoregressive process in a mathematical model based on coupled differential equations in order to obtain the tachograms and the electrocardiogram signals of young adults with normal heartbeats. Our results are compared with experimental tachogram by means of Poincaré plot and dentrended fluctuation analysis. We verify that the results from the model with autoregressive process show good agreement with experimental measures from tachogram generated by electrical activity of the heartbeat. With the tachogram we build the electrocardiogram by means of coupled differential equations.

The Cusp Catastrophe Model as Cross-Sectional and Longitudinal Mixture Structural Equation Models

PubMed Central

Chow, Sy-Miin; Witkiewitz, Katie; Grasman, Raoul P. P. P.; Maisto, Stephen A.

2015-01-01

Catastrophe theory (Thom, 1972, 1993) is the study of the many ways in which continuous changes in a system’s parameters can result in discontinuous changes in one or several outcome variables of interest. Catastrophe theory–inspired models have been used to represent a variety of change phenomena in the realm of social and behavioral sciences. Despite their promise, widespread applications of catastrophe models have been impeded, in part, by difficulties in performing model fitting and model comparison procedures. We propose a new modeling framework for testing one kind of catastrophe model — the cusp catastrophe model — as a mixture structural equation model (MSEM) when cross-sectional data are available; or alternatively, as an MSEM with regime-switching (MSEM-RS) when longitudinal panel data are available. The proposed models and the advantages offered by this alternative modeling framework are illustrated using two empirical examples and a simulation study. PMID:25822209

Investigation of flood routing by a dynamic wave model in trapezoidal channels

NASA Astrophysics Data System (ADS)

Sulistyono, B. A.; Wiryanto, L. H.

2017-08-01

The problems of flood wave propagation, in bodies of waters, cause by intense rains or breaking of control structures, represent a great challenge in the mathematical modeling processes. This research concerns about the development and application of a mathematical model based on the Saint Venant's equations, to study the behavior of the propagation of a flood wave in trapezoidal channels. In these equations, the momentum equation transforms to partial differential equation which has two parameters related to cross-sectional area and discharge of the channel. These new formulas have been solved by using an explicit finite difference scheme. In computation procedure, after computing the discharge from the momentum equation, the cross-sectional area will be obtained from the continuity equation for a given point of channel. To evaluate the behavior of the control variables, several scenarios for the main channel as well as for flood waves are considered and different simulations are performed. The simulations demonstrate that for the same bed width, the peak discharge in trapezoidal channel smaller than in rectangular one at a specific distance along the channel length and so, that roughness coefficient and bed slope of the channel play a strong game on the behavior of the flood wave propagation.

A one-step method for modelling longitudinal data with differential equations.

PubMed

Hu, Yueqin; Treinen, Raymond

2018-04-06

Differential equation models are frequently used to describe non-linear trajectories of longitudinal data. This study proposes a new approach to estimate the parameters in differential equation models. Instead of estimating derivatives from the observed data first and then fitting a differential equation to the derivatives, our new approach directly fits the analytic solution of a differential equation to the observed data, and therefore simplifies the procedure and avoids bias from derivative estimations. A simulation study indicates that the analytic solutions of differential equations (ASDE) approach obtains unbiased estimates of parameters and their standard errors. Compared with other approaches that estimate derivatives first, ASDE has smaller standard error, larger statistical power and accurate Type I error. Although ASDE obtains biased estimation when the system has sudden phase change, the bias is not serious and a solution is also provided to solve the phase problem. The ASDE method is illustrated and applied to a two-week study on consumers' shopping behaviour after a sale promotion, and to a set of public data tracking participants' grammatical facial expression in sign language. R codes for ASDE, recommendations for sample size and starting values are provided. Limitations and several possible expansions of ASDE are also discussed. © 2018 The British Psychological Society.

An algorithm to generate input data from meteorological and space shuttle observations to validate a CH4-CO model

NASA Technical Reports Server (NTRS)

Peters, L. K.; Yamanis, J.

1981-01-01

Objective procedures to analyze data from meteorological and space shuttle observations to validate a three dimensional model were investigated. The transport and chemistry of carbon monoxide and methane in the troposphere were studied. Four aspects were examined: (1) detailed evaluation of the variational calculus procedure, with the equation of continuity as a strong constraint, for adjustment of global tropospheric wind fields; (2) reduction of the National Meteorological Center (NMC) data tapes for data input to the OSTA-1/MAPS Experiment; (3) interpolation of the NMC Data for input to the CH4-CO model; and (4) temporal and spatial interpolation procedures of the CO measurements from the OSTA-1/MAPS Experiment to generate usable contours of the data.

Computing the modal mass from the state space model in combined experimental-operational modal analysis

NASA Astrophysics Data System (ADS)

Cara, Javier

2016-05-01

Modal parameters comprise natural frequencies, damping ratios, modal vectors and modal masses. In a theoretic framework, these parameters are the basis for the solution of vibration problems using the theory of modal superposition. In practice, they can be computed from input-output vibration data: the usual procedure is to estimate a mathematical model from the data and then to compute the modal parameters from the estimated model. The most popular models for input-output data are based on the frequency response function, but in recent years the state space model in the time domain has become popular among researchers and practitioners of modal analysis with experimental data. In this work, the equations to compute the modal parameters from the state space model when input and output data are available (like in combined experimental-operational modal analysis) are derived in detail using invariants of the state space model: the equations needed to compute natural frequencies, damping ratios and modal vectors are well known in the operational modal analysis framework, but the equation needed to compute the modal masses has not generated much interest in technical literature. These equations are applied to both a numerical simulation and an experimental study in the last part of the work.

Averaging problem in general relativity, macroscopic gravity and using Einstein's equations in cosmology.

NASA Astrophysics Data System (ADS)

Zalaletdinov, R. M.

1998-04-01

The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the geometry of macroscopic space-time, which follows from averaging Cartan's structure equations, is described and the correlation tensors present in the theory are discussed. The macroscopic field equations (averaged Einstein's equations) derived in the framework of the approach are presented and their structure is analysed. The correspondence principle for macroscopic gravity is formulated and a definition of the stress-energy tensor for the macroscopic gravitational field is proposed. It is shown that the physical meaning of using Einstein's equations with a hydrodynamic stress-energy tensor in looking for cosmological models means neglecting all gravitational field correlations. The system of macroscopic gravity equations to be solved when the correlations are taken into consideration is given and described.

Fully-coupled analysis of jet mixing problems. Part 1. Shock-capturing model, SCIPVIS

NASA Technical Reports Server (NTRS)

Dash, S. M.; Wolf, D. E.

1984-01-01

A computational model, SCIPVIS, is described which predicts the multiple cell shock structure in imperfectly expanded, turbulent, axisymmetric jets. The model spatially integrates the parabolized Navier-Stokes jet mixing equations using a shock-capturing approach in supersonic flow regions and a pressure-split approximation in subsonic flow regions. The regions are coupled using a viscous-characteristic procedure. Turbulence processes are represented via the solution of compressibility-corrected two-equation turbulence models. The formation of Mach discs in the jet and the interactive analysis of the wake-like mixing process occurring behind Mach discs is handled in a rigorous manner. Calculations are presented exhibiting the fundamental interactive processes occurring in supersonic jets and the model is assessed via comparisons with detailed laboratory data for a variety of under- and overexpanded jets.

From integrability to conformal symmetry: Bosonic superconformal Toda theories

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

Bo-Yu Hou; Liu Chao

In this paper the authors study the conformal integrable models obtained from conformal reductions of WZNW theory associated with second order constraints. These models are called bosonic superconformal Toda models due to their conformal spectra and their resemblance to the usual Toda theories. From the reduction procedure they get the equations of motion and the linearized Lax equations in a generic Z gradation of the underlying Lie algebra. Then, in the special case of principal gradation, they derive the classical r matrix, fundamental Poisson relation, exchange algebra of chiral operators and find out the classical vertex operators. The result showsmore » that their model is very similar to the ordinary Toda theories in that one can obtain various conformal properties of the model from its integrability.« less

Hamilton-Jacobi modelling of relative motion for formation flying.

PubMed

Kolemen, Egemen; Kasdin, N Jeremy; Gurfil, Pini

2005-12-01

A precise analytic model for the relative motion of a group of satellites in slightly elliptic orbits is introduced. With this aim, we describe the relative motion of an object relative to a circular or slightly elliptic reference orbit in the rotating Hill frame via a low-order Hamiltonian, and solve the Hamilton-Jacobi equation. This results in a first-order solution to the relative motion identical to the Clohessy-Wiltshire approach; here, however, rather than using initial conditions as our constants of the motion, we utilize the canonical momenta and coordinates. This allows us to treat perturbations in an identical manner, as in the classical Delaunay formulation of the two-body problem. A precise analytical model for the base orbit is chosen with the included effect of zonal harmonics (J(2), J(3), J(4)). A Hamiltonian describing the real relative motion is formed and by differing this from the nominal Hamiltonian, the perturbing Hamiltonian is obtained. Using the Hamilton equations, the variational equations for the new constants are found. In a manner analogous to the center manifold reduction procedure, the non-periodic part of the motion is canceled through a magnitude analysis leading to simple boundedness conditions that cancel the drift terms due to the higher order perturbations. Using this condition, the variational equations are integrated to give periodic solutions that closely approximate the results from numerical integration (1 mm/per orbit for higher order and eccentricity perturbations and 30 cm/per orbit for zonal perturbations). This procedure provides a compact and insightful analytic description of the resulting relative motion.

Generalized Flip-Flop Input Equations Based on a Four-Valued Boolean Algebra

NASA Technical Reports Server (NTRS)

Tucker, Jerry H.; Tapia, Moiez A.

1996-01-01

A procedure is developed for obtaining generalized flip-flop input equations, and a concise method is presented for representing these equations. The procedure is based on solving a four-valued characteristic equation of the flip-flop, and can encompass flip-flops that are too complex to approach intuitively. The technique is presented using Karnaugh maps, but could easily be implemented in software.

Approximate furrow infiltration model for time-variable ponding depth

USDA-ARS?s Scientific Manuscript database

A methodology is proposed for estimating furrow infiltration under time-variable ponding depth conditions. The methodology approximates the solution to the two-dimensional Richards equation, and is a modification of a procedure that was originally proposed for computing infiltration under constant ...

Evidence Regarding the Internal Structure: Confirmatory Factor Analysis

ERIC Educational Resources Information Center

Lewis, Todd F.

2017-01-01

American Educational Research Association (AERA) standards stipulate that researchers show evidence of the internal structure of instruments. Confirmatory factor analysis (CFA) is one structural equation modeling procedure designed to assess construct validity of assessments that has broad applicability for counselors interested in instrument…

Displaying Colors of Specified Chrominance on a Color Graphics Display.

DTIC Science & Technology

1982-12-01

coordinates (such as Commission Internationale de l’Eclairage CIEXYZ coordinates). This report contains the description of a procedure for displaying...colors of known chrominance as specified by CIEXYZ coordinates. The procedure makes use of models of a color graphics system intensity (bits) to lumi...coordinates (e.g., CIELUV -1976 CT contrast equations as described in Robertson, 1977). Thus, the results of most efforts to specify a set of colors to

CAN-DO, CFD-based Aerodynamic Nozzle Design and Optimization program for supersonic/hypersonic wind tunnels

NASA Technical Reports Server (NTRS)

Korte, John J.; Kumar, Ajay; Singh, D. J.; White, J. A.

1992-01-01

A design program is developed which incorporates a modern approach to the design of supersonic/hypersonic wind-tunnel nozzles. The approach is obtained by the coupling of computational fluid dynamics (CFD) with design optimization. The program can be used to design a 2D or axisymmetric, supersonic or hypersonic, wind-tunnel nozzles that can be modeled with a calorically perfect gas. The nozzle design is obtained by solving a nonlinear least-squares optimization problem (LSOP). The LSOP is solved using an iterative procedure which requires intermediate flowfield solutions. The nozzle flowfield is simulated by solving the Navier-Stokes equations for the subsonic and transonic flow regions and the parabolized Navier-Stokes equations for the supersonic flow regions. The advantages of this method are that the design is based on the solution of the viscous equations eliminating the need to make separate corrections to a design contour, and the flexibility of applying the procedure to different types of nozzle design problems.

Digital computer simulation of inductor-energy-storage dc-to-dc converters with closed-loop regulators

NASA Technical Reports Server (NTRS)

Ohri, A. K.; Owen, H. A.; Wilson, T. G.; Rodriguez, G. E.

1974-01-01

The simulation of converter-controller combinations by means of a flexible digital computer program which produces output to a graphic display is discussed. The procedure is an alternative to mathematical analysis of converter systems. The types of computer programming involved in the simulation are described. Schematic diagrams, state equations, and output equations are displayed for four basic forms of inductor-energy-storage dc to dc converters. Mathematical models are developed to show the relationship of the parameters.

Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements.

PubMed

Leander, Jacob; Lundh, Torbjörn; Jirstrand, Mats

2014-05-01

In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh-Nagumo model for excitable media and the Lotka-Volterra predator-prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Kwak, Dochan

1999-01-01

A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finite volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5th) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5th-order upwind differencing and a modified production term in the Baldwin-Barth one-equation turbulence model are used with adequate grid resolution.

Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.

PubMed

Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C

2011-06-01

The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.

Mixed models and reduction method for dynamic analysis of anisotropic shells

NASA Technical Reports Server (NTRS)

Noor, A. K.; Peters, J. M.

1985-01-01

A time-domain computational procedure is presented for predicting the dynamic response of laminated anisotropic shells. The two key elements of the procedure are: (1) use of mixed finite element models having independent interpolation (shape) functions for stress resultants and generalized displacements for the spatial discretization of the shell, with the stress resultants allowed to be discontinuous at interelement boundaries; and (2) use of a dynamic reduction method, with the global approximation vectors consisting of the static solution and an orthogonal set of Lanczos vectors. The dynamic reduction is accomplished by means of successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate the global approximation vectors. Then the Rayleigh-Ritz technique is used to generate a reduced system of ordinary differential equations in the amplitudes of these modes. The temporal integration of the reduced differential equations is performed by using an explicit half-station central difference scheme (Leap-frog method). The effectiveness of the proposed procedure is demonstrated by means of a numerical example and its advantages over reduction methods used with the displacement formulation are discussed.

Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.

2017-11-01

An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary functions and/or arbitrary constant parameters), using the software package GeM for Maple. Application of equivalence transformations to the reduction of the number of arbitrary elements in a given system of equations is discussed, and several examples are considered. The first computational example of generalized equivalence transformations where the transformation of the dependent variable involves an arbitrary constitutive function is presented. As a detailed physical example, a three-parameter family of nonlinear wave equations describing finite anti-plane shear displacements of an incompressible hyperelastic fiber-reinforced medium is considered. Equivalence transformations are computed and employed to radically simplify the model for an arbitrary fiber direction, invertibly reducing the model to a simple form that corresponds to a special fiber direction, and involves no arbitrary elements. The presented computation algorithm is applicable to wide classes of systems of differential equations containing arbitrary elements.

Estimation of Flood-Frequency Discharges for Rural, Unregulated Streams in West Virginia

USGS Publications Warehouse

Wiley, Jeffrey B.; Atkins, John T.

2010-01-01

Flood-frequency discharges were determined for 290 streamgage stations having a minimum of 9 years of record in West Virginia and surrounding states through the 2006 or 2007 water year. No trend was determined in the annual peaks used to calculate the flood-frequency discharges. Multiple and simple least-squares regression equations for the 100-year (1-percent annual-occurrence probability) flood discharge with independent variables that describe the basin characteristics were developed for 290 streamgage stations in West Virginia and adjacent states. The regression residuals for the models were evaluated and used to define three regions of the State, designated as Eastern Panhandle, Central Mountains, and Western Plateaus. Exploratory data analysis procedures identified 44 streamgage stations that were excluded from the development of regression equations representative of rural, unregulated streams in West Virginia. Regional equations for the 1.1-, 1.5-, 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year flood discharges were determined by generalized least-squares regression using data from the remaining 246 streamgage stations. Drainage area was the only significant independent variable determined for all equations in all regions. Procedures developed to estimate flood-frequency discharges on ungaged streams were based on (1) regional equations and (2) drainage-area ratios between gaged and ungaged locations on the same stream. The procedures are applicable only to rural, unregulated streams within the boundaries of West Virginia that have drainage areas within the limits of the stations used to develop the regional equations (from 0.21 to 1,461 square miles in the Eastern Panhandle, from 0.10 to 1,619 square miles in the Central Mountains, and from 0.13 to 1,516 square miles in the Western Plateaus). The accuracy of the equations is quantified by measuring the average prediction error (from 21.7 to 56.3 percent) and equivalent years of record (from 2.0 to 70.9 years).

Scaling Laws Applied to a Modal Formulation of the Aeroservoelastic Equations

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S.

2002-01-01

A method of scaling is described that easily converts the aeroelastic equations of motion of a full-sized aircraft into ones of a wind-tunnel model. To implement the method, a set of rules is provided for the conversion process involving matrix operations with scale factors. In addition, a technique for analytically incorporating a spring mounting system into the aeroelastic equations is also presented. As an example problem, a finite element model of a full-sized aircraft is introduced from the High Speed Research (HSR) program to exercise the scaling method. With a set of scale factor values, a brief outline is given of a procedure to generate the first-order aeroservoelastic analytical model representing the wind-tunnel model. To verify the scaling process as applied to the example problem, the root-locus patterns from the full-sized vehicle and the wind-tunnel model are compared to see if the root magnitudes scale with the frequency scale factor value. Selected time-history results are given from a numerical simulation of an active-controlled wind-tunnel model to demonstrate the utility of the scaling process.

Symbolic generation of elastic rotor blade equations using a FORTRAN processor and numerical study on dynamic inflow effects on the stability of helicopter rotors

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.

1986-01-01

The process of performing an automated stability analysis for an elastic-bladed helicopter rotor is discussed. A symbolic manipulation program, written in FORTRAN, is used to aid in the derivation of the governing equations of motion for the rotor. The blades undergo coupled bending and torsional deformations. Two-dimensional quasi-steady aerodynamics below stall are used. Although reversed flow effects are neglected, unsteady effects, modeled as dynamic inflow are included. Using a Lagrangian approach, the governing equations are derived in generalized coordinates using the symbolic program. The program generates the steady and perturbed equations and writes into subroutines to be called by numerical routines. The symbolic program can operate on both expressions and matrices. For the case of hovering flight, the blade and dynamic inflow equations are converted to equations in a multiblade coordinate system by rearranging the coefficients of the equations. For the case of forward flight, the multiblade equations are obtained through the symbolic program. The final multiblade equations are capable of accommodating any number of elastic blade modes. The computer implementation of this procedure consists of three stages: (1) the symbolic derivation of equations; (2) the coding of the equations into subroutines; and (3) the numerical study after identifying mass, damping, and stiffness coefficients. Damping results are presented in hover and in forward flight with and without dynamic inflow effects for various rotor blade models, including rigid blade lag-flap, elastic flap-lag, flap-lag-torsion, and quasi-static torsion. Results from dynamic inflow effects which are obtained from a lift deficiency function for a quasi-static inflow model in hover are also presented.

A mathematical approach to molecular organization and proteolytic disintegration of bacterial inclusion bodies.

PubMed

Cubarsi, R; Carrió, M M; Villaverde, A

2005-09-01

The in vivo proteolytic digestion of bacterial inclusion bodies (IBs) and the kinetic analysis of the resulting protein fragments is an interesting approach to investigate the molecular organization of these unconventional protein aggregates. In this work, we describe a set of mathematical instruments useful for such analysis and interpretation of observed data. These methods combine numerical estimation of digestion rate and approximation of its high-order derivatives, modelling of fragmentation events from a mixture of Poisson processes associated with differentiated protein species, differential equations techniques in order to estimate the mixture parameters, an iterative predictor-corrector algorithm for describing the flow diagram along the cascade process, as well as least squares procedures with minimum variance estimates. The models are formulated and compared with data, and successively refined to better match experimental observations. By applying such procedures as well as newer improved algorithms of formerly developed equations, it has been possible to model, for two kinds of bacterially produced aggregation prone recombinant proteins, their cascade digestion process that has revealed intriguing features of the IB-forming polypeptides.

On an integro-differential equation model for the study of the response of an acoustically coupled panel

NASA Technical Reports Server (NTRS)

Yen, D. H. Y.; Maestrello, L.; Padula, S.

1975-01-01

The response of a clamped panel to supersonically convected turbulence is considered. A theoretical model in the form of an integro-differential equation is employed that takes into account the coupling between the panel motion and the surrounding acoustic medium. The kernels of the integrals, which represent induced pressures due to the panel motion, are Green's functions for sound radiations under various moving and stationary sources. An approximate analysis is made by following a finite-element Ritz-Galerkin procedure. Preliminary numerical results, in agreement with experimental findings, indicate that the acoustic damping is the controlling mechanism of the response.

Crop status evaluations and yield predictions

NASA Technical Reports Server (NTRS)

Haun, J. R.

1975-01-01

A model was developed for predicting the day 50 percent of the wheat crop is planted in North Dakota. This model incorporates location as an independent variable. The Julian date when 50 percent of the crop was planted for the nine divisions of North Dakota for seven years was regressed on the 49 variables through the step-down multiple regression procedure. This procedure begins with all of the independent variables and sequentially removes variables that are below a predetermined level of significance after each step. The prediction equation was tested on daily data. The accuracy of the model is considered satisfactory for finding the historic dates on which to initiate yield prediction model. Growth prediction models were also developed for spring wheat.

Why does shear banding behave like first-order phase transitions? Derivation of a potential from a mechanical constitutive model.

PubMed

Sato, K; Yuan, X-F; Kawakatsu, T

2010-02-01

Numerous numerical and experimental evidence suggest that shear banding behavior looks like first-order phase transitions. In this paper, we demonstrate that this correspondence is actually established in the so-called non-local diffusive Johnson-Segalman model (the DJS model), a typical mechanical constitutive model that has been widely used for describing shear banding phenomena. In the neighborhood of the critical point, we apply the reduction procedure based on the center manifold theory to the governing equations of the DJS model. As a result, we obtain a time evolution equation of the flow field that is equivalent to the time-dependent Ginzburg-Landau (TDGL) equations for modeling thermodynamic first-order phase transitions. This result, for the first time, provides a mathematical proof that there is an analogy between the mechanical instability and thermodynamic phase transition at least in the vicinity of the critical point of the shear banding of DJS model. Within this framework, we can clearly distinguish the metastable branch in the stress-strain rate curve around the shear banding region from the globally stable branch. A simple extension of this analysis to a class of more general constitutive models is also discussed. Numerical simulations for the original DJS model and the reduced TDGL equation is performed to confirm the range of validity of our reduction theory.

Equating Two Forms of a Criterion-Referenced Test by Using Norm Referenced Data: An Illustration of Two Methods.

ERIC Educational Resources Information Center

Garcia-Quintana, Roan A.; Johnson, Lynne M.

Three different computational procedures for equating two forms of a test were applied to a pair of mathematics tests to compare the results of the three procedures. The tests that were being equated were two forms of the SRA Mastery Mathematics Tests. The common, linking test used for equating was the Comprehensive Tests of Basic Skills, Form S,…

Lagrangian averaging, nonlinear waves, and shock regularization

NASA Astrophysics Data System (ADS)

Bhat, Harish S.

In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in both material and spatial frames. Writing the resulting equations of motion requires certain Lie-algebraic calculations that we carry out in detail for expository purposes. Next, we extend the derivation of the Lagrangian averaged Euler (LAE-alpha) equations to the case of barotropic compressible flows. The derivation in this thesis involves averaging over a tube of trajectories etaepsilon centered around a given Lagrangian flow eta. With this tube framework, the LAE-alpha equations are derived by following a simple procedure: start with a given action, expand via Taylor series in terms of small-scale fluid fluctuations xi, truncate, average, and then model those terms that are nonlinear functions of xi. We then analyze a one-dimensional subcase of the general models derived above. We prove the existence of a large family of traveling wave solutions. Computing the dispersion relation for this model, we find it is nonlinear, implying that the equation is dispersive. We carry out numerical experiments that show that the model possesses smooth, bounded solutions that display interesting pattern formation. Finally, we examine a Hamiltonian partial differential equation (PDE) that regularizes the inviscid Burgers equation without the addition of standard viscosity. Here alpha is a small parameter that controls a nonlinear smoothing term that we have added to the inviscid Burgers equation. We show the existence of a large family of traveling front solutions. We analyze the initial-value problem and prove well-posedness for a certain class of initial data. We prove that in the zero-alpha limit, without any standard viscosity, solutions of the PDE converge strongly to weak solutions of the inviscid Burgers equation. We provide numerical evidence that this limit satisfies an entropy inequality for the inviscid Burgers equation. We demonstrate a Hamiltonian structure for the PDE.

Transonic Navier-Stokes solutions of three-dimensional afterbody flows

NASA Technical Reports Server (NTRS)

Compton, William B., III; Thomas, James L.; Abeyounis, William K.; Mason, Mary L.

1989-01-01

The performance of a three-dimensional Navier-Stokes solution technique in predicting the transonic flow past a nonaxisymmetric nozzle was investigated. The investigation was conducted at free-stream Mach numbers ranging from 0.60 to 0.94 and an angle of attack of 0 degrees. The numerical solution procedure employs the three-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations written in strong conservation form, a thin layer assumption, and the Baldwin-Lomax turbulence model. The equations are solved by using the finite-volume principle in conjunction with an approximately factored upwind-biased numerical algorithm. In the numerical procedure, the jet exhaust is represented by a solid sting. Wind-tunnel data with the jet exhaust simulated by high pressure air were also obtained to compare with the numerical calculations.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

Higher groupoid bundles, higher spaces, and self-dual tensor field equations

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Sämann, Christian; Wolf, Martin

2016-08-01

We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general class of (higher) spaces comprising presentable differentiable stacks, as e.g. orbifolds. We start off with a self-contained review on simplicial sets as models of $(\\infty,1)$-categories. We then discuss principal bundles in terms of simplicial maps and their homotopies. We explain in detail a differentiation procedure, suggested by Severa, that maps higher groupoids to $L_\\infty$-algebroids. Generalising this procedure, we define connections for higher groupoid bundles. As an application, we obtain six-dimensional superconformal field theories via a Penrose-Ward transform of higher groupoid bundles over a twistor space. This construction reduces the search for non-Abelian self-dual tensor field equations in six dimensions to a search for the appropriate (higher) gauge structure. The treatment aims to be accessible to theoretical physicists.

FAST SIMULATION OF SOLID TUMORS THERMAL ABLATION TREATMENTS WITH A 3D REACTION DIFFUSION MODEL *

PubMed Central

BERTACCINI, DANIELE; CALVETTI, DANIELA

2007-01-01

An efficient computational method for near real-time simulation of thermal ablation of tumors via radio frequencies is proposed. Model simulations of the temperature field in a 3D portion of tissue containing the tumoral mass for different patterns of source heating can be used to design the ablation procedure. The availability of a very efficient computational scheme makes it possible update the predicted outcome of the procedure in real time. In the algorithms proposed here a discretization in space of the governing equations is followed by an adaptive time integration based on implicit multistep formulas. A modification of the ode15s MATLAB function which uses Krylov space iterative methods for the solution of for the linear systems arising at each integration step makes it possible to perform the simulations on standard desktop for much finer grids than using the built-in ode15s. The proposed algorithm can be applied to a wide class of nonlinear parabolic differential equations. PMID:17173888

A Constitutive Model for the Inelastic Multiaxial Cyclic Response of a Nickel Base Superalloy Rene 80. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Ramaswamy, V. G.

