Analysis of latency performance of bluetooth low energy (BLE) networks.
Cho, Keuchul; Park, Woojin; Hong, Moonki; Park, Gisu; Cho, Wooseong; Seo, Jihoon; Han, Kijun
2015-01-01
Bluetooth Low Energy (BLE) is a short-range wireless communication technology aiming at low-cost and low-power communication. The performance evaluation of classical Bluetooth device discovery have been intensively studied using analytical modeling and simulative methods, but these techniques are not applicable to BLE, since BLE has a fundamental change in the design of the discovery mechanism, including the usage of three advertising channels. Recently, there several works have analyzed the topic of BLE device discovery, but these studies are still far from thorough. It is thus necessary to develop a new, accurate model for the BLE discovery process. In particular, the wide range settings of the parameters introduce lots of potential for BLE devices to customize their discovery performance. This motivates our study of modeling the BLE discovery process and performing intensive simulation. This paper is focused on building an analytical model to investigate the discovery probability, as well as the expected discovery latency, which are then validated via extensive experiments. Our analysis considers both continuous and discontinuous scanning modes. We analyze the sensitivity of these performance metrics to parameter settings to quantitatively examine to what extent parameters influence the performance metric of the discovery processes. PMID:25545266
Analysis of Latency Performance of Bluetooth Low Energy (BLE) Networks
Cho, Keuchul; Park, Woojin; Hong, Moonki; Park, Gisu; Cho, Wooseong; Seo, Jihoon; Han, Kijun
2015-01-01
Bluetooth Low Energy (BLE) is a short-range wireless communication technology aiming at low-cost and low-power communication. The performance evaluation of classical Bluetooth device discovery have been intensively studied using analytical modeling and simulative methods, but these techniques are not applicable to BLE, since BLE has a fundamental change in the design of the discovery mechanism, including the usage of three advertising channels. Recently, there several works have analyzed the topic of BLE device discovery, but these studies are still far from thorough. It is thus necessary to develop a new, accurate model for the BLE discovery process. In particular, the wide range settings of the parameters introduce lots of potential for BLE devices to customize their discovery performance. This motivates our study of modeling the BLE discovery process and performing intensive simulation. This paper is focused on building an analytical model to investigate the discovery probability, as well as the expected discovery latency, which are then validated via extensive experiments. Our analysis considers both continuous and discontinuous scanning modes. We analyze the sensitivity of these performance metrics to parameter settings to quantitatively examine to what extent parameters influence the performance metric of the discovery processes. PMID:25545266
Regularized Structural Equation Modeling
Jacobucci, Ross; Grimm, Kevin J.; McArdle, John J.
2016-01-01
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM’s utility. PMID:27398019
Structural Equation Model Trees
ERIC Educational Resources Information Center
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2015-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model. PMID:22984789
Generalized Multilevel Structural Equation Modeling
ERIC Educational Resources Information Center
Rabe-Hesketh, Sophia; Skrondal, Anders; Pickles, Andrew
2004-01-01
A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent…
Modelling by Differential Equations
ERIC Educational Resources Information Center
Chaachoua, Hamid; Saglam, Ayse
2006-01-01
This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…
Research on two equation models
NASA Technical Reports Server (NTRS)
Yang, Z.
1993-01-01
The k-epsilon model is the most widely used turbulence model in engineering calculations. However, the model has several deficiencies that need to be fixed. This document presents improvements to the capabilities of the k-epsilon model in the following areas: a Galilean and tensorial invariant k-epsilon model for near wall turbulence; a new set of wall functions for attached flows; a new model equation for the dissipation rate, which has a better theoretical basis, contains the contribution of flow inhomogeneity, and captures the effect of the pressure gradient accurately; and a better model for bypass transition due to freestream turbulence.
Model Equations: "Black Box" Reconstruction
NASA Astrophysics Data System (ADS)
Bezruchko, Boris P.; Smirnov, Dmitry A.
Black box reconstruction is both the most difficult and the most tempting modelling problem when any prior information about an appropriate model structure is lacking. An intriguing thing is that a model capable of reproducing an observed behaviour or predicting further evolution should be obtained only from an observed time series, i.e. "from nothing" at first sight. Chances for a success are not large. Even more so, a "good" model would become a valuable tool to characterise an object and understand its dynamics. Lack of prior information causes one to utilise universal model structures, e.g. artificial neural networks, radial basis functions and algebraic polynomials are included in the right-hand sides of dynamical model equations. Such models are often multi-dimensional and involve quite many free parameters.
One-Equation Algebraic Model Of Turbulence
NASA Technical Reports Server (NTRS)
Baldwin, B. S.; Barth, T. J.
1993-01-01
One-equation model of turbulence based on standard equations of k-epsilon model of turbulence, where k is turbulent energy and e is rate of dissipation of k. Derivation of one-equation model motivated partly by inaccuracies of flows computed by some Navier-Stokes-equations-solving algorithms incorporating algebraic models of turbulence. Satisfies need to avoid having to determine algebraic length scales.
The Specific Analysis of Structural Equation Models
ERIC Educational Resources Information Center
McDonald, Roderick P.
2004-01-01
Conventional structural equation modeling fits a covariance structure implied by the equations of the model. This treatment of the model often gives misleading results because overall goodness of fit tests do not focus on the specific constraints implied by the model. An alternative treatment arising from Pearl's directed acyclic graph theory…
Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models
ERIC Educational Resources Information Center
Song, Xin-Yuan; Xia, Ye-Mao; Pan, Jun-Hao; Lee, Sik-Yum
2011-01-01
Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…
Congeneric Models and Levine's Linear Equating Procedures.
ERIC Educational Resources Information Center
Brennan, Robert L.
In 1955, R. Levine introduced two linear equating procedures for the common-item non-equivalent populations design. His procedures make the same assumptions about true scores; they differ in terms of the nature of the equating function used. In this paper, two parameterizations of a classical congeneric model are introduced to model the variables…
Modeling Projects in a Differential Equations Course.
ERIC Educational Resources Information Center
Claus-McGahan, Elly
1998-01-01
Discusses the value of student-designed, in-depth, modeling projects in a differential equations course and how to prepare students. Provides excerpts from worksheets, a list of computer software for Macintosh that can be used in teaching differential equations, and an annotated bibliography. (Author/ASK)
Stochastic differential equation model to Prendiville processes
Granita; Bahar, Arifah
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Multiplicity Control in Structural Equation Modeling
ERIC Educational Resources Information Center
Cribbie, Robert A.
2007-01-01
Researchers conducting structural equation modeling analyses rarely, if ever, control for the inflated probability of Type I errors when evaluating the statistical significance of multiple parameters in a model. In this study, the Type I error control, power and true model rates of famsilywise and false discovery rate controlling procedures were…
Differential equation models for sharp threshold dynamics.
Schramm, Harrison C; Dimitrov, Nedialko B
2014-01-01
We develop an extension to differential equation models of dynamical systems to allow us to analyze probabilistic threshold dynamics that fundamentally and globally change system behavior. We apply our novel modeling approach to two cases of interest: a model of infectious disease modified for malware where a detection event drastically changes dynamics by introducing a new class in competition with the original infection; and the Lanchester model of armed conflict, where the loss of a key capability drastically changes the effectiveness of one of the sides. We derive and demonstrate a step-by-step, repeatable method for applying our novel modeling approach to an arbitrary system, and we compare the resulting differential equations to simulations of the system's random progression. Our work leads to a simple and easily implemented method for analyzing probabilistic threshold dynamics using differential equations. PMID:24184349
Causality, Confirmation, Credulity, and Structural Equation Modeling.
ERIC Educational Resources Information Center
Biddle, Bruce J.; Marlin, Marjorie M.
1987-01-01
Defines structural equation modeling (SEM) and points out its relation to other more familiar data-analytic techniques, as well as some of the potentials and pitfalls of SEM in the analysis of developmental data. Discussion focuses on causal modeling, path diagrams, ordinary least-squares regression analysis, and powerful methods for model…
A Brief Guide to Structural Equation Modeling
ERIC Educational Resources Information Center
Weston, Rebecca; Gore, Paul A., Jr.
2006-01-01
To complement recent articles in this journal on structural equation modeling (SEM) practice and principles by Martens and by Quintana and Maxwell, respectively, the authors offer a consumer's guide to SEM. Using an example derived from theory and research on vocational psychology, the authors outline six steps in SEM: model specification,…
Mediation from Multilevel to Structural Equation Modeling
MacKinnon, David P.; Valente, Matthew J.
2016-01-01
Background/Aims The purpose of this article is to outline multilevel structural equation modeling (MSEM) for mediation analysis of longitudinal data. The introduction of mediating variables can improve experimental and nonexperimental studies of child growth in several ways as discussed throughout this article. Single-mediator individual-level and multilevel mediation models illustrate several current issues in the estimation of mediation with longitudinal data. The strengths of incorporating structural equation modeling (SEM) with multilevel mediation modeling are described. Summary and Key Messages Longitudinal mediation models are pervasive in many areas of research including child growth. Longitudinal mediation models are ideally modeled as repeated measurements clustered within individuals. Further, the combination of MSEM and SEM provides an ideal approach for several reasons, including the ability to assess effects at different levels of analysis, incorporation of measurement error and possible random effects that vary across individuals. PMID:25413658
Experiences with two-equation turbulence models
NASA Technical Reports Server (NTRS)
Singhal, Ashok K.; Lai, Yong G.; Avva, Ram K.
1995-01-01
This viewgraph presentation discusses the following: introduction to CFD Research Corporation; experiences with two-equation models - models used, numerical difficulties, validation and applications, and strengths and weaknesses; and answers to three questions posed by the workshop organizing committee - what are your customers telling you, what are you doing in-house, and how can NASA-CMOTT (Center for Modeling of Turbulence and Transition) help.
Sandia Equation of State Model Library
Energy Science and Technology Software Center (ESTSC)
2013-08-29
The software provides a general interface for querying thermodynamic states of material models along with implementation of both general and specific equation of state models. In particular, models are provided for the IAPWS-IF97 and IAPWS95 water standards as well as the associated water standards for viscosity, thermal conductivity, and surface tension. The interface supports implementation of models in a variety of independent variable spaces. Also, model support routines are included that allow for coupling ofmore » models and determination and representation of phase boundaries.« less
Sandia Equation of State Model Library
Carpenter, John H.
2013-08-29
The software provides a general interface for querying thermodynamic states of material models along with implementation of both general and specific equation of state models. In particular, models are provided for the IAPWS-IF97 and IAPWS95 water standards as well as the associated water standards for viscosity, thermal conductivity, and surface tension. The interface supports implementation of models in a variety of independent variable spaces. Also, model support routines are included that allow for coupling of models and determination and representation of phase boundaries.
Structural Equation Modeling in Rehabilitation Counseling Research
ERIC Educational Resources Information Center
Chan, Fong; Lee, Gloria K.; Lee, Eun-Jeong; Kubota, Coleen; Allen, Chase A.
2007-01-01
Structural equation modeling (SEM) has become increasingly popular in counseling, psychology, and rehabilitation research. The purpose of this article is to provide an overview of the basic concepts and applications of SEM in rehabilitation counseling research using the AMOS statistical software program.
Asymptotic-preserving Boltzmann model equations for binary gas mixture
NASA Astrophysics Data System (ADS)
Liu, Sha; Liang, Yihua
2016-02-01
An improved system of Boltzmann model equations is developed for binary gas mixture. This system of model equations has a complete asymptotic preserving property that can strictly recover the Navier-Stokes equations in the continuum limit with the correct constitutive relations and the correct viscosity, thermal conduction, diffusion, and thermal diffusion coefficients. In this equation system, the self- and cross-collision terms in Boltzmann equations are replaced by single relaxation terms. In monocomponent case, this system of equations can be reduced to the commonly used Shakhov equation. The conservation property and the H theorem which are important for model equations are also satisfied by this system of model equations.
Asymptotic-preserving Boltzmann model equations for binary gas mixture.
Liu, Sha; Liang, Yihua
2016-02-01
An improved system of Boltzmann model equations is developed for binary gas mixture. This system of model equations has a complete asymptotic preserving property that can strictly recover the Navier-Stokes equations in the continuum limit with the correct constitutive relations and the correct viscosity, thermal conduction, diffusion, and thermal diffusion coefficients. In this equation system, the self- and cross-collision terms in Boltzmann equations are replaced by single relaxation terms. In monocomponent case, this system of equations can be reduced to the commonly used Shakhov equation. The conservation property and the H theorem which are important for model equations are also satisfied by this system of model equations. PMID:26986408
Bayesian Data-Model Fit Assessment for Structural Equation Modeling
ERIC Educational Resources Information Center
Levy, Roy
2011-01-01
Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…
Partial differential equation models in macroeconomics.