1986-01-01

The objective was to develop unified constitutive equations which can model a variety of nonlinear material phenomena observed in Rene 80 at elevated temperatures. A constitutive model was developed based on back stress and drag stress. The tensorial back stress was used to model directional effects; whereas, the scalar drag stress was used to model isotropic effects and cyclic hardening or softening. A flow equation and evolution equations for the state variables were developed in multiaxial form. Procedures were developed to generate the material parameters. The model predicted very well the monotonic tensile, cyclic, creep, and stress relaxation behavior of Rene 80 at 982 C. The model was then extended to 871, 760, and 538 C. It was shown that strain rate dependent behavior at high temperatures and strain rate independent behavior at the lower temperatures could be predicted very well. A large number of monotonic tensile, creep, stress relation, and cyclic experiments were predicted. The multiaxial capabilities of the model were verified extensively for combined tension/torsion experiments. The prediction of the model agreed very well for proportional, nonproportional, and pure shear cyclic loading conditions at 982 and 871 C.

A low diffusive Lagrange-remap scheme for the simulation of violent air-water free-surface flows

NASA Astrophysics Data System (ADS)

Bernard-Champmartin, Aude; De Vuyst, Florian

2014-10-01

In 2002, Després and Lagoutière [17] proposed a low-diffusive advection scheme for pure transport equation problems, which is particularly accurate for step-shaped solutions, and thus suited for interface tracking procedure by a color function. This has been extended by Kokh and Lagoutière [28] in the context of compressible multifluid flows using a five-equation model. In this paper, we explore a simplified variant approach for gas-liquid three-equation models. The Eulerian numerical scheme has two ingredients: a robust remapped Lagrange solver for the solution of the volume-averaged equations, and a low diffusive compressive scheme for the advection of the gas mass fraction. Numerical experiments show the performance of the computational approach on various flow reference problems: dam break, sloshing of a tank filled with water, water-water impact and finally a case of Rayleigh-Taylor instability. One of the advantages of the present interface capturing solver is its natural implementation on parallel processors or computers.

Numerical Calculations of 3-D High-Lift Flows and Comparison with Experiment

NASA Technical Reports Server (NTRS)

Compton, William B, III

2015-01-01

Solutions were obtained with the Navier-Stokes CFD code TLNS3D to predict the flow about the NASA Trapezoidal Wing, a high-lift wing composed of three elements: the main-wing element, a deployed leading-edge slat, and a deployed trailing-edge flap. Turbulence was modeled by the Spalart-Allmaras one-equation turbulence model. One case with massive separation was repeated using Menter's two-equation SST (Menter's Shear Stress Transport) k-omega turbulence model in an attempt to improve the agreement with experiment. The investigation was conducted at a free stream Mach number of 0.2, and at angles of attack ranging from 10.004 degrees to 34.858 degrees. The Reynolds number based on the mean aerodynamic chord of the wing was 4.3 x 10 (sup 6). Compared to experiment, the numerical procedure predicted the surface pressures very well at angles of attack in the linear range of the lift. However, computed maximum lift was 5% low. Drag was mainly under predicted. The procedure correctly predicted several well-known trends and features of high-lift flows, such as off-body separation. The two turbulence models yielded significantly different solutions for the repeated case.

Robustness of fit indices to outliers and leverage observations in structural equation modeling.

PubMed

Yuan, Ke-Hai; Zhong, Xiaoling

2013-06-01

Normal-distribution-based maximum likelihood (NML) is the most widely used method in structural equation modeling (SEM), although practical data tend to be nonnormally distributed. The effect of nonnormally distributed data or data contamination on the normal-distribution-based likelihood ratio (LR) statistic is well understood due to many analytical and empirical studies. In SEM, fit indices are used as widely as the LR statistic. In addition to NML, robust procedures have been developed for more efficient and less biased parameter estimates with practical data. This article studies the effect of outliers and leverage observations on fit indices following NML and two robust methods. Analysis and empirical results indicate that good leverage observations following NML and one of the robust methods lead most fit indices to give more support to the substantive model. While outliers tend to make a good model superficially bad according to many fit indices following NML, they have little effect on those following the two robust procedures. Implications of the results to data analysis are discussed, and recommendations are provided regarding the use of estimation methods and interpretation of fit indices. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

A Sub-filter Scale Noise Equation far Hybrid LES Simulations

NASA Technical Reports Server (NTRS)

Goldstein, Marvin E.

2006-01-01

Hybrid LES/subscale modeling approaches have an important advantage over the current noise prediction methods in that they only involve modeling of the relatively universal subscale motion and not the configuration dependent larger scale turbulence . Previous hybrid approaches use approximate statistical techniques or extrapolation methods to obtain the requisite information about the sub-filter scale motion. An alternative approach would be to adopt the modeling techniques used in the current noise prediction methods and determine the unknown stresses from experimental data. The present paper derives an equation for predicting the sub scale sound from information that can be obtained with currently available experimental procedures. The resulting prediction method would then be intermediate between the current noise prediction codes and previously proposed hybrid techniques.

Prediction of hydrodynamics and chemistry of confined turbulent methane-air flames with attention to formation of oxides of nitrogen

NASA Technical Reports Server (NTRS)

Elghobashi, S.; Spalding, D. B.; Srivatsa, S. K.

1977-01-01

A formulation of the governing partial differential equations for fluid flow and reacting chemical species in a tubular combustor is presented. A numerical procedure for the solution of the governing differential equations is described, and models for chemical equilibrium and chemical kinetics calculations are presented. The chemical equilibrium model is used to characterize the hydrocarbon reactions. The chemical kinetics model is used to predict the concentrations of the oxides of nitrogen. The combustor consists of a cylindrical duct of varying cross sections with concentric streams of gaseous fuel and air entering the duct at one end. Four sample cases with specified inlet and boundary conditions are considered, and the results are discussed

A thought construction of working perpetuum mobile of the second kind

NASA Astrophysics Data System (ADS)

Čápek, V.; Bok, J.

1999-12-01

The previously published model of the isothermal Maxwell demon as one of models of open quantum systems endowed with the faculty of selforganization is reconstructed here. It describes an open quantum system interacting with a single thermodynamic bath but otherwise not aided from outside. Its activity is given by the standard linear Liouville equation for the system and bath. Owing to its selforganization property, the model then yields cyclic conversion of heat from the bath into mechanical work without compensation. Hence, it provides an explicit thought construction of perpetuum mobile of the second kind, contradicting thus the Thomson formulation of the second law of thermodynamics. No approximation is involved as a special scaling procedure is used which makes the employed kinetic equations exact.

Differential geometry based solvation model. III. Quantum formulation

PubMed Central

Chen, Zhan; Wei, Guo-Wei

2011-01-01

Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model. PMID:22112067

Structural equation modeling: building and evaluating causal models: Chapter 8

USGS Publications Warehouse

Grace, James B.; Scheiner, Samuel M.; Schoolmaster, Donald R.

2015-01-01

Scientists frequently wish to study hypotheses about causal relationships, rather than just statistical associations. This chapter addresses the question of how scientists might approach this ambitious task. Here we describe structural equation modeling (SEM), a general modeling framework for the study of causal hypotheses. Our goals are to (a) concisely describe the methodology, (b) illustrate its utility for investigating ecological systems, and (c) provide guidance for its application. Throughout our presentation, we rely on a study of the effects of human activities on wetland ecosystems to make our description of methodology more tangible. We begin by presenting the fundamental principles of SEM, including both its distinguishing characteristics and the requirements for modeling hypotheses about causal networks. We then illustrate SEM procedures and offer guidelines for conducting SEM analyses. Our focus in this presentation is on basic modeling objectives and core techniques. Pointers to additional modeling options are also given.

The Routine Fitting of Kinetic Data to Models

PubMed Central

Berman, Mones; Shahn, Ezra; Weiss, Marjory F.

1962-01-01

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible. PMID:13867975

Coarse mesh and one-cell block inversion based diffusion synthetic acceleration

NASA Astrophysics Data System (ADS)

Kim, Kang-Seog

DSA (Diffusion Synthetic Acceleration) has been developed to accelerate the SN transport iteration. We have developed solution techniques for the diffusion equations of FLBLD (Fully Lumped Bilinear Discontinuous), SCB (Simple Comer Balance) and UCB (Upstream Corner Balance) modified 4-step DSA in x-y geometry. Our first multi-level method includes a block Gauss-Seidel iteration for the discontinuous diffusion equation, uses the continuous diffusion equation derived from the asymptotic analysis, and avoids void cell calculation. We implemented this multi-level procedure and performed model problem calculations. The results showed that the FLBLD, SCB and UCB modified 4-step DSA schemes with this multi-level technique are unconditionally stable and rapidly convergent. We suggested a simplified multi-level technique for FLBLD, SCB and UCB modified 4-step DSA. This new procedure does not include iterations on the diffusion calculation or the residual calculation. Fourier analysis results showed that this new procedure was as rapidly convergent as conventional modified 4-step DSA. We developed new DSA procedures coupled with 1-CI (Cell Block Inversion) transport which can be easily parallelized. We showed that 1-CI based DSA schemes preceded by SI (Source Iteration) are efficient and rapidly convergent for LD (Linear Discontinuous) and LLD (Lumped Linear Discontinuous) in slab geometry and for BLD (Bilinear Discontinuous) and FLBLD in x-y geometry. For 1-CI based DSA without SI in slab geometry, the results showed that this procedure is very efficient and effective for all cases. We also showed that 1-CI based DSA in x-y geometry was not effective for thin mesh spacings, but is effective and rapidly convergent for intermediate and thick mesh spacings. We demonstrated that the diffusion equation discretized on a coarse mesh could be employed to accelerate the transport equation. Our results showed that coarse mesh DSA is unconditionally stable and is as rapidly convergent as fine mesh DSA in slab geometry. For x-y geometry our coarse mesh DSA is very effective for thin and intermediate mesh spacings independent of the scattering ratio, but is not effective for purely scattering problems and high aspect ratio zoning. However, if the scattering ratio is less than about 0.95, this procedure is very effective for all mesh spacing.

Sensitivity of the model error parameter specification in weak-constraint four-dimensional variational data assimilation

NASA Astrophysics Data System (ADS)

Shaw, Jeremy A.; Daescu, Dacian N.

2017-08-01

This article presents the mathematical framework to evaluate the sensitivity of a forecast error aspect to the input parameters of a weak-constraint four-dimensional variational data assimilation system (w4D-Var DAS), extending the established theory from strong-constraint 4D-Var. Emphasis is placed on the derivation of the equations for evaluating the forecast sensitivity to parameters in the DAS representation of the model error statistics, including bias, standard deviation, and correlation structure. A novel adjoint-based procedure for adaptive tuning of the specified model error covariance matrix is introduced. Results from numerical convergence tests establish the validity of the model error sensitivity equations. Preliminary experiments providing a proof-of-concept are performed using the Lorenz multi-scale model to illustrate the theoretical concepts and potential benefits for practical applications.

Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation.

PubMed

Hu, Xiao-Rui; Lou, Sen-Yue; Chen, Yong

2012-05-01

In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painlevé II solutions.

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

NASA Astrophysics Data System (ADS)

Troisi, Antonio

2017-03-01

Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f( R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R)=f_0R^n the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions.

Numerical modelling of multiphase liquid-vapor-gas flows with interfaces and cavitation

NASA Astrophysics Data System (ADS)

Pelanti, Marica

2017-11-01

We are interested in the simulation of multiphase flows where the dynamical appearance of vapor cavities and evaporation fronts in a liquid is coupled to the dynamics of a third non-condensable gaseous phase. We describe these flows by a single-velocity three-phase compressible flow model composed of the phasic mass and total energy equations, the volume fraction equations, and the mixture momentum equation. The model includes stiff mechanical and thermal relaxation source terms for all the phases, and chemical relaxation terms to describe mass transfer between the liquid and vapor phases of the species that may undergo transition. The flow equations are solved by a mixture-energy-consistent finite volume wave propagation scheme, combined with simple and robust procedures for the treatment of the stiff relaxation terms. An analytical study of the characteristic wave speeds of the hierarchy of relaxed models associated to the parent model system is also presented. We show several numerical experiments, including two-dimensional simulations of underwater explosive phenomena where highly pressurized gases trigger cavitation processes close to a rigid surface or to a free surface. This work was supported by the French Government Grant DGA N. 2012.60.0011.00.470.75.01, and partially by the Norwegian Grant RCN N. 234126/E30.

A Procedure for Structural Weight Estimation of Single Stage to Orbit Launch Vehicles (Interim User's Manual)

NASA Technical Reports Server (NTRS)

Martinovic, Zoran N.; Cerro, Jeffrey A.

2002-01-01

This is an interim user's manual for current procedures used in the Vehicle Analysis Branch at NASA Langley Research Center, Hampton, Virginia, for launch vehicle structural subsystem weight estimation based on finite element modeling and structural analysis. The process is intended to complement traditional methods of conceptual and early preliminary structural design such as the application of empirical weight estimation or application of classical engineering design equations and criteria on one dimensional "line" models. Functions of two commercially available software codes are coupled together. Vehicle modeling and analysis are done using SDRC/I-DEAS, and structural sizing is performed with the Collier Research Corp. HyperSizer program.

A model for the value of a business, some optimization problems in its operating procedures and the valuation of its debt

NASA Astrophysics Data System (ADS)

1997-12-01

In this paper we present a model for the value of a firm based on observable variables and parameters: the annual turnover, the expenses, interest rates. This value is the solution of a parabolic partial differential equation. We show how the value of the company depends on its legal status such as its liability (that is, whether it is a Limited Company or a sole trader/partnership). We give examples of how the operating procedures can be optimized (for example, whether the firm should close down, relocate etc.). Finally, we show how the model can be used to value the debt issued by the firm.

Formulation of a General Technique for Predicting Pneumatic Attenuation Errors in Airborne Pressure Sensing Devices

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.

1988-01-01

Presented is a mathematical model derived from the Navier-Stokes equations of momentum and continuity, which may be accurately used to predict the behavior of conventionally mounted pneumatic sensing systems subject to arbitrary pressure inputs. Numerical techniques for solving the general model are developed. Both step and frequency response lab tests were performed. These data are compared with solutions of the mathematical model and show excellent agreement. The procedures used to obtain the lab data are described. In-flight step and frequency response data were obtained. Comparisons with numerical solutions of the math model show good agreement. Procedures used to obtain the flight data are described. Difficulties encountered with obtaining the flight data are discussed.

An Engineering Solution for Solving Mesh Size Effects in the Simulation of Delamination with Cohesive Zone Models

NASA Technical Reports Server (NTRS)

Turon, A.; Davila, C. G.; Camanho, P. P.; Costa, J.

2007-01-01

This paper presents a methodology to determine the parameters to be used in the constitutive equations of Cohesive Zone Models employed in the simulation of delamination in composite materials by means of decohesion finite elements. A closed-form expression is developed to define the stiffness of the cohesive layer. A novel procedure that allows the use of coarser meshes of decohesion elements in large-scale computations is also proposed. The procedure ensures that the energy dissipated by the fracture process is computed correctly. It is shown that coarse-meshed models defined using the approach proposed here yield the same results as the models with finer meshes normally used for the simulation of fracture processes.

Automated analysis of biological oscillator models using mode decomposition.

PubMed

Konopka, Tomasz

2011-04-01

Oscillating signals produced by biological systems have shapes, described by their Fourier spectra, that can potentially reveal the mechanisms that generate them. Extracting this information from measured signals is interesting for the validation of theoretical models, discovery and classification of interaction types, and for optimal experiment design. An automated workflow is described for the analysis of oscillating signals. A software package is developed to match signal shapes to hundreds of a priori viable model structures defined by a class of first-order differential equations. The package computes parameter values for each model by exploiting the mode decomposition of oscillating signals and formulating the matching problem in terms of systems of simultaneous polynomial equations. On the basis of the computed parameter values, the software returns a list of models consistent with the data. In validation tests with synthetic datasets, it not only shortlists those model structures used to generate the data but also shows that excellent fits can sometimes be achieved with alternative equations. The listing of all consistent equations is indicative of how further invalidation might be achieved with additional information. When applied to data from a microarray experiment on mice, the procedure finds several candidate model structures to describe interactions related to the circadian rhythm. This shows that experimental data on oscillators is indeed rich in information about gene regulation mechanisms. The software package is available at http://babylone.ulb.ac.be/autoosc/.

Terrestrial gravity data analysis for interim gravity model improvement

NASA Technical Reports Server (NTRS)

1987-01-01

This is the first status report for the Interim Gravity Model research effort that was started on June 30, 1986. The basic theme of this study is to develop appropriate models and adjustment procedures for estimating potential coefficients from terrestrial gravity data. The plan is to use the latest gravity data sets to produce coefficient estimates as well as to provide normal equations to NASA for use in the TOPEX/POSEIDON gravity field modeling program.

Using the Multilayer Free-Surface Flow Model to Solve Wave Problems

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

Prokof’ev, V. A., E-mail: ProkofyevVA@vniig.ru

2017-01-15

A method is presented for changing over from a single-layer shallow-water model to a multilayer model with hydrostatic pressure profile and, then, to a multilayer model with nonhydrostatic pressure profile. The method does not require complex procedures for solving the discrete Poisson’s equation and features high computation efficiency. The results of validating the algorithm against experimental data critical for the numerical dissipation of the numerical scheme are presented. Examples are considered.

Bilateral effects of hospital patient-safety procedures on nurses' job satisfaction.

PubMed

Inoue, T; Karima, R; Harada, K

2017-09-01

The aim of this study was to examine how hospital patient-safety procedures affect the job satisfaction of hospital nurses. Additionally, we investigated the association between perceived autonomy and hospital patient-safety procedures and job satisfaction. Recently, measures for patient safety have been recognized as an essential requirement in hospitals. Hospital patient-safety procedures may enhance the job satisfaction of nurses by improving the quality of their work. However, such procedures may also decrease their job satisfaction by imposing excessive stress on nurses because they cannot make mistakes. The participants included 537 nurses at 10 private hospitals in Japan (The surveys were collected from March to July 2012). Factors related to hospital patient-safety procedures were demonstrated using factor analysis, and the associations between these factors and nurses' self-perceived autonomy and job satisfaction were examined using structural equation modelling. Five factors regarding hospital patient-safety procedures were extracted. Additionally, structural equation modelling revealed statistically significant associations between these factors and the nurses' self-perceived autonomy and job satisfaction. The findings showed that nurses' perceived autonomy of the workplace enhanced their job satisfaction and that their perceptions of hospital patient-safety procedures promoted their job satisfaction. However, some styles of chief nurses' leadership regarding patient safety restrict nurses' independent and autonomous decision-making and actions, resulting in a lowering of job satisfaction. This study demonstrated that hospital patient-safety procedures have ambiguous effects on nurses' job satisfaction. In particular, chief nurses' leadership relating to patient safety can have a positive or negative effect on nurses' job satisfaction. The findings indicated that hospital managers should demonstrate positive attitudes to improve patient safety for nurses' job satisfaction. In addition, policymakers in the hospitals should consider that chief nurses' leadership styles may reduce autonomy and suppress nurses' job satisfaction. © 2017 The Authors International Nursing Review published by John Wiley & Sons Ltd on behalf of International Council of Nurses.

Development of numerical techniques for simulation of magnetogasdynamics and hypersonic chemistry

NASA Astrophysics Data System (ADS)

Damevin, Henri-Marie

Magnetogasdynamics, the science concerned with the mutual interaction between electromagnetic field and flow of electrically conducting gas, offers promising advances in flow control and propulsion of future hypersonic vehicles. Numerical simulations are essential for understanding phenomena, and for research and development. The current dissertation is devoted to the development and validation of numerical algorithms for the solution of multidimensional magnetogasdynamic equations and the simulation of hypersonic high-temperature effects. Governing equations are derived, based on classical magnetogasdynamic assumptions. Two sets of equations are considered, namely the full equations and equations in the low magnetic Reynolds number approximation. Equations are expressed in a suitable formulation for discretization by finite differences in a computational space. For the full equations, Gauss law for magnetism is enforced using Powell's methodology. The time integration method is a four-stage modified Runge-Kutta scheme, amended with a Total Variation Diminishing model in a postprocessing stage. The eigensystem, required for the Total Variation Diminishing scheme, is derived in generalized three-dimensional coordinate system. For the simulation of hypersonic high-temperature effects, two chemical models are utilized, namely a nonequilibrium model and an equilibrium model. A loosely coupled approach is implemented to communicate between the magnetogasdynamic equations and the chemical models. The nonequilibrium model is a one-temperature, five-species, seventeen-reaction model solved by an implicit flux-vector splitting scheme. The chemical equilibrium model computes thermodynamics properties using curve fit procedures. Selected results are provided, which explore the different features of the numerical algorithms. The shock-capturing properties are validated for shock-tube simulations using numerical solutions reported in the literature. The computations of superfast flows over corners and in convergent channels demonstrate the performances of the algorithm in multiple dimensions. The implementation of diffusion terms is validated by solving the magnetic Rayleigh problem and Hartmann problem, for which analytical solutions are available. Prediction of blunt-body type flow are investigated and compared with numerical solutions reported in the literature. The effectiveness of the chemical models for hypersonic flow over blunt body is examined in various flow conditions. It is shown that the proposed schemes perform well in a variety of test cases, though some limitations have been identified.

Finite element solution of transient fluid-structure interaction problems

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Cheng, Raymond S.; Hambric, Stephen A.

1991-01-01

A finite element approach using NASTRAN is developed for solving time-dependent fluid-structure interaction problems, with emphasis on the transient scattering of acoustic waves from submerged elastic structures. Finite elements are used for modeling both structure and fluid domains to facilitate the graphical display of the wave motion through both media. For the liquid, the use of velocity potential as the fundamental unknown results in a symmetric matrix equation. The approach is illustrated for the problem of transient scattering from a submerged elastic spherical shell subjected to an incident tone burst. The use of an analogy between the equations of elasticity and the wave equation of acoustics, a necessary ingredient to the procedure, is summarized.

Compliance matrices for cracked bodies

NASA Technical Reports Server (NTRS)

Ballarini, R.

1986-01-01

An algorithm is developed to construct the compliance matrix for a cracked solid in the integral-equation formulation of two-dimensional linear-elastic fracture mechanics. The integral equation is reduced to a system of algebraic equations for unknown values of the dislocation-density function at discrete points on the interval from -1 to 1, using the numerical procedure described by Gerasoulis (1982). Sample numerical results are presented, and it is suggested that the algorithm is especially useful in cases where iterative solutions are required; e.g., models of fiber-reinforced concrete, rocks, or ceramics where microcracking, fiber bridging, and other nonlinear effects are treated as nonlinear springs along the crack surfaces (Ballarini et al., 1984).

On the Yakhot-Orszag renormalization group method for deriving turbulence statistics and models

NASA Technical Reports Server (NTRS)

Smith, L. M.; Reynolds, W. C.

1992-01-01

An independent, comprehensive, critical review of the 'renormalization group' (RNG) theory of turbulence developed by Yakhot and Orszag (1986) is provided. Their basic theory for the Navier-Stokes equations is confirmed, and approximations in the scale removal procedure are discussed. The YO derivations of the velocity-derivative skewness and the transport equation for the energy dissipation rate are examined. An algebraic error in the derivation of the skewness is corrected. The corrected RNG skewness value of -0.59 is in agreement with experiments at moderate Reynolds numbers. Several problems are identified in the derivation of the energy dissipation rate equations which suggest that the derivation should be reformulated.

On the Solution of the Three-Dimensional Flowfield About a Flow-Through Nacelle. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Compton, William Bernard

1985-01-01

The solution of the three dimensional flow field for a flow through nacelle was studied. Both inviscid and viscous inviscid interacting solutions were examined. Inviscid solutions were obtained with two different computational procedures for solving the three dimensional Euler equations. The first procedure employs an alternating direction implicit numerical algorithm, and required the development of a complete computational model for the nacelle problem. The second computational technique employs a fourth order Runge-Kutta numerical algorithm which was modified to fit the nacelle problem. Viscous effects on the flow field were evaluated with a viscous inviscid interacting computational model. This model was constructed by coupling the explicit Euler solution procedure with a flag entrainment boundary layer solution procedure in a global iteration scheme. The computational techniques were used to compute the flow field for a long duct turbofan engine nacelle at free stream Mach numbers of 0.80 and 0.94 and angles of attack of 0 and 4 deg.

Construct validity of the Chinese version of the Self-care of Heart Failure Index determined using structural equation modeling.

PubMed

Kang, Xiaofeng; Dennison Himmelfarb, Cheryl R; Li, Zheng; Zhang, Jian; Lv, Rong; Guo, Jinyu

2015-01-01

The Self-care of Heart Failure Index (SCHFI) is an empirically tested instrument for measuring the self-care of patients with heart failure. The aim of this study was to develop a simplified Chinese version of the SCHFI and provide evidence for its construct validity. A total of 182 Chinese with heart failure were surveyed. A 2-step structural equation modeling procedure was applied to test construct validity. Factor analysis showed 3 factors explaining 43% of the variance. Structural equation model confirmed that self-care maintenance, self-care management, and self-care confidence are indeed indicators of self-care, and self-care confidence was a positive and equally strong predictor of self-care maintenance and self-care management. Moreover, self-care scores were correlated with the Partners in Health Scale, indicating satisfactory concurrent validity. The Chinese version of the SCHFI is a theory-based instrument for assessing self-care of Chinese patients with heart failure.

Identifying parameter regions for multistationarity

PubMed Central

Conradi, Carsten; Mincheva, Maya; Wiuf, Carsten

2017-01-01

Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria. The procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity. PMID:28972969

Cattell-Horn-Carroll Cognitive Abilities and Reading Achievement

ERIC Educational Resources Information Center

Benson, Nicholas

2008-01-01

Structural equation modeling procedures are applied to the standardization sample of the Woodcock-Johnson III to simultaneously estimate the effects of a psychometric general factor (g), specific cognitive abilities, and reading skills on reading achievement. The results of this study indicate that g has a strong direct relationship with basic…

Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

NASA Technical Reports Server (NTRS)

Jongen, T.; Gatski, T. B.

1997-01-01

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

Recursive thoughts on the simulation of the flexible multibody dynamics of slender offshore structures

NASA Astrophysics Data System (ADS)

Schilder, J.; Ellenbroek, M.; de Boer, A.

2017-12-01

In this work, the floating frame of reference formulation is used to create a flexible multibody model of slender offshore structures such as pipelines and risers. It is shown that due to the chain-like topology of the considered structures, the equation of motion can be expressed in terms of absolute interface coordinates. In the presented form, kinematic constraint equations are satisfied explicitly and the Lagrange multipliers are eliminated from the equations. Hence, the structures can be conveniently coupled to finite element or multibody models of for example seabed and vessel. The chain-like topology enables the efficient use of recursive solution procedures for both transient dynamic analysis and equilibrium analysis. For this, the transfer matrix method is used. In order to improve the convergence of the equilibrium analysis, the analytical solution of an ideal catenary is used as an initial configuration, reducing the number of required iterations.

Rotor dynamic simulation and system identification methods for application to vacuum whirl data

NASA Technical Reports Server (NTRS)

Berman, A.; Giansante, N.; Flannelly, W. G.