Achdou, Yves; Buera, Francisco J; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin
2014-11-13
The purpose of this article is to get mathematicians interested in studying a number of partial differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time, they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research. PMID:25288811
A New Reynolds Stress Algebraic Equation Model
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.
1994-01-01
A general turbulent constitutive relation is directly applied to propose a new Reynolds stress algebraic equation model. In the development of this model, the constraints based on rapid distortion theory and realizability (i.e. the positivity of the normal Reynolds stresses and the Schwarz' inequality between turbulent velocity correlations) are imposed. Model coefficients are calibrated using well-studied basic flows such as homogeneous shear flow and the surface flow in the inertial sublayer. The performance of this model is then tested in complex turbulent flows including the separated flow over a backward-facing step and the flow in a confined jet. The calculation results are encouraging and point to the success of the present model in modeling turbulent flows with complex geometries.
Structural equation modeling: strengths, limitations, and misconceptions.
Tomarken, Andrew J; Waller, Niels G
2005-01-01
Because structural equation modeling (SEM) has become a very popular data-analytic technique, it is important for clinical scientists to have a balanced perception of its strengths and limitations. We review several strengths of SEM, with a particular focus on recent innovations (e.g., latent growth modeling, multilevel SEM models, and approaches for dealing with missing data and with violations of normality assumptions) that underscore how SEM has become a broad data-analytic framework with flexible and unique capabilities. We also consider several limitations of SEM and some misconceptions that it tends to elicit. Major themes emphasized are the problem of omitted variables, the importance of lower-order model components, potential limitations of models judged to be well fitting, the inaccuracy of some commonly used rules of thumb, and the importance of study design. Throughout, we offer recommendations for the conduct of SEM analyses and the reporting of results. PMID:17716081
Model Specification Searches in Structural Equation Modeling Using Tabu Search.
ERIC Educational Resources Information Center
Marcoulides, George A.; Drezner, Zvi; Schumacker, Randall E.
1998-01-01
Introduces an alternative structural equation modeling (SEM) specification search approach based on the Tabu search procedure. Using data with known structure, the procedure is illustrated, and its capabilities for specification searches in SEM are demonstrated. (Author/SLD)
Wave equation modelling using Julia programming language
NASA Astrophysics Data System (ADS)
Kim, Ahreum; Ryu, Donghyun; Ha, Wansoo
2016-04-01
Julia is a young high-performance dynamic programming language for scientific computations. It provides an extensive mathematical function library, a clean syntax and its own parallel execution model. We developed 2d wave equation modeling programs using Julia and C programming languages and compared their performance. We used the same modeling algorithm for the two modeling programs. We used Julia version 0.3.9 in this comparison. We declared data type of function arguments and used inbounds macro in the Julia program. Numerical results showed that the C programs compiled with Intel and GNU compilers were faster than Julia program, about 18% and 7%, respectively. Taking the simplicity of dynamic programming language into consideration, Julia can be a novel alternative of existing statically typed programming languages.
Parameter Estimation of Partial Differential Equation Models
Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J.; Maity, Arnab
2013-01-01
Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data. PMID:24363476
Parameter Estimation of Partial Differential Equation Models.
Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab
2013-01-01
Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data. PMID:24363476
Exploratory structural equation modeling of personality data.
Booth, Tom; Hughes, David J
2014-06-01
The current article compares the use of exploratory structural equation modeling (ESEM) as an alternative to confirmatory factor analytic (CFA) models in personality research. We compare model fit, factor distinctiveness, and criterion associations of factors derived from ESEM and CFA models. In Sample 1 (n = 336) participants completed the NEO-FFI, the Trait Emotional Intelligence Questionnaire-Short Form, and the Creative Domains Questionnaire. In Sample 2 (n = 425) participants completed the Big Five Inventory and the depression and anxiety scales of the General Health Questionnaire. ESEM models provided better fit than CFA models, but ESEM solutions did not uniformly meet cutoff criteria for model fit. Factor scores derived from ESEM and CFA models correlated highly (.91 to .99), suggesting the additional factor loadings within the ESEM model add little in defining latent factor content. Lastly, criterion associations of each personality factor in CFA and ESEM models were near identical in both inventories. We provide an example of how ESEM and CFA might be used together in improving personality assessment. PMID:24682748
The reservoir model: a differential equation model of psychological regulation.
Deboeck, Pascal R; Bergeman, C S
2013-06-01
Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might "add up" over time (e.g., life stressors, inputs), but individuals simultaneously take action to "blow off steam" (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the "height" (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging. PMID:23527605
A Realizable Reynolds Stress Algebraic Equation Model
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.
1993-01-01
The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.
Transfer equations for modeling interrill erosion
NASA Astrophysics Data System (ADS)
Bako Amina, Nouhou; Frédéric, Darboux; François, James; Carine, Lucas
2016-04-01
Numerous models are available for matter transfer along an hillslope. They are usually process-specific, requiring to use several models to simulate transfers along an hillslope. To overcome this issue, we develop a new model valid for chemical (nutrients, pollutants, dissolved carbon) and particle transfers by water. It is able to simulate both interrill and rill erosion. This new equation encompasses the previous models of Gao et al. (2004), Hairsine and Rose (1992, 1991) and Lajeunesse et al. (2013) in a single and unified form. We show that it can account for multi-class particle transport able to simulate both linear and non-linear behaviors. Surface conditions (crusts) is accounted for, making possible for space and time changes of soil properties. For the calibration of the model, specific laboratory experiments have been carried out to validate the effect of rainfall on travel distance of particles. These experiments allow to separate detachment by raindrops from the agitation of the flow by the drops. Different particle sizes and rainfall kinetic energies are investigated. The results assess the exact role of rainfall on sediment transport. Our new model is able to represent adequately these experimental results.
A discrete model of a modified Burgers' partial differential equation
NASA Technical Reports Server (NTRS)
Mickens, R. E.; Shoosmith, J. N.
1990-01-01
A new finite-difference scheme is constructed for a modified Burger's equation. Three special cases of the equation are considered, and the 'exact' difference schemes for the space- and time-independent forms of the equation are presented, along with the diffusion-free case of Burger's equation modeled by a difference equation. The desired difference scheme is then obtained by imposing on any difference model of the initial equation the requirement that, in the appropriate limits, its difference scheme must reduce the results of the obtained equations.
Teaching Modeling with Partial Differential Equations: Several Successful Approaches
ERIC Educational Resources Information Center
Myers, Joseph; Trubatch, David; Winkel, Brian
2008-01-01
We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…
Model Comparison of Nonlinear Structural Equation Models with Fixed Covariates.
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan
2003-01-01
Proposed a new nonlinear structural equation model with fixed covariates to deal with some complicated substantive theory and developed a Bayesian path sampling procedure for model comparison. Illustrated the approach with an illustrative example using data from an international study. (SLD)
Robust estimation for ordinary differential equation models.
Cao, J; Wang, L; Xu, J
2011-12-01
Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. We propose a robust method to address this problem. The dynamic process is represented with a nonparametric function, which is a linear combination of basis functions. The nonparametric function is estimated by a robust penalized smoothing method. The penalty term is defined with the parametric ODE model, which controls the roughness of the nonparametric function and maintains the fidelity of the nonparametric function to the ODE model. The basis coefficients and ODE parameters are estimated in two nested levels of optimization. The coefficient estimates are treated as an implicit function of ODE parameters, which enables one to derive the analytic gradients for optimization using the implicit function theorem. Simulation studies show that the robust method gives satisfactory estimates for the ODE parameters from noisy data with outliers. The robust method is demonstrated by estimating a predator-prey ODE model from real ecological data. PMID:21401565
Alternative field representations and integral equations for modeling inhomogeneous dielectrics
NASA Technical Reports Server (NTRS)
Volakis, John L.
1992-01-01
New volume and volume-surface integral equations are presented for modeling inhomogeneous dielectric regions. The presented integral equations result in more efficient numerical implementations and should, therefore, be useful in a variety of electromagnetic applications.
Hu, Zhangli; Fan, Zhun; Zhao, Zhonglin; Chen, Jun; Li, Jiancheng
2012-01-01
The mitochondrial expression of exogenous antibiotic resistance genes has not been demonstrated successfully to date, which has limited the development of antibiotic resistance genes as selectable markers for mitochondrial site-directed transformation in Chlamydomonas reinhardtii. In this work, the plasmid pBSLPNCB was constructed by inserting the gene ble of Streptoalloteichus hindustanus (Sh ble), encoding a small (14-kilodalton) protective protein into the site between TERMINVREP-Left repeats and the cob gene in a fragment of mitochondrial DNA (mtDNA) of C. reinhardtii. The fusion DNA-construct, which contained TERMINVREP-Left, Sh ble, cob, and partial nd4 sequence, were introduced into the mitochondria of the respiratory deficient dum-1 mutant CC-2654 of C. reinhardtii by biolistic particle delivery system. A large number of transformants were obtained after eight weeks in the dark. Subsequent subculture of the transformants on the selection TAP media containing 3 ìg/mL Zeomycin for 12 months resulted in genetically modified transgenic algae MT-Bs. Sequencing and Southern analyses on the mitochondrial genome of the different MT-B lines revealed that Sh ble gene had been integrated into the mitochondrial genome of C. reinhardtii. Both Western blot, using the anti-BLE monoclonal antibody, and Zeomycin tolerance analysis confirmed the presence of BLE protein in the transgenic algal cells. It indicates that the Sh ble gene can be stably expressed in the mitochondria of C. reinhardtii. PMID:22530046
USING STRUCTURAL EQUATION MODELING TO INVESTIGATE RELATIONSHIPS AMONG ECOLOGICAL VARIABLES
This paper gives an introductory account of Structural Equation Modeling (SEM) and demonstrates its application using LISREL< with a model utilizing environmental data. Using nine EMAP data variables, we analyzed their correlation matrix with an SEM model. The model characterized...
Fitting ARMA Time Series by Structural Equation Models.
ERIC Educational Resources Information Center
van Buuren, Stef
1997-01-01
This paper outlines how the stationary ARMA (p,q) model (G. Box and G. Jenkins, 1976) can be specified as a structural equation model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. The method is applied to three problem types. (SLD)
Parameter Estimates in Differential Equation Models for Chemical Kinetics
ERIC Educational Resources Information Center
Winkel, Brian
2011-01-01
We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…
BLE protection scheme for light-trail WDM mesh networks
NASA Astrophysics Data System (ADS)
Xing, Junwei; Wang, Hongxiang; Ji, Yuefeng
2007-11-01
Light-trail is a solution to providing high resource utilization and sub-wavelength support [1]. A light-trail is a multi-point light-path, such that multiple users can take part in communication along the trail, through time (differentiated) non-overlapping connections. This multi-point flow model leads to a new set of problems in the area of protecting and restoring light-trail based networks. Conventional link protection which just protects the existed connection in the light-trail at the time of the failure is not sufficient for light-trails because of the potential of having multiple possible source-destination pairs in the same trail over time. The fact is demonstrated and explained detailedly in [4]. In this paper, a novel protection mechanism is proposed for light-trail WDM mesh network, which is Backup Light-trail Expending scheme. Subsequently the performance of this scheme is evaluated and compared to conventional Connection Dedicated Protection Scheme. Numerical results obtained by simulation indicate that, Backup Light-trail Expending Scheme has a faster restoration time and better wavelength utilization.
Equating Parameter Estimates from the Generalized Graded Unfolding Model.
ERIC Educational Resources Information Center
Roberts, James S.
Three common methods for equating parameter estimates from binary item response theory models are extended to the generalized grading unfolding model (GGUM). The GGUM is an item response model in which single-peaked, nonmonotonic expected value functions are implemented for polytomous responses. GGUM parameter estimates are equated using extended…
Dynamic hysteresis modeling including skin effect using diffusion equation model
NASA Astrophysics Data System (ADS)
Hamada, Souad; Louai, Fatima Zohra; Nait-Said, Nasreddine; Benabou, Abdelkader
2016-07-01
An improved dynamic hysteresis model is proposed for the prediction of hysteresis loop of electrical steel up to mean frequencies, taking into account the skin effect. In previous works, the analytical solution of the diffusion equation for low frequency (DELF) was coupled with the inverse static Jiles-Atherton (JA) model in order to represent the hysteresis behavior for a lamination. In the present paper, this approach is improved to ensure the reproducibility of measured hysteresis loops at mean frequency. The results of simulation are compared with the experimental ones. The selected results for frequencies 50 Hz, 100 Hz, 200 Hz and 400 Hz are presented and discussed.
Approximate flash calculations for equation-of-state compositional models
Nghiem, L.X.; Li, Y.K.
1985-02-01
An approximate method for flash calculations (AFC) with an equation of state is presented. The equations for AFC are obtained by linearizing the thermodynamic equilibrium equations at an equilibrium condition termed reference condition. The AFC equations are much simpler than the actual equations for flash calculations and yet give almost the same results. A procedure for generating new reference conditions to keep the AFC results close to the true flash calculation (TFC) results is described. AFC is compared to TFC in the calculation of standard laboratory tests and in the simulation of gas injection processes with a composition model. Excellent results are obtained with AFC in less than half the original execution time.
Dirac Equation for Electrodynamic Model Particle
NASA Astrophysics Data System (ADS)
Zheng-Johansson, J. X.
2008-03-01
We set up the Maxwell's equations and subsequently the classical wave equations for the electromagnetic waves which together with their generating source, an oscillatory charge of zero rest mass, make up a particle travelling at velocity v as with the charge in the fields of an external scalar and vector potentials. The direct solutions in constant external field are Doppler-displaced plane waves propagating at the velocity of light c; at the de Broglie wavelength scale and expressed in terms of the dynamically equivalent and appropriate geometric mean wave variables, these render as functons identical to the space-time functions of the Dirac spinor, and these are identical to the de Broglie phase waves given previously from explicit superposition. For two spin-half particles of a common set of space-time functions constrained with antisymmetric spin functions as follows the Pauli principle for same charges and as separately indirectly induced based on experiment for opposite charges, the complete wave functions are identical to a Dirac spinor. The back-substitution of the so explicitly determined complete wave functions in the corresponding classical wave equations of the two particles, subjected further to reductions appropriate for the stationary- state particle motion and to rotation invariance when in three dimensions, give a Dirac equation set; the procedure and conclusion are directly extendible to arbitrarily varying potentials by use of the Furious theorem and to three dimensions (full paper: QTS5).
Dirac equation for electrodynamic model particles
NASA Astrophysics Data System (ADS)
Zheng-Johansson, J. X.
2008-08-01
We set up the Maxwell's equations and subsequently the classical wave equations for the electromagnetic waves which together with their generating source, an oscillatory charge of zero rest mass in general travelling, make up a particle travelling similarly as the source at velocity ν in the field of an external scalar and vector potentials. The direct solutions in constant external field are Doppler-displaced plane waves propagating at the velocity of light c; at the de Broglie wavelength scale and expressed in terms of the dynamically equivalent and appropriate geometric mean wave variables, these render as functions identical to the space-time functions of a corresponding Dirac spinor, and in turn identical to de Broglie phase waves previously obtained from explicit superposition. For two spin-half particles of a common set of space-time functions constrained with antisymmetric spin functions as follows the Pauli principle for same charges and as separately indirectly induced based on experiment for opposite charges, the complete wave functions are identical to the Dirac spinor. The back-substitution of the so explicitly determined complete wave functions in the corresponding classical wave equations of the two particles, subjected further to reductions appropriate for the stationary-state particle motion and to rotation invariance when in three dimensions, give a Dirac equation set; the procedure and conclusion are directly extendible to arbitrarily varying potentials by use of the Furious theorem and to particle motions in three dimensions by virtue of the characteristics of de Broglie particle motion. Through the derivation of the Dirac equation, the study hopes to lend insight into the connections between the Dirac wave functions and the electrodynamic components of simple particles under the government by the well established basic laws of electrodynamics.
A Structural Equation Modeling Analysis of Influences on Juvenile Delinquency
ERIC Educational Resources Information Center
Barrett, David E.; Katsiyannis, Antonis; Zhang, Dalun; Zhang, Dake
2014-01-01
This study examined influences on delinquency and recidivism using structural equation modeling. The sample comprised 199,204 individuals: 99,602 youth whose cases had been processed by the South Carolina Department of Juvenile Justice and a matched control group of 99,602 youth without juvenile records. Structural equation modeling for the…
Two Rules of Identification for Structural Equation Models
ERIC Educational Resources Information Center
Bollen, Kenneth A.; Davis, Walter R.
2009-01-01
Identification of structural equation models remains a challenge to many researchers. Although empirical tests of identification are readily available in structural equation modeling software, these examine local identification and rely on sample estimates of parameters. Rules of identification are available, but do not include all models…
A Hybrid Method of Moment Equations and Rate Equations to Modeling Gas-Grain Chemistry
NASA Astrophysics Data System (ADS)
Pei, Y.; Herbst, E.
2011-05-01
Grain surfaces play a crucial role in catalyzing many important chemical reactions in the interstellar medium (ISM). The deterministic rate equation (RE) method has often been used to simulate the surface chemistry. But this method becomes inaccurate when the number of reacting particles per grain is typically less than one, which can occur in the ISM. In this condition, stochastic approaches such as the master equations are adopted. However, these methods have mostly been constrained to small chemical networks due to the large amounts of processor time and computer power required. In this study, we present a hybrid method consisting of the moment equation approximation to the stochastic master equation approach and deterministic rate equations to treat a gas-grain model of homogeneous cold cloud cores with time-independent physical conditions. In this model, we use the standard OSU gas phase network (version OSU2006V3) which involves 458 gas phase species and more than 4000 reactions, and treat it by deterministic rate equations. A medium-sized surface reaction network which consists of 21 species and 19 reactions accounts for the productions of stable molecules such as H_2O, CO, CO_2, H_2CO, CH_3OH, NH_3 and CH_4. These surface reactions are treated by a hybrid method of moment equations (Barzel & Biham 2007) and rate equations: when the abundance of a surface species is lower than a specific threshold, say one per grain, we use the ``stochastic" moment equations to simulate the evolution; when its abundance goes above this threshold, we use the rate equations. A continuity technique is utilized to secure a smooth transition between these two methods. We have run chemical simulations for a time up to 10^8 yr at three temperatures: 10 K, 15 K, and 20 K. The results will be compared with those generated from (1) a completely deterministic model that uses rate equations for both gas phase and grain surface chemistry, (2) the method of modified rate equations (Garrod
Landscape evolution models: A review of their fundamental equations
NASA Astrophysics Data System (ADS)
Chen, Alex; Darbon, Jérôme; Morel, Jean-Michel
2014-08-01
This paper reviews the main physical laws proposed in landscape evolution models (LEMs). It discusses first the main partial differential equations involved in these models and their variants. These equations govern water runoff, stream incision, regolith-bedrock interaction, hillslope evolution, and sedimentation. A synthesis of existing LEMs is proposed. It proposes three models with growing complexity and with a growing number of components: two-equation models with only two components, governing water and bedrock evolution; three-equation models with three components where water, bedrock, and sediment interact; and finally models with four equations and four interacting components, namely water, bedrock, suspended sediment, and regolith. This analysis is not a mere compilation of existing LEMs. It attempts at giving the simplest and most general physically consistent set of equations, coping with all requirements stated in LEMs and LEM software. Three issues are in particular addressed and hopefully resolved. The first one is a correct formulation of the water transport equation down slopes. A general formulation for this equation is proposed, coping not only with the simplest form computing the drainage area but also with a sound energy dissipation argument associated with the Saint-Venant shallow water equations. The second issue arises from the coexistence of two competing modes, namely the detachment-limited erosion mode on hillslopes, and the transport-limited sediment transport on river beds. The third issue (linked to the second) is the fact that no conservation law is available for material in these two modes. A simple solution proposed to resolve these issues is the introduction, as suggested by several authors, of an additional variable for suspended sediment load in water. With only three variables and three equations, the above-mentioned contradictions seem to be eliminated. Several numerical experiments on real digital elevation models (DEMs
Structural Equation Model of Adolescent Delinquency.
ERIC Educational Resources Information Center
Whiteside, Leanne; And Others
This study of 1,093 public high school students was designed to test an integrated theoretical model of delinquency, consisting of elements of social control and social learning theories, with LISREL procedures. The model confirmed with LISREL was very similar to the hypothesized model. The hypothesized model was fitted to data on one random…
Student Difficulties with Units in Differential Equations in Modelling Contexts
ERIC Educational Resources Information Center
Rowland, David R.
2006-01-01
First-year undergraduate engineering students' understanding of the units of factors and terms in first-order ordinary differential equations used in modelling contexts was investigated using diagnostic quiz questions. Few students appeared to realize that the units of each term in such equations must be the same, or if they did, nevertheless…
Skyrme models and nuclear matter equation of state
NASA Astrophysics Data System (ADS)
Adam, C.; Haberichter, M.; Wereszczynski, A.
2015-11-01
We investigate the role of pressure in a class of generalized Skyrme models. We introduce pressure as the trace of the spatial part of the energy-momentum tensor and show that it obeys the usual thermodynamical relation. Then, we compute analytically the mean-field equation of state in the high- and medium-pressure regimes by applying topological bounds on compact domains. The equation of state is further investigated numerically for the charge-one Skyrmions. We identify which term in a generalized Skyrme model is responsible for which part in the equation of state. Further, we compare our findings with the corresponding results in the Walecka model.
Implementing Restricted Maximum Likelihood Estimation in Structural Equation Models
ERIC Educational Resources Information Center
Cheung, Mike W.-L.
2013-01-01
Structural equation modeling (SEM) is now a generic modeling framework for many multivariate techniques applied in the social and behavioral sciences. Many statistical models can be considered either as special cases of SEM or as part of the latent variable modeling framework. One popular extension is the use of SEM to conduct linear mixed-effects…
Fractal ladder models and power law wave equations
Kelly, James F.; McGough, Robert J.
2009-01-01
The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters. PMID:19813816
Finite Feedback Cycling in Structural Equation Models
ERIC Educational Resources Information Center
Hayduk, Leslie A.
2009-01-01
In models containing reciprocal effects, or longer causal loops, the usual effect estimates assume that any effect touching a loop initiates an infinite cycling of effects around that loop. The real world, in contrast, might permit only finite feedback cycles. I use a simple hypothetical model to demonstrate that if the world permits only a few…
Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order
Favalli, Andrea; Croft, Stephen; Santi, Peter
2015-06-15
Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclear data constants by a series of coupled algebraic equations – the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This study represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.
Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order
Favalli, Andrea; Croft, Stephen; Santi, Peter
2015-06-15
Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclearmore » data constants by a series of coupled algebraic equations – the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This study represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.« less
Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order
NASA Astrophysics Data System (ADS)
Favalli, Andrea; Croft, Stephen; Santi, Peter
2015-09-01
Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclear data constants by a series of coupled algebraic equations - the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This work represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.
A critical comparison of two-equation turbulence models
NASA Technical Reports Server (NTRS)
Lang, N. J.; Shih, T. H.
1991-01-01
Several two-equation models were proposed and tested against benchmark flows by various researchers. For each study, different numerical methods or codes were used to obtain the results which were reported to be an improvement over other models. However, these comparisons may be overshadowed by the different numerical schemes used to obtain the results. With this in mind, several existing two-equation turbulence models, including k-epsilon, k-tau, k-omega, and q-omega models, are implemented into a common flow solver code for near wall turbulent flows. The quality of each model is based on several criteria, including robustness and accuracy of predicting the turbulent quantities.
An Extended Equation of State Modeling Method I. Pure Fluids
NASA Astrophysics Data System (ADS)
Scalabrin, G.; Bettio, L.; Marchi, P.; Piazza, L.; Richon, D.
2006-09-01
A new technique is proposed here to represent the thermodynamic surface of a pure fluid in the fundamental Helmholtz energy form. The peculiarity of the present method is the extension of a generic equation of state for the target fluid, which is assumed as the basic equation, through the distortion of its independent variables by individual shape functions, which are represented by a neural network used as function approximator. The basic equation of state for the target fluid can have the simple functional form of a cubic equation, as, for instance, the Soave-Redlich-Kwong equation assumed in the present study. A set of nine fluids including hydrocarbons, haloalkane refrigerants, and strongly polar substances has been considered. For each of them the model has been regressed and then validated against volumetric and caloric properties generated in the vapor, liquid, and supercritical regions from highly accurate dedicated equations of state. In comparison with the underlying cubic equation of state, the prediction accuracy is improved by a factor between 10 and 100, depending on the property and on the region. It has been verified that about 100 density experimental points, together with from 10 to 20 coexistence data, are sufficient to guarantee high prediction accuracy for different thermodynamic properties. The method is a promising modeling technique for the heuristic development of multiparameter dedicated equations of state from experimental data.