1980-01-01

Methods of using rotor vacuum whirl data to improve the ability to model helicopter rotors were developed. The work consisted of the formulation of the equations of motion of elastic blades on a hub using a Galerkin method; the development of a general computer program for simulation of these equations; the study and implementation of a procedure for determining physical parameters based on measured data; and the application of a method for computing the normal modes and natural frequencies based on test data.

Finite element analysis and computer graphics visualization of flow around pitching and plunging airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.

1973-01-01

A general computational method for analyzing unsteady flow around pitching and plunging airfoils was developed. The finite element method was applied in developing an efficient numerical procedure for the solution of equations describing the flow around airfoils. The numerical results were employed in conjunction with computer graphics techniques to produce visualization of the flow. The investigation involved mathematical model studies of flow in two phases: (1) analysis of a potential flow formulation and (2) analysis of an incompressible, unsteady, viscous flow from Navier-Stokes equations.

Renormalization group methods for the Reynolds stress transport equations

NASA Technical Reports Server (NTRS)

Rubinstein, R.

1992-01-01

The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

Analysis of energy states in modulation doped multiquantum well heterostructures

NASA Technical Reports Server (NTRS)

Ji, G.; Henderson, T.; Peng, C. K.; Huang, D.; Morkoc, H.

1990-01-01

A precise and effective numerical procedure to model the band diagram of modulation doped multiquantum well heterostructures is presented. This method is based on a self-consistent iterative solution of the Schroedinger equation and the Poisson equation. It can be used rather easily in any arbitrary modulation-doped structure. In addition to confined energy subbands, the unconfined states can be calculated as well. Examples on realistic device structures are given to demonstrate capabilities of this procedure. The numerical results are in good agreement with experiments. With the aid of this method the transitions involving both the confined and unconfined conduction subbands in a modulation doped AlGaAs/GaAs superlattice, and in a strained layer InGaAs/GaAs superlattice are identified. These results represent the first observation of unconfined transitions in modulation doped multiquantum well structures.

Procedures for experimental measurement and theoretical analysis of large plastic deformations

NASA Technical Reports Server (NTRS)

Morris, R. E.

1974-01-01

Theoretical equations are derived and analytical procedures are presented for the interpretation of experimental measurements of large plastic strains in the surface of a plate. Orthogonal gage lengths established on the metal surface are measured before and after deformation. The change in orthogonality after deformation is also measured. Equations yield the principal strains, deviatoric stresses in the absence of surface friction forces, true stresses if the stress normal to the surface is known, and the orientation angle between the deformed gage line and the principal stress-strain axes. Errors in the measurement of nominal strains greater than 3 percent are within engineering accuracy. Applications suggested for this strain measurement system include the large-strain-stress analysis of impact test models, burst tests of spherical or cylindrical pressure vessels, and to augment small-strain instrumentation tests where large strains are anticipated.

HCMM satellite follow-on investigation no. 25. Soil moisture and heat budget evalution in selected European zones of agricultural and environmental interest (TELLUS project)

NASA Technical Reports Server (NTRS)

1980-01-01

A simple procedure to evaluate actual evaporation was derived by linearizing the surface energy balance equation, using Taylor's expansion. The original multidimensional hypersurface could be reduced to a linear relationship between evaporation and surface temperature or to a surface relationship involving evaporation, surface temperature and albedo. This procedure permits a rapid sensitivity analysis of the surface energy balance equation as well as a speedy mapping of evaporation from remotely sensed surface temperatures and albedo. Comparison with experimental data yielded promising results. The validity of evapotranspiration and soil moisture models in semiarid conditions was tested. Wheat was the crop chosen for a continuous measurement campaign made in the south of Italy. Radiometric, micrometeorologic, agronomic and soil data were collected for processing and interpretation.

Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory

ERIC Educational Resources Information Center

Brossman, Bradley Grant

2010-01-01

The purpose of this research was to develop observed score and true score equating procedures to be used in conjunction with the Multidimensional Item Response Theory (MIRT) framework. Currently, MIRT scale linking procedures exist to place item parameter estimates and ability estimates on the same scale after separate calibrations are conducted.…

Identifyability measures to select the parameters to be estimated in a solid-state fermentation distributed parameter model.

PubMed

da Silveira, Christian L; Mazutti, Marcio A; Salau, Nina P G

2016-07-08

Process modeling can lead to of advantages such as helping in process control, reducing process costs and product quality improvement. This work proposes a solid-state fermentation distributed parameter model composed by seven differential equations with seventeen parameters to represent the process. Also, parameters estimation with a parameters identifyability analysis (PIA) is performed to build an accurate model with optimum parameters. Statistical tests were made to verify the model accuracy with the estimated parameters considering different assumptions. The results have shown that the model assuming substrate inhibition better represents the process. It was also shown that eight from the seventeen original model parameters were nonidentifiable and better results were obtained with the removal of these parameters from the estimation procedure. Therefore, PIA can be useful to estimation procedure, since it may reduce the number of parameters that can be evaluated. Further, PIA improved the model results, showing to be an important procedure to be taken. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:905-917, 2016. © 2016 American Institute of Chemical Engineers.

Modeling and analysis of the space shuttle nose-gear tire with semianalytic finite elements

NASA Technical Reports Server (NTRS)

Kim, Kyun O.; Noor, Ahmed K.; Tanner, John A.

1990-01-01

A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The Space Shuttle Orbiter nose gear tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynominals in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell. Numerical results of the Space Shuttle Orbiter nose gear tire model are compared with experimental measurements of the tire subjected to inflation loading.

Evaluating operational vacuum for landfill biogas extraction.

PubMed

Fabbricino, Massimiliano

2007-01-01

This manuscript proposes a practical methodology for estimating the operational vacuum for landfill biogas extraction from municipal landfills. The procedure is based on two sub-models which simulate landfill gas production from organic waste decomposition and distribution of gas pressure and gas movement induced by suction at a blower station. The two models are coupled in a single mass balance equation, obtaining a relationship between the operational vacuum and the amount of landfill gas that can be extracted from an assigned system of vertical wells. To better illustrate the procedure, it is applied to a case study, where a good agreement between simulated and measured data, within +/- 30%, is obtained.

A new statistical method for transfer coefficient calculations in the framework of the general multiple-compartment model of transport for radionuclides in biological systems.

PubMed

Garcia, F; Arruda-Neto, J D; Manso, M V; Helene, O M; Vanin, V R; Rodriguez, O; Mesa, J; Likhachev, V P; Filho, J W; Deppman, A; Perez, G; Guzman, F; de Camargo, S P

1999-10-01

A new and simple statistical procedure (STATFLUX) for the calculation of transfer coefficients of radionuclide transport to animals and plants is proposed. The method is based on the general multiple-compartment model, which uses a system of linear equations involving geometrical volume considerations. By using experimentally available curves of radionuclide concentrations versus time, for each animal compartment (organs), flow parameters were estimated by employing a least-squares procedure, whose consistency is tested. Some numerical results are presented in order to compare the STATFLUX transfer coefficients with those from other works and experimental data.

Iterative procedures for space shuttle main engine performance models

NASA Technical Reports Server (NTRS)

Santi, L. Michael

1989-01-01

Performance models of the Space Shuttle Main Engine (SSME) contain iterative strategies for determining approximate solutions to nonlinear equations reflecting fundamental mass, energy, and pressure balances within engine flow systems. Both univariate and multivariate Newton-Raphson algorithms are employed in the current version of the engine Test Information Program (TIP). Computational efficiency and reliability of these procedures is examined. A modified trust region form of the multivariate Newton-Raphson method is implemented and shown to be superior for off nominal engine performance predictions. A heuristic form of Broyden's Rank One method is also tested and favorable results based on this algorithm are presented.

Prediction of hydrodynamics and chemistry of confined turbulent methane-air frames in a two concentric tube combustor

NASA Technical Reports Server (NTRS)

Markatos, N. C.; Spalding, D. B.; Srivatsa, S. K.

1978-01-01

A formulation of the governing partial differential equations for fluid flow and reacting chemical species in a two-concentric-tube combustor is presented. A numerical procedure for the solution of the governing differential equations is described and models for chemical-equilibrium and chemical-kinetics calculations are presented. The chemical-equilibrium model is used to characterize the hydrocarbon reactions. The chemical-kinetics model is used to predict the concentrations of the oxides of nitrogen. The combustor considered consists of two coaxial ducts. Concentric streams of gaseous fuel and air enter the inlet duct at one end; the flow then reverses and flows out through the outer duct. Two sample cases with specified inlet and boundary conditions are considered and the results are discussed.

Chain pooling to minimize prediction error in subset regression. [Monte Carlo studies using population models

NASA Technical Reports Server (NTRS)

Holms, A. G.

1974-01-01

Monte Carlo studies using population models intended to represent response surface applications are reported. Simulated experiments were generated by adding pseudo random normally distributed errors to population values to generate observations. Model equations were fitted to the observations and the decision procedure was used to delete terms. Comparison of values predicted by the reduced models with the true population values enabled the identification of deletion strategies that are approximately optimal for minimizing prediction errors.

Turbulence modeling for hypersonic flight

NASA Technical Reports Server (NTRS)

Bardina, Jorge E.

1992-01-01

The objective of the present work is to develop, verify, and incorporate two equation turbulence models which account for the effect of compressibility at high speeds into a three dimensional Reynolds averaged Navier-Stokes code and to provide documented model descriptions and numerical procedures so that they can be implemented into the National Aerospace Plane (NASP) codes. A summary of accomplishments is listed: (1) Four codes have been tested and evaluated against a flat plate boundary layer flow and an external supersonic flow; (2) a code named RANS was chosen because of its speed, accuracy, and versatility; (3) the code was extended from thin boundary layer to full Navier-Stokes; (4) the K-omega two equation turbulence model has been implemented into the base code; (5) a 24 degree laminar compression corner flow has been simulated and compared to other numerical simulations; and (6) work is in progress in writing the numerical method of the base code including the turbulence model.

Finding identifiable parameter combinations in nonlinear ODE models and the rational reparameterization of their input-output equations.

PubMed

Meshkat, Nicolette; Anderson, Chris; Distefano, Joseph J

2011-09-01

When examining the structural identifiability properties of dynamic system models, some parameters can take on an infinite number of values and yet yield identical input-output data. These parameters and the model are then said to be unidentifiable. Finding identifiable combinations of parameters with which to reparameterize the model provides a means for quantitatively analyzing the model and computing solutions in terms of the combinations. In this paper, we revisit and explore the properties of an algorithm for finding identifiable parameter combinations using Gröbner Bases and prove useful theoretical properties of these parameter combinations. We prove a set of M algebraically independent identifiable parameter combinations can be found using this algorithm and that there exists a unique rational reparameterization of the input-output equations over these parameter combinations. We also demonstrate application of the procedure to a nonlinear biomodel. Copyright © 2011 Elsevier Inc. All rights reserved.

Estimating Selected Streamflow Statistics Representative of 1930-2002 in West Virginia

USGS Publications Warehouse

Wiley, Jeffrey B.

2008-01-01

Regional equations and procedures were developed for estimating 1-, 3-, 7-, 14-, and 30-day 2-year; 1-, 3-, 7-, 14-, and 30-day 5-year; and 1-, 3-, 7-, 14-, and 30-day 10-year hydrologically based low-flow frequency values for unregulated streams in West Virginia. Regional equations and procedures also were developed for estimating the 1-day, 3-year and 4-day, 3-year biologically based low-flow frequency values; the U.S. Environmental Protection Agency harmonic-mean flows; and the 10-, 25-, 50-, 75-, and 90-percent flow-duration values. Regional equations were developed using ordinary least-squares regression using statistics from 117 U.S. Geological Survey continuous streamflow-gaging stations as dependent variables and basin characteristics as independent variables. Equations for three regions in West Virginia - North, South-Central, and Eastern Panhandle - were determined. Drainage area, precipitation, and longitude of the basin centroid are significant independent variables in one or more of the equations. Estimating procedures are presented for determining statistics at a gaging station, a partial-record station, and an ungaged location. Examples of some estimating procedures are presented.

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

NASA Technical Reports Server (NTRS)

Grove, R. D.; Bowles, R. L.; Mayhew, S. C.

1972-01-01

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Comparative Study of Advanced Turbulence Models for Turbomachinery

NASA Technical Reports Server (NTRS)

Hadid, Ali H.; Sindir, Munir M.

1996-01-01

A computational study has been undertaken to study the performance of advanced phenomenological turbulence models coded in a modular form to describe incompressible turbulent flow behavior in two dimensional/axisymmetric and three dimensional complex geometry. The models include a variety of two equation models (single and multi-scale k-epsilon models with different near wall treatments) and second moment algebraic and full Reynolds stress closure models. These models were systematically assessed to evaluate their performance in complex flows with rotation, curvature and separation. The models are coded as self contained modules that can be interfaced with a number of flow solvers. These modules are stand alone satellite programs that come with their own formulation, finite-volume discretization scheme, solver and boundary condition implementation. They will take as input (from any generic Navier-Stokes solver) the velocity field, grid (structured H-type grid) and computational domain specification (boundary conditions), and will deliver, depending on the model used, turbulent viscosity, or the components of the Reynolds stress tensor. There are separate 2D/axisymmetric and/or 3D decks for each module considered. The modules are tested using Rocketdyn's proprietary code REACT. The code utilizes an efficient solution procedure to solve Navier-Stokes equations in a non-orthogonal body-fitted coordinate system. The differential equations are discretized over a finite-volume grid using a non-staggered variable arrangement and an efficient solution procedure based on the SIMPLE algorithm for the velocity-pressure coupling is used. The modules developed have been interfaced and tested using finite-volume, pressure-correction CFD solvers which are widely used in the CFD community. Other solvers can also be used to test these modules since they are independently structured with their own discretization scheme and solver methodology. Many of these modules have been independently tested by Professor C.P. Chen and his group at the University of Alabama at Huntsville (UAH) by interfacing them with own flow solver (MAST).

HYDRA-II: A hydrothermal analysis computer code: Volume 2, User's manual

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

McCann, R.A.; Lowery, P.S.; Lessor, D.L.

1987-09-01

HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite-difference solution in cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equations formore » conservation of momentum incorporate directional porosities and permeabilities that are available to model solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits modeling of orthotropic physical properties and film resistances. Several automated methods are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. Volume 1 - Equations and Numerics describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. This volume, Volume 2 - User's Manual, contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a sample problem. The final volume, Volume 3 - Verification/Validation Assessments, provides a comparison between the analytical solution and the numerical simulation for problems with a known solution. 6 refs.« less

Modeling the pressure inactivation of Escherichia coli and Salmonella typhimurium in sapote mamey ( Pouteria sapota (Jacq.) H.E. Moore & Stearn) pulp.

PubMed

Saucedo-Reyes, Daniela; Carrillo-Salazar, José A; Román-Padilla, Lizbeth; Saucedo-Veloz, Crescenciano; Reyes-Santamaría, María I; Ramírez-Gilly, Mariana; Tecante, Alberto

2018-03-01

High hydrostatic pressure inactivation kinetics of Escherichia coli ATCC 25922 and Salmonella enterica subsp. enterica serovar Typhimurium ATCC 14028 ( S. typhimurium) in a low acid mamey pulp at four pressure levels (300, 350, 400, and 450 MPa), different exposure times (0-8 min), and temperature of 25 ± 2℃ were obtained. Survival curves showed deviations from linearity in the form of a tail (upward concavity). The primary models tested were the Weibull model, the modified Gompertz equation, and the biphasic model. The Weibull model gave the best goodness of fit ( R 2 adj  > 0.956, root mean square error < 0.290) in the modeling and the lowest Akaike information criterion value. Exponential-logistic and exponential decay models, and Bigelow-type and an empirical models for b'( P) and n( P) parameters, respectively, were tested as alternative secondary models. The process validation considered the two- and one-step nonlinear regressions for making predictions of the survival fraction; both regression types provided an adequate goodness of fit and the one-step nonlinear regression clearly reduced fitting errors. The best candidate model according to the Akaike theory information, with better accuracy and more reliable predictions was the Weibull model integrated by the exponential-logistic and exponential decay secondary models as a function of time and pressure (two-step procedure) or incorporated as one equation (one-step procedure). Both mathematical expressions were used to determine the t d parameter, where the desired reductions ( 5D) (considering d = 5 ( t 5 ) as the criterion of 5 Log 10 reduction (5 D)) in both microorganisms are attainable at 400 MPa for 5.487 ± 0.488 or 5.950 ± 0.329 min, respectively, for the one- or two-step nonlinear procedure.

Volatilization of organic compounds from streams

USGS Publications Warehouse

Rathburn, R.E.; Tai, D.Y.

1982-01-01

Mass-transfer coefficients for the volatilization of ethylene and propane were correlated with the hydraulic and geometric properties of seven streams, and predictive equations were developed. The equations were evaluated using a normalized root-mean-square error as the criterion of comparison. The two best equations were a two-variable equation containing the energy dissipated per unit mass per unit time and the average depth of flow and a three-variable equation containing the average velocity, the average depth of flow, and the slope of the stream. Procedures for adjusting the ethylene and propane coefficients for other organic compounds were evaluated. These procedures are based on molecular diffusivity, molecular diameter, or molecular weight. Because of limited data, none of these procedures have been extensively verified. Therefore, until additional data become available, it is suggested that the mass-transfer coefficient be assumed to be inversely proportional to the square root of the molecular weight.

The numerical evaluation of maximum-likelihood estimates of the parameters for a mixture of normal distributions from partially identified samples

NASA Technical Reports Server (NTRS)

Walker, H. F.

1976-01-01

Likelihood equations determined by the two types of samples which are necessary conditions for a maximum-likelihood estimate were considered. These equations suggest certain successive approximations iterative procedures for obtaining maximum likelihood estimates. The procedures, which are generalized steepest ascent (deflected gradient) procedures, contain those of Hosmer as a special case.

Theory and modeling of atmospheric turbulence, part 1

NASA Technical Reports Server (NTRS)

1984-01-01

The cascade transfer which is the only function to describe the mode coupling as the result of the nonlinear hydrodynamic state of turbulence is discussed. A kinetic theory combined with a scaling procedure was developed. The transfer function governs the non-linear mode coupling in strong turbulence. The master equation is consistent with the hydrodynamical system that describes the microdynamic state of turbulence and has the advantages to be homogeneous and have fewer nonlinear terms. The modes are scaled into groups to decipher the governing transport processes and statistical characteristics. An equation of vorticity transport describes the microdynamic state of two dimensional, isotropic and homogeneous, geostrophic turbulence. The equation of evolution of the macrovorticity is derived from group scaling in the form of the Fokker-Planck equation with memory. The microdynamic state of turbulence is transformed into the Liouville equation to derive the kinetic equation of the singlet distribution in turbulence. The collision integral contains a memory, which is analyzed with pair collision and the multiple collision. Two other kinetic equations are developed in parallel for the propagator and the transition probability for the interaction among the groups.

Note: Model identification and analysis of bivalent analyte surface plasmon resonance data.

PubMed

Tiwari, Purushottam Babu; Üren, Aykut; He, Jin; Darici, Yesim; Wang, Xuewen

2015-10-01

Surface plasmon resonance (SPR) is a widely used, affinity based, label-free biophysical technique to investigate biomolecular interactions. The extraction of rate constants requires accurate identification of the particular binding model. The bivalent analyte model involves coupled non-linear differential equations. No clear procedure to identify the bivalent analyte mechanism has been established. In this report, we propose a unique signature for the bivalent analyte model. This signature can be used to distinguish the bivalent analyte model from other biphasic models. The proposed method is demonstrated using experimentally measured SPR sensorgrams.

A generalized reaction diffusion model for spatial structure formed by motile cells.

PubMed

Ochoa, F L

1984-01-01

A non-linear stability analysis using a multi-scale perturbation procedure is carried out on a model of a generalized reaction diffusion mechanism which involves only a single equation but which nevertheless exhibits bifurcation to non-uniform states. The patterns generated by this model by variation in a parameter related to the scalar dimensions of domain of definition, indicate its capacity to represent certain key morphogenetic features of multicellular systems formed by motile cells.

A computational procedure for large rotational motions in multibody dynamics

NASA Technical Reports Server (NTRS)

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

1987-01-01

A computational procedure suitable for the solution of equations of motion for multibody systems is presented. The present procedure adopts a differential partitioning of the translational motions and the rotational motions. The translational equations of motion are then treated by either a conventional explicit or an implicit direct integration method. A principle feature of this procedure is a nonlinearly implicit algorithm for updating rotations via the Euler four-parameter representation. This procedure is applied to the rolling of a sphere through a specific trajectory, which shows that it yields robust solutions.

Robust decentralized power system controller design: Integrated approach

NASA Astrophysics Data System (ADS)

Veselý, Vojtech

2017-09-01

A unique approach to the design of gain scheduled controller (GSC) is presented. The proposed design procedure is based on the Bellman-Lyapunov equation, guaranteed cost and robust stability conditions using the parameter dependent quadratic stability approach. The obtained feasible design procedures for robust GSC design are in the form of BMI with guaranteed convex stability conditions. The obtained design results and their properties are illustrated in the simultaneously design of controllers for simple model (6-order) turbogenerator. The results of the obtained design procedure are a PI automatic voltage regulator (AVR) for synchronous generator, a PI governor controller and a power system stabilizer for excitation system.

On a perturbed Sparre Andersen risk model with multi-layer dividend strategy

NASA Astrophysics Data System (ADS)

Yang, Hu; Zhang, Zhimin

2009-10-01

In this paper, we consider a perturbed Sparre Andersen risk model, in which the inter-claim times are generalized Erlang(n) distributed. Under the multi-layer dividend strategy, piece-wise integro-differential equations for the discounted penalty functions are derived, and a recursive approach is applied to express the solutions. A numerical example to calculate the ruin probabilities is given to illustrate the solution procedure.

A linearized Euler analysis of unsteady flows in turbomachinery

NASA Technical Reports Server (NTRS)

Hall, Kenneth C.; Crawley, Edward F.

1987-01-01

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

A composite velocity procedure for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1982-01-01

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

On supporting students' understanding of solving linear equation by using flowchart

NASA Astrophysics Data System (ADS)

Toyib, Muhamad; Kusmayadi, Tri Atmojo; Riyadi

2017-05-01

The aim of this study was to support 7th graders to gradually understand the concepts and procedures of solving linear equation. Thirty-two 7th graders of a Junior High School in Surakarta, Indonesia were involved in this study. Design research was used as the research approach to achieve the aim. A set of learning activities in solving linear equation with one unknown were designed based on Realistic Mathematics Education (RME) approach. The activities were started by playing LEGO to find a linear equation then solve the equation by using flowchart. The results indicate that using the realistic problems, playing LEGO could stimulate students to construct linear equation. Furthermore, Flowchart used to encourage students' reasoning and understanding on the concepts and procedures of solving linear equation with one unknown.

Applying transfer matrix method to the estimation of the modal characteristics of the NASA Mini-Mass Truss

NASA Technical Reports Server (NTRS)

Shen, Ji-Yao; Taylor, Lawrence W., Jr.

1994-01-01

It is beneficial to use a distributed parameter model for large space structures because the approach minimizes the number of model parameters. Holzer's transfer matrix method provides a useful means to simplify and standardize the procedure for solving the system of partial differential equations. Any large space structures can be broken down into sub-structures with simple elastic and dynamical properties. For each single element, such as beam, tether, or rigid body, we can derive the corresponding transfer matrix. Combining these elements' matrices enables the solution of the global system equations. The characteristics equation can then be formed by satisfying the appropriate boundary conditions. Then natural frequencies and mode shapes can be determined by searching the roots of the characteristic equation at frequencies within the range of interest. This paper applies this methodology, and the maximum likelihood estimation method, to refine the modal characteristics of the NASA Mini-Mast Truss by successively matching the theoretical response to the test data of the truss. The method is being applied to more complex configurations.

Dimensionality of organizational justice in a call center context.

PubMed

Flint, Douglas; Haley, Lynn M; McNally, Jeffrey J

2012-04-01

Summary.-Employees in three call centers were surveyed about their perceptions of organizational justice. Four factors were measured: distributive justice, procedural justice, interpersonal justice, and informational justice. Structural equation modeling was employed to test whether a two-, three-, or four-factor model best fit the call center data. A three-factor model of distributive, procedural, and informational justice provided the best fit to these data. The three-factor model that showed the best fit does not conform to any of the more traditional models identified in the organizational justice literature. This implies that the context in which organizational justice is measured may play a role in identifying which justice factors are relevant to employees. Findings add to the empirical evidence on the dimensionality of organizational justice and imply that dimensionality of organizational justice is more context-dependent than previously thought.

Influence of Learner Beliefs and Gender on the Motivating Power of L2 Selves

ERIC Educational Resources Information Center

Yashima, Tomoko; Nishida, Rieko; Mizumoto, Atsushi

2017-01-01

This study investigates 3 unexplored issues regarding Second Language (L2) Motivational Self System theory. It further validates the theory using multiple structural equation modeling (SEM) along with a procedure comparing the strength of corresponding paths. Japanese university freshmen (N = 2,631) responded to a questionnaire and took the…

Generating Nonnormal Multivariate Data Using Copulas: Applications to SEM

ERIC Educational Resources Information Center

Mair, Patrick; Satorra, Albert; Bentler, Peter M.

2012-01-01

This article develops a procedure based on copulas to simulate multivariate nonnormal data that satisfy a prespecified variance-covariance matrix. The covariance matrix used can comply with a specific moment structure form (e.g., a factor analysis or a general structural equation model). Thus, the method is particularly useful for Monte Carlo…

Happy Spouses, Happy Parents? Family Relationships among Finnish and Dutch Dual Earners

ERIC Educational Resources Information Center

Malinen, Kaisa; Kinnunen, Ulla; Tolvanen, Asko; Ronka, Anna; Wierda-Boer, Hilde; Gerris, Jan

2010-01-01

In this study links between spousal and parent-child relationships among Finnish (n = 157 couples) and Dutch (n = 276 couples) dual earners with young children were examined using paired questionnaire data. Variable-oriented analyses (structural equation modeling with a multigroup procedure) supported the spillover hypothesis, as higher levels of…

Recombinant Enaction: Manipulatives Generate New Procedures in the Imagination, by Extending and Recombining Action Spaces

ERIC Educational Resources Information Center

Rahaman, Jeenath; Agrawal, Harshit; Srivastava, Nisheeth; Chandrasekharan, Sanjay

2018-01-01

Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation-based…

A finite element approach for solution of the 3D Euler equations

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Ramakrishnan, R.; Dechaumphai, P.

1986-01-01

Prediction of thermal deformations and stresses has prime importance in the design of the next generation of high speed flight vehicles. Aerothermal load computations for complex three-dimensional shapes necessitate development of procedures to solve the full Navier-Stokes equations. This paper details the development of a three-dimensional inviscid flow approach which can be extended for three-dimensional viscous flows. A finite element formulation, based on a Taylor series expansion in time, is employed to solve the compressible Euler equations. Model generation and results display are done using a commercially available program, PATRAN, and vectorizing strategies are incorporated to ensure computational efficiency. Sample problems are presented to demonstrate the validity of the approach for analyzing high speed compressible flows.

Filtering of non-linear instabilities

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1978-01-01

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown that these problems can be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate filtering can reduce the intensity of these oscillations and possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and nonconservation differencing. The entire spectrum of filtered equations retains a three point character as well as second order spatial accuracy. Burgers equation was considered as a model.