Development of one-equation transition/turbulence models
Edwards, J.R.; Roy, C.J.; Blottner, F.G.; Hassan, H.A.
2000-01-14
This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity--transport equation for nonturbulent fluctuation growth based on that proposed by Warren and Hassan is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittency function based on the work of Dhawan and Narasimha. The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the grid-dependence of selected predictions is analyzed.
Modeling Meandering Channel by Two-Dimensional Shallow Water Equations
NASA Astrophysics Data System (ADS)
Yu, C.; Duan, J. G.
2014-12-01
This research is to simulate the process of channel meandering using a two-dimensional depth-averaged hydrodynamic model. The multiple interactions between unsteady flow, turbulence, secondary flow, nonequilibrium sediment transport and bank erosion are considered by the model. The governing equations are the 2D depth-averaged Reynolds-averaged Navier-Stokes (2D-RANS) equations and the Exner equation for bed elevation evolution. The Reynolds stresses are calculated by the k-ɛ turbulence model. The secondary flow, is modeled by the dispersion terms in momentum equations. The spatial lag between the instantaneous flow properties and the rate of sediment transport is simulated by the nonequilibrium sediment transport model. During the process of adaptation, the sediment transport rate gradually develops into the transport capacity of a given flow condition. The evolution of channel bed and bank is modeled by the general Exner equation that accounts for both vertical deformation of bed elevation as well as lateral migration of bank. The system of governing equations is solved by a semi-implicit finite volume method over the Cartesian mesh. The advective fluxes across each cell interface are simultaneously calculated by the extended HLL Riemann solver. At each time step, the diffusion terms in the governing equations are solved by the implicit Euler scheme. The source terms are discretized in a well-balanced way to retain the C-property of the proposed model. Application of the model to different test cases indicates that the model can correctly simulate different phases of meandering channel evolution which include streamwise migration, transverse migration and rotation of channel bends.
Introduction to Structural Equation Modeling: Issues and Practical Considerations
ERIC Educational Resources Information Center
Lei, Pui-Wa; Wu, Qiong
2007-01-01
Structural equation modeling (SEM) is a versatile statistical modeling tool. Its estimation techniques, modeling capacities, and breadth of applications are expanding rapidly. This module introduces some common terminologies. General steps of SEM are discussed along with important considerations in each step. Simple examples are provided to…
Parameter Estimates in Differential Equation Models for Population Growth
ERIC Educational Resources Information Center
Winkel, Brian J.
2011-01-01
We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist,…
Structural Equation Modeling Diagnostics Using R Package Semdiag and EQS
ERIC Educational Resources Information Center
Yuan, Ke-Hai; Zhang, Zhiyong
2012-01-01
Yuan and Hayashi (2010) introduced 2 scatter plots for model and data diagnostics in structural equation modeling (SEM). However, the generation of the plots requires in-depth understanding of their underlying technical details. This article develops and introduces an R package semdiag for easily drawing the 2 plots. With a model specified in EQS…
Latent Growth Curves within Developmental Structural Equation Models.
ERIC Educational Resources Information Center
McArdle, J. J.; Epstein, David
1987-01-01
Uses structural equation modeling to combine traditional ideas from repeated-measures ANOVA with some traditional ideas from longitudinal factor analysis. The model describes a latent growth curve model that permits the estimation of parameters representing individual and group dynamics. (Author/RH)
People Are Variables Too: Multilevel Structural Equations Modeling
ERIC Educational Resources Information Center
Mehta, Paras D.; Neale, Michael C.
2005-01-01
The article uses confirmatory factor analysis (CFA) as a template to explain didactically multilevel structural equation models (ML-SEM) and to demonstrate the equivalence of general mixed-effects models and ML-SEM. An intuitively appealing graphical representation of complex ML-SEMs is introduced that succinctly describes the underlying model and…
Structural Equation Modelling: A Primer for Music Education Researchers
ERIC Educational Resources Information Center
Teo, Timothy
2010-01-01
Structural equation modelling (SEM) is a method for analysis of multivariate data from both non-experimental and experimental research. The method combines a structural model linking latent variables and a measurement model linking observed variables with latent variables. Its use in social science and educational research has grown since the…
Case Residuals in Structural Equation Modeling
ERIC Educational Resources Information Center
Cardinale, John
2011-01-01
From the beginning, lead methodologists in psychometrics and quantitative psychology have been well aware of the problems of fitting structural and confirmatory factor models. The question we approach in our research is how to best detect this misfit and how to identify specific sources of misfit by scrutinizing the data at the case level. Since…
Lattice Boltzmann model for generalized nonlinear wave equations
NASA Astrophysics Data System (ADS)
Lai, Huilin; Ma, Changfeng
2011-10-01
In this paper, a lattice Boltzmann model is developed to solve a class of the nonlinear wave equations. Through selecting equilibrium distribution function and an amending function properly, the governing evolution equation can be recovered correctly according to our proposed scheme, in which the Chapman-Enskog expansion is employed. We validate the algorithm on some problems where analytic solutions are available, including the second-order telegraph equation, the nonlinear Klein-Gordon equation, and the damped, driven sine-Gordon equation. It is found that the numerical results agree well with the analytic solutions, which indicates that the present algorithm is very effective and can be used to solve more general nonlinear problems.
Approximate flash calculations for equation-of-state compositional models--
Nghiem, L.X.; Li, Y.K. )
1990-02-01
An approximate flash-calculation (AFC) method with an equation of state (EOS) is presented. The equations for AFC are obtained by linearizing the thermodynamic equilibrium equations at an equilibrium condition called the reference condition. The AFC equations are much simpler than the actual equations for flash calculations and yet give almost the same results. A procedure for generating new reference conditions to keep the AFC results close to the true flash-calculation (TFC) results is described. AFC is compared with TFC in the calculation of standard laboratory tests and in the simulation of gas-injection processes with a compositional model. Excellent results are obtained with AFC in less than half the original execution time.
The Landau-Lifshitz equation in atomistic models
NASA Astrophysics Data System (ADS)
Ellis, M. O. A.; Evans, R. F. L.; Ostler, T. A.; Barker, J.; Atxitia, U.; Chubykalo-Fesenko, O.; Chantrell, R. W.
2015-09-01
The Landau-Lifshitz (LL) equation, originally proposed at the macrospin level, is increasingly used in Atomistic Spin Dynamic (ASD) models. These models are based on a spin Hamiltonian featuring atomic spins of fixed length, with the exchange introduced using the Heisenberg formalism. ASD models are proving a powerful approach to the fundamental understanding of ultrafast magnetization dynamics, including the prediction of the thermally induced magnetization switching phenomenon in which the magnetization is reversed using an ultra-fast laser pulse in the absence of an externally applied field. This paper outlines the ASD model approach and considers the role and limitations of the LL equation in this context.
Quantum hydrodynamic model by moment closure of Wigner equation
NASA Astrophysics Data System (ADS)
Cai, Zhenning; Fan, Yuwei; Li, Ruo; Lu, Tiao; Wang, Yanli
2012-10-01
In this paper, we derive the quantum hydrodynamics models based on the moment closure of the Wigner equation. The moment expansion adopted is of the Grad type first proposed by Grad ["On the kinetic theory of rarefied gases," Commun. Pure Appl. Math. 2(4), 331-407 (1949), 10.1002/cpa.3160020403]. The Grad's moment method was originally developed for the Boltzmann equation. Recently, a regularization method for the Grad's moment system of the Boltzmann equation was proposed by Cai et al. [Commun. Pure Appl. Math. "Globally hyperbolic regularization of Grad's moment system" (in press)] to achieve the global hyperbolicity so that the local well-posedness of the moment system is attained. With the moment expansion of the Wigner function, the drift term in the Wigner equation has exactly the same moment representation as in the Boltzmann equation, thus the regularization applies. The moment expansion of the nonlocal Wigner potential term in the Wigner equation turns out to be a linear source term, which can only induce very mild growth of the solution. As a result, the local well-posedness of the regularized moment system for the Wigner equation remains as for the Boltzmann equation.
An Extended Equation of State Modeling Method II. Mixtures
NASA Astrophysics Data System (ADS)
Scalabrin, G.; Marchi, P.; Stringari, P.; Richon, D.
2006-09-01
This work is the extension of previous work dedicated to pure fluids. The same method is extended to the representation of thermodynamic properties of a mixture through a fundamental equation of state in terms of the Helmholtz energy. The proposed technique exploits the extended corresponding-states concept of distorting the independent variables of a dedicated equation of state for a reference fluid using suitable scale factor functions to adapt the equation to experimental data of a target system. An existing equation of state for the target mixture is used instead of an equation for the reference fluid, completely avoiding the need for a reference fluid. In particular, a Soave-Redlich-Kwong cubic equation with van der Waals mixing rules is chosen. The scale factors, which are functions of temperature, density, and mole fraction of the target mixture, are expressed in the form of a multilayer feedforward neural network, whose coefficients are regressed by minimizing a suitable objective function involving different kinds of mixture thermodynamic data. As a preliminary test, the model is applied to five binary and two ternary haloalkane mixtures, using data generated from existing dedicated equations of state for the selected mixtures. The results show that the method is robust and straightforward for the effective development of a mixture- specific equation of state directly from experimental data.
Shock-wave structure using nonlinear model Boltzmann equations.
NASA Technical Reports Server (NTRS)
Segal, B. M.; Ferziger, J. H.
1972-01-01
The structure of strong plane shock waves in a perfect monatomic gas was studied using four nonlinear models of the Boltzmann equation. The models involved the use of a simplified collision operator with velocity-independent collision frequency, in place of the complicated Boltzmann collision operator. The models employed were the BGK and ellipsoidal models developed by earlier authors, and the polynomial and trimodal gain function models developed during the work. An exact set of moment equations was derived for the density, velocity, temperature, viscous stress, and heat flux within the shock. This set was reduced to a pair of coupled nonlinear integral equations and solved using specially adapted numerical techniques. A new and simple Gauss-Seidel iteration was developed during the work and found to be as efficient as the best earlier iteration methods.
Revised predictive equations for salt intrusion modelling in estuaries
NASA Astrophysics Data System (ADS)
Gisen, J. I. A.; Savenije, H. H. G.; Nijzink, R. C.
2015-01-01
For one-dimensional salt intrusion models to be predictive, we need predictive equations to link model parameters to observable hydraulic and geometric variables. The one-dimensional model of Savenije (1993b) made use of predictive equation for the Van der Burgh coefficient K and the dispersion at the seaward boundary D0. Here we have improved these equations by using an expanded database, including new previously un-surveyed estuaries. Furthermore, we derived a revised predictive equation for the dispersion at tidal average (TA) condition and with the boundary situated at the well identifiable inflection point where the estuary changes from wave-dominated to tide-dominated geometry. We used 89 salinity profiles in 30 estuaries (including 7 recently studied estuaries in Malaysia), and empirically derived a range of equations using various combinations of dimensionless parameters. We split our data in two separated datasets: (1) with more reliable data for calibration, and (2) with less reliable data for validation. The dimensionless parameters that gave the best performance depended on the geometry, tidal strength, friction and the Richardson Number. The limitation of the equations is that the friction is generally unknown. In order to overcome this problem, a coupling has been made with the analytical hydraulic model of Cai et al. (2012), which makes use of observed tidal damping and by which the friction can be determined.
Revised predictive equations for salt intrusion modelling in estuaries
NASA Astrophysics Data System (ADS)
Gisen, J. I. A.; Savenije, H. H. G.; Nijzink, R. C.
2015-06-01
For one-dimensional salt intrusion models to be predictive, we need predictive equations to link model parameters to observable hydraulic and geometric variables. The one-dimensional model of Savenije (1993b) made use of predictive equations for the Van der Burgh coefficient K and the dispersion at the seaward boundary D0. Here we have improved these equations by using an expanded database, including new previously un-surveyed estuaries. Furthermore, we derived a revised predictive equation for the dispersion at tidal average condition and with the boundary situated at the well identifiable inflection point where the estuary changes from wave-dominated to tide-dominated geometry. We used 89 salinity profiles in 30 estuaries (including seven recently studied estuaries in Malaysia), and empirically derived a range of equations using various combinations of dimensionless parameters. We split our data in two separated data sets: (1) with more reliable data for calibration, and (2) with less reliable data for validation. The dimensionless parameters that gave the best performance depended on the geometry, tidal strength, friction and the Richardson number. The limitation of the equations is that the friction is generally unknown. In order to overcome this problem, a coupling has been made with the analytical hydraulic model of Cai et al. (2012), which makes use of observed tidal damping and by which the friction can be determined.
Modeling adsorption with lattice Boltzmann equation.
Guo, Long; Xiao, Lizhi; Shan, Xiaowen; Zhang, Xiaoling
2016-01-01
The research of adsorption theory has recently gained renewed attention due to its critical relevance to a number of trending industrial applications, hydrogen storage and shale gas exploration for instance. The existing theoretical foundation, laid mostly in the early twentieth century, was largely based on simple heuristic molecular interaction models and static interaction potential which, although being insightful in illuminating the fundamental mechanisms, are insufficient for computations with realistic adsorbent structure and adsorbate hydrodynamics, both critical for real-life applications. Here we present and validate a novel lattice Boltzmann model incorporating both adsorbate-adsorbate and adsorbate-adsorbent interactions with hydrodynamics which, for the first time, allows adsorption to be computed with real-life details. Connection with the classic Ono-Kondo lattice theory is established and various adsorption isotherms, both within and beyond the IUPAC classification are observed as a pseudo-potential is varied. This new approach not only enables an important physical to be simulated for real-life applications, but also provides an enabling theoretical framework within which the fundamentals of adsorption can be studied. PMID:27256325
Modeling adsorption with lattice Boltzmann equation
Guo, Long; Xiao, Lizhi; Shan, Xiaowen; Zhang, Xiaoling
2016-01-01
The research of adsorption theory has recently gained renewed attention due to its critical relevance to a number of trending industrial applications, hydrogen storage and shale gas exploration for instance. The existing theoretical foundation, laid mostly in the early twentieth century, was largely based on simple heuristic molecular interaction models and static interaction potential which, although being insightful in illuminating the fundamental mechanisms, are insufficient for computations with realistic adsorbent structure and adsorbate hydrodynamics, both critical for real-life applications. Here we present and validate a novel lattice Boltzmann model incorporating both adsorbate-adsorbate and adsorbate-adsorbent interactions with hydrodynamics which, for the first time, allows adsorption to be computed with real-life details. Connection with the classic Ono-Kondo lattice theory is established and various adsorption isotherms, both within and beyond the IUPAC classification are observed as a pseudo-potential is varied. This new approach not only enables an important physical to be simulated for real-life applications, but also provides an enabling theoretical framework within which the fundamentals of adsorption can be studied. PMID:27256325
Computational modeling of femtosecond optical solitons from Maxwell's equations
NASA Technical Reports Server (NTRS)
Goorjian, Peter M.; Taflove, Allen; Joseph, Rose M.; Hagness, Susan C.
1992-01-01
An algorithm is developed that permits the direct time integration of full-vector nonlinear Maxwell's equations. This capability permits the modeling of both linear and nonlinear instantaneous and dispersive effects in the electric polarization in material media. The modeling of the optical carrier is retained. The fundamental innovation is to notice that it is possible to treat the linear and nonlinear convolution integrals, which describe the dispersion, as new dependent variables. A coupled system of nonlinear second-order ordinary differential equations can then be derived for the linear and nonlinear convolution integrals, by differentiating them in the time domain. These equations, together with Maxwell's equations, are solved to determine the electromagnetic fields in nonlinear dispersive media. Results are presented of calculations in one dimension of the propagation and collision of femtosecond electromagnetic solitons that retain the optical carrier, taking into account as the Kerr and Raman interactions.
Generalized cable equation model for myelinated nerve fiber.
Einziger, Pinchas D; Livshitz, Leonid M; Mizrahi, Joseph
2005-10-01
Herein, the well-known cable equation for nonmyelinated axon model is extended analytically for myelinated axon formulation. The myelinated membrane conductivity is represented via the Fourier series expansion. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficients, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the entire periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent nonmyelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the myelinated axon model. Hill's equation is explicitly integrated for the specific choice of piecewise constant membrane conductivity profile, thereby resulting in an explicit closed form expression for the transmembrane potential in terms of trigonometric functions. The Floquet's modes are recognized as the nerve fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model, provided that the periodic membrane point-wise passivity constraint is properly modified. Indeed, the modified condition, enforcing the periodic membrane passivity constraint on the average conductivity only leads, for the first time, to the inclusion of the nerve fiber activation modes in our novel model. The validity of the generalized transmission-line and cable equation models for a myelinated nerve fiber, is verified herein through a rigorous Green's function formulation and numerical simulations for transmembrane potential induced in three-dimensional myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our
A Multiple Equation Model of Demand for Health Care
Wirick, Grover C.
1966-01-01
Planning health care facilities for the future requires a means of estimating future consumption of services. Demand for medical care is looked upon as demand for separate components (hospital, doctor, dentist, medicine, other) rather than for a single, homogeneous product. A simultaneous equation model is proposed, and measures representing the forces thought to influence consumption (need, realization, motivation, resources, and availability of service) are fitted into the five equations. An optimized analysis variance method is employed on data from a sample survey of Michigan's population in 1958 to obtain single equation estimates of the five demand functions as a preliminary test of the model. The optimizing feature, which also includes an examination of complex interactions, retains variables in the equation on the basis of their estimating ability. The results indicate that a high degree of joint dependency exists among the components and that a simultaneous equation model is warranted. The study, intended as a research design, also reveals considerable variety in component equations, certain relevant and irrelevant variables, several important interactions, and a need for refining some measures in future studies. PMID:5971639
Flow equations for the ionic Hubbard model
NASA Astrophysics Data System (ADS)
Hafez, Mohsen; Jafari, S. A.; Abolhassani, M. R.
2009-12-01
Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H, we employ Continuous Unitary Transformations (CUT) to obtain a “classical” effective Hamiltonian in which hopping term has been renormalized to zero. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed Δ, as U increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing U, first transition occurs at U=Uc_1, where spin and charge gaps both vanish and remain zero up to U=Uc_2. A gap-less state in charge and spin sectors characterizes a metal. For U>Uc_2 spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.
Transonic Turbulent Flow Predictions With Two-Equation Turbulence Models
NASA Technical Reports Server (NTRS)
Liou, William W.; Shih, Tsan-Hsing
1996-01-01
Solutions of the Favre-averaged Navier-Stokes equations for two well-documented transonic turbulent flows are compared in detail with existing experimental data. While the boundary layer in the first case remains attached, a region of extensive flow separation has been observed in the second case. Two recently developed k-epsilon, two-equation, eddy-viscosity models are used to model the turbulence field. These models satisfy the realizability constraints of the Reynolds stresses. Comparisons with the measurements are made for the wall pressure distribution, the mean streamwise velocity profiles, and turbulent quantities. Reasonably good agreement is obtained with the experimental data.
Multiplicity Control in Structural Equation Modeling: Incorporating Parameter Dependencies
ERIC Educational Resources Information Center
Smith, Carrie E.; Cribbie, Robert A.
2013-01-01
When structural equation modeling (SEM) analyses are conducted, significance tests for all important model relationships (parameters including factor loadings, covariances, etc.) are typically conducted at a specified nominal Type I error rate ([alpha]). Despite the fact that many significance tests are often conducted in SEM, rarely is…
A Note on Structural Equation Modeling Estimates of Reliability
ERIC Educational Resources Information Center
Yang, Yanyun; Green, Samuel B.
2010-01-01
Reliability can be estimated using structural equation modeling (SEM). Two potential problems with this approach are that estimates may be unstable with small sample sizes and biased with misspecified models. A Monte Carlo study was conducted to investigate the quality of SEM estimates of reliability by themselves and relative to coefficient…
A Structural Equation Model for Predicting Business Student Performance
ERIC Educational Resources Information Center
Pomykalski, James J.; Dion, Paul; Brock, James L.
2008-01-01
In this study, the authors developed a structural equation model that accounted for 79% of the variability of a student's final grade point average by using a sample size of 147 students. The model is based on student grades in 4 foundational business courses: introduction to business, macroeconomics, statistics, and using databases. Educators and…
A Bayesian Approach for Analyzing Longitudinal Structural Equation Models
ERIC Educational Resources Information Center
Song, Xin-Yuan; Lu, Zhao-Hua; Hser, Yih-Ing; Lee, Sik-Yum
2011-01-01
This article considers a Bayesian approach for analyzing a longitudinal 2-level nonlinear structural equation model with covariates, and mixed continuous and ordered categorical variables. The first-level model is formulated for measures taken at each time point nested within individuals for investigating their characteristics that are dynamically…
A Structural Equation Model of Expertise in College Physics
ERIC Educational Resources Information Center
Taasoobshirazi, Gita; Carr, Martha
2009-01-01
A model of expertise in physics was tested on a sample of 374 college students in 2 different level physics courses. Structural equation modeling was used to test hypothesized relationships among variables linked to expert performance in physics including strategy use, pictorial representation, categorization skills, and motivation, and these…
Analyzing Mixed-Dyadic Data Using Structural Equation Models
ERIC Educational Resources Information Center
Peugh, James L.; DiLillo, David; Panuzio, Jillian
2013-01-01
Mixed-dyadic data, collected from distinguishable (nonexchangeable) or indistinguishable (exchangeable) dyads, require statistical analysis techniques that model the variation within dyads and between dyads appropriately. The purpose of this article is to provide a tutorial for performing structural equation modeling analyses of cross-sectional…
Testing Structural Equation Models or Detection of Misspecifications?
ERIC Educational Resources Information Center
Saris, Willem E.; Satorra, Albert; van der Veld, William M.
2009-01-01
Assessing the correctness of a structural equation model is essential to avoid drawing incorrect conclusions from empirical research. In the past, the chi-square test was recommended for assessing the correctness of the model but this test has been criticized because of its sensitivity to sample size. As a reaction, an abundance of fit indexes…
Climate Modeling in the Calculus and Differential Equations Classroom
ERIC Educational Resources Information Center
Kose, Emek; Kunze, Jennifer
2013-01-01
Students in college-level mathematics classes can build the differential equations of an energy balance model of the Earth's climate themselves, from a basic understanding of the background science. Here we use variable albedo and qualitative analysis to find stable and unstable equilibria of such a model, providing a problem or perhaps a…
A Structural Equation Model of Conceptual Change in Physics
ERIC Educational Resources Information Center
Taasoobshirazi, Gita; Sinatra, Gale M.
2011-01-01
A model of conceptual change in physics was tested on introductory-level, college physics students. Structural equation modeling was used to test hypothesized relationships among variables linked to conceptual change in physics including an approach goal orientation, need for cognition, motivation, and course grade. Conceptual change in physics…
Bayesian Semiparametric Structural Equation Models with Latent Variables
ERIC Educational Resources Information Center
Yang, Mingan; Dunson, David B.
2010-01-01
Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In…
An evolution equation modeling inversion of tulip flames
Dold, J.W.; Joulin, G.
1995-02-01
The authors attempt to reduce the number of physical ingredients needed to model the phenomenon of tulip-flame inversion to a bare minimum. This is achieved by synthesizing the nonlinear, first-order Michelson-Sivashinsky (MS) equation with the second order linear dispersion relation of Landau and Darrieus, which adds only one extra term to the MS equation without changing any of its stationary behavior and without changing its dynamics in the limit of small density change when the MS equation is asymptotically valid. However, as demonstrated by spectral numerical solutions, the resulting second-order nonlinear evolution equation is found to describe the inversion of tulip flames in good qualitative agreement with classical experiments on the phenomenon. This shows that the combined influences of front curvature, geometric nonlinearity and hydrodynamic instability (including its second-order, or inertial effects, which are an essential result of vorticity production at the flame front) are sufficient to reproduce the inversion process.
Computerized power supply analysis: State equation generation and terminal models
NASA Technical Reports Server (NTRS)
Garrett, S. J.
1978-01-01
To aid engineers that design power supply systems two analysis tools that can be used with the state equation analysis package were developed. These tools include integration routines that start with the description of a power supply in state equation form and yield analytical results. The first tool uses a computer program that works with the SUPER SCEPTRE circuit analysis program and prints the state equation for an electrical network. The state equations developed automatically by the computer program are used to develop an algorithm for reducing the number of state variables required to describe an electrical network. In this way a second tool is obtained in which the order of the network is reduced and a simpler terminal model is obtained.
On the limiters of two-equation turbulence models
NASA Astrophysics Data System (ADS)
Park, Chang Hwan; Park, Seung O.
2005-01-01
When two-equation turbulence models are used, unrealistically large values of turbulence variables can appear due to the infringement of a realizability condition or to numerical error. To cure this in practical calculations, various limiters on the source terms are often employed. In the present work, a mathematically correct bound for eddy viscosity is obtained from the realizability condition itself. From this, realizability bounds for several terms of model equations are given. The effects of various bounds including the present one, are investigated on the predictions of fundamental flows including simple shear flows, supersonic compression ramp flow and supersonic base flow. It is shown that the limiter affects the prediction very significantly.