Strong nonlinear rupture theory of thin free liquid films

NASA Astrophysics Data System (ADS)

Chi-Chuan, Hwang; Jun-Liang, Chen; Li-Fu, Shen; Cheng-I, Weng

1996-02-01

A simplified governing equation with high-order effects is formulated after a procedure of evaluating the order of magnitude. Furthermore, the nonlinear evolution equations are derived by the Kármán-Polhausen integral method with a specified velocity profile. Particularly, the effects of surface tension, van der Waals potential, inertia and high-order viscous dissipation are taken into consideration in these equation. The numerical results reveal that the rupture time of free film is much shorter than that of a film on a flat plate. It is shown that because of a more complete high-order viscous dissipation effect discussed in the present study, the rupture process of present model is slower than is predicted by the high-order long wave theory.

Numerical Solution of the Gyrokinetic Poisson Equation in TEMPEST

NASA Astrophysics Data System (ADS)

Dorr, Milo; Cohen, Bruce; Cohen, Ronald; Dimits, Andris; Hittinger, Jeffrey; Kerbel, Gary; Nevins, William; Rognlien, Thomas; Umansky, Maxim; Xiong, Andrew; Xu, Xueqiao

2006-10-01

The gyrokinetic Poisson (GKP) model in the TEMPEST continuum gyrokinetic edge plasma code yields the electrostatic potential due to the charge density of electrons and an arbitrary number of ion species including the effects of gyroaveraging in the limit kρ1. The TEMPEST equations are integrated as a differential algebraic system involving a nonlinear system solve via Newton-Krylov iteration. The GKP preconditioner block is inverted using a multigrid preconditioned conjugate gradient (CG) algorithm. Electrons are treated as kinetic or adiabatic. The Boltzmann relation in the adiabatic option employs flux surface averaging to maintain neutrality within field lines and is solved self-consistently with the GKP equation. A decomposition procedure circumvents the near singularity of the GKP Jacobian block that otherwise degrades CG convergence.

Microscale Procedure for Inorganic Qualitative Analysis with Emphasis on Writing Equations: Chemical Fingerprinting Applied to the "n"-bottle Problem of Matching Samples with Their Formulas

ERIC Educational Resources Information Center

Sattsangi, Prem D.

2014-01-01

A laboratory method for teaching inorganic qualitative analysis and chemical equations is described. The experiment has been designed to focus attention on cations and anions that react to form products. This leads to a logical approach to understand and write chemical equations. The procedure uses 3 mL plastic micropipettes to store and deliver…

I. Excluded volume effects in Ising cluster distributions and nuclear multifragmentation. II. Multiple-chance effects in alpha-particle evaporation

NASA Astrophysics Data System (ADS)

Breus, Dimitry Eugene

In Part I, geometric clusters of the Ising model are studied as possible model clusters for nuclear multifragmentation. These clusters may not be considered as non-interacting (ideal gas) due to excluded volume effect which predominantly is the artifact of the cluster's finite size. Interaction significantly complicates the use of clusters in the analysis of thermodynamic systems. Stillinger's theory is used as a basis for the analysis, which within the RFL (Reiss, Frisch, Lebowitz) fluid-of-spheres approximation produces a prediction for cluster concentrations well obeyed by geometric clusters of the Ising model. If thermodynamic condition of phase coexistence is met, these concentrations can be incorporated into a differential equation procedure of moderate complexity to elucidate the liquid-vapor phase diagram of the system with cluster interaction included. The drawback of increased complexity is outweighted by the reward of greater accuracy of the phase diagram, as it is demonstrated by the Ising model. A novel nuclear-cluster analysis procedure is developed by modifying Fisher's model to contain cluster interaction and employing the differential equation procedure to obtain thermodynamic variables. With this procedure applied to geometric clusters, the guidelines are developed to look for excluded volume effect in nuclear multifragmentation. In Part II, an explanation is offered for the recently observed oscillations in the energy spectra of alpha-particles emitted from hot compound nuclei. Contrary to what was previously expected, the oscillations are assumed to be caused by the multiple-chance nature of alpha-evaporation. In a semi-empirical fashion this assumption is successfully confirmed by a technique of two-spectra decomposition which treats experimental alpha-spectra as having contributions from at least two independent emitters. Building upon the success of the multiple-chance explanation of the oscillations, Moretto's single-chance evaporation theory is augmented to include multiple-chance emission and tested on experimental data to yield positive results.

Poisson-Boltzmann-Nernst-Planck model

NASA Astrophysics Data System (ADS)

Zheng, Qiong; Wei, Guo-Wei

2011-05-01

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.

Poisson-Boltzmann-Nernst-Planck model

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

Zheng Qiong; Wei Guowei; Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species inmore » the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.« less

Poisson–Boltzmann–Nernst–Planck model

PubMed Central

Zheng, Qiong; Wei, Guo-Wei

2011-01-01

The Poisson–Nernst–Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst–Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst–Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst–Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson–Boltzmann and Nernst–Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current–voltage (I–V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I–V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. PMID:21599038

Poisson-Boltzmann-Nernst-Planck model.

PubMed

Zheng, Qiong; Wei, Guo-Wei

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. © 2011 American Institute of Physics.

Numerical modeling for dilute and dense sprays

NASA Technical Reports Server (NTRS)

Chen, C. P.; Kim, Y. M.; Shang, H. M.; Ziebarth, J. P.; Wang, T. S.

1992-01-01

We have successfully implemented a numerical model for spray-combustion calculations. In this model, the governing gas-phase equations in Eulerian coordinate are solved by a time-marching multiple pressure correction procedure based on the operator-splitting technique. The droplet-phase equations in Lagrangian coordinate are solved by a stochastic discrete particle technique. In order to simplify the calculation procedure for the circulating droplets, the effective conductivity model is utilized. The k-epsilon models are utilized to characterize the time and length scales of the gas phase in conjunction with turbulent modulation by droplets and droplet dispersion by turbulence. This method entails random sampling of instantaneous gas flow properties and the stochastic process requires a large number of computational parcels to produce the satisfactory dispersion distributions even for rather dilute sprays. Two major improvements in spray combustion modelings were made. Firstly, we have developed a probability density function approach in multidimensional space to represent a specific computational particle. Secondly, we incorporate the Taylor Analogy Breakup (TAB) model for handling the dense spray effects. This breakup model is based on the reasonable assumption that atomization and drop breakup are indistinguishable processes within a dense spray near the nozzle exit. Accordingly, atomization is prescribed by injecting drops which have a characteristic size equal to the nozzle exit diameter. Example problems include the nearly homogeneous and inhomogeneous turbulent particle dispersion, and the non-evaporating, evaporating, and burning dense sprays. Comparison with experimental data will be discussed in detail.

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

NASA Technical Reports Server (NTRS)

Gordnier, R. E.; Rubin, S. G.

1986-01-01

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible flow equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential-like function. This provides for an efficient solution procedure that is locally representative of both asymptotic inviscid and boundary layer theories. A modified conservative form of the axial momentum equation that is required to obtain rotational solutions in the inviscid region is presented and a combined conservation/nonconservation form is applied for evaluation of the reduced Navier-Stokes (RNS), Euler and potential equations. A variety of results is presented and the effects of the approximations on entropy production, shock capturing, and viscous interaction are discussed.

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

Marra, Valerio; Kolb, Edward W.; Matarrese, Sabino

We analyze a toy Swiss-cheese cosmological model to study the averaging problem. In our Swiss-cheese model, the cheese is a spatially flat, matter only, Friedmann-Robertson-Walker solution (i.e., the Einstein-de Sitter model), and the holes are constructed from a Lemaitre-Tolman-Bondi solution of Einstein's equations. We study the propagation of photons in the Swiss-cheese model, and find a phenomenological homogeneous model to describe observables. Following a fitting procedure based on light-cone averages, we find that the expansion scalar is unaffected by the inhomogeneities (i.e., the phenomenological homogeneous model is the cheese model). This is because of the spherical symmetry of the model;more » it is unclear whether the expansion scalar will be affected by nonspherical voids. However, the light-cone average of the density as a function of redshift is affected by inhomogeneities. The effect arises because, as the universe evolves, a photon spends more and more time in the (large) voids than in the (thin) high-density structures. The phenomenological homogeneous model describing the light-cone average of the density is similar to the {lambda}CDM concordance model. It is interesting that, although the sole source in the Swiss-cheese model is matter, the phenomenological homogeneous model behaves as if it has a dark-energy component. Finally, we study how the equation of state of the phenomenological homogeneous model depends on the size of the inhomogeneities, and find that the equation-of-state parameters w{sub 0} and w{sub a} follow a power-law dependence with a scaling exponent equal to unity. That is, the equation of state depends linearly on the distance the photon travels through voids. We conclude that, within our toy model, the holes must have a present size of about 250 Mpc to be able to mimic the concordance model.« less

The nonlinear modified equation approach to analyzing finite difference schemes

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1981-01-01

The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

Preconditioned conjugate residual methods for the solution of spectral equations

NASA Technical Reports Server (NTRS)

Wong, Y. S.; Zang, T. A.; Hussaini, M. Y.

1986-01-01

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Three-Dimensional Navier-Stokes Method with Two-Equation Turbulence Models for Efficient Numerical Simulation of Hypersonic Flows

NASA Technical Reports Server (NTRS)

Bardina, J. E.

1994-01-01

A new computational efficient 3-D compressible Reynolds-averaged implicit Navier-Stokes method with advanced two equation turbulence models for high speed flows is presented. All convective terms are modeled using an entropy satisfying higher-order Total Variation Diminishing (TVD) scheme based on implicit upwind flux-difference split approximations and arithmetic averaging procedure of primitive variables. This method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent Navier-Stokes procedures to solve flows with mixed supersonic and subsonic zones, including streamwise separated flows. Its robust stability derives from a combination of conservative implicit upwind flux-difference splitting with Roe's property U to provide accurate shock capturing capability that non-conservative schemes do not guarantee, alternating symmetric Gauss-Seidel 'method of planes' relaxation procedure coupled with a three-dimensional two-factor diagonal-dominant approximate factorization scheme, TVD flux limiters of higher-order flux differences satisfying realizability, and well-posed characteristic-based implicit boundary-point a'pproximations consistent with the local characteristics domain of dependence. The efficiency of the method is highly increased with Newton Raphson acceleration which allows convergence in essentially one forward sweep for supersonic flows. The method is verified by comparing with experiment and other Navier-Stokes methods. Here, results of adiabatic and cooled flat plate flows, compression corner flow, and 3-D hypersonic shock-wave/turbulent boundary layer interaction flows are presented. The robust 3-D method achieves a better computational efficiency of at least one order of magnitude over the CNS Navier-Stokes code. It provides cost-effective aerodynamic predictions in agreement with experiment, and the capability of predicting complex flow structures in complex geometries with good accuracy.

Helicopter vibration suppression using simple pendulum absorbers on the rotor blade

NASA Technical Reports Server (NTRS)

Hamouda, M.-N. H.; Pierce, G. A.

1981-01-01

A design procedure is presented for the installation of simple pendulums on the blades of a helicopter rotor to suppress the root reactions. The procedure consists of a frequency response analysis for a hingeless rotor blade excited by a harmonic variation of spanwise airload distributions during forward flight, as well as a concentrated load at the tip. The structural modeling of the blade provides for elastic degrees of freedom in flap and lead-lag bending plus torsion. Simple flap and lead-lag pendulums are considered individually. Using a rational order scheme, the general nonlinear equations of motion are linearized. A quasi-steady aerodynamic representation is used in the formation of the airloads. The solution of the system equations derives from their representation as a transfer matrix. The results include the effect of pendulum tuning on the minimization of the hub reactions.

Computer simulations of phase field drops on super-hydrophobic surfaces

NASA Astrophysics Data System (ADS)

Fedeli, Livio

2017-09-01

We present a novel quasi-Newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena. We perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes. Moreover, we discuss the conditions that, on a theoretical level, guarantee the convergence of this method. At each iterative step, a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess. Discretization performs through cell-centered finite differences. The resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi-grid techniques. The final code achieves three-dimensional, realistic computer experiments comparable to those produced in laboratory settings. This code offers not only new insights into the phenomenology of super-hydrophobicity, but also serves as a reliable predictive tool for the study of hydrophobic surfaces.

Investigation of aerodynamic characteristics of subsonic wings

NASA Technical Reports Server (NTRS)

Dejarnette, F. R.; Frink, N. T.

1979-01-01

An analytical strake design procedure is investigated. A numerical solution to the governing strake design equation is used to generate a series of strakes which are tested in a water tunnel to study their vortex breakdown characteristics. The strakes are scaled for use on a half-scale model of the NASA-LaRC general research fuselage with a 44 degrees trapezoidal wing. An analytical solution to the governing design equation is obtained. The strake design procedure relates the potential-flow leading-edge suction and pressure distributions to vortex stability. Several suction distributions are studied and those which are more triangular and peak near the tip generate strakes that reach higher angles of attack before vortex breakdown occurs at the wing trailing edge. For the same suction distribution, a conical rather than three dimensional pressure specification results in a better strake shape as judged from its vortex breakdown characteristics.

Flowfield computation of entry vehicles

NASA Technical Reports Server (NTRS)

Prabhu, Dinesh K.

1990-01-01

The equations governing the multidimensional flow of a reacting mixture of thermally perfect gasses were derived. The modeling procedures for the various terms of the conservation laws are discussed. A numerical algorithm, based on the finite-volume approach, to solve these conservation equations was developed. The advantages and disadvantages of the present numerical scheme are discussed from the point of view of accuracy, computer time, and memory requirements. A simple one-dimensional model problem was solved to prove the feasibility and accuracy of the algorithm. A computer code implementing the above algorithm was developed and is presently being applied to simple geometries and conditions. Once the code is completely debugged and validated, it will be used to compute the complete unsteady flow field around the Aeroassist Flight Experiment (AFE) body.

Modeling of atomization and distribution of drop-liquid fuel in unsteady swirling flows in a combustion chamber and free space

NASA Astrophysics Data System (ADS)

Sviridenkov, A. A.; Toktaliev, P. D.; Tretyakov, V. V.

2018-03-01

Numerical and experimental research of atomization and propagation of drop-liquid phase in swirling flow behind the frontal device of combustion chamber was performed. Numerical procedure was based on steady and unsteady Reynolds equations solution. It's shown that better agreement with experimental data could be obtained with unsteady approach. Fractional time step method was implemented to solve Reynolds equations. Models of primary and secondary breakup of liquid fuel jet in swirling flows are formulated and tested. Typical mean sizes of fuel droplets for base operational regime of swirling device and combustion chamber were calculated. Comparison of main features of internal swirling flow in combustion chamber with unbounded swirling flow was made.

A Comparative Analysis of Pre-Equating and Post-Equating in a Large-Scale Assessment, High Stakes Examination

ERIC Educational Resources Information Center

Ojerinde, Dibu; Popoola, Omokunmi; Onyeneho, Patrick; Egberongbe, Aminat

2016-01-01

Statistical procedure used in adjusting test score difficulties on test forms is known as "equating". Equating makes it possible for various test forms to be used interchangeably. In terms of where the equating method fits in the assessment cycle, there are pre-equating and post-equating methods. The major benefits of pre-equating, when…

Multiplicative noise removal through fractional order tv-based model and fast numerical schemes for its approximation

NASA Astrophysics Data System (ADS)

Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad

2017-07-01

This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.

Full-envelope aerodynamic modeling of the Harrier aircraft

NASA Technical Reports Server (NTRS)

Mcnally, B. David

1986-01-01

A project to identify a full-envelope model of the YAV-8B Harrier using flight-test and parameter identification techniques is described. As part of the research in advanced control and display concepts for V/STOL aircraft, a full-envelope aerodynamic model of the Harrier is identified, using mathematical model structures and parameter identification methods. A global-polynomial model structure is also used as a basis for the identification of the YAV-8B aerodynamic model. State estimation methods are used to ensure flight data consistency prior to parameter identification.Equation-error methods are used to identify model parameters. A fixed-base simulator is used extensively to develop flight test procedures and to validate parameter identification software. Using simple flight maneuvers, a simulated data set was created covering the YAV-8B flight envelope from about 0.3 to 0.7 Mach and about -5 to 15 deg angle of attack. A singular value decomposition implementation of the equation-error approach produced good parameter estimates based on this simulated data set.

Model fit evaluation in multilevel structural equation models

PubMed Central

Ryu, Ehri

2014-01-01

Assessing goodness of model fit is one of the key questions in structural equation modeling (SEM). Goodness of fit is the extent to which the hypothesized model reproduces the multivariate structure underlying the set of variables. During the earlier development of multilevel structural equation models, the “standard” approach was to evaluate the goodness of fit for the entire model across all levels simultaneously. The model fit statistics produced by the standard approach have a potential problem in detecting lack of fit in the higher-level model for which the effective sample size is much smaller. Also when the standard approach results in poor model fit, it is not clear at which level the model does not fit well. This article reviews two alternative approaches that have been proposed to overcome the limitations of the standard approach. One is a two-step procedure which first produces estimates of saturated covariance matrices at each level and then performs single-level analysis at each level with the estimated covariance matrices as input (Yuan and Bentler, 2007). The other level-specific approach utilizes partially saturated models to obtain test statistics and fit indices for each level separately (Ryu and West, 2009). Simulation studies (e.g., Yuan and Bentler, 2007; Ryu and West, 2009) have consistently shown that both alternative approaches performed well in detecting lack of fit at any level, whereas the standard approach failed to detect lack of fit at the higher level. It is recommended that the alternative approaches are used to assess the model fit in multilevel structural equation model. Advantages and disadvantages of the two alternative approaches are discussed. The alternative approaches are demonstrated in an empirical example. PMID:24550882

A BRST gauge-fixing procedure for Yang Mills theory on sphere

NASA Astrophysics Data System (ADS)

Banerjee, Rabin; Deguchi, Shinichi

2006-01-01

A gauge-fixing procedure for the Yang-Mills theory on an n-dimensional sphere (or a hypersphere) is discussed in a systematic manner. We claim that Adler's gauge-fixing condition used in massless Euclidean QED on a hypersphere is not conventional because of the presence of an extra free index, and hence is unfavorable for the gauge-fixing procedure based on the BRST invariance principle (or simply BRST gauge-fixing procedure). Choosing a suitable gauge condition, which is proved to be equivalent to a generalization of Adler's condition, we apply the BRST gauge-fixing procedure to the Yang-Mills theory on a hypersphere to obtain consistent results. Field equations for the Yang-Mills field and associated fields are derived in manifestly O (n + 1) covariant or invariant forms. In the large radius limit, these equations reproduce the corresponding field equations defined on the n-dimensional flat space.

An analytical procedure and automated computer code used to design model nozzles which meet MSFC base pressure similarity parameter criteria. [space shuttle

NASA Technical Reports Server (NTRS)

Sulyma, P. R.

1980-01-01

Fundamental equations and similarity definition and application are described as well as the computational steps of a computer program developed to design model nozzles for wind tunnel tests conducted to define power-on aerodynamic characteristics of the space shuttle over a range of ascent trajectory conditions. The computer code capabilities, a user's guide for the model nozzle design program, and the output format are examined. A program listing is included.

Synthesis of Railroad Design Methods, Track Response Models, and Evaluation Methods for Military Railroads.

DTIC Science & Technology

1985-03-01

economically justified. For main lines, access tracks, heavy traffic tracks, and tracks where the de- sign train speed is greater than 40 mph, TM 5... analysis 35. The beam-on-elastic-foundation model is the key to the AREA design procedure. Kerr in "Problems and Needs in Track Structure Design and... Analysis " (Kerr 1977) presents an outline of the development of this model for analysis of track structures. The fundamental differential equation which

Research procedure for buck-boost converter for small electric vehicles

NASA Astrophysics Data System (ADS)

Vacheva, Gergana; Hinov, Nikolay; Penev, Dimitar

2017-12-01

In the current paper is developed a mathematical model realized in Matlab for describing a buck-boost converter for control of small electric vehicle. The model is presented with differential equations which describes the processes in the converter. Through the research of this model it can be accomplished the optimal work mode of a small electric vehicles. The proposed converter can be used in a wide range of applications like small electric vehicles, smart grids and different systems for energy storage.

Period of vibration of axially vibrating truly nonlinear rod

NASA Astrophysics Data System (ADS)

Cveticanin, L.

2016-07-01

In this paper the axial vibration of a muscle whose fibers are parallel to the direction of muscle compression is investigated. The model is a clamped-free rod with a strongly nonlinear elastic property. Axial vibration is described by a nonlinear partial differential equation. A solution of the equation is constructed for special initial conditions by using the method of separation of variables. The partial differential equation is separated into two uncoupled strongly nonlinear second order differential equations. Both equations, with displacement function and with time function are exactly determined. Exact solutions are given in the form of inverse incomplete and inverse complete Beta function. Using boundary and initial conditions, the frequency of vibration is obtained. It has to be mentioned that the determined frequency represents the exact analytic description for the axially vibrating truly nonlinear clamped-free rod. The procedure suggested in this paper is applied for calculation of the frequency of the longissimus dorsi muscle of a cow. The influence of elasticity order and elasticity coefficient on the frequency property is tested.

Kinetic model of turbulence in an incompressible fluid

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1978-01-01

A statistical description of turbulence in an incompressible fluid obeying the Navier-Stokes equations is proposed, where pressure is regarded as a potential for the interaction between fluid elements. A scaling procedure divides a fluctuation into three ranks representing the three transport processes of macroscopic evolution, transport property, and relaxation. Closure is obtained by relaxation, and a kinetic equation is obtained for the fluctuation of the macroscopic rank of the distribution function. The solution gives the transfer function and eddy viscosity. When applied to the inertia subrange of the energy spectrum the analysis recovers the Kolmogorov law and its numerical coefficient.

Bright, dark, and mixed vector soliton solutions of the general coupled nonlinear Schrödinger equations.

PubMed

Agalarov, Agalar; Zhulego, Vladimir; Gadzhimuradov, Telman

2015-04-01

The reduction procedure for the general coupled nonlinear Schrödinger (GCNLS) equations with four-wave mixing terms is proposed. It is shown that the GCNLS system is equivalent to the well known integrable families of the Manakov and Makhankov U(n,m)-vector models. This equivalence allows us to construct bright-bright and dark-dark solitons and a quasibreather-dark solution with unconventional dynamics: the density of the first component oscillates in space and time, whereas the density of the second component does not. The collision properties of solitons are also studied.

Evaluation of a research circulation control airfoil using Navier-Stokes methods

NASA Technical Reports Server (NTRS)

Shrewsbury, George D.

1987-01-01

The compressible Reynolds time averaged Navier-Stokes equations were used to obtain solutions for flows about a two dimensional circulation control airfoil. The governing equations were written in conservation form for a body-fitted coordinate system and solved using an Alternating Direction Implicit (ADI) procedure. A modified algebraic eddy viscosity model was used to define the turbulent characteristics of the flow, including the wall jet flow over the Coanda surface at the trailing edge. Numerical results are compared to experimental data obtained for a research circulation control airfoil geometry. Excellent agreement with the experimental results was obtained.

Fourth order scheme for wavelet based solution of Black-Scholes equation

NASA Astrophysics Data System (ADS)

Finěk, Václav

2017-12-01

The present paper is devoted to the numerical solution of the Black-Scholes equation for pricing European options. We apply the Crank-Nicolson scheme with Richardson extrapolation for time discretization and Hermite cubic spline wavelets with four vanishing moments for space discretization. This scheme is the fourth order accurate both in time and in space. Computational results indicate that the Crank-Nicolson scheme with Richardson extrapolation significantly decreases the amount of computational work. We also numerically show that optimal convergence rate for the used scheme is obtained without using startup procedure despite the data irregularities in the model.

Determination of macro-scale soil properties from pore-scale structures: model derivation.

PubMed

Daly, K R; Roose, T

2018-01-01

In this paper, we use homogenization to derive a set of macro-scale poro-elastic equations for soils composed of rigid solid particles, air-filled pore space and a poro-elastic mixed phase. We consider the derivation in the limit of large deformation and show that by solving representative problems on the micro-scale we can parametrize the macro-scale equations. To validate the homogenization procedure, we compare the predictions of the homogenized equations with those of the full equations for a range of different geometries and material properties. We show that the results differ by [Formula: see text] for all cases considered. The success of the homogenization scheme means that it can be used to determine the macro-scale poro-elastic properties of soils from the underlying structure. Hence, it will prove a valuable tool in both characterization and optimization.

Filtering of non-linear instabilities. [from finite difference solution of fluid dynamics equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1979-01-01

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown here that these problems can in fact be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate 'filtering' can reduce the intensity of these oscillations and in some cases possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and non-conservation differencing. The entire spectrum of filtered equations retains a three-point character as well as second-order spatial accuracy. Burgers equation has been considered as a model. Several filters are examined in detail, and smooth solutions have been obtained for extremely large cell Reynolds numbers.

Treating convection in sequential solvers

NASA Technical Reports Server (NTRS)

Shyy, Wei; Thakur, Siddharth

1992-01-01

The treatment of the convection terms in the sequential solver, a standard procedure found in virtually all pressure based algorithms, to compute the flow problems with sharp gradients and source terms is investigated. Both scalar model problems and one-dimensional gas dynamics equations have been used to study the various issues involved. Different approaches including the use of nonlinear filtering techniques and adoption of TVD type schemes have been investigated. Special treatments of the source terms such as pressure gradients and heat release have also been devised, yielding insight and improved accuracy of the numerical procedure adopted.

Development of renormalization group analysis of turbulence

NASA Technical Reports Server (NTRS)

Smith, L. M.

1990-01-01

The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.

Procedural justice, supervisor autonomy support, work satisfaction, organizational identification and job performance: the mediating role of need satisfaction and perceived organizational support.

PubMed

Gillet, Nicolas; Colombat, Philippe; Michinov, Estelle; Pronost, Anne-Marie; Fouquereau, Evelyne

2013-11-01

To test a model linking procedural justice, supervisor autonomy support, need satisfaction, organizational support, work satisfaction, organizational identification and job performance. Research in industrial and organizational psychology has shown that procedural justice and supervisor autonomy support lead to positive outcomes. However, very little research related to this subject has been conducted in healthcare settings. Moreover, few studies have examined mechanisms that could account for these positive relationships. A cross-sectional correlational design was used. Convenience sampling was used and a sample of 500 nurses working in haematology, oncology and haematology/oncology units in France was surveyed in 2011. The final sample consisted of 323 nurses (64.6% response rate). The hypothesized model was tested using structural equation modelling. Procedural justice and supervisor autonomy support significantly and positively influenced need satisfaction and perceived organizational support, which in turn positively predicted work satisfaction, organizational identification and job performance. Organizations could deliver training programmes for their managers aimed at enhancing the use of fair procedures in allocating outcomes and developing their autonomy-supportive behaviours to improve nurses' work satisfaction, organizational identification and job performance. © 2013 Blackwell Publishing Ltd.

Steady inviscid transonic flows over planar airfoils: A search for a simplified procedure

NASA Technical Reports Server (NTRS)

Magnus, R.; Yoshihara, H.

1973-01-01

A finite difference procedure based upon a system of unsteady equations in proper conservation form with either exact or small disturbance steady terms is used to calculate the steady flows over several classes of airfoils. The airfoil condition is fulfilled on a slab whose upstream extremity is a semi-circle overlaying the airfoil leading edge circle. The limitations of the small disturbance equations are demonstrated in an extreme example of a blunt-nosed, aft-cambered airfoil. The necessity of using the equations in proper conservation form to capture the shock properly is stressed. Ability of the steady relaxation procedures to capture the shock is briefly examined.

Item response theory - A first approach

NASA Astrophysics Data System (ADS)

Nunes, Sandra; Oliveira, Teresa; Oliveira, Amílcar

2017-07-01

The Item Response Theory (IRT) has become one of the most popular scoring frameworks for measurement data, frequently used in computerized adaptive testing, cognitively diagnostic assessment and test equating. According to Andrade et al. (2000), IRT can be defined as a set of mathematical models (Item Response Models - IRM) constructed to represent the probability of an individual giving the right answer to an item of a particular test. The number of Item Responsible Models available to measurement analysis has increased considerably in the last fifteen years due to increasing computer power and due to a demand for accuracy and more meaningful inferences grounded in complex data. The developments in modeling with Item Response Theory were related with developments in estimation theory, most remarkably Bayesian estimation with Markov chain Monte Carlo algorithms (Patz & Junker, 1999). The popularity of Item Response Theory has also implied numerous overviews in books and journals, and many connections between IRT and other statistical estimation procedures, such as factor analysis and structural equation modeling, have been made repeatedly (Van der Lindem & Hambleton, 1997). As stated before the Item Response Theory covers a variety of measurement models, ranging from basic one-dimensional models for dichotomously and polytomously scored items and their multidimensional analogues to models that incorporate information about cognitive sub-processes which influence the overall item response process. The aim of this work is to introduce the main concepts associated with one-dimensional models of Item Response Theory, to specify the logistic models with one, two and three parameters, to discuss some properties of these models and to present the main estimation procedures.

Experimental Validation of a Coupled Fluid-Multibody Dynamics Model for Tanker Trucks

DTIC Science & Technology

2007-11-08

order to accurately predict the dynamic response of tanker trucks, the model must accurately account for the following effects : • Incompressible...computational code which uses a time- accurate explicit solution procedure is used to solve both the solid and fluid equations of motion. Many commercial...position vector, τ is the deviatoric stress tensor, D is the rate of deformation tensor, f r is the body force vector, r is the artificial

Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector

NASA Technical Reports Server (NTRS)

Wu, Jie-Zhi; Zhou, Ye; Wu, Jian-Ming

1996-01-01

We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds stress transport equation.

Aeroelastic Stability of Rotor Blades Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Chopra, I.; Sivaneri, N.

1982-01-01

The flutter stability of flap bending, lead-lag bending, and torsion of helicopter rotor blades in hover is investigated using a finite element formulation based on Hamilton's principle. The blade is divided into a number of finite elements. Quasi-steady strip theory is used to evaluate the aerodynamic loads. The nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The equations of motion are linearized assuming blade motion to be a small perturbation about the steady deflected shape. The normal mode method based on the coupled rotating natural modes is used to reduce the number of equations in the flutter analysis. First the formulation is applied to single-load-path blades (articulated and hingeless blades). Numerical results show very good agreement with existing results obtained using the modal approach. The second part of the application concerns multiple-load-path blades, i.e. bearingless blades. Numerical results are presented for several analytical models of the bearingless blade. Results are also obtained using an equivalent beam approach wherein a bearingless blade is modelled as a single beam with equivalent properties. Results show the equivalent beam model.

Estimation of the Reactive Flow Model Parameters for an Ammonium Nitrate-Based Emulsion Explosive Using Genetic Algorithms

NASA Astrophysics Data System (ADS)

Ribeiro, J. B.; Silva, C.; Mendes, R.

2010-10-01

A real coded genetic algorithm methodology that has been developed for the estimation of the parameters of the reaction rate equation of the Lee-Tarver reactive flow model is described in detail. This methodology allows, in a single optimization procedure, using only one experimental result and, without the need of any starting solution, to seek the 15 parameters of the reaction rate equation that fit the numerical to the experimental results. Mass averaging and the plate-gap model have been used for the determination of the shock data used in the unreacted explosive JWL equation of state (EOS) assessment and the thermochemical code THOR retrieved the data used in the detonation products' JWL EOS assessments. The developed methodology was applied for the estimation of the referred parameters for an ammonium nitrate-based emulsion explosive using poly(methyl methacrylate) (PMMA)-embedded manganin gauge pressure-time data. The obtained parameters allow a reasonably good description of the experimental data and show some peculiarities arising from the intrinsic nature of this kind of composite explosive.

Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Jia, Shu-Liang; Huang, Qian-Min; Lan, Zhong-Zhou

2016-11-01

In this paper, a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation is investigated, which has been presented as a model for the shallow water wave in fluids or the electrostatic wave potential in plasmas. By virtue of the binary Bell polynomials, the bilinear form of this equation is obtained. With the aid of the bilinear form, N -soliton solutions are obtained by the Hirota method, periodic wave solutions are constructed via the Riemann theta function, and breather wave solutions are obtained according to the extended homoclinic test approach. Travelling waves are constructed by the polynomial expansion method as well. Then, the relations between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure. Furthermore, we obtain some new solutions of this equation by the standard extended homoclinic test approach. Finally, we give a generalized form of this equation, and find that similar analytical solutions can be obtained from the generalized equation with arbitrary coefficients.

To Parcel or Not To Parcel: Exploring the Question, Weighing the Merits.

ERIC Educational Resources Information Center

Little, Todd D.; Cunningham, William A.; Shahar, Golan; Widaman, Keith F.

2002-01-01

Studied the evidence for the practice of using parcels of item as manifest variables in structural equation modeling procedures. Findings suggest that the unconsidered use of parcels is never warranted, but the considered use of parcels cannot be dismissed out of hand. Describes a number of parceling techniques and their strengths and weaknesses.…

Meaning-Related and Print-Related Interactions between Preschoolers and Parents during Shared Book Reading and Their Associations with Emergent Literacy Skills

ERIC Educational Resources Information Center

Han, Jisu; Neuharth-Pritchett, Stacey

2015-01-01

This study examined interactions between preschool children and parents during shared book reading by analyzing parental self-report data. Using confirmatory factor analytic procedures and structural equation modeling, this study developed a scale measuring meaning-related and print-related reading interactions and examined their associations with…

Testing for Measurement and Structural Equivalence in Large-Scale Cross-Cultural Studies: Addressing the Issue of Nonequivalence

ERIC Educational Resources Information Center

Byrne, Barbara M.; van de Vijver, Fons J. R.

2010-01-01

A critical assumption in cross-cultural comparative research is that the instrument measures the same construct(s) in exactly the same way across all groups (i.e., the instrument is measurement and structurally equivalent). Structural equation modeling (SEM) procedures are commonly used in testing these assumptions of multigroup equivalence.…

A complete multifluid model for bipolar semiconductors, with interacting carriers, phonons, and photons

NASA Astrophysics Data System (ADS)

Rossani, A.

2017-12-01

If electrons (e) and holes (h) in metals or semiconductors are heated to the temperatures T_e and T_h greater than the lattice temperature, the electron-phonon interaction causes energy relaxation. In the non-uniform case a momentum relaxation occurs as well. In view of such an application, a new model, based on an asymptotic procedure for solving the kinetic equations of carriers, phonons, and photons, is proposed, which gives naturally the displaced Maxwellian at the leading order. Several generation-recombination (GR) events occur in bipolar semiconductors. In the presence of photons the most important ones are the radiative GR events, direct, indirect, and exciton-catalyzed. Phonons and photons are treated here as a participating species, with their own equation. All the phonon-photon interactions are accounted for. Moreover, carrier-photon (Compton) interactions are introduced, which make complete the model. After that, balance equations for the electron number, hole number, energy densities, and momentum densities are constructed, which constitute now a system of macroscopic equations for the chemical potentials (carriers), the temperatures (carriers and bosons), and the drift velocities (carriers and bosons). In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered, even in the presence of an external magnetic field.

Enthalpy measurement of coal-derived liquids. Technical progress report, August-October 1982

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

Kidnay, A.J.; Yesavage, V.F.

The correlational effort on the coal syncrudes and model compounds has been proceeding along two fronts. The first involves experimental work on a correlating factor for association in the liquids and the second involves an investigation of the modeling capabilities of cubic equations of state. The first area of investigation is the experimental measurement of a correlating factor for assocition in coal liquids. The procedure involves molecular weight measurement by freezing point depression. To facilitate these measurements, a simple Beckman freezing point depression apparatus is being currently modified to increase the accuracy, speed, and ease of measurement. The second areamore » of effort has involved establishing a set of cubic equations of state which can adequately model the enthalpy departures of quinoline and m-cresol. To this effort, a number of standard and association specific equations of state have been tested against a data base of previously measured enthalpy departures of m-cresol and quinoline. It has been found that these equations do quantitatively a poor job on m-cresol and quinoline. These problems are probably due to the highly polar nature of m-cresol and to a lesser extent quinoline, and to the poor quality of critical parameters for quinoline.« less

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M. S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.

A Graphical Approach to Evaluating Equating Using Test Characteristic Curves

ERIC Educational Resources Information Center

Wyse, Adam E.; Reckase, Mark D.

2011-01-01

An essential concern in the application of any equating procedure is determining whether tests can be considered equated after the tests have been placed onto a common scale. This article clarifies one equating criterion, the first-order equity property of equating, and develops a new method for evaluating equating that is linked to this…

Piezoelectric Actuator Modeling Using MSC/NASTRAN and MATLAB

NASA Technical Reports Server (NTRS)

Reaves, Mercedes C.; Horta, Lucas G.

2003-01-01

This paper presents a procedure for modeling structures containing piezoelectric actuators using MSCMASTRAN and MATLAB. The paper describes the utility and functionality of one set of validated modeling tools. The tools described herein use MSCMASTRAN to model the structure with piezoelectric actuators and a thermally induced strain to model straining of the actuators due to an applied voltage field. MATLAB scripts are used to assemble the dynamic equations and to generate frequency response functions. The application of these tools is discussed using a cantilever aluminum beam with a surface mounted piezoelectric actuator as a sample problem. Software in the form of MSCINASTRAN DMAP input commands, MATLAB scripts, and a step-by-step procedure to solve the example problem are provided. Analysis results are generated in terms of frequency response functions from deflection and strain data as a function of input voltage to the actuator.

[The bullied who bullies: the reciprocal relationship between victim and aggressor in workplace bullying situations].

PubMed

Rodríguez Muñoz, Alfredo; Moreno Jiménez, Bernardo; Baillien, Elfi; Sanz Vergel, Ana Isabel; Moreno López, Ynomig

2012-01-01

The aim of this study was to explore longitudinal relationships between organizational factors (workload and procedural justice) and targets and perpetrators of workplace bullying. We compared several causal models (baseline or stability, normal, reversed and reciprocal models). The sample comprised 286 employees from two companies in Madrid, and we used a time-lag of one year. Results of structural equation modeling analyses showed that reciprocal model fit the data the best. We found that T1 workload was related positively to T2 target of bullying, and T1 procedural justice was related negatively to T2 target of bullying. There was a significant reverse effect of T1 target of bullying on T2 workload. Furthermore, we found a reciprocal relationship between being the target and the perpetrator of bullying. Overall, these findings emphasize the need to extend the traditional causal models of workplace bullying to more dynamic approaches.

Lumley's PODT definition of large eddies and a trio of numerical procedures. [Proper Orthogonal Decomposition Theorem

NASA Technical Reports Server (NTRS)

Payne, Fred R.

1992-01-01

Lumley's 1967 Moscow paper provided, for the first time, a completely rational definition of the physically-useful term 'large eddy', popular for a half-century. The numerical procedures based upon his results are: (1) PODT (Proper Orthogonal Decomposition Theorem), which extracts the Large Eddy structure of stochastic processes from physical or computer simulation two-point covariances, and 2) LEIM (Large-Eddy Interaction Model), a predictive scheme for the dynamical large eddies based upon higher order turbulence modeling. Earlier Lumley's work (1964) forms the basis for the final member of the triad of numerical procedures: this predicts the global neutral modes of turbulence which have surprising agreement with both structural eigenmodes and those obtained from the dynamical equations. The ultimate goal of improved engineering design tools for turbulence may be near at hand, partly due to the power and storage of 'supermicrocomputer' workstations finally becoming adequate for the demanding numerics of these procedures.

Validation of a heteroscedastic hazards regression model.

PubMed

Wu, Hong-Dar Isaac; Hsieh, Fushing; Chen, Chen-Hsin

2002-03-01

A Cox-type regression model accommodating heteroscedasticity, with a power factor of the baseline cumulative hazard, is investigated for analyzing data with crossing hazards behavior. Since the approach of partial likelihood cannot eliminate the baseline hazard, an overidentified estimating equation (OEE) approach is introduced in the estimation procedure. It by-product, a model checking statistic, is presented to test for the overall adequacy of the heteroscedastic model. Further, under the heteroscedastic model setting, we propose two statistics to test the proportional hazards assumption. Implementation of this model is illustrated in a data analysis of a cancer clinical trial.

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

NASA Astrophysics Data System (ADS)

Ansari, R.; Faraji Oskouie, M.; Gholami, R.

2016-01-01

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

VS2DI: Model use, calibration, and validation

USGS Publications Warehouse

Healy, Richard W.; Essaid, Hedeff I.

2012-01-01

VS2DI is a software package for simulating water, solute, and heat transport through soils or other porous media under conditions of variable saturation. The package contains a graphical preprocessor for constructing simulations, a postprocessor for displaying simulation results, and numerical models that solve for flow and solute transport (VS2DT) and flow and heat transport (VS2DH). Flow is described by the Richards equation, and solute and heat transport are described by advection-dispersion equations; the finite-difference method is used to solve these equations. Problems can be simulated in one, two, or three (assuming radial symmetry) dimensions. This article provides an overview of calibration techniques that have been used with VS2DI; included is a detailed description of calibration procedures used in simulating the interaction between groundwater and a stream fed by drainage from agricultural fields in central Indiana. Brief descriptions of VS2DI and the various types of problems that have been addressed with the software package are also presented.

Prediction of composite thermal behavior made simple

NASA Technical Reports Server (NTRS)

Chamis, C. C.

1981-01-01

A convenient procedure is described to determine the thermal behavior (thermal expansion coefficients and thermal stresses) of angleplied fiber composites using a pocket calculator. The procedure consists of equations and appropriate graphs for various ( + or - theta) ply combinations. These graphs present reduced stiffness and thermal expansion coefficients as functions of (+ or - theta) in order to simplify and expedite the use of the equations. The procedure is applicable to all types of balanced, symmetric fiber composites including interply and intraply hybrids. The versatility and generality of the procedure is illustrated using several step-by-step numerical examples.

On the equivalence of the dual-wavelength and polarimetric equations for estimation of the raindrop size distribution

NASA Technical Reports Server (NTRS)

Meneghini, Robert; Liao, Liang

2006-01-01

In writing the integral equations for the median mass diameter and particle concentration, or comparable parameters of the raindrop size distribution, it is apparent that when attenuation effects are included, the forms of the equations for polarimetric and dual wavelength radars are identical. In both sets of equations, differences in the backscattering and extinction cross sections appear: in the polarimetric equations, the differences are taken with respect polarization at a fixed frequency while for the dual wavelength equations, the differences are taken with respect to wavelength at a fixed polarization. Because the forms of the equations are the same, the ways in which they can be solved are similar as well. To avoid instabilities in the forward recursion procedure, the equations can be expressed in the form of a final-value. Solving the equations in this way traditionally has required estimates of the path attenuations to the final gate: either the attenuations at horizontal and vertical polarizations at the same frequency or attenuations at two frequencies with the same polarization. This has been done for dual-frequency (air/spaceborne case) and polarimetric radars by the respective use of the surface reference technique and the differential phase shift. An alternative to solving the constrained version of the equations is an iterative procedure recently proposed in which independent estimates of path attenuation are not required. Although the procedure has limitations, it appears to be quite useful. Simulations of the retrievals help clarify the relationship between the constrained and unconstrained approaches and their application to the polarimetric and dual-wavelength equations.

Collision partner selection schemes in DSMC: From micro/nano flows to hypersonic flows

NASA Astrophysics Data System (ADS)

Roohi, Ehsan; Stefanov, Stefan

2016-10-01

The motivation of this review paper is to present a detailed summary of different collision models developed in the framework of the direct simulation Monte Carlo (DSMC) method. The emphasis is put on a newly developed collision model, i.e., the Simplified Bernoulli trial (SBT), which permits efficient low-memory simulation of rarefied gas flows. The paper starts with a brief review of the governing equations of the rarefied gas dynamics including Boltzmann and Kac master equations and reiterates that the linear Kac equation reduces to a non-linear Boltzmann equation under the assumption of molecular chaos. An introduction to the DSMC method is provided, and principles of collision algorithms in the DSMC are discussed. A distinction is made between those collision models that are based on classical kinetic theory (time counter, no time counter (NTC), and nearest neighbor (NN)) and the other class that could be derived mathematically from the Kac master equation (pseudo-Poisson process, ballot box, majorant frequency, null collision, Bernoulli trials scheme and its variants). To provide a deeper insight, the derivation of both collision models, either from the principles of the kinetic theory or the Kac master equation, is provided with sufficient details. Some discussions on the importance of subcells in the DSMC collision procedure are also provided and different types of subcells are presented. The paper then focuses on the simplified version of the Bernoulli trials algorithm (SBT) and presents a detailed summary of validation of the SBT family collision schemes (SBT on transient adaptive subcells: SBT-TAS, and intelligent SBT: ISBT) in a broad spectrum of rarefied gas-flow test cases, ranging from low speed, internal micro and nano flows to external hypersonic flow, emphasizing first the accuracy of these new collision models and second, demonstrating that the SBT family scheme, if compared to other conventional and recent collision models, requires smaller number of particles per cell to obtain sufficiently accurate solutions.

Physical processes in the strong magnetic fields of accreting neutron stars

NASA Technical Reports Server (NTRS)

Meszaros, P.

1984-01-01

Analytical formulae are fitted to observational data on physical processes occurring in strong magnetic fields surrounding accreting neutron stars. The propagation of normal modes in the presence of a quantizing magnetic field is discussed in terms of a wave equation in Fourier space, quantum electrodynamic effects, polarization and mode ellipticity. The results are applied to calculating the Thomson scattering, bremsstrahlung and Compton scattering cross-sections, which are a function of the frequency, angle and polarization of the magnetic field. Numerical procedures are explored for solving the radiative transfer equations. When applied to modeling X ray pulsars, a problem arises in the necessity to couple the magnetic angle and frequency dependence of the cross-sections with the hydrodynamic equations. The use of time-dependent averaging and approximation techniques is indicated.

First principles pulse pile-up balance equation and fast deterministic solution

NASA Astrophysics Data System (ADS)

Sabbatucci, Lorenzo; Fernández, Jorge E.

2017-08-01

Pulse pile-up (PPU) is an always present effect which introduces a distortion into the spectrum measured with radiation detectors and that worsen with the increasing emission rate of the radiation source. It is fully ascribable to the pulse handling circuitry of the detector and it is not comprised in the detector response function which is well explained by a physical model. The PPU changes both the number and the height of the recorded pulses, which are related, respectively, with the number of detected particles and their energy. In the present work, it is derived a first principles balance equation for second order PPU to obtain a post-processing correction to apply to X-ray measurements. The balance equation is solved for the particular case of rectangular pulse shape using a deterministic iterative procedure for which it will be shown the convergence. The proposed method, deterministic rectangular PPU (DRPPU), requires minimum amount of information and, as example, it is applied to a solid state Si detector with active or off-line PPU suppression circuitry. A comparison shows that the results obtained with this fast and simple approach are comparable to those from the more sophisticated procedure using precise detector pulse shapes.

Inverse scattering transform analysis of rogue waves using local periodization procedure

NASA Astrophysics Data System (ADS)

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-07-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.

Inverse scattering transform analysis of rogue waves using local periodization procedure

PubMed Central

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-01-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra. PMID:27385164

Strengthening safety compliance in nuclear power operations: a role-based approach.

PubMed

Martínez-Córcoles, Mario; Gracia, Francisco J; Tomás, Inés; Peiró, José M

2014-07-01

Safety compliance is of paramount importance in guaranteeing the safe running of nuclear power plants. However, it depends mostly on procedures that do not always involve the safest outcomes. This article introduces an empirical model based on the organizational role theory to analyze the influence of legitimate sources of expectations (procedures formalization and leadership) on workers' compliance behaviors. The sample was composed of 495 employees from two Spanish nuclear power plants. Structural equation analysis showed that, in spite of some problematic effects of proceduralization (such as role conflict and role ambiguity), procedure formalization along with an empowering leadership style lead to safety compliance by clarifying a worker's role in safety. Implications of these findings for safety research are outlined, as well as their practical implications. © 2014 Society for Risk Analysis.

Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes

NASA Astrophysics Data System (ADS)

Kyriakopoulos, Charalampos; Grossmann, Gerrit; Wolf, Verena; Bortolussi, Luca

2018-01-01

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree kmax of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large kmax. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.

A conservative fully implicit algorithm for predicting slug flows

NASA Astrophysics Data System (ADS)

Krasnopolsky, Boris I.; Lukyanov, Alexander A.

2018-02-01

An accurate and predictive modelling of slug flows is required by many industries (e.g., oil and gas, nuclear engineering, chemical engineering) to prevent undesired events potentially leading to serious environmental accidents. For example, the hydrodynamic and terrain-induced slugging leads to unwanted unsteady flow conditions. This demands the development of fast and robust numerical techniques for predicting slug flows. The presented in this paper study proposes a multi-fluid model and its implementation method accounting for phase appearance and disappearance. The numerical modelling of phase appearance and disappearance presents a complex numerical challenge for all multi-component and multi-fluid models. Numerical challenges arise from the singular systems of equations when some phases are absent and from the solution discontinuity when some phases appear or disappear. This paper provides a flexible and robust solution to these issues. A fully implicit formulation described in this work enables to efficiently solve governing fluid flow equations. The proposed numerical method provides a modelling capability of phase appearance and disappearance processes, which is based on switching procedure between various sets of governing equations. These sets of equations are constructed using information about the number of phases present in the computational domain. The proposed scheme does not require an explicit truncation of solutions leading to a conservative scheme for mass and linear momentum. A transient two-fluid model is used to verify and validate the proposed algorithm for conditions of hydrodynamic and terrain-induced slug flow regimes. The developed modelling capabilities allow to predict all the major features of the experimental data, and are in a good quantitative agreement with them.

A new limiting procedure for discontinuous Galerkin methods applied to compressible multiphase flows with shocks and interfaces

NASA Astrophysics Data System (ADS)

Henry de Frahan, Marc T.; Varadan, Sreenivas; Johnsen, Eric

2015-01-01

Although the Discontinuous Galerkin (DG) method has seen widespread use for compressible flow problems in a single fluid with constant material properties, it has yet to be implemented in a consistent fashion for compressible multiphase flows with shocks and interfaces. Specifically, it is challenging to design a scheme that meets the following requirements: conservation, high-order accuracy in smooth regions and non-oscillatory behavior at discontinuities (in particular, material interfaces). Following the interface-capturing approach of Abgrall [1], we model flows of multiple fluid components or phases using a single equation of state with variable material properties; discontinuities in these properties correspond to interfaces. To represent compressible phenomena in solids, liquids, and gases, we present our analysis for equations of state belonging to the Mie-Grüneisen family. Within the DG framework, we propose a conservative, high-order accurate, and non-oscillatory limiting procedure, verified with simple multifluid and multiphase problems. We show analytically that two key elements are required to prevent spurious pressure oscillations at interfaces and maintain conservation: (i) the transport equation(s) describing the material properties must be solved in a non-conservative weak form, and (ii) the suitable variables must be limited (density, momentum, pressure, and appropriate properties entering the equation of state), coupled with a consistent reconstruction of the energy. Further, we introduce a physics-based discontinuity sensor to apply limiting in a solution-adaptive fashion. We verify this approach with one- and two-dimensional problems with shocks and interfaces, including high pressure and density ratios, for fluids obeying different equations of state to illustrate the robustness and versatility of the method. The algorithm is implemented on parallel graphics processing units (GPU) to achieve high speedup.

A semi-direct procedure using a local relaxation factor and its application to an internal flow problem

NASA Technical Reports Server (NTRS)

Chang, S. C.

1984-01-01

Generally, fast direct solvers are not directly applicable to a nonseparable elliptic partial differential equation. This limitation, however, is circumvented by a semi-direct procedure, i.e., an iterative procedure using fast direct solvers. An efficient semi-direct procedure which is easy to implement and applicable to a variety of boundary conditions is presented. The current procedure also possesses other highly desirable properties, i.e.: (1) the convergence rate does not decrease with an increase of grid cell aspect ratio, and (2) the convergence rate is estimated using the coefficients of the partial differential equation being solved.

Voice, perceived fairness, agency trust, and acceptance of management decisions among Minnesota anglers

USGS Publications Warehouse

Schroeder, Susan A.; Fulton, David C.

2017-01-01

Although researchers agree that public participation in natural resource decision making is critical to institutional acceptance by stakeholders and the general public, the processes to gain public perceptions of fairness, agency trust, and acceptance of management decisions are not clear. Using results from a mail survey of Minnesota resident anglers, we used structural equation modeling to examine how instrumental versus symbolic motives related to anglers’ perceptions of agency fairness, trustworthiness, and ultimately acceptance of fisheries management decisions. We applied laboratory research on relationships among procedural fairness, trust, and management acceptance, and then tested models incorporating anglers’ perceptions of voice for anglers and nonanglers in management decisions. Results suggested that trust fully mediated the relationship between procedural fairness and management acceptance. Angler perceptions of angler and nonangler voice both related to views of procedural fairness, but angler voice was more strongly related and was also significantly related to acceptance of management decisions.

Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint

NASA Technical Reports Server (NTRS)

Li, Y.; Navon, I. M.; Courtier, P.; Gauthier, P.

1993-01-01

An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.

Light propagation in the averaged universe

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

Bagheri, Samae; Schwarz, Dominik J., E-mail: s_bagheri@physik.uni-bielefeld.de, E-mail: dschwarz@physik.uni-bielefeld.de

Cosmic structures determine how light propagates through the Universe and consequently must be taken into account in the interpretation of observations. In the standard cosmological model at the largest scales, such structures are either ignored or treated as small perturbations to an isotropic and homogeneous Universe. This isotropic and homogeneous model is commonly assumed to emerge from some averaging process at the largest scales. We assume that there exists an averaging procedure that preserves the causal structure of space-time. Based on that assumption, we study the effects of averaging the geometry of space-time and derive an averaged version of themore » null geodesic equation of motion. For the averaged geometry we then assume a flat Friedmann-Lemaître (FL) model and find that light propagation in this averaged FL model is not given by null geodesics of that model, but rather by a modified light propagation equation that contains an effective Hubble expansion rate, which differs from the Hubble rate of the averaged space-time.« less

A numerical and experimental study on the nonlinear evolution of long-crested irregular waves

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

Goullet, Arnaud; Choi, Wooyoung; Division of Ocean Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701

2011-01-15

The spatial evolution of nonlinear long-crested irregular waves characterized by the JONSWAP spectrum is studied numerically using a nonlinear wave model based on a pseudospectral (PS) method and the modified nonlinear Schroedinger (MNLS) equation. In addition, new laboratory experiments with two different spectral bandwidths are carried out and a number of wave probe measurements are made to validate these two wave models. Strongly nonlinear wave groups are observed experimentally and their propagation and interaction are studied in detail. For the comparison with experimental measurements, the two models need to be initialized with care and the initialization procedures are described. Themore » MNLS equation is found to approximate reasonably well for the wave fields with a relatively smaller Benjamin-Feir index, but the phase error increases as the propagation distance increases. The PS model with different orders of nonlinear approximation is solved numerically, and it is shown that the fifth-order model agrees well with our measurements prior to wave breaking for both spectral bandwidths.« less

Fiber Composite Sandwich Thermostructural Behavior: Computational Simulation

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Aiello, R. A.; Murthy, P. L. N.