ERIC Educational Resources Information Center
Wongbundhit, Yuwadee
Two approaches for conceptualizing and estimating a contextual model for analyzing student achievement are the separate equation approach and the single equation approach. The separate equation method determines the relationship between the individual-level independent variable and the individual-level dependent variable within each group. It then…
Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling
Ye, Hao; Beamish, Richard J.; Glaser, Sarah M.; Grant, Sue C. H.; Hsieh, Chih-hao; Richards, Laura J.; Schnute, Jon T.; Sugihara, George
2015-01-01
It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner–recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts. PMID:25733874
Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling.
Ye, Hao; Beamish, Richard J; Glaser, Sarah M; Grant, Sue C H; Hsieh, Chih-Hao; Richards, Laura J; Schnute, Jon T; Sugihara, George
2015-03-31
It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner-recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts. PMID:25733874
Modelling biochemical reaction systems by stochastic differential equations with reflection.
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
2016-05-01
In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. PMID:26920245
A lattice Boltzmann model for the Burgers-Fisher equation.
Zhang, Jianying; Yan, Guangwu
2010-06-01
A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. PMID:20590325
Langevin equation model of dispersion in the convective boundary layer
Nasstrom, J S
1998-08-01
This dissertation presents the development and evaluation of a Lagrangian stochastic model of vertical dispersion of trace material in the convective boundary layer (CBL). This model is based on a Langevin equation of motion for a fluid particle, and assumes the fluid vertical velocity probability distribution is skewed and spatially homogeneous. This approach can account for the effect of large-scale, long-lived turbulent structures and skewed vertical velocity distributions found in the CBL. The form of the Langevin equation used has a linear (in velocity) deterministic acceleration and a skewed randomacceleration. For the case of homogeneous fluid velocity statistics, this ""linear-skewed" Langevin equation can be integrated explicitly, resulting in a relatively efficient numerical simulation method. It is shown that this approach is more efficient than an alternative using a "nonlinear-Gaussian" Langevin equation (with a nonlinear deterministic acceleration and a Gaussian random acceleration) assuming homogeneous turbulence, and much more efficient than alternative approaches using Langevin equation models assuming inhomogeneous turbulence. "Reflection" boundary conditions for selecting a new velocity for a particle that encounters a boundary at the top or bottom of the CBL were investigated. These include one method using the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated, and two alternatives in which the magnitudes of these velocities are negatively correlated and uncorrelated. The constraint that spatial and velocity distributions of a well-mixed tracer must be the same as those of the fluid, was used to develop the Langevin equation models and the reflection boundary conditions. The two Langevin equation models and three reflection methods were successfully tested using cases for which exact, analytic statistical properties of particle velocity and position are known, including well
Numerical modelling in biosciences using delay differential equations
NASA Astrophysics Data System (ADS)
Bocharov, Gennadii A.; Rihan, Fathalla A.
2000-12-01
Our principal purposes here are (i) to consider, from the perspective of applied mathematics, models of phenomena in the biosciences that are based on delay differential equations and for which numerical approaches are a major tool in understanding their dynamics, (ii) to review the application of numerical techniques to investigate these models. We show that there are prima facie reasons for using such models: (i) they have a richer mathematical framework (compared with ordinary differential equations) for the analysis of biosystem dynamics, (ii) they display better consistency with the nature of certain biological processes and predictive results. We analyze both the qualitative and quantitative role that delays play in basic time-lag models proposed in population dynamics, epidemiology, physiology, immunology, neural networks and cell kinetics. We then indicate suitable computational techniques for the numerical treatment of mathematical problems emerging in the biosciences, comparing them with those implemented by the bio-modellers.
Analysis of two-equation turbulence models for recirculating flows
NASA Technical Reports Server (NTRS)
Thangam, S.
1991-01-01
The two-equation kappa-epsilon model is used to analyze turbulent separated flow past a backward-facing step. It is shown that if the model constraints are modified to be consistent with the accepted energy decay rate for isotropic turbulence, the dominant features of the flow field, namely the size of the separation bubble and the streamwise component of the mean velocity, can be accurately predicted. In addition, except in the vicinity of the step, very good predictions for the turbulent shear stress, the wall pressure, and the wall shear stress are obtained. The model is also shown to provide good predictions for the turbulence intensity in the region downstream of the reattachment point. Estimated long time growth rates for the turbulent kinetic energy and dissipation rate of homogeneous shear flow are utilized to develop an optimal set of constants for the two equation kappa-epsilon model. The physical implications of the model performance are also discussed.
Building Context with Tumor Growth Modeling Projects in Differential Equations
ERIC Educational Resources Information Center
Beier, Julie C.; Gevertz, Jana L.; Howard, Keith E.
2015-01-01
The use of modeling projects serves to integrate, reinforce, and extend student knowledge. Here we present two projects related to tumor growth appropriate for a first course in differential equations. They illustrate the use of problem-based learning to reinforce and extend course content via a writing or research experience. Here we discuss…
Maximum Likelihood Estimation of Nonlinear Structural Equation Models.
ERIC Educational Resources Information Center
Lee, Sik-Yum; Zhu, Hong-Tu
2002-01-01
Developed an EM type algorithm for maximum likelihood estimation of a general nonlinear structural equation model in which the E-step is completed by a Metropolis-Hastings algorithm. Illustrated the methodology with results from a simulation study and two real examples using data from previous studies. (SLD)
Local Influence Analysis of Nonlinear Structural Equation Models
ERIC Educational Resources Information Center
Lee, Sik-Yum; Tang, Nian-Sheng
2004-01-01
By regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm, we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model. The basic building blocks of local influence analysis…
The Use of Structural Equation Modeling in Counseling Psychology Research
ERIC Educational Resources Information Center
Martens, Matthew P.
2005-01-01
Structural equation modeling (SEM) has become increasingly popular for analyzing data in the social sciences, although several broad reviews of psychology journals suggest that many SEM researchers engage in questionable practices when using the technique. The purpose of this study is to review and critique the use of SEM in counseling psychology…
Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
ERIC Educational Resources Information Center
Yuan, Ke-Hai; Zhang, Zhiyong
2012-01-01
The paper develops a two-stage robust procedure for structural equation modeling (SEM) and an R package "rsem" to facilitate the use of the procedure by applied researchers. In the first stage, M-estimates of the saturated mean vector and covariance matrix of all variables are obtained. Those corresponding to the substantive variables are then…
Gender Differences in Explaining Grades Using Structural Equation Modeling
ERIC Educational Resources Information Center
Ruban, Lilia M.; McCoach, D. Betsy
2005-01-01
This study examined the differential impacts of SAT scores and high school rank, college academic level, motivational variables, and self-regulatory variables in explaining variance in the academic achievement of male and female collegians using structural equation modeling and multiple groups analyses. Significantly, in light of earlier research,…
Structural Equation Modeling Reporting Practices for Language Assessment
ERIC Educational Resources Information Center
Ockey, Gary J.; Choi, Ikkyu
2015-01-01
Studies that use structural equation modeling (SEM) techniques are increasingly encountered in the language assessment literature. This popularity has created the need for a set of guidelines that can indicate what should be included in a research report and make it possible for research consumers to judge the appropriateness of the…
Sensitivity Analysis in Structural Equation Models: Cases and Their Influence
ERIC Educational Resources Information Center
Pek, Jolynn; MacCallum, Robert C.
2011-01-01
The detection of outliers and influential observations is routine practice in linear regression. Despite ongoing extensions and development of case diagnostics in structural equation models (SEM), their application has received limited attention and understanding in practice. The use of case diagnostics informs analysts of the uncertainty of model…
Linking Models: Reasoning from Patterns to Tables and Equations
ERIC Educational Resources Information Center
Switzer, J. Matt
2013-01-01
Patterns are commonly used in middle years mathematics classrooms to teach students about functions and modelling with tables, graphs, and equations. Grade 6 students are expected to, "continue and create sequences involving whole numbers, fractions and decimals," and "describe the rule used to create the sequence." (Australian…
Asymptotic behaviour of the Boltzmann equation as a cosmological model
NASA Astrophysics Data System (ADS)
Lee, Ho
2016-08-01
As a Newtonian cosmological model the Vlasov-Poisson-Boltzmann system is considered, and a slightly modified Boltzmann equation, which describes the stability of an expanding universe, is derived. Asymptotic behaviour of solutions turns out to depend on the expansion of the universe, and in this paper we consider the soft potential case and will obtain asymptotic behaviour.
Model Lorentz-like equation with continuous spectrum
NASA Astrophysics Data System (ADS)
Dudyński, Marek
2016-07-01
We present a new model of the Lorentz gas kinetic equation for a system where the integral collision operator has a spectrum consisting of a continuous and discrete part. The spectral gap between the two kinds of the spectrum is an adjustable parameter of the model. This allows for the analysis of the existence and property of the hydrodynamical eigenstates and the meaning of the Grad's method of moments for the transition between hard and soft interactions.
Lattice Boltzmann model for a steady radiative transfer equation.
Yi, Hong-Liang; Yao, Feng-Ju; Tan, He-Ping
2016-08-01
A complete lattice Boltzmann model (LBM) is proposed for the steady radiative transfer equation (RTE). The RTE can be regarded as a pure convection equation with a source term. To derive the expressions for the equilibrium distribution function and the relaxation time, an artificial isotropic diffusion term is introduced to form a convection-diffusion equation. When the dimensionless relaxation time has a value of 0.5, the lattice Boltzmann equation (LBE) is exactly applicable to the original steady RTE. We also perform a multiscale analysis based on the Chapman-Enskog expansion to recover the macroscopic RTE from the mesoscopic LBE. The D2Q9 model is used to solve the LBE, and the numerical results obtained by the LBM are comparable to the results obtained by other methods or analytical solutions, which demonstrates that the proposed model is highly accurate and stable in simulating multidimensional radiative transfer. In addition, we find that the convergence rate of the LBM depends on the transport properties of RTE: for diffusion-dominated RTE with a large optical thickness, the LBM shows a second-order convergence rate in space, while for convection-dominated RTE with a small optical thickness, a lower convergence rate is observed. PMID:27627417
Development of a One-Equation Transition/Turbulence Model
EDWARDS,JACK R.; ROY,CHRISTOPHER J.; BLOTTNER,FREDERICK G.; HASSAN,HASSAN A.
2000-09-26
This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity - transport equation for non-turbulent fluctuation growth based on that proposed by Warren and Hassan (Journal of Aircraft, Vol. 35, No. 5) is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittence function based on the work of Dhawan and Narasimha (Journal of Fluid Mechanics, Vol. 3, No. 4). The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the spatial accuracy of selected predictions is analyzed.
New Kinematic Model in comparing with Langevin equation and Fokker Planck Equation
NASA Astrophysics Data System (ADS)
Lee, Kyoung; Wang, Zhijian; Gardner, Robin
2010-03-01
An analytic approximate solution of New Kinematic Model with the boundary conditions is developed for the incompressible packing condition in Pebble Bed Reactors. It is based on velocity description of the packing density in the hopper. The packing structure can be presented with a jamming phenomenon from flow types. The gravity-driven macroscopic motions are governed not only by the geometry and external boundary conditions of silos and hoppers, but by flow prosperities of granular materials, such as friction, viscosity and porosity. The analytical formulas for the quasi-linear diffusion and convection coefficients of the velocity profile are obtained. Since it was found that the New Kinematic Model is dependent upon the granular packing density distribution, we are motivated to study the Langevin equation with friction under the influence of the Gravitational field. We also discuss the relation with the Fokker Planck Equation using Detailed balance and Metropolis-Hastings Algorithm. Markov chain Monte Carlo methods are shown to be a non-Maxwellian distribution function with the mean velocity of the field particles having an effective temperature.
The truncation model of the derivative nonlinear Schroedinger equation
Sanchez-Arriaga, G.; Hada, T.; Nariyuki, Y.