1986-01-01

Several computational levels of progressive sophistication/simplification are described to computationally simulate composite sandwich hygral, thermal, and structural behavior. The computational levels of sophistication include: (1) three-dimensional detailed finite element modeling of the honeycomb, the adhesive and the composite faces; (2) three-dimensional finite element modeling of the honeycomb assumed to be an equivalent continuous, homogeneous medium, the adhesive and the composite faces; (3) laminate theory simulation where the honeycomb (metal or composite) is assumed to consist of plies with equivalent properties; and (4) derivations of approximate, simplified equations for thermal and mechanical properties by simulating the honeycomb as an equivalent homogeneous medium. The approximate equations are combined with composite hygrothermomechanical and laminate theories to provide a simple and effective computational procedure for simulating the thermomechanical/thermostructural behavior of fiber composite sandwich structures.

A rational approach to the use of Prandtl's mixing length model in free turbulent shear flow calculations

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Bushnell, D. M.

1973-01-01

Prandtl's basic mixing length model was used to compute 22 test cases on free turbulent shear flows. The calculations employed appropriate algebraic length scale equations and single values of mixing length constant for planar and axisymmetric flows, respectively. Good agreement with data was obtained except for flows, such as supersonic free shear layers, where large sustained sensitivity changes occur. The inability to predict the more gradual mixing in these flows is tentatively ascribed to the presence of a significant turbulence-induced transverse static pressure gradient which is neglected in conventional solution procedures. Some type of an equation for length scale development was found to be necessary for successful computation of highly nonsimilar flow regions such as jet or wake development from thick wall flows.

Methods for parameter identification in oscillatory networks and application to cortical and thalamic 600 Hz activity.

PubMed

Leistritz, L; Suesse, T; Haueisen, J; Hilgenfeld, B; Witte, H

2006-01-01

Directed information transfer in the human brain occurs presumably by oscillations. As of yet, most approaches for the analysis of these oscillations are based on time-frequency or coherence analysis. The present work concerns the modeling of cortical 600 Hz oscillations, localized within the Brodmann Areas 3b and 1 after stimulation of the nervus medianus, by means of coupled differential equations. This approach leads to the so-called parameter identification problem, where based on a given data set, a set of unknown parameters of a system of ordinary differential equations is determined by special optimization procedures. Some suitable algorithms for this task are presented in this paper. Finally an oscillatory network model is optimally fitted to the data taken from ten volunteers.

Estimation of homogeneous nucleation flux via a kinetic model

NASA Technical Reports Server (NTRS)

Wilcox, C. F.; Bauer, S. H.

1991-01-01

The proposed kinetic model for condensation under homogeneous conditions, and the onset of unidirectional cluster growth in supersaturated gases, does not suffer from the conceptual flaws that characterize classical nucleation theory. When a full set of simultaneous rate equation is solved, a characteristic time emerges, for each cluster size, at which the production rate, and its rate of conversion to the next size (n + 1) are equal. Procedures for estimating the essential parameters are proposed; condensation fluxes J(kin) exp ss are evaluated. Since there are practical limits to the cluster size that can be incorporated in the set of simultaneous first-order differential equations, a code was developed for computing an approximate J(th) exp ss based on estimates of a 'constrained equilibrium' distribution, and identification of its minimum.

Asymptotically safe standard model extensions?

NASA Astrophysics Data System (ADS)

Pelaggi, Giulio Maria; Plascencia, Alexis D.; Salvio, Alberto; Sannino, Francesco; Smirnov, Juri; Strumia, Alessandro

2018-05-01

We consider theories with a large number NF of charged fermions and compute the renormalization group equations for the gauge, Yukawa and quartic couplings resummed at leading order in 1 /NF. We construct extensions of the standard model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.

Physical interrelation between Fokker-Planck and random walk models with application to Coulomb interactions.

NASA Technical Reports Server (NTRS)

Englert, G. W.

1971-01-01

A model of the random walk is formulated to allow a simple computing procedure to replace the difficult problem of solution of the Fokker-Planck equation. The step sizes and probabilities of taking steps in the various directions are expressed in terms of Fokker-Planck coefficients. Application is made to many particle systems with Coulomb interactions. The relaxation of a highly peaked velocity distribution of particles to equilibrium conditions is illustrated.

The associations between perceived distributive, procedural, and interactional organizational justice, self-rated health and burnout.

PubMed

Liljegren, Mats; Ekberg, Kerstin

2009-01-01

The aim of the present study was to examine the cross-sectional and 2-year longitudinal associations between perceived organizational justice, self-rated health and burnout. The study used questionnaire data from 428 Swedish employment officers and the data was analyzed with Structural Equation Modeling, SEM. Two different models were tested: a global organizational justice model (with and without correlated measurement errors) and a differentiated (distributive, procedural and interactional organizational justice) justice model (with and without correlated measurement errors). The global justice model with autocorrelations had the most satisfactory goodness-of-fit indices. Global justice showed statistically significant (p < 0.01) cross-sectional (0.80 {mle 0.84) and longitudinal positive associations (0.76 mle 0.82) between organizational justice and self-rated health, and significant (p < 0.01) negative associations between organizational justice and burnout (cross-sectional: mle = -0.85, longitudinal -0.83 mle -0.84). The global justice construct showed better goodness-of-fit indices than the threefold justice construct but a differentiated organizational justice concept could give valuable information about health related risk factors: if they are structural (distributive justice), procedural (procedural justice) or inter-personal (interactional justice). The two approaches to study organizational justice should therefore be regarded as complementary rather than exclusive.

A diagnostic model to estimate winds and small-scale drag from Mars Observer PMIRR data

NASA Technical Reports Server (NTRS)

Barnes, J. R.

1993-01-01

Theoretical and modeling studies indicate that small-scale drag due to breaking gravity waves is likely to be of considerable importance for the circulation in the middle atmospheric region (approximately 40-100 km altitude) on Mars. Recent earth-based spectroscopic observations have provided evidence for the existence of circulation features, in particular, a warm winter polar region, associated with gravity wave drag. Since the Mars Observer PMIRR experiment will obtain temperature profiles extending from the surface up to about 80 km altitude, it will be extensively sampling middle atmospheric regions in which gravity wave drag may play a dominant role. Estimating the drag then becomes crucial to the estimation of the atmospheric winds from the PMIRR-observed temperatures. An interative diagnostic model based upon one previously developed and tested with earth satellite temperature data will be applied to the PMIRR measurements to produce estimates of the small-scale zonal drag and three-dimensional wind fields in the Mars middle atmosphere. This model is based on the primitive equations, and can allow for time dependence (the time tendencies used may be based upon those computed in a Fast Fourier Mapping procedure). The small-scale zonal drag is estimated as the residual in the zonal momentum equation; the horizontal winds having first been estimated from the meridional momentum equation and the continuity equation. The scheme estimates the vertical motions from the thermodynamic equation, and thus needs estimates of the diabatic heating based upon the observed temperatures. The latter will be generated using a radiative model. It is hoped that the diagnostic scheme will be able to produce good estimates of the zonal gravity wave drag in the Mars middle atmosphere, estimates that can then be used in other diagnostic or assimilation efforts, as well as more theoretical studies.

Bi-Factor MIRT Observed-Score Equating for Mixed-Format Tests

ERIC Educational Resources Information Center

Lee, Guemin; Lee, Won-Chan

2016-01-01

The main purposes of this study were to develop bi-factor multidimensional item response theory (BF-MIRT) observed-score equating procedures for mixed-format tests and to investigate relative appropriateness of the proposed procedures. Using data from a large-scale testing program, three types of pseudo data sets were formulated: matched samples,…

Using Kernel Equating to Assess Item Order Effects on Test Scores

ERIC Educational Resources Information Center

Moses, Tim; Yang, Wen-Ling; Wilson, Christine

2007-01-01

This study explored the use of kernel equating for integrating and extending two procedures proposed for assessing item order effects in test forms that have been administered to randomly equivalent groups. When these procedures are used together, they can provide complementary information about the extent to which item order effects impact test…

Theory and application of an approximate model of saltwater upconing in aquifers

USGS Publications Warehouse

McElwee, C.; Kemblowski, M.

1990-01-01

Motion and mixing of salt water and fresh water are vitally important for water-resource development throughout the world. An approximate model of saltwater upconing in aquifers is developed, which results in three non-linear coupled equations for the freshwater zone, the saltwater zone, and the transition zone. The description of the transition zone uses the concept of a boundary layer. This model invokes some assumptions to give a reasonably tractable model, considerably better than the sharp interface approximation but considerably simpler than a fully three-dimensional model with variable density. We assume the validity of the Dupuit-Forchheimer approximation of horizontal flow in each layer. Vertical hydrodynamic dispersion into the base of the transition zone is assumed and concentration of the saltwater zone is assumed constant. Solute in the transition zone is assumed to be moved by advection only. Velocity and concentration are allowed to vary vertically in the transition zone by using shape functions. Several numerical techniques can be used to solve the model equations, and simple analytical solutions can be useful in validating the numerical solution procedures. We find that the model equations can be solved with adequate accuracy using the procedures presented. The approximate model is applied to the Smoky Hill River valley in central Kansas. This model can reproduce earlier sharp interface results as well as evaluate the importance of hydrodynamic dispersion for feeding salt water to the river. We use a wide range of dispersivity values and find that unstable upconing always occurs. Therefore, in this case, hydrodynamic dispersion is not the only mechanism feeding salt water to the river. Calculations imply that unstable upconing and hydrodynamic dispersion could be equally important in transporting salt water. For example, if groundwater flux to the Smoky Hill River were only about 40% of its expected value, stable upconing could exist where hydrodynamic dispersion into a transition zone is the primary mechanism for moving salt water to the river. The current model could be useful in situations involving dense saltwater layers. ?? 1990.

Determination of equivalent sound speed profiles for ray tracing in near-ground sound propagation.

PubMed

Prospathopoulos, John M; Voutsinas, Spyros G

2007-09-01

The determination of appropriate sound speed profiles in the modeling of near-ground propagation using a ray tracing method is investigated using a ray tracing model which is capable of performing axisymmetric calculations of the sound field around an isolated source. Eigenrays are traced using an iterative procedure which integrates the trajectory equations for each ray launched from the source at a specific direction. The calculation of sound energy losses is made by introducing appropriate coefficients to the equations representing the effect of ground and atmospheric absorption and the interaction with the atmospheric turbulence. The model is validated against analytical and numerical predictions of other methodologies for simple cases, as well as against measurements for nonrefractive atmospheric environments. A systematic investigation for near-ground propagation in downward and upward refractive atmosphere is made using experimental data. Guidelines for the suitable simulation of the wind velocity profile are derived by correlating predictions with measurements.

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Luo, Li-Shi

2007-01-01

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

Computational analysis of the SSME fuel preburner flow

NASA Technical Reports Server (NTRS)

Wang, T. S.; Farmer, R. C.

1986-01-01

A computational fluid dynamics model which simulates the steady state operation of the SSME fuel preburner is developed. Specifically, the model will be used to quantify the flow factors which cause local hot spots in the fuel preburner in order to recommend experiments whereby the control of undesirable flow features can be demonstrated. The results of a two year effort to model the preburner are presented. In this effort, investigating the fuel preburner flowfield, the appropriate transport equations were numerically solved for both an axisymmetric and a three-dimensional configuration. Continuum's VAST (Variational Solution of the Transport equations) code, in conjunction with the CM-1000 Engineering Analysis Workstation and the NASA/Ames CYBER 205, was used to perform the required calculations. It is concluded that the preburner operational anomalies are not due to steady state phenomena and must, therefore, be related to transient operational procedures.

Nonlocal equation for the superconducting gap parameter

NASA Astrophysics Data System (ADS)

Simonucci, S.; Strinati, G. Calvanese

2017-08-01

The properties are considered in detail of a nonlocal (integral) equation for the superconducting gap parameter, which is obtained by a coarse-graining procedure applied to the Bogoliubov-de Gennes (BdG) equations over the whole coupling-versus-temperature phase diagram associated with the superfluid phase. It is found that the limiting size of the coarse-graining procedure, which is dictated by the range of the kernel of this integral equation, corresponds to the size of the Cooper pairs over the whole coupling-versus-temperature phase diagram up to the critical temperature, even when Cooper pairs turn into composite bosons on the BEC side of the BCS-BEC crossover. A practical method is further implemented to solve numerically this integral equation in an efficient way, which is based on a novel algorithm for calculating the Fourier transforms. Application of this method to the case of an isolated vortex, throughout the BCS-BEC crossover and for all temperatures in the superfluid phase, helps clarifying the nature of the length scales associated with a single vortex and the kinds of details that are in practice disposed off by the coarse-graining procedure on the BdG equations.

Nonlinearity and Strain-Rate Dependence in the Deformation Response of Polymer Matrix Composites Modeled

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.

2000-01-01

There has been no accurate procedure for modeling the high-speed impact of composite materials, but such an analytical capability will be required in designing reliable lightweight engine-containment systems. The majority of the models in use assume a linear elastic material response that does not vary with strain rate. However, for containment systems, polymer matrix composites incorporating ductile polymers are likely to be used. For such a material, the deformation response is likely to be nonlinear and to vary with strain rate. An analytical model has been developed at the NASA Glenn Research Center at Lewis Field that incorporates both of these features. A set of constitutive equations that was originally developed to analyze the viscoplastic deformation of metals (Ramaswamy-Stouffer equations) was modified to simulate the nonlinear, rate-dependent deformation of polymers. Specifically, the effects of hydrostatic stresses on the inelastic response, which can be significant in polymers, were accounted for by a modification of the definition of the effective stress. The constitutive equations were then incorporated into a composite micromechanics model based on the mechanics of materials theory. This theory predicts the deformation response of a composite material from the properties and behavior of the individual constituents. In this manner, the nonlinear, rate-dependent deformation response of a polymer matrix composite can be predicted.

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation (ODE) Models with Mixed Effects

PubMed Central

Chow, Sy-Miin; Bendezú, Jason J.; Cole, Pamela M.; Ram, Nilam

2016-01-01

Several approaches currently exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA), generalized local linear approximation (GLLA), and generalized orthogonal local derivative approximation (GOLD). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children’s self-regulation. PMID:27391255

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects.

PubMed

Chow, Sy-Miin; Bendezú, Jason J; Cole, Pamela M; Ram, Nilam

2016-01-01

Several approaches exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA; Ramsay & Silverman, 2005 ), generalized local linear approximation (GLLA; Boker, Deboeck, Edler, & Peel, 2010 ), and generalized orthogonal local derivative approximation (GOLD; Deboeck, 2010 ). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo (MC) study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children's self-regulation.

Study of the flow field past dimpled aerodynamic surfaces: numerical simulation and experimental verification

NASA Astrophysics Data System (ADS)

Binci, L.; Clementi, G.; D'Alessandro, V.; Montelpare, S.; Ricci, R.

2017-11-01

This work presents the study of the flow field past of dimpled laminar airfoil. Fluid dynamic behaviour of these elements has been not still deeply studied in the scientific community. Therefore Computational Fluid-Dynamics (CFD) is here used to analyze the flow field induced by dimples on the NACA 64-014A laminar airfoil at Re = 1.75 · 105 at α = 0°. Reynolds Averaged Navier-Stokes (RANS) equations and Large-Eddy Simulations (LES) were compared with wind tunnel measurements in order to evaluate their effectiveness in the modeling this kind of flow field. LES equations were solved using a specifically developed OpenFOAM solver adopting an L-stable Singly Diagonally Implicit Runge-Kutta (SDIRK) technique with an iterated PISO-like procedure for handling pressure-velocity coupling within each RK stage. Dynamic Smagorinsky subgrid model was employed. LES results provided good agreement with experimental data, while RANS equations closed with \\[k-ω -γ -\\overset{}{\\mathop{{{\\operatorname{Re}}θ, \\text{t}}}} \\] approach overstimates laminar separation bubble (LSB) extension of dimpled and un-dimpled configurations. Moreover, through skin friction coefficient analysis, we found a different representation of the turbulent zone between the numerical models; indeed, with RANS model LSB seems to be divided in two different parts, meanwhile LES model shows a LSB global reduction.

Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1993-01-01

The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.

Shock temperature dependent rate law for plastic bonded explosives

NASA Astrophysics Data System (ADS)

Aslam, Tariq D.

2018-04-01

A reactive flow model for the tri-amino-tri-nitro-benzene (TATB) based plastic bonded explosive PBX 9502 (95% TATB, 5% polymeric binder Kel-F 800) is presented. This newly devised model is based primarily on the shock temperature of the material, along with local pressure, and accurately models a broader range of detonation and initiation scenarios. Specifically, sensitivity changes to the initial explosive temperature are accounted for naturally and with a single set of parameters. The equation of state forms for the reactants and products, as well as the thermodynamic closure of pressure and temperature equilibration, are carried over from the Wescott-Stewart-Davis (WSD) model [Wescott et al., J. Appl. Phys. 98, 053514 (2005) and "Modeling detonation diffraction and dead zones in PBX-9502," in Proceedings of the Thirteenth International Detonation Symposium (2006)]. This newly devised model, with Arrhenius state dependence on the shock temperature, based on the WSD equation of states, is denoted by AWSD. Modifying an existing implementation of the WSD model to the AWSD model in a hydrocode is a rather straightforward procedure.

Extracting surface diffusion coefficients from batch adsorption measurement data: application of the classic Langmuir kinetics model.

PubMed

Chu, Khim Hoong

2017-11-09

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6  cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.

Beyond discounting: possible experimental models of impulse control.

PubMed

Monterosso, J; Ainslie, G

1999-10-01

Animal studies of impulsivity have typically used one of three models: a delay of reward procedure, a differential reinforcement for low rate responding (DRL) procedure, or an autoshaping procedure. In each of these paradigms, we argue, measurement of impulsivity is implicitly or explicitly equated with the effect delay has on the value of reward. The steepness by which delay diminishes value (the temporal discount function) is treated as an index of impulsivity. In order to provide a better analog of human impulsivity, this model needs to be expanded to include the converse of impulsivity - self-control. Through mechanisms such as committing to long range interests before the onset of temptation, or through bundling individual choices into classes of choices that are made at once, human decision-making can often look far less myopic than single trial experiments predict. For people, impulsive behavior may be more often the result of the breakdown of self-control mechanisms than of steep discount functions. Existing animal models of self-control are discussed, and future directions are suggested for psychopharmacological research.

Eigenspace perturbations for structural uncertainty estimation of turbulence closure models

NASA Astrophysics Data System (ADS)

Jofre, Lluis; Mishra, Aashwin; Iaccarino, Gianluca

2017-11-01

With the present state of computational resources, a purely numerical resolution of turbulent flows encountered in engineering applications is not viable. Consequently, investigations into turbulence rely on various degrees of modeling. Archetypal amongst these variable resolution approaches would be RANS models in two-equation closures, and subgrid-scale models in LES. However, owing to the simplifications introduced during model formulation, the fidelity of all such models is limited, and therefore the explicit quantification of the predictive uncertainty is essential. In such scenario, the ideal uncertainty estimation procedure must be agnostic to modeling resolution, methodology, and the nature or level of the model filter. The procedure should be able to give reliable prediction intervals for different Quantities of Interest, over varied flows and flow conditions, and at diametric levels of modeling resolution. In this talk, we present and substantiate the Eigenspace perturbation framework as an uncertainty estimation paradigm that meets these criteria. Commencing from a broad overview, we outline the details of this framework at different modeling resolution. Thence, using benchmark flows, along with engineering problems, the efficacy of this procedure is established. This research was partially supported by NNSA under the Predictive Science Academic Alliance Program (PSAAP) II, and by DARPA under the Enabling Quantification of Uncertainty in Physical Systems (EQUiPS) project (technical monitor: Dr Fariba Fahroo).

ESTIMATION OF CONSTANT AND TIME-VARYING DYNAMIC PARAMETERS OF HIV INFECTION IN A NONLINEAR DIFFERENTIAL EQUATION MODEL.

PubMed

Liang, Hua; Miao, Hongyu; Wu, Hulin

2010-03-01

Modeling viral dynamics in HIV/AIDS studies has resulted in deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper, we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies. We applied the proposed techniques to estimate the key HIV viral dynamic parameters for two individual AIDS patients treated with antiretroviral therapies. We demonstrate that HIV viral dynamics can be well characterized and quantified for individual patients. As a result, personalized treatment decision based on viral dynamic models is possible.

Coolant side heat transfer with rotation: User manual for 3D-TEACH with rotation

NASA Technical Reports Server (NTRS)

Syed, S. A.; James, R. H.

1989-01-01

This program solves the governing transport equations in Reynolds average form for the flow of a 3-D, steady state, viscous, heat conducting, multiple species, single phase, Newtonian fluid with combustion. The governing partial differential equations are solved in physical variables in either a Cartesian or cylindrical coordinate system. The effects of rotation on the momentum and enthalpy calculations modeled in Cartesian coordinates are examined. The flow of the fluid should be confined and subsonic with a maximum Mach number no larger than 0.5. This manual describes the operating procedures and input details for executing a 3D-TEACH computation.

The Motion of a Leaking Oscillator: A Study for the Physics Class

ERIC Educational Resources Information Center

Rodrigues, Hilário; Panza, Nelson; Portes, Dirceu; Soares, Alexandre

2014-01-01

This paper is essentially about the general form of Newton's second law for variable mass problems. We develop a model for describing the motion of the one-dimensional oscillator with a variable mass within the framework of classroom physics. We present a simple numerical procedure for the solution of the equation of motion of the system to…

On the dynamics of some grid adaption schemes

NASA Technical Reports Server (NTRS)

Sweby, Peter K.; Yee, Helen C.

1994-01-01

The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.

Probable flood predictions in ungauged coastal basins of El Salvador

USGS Publications Warehouse

Friedel, M.J.; Smith, M.E.; Chica, A.M.E.; Litke, D.

2008-01-01

A regionalization procedure is presented and used to predict probable flooding in four ungauged coastal river basins of El Salvador: Paz, Jiboa, Grande de San Miguel, and Goascoran. The flood-prediction problem is sequentially solved for two regions: upstream mountains and downstream alluvial plains. In the upstream mountains, a set of rainfall-runoff parameter values and recurrent peak-flow discharge hydrographs are simultaneously estimated for 20 tributary-basin models. Application of dissimilarity equations among tributary basins (soft prior information) permitted development of a parsimonious parameter structure subject to information content in the recurrent peak-flow discharge values derived using regression equations based on measurements recorded outside the ungauged study basins. The estimated joint set of parameter values formed the basis from which probable minimum and maximum peak-flow discharge limits were then estimated revealing that prediction uncertainty increases with basin size. In the downstream alluvial plain, model application of the estimated minimum and maximum peak-flow hydrographs facilitated simulation of probable 100-year flood-flow depths in confined canyons and across unconfined coastal alluvial plains. The regionalization procedure provides a tool for hydrologic risk assessment and flood protection planning that is not restricted to the case presented herein. ?? 2008 ASCE.

Variable-free exploration of stochastic models: a gene regulatory network example.

PubMed

Erban, Radek; Frewen, Thomas A; Wang, Xiao; Elston, Timothy C; Coifman, Ronald; Nadler, Boaz; Kevrekidis, Ioannis G

2007-04-21

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [R. Erban et al., J. Chem. Phys. 124, 084106 (2006)] the authors assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e., effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [R. Coifman et al., Proc. Natl. Acad. Sci. U.S.A. 102, 7426 (2005)] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free, coarse-grained computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables.

Incorporating interfacial phenomena in solidification models

NASA Technical Reports Server (NTRS)

Beckermann, Christoph; Wang, Chao Yang

1994-01-01

A general methodology is available for the incorporation of microscopic interfacial phenomena in macroscopic solidification models that include diffusion and convection. The method is derived from a formal averaging procedure and a multiphase approach, and relies on the presence of interfacial integrals in the macroscopic transport equations. In a wider engineering context, these techniques are not new, but their application in the analysis and modeling of solidification processes has largely been overlooked. This article describes the techniques and demonstrates their utility in two examples in which microscopic interfacial phenomena are of great importance.

On spatial mutation-selection models

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

Kondratiev, Yuri, E-mail: kondrat@math.uni-bielefeld.de; Kutoviy, Oleksandr, E-mail: kutoviy@math.uni-bielefeld.de, E-mail: kutovyi@mit.edu; Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

2013-11-15

We discuss the selection procedure in the framework of mutation models. We study the regulation for stochastically developing systems based on a transformation of the initial Markov process which includes a cost functional. The transformation of initial Markov process by cost functional has an analytic realization in terms of a Kimura-Maruyama type equation for the time evolution of states or in terms of the corresponding Feynman-Kac formula on the path space. The state evolution of the system including the limiting behavior is studied for two types of mutation-selection models.

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

NASA Astrophysics Data System (ADS)

Kilcrease, D. P.; Brookes, S.

2013-12-01

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. A simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure for the Born cross-sections that employs the Elwert-Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. We also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.

A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.; Lee, Henry

2014-01-01

The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no indication in Ref. II that the gaps are explicitly modeled as in Ref. 6. Computations using overset grids are reported in Ref. 12 for a case by adding moving control surface to an existing blade but with no validation either with an experiment or another computation.

Simplification and Transformation of ASTM F1292 Measurement Procedure for Fall Accident Injury Criteria

PubMed Central

KATO, Maki; SHIMODAIRA, Yoshie; SATO, Takeshi; IIDA, Hiromi

2014-01-01

Abstract: Protecting children from injuries caused by fall accidents from playground equipment is important. Therefore, measures toward minimizing the risk of fall accident injuries are required. The risk of injury can be evaluated using ASTM F1292. In this test, G-max and the HIC are used to estimate the risk of injury. However, the measurement procedure is too complicated for application to a large number of installed equipment. F1292 requires simplified by reducing the number of phases, even with a small risk of loss in accuracy. With this in mind, this study proposes a shortened measurement procedure and a transformation equation to estimate the risk as same as F1292. As the result of experiments, it was revealed that G-max and the HIC values for both procedures linearly increase with drop height. The differences in outcomes between the regression equations of the standardized procedure and those of the shortened procedure can be used as a correction value. They can be added to the value measured by the shortened procedure. This suggests that the combination of the shortened procedure and transformation equation would be equivalent to F1292, with the advantage of being more easily and efficiently applied to the evaluation of installed playground equipment. PMID:25088989

Simplification and transformation of ASTM F1292 measurement procedure for fall accident injury criteria.

PubMed

Kato, Maki; Shimodaira, Yoshie; Sato, Takeshi; Iida, Hiromi

2014-01-01

Protecting children from injuries caused by fall accidents from playground equipment is important. Therefore, measures toward minimizing the risk of fall accident injuries are required. The risk of injury can be evaluated using ASTM F1292. In this test, G-max and the HIC are used to estimate the risk of injury. However, the measurement procedure is too complicated for application to a large number of installed equipment. F1292 requires simplified by reducing the number of phases, even with a small risk of loss in accuracy. With this in mind, this study proposes a shortened measurement procedure and a transformation equation to estimate the risk as same as F1292. As the result of experiments, it was revealed that G-max and the HIC values for both procedures linearly increase with drop height. The differences in outcomes between the regression equations of the standardized procedure and those of the shortened procedure can be used as a correction value. They can be added to the value measured by the shortened procedure. This suggests that the combination of the shortened procedure and transformation equation would be equivalent to F1292, with the advantage of being more easily and efficiently applied to the evaluation of installed playground equipment.

Nonlinear estimation of parameters in biphasic Arrhenius plots.

PubMed

Puterman, M L; Hrboticky, N; Innis, S M

1988-05-01

This paper presents a formal procedure for the statistical analysis of data on the thermotropic behavior of membrane-bound enzymes generated using the Arrhenius equation and compares the analysis to several alternatives. Data is modeled by a bent hyperbola. Nonlinear regression is used to obtain estimates and standard errors of the intersection of line segments, defined as the transition temperature, and slopes, defined as energies of activation of the enzyme reaction. The methodology allows formal tests of the adequacy of a biphasic model rather than either a single straight line or a curvilinear model. Examples on data concerning the thermotropic behavior of pig brain synaptosomal acetylcholinesterase are given. The data support the biphasic temperature dependence of this enzyme. The methodology represents a formal procedure for statistical validation of any biphasic data and allows for calculation of all line parameters with estimates of precision.

Estimation of liquefaction-induced lateral spread from numerical modeling and its application

NASA Astrophysics Data System (ADS)

Meng, Xianhong

A noncoupled numerical procedure was developed using a scheme of pore water generation that causes shear modulus degradation and shear strength degradation resulting from earthquake cyclic motion. The designed Fast Lagrangian Analysis of Continua (FLAC) model procedure was tested using the liquefaction-induced lateral spread and ground response for Wildlife and Kobe sites. Sixteen well-documented case histories of lateral spread were reviewed and modeled using the modeling procedure. The dynamic residual strength ratios were back-calculated by matching the predicted displacement with the measured lateral spread, or with the displacement predicted by the Yound et al. model. Statistical analysis on the modeling results and soil properties show that most significant parameters governing the residual strength of the liquefied soil are the SPT blow count, fine content and soil particle size of the lateral spread layer. A regression equation was developed to express the residual strength values with these soil properties. Overall, this research demonstrated that a calibrated numerical model can predict the first order effectiveness of liquefaction-induced lateral spread using relatively simple parameters obtained from routine geotechnical investigation. In addition, the model can be used to plan a soil improvement program for cases where liquefaction remediation is needed. This allows the model to be used for design purposes at bridge approaches structured on liquefiable materials.

Numerical solutions of a control problem governed by functional differential equations

NASA Technical Reports Server (NTRS)

Banks, H. T.; Thrift, P. R.; Burns, J. A.; Cliff, E. M.

1978-01-01

A numerical procedure is proposed for solving optimal control problems governed by linear retarded functional differential equations. The procedure is based on the idea of 'averaging approximations', due to Banks and Burns (1975). For illustration, numerical results generated on an IBM 370/158 computer, which demonstrate the rapid convergence of the method are presented.

Pedagogical Implications in the Thermal Analysis of Uniform Annular Fins: Alternative Analytic Solutions by Series.

ERIC Educational Resources Information Center

Campo, Antonio; Rodriguez, Franklin

1998-01-01

Presents two alternative computational procedures for solving the modified Bessel equation of zero order: the Frobenius method, and the power series method coupled with a curve fit. Students in heat transfer courses can benefit from these alternative procedures; a course on ordinary differential equations is the only mathematical background that…

Validating proposed migration equation and parameters' values as a tool to reproduce and predict 137Cs vertical migration activity in Spanish soils.

PubMed

Olondo, C; Legarda, F; Herranz, M; Idoeta, R

2017-04-01

This paper shows the procedure performed to validate the migration equation and the migration parameters' values presented in a previous paper (Legarda et al., 2011) regarding the migration of 137 Cs in Spanish mainland soils. In this paper, this model validation has been carried out checking experimentally obtained activity concentration values against those predicted by the model. This experimental data come from the measured vertical activity profiles of 8 new sampling points which are located in northern Spain. Before testing predicted values of the model, the uncertainty of those values has been assessed with the appropriate uncertainty analysis. Once establishing the uncertainty of the model, both activity concentration values, experimental versus model predicted ones, have been compared. Model validation has been performed analyzing its accuracy, studying it as a whole and also at different depth intervals. As a result, this model has been validated as a tool to predict 137 Cs behaviour in a Mediterranean environment. Copyright © 2017 Elsevier Ltd. All rights reserved.

How to Find a Bug in Ten Thousand Lines Transport Solver? Outline of Experiences from AN Advection-Diffusion Code Verification

NASA Astrophysics Data System (ADS)

Zamani, K.; Bombardelli, F.

2011-12-01

Almost all natural phenomena on Earth are highly nonlinear. Even simplifications to the equations describing nature usually end up being nonlinear partial differential equations. Transport (ADR) equation is a pivotal equation in atmospheric sciences and water quality. This nonlinear equation needs to be solved numerically for practical purposes so academicians and engineers thoroughly rely on the assistance of numerical codes. Thus, numerical codes require verification before they are utilized for multiple applications in science and engineering. Model verification is a mathematical procedure whereby a numerical code is checked to assure the governing equation is properly solved as it is described in the design document. CFD verification is not a straightforward and well-defined course. Only a complete test suite can uncover all the limitations and bugs. Results are needed to be assessed to make a distinction between bug-induced-defect and innate limitation of a numerical scheme. As Roache (2009) said, numerical verification is a state-of-the-art procedure. Sometimes novel tricks work out. This study conveys the synopsis of the experiences we gained during a comprehensive verification process which was done for a transport solver. A test suite was designed including unit tests and algorithmic tests. Tests were layered in complexity in several dimensions from simple to complex. Acceptance criteria defined for the desirable capabilities of the transport code such as order of accuracy, mass conservation, handling stiff source term, spurious oscillation, and initial shape preservation. At the begining, mesh convergence study which is the main craft of the verification is performed. To that end, analytical solution of ADR equation gathered. Also a new solution was derived. In the more general cases, lack of analytical solution could be overcome through Richardson Extrapolation and Manufactured Solution. Then, two bugs which were concealed during the mesh convergence study uncovered with the method of false injection and visualization of the results. Symmetry had dual functionality: there was a bug, which was hidden due to the symmetric nature of a test (it was detected afterward utilizing artificial false injection), on the other hand self-symmetry was used to design a new test, and in a case the analytical solution of the ADR equation was unknown. Assisting subroutines designed to check and post-process conservation of mass and oscillatory behavior. Finally, capability of the solver also checked for stiff reaction source term. The above test suite not only was a decent tool of error detection but also it provided a thorough feedback on the ADR solvers limitations. Such information is the crux of any rigorous numerical modeling for a modeler who deals with surface/subsurface pollution transport.

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M.-S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.

Evaluation of the National Research Council (2001) dairy model and derivation of new prediction equations. 1. Digestibility of fiber, fat, protein, and nonfiber carbohydrate.

PubMed

White, R R; Roman-Garcia, Y; Firkins, J L; VandeHaar, M J; Armentano, L E; Weiss, W P; McGill, T; Garnett, R; Hanigan, M D

2017-05-01

Evaluation of ration balancing systems such as the National Research Council (NRC) Nutrient Requirements series is important for improving predictions of animal nutrient requirements and advancing feeding strategies. This work used a literature data set (n = 550) to evaluate predictions of total-tract digested neutral detergent fiber (NDF), fatty acid (FA), crude protein (CP), and nonfiber carbohydrate (NFC) estimated by the NRC (2001) dairy model. Mean biases suggested that the NRC (2001) lactating cow model overestimated true FA and CP digestibility by 26 and 7%, respectively, and under-predicted NDF digestibility by 16%. All NRC (2001) estimates had notable mean and slope biases and large root mean squared prediction error (RMSPE), and concordance (CCC) ranged from poor to good. Predicting NDF digestibility with independent equations for legumes, corn silage, other forages, and nonforage feeds improved CCC (0.85 vs. 0.76) compared with the re-derived NRC (2001) equation form (NRC equation with parameter estimates re-derived against this data set). Separate FA digestion coefficients were derived for different fat supplements (animal fats, oils, and other fat types) and for the basal diet. This equation returned improved (from 0.76 to 0.94) CCC compared with the re-derived NRC (2001) equation form. Unique CP digestibility equations were derived for forages, animal protein feeds, plant protein feeds, and other feeds, which improved CCC compared with the re-derived NRC (2001) equation form (0.74 to 0.85). New NFC digestibility coefficients were derived for grain-specific starch digestibilities, with residual organic matter assumed to be 98% digestible. A Monte Carlo cross-validation was performed to evaluate repeatability of model fit. In this procedure, data were randomly subsetted 500 times into derivation (60%) and evaluation (40%) data sets, and equations were derived using the derivation data and then evaluated against the independent evaluation data. Models derived with random study effects demonstrated poor repeatability of fit in independent evaluation. Similar equations derived without random study effects showed improved fit against independent data and little evidence of biased parameter estimates associated with failure to include study effects. The equations derived in this analysis provide interesting insight into how NDF, starch, FA, and CP digestibilities are affected by intake, feed type, and diet composition. The Authors. Published by the Federation of Animal Science Societies and Elsevier Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Numerical simulation of the generation mechanism of axisymmetric supersonic jet screech tones

NASA Astrophysics Data System (ADS)

Li, X. D.; Gao, J. H.

2005-08-01

In this paper an axisymmetric computational aeroacoustic procedure is developed to investigate the generation mechanism of axisymmetric supersonic jet screech tones. The axisymmetric Navier-Stokes equations and the two equations standard k-ɛ turbulence model modified by Turpin and Troyes ["Validation of a two-equation turbulence model for axisymmetric reacting and non-reaction flows," AIAA Paper No. 2000-3463 (2000)] are solved in the generalized curvilinear coordinate system. A generalized wall function is applied in the nozzle exit wall region. The dispersion-relation-preserving scheme is applied for space discretization. The 2N storage low-dissipation and low-dispersion Runge-Kutta scheme is employed for time integration. Much attention is paid to far-field boundary conditions and turbulence model. The underexpanded axisymmetric supersonic jet screech tones are simulated over the Mach number from 1.05 to 1.2. Numerical results are presented and compared with the experimental data by other researchers. The simulated wavelengths of A0, A1, A2, and B modes and part of simulated amplitudes agree very well with the measurement data by Ponton and Seiner ["The effects of nozzle exit lip thickness on plume resonance," J. Sound Vib. 154, 531 (1992)]. In particular, the phenomena of modes jumping have been captured correctly although the numerical procedure has to be improved to predict the amplitudes of supersonic jet screech tones more accurately. Furthermore, the phenomena of shock motions are analyzed. The predicted splitting and combination of shock cells are similar with the experimental observations of Panda ["Shock oscillation in underexpanded screeching jets," J. Fluid. Mech. 363, 173 (1998)]. Finally, the receptivity process is numerically studied and analyzed. It is shown that the receptivity zone is associated with the initial thin shear layer, and the incoming and reflected sound waves.

On the solution of evolution equations based on multigrid and explicit iterative methods

NASA Astrophysics Data System (ADS)

Zhukov, V. T.; Novikova, N. D.; Feodoritova, O. B.

2015-08-01

Two schemes for solving initial-boundary value problems for three-dimensional parabolic equations are studied. One is implicit and is solved using the multigrid method, while the other is explicit iterative and is based on optimal properties of the Chebyshev polynomials. In the explicit iterative scheme, the number of iteration steps and the iteration parameters are chosen as based on the approximation and stability conditions, rather than on the optimization of iteration convergence to the solution of the implicit scheme. The features of the multigrid scheme include the implementation of the intergrid transfer operators for the case of discontinuous coefficients in the equation and the adaptation of the smoothing procedure to the spectrum of the difference operators. The results produced by these schemes as applied to model problems with anisotropic discontinuous coefficients are compared.

Computation of confined coflow jets with three turbulence models

NASA Technical Reports Server (NTRS)

Zhu, J.; Shih, T. H.

1993-01-01

A numerical study of confined jets in a cylindrical duct is carried out to examine the performance of two recently proposed turbulence models: an RNG-based K-epsilon model and a realizable Reynolds stress algebraic equation model. The former is of the same form as the standard K-epsilon model but has different model coefficients. The latter uses an explicit quadratic stress-strain relationship to model the turbulent stresses and is capable of ensuring the positivity of each turbulent normal stress. The flow considered involves recirculation with unfixed separation and reattachment points and severe adverse pressure gradients, thereby providing a valuable test of the predictive capability of the models for complex flows. Calculations are performed with a finite-volume procedure. Numerical credibility of the solutions is ensured by using second-order accurate differencing schemes and sufficiently fine grids. Calculations with the standard K-epsilon model are also made for comparison. Detailed comparisons with experiments show that the realizable Reynolds stress algebraic equation model consistently works better than does the standard K-epsilon model in capturing the essential flow features, while the RNG-based K-epsilon model does not seem to give improvements over the standard K-epsilon model under the flow conditions considered.

Analysis of aircraft tires via semianalytic finite elements

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Kim, Kyun O.; Tanner, John A.

1990-01-01

A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynomials in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell.

Travelling wave solutions of the homogeneous one-dimensional FREFLO model

NASA Astrophysics Data System (ADS)

Huang, B.; Hong, J. Y.; Jing, G. Q.; Niu, W.; Fang, L.

2018-01-01

Presently there is quite few analytical studies in traffic flows due to the non-linearity of the governing equations. In the present paper we introduce travelling wave solutions for the homogeneous one-dimensional FREFLO model, which are expressed in the form of series and describe the procedure that vehicles/pedestrians move with a negative velocity and decelerate until rest, then accelerate inversely to positive velocities. This method is expect to be extended to more complex situations in the future.

A probabilistic approach to photovoltaic generator performance prediction

NASA Astrophysics Data System (ADS)

Khallat, M. A.; Rahman, S.

1986-09-01

A method for predicting the performance of a photovoltaic (PV) generator based on long term climatological data and expected cell performance is described. The equations for cell model formulation are provided. Use of the statistical model for characterizing the insolation level is discussed. The insolation data is fitted to appropriate probability distribution functions (Weibull, beta, normal). The probability distribution functions are utilized to evaluate the capacity factors of PV panels or arrays. An example is presented revealing the applicability of the procedure.

Renormalization Group scale-setting in astrophysical systems

NASA Astrophysics Data System (ADS)

Domazet, Silvije; Štefančić, Hrvoje

2011-09-01

A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.

Dynamic reduction with applications to mathematical biology and other areas.

PubMed

Sacker, Robert J; Von Bremen, Hubertus F

2007-10-01

In a difference or differential equation one is usually interested in finding solutions having certain properties, either intrinsic properties (e.g. bounded, periodic, almost periodic) or extrinsic properties (e.g. stable, asymptotically stable, globally asymptotically stable). In certain instances it may happen that the dependence of these equations on the state variable is such that one may (1) alter that dependency by replacing part of the state variable by a function from a class having some of the above properties and (2) solve the 'reduced' equation for a solution having the remaining properties and lying in the same class. This then sets up a mapping Τ of the class into itself, thus reducing the original problem to one of finding a fixed point of the mapping. The procedure is applied to obtain a globally asymptotically stable periodic solution for a system of difference equations modeling the interaction of wild and genetically altered mosquitoes in an environment yielding periodic parameters. It is also shown that certain coupled periodic systems of difference equations may be completely decoupled so that the mapping Τ is established by solving a set of scalar equations. Periodic difference equations of extended Ricker type and also rational difference equations with a finite number of delays are also considered by reducing them to equations without delays but with a larger period. Conditions are given guaranteeing the existence and global asymptotic stability of periodic solutions.

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

NASA Astrophysics Data System (ADS)

Thomas, Philipp; Straube, Arthur V.; Grima, Ramon

2010-11-01

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.

A Procedure for Deriving Formulas to Convert Transition Rates to Probabilities for Multistate Markov Models.

PubMed

Jones, Edmund; Epstein, David; García-Mochón, Leticia

2017-10-01

For health-economic analyses that use multistate Markov models, it is often necessary to convert from transition rates to transition probabilities, and for probabilistic sensitivity analysis and other purposes it is useful to have explicit algebraic formulas for these conversions, to avoid having to resort to numerical methods. However, if there are four or more states then the formulas can be extremely complicated. These calculations can be made using packages such as R, but many analysts and other stakeholders still prefer to use spreadsheets for these decision models. We describe a procedure for deriving formulas that use intermediate variables so that each individual formula is reasonably simple. Once the formulas have been derived, the calculations can be performed in Excel or similar software. The procedure is illustrated by several examples and we discuss how to use a computer algebra system to assist with it. The procedure works in a wide variety of scenarios but cannot be employed when there are several backward transitions and the characteristic equation has no algebraic solution, or when the eigenvalues of the transition rate matrix are very close to each other.

Applying constraints on model-based methods: Estimation of rate constants in a second order consecutive reaction

NASA Astrophysics Data System (ADS)

Kompany-Zareh, Mohsen; Khoshkam, Maryam

2013-02-01

This paper describes estimation of reaction rate constants and pure ultraviolet/visible (UV-vis) spectra of the component involved in a second order consecutive reaction between Ortho-Amino benzoeic acid (o-ABA) and Diazoniom ions (DIAZO), with one intermediate. In the described system, o-ABA was not absorbing in the visible region of interest and thus, closure rank deficiency problem did not exist. Concentration profiles were determined by solving differential equations of the corresponding kinetic model. In that sense, three types of model-based procedures were applied to estimate the rate constants of the kinetic system, according to Levenberg/Marquardt (NGL/M) algorithm. Original data-based, Score-based and concentration-based objective functions were included in these nonlinear fitting procedures. Results showed that when there is error in initial concentrations, accuracy of estimated rate constants strongly depends on the type of applied objective function in fitting procedure. Moreover, flexibility in application of different constraints and optimization of the initial concentrations estimation during the fitting procedure were investigated. Results showed a considerable decrease in ambiguity of obtained parameters by applying appropriate constraints and adjustable initial concentrations of reagents.

The use of elements of the Stewart model (Strong Ion Approach) for the diagnostics of respiratory acidosis on the basis of the calculation of a value of a modified anion gap (AGm) in brachycephalic dogs.

PubMed

Sławuta, P; Glińska-Suchocka, K; Cekiera, A

2015-01-01

Apart from the HH equation, the acid-base balance of an organism is also described by the Stewart model, which assumes that the proper insight into the ABB of the organism is given by an analysis of: pCO2, the difference of concentrations of strong cations and anions in the blood serum - SID, and the total concentration of nonvolatile weak acids - Acid total. The notion of an anion gap (AG), or the apparent lack of ions, is closely related to the acid-base balance described according to the HH equation. Its value mainly consists of negatively charged proteins, phosphates, and sulphates in blood. In the human medicine, a modified anion gap is used, which, including the concentration of the protein buffer of blood, is, in fact, the combination of the apparent lack of ions derived from the classic model and the Stewart model. In brachycephalic dogs, respiratory acidosis often occurs, which is caused by an overgrowth of the soft palate, making it impossible for a free air flow and causing an increase in pCO2--carbonic acid anhydride The aim of the present paper was an attempt to answer the question whether, in the case of systemic respiratory acidosis, changes in the concentration of buffering ions can also be seen. The study was carried out on 60 adult dogs of boxer breed in which, on the basis of the results of endoscopic examination, a strong overgrowth of the soft palate requiring a surgical correction was found. For each dog, the value of the anion gap before and after the palate correction procedure was calculated according to the following equation: AG = ([Na+ mmol/l] + [K+ mmol/l])--([Cl- mmol/l]+ [HCO3- mmol/l]) as well as the value of the modified AG--according to the following equation: AGm = calculated AG + 2.5 x (albumins(r)--albumins(d)). The values of AG calculated for the dogs before and after the procedure fell within the limits of the reference values and did not differ significantly whereas the values of AGm calculated for the dogs before and after the procedure differed from each other significantly. 1) On the basis of the values of AGm obtained it should be stated that in spite of finding respiratory acidosis in the examined dogs, changes in ion concentration can also be seen, which, according to the Stewart theory, compensate metabolic ABB disorders 2) In spite of the fact that all the values used for calculation of AGm were within the limits of reference values, the values of AGm in dogs before and after the soft palate correction procedure differed from each other significantly, which proves high sensitivity and usefulness of the AGm calculation as a diagnostic method.

Enhanced model for determining the number of graphene layers and their distribution from X-ray diffraction data

PubMed Central

Ademi, Abdulakim; Grozdanov, Anita; Paunović, Perica; Dimitrov, Aleksandar T

2015-01-01

Summary A model consisting of an equation that includes graphene thickness distribution is used to calculate theoretical 002 X-ray diffraction (XRD) peak intensities. An analysis was performed upon graphene samples produced by two different electrochemical procedures: electrolysis in aqueous electrolyte and electrolysis in molten salts, both using a nonstationary current regime. Herein, the model is enhanced by a partitioning of the corresponding 2θ interval, resulting in significantly improved accuracy of the results. The model curves obtained exhibit excellent fitting to the XRD intensities curves of the studied graphene samples. The employed equation parameters make it possible to calculate the j-layer graphene region coverage of the graphene samples, and hence the number of graphene layers. The results of the thorough analysis are in agreement with the calculated number of graphene layers from Raman spectra C-peak position values and indicate that the graphene samples studied are few-layered. PMID:26665083

Sharply curved turn around duct flow predictions using spectral partitioning of the turbulent kinetic energy and a pressure modified wall law

NASA Technical Reports Server (NTRS)

Santi, L. Michael

1986-01-01

Computational predictions of turbulent flow in sharply curved 180 degree turn around ducts are presented. The CNS2D computer code is used to solve the equations of motion for two-dimensional incompressible flows transformed to a nonorthogonal body-fitted coordinate system. This procedure incorporates the pressure velocity correction algorithm SIMPLE-C to iteratively solve a discretized form of the transformed equations. A multiple scale turbulence model based on simplified spectral partitioning is employed to obtain closure. Flow field predictions utilizing the multiple scale model are compared to features predicted by the traditional single scale k-epsilon model. Tuning parameter sensitivities of the multiple scale model applied to turn around duct flows are also determined. In addition, a wall function approach based on a wall law suitable for incompressible turbulent boundary layers under strong adverse pressure gradients is tested. Turn around duct flow characteristics utilizing this modified wall law are presented and compared to results based on a standard wall treatment.

Simplified procedures for correlation of experimentally measured and predicted thrust chamber performance

NASA Technical Reports Server (NTRS)

Powell, W. B.

1973-01-01

Thrust chamber performance is evaluated in terms of an analytical model incorporating all the loss processes that occur in a real rocket motor. The important loss processes in the real thrust chamber were identified, and a methodology and recommended procedure for predicting real thrust chamber vacuum specific impulse were developed. Simplified equations for the calculation of vacuum specific impulse are developed to relate the delivered performance (both vacuum specific impulse and characteristic velocity) to the ideal performance as degraded by the losses corresponding to a specified list of loss processes. These simplified equations enable the various performance loss components, and the corresponding efficiencies, to be quantified separately (except that interaction effects are arbitrarily assigned in the process). The loss and efficiency expressions presented can be used to evaluate experimentally measured thrust chamber performance, to direct development effort into the areas most likely to yield improvements in performance, and as a basis to predict performance of related thrust chamber configurations.

Plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a coated circular inclusion

NASA Astrophysics Data System (ADS)

Hoh, H. J.; Xiao, Z. M.; Luo, J.

2010-09-01

An analytical investigation on the plastic zone size of a crack near a coated circular inclusion under three different loading conditions of uniaxial tension, uniform tension and pure shear was carried out. Both the crack and coated circular inclusion are embedded in an infinite matrix, with the crack oriented along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small-scale yielding [J. Mech. Phys. Solids 8 (1960) p. 100], two thin strips of yielded plastic zones are introduced at both crack tips. Using the solution for a coated circular inclusion interacting with a single dislocation as the Green's function, the physical problem is formulated into a set of singular integral equations. Using the method of Erdogan and Gupta [Q. J. Appl. Math. 29 (1972) p. 525] and iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacement.

Thermodynamic and Mechanic Consideration on the stability of Anti-symmetric Schaefer’s equation

NASA Astrophysics Data System (ADS)

Suriamihardja, D. A.; Amiruddin; Saaduddin

2018-03-01

Schaefer’s equation relates an interaction between population of fishes and the number of units of fishing effort. The population growth of fishes is reduced by the number of units of fishing effort, while the population growth of units of fishing effort depends on the existence of fishes. This paper aims to examine the stability of an anti-symmetric Schaefer’s equation through thermodynamic and mechanic procedure using a formula of entropy production near equilibrium which is recognized as Onsager’s relation. The results confirm that entropic approach (thermodynamics) and dissipative approach (mechanics) are usable to be applied as Lyapunov’s procedure in examining the stability of systems of differential equations.

Estimating design-flood discharges for streams in Iowa using drainage-basin and channel-geometry characteristics

USGS Publications Warehouse

Eash, D.A.

1993-01-01

Procedures provided for applying the drainage-basin and channel-geometry regression equations depend on whether the design-flood discharge estimate is for a site on an ungaged stream, an ungaged site on a gaged stream, or a gaged site. When both a drainage-basin and a channel-geometry regression-equation estimate are available for a stream site, a procedure is presented for determining a weighted average of the two flood estimates. The drainage-basin regression equations are applicable to unregulated rural drainage areas less than 1,060 square miles, and the channel-geometry regression equations are applicable to unregulated rural streams in Iowa with stabilized channels.

General relativistic hydrodynamics with Adaptive-Mesh Refinement (AMR) and modeling of accretion disks

NASA Astrophysics Data System (ADS)

Donmez, Orhan

We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.

Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes.

PubMed

Kyriakopoulos, Charalampos; Grossmann, Gerrit; Wolf, Verena; Bortolussi, Luca

2018-01-01

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree k_{max} of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large k_{max}. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.

Implementation of 3-D isoparametric finite elements on supercomputer for the formulation of recursive dynamical equations of multi-body systems

NASA Technical Reports Server (NTRS)

Shareef, N. H.; Amirouche, F. M. L.

1991-01-01

A computational algorithmic procedure is developed and implemented for the dynamic analysis of a multibody system with rigid/flexible interconnected bodies. The algorithm takes into consideration the large rotation/translation and small elastic deformations associated with the rigid-body degrees of freedom and the flexibility of the bodies in the system respectively. Versatile three-dimensional isoparametric brick elements are employed for the modeling of the geometric configurations of the bodies. The formulation of the recursive dynamical equations of motion is based on the recursive Kane's equations, strain energy concepts, and the techniques of component mode synthesis. In order to minimize CPU-intensive matrix multiplication operations and speed up the execution process, the concepts of indexed arrays is utilized in the formulation of the equations of motion. A spin-up maneuver of a space robot with three flexible links carrying a solar panel is used as an illustrative example.

Transport of water and ions in partially water-saturated porous media. Part 1. Constitutive equations

NASA Astrophysics Data System (ADS)

Revil, A.

2017-05-01

I developed a model of cross-coupled flow in partially saturated porous media based on electrokinetic coupling including the effect of ion filtration (normal and reverse osmosis) and the multi-component nature of the pore water (wetting) phase. The model also handles diffusion and membrane polarization but is valid only for saturations above the irreducible water saturation. I start with the local Nernst-Planck and Stokes equations and I use a volume-averaging procedure to obtain the generalized Ohm, Fick, and Darcy equations with cross-coupling terms at the scale of a representative elementary volume of the porous rock. These coupling terms obey Onsager's reciprocity, which is a required condition, at the macroscale, to keep the total dissipation function of the system positive. Rather than writing the electrokinetic terms in terms of zeta potential (the double layer electrical potential on the slipping plane located in the pore water), I developed the model in terms of an effective charge density dragged by the flow of the pore water. This effective charge density is found to be strongly controlled by the permeability and the water saturation. I also developed an electrical conductivity equation including the effect of saturation on both bulk and surface conductivities, the surface conductivity being associated with electromigration in the electrical diffuse layer coating the grains. This surface conductivity depends on the CEC of the porous material.