2009-04-15
The derivative nonlinear Schroedinger (DNLS) equation is explored using a truncation model with three resonant traveling waves. In the conservative case, the system derives from a time-independent Hamiltonian function with only one degree of freedom and the solutions can be written using elliptic functions. In spite of its low dimensional order, the truncation model preserves some features from the DNLS equation. In particular, the modulational instability criterion fits with the existence of two hyperbolic fixed points joined by a heteroclinic orbit that forces the exchange of energy between the three waves. On the other hand, numerical integrations of the DNLS equation show that the truncation model fails when wave energy is increased or left-hand polarized modulational unstable modes are present. When dissipative and growth terms are added the system exhibits a very complex dynamics including appearance of several attractors, period doubling bifurcations leading to chaos as well as other nonlinear phenomenon. In this case, the validity of the truncation model depends on the strength of the dissipation and the kind of attractor investigated.
Non-Equilibrium Turbulence and Two-Equation Modeling
NASA Technical Reports Server (NTRS)
Rubinstein, Robert
2011-01-01
Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.
Annotated bibliography of structural equation modelling: technical work.
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). PMID:1873237
Modeling tree crown dynamics with 3D partial differential equations.
Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry
2014-01-01
We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications. PMID:25101095
Immersed boundary method for Boltzmann model kinetic equations
NASA Astrophysics Data System (ADS)
Pekardan, Cem; Chigullapalli, Sruti; Sun, Lin; Alexeenko, Alina
2012-11-01
Three different immersed boundary method formulations are presented for Boltzmann model kinetic equations such as Bhatnagar-Gross-Krook (BGK) and Ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model equations. 1D unsteady IBM solution for a moving piston is compared with the DSMC results and 2D quasi-steady microscale gas damping solutions are verified by a conformal finite volume method solver. Transient analysis for a sinusoidally moving beam is also carried out for the different pressure conditions (1 atm, 0.1 atm and 0.01 atm) corresponding to Kn=0.05,0.5 and 5. Interrelaxation method (Method 2) is shown to provide a faster convergence as compared to the traditional interpolation scheme used in continuum IBM formulations. Unsteady damping in rarefied regime is characterized by a significant phase-lag which is not captured by quasi-steady approximations.
Numerical Solution of a Model Equation of Price Formation
NASA Astrophysics Data System (ADS)
Chernogorova, T.; Vulkov, L.
2009-10-01
The paper [2] is devoted to the effect of reconciling the classical Black-Sholes theory of option pricing and hedging with various phenomena observed in the markets such as the influence of trading and hedging on the dynamics of an asset. Here we will discuss the numerical solution of initial boundary-value problems to a model equation of the theory. The lack of regularity in the solution as a result from Dirac delta coefficient reduces the accuracy in the numerical computations. First, we apply the finite volume method to discretize the differential problem. Second, we implement a technique of local regularization introduced by A-K. Tornberg and B. Engquist [7] for handling this equation. We derived the numerical regularization process into two steps: the Dirac delta function is regularized and then the regularized differential equation is discretized by difference schemes. Using the discrete maximum principle a priori bounds are obtained for the difference equations that imply stability and convergence of difference schemes for the problem under consideration. Numerical experiments are discussed.
Modeling Inflation Using a Non-Equilibrium Equation of Exchange
NASA Technical Reports Server (NTRS)
Chamberlain, Robert G.
2013-01-01
Inflation is a change in the prices of goods that takes place without changes in the actual values of those goods. The Equation of Exchange, formulated clearly in a seminal paper by Irving Fisher in 1911, establishes an equilibrium relationship between the price index P (also known as "inflation"), the economy's aggregate output Q (also known as "the real gross domestic product"), the amount of money available for spending M (also known as "the money supply"), and the rate at which money is reused V (also known as "the velocity of circulation of money"). This paper offers first a qualitative discussion of what can cause these factors to change and how those causes might be controlled, then develops a quantitative model of inflation based on a non-equilibrium version of the Equation of Exchange. Causal relationships are different from equations in that the effects of changes in the causal variables take time to play out-often significant amounts of time. In the model described here, wages track prices, but only after a distributed lag. Prices change whenever the money supply, aggregate output, or the velocity of circulation of money change, but only after a distributed lag. Similarly, the money supply depends on the supplies of domestic and foreign money, which depend on the monetary base and a variety of foreign transactions, respectively. The spreading of delays mitigates the shocks of sudden changes to important inputs, but the most important aspect of this model is that delays, which often have dramatic consequences in dynamic systems, are explicitly incorporated.macroeconomics, inflation, equation of exchange, non-equilibrium, Athena Project
One-way nesting for a primitive equation ocean model
NASA Technical Reports Server (NTRS)
Blake, D. W.
1991-01-01
Prognostic numerical models for atmospheric and oceanic circulations require initial fields, boundary conditions, and forcing functions in addition to a consistent set of partial differential equations, including a state relation and equations expressing conservation of mass, momentum, and energy. Depending on the horizontal domain to be modeled, the horizontal boundary conditions are either physically obvious or extremely difficult to specify consistently. If the entire atmosphere is modeled, periodic horizontal boundary conditions are appropriate. On the other hand, the physical horizontal boundaries on the entire ocean are solid walls. Obviously, the normal velocity at a solid wall is zero while the specification of the tangential velocity depends on the mathematical treatment of the horizontal viscous terms. Limitations imposed by computer capacity and cost, as well as research interests, have led to the use of limited area models to study flows in the atmosphere and ocean. The limited area models do not have physical horizontal boundaries, merely numerical ones. Correctly determining these open boundary conditions for limited-area numerical models has both intrigued and frustrated numerical modelers for decades. One common approach is to use the closed or solid wall boundary conditions for a limited-area model. The argument given for this approach is that the boundary conditions affect flow near the walls but that none of these effects are propagated into the interior. Therefore, one chooses a big enough domain that the central region of interest is not corrupted by the boundary flow. Research in progress to model the North Atlantic circulation vividly illustrates the pitfalls of this approach. Two model runs are compared: (1) the southern boundary at 20S between latitudes 0 and 40W is artificially closed; and (2) the same boundary is specified as open with an inward transport of 15 Sv (determined from a global model with the same physics) uniformly spread
ERIC Educational Resources Information Center
González, B. Jorge; von Davier, Matthias
2013-01-01
Based on Lord's criterion of equity of equating, van der Linden (this issue) revisits the so-called local equating method and offers alternative as well as new thoughts on several topics including the types of transformations, symmetry, reliability, and population invariance appropriate for equating. A remarkable aspect is to define equating…
Modeling taper charge with a non-linear equation
NASA Technical Reports Server (NTRS)
Mcdermott, P. P.
1985-01-01
Work aimed at modeling the charge voltage and current characteristics of nickel-cadmium cells subject to taper charge is presented. Work reported at previous NASA Battery Workshops has shown that the voltage of cells subject to constant current charge and discharge can be modeled very accurately with the equation: voltage = A + (B/(C-X)) + De to the -Ex where A, B, D, and E are fit parameters and x is amp-hr of charge removed during discharge or returned during charge. In a constant current regime, x is also equivalent to time on charge or discharge.
Integral equation model for warm and hot dense mixtures.
Starrett, C E; Saumon, D; Daligault, J; Hamel, S
2014-09-01
In a previous work [C. E. Starrett and D. Saumon, Phys. Rev. E 87, 013104 (2013)] a model for the calculation of electronic and ionic structures of warm and hot dense matter was described and validated. In that model the electronic structure of one atom in a plasma is determined using a density-functional-theory-based average-atom (AA) model and the ionic structure is determined by coupling the AA model to integral equations governing the fluid structure. That model was for plasmas with one nuclear species only. Here we extend it to treat plasmas with many nuclear species, i.e., mixtures, and apply it to a carbon-hydrogen mixture relevant to inertial confinement fusion experiments. Comparison of the predicted electronic and ionic structures with orbital-free and Kohn-Sham molecular dynamics simulations reveals excellent agreement wherever chemical bonding is not significant. PMID:25314550
New Equation of State Models for Hydrodynamic Applications
NASA Astrophysics Data System (ADS)
Young, David A.; Barbee, Troy W., III; Rogers, Forrest J.
1997-07-01
Accurate models of the equation of state of matter at high pressures and temperatures are increasingly required for hydrodynamic simulations. We have developed two new approaches to accurate EOS modeling: 1) ab initio phonons from electron band structure theory for condensed matter and 2) the ACTEX dense plasma model for ultrahigh pressure shocks. We have studied the diamond and high pressure phases of carbon with the ab initio model and find good agreement between theory and experiment for shock Hugoniots, isotherms, and isobars. The theory also predicts a comprehensive phase diagram for carbon. For ultrahigh pressure shock states, we have studied the comparison of ACTEX theory with experiments for deuterium, beryllium, polystyrene, water, aluminum, and silicon dioxide. The agreement is good, showing that complex multispecies plasmas are treated adequately by the theory. These models will be useful in improving the numerical EOS tables used by hydrodynamic codes.
Modeling rapid mass movements using the shallow water equations
NASA Astrophysics Data System (ADS)
Hergarten, S.; Robl, J.
2014-11-01
We propose a new method to model rapid mass movements on complex topography using the shallow water equations in Cartesian coordinates. These equations are the widely used standard approximation for the flow of water in rivers and shallow lakes, but the main prerequisite for their application - an almost horizontal fluid table - is in general not satisfied for avalanches and debris flows in steep terrain. Therefore, we have developed appropriate correction terms for large topographic gradients. In this study we present the mathematical formulation of these correction terms and their implementation in the open source flow solver GERRIS. This novel approach is evaluated by simulating avalanches on synthetic and finally natural topographies and the widely used Voellmy flow resistance law. The results are tested against analytical solutions and the commercial avalanche model RAMMS. The overall results are in excellent agreement with the reference system RAMMS, and the deviations between the different models are far below the uncertainties in the determination of the relevant fluid parameters and involved avalanche volumes in reality. As this code is freely available and open source, it can be easily extended by additional fluid models or source areas, making this model suitable for simulating several types of rapid mass movements. It therefore provides a valuable tool assisting regional scale natural hazard studies.
Modeling of Flow Transition Using an Intermittency Transport Equation
NASA Technical Reports Server (NTRS)
Suzen, Y. B.; Huang, P. G.
1999-01-01
A new transport equation for intermittency factor is proposed to model transitional flows. The intermittent behavior of the transitional flows is incorporated into the computations by modifying the eddy viscosity, mu(sub t), obtainable from a turbulence model, with the intermittency factor, gamma: mu(sub t, sup *) = gamma.mu(sub t). In this paper, Menter's SST model (Menter, 1994) is employed to compute mu(sub t) and other turbulent quantities. The proposed intermittency transport equation can be considered as a blending of two models - Steelant and Dick (1996) and Cho and Chung (1992). The former was proposed for near-wall flows and was designed to reproduce the streamwise variation of the intermittency factor in the transition zone following Dhawan and Narasimha correlation (Dhawan and Narasimha, 1958) and the latter was proposed for free shear flows and was used to provide a realistic cross-stream variation of the intermittency profile. The new model was used to predict the T3 series experiments assembled by Savill (1993a, 1993b) including flows with different freestream turbulence intensities and two pressure-gradient cases. For all test cases good agreements between the computed results and the experimental data are observed.
Two-equation turbulence modeling for 3-D hypersonic flows
NASA Technical Reports Server (NTRS)
Bardina, J. E.; Coakley, T. J.; Marvin, J. G.
1992-01-01
An investigation to verify, incorporate and develop two-equation turbulence models for three-dimensional high speed flows is presented. The current design effort of hypersonic vehicles has led to an intensive study of turbulence models for compressible hypersonic flows. This research complements an extensive review of experimental data and the current development of 2D turbulence models. The review of experimental data on 2D and 3D flows includes complex hypersonic flows with pressure profiles, skin friction, wall heat transfer, and turbulence statistics data. In a parallel effort, turbulence models for high speed flows have been tested against flat plate boundary layers, and are being tested against the 2D database. In the present paper, we present the results of 3D Navier-Stokes numerical simulations with an improved k-omega two-equation turbulence model against experimental data and empirical correlations of an adiabatic flat plate boundary layer, a cold wall flat plate boundary layer, and a 3D database flow, the interaction of an oblique shock wave and a thick turbulent boundary layer with a free stream Mach number = 8.18 and Reynolds number = 5 x 10 to the 6th.
Validation of two-equation turbulence models for propulsion flowfields
NASA Technical Reports Server (NTRS)
Deshpande, Manish; Venkateswaran, S.; Merkle, Charles L.