Dynamic response of a collidant impacting a low pressure airbag

NASA Astrophysics Data System (ADS)

Dreher, Peter A.

There are many uses of low pressure airbags, both military and commercial. Many of these applications have been hampered by inadequate and inaccurate modeling tools. This dissertation contains the derivation of a four degree-of-freedom system of differential equations from physical laws of mass and energy conservation, force equilibrium, and the Ideal Gas Law. Kinematic equations were derived to model a cylindrical airbag as a single control volume impacted by a parallelepiped collidant. An efficient numerical procedure was devised to solve the simplified system of equations in a manner amenable to discovering design trends. The largest public airbag experiment, both in scale and scope, was designed and built to collect data on low-pressure airbag responses, otherwise unavailable in the literature. The experimental results were compared to computational simulations to validate the simplified numerical model. Experimental response trends are presented that will aid airbag designers. The two objectives of using a low pressure airbag to demonstrate the feasibility to (1) accelerate a munition to 15 feet per second velocity from a bomb bay, and (2) decelerate humans hitting trucks below the human tolerance level of 50 G's, were both met.

A procedure to construct exact solutions of nonlinear fractional differential equations.

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

NASA Astrophysics Data System (ADS)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

Comprehensive analysis of heat transfer of gold-blood nanofluid (Sisko-model) with thermal radiation

NASA Astrophysics Data System (ADS)

Eid, Mohamed R.; Alsaedi, Ahmed; Muhammad, Taseer; Hayat, Tasawar

Characteristics of heat transfer of gold nanoparticles (Au-NPs) in flow past a power-law stretching surface are discussed. Sisko bio-nanofluid flow (with blood as a base fluid) in existence of non-linear thermal radiation is studied. The resulting equations system is abbreviated to model the suggested problem in non-linear PDEs. Along with initial and boundary-conditions, the equations are made non-dimensional and then resolved numerically utilizing 4th-5th order Runge-Kutta-Fehlberg (RKF45) technique with shooting integration procedure. Various flow quantities behaviors are examined for parametric consideration such as the Au-NPs volume fraction, the exponentially stretching and thermal radiation parameters. It is observed that radiation drives to shortage the thermal boundary-layer thickness and therefore resulted in better heat transfer at surface.

Numerical Limitations of 1D Hydraulic Models Using MIKE11 or HEC-RAS software - Case study of Baraolt River, Romania

NASA Astrophysics Data System (ADS)

Andrei, Armas; Robert, Beilicci; Erika, Beilicci

2017-10-01

MIKE 11 is an advanced hydroinformatic tool, a professional engineering software package for simulation of one-dimensional flows in estuaries, rivers, irrigation systems, channels and other water bodies. MIKE 11 is a 1-dimensional river model. It was developed by DHI Water · Environment · Health, Denmark. The basic computational procedure of HEC-RAS for steady flow is based on the solution of the one-dimensional energy equation. Energy losses are evaluated by friction and contraction / expansion. The momentum equation may be used in situations where the water surface profile is rapidly varied. These situations include hydraulic jumps, hydraulics of bridges, and evaluating profiles at river confluences. For unsteady flow, HEC-RAS solves the full, dynamic, 1-D Saint Venant Equation using an implicit, finite difference method. The unsteady flow equation solver was adapted from Dr. Robert L. Barkau’s UNET package. Fluid motion is controlled by the basic principles of conservation of mass, energy and momentum, which form the basis of fluid mechanics and hydraulic engineering. Complex flow situations must be solved using empirical approximations and numerical models, which are based on derivations of the basic principles (backwater equation, Navier-Stokes equation etc.). All numerical models are required to make some form of approximation to solve these principles, and consequently all have their limitations. The study of hydraulics and fluid mechanics is founded on the three basic principles of conservation of mass, energy and momentum. Real-life situations are frequently too complex to solve without the aid of numerical models. There is a tendency among some engineers to discard the basic principles taught at university and blindly assume that the results produced by the model are correct. Regardless of the complexity of models and despite the claims of their developers, all numerical models are required to make approximations. These may be related to geometric limitations, numerical simplification, or the use of empirical correlations. Some are obvious: one-dimensional models must average properties over the two remaining directions. It is the less obvious and poorly advertised approximations that pose the greatest threat to the novice user. Some of these, such as the inability of one-dimensional unsteady models to simulate supercritical flow can cause significant inaccuracy in the model predictions.

A Lumped Computational Model for Sodium Sulfur Battery Analysis

NASA Astrophysics Data System (ADS)

Wu, Fan

Due to the cost of materials and time consuming testing procedures, development of new batteries is a slow and expensive practice. The purpose of this study is to develop a computational model and assess the capabilities of such a model designed to aid in the design process and control of sodium sulfur batteries. To this end, a transient lumped computational model derived from an integral analysis of the transport of species, energy and charge throughout the battery has been developed. The computation processes are coupled with the use of Faraday's law, and solutions for the species concentrations, electrical potential and current are produced in a time marching fashion. Properties required for solving the governing equations are calculated and updated as a function of time based on the composition of each control volume. The proposed model is validated against multi- dimensional simulations and experimental results from literatures, and simulation results using the proposed model is presented and analyzed. The computational model and electrochemical model used to solve the equations for the lumped model are compared with similar ones found in the literature. The results obtained from the current model compare favorably with those from experiments and other models.

Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge.

PubMed

Schneider, Michael; Rittle-Johnson, Bethany; Star, Jon R

2011-11-01

Competence in many domains rests on children developing conceptual and procedural knowledge, as well as procedural flexibility. However, research on the developmental relations between these different types of knowledge has yielded unclear results, in part because little attention has been paid to the validity of the measures or to the effects of prior knowledge on the relations. To overcome these problems, we modeled the three constructs in the domain of equation solving as latent factors and tested (a) whether the predictive relations between conceptual and procedural knowledge were bidirectional, (b) whether these interrelations were moderated by prior knowledge, and (c) how both constructs contributed to procedural flexibility. We analyzed data from 2 measurement points each from two samples (Ns = 228 and 304) of middle school students who differed in prior knowledge. Conceptual and procedural knowledge had stable bidirectional relations that were not moderated by prior knowledge. Both kinds of knowledge contributed independently to procedural flexibility. The results demonstrate how changes in complex knowledge structures contribute to competence development.

TOPICAL REVIEW: Nonlinear aspects of the renormalization group flows of Dyson's hierarchical model

NASA Astrophysics Data System (ADS)

Meurice, Y.

2007-06-01

We review recent results concerning the renormalization group (RG) transformation of Dyson's hierarchical model (HM). This model can be seen as an approximation of a scalar field theory on a lattice. We introduce the HM and show that its large group of symmetry simplifies drastically the blockspinning procedure. Several equivalent forms of the recursion formula are presented with unified notations. Rigourous and numerical results concerning the recursion formula are summarized. It is pointed out that the recursion formula of the HM is inequivalent to both Wilson's approximate recursion formula and Polchinski's equation in the local potential approximation (despite the very small difference with the exponents of the latter). We draw a comparison between the RG of the HM and functional RG equations in the local potential approximation. The construction of the linear and nonlinear scaling variables is discussed in an operational way. We describe the calculation of non-universal critical amplitudes in terms of the scaling variables of two fixed points. This question appears as a problem of interpolation between these fixed points. Universal amplitude ratios are calculated. We discuss the large-N limit and the complex singularities of the critical potential calculable in this limit. The interpolation between the HM and more conventional lattice models is presented as a symmetry breaking problem. We briefly introduce models with an approximate supersymmetry. One important goal of this review is to present a configuration space counterpart, suitable for lattice formulations, of functional RG equations formulated in momentum space (often called exact RG equations and abbreviated ERGE).

Masses from an inhomogeneous partial difference equation with higher-order isospin contributions

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

Masson, P.J.; Jaenecke, J.

In the present work, a mass equation obtained as the solution of an inhomogeneous partial difference equation is used to predict masses of unknown neutron-rich and proton-rich nuclei. The inhomogeneous source terms contain shell-dependent symmetry energy expressions (quadratic in isospin), and include, as well, an independently derived shell-model Coulomb energy equation which describes all known Coulomb displacement energies with a standarad deviation of sigma/sub c/ = 41 keV. Perturbations of higher order in isospin, previously recognized as a cause of systematic effects in long-range mass extrapolations, are also incorporated. The most general solutions of the inhomogeneous difference equation have beenmore » deduced from a chi/sup 2/-minimization procedure based on the recent atomic mass adjustment of Wapstra, Audi, and Hoekstra. Subjecting the solutions further to the condition of charge symmetry preserves the accuracy of Coulomb energies and allows mass predictions for nuclei with both Ngreater than or equal toZ and Z>N. The solutions correspond to a mass equation with 470 parameters. Using this equation, 4385 mass values have been calculated for nuclei with Agreater than or equal to16 (except N = Z = odd for A<40), with a standard deviation of sigma/sub m/ = 194 keV from the experimental masses. copyright 1988 Academic Press, Inc.« less

Improving the performance of the mass transfer-based reference evapotranspiration estimation approaches through a coupled wavelet-random forest methodology

NASA Astrophysics Data System (ADS)

Shiri, Jalal

2018-06-01

Among different reference evapotranspiration (ETo) modeling approaches, mass transfer-based methods have been less studied. These approaches utilize temperature and wind speed records. On the other hand, the empirical equations proposed in this context generally produce weak simulations, except when a local calibration is used for improving their performance. This might be a crucial drawback for those equations in case of local data scarcity for calibration procedure. So, application of heuristic methods can be considered as a substitute for improving the performance accuracy of the mass transfer-based approaches. However, given that the wind speed records have usually higher variation magnitudes than the other meteorological parameters, application of a wavelet transform for coupling with heuristic models would be necessary. In the present paper, a coupled wavelet-random forest (WRF) methodology was proposed for the first time to improve the performance accuracy of the mass transfer-based ETo estimation approaches using cross-validation data management scenarios in both local and cross-station scales. The obtained results revealed that the new coupled WRF model (with the minimum scatter index values of 0.150 and 0.192 for local and external applications, respectively) improved the performance accuracy of the single RF models as well as the empirical equations to great extent.

Mean Field Analysis of Large-Scale Interacting Populations of Stochastic Conductance-Based Spiking Neurons Using the Klimontovich Method

NASA Astrophysics Data System (ADS)

Gandolfo, Daniel; Rodriguez, Roger; Tuckwell, Henry C.

2017-03-01

We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions (PPD) which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the PPDs. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean-Vlasov-Fokker-Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from PPDs are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained for networks of Fitzhugh-Nagumo model neurons, which are often used to approximate Hodgkin-Huxley model neurons, the theory can be readily applied to networks of general conductance-based model neurons of arbitrary dimension.

New type of a generalized variable-coefficient Kadomtsev-Petviashvili equation with self-consistent sources and its Grammian-type solutions

NASA Astrophysics Data System (ADS)

Zhang, Yi; Xu, Yue; Ma, Kun

2016-08-01

In this paper, the variable-coefficient Kadomtsev-Petviashvili (vcKP) equation with self-consistent sources is presented by two different methods, one is the source generation procedure, the other is the Pfaffianization procedure, and the solutions for the two new coupled systems are given through Grammian-type Pfaffian determinants.

An Exploration of a Quantitative Reasoning Instructional Approach to Linear Equations in Two Variables with Community College Students

ERIC Educational Resources Information Center

Belue, Paul T.; Cavey, Laurie Overman; Kinzel, Margaret T.

2017-01-01

In this exploratory study, we examined the effects of a quantitative reasoning instructional approach to linear equations in two variables on community college students' conceptual understanding, procedural fluency, and reasoning ability. This was done in comparison to the use of a traditional procedural approach for instruction on the same topic.…

40 CFR 63.8234 - What equations and procedures must I use for the initial compliance demonstration?

Code of Federal Regulations, 2010 CFR

2010-07-01

... What equations and procedures must I use for the initial compliance demonstration? (a) By-product... Megagram of chlorine production (g Hg/Mg Cl2) of chlorine produced from all by-product hydrogen streams and...) Determine the mercury emission rate for each test run in grams per day for each by-product hydrogen stream...

40 CFR 63.8243 - What equations and procedures must I use to demonstrate continuous compliance?

Code of Federal Regulations, 2010 CFR

2010-07-01

....8243 What equations and procedures must I use to demonstrate continuous compliance? (a) By-product... determine the g Hg/Mg Cl2 produced from all by-product hydrogen streams and all end box ventilation system... weekly mercury emission rate in grams per week for each by-product hydrogen stream and for each end box...

Direct computation of thermodynamic properties of chemically reacting air with consideration to CFD

NASA Astrophysics Data System (ADS)

Iannelli, Joe

2003-10-01

This paper details a two-equation procedure to calculate exactly mass and mole fractions, pressure, temperature, specific heats, speed of sound and the thermodynamic and jacobian partial derivatives of pressure and temperature for a five-species chemically reacting equilibrium air. The procedure generates these thermodynamic properties using as independent variables either pressure and temperature or density and internal energy, for CFD applications. An original element in this procedure consists in the exact physically meaningful solution of the mass-fraction and mass-action equations. Air-equivalent molecular masses for oxygen and nitrogen are then developed to account, within a mixture of only oxygen and nitrogen, for the presence of carbon dioxide, argon and the other noble gases within atmospheric air. The mathematical formulation also introduces a versatile system non-dimensionalization that makes the procedure uniformly applicable to flows ranging from shock-tube flows with zero initial velocity to aerothermodynamic flows with supersonic/hypersonic free-stream Mach numbers. Over a temperature range of more than 10000 K and pressure and density ranges corresponding to an increase in altitude in standard atmosphere of 30000 m above sea level, the predicted distributions of mole fractions, constant-volume specific heat, and speed of sound for the model five species agree with independently published results, and all the calculated thermodynamic properties, including their partial derivatives, remain continuous, smooth, and physically meaningful.

Enhanced Decision Analysis Support System.

DTIC Science & Technology

1981-03-01

autorrares "i., the method for determining preferences when multiple and competing attributes are involved. Worth assessment is used as the model which...1967 as a method for determining preferenoe when multiple and competing attributes are involved (Rf 10). The tern worth can be - equated to other... competing objectives. After some discussion, the group decided that the problem could best be decided using the worth assessment procedure. They

The Economic Impact of Eight Cultural Institutions on the Economy of the St. Louis SMSA. Technical Supplement. Volume I [and] Volume II--Appendices.

ERIC Educational Resources Information Center

Cwi, David; Smith, D. Alden

The research methods, procedures, and data for determining the impact of eight cultural institutions on the St. Louis (Missouri) economy (1978) are outlined. A 30-equation model was used to identify a variety of effects on local businesses, government, and individuals. Researchers examined internal records of the eight institutions as well as…

Rigorous Model Reduction for a Damped-Forced Nonlinear Beam Model: An Infinite-Dimensional Analysis

NASA Astrophysics Data System (ADS)

Kogelbauer, Florian; Haller, George

2018-06-01

We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of the linearized beam equation. Reduction in the governing PDE to SSMs provides an explicit low-dimensional model which captures the correct asymptotics of the full, infinite-dimensional dynamics. Our approach is general enough to admit extensions to other types of continuum vibrations. The model-reduction procedure we employ also gives guidelines for a mathematically self-consistent modeling of damping in PDEs describing structural vibrations.

Two approaches to forecast Ebola synthetic epidemics.

PubMed

Champredon, David; Li, Michael; Bolker, Benjamin M; Dushoff, Jonathan

2018-03-01

We use two modelling approaches to forecast synthetic Ebola epidemics in the context of the RAPIDD Ebola Forecasting Challenge. The first approach is a standard stochastic compartmental model that aims to forecast incidence, hospitalization and deaths among both the general population and health care workers. The second is a model based on the renewal equation with latent variables that forecasts incidence in the whole population only. We describe fitting and forecasting procedures for each model and discuss their advantages and drawbacks. We did not find that one model was consistently better in forecasting than the other. Copyright © 2017 The Author(s). Published by Elsevier B.V. All rights reserved.

Numerical solution of quadratic matrix equations for free vibration analysis of structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

Scilab software as an alternative low-cost computing in solving the linear equations problem

NASA Astrophysics Data System (ADS)

Agus, Fahrul; Haviluddin

2017-02-01

Numerical computation packages are widely used both in teaching and research. These packages consist of license (proprietary) and open source software (non-proprietary). One of the reasons to use the package is a complexity of mathematics function (i.e., linear problems). Also, number of variables in a linear or non-linear function has been increased. The aim of this paper was to reflect on key aspects related to the method, didactics and creative praxis in the teaching of linear equations in higher education. If implemented, it could be contribute to a better learning in mathematics area (i.e., solving simultaneous linear equations) that essential for future engineers. The focus of this study was to introduce an additional numerical computation package of Scilab as an alternative low-cost computing programming. In this paper, Scilab software was proposed some activities that related to the mathematical models. In this experiment, four numerical methods such as Gaussian Elimination, Gauss-Jordan, Inverse Matrix, and Lower-Upper Decomposition (LU) have been implemented. The results of this study showed that a routine or procedure in numerical methods have been created and explored by using Scilab procedures. Then, the routine of numerical method that could be as a teaching material course has exploited.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram.

Computational benefits using artificial intelligent methodologies for the solution of an environmental design problem: saltwater intrusion.

PubMed

Papadopoulou, Maria P; Nikolos, Ioannis K; Karatzas, George P

2010-01-01

Artificial Neural Networks (ANNs) comprise a powerful tool to approximate the complicated behavior and response of physical systems allowing considerable reduction in computation time during time-consuming optimization runs. In this work, a Radial Basis Function Artificial Neural Network (RBFN) is combined with a Differential Evolution (DE) algorithm to solve a water resources management problem, using an optimization procedure. The objective of the optimization scheme is to cover the daily water demand on the coastal aquifer east of the city of Heraklion, Crete, without reducing the subsurface water quality due to seawater intrusion. The RBFN is utilized as an on-line surrogate model to approximate the behavior of the aquifer and to replace some of the costly evaluations of an accurate numerical simulation model which solves the subsurface water flow differential equations. The RBFN is used as a local approximation model in such a way as to maintain the robustness of the DE algorithm. The results of this procedure are compared to the corresponding results obtained by using the Simplex method and by using the DE procedure without the surrogate model. As it is demonstrated, the use of the surrogate model accelerates the convergence of the DE optimization procedure and additionally provides a better solution at the same number of exact evaluations, compared to the original DE algorithm.

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

Forecasting transitions in systems with high-dimensional stochastic complex dynamics: a linear stability analysis of the tangled nature model.

PubMed

Cairoli, Andrea; Piovani, Duccio; Jensen, Henrik Jeldtoft

2014-12-31

We propose a new procedure to monitor and forecast the onset of transitions in high-dimensional complex systems. We describe our procedure by an application to the tangled nature model of evolutionary ecology. The quasistable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean-field equations. Numerical analysis of the high-dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with a positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean-field approximation is found to be a good early warning of the transitions occurring intermittently.

Extended Weyl invariance in a bimetric model and partial masslessness

NASA Astrophysics Data System (ADS)

Hassan, S. F.; Schmidt-May, Angnis; von Strauss, Mikael

2016-01-01

We revisit a particular ghost-free bimetric model which is related to both partial masslessness (PM) and conformal gravity. Linearly, the model propagates six instead of seven degrees of freedom not only around de Sitter but also around flat spacetime. Nonlinearly, the equations of motion can be recast in the form of expansions in powers of curvatures, and exhibit a remarkable amount of structure. In this form, the equations are shown to be invariant under scalar gauge transformations, at least up to six orders in derivatives, the lowest order term being a Weyl scaling of the metrics. The terms at two-derivative order reproduce the usual PM gauge transformations on de Sitter backgrounds. At the four-derivative order, a potential obstruction that could destroy the symmetry is shown to vanish. This in turn guarantees the gauge invariance to at least six-orders in derivatives. This is equivalent to adding up to ten-derivative corrections to conformal gravity. More generally, we outline a procedure for constructing the gauge transformations order by order as an expansion in derivatives and comment on the validity and limitations of the procedure. We also discuss recent arguments against the existence of a PM gauge symmetry in bimetric theory and show that, at least in their present form, they are evaded by the model considered here. Finally, we argue that a bimetric approach to PM theory is more promising than one based on the existence of a fundamental PM field.

Equations for Automotive-Transmission Performance

NASA Technical Reports Server (NTRS)

Chazanoff, S.; Aston, M. B.; Chapman, C. P.

1984-01-01

Curve-fitting procedure ensures high confidence levels. Threedimensional plot represents performance of small automatic transmission coasting in second gear. In equation for plot, PL power loss, S speed and T torque. Equations applicable to manual and automatic transmissions over wide range of speed, torque, and efficiency.

The antecedents of buyers' perceived justice in online markets.

PubMed

Chiu, Shun-Po; Chou, Huey-Wen; Chiu, Chao-Min

2013-07-01

The success of a business largely depends upon customers' intentions to continue to purchase, but this can be a challenge for vendors in online markets. This study proposes a model which identifies an initial set of justice antecedents and evaluates their relation to perceived justice, trust, and repurchase intention in online markets. The theoretical model is tested by using structural equation modeling on a data set of 424 buyers in Yahoo! Kimo online auction market. The results demonstrate that three dimensions of justice (distributive, procedural, and interactional) are positively and significantly related to trust, which in turn affects buyers' intention to repurchase. Moreover, among the three dimensions of justice judgments, distributive justice and interactional justice are relatively more important than procedural justice in predicting buyers' trust in sellers. In terms of the antecedents of justice, this study provides evidence that product quality and delivery performance are significantly related to distributive justice, while information quality and contact channel are important antecedents of procedural justice. This study also finds that responsiveness is important in enhancing buyers' judgments of interactional justice.

Population dynamics of minimally cognitive individuals. Part I: Introducing knowledge into the dynamics

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

Schmieder, R.W.

The author presents a new approach for modeling the dynamics of collections of objects with internal structure. Based on the fact that the behavior of an individual in a population is modified by its knowledge of other individuals, a procedure for accounting for knowledge in a population of interacting objects is presented. It is assumed that each object has partial (or complete) knowledge of some (or all) other objects in the population. The dynamical equations for the objects are then modified to include the effects of this pairwise knowledge. This procedure has the effect of projecting out what the populationmore » will do from the much larger space of what it could do, i.e., filtering or smoothing the dynamics by replacing the complex detailed physical model with an effective model that produces the behavior of interest. The procedure therefore provides a minimalist approach for obtaining emergent collective behavior. The use of knowledge as a dynamical quantity, and its relationship to statistical mechanics, thermodynamics, information theory, and cognition microstructure are discussed.« less

A Comparative Study of Some Dynamic Stall Models

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Kaza, K. R. V.

1987-01-01

Three semi-empirical aerodynamic stall models are compared with respect to their lift and moment hysteresis loop prediction, limit cycle behavior, easy implementation, and feasibility in developing the parameters required for stall flutter prediction of advanced turbines. For the comparison of aeroelastic response prediction including stall, a typical section model and a plate structural model are considered. The response analysis includes both plunging and pitching motions of the blades. In model A, a correction to the angle of attack is applied when the angle of attack exceeds the static stall angle. In model B, a synthesis procedure is used for angles of attack above static stall angles and the time history effects are accounted through the Wagner function. In both models the life and moment coefficients for angle of attack below stall are obtained from tabular data for a given Mach number and angle of attack. In model C, referred to an the ONERA model, the life and moment coefficients are given in the form of two differential equations, one for angles below stall, and the other for angles above stall. The parameters of those equations are nonlinear functions of the angle of attack.

Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation.

PubMed

Zhang, Raoyang; Shan, Xiaowen; Chen, Hudong

2006-10-01

We present a further theoretical extension to the kinetic-theory-based formulation of the lattice Boltzmann method of Shan [J. Fluid Mech. 550, 413 (2006)]. In addition to the higher-order projection of the equilibrium distribution function and a sufficiently accurate Gauss-Hermite quadrature in the original formulation, a regularization procedure is introduced in this paper. This procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the Galerkin sense. Using this formulation, we construct a specific lattice Boltzmann model that accurately incorporates up to third-order hydrodynamic moments. Numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice Boltzmann models, so that fluid flows at finite Knudsen number Kn can be more quantitatively simulated. Results from force-driven Poiseuille flow simulations predict the Knudsen's minimum and the asymptotic behavior of flow flux at large Kn.

Numerical simulation of the pollution formed by exhaust jets at the ground running procedure

NASA Astrophysics Data System (ADS)

Korotaeva, T. A.; Turchinovich, A. O.

2016-10-01

The paper presents an approach that is new for aviation-related ecology. The approach allows defining spatial distribution of pollutant concentrations released at engine ground running procedure (GRP) using full gas-dynamic models. For the first time such a task is modeled in three-dimensional approximation in the framework of the numerical solution of the Navier-Stokes equations with taking into account a kinetic model of interaction between the components of engine exhaust and air. The complex pattern of gas-dynamic flow that occurs at the flow around an aircraft with the jet exhausts that interact with each other, air, jet blast deflector (JBD), and surface of the airplane has been studied in the present work. The numerical technique developed for calculating the concentrations of pollutants produced at the GRP stage permits to define level, character, and area of contamination more reliable and increase accuracy in definition of sanitary protection zones.

Identification of the heat transfer coefficient in the two-dimensional model of binary alloy solidification

NASA Astrophysics Data System (ADS)

Hetmaniok, Edyta; Hristov, Jordan; Słota, Damian; Zielonka, Adam

2017-05-01

The paper presents the procedure for solving the inverse problem for the binary alloy solidification in a two-dimensional space. This is a continuation of some previous works of the authors investigating a similar problem but in the one-dimensional domain. Goal of the problem consists in identification of the heat transfer coefficient on boundary of the region and in reconstruction of the temperature distribution inside the considered region in case when the temperature measurements in selected points of the alloy are known. Mathematical model of the problem is based on the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependance on the concentration of the alloy component. For describing this concentration the Scheil model is used. Investigated procedure involves also the parallelized Ant Colony Optimization algorithm applied for minimizing a functional expressing the error of approximate solution.

A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, J.-S.; Chen, K.-H.; Choi, Y.

1992-01-01

A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables as unknowns. Real gas properties and equilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, nonreacting flow in a model double annular combustor, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.

Finite-element solutions for geothermal systems

NASA Technical Reports Server (NTRS)

Chen, J. C.; Conel, J. E.

1977-01-01

Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.

Davidenko’s Method for the Solution of Nonlinear Operator Equations.

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), OPERATORS(MATHEMATICS), BANACH SPACE , MAPPING (TRANSFORMATIONS), NUMERICAL METHODS AND PROCEDURES, INTEGRALS, SET THEORY, CONVERGENCE, MATRICES(MATHEMATICS)

Insights.

ERIC Educational Resources Information Center

Bogner, Donna, Ed.

1990-01-01

Presented is an approach to solving oxidation-reduction reactions. The advantage of this procedure for both acidic and basic equations is stressed and emphasizes the electrical nature of redox equations. (KR)