1994-01-01
The objective of the study is to assess the capability of two-equation turbulence models for simulating propulsion-related flowfields. The standard kappa-epsilon model with Chien's low Reynolds number formulation for near-wall effects is used as the baseline turbulence model. Several experimental test cases, representative of rocket combustor internal flowfields, are used to catalog the performance of the baseline model. Specific flowfields considered here include recirculating flow behind a backstep, mixing between coaxial jets and planar shear layers. Since turbulence solutions are notoriously dependent on grid and numerical methodology, the effects of grid refinement and artificial dissipation on numerical accuracy are studied. In the latter instance, computational results obtained with several central-differenced and upwind-based formulations are compared. Based on these results, improved turbulence modes such as enhanced kappa-epsilon models as well as other two-equation formulations (e.g., kappa-omega) are being studied. In addition, validation of swirling and reacting flowfields are also currently underway.
On the Connection Between One-and Two-Equation Models of Turbulence
NASA Technical Reports Server (NTRS)
Menter, F. R.; Rai, Man Mohan (Technical Monitor)
1994-01-01
A formalism will be presented that allows the transformation of two-equation eddy viscosity turbulence models into one-equation models. The transformation is based on an assumption that is widely accepted over a large range of boundary layer flows and that has been shown to actually improve predictions when incorporated into two-equation models of turbulence. Based on that assumption, a new one-equation turbulence model will be derived. The new model will be tested in great detail against a previously introduced one-equation model and against its parent two-equation model.
Mickens, R.E.
1997-12-12
The major thrust of this proposal was to continue our investigations of so-called non-standard finite-difference schemes as formulated by other authors. These schemes do not follow the standard rules used to model continuous differential equations by discrete difference equations. The two major aspects of this procedure consist of generalizing the definition of the discrete derivative and using a nonlocal model (on the computational grid or lattice) for nonlinear terms that may occur in the differential equations. Our aim was to investigate the construction of nonstandard finite-difference schemes for several classes of ordinary and partial differential equations. These equations are simple enough to be tractable, yet, have enough complexity to be both mathematically and scientifically interesting. It should be noted that all of these equations differential equations model some physical phenomena under an appropriate set of experimental conditions. The major goal of the project was to better understand the process of constructing finite-difference models for differential equations. In particular, it demonstrates the value of using nonstandard finite-difference procedures. A secondary goal was to construct and study a variety of analytical techniques that can be used to investigate the mathematical properties of the obtained difference equations. These mathematical procedures are of interest in their own right and should be a valuable contribution to the mathematics research literature in difference equations. All of the results obtained from the research done under this project have been published in the relevant research/technical journals or submitted for publication. Our expectation is that these results will lead to improved finite difference schemes for the numerical integration of both ordinary and partial differential equations. Section G of the Appendix gives a concise summary of the major results obtained under funding by the grant.
On an evolution equation in a cell motility model
NASA Astrophysics Data System (ADS)
Mizuhara, Matthew S.; Berlyand, Leonid; Rybalko, Volodymyr; Zhang, Lei
2016-04-01
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells on a substrate. The key issue is the evolution of the cell membrane (interface curve) which involves shape change and net motion. This issue can be addressed both qualitatively and quantitatively by studying the evolution equation of the sharp interface limit for this system. However, this equation is non-linear and non-local and existence of solutions presents a significant analytical challenge. We establish existence of solutions for a wide class of initial data in the so-called subcritical regime. Existence is proved in a two step procedure. First, for smooth (H2) initial data we use a regularization technique. Second, we consider non-smooth initial data that are more relevant from the application point of view. Here, uniform estimates on the time when solutions exist rely on a maximum principle type argument. We also explore the long time behavior of the model using both analytical and numerical tools. We prove the nonexistence of traveling wave solutions with nonzero velocity. Numerical experiments show that presence of non-linearity and asymmetry of the initial curve results in a net motion which distinguishes it from classical volume preserving curvature motion. This is done by developing an algorithm for efficient numerical resolution of the non-local term in the evolution equation.
Modeling Dynamic Functional Neuroimaging Data Using Structural Equation Modeling
ERIC Educational Resources Information Center
Price, Larry R.; Laird, Angela R.; Fox, Peter T.; Ingham, Roger J.
2009-01-01
The aims of this study were to present a method for developing a path analytic network model using data acquired from positron emission tomography. Regions of interest within the human brain were identified through quantitative activation likelihood estimation meta-analysis. Using this information, a "true" or population path model was then…
Low Reynolds number two-equation modeling of turbulent flows
NASA Technical Reports Server (NTRS)
Michelassi, V.; Shih, T.-H.
1991-01-01
A k-epsilon model that accounts for viscous and wall effects is presented. The proposed formulation does not contain the local wall distance thereby making very simple the application to complex geometries. The formulation is based on an existing k-epsilon model that proved to fit very well with the results of direct numerical simulation. The new form is compared with nine different two-equation models and with direct numerical simulation for a fully developed channel flow at Re = 3300. The simple flow configuration allows a comparison free from numerical inaccuracies. The computed results prove that few of the considered forms exhibit a satisfactory agreement with the channel flow data. The model shows an improvement with respect to the existing formulations.
Bayesian structural equation modeling in sport and exercise psychology.
Stenling, Andreas; Ivarsson, Andreas; Johnson, Urban; Lindwall, Magnus
2015-08-01
Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach. PMID:26442771
The remarkable ability of turbulence model equations to describe transition
NASA Technical Reports Server (NTRS)
Wilcox, David C.
1992-01-01
This paper demonstrates how well the k-omega turbulence model describes the nonlinear growth of flow instabilities from laminar flow into the turbulent flow regime. Viscous modifications are proposed for the k-omega model that yield close agreement with measurements and with Direct Numerical Simulation results for channel and pipe flow. These modifications permit prediction of subtle sublayer details such as maximum dissipation at the surface, k approximately y(exp 2) as y approaches 0, and the sharp peak value of k near the surface. With two transition specific closure coefficients, the model equations accurately predict transition for an incompressible flat-plate boundary layer. The analysis also shows why the k-epsilon model is so difficult to use for predicting transition.
Mesoscale Eddy Parameterization in an Idealized Primitive Equations Model
NASA Astrophysics Data System (ADS)
Anstey, J.; Zanna, L.
2014-12-01
Large-scale ocean currents such as the Gulf Stream and Kuroshio Extension are strongly influenced by mesoscale eddies, which have spatial scales of order 10-100 km. The effects of these eddies are poorly represented in many state-of-the-art ocean general circulation models (GCMs) due to the inadequate spatial resolution of these models. In this study we examine the response of the large-scale ocean circulation to the rectified effects of eddy forcing - i.e., the role played by surface-intensified mesoscale eddies in sustaining and modulating an eastward jet that separates from an intense western boundary current (WBC). For this purpose a primitive equations ocean model (the MITgcm) in an idealized wind-forced double-gyre configuration is integrated at eddy-resolving resolution to reach a forced-dissipative equilibrium state that captures the essential dynamics of WBC-extension jets. The rectified eddy forcing is diagnosed as a stochastic function of the large-scale state, this being characterized by the manner in which potential vorticity (PV) contours become deformed. Specifically, a stochastic function based on the Laplacian of the material rate of change of PV is examined in order to compare the primitive equations results with those of a quasi-geostrophic model in which this function has shown some utility as a parameterization of eddy effects (Porta Mana and Zanna, 2014). The key question is whether an eddy parameterization based on quasi-geostrophic scaling is able to carry over to a system in which this scaling is not imposed (i.e. the primitive equations), in which unbalanced motions occur.
Duan, Aiguo; Zhang, Jianguo; Zhang, Xiongqing; He, Caiyun
2015-01-01
In this study, seven popular equations, including 3-parameter Weibull, 2-parameter Weibull, Gompertz, Logistic, Mitscherlich, Korf and R distribution, were used to model stand diameter distributions for exploring the relationship between the equations' inflection point attributes and model accuracy. A database comprised of 146 diameter frequency distributions of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) plantations was used to demonstrate model fitting and comparison. Results showed that the inflection points of the stand diameter cumulative percentage distribution ranged from 0.4 to 0.6, showing a 1/2 close rule. The equation's inflection point attribute was strongly related to its model accuracy. Equation with an inflection point showed much higher accuracy than that without an inflection point. The larger the effective inflection point interval of the fitting curve of the equation was, and the closer the inflection point was to 0.5 for the equations with fixed inflection points, the higher the equation's accuracy was. It could be found that the equation's inflection point had close relationship with skewness of diameter distribution and stand age, stand density, which provided a scientific basis for model selection of a stand diameter distribution for Chinese fir plantations and other tree species. PMID:26016995
Integrable cosmological models from higher dimensional Einstein equations
Sano, Masakazu; Suzuki, Hisao
2007-09-15
We consider the cosmological models for the higher dimensional space-time which includes the curvatures of our space as well as the curvatures of the internal space. We find that the condition for the integrability of the cosmological equations is that the total space-time dimensions are D=10 or D=11 which is exactly the conditions for superstrings or M theory. We obtain analytic solutions with generic initial conditions in the four-dimensional Einstein frame and study the accelerating universe when both our space and the internal space have negative curvatures.
New equation of state model for hydrodynamic applications
Young, D.A.; Barbee, T.W. III; Rogers, F.J.
1997-07-01
Two new theoretical methods for computing the equation of state of hot, dense matter are discussed.The ab initio phonon theory gives a first-principles calculation of lattice frequencies, which can be used to compare theory and experiment for isothermal and shock compression of solids. The ACTEX dense plasma theory has been improved to allow it to be compared directly with ultrahigh pressure shock data on low-Z materials. The comparisons with experiment are good, suggesting that these models will be useful in generating global EOS tables for hydrodynamic simulations.
Partial differential equation models in the socio-economic sciences
Burger, Martin; Caffarelli, Luis; Markowich, Peter A.
2014-01-01
Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences. The application of PDEs in the latter is a promising field, but widely quite open and leading to a variety of novel mathematical challenges. In this introductory article of the Theme Issue, we will provide an overview of the field and its recent boosting topics. Moreover, we will put the contributions to the Theme Issue in an appropriate perspective. PMID:25288814
New equation of state models for hydrodynamic applications
NASA Astrophysics Data System (ADS)
Young, David A.; Barbee, Troy W.; Rogers, Forrest J.
1998-07-01
Two new theoretical methods for computing the equation of state of hot, dense matter are discussed. The ab initio phonon theory gives a first-principles calculation of lattice frequencies, which can be used to compare theory and experiment for isothermal and shock compression of solids. The ACTEX dense plasma theory has been improved to allow it to be compared directly with ultrahigh pressure shock data on low-Z materials. The comparisons with experiment are good, suggesting that these models will be useful in generating global EOS tables for hydrodynamic simulations.
A one-equation turbulence model for recirculating flows
NASA Astrophysics Data System (ADS)
Zhang, Yang; Bai, JunQiang; Xu, JingLei; Li, Yi
2016-06-01
A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is computed from a recalibrated Bradshaw's assumption that the constant a 1 = 0.31 is recalibrated to a function based on a set of direct numerical simulation (DNS) data. The values of dissipation of turbulent kinetic energy consist of the near-wall part and isotropic part, and the isotropic part involves the von Karman length scale as the turbulent length scale. The performance of the new model is evaluated by the results from DNS for fully developed turbulence channel flow with a wide range of Reynolds numbers. However, the computed result of the recirculating flow at the separated bubble of NACA4412 demonstrates that an increase is needed on the turbulent dissipation, and this leads to an advanced tuning on the self-adjusted function. The improved model predicts better results in both the non-equilibrium and equilibrium flows, e.g. channel flows, backward-facing step flow and hump in a channel.
Structural Equation Modeling: Applications in ecological and evolutionary biology research
Pugesek, Bruce H.; von Eye, Alexander; Tomer, Adrian
2003-01-01
This book presents an introduction to the methodology of structural equation modeling, illustrates its use, and goes on to argue that it has revolutionary implications for the study of natural systems. A major theme of this book is that we have, up to this point, attempted to study systems primarily using methods (such as the univariate model) that were designed only for considering individual processes. Understanding systems requires the capacity to examine simultaneous influences and responses. Structural equation modeling (SEM) has such capabilities. It also possesses many other traits that add strength to its utility as a means of making scientific progress. In light of the capabilities of SEM, it can be argued that much of ecological theory is currently locked in an immature state that impairs its relevance. It is further argued that the principles of SEM are capable of leading to the development and evaluation of multivariate theories of the sort vitally needed for the conservation of natural systems. Supplementary information can be found at the authors website, http://www.jamesbgrace.com/. Details why multivariate analyses should be used to study ecological systems Exposes unappreciated weakness in many current popular analyses Emphasizes the future methodological developments needed to advance our understanding of ecological systems.
Computationally efficient statistical differential equation modeling using homogenization
Hooten, Mevin B.; Garlick, Martha J.; Powell, James A.
2013-01-01
Statistical models using partial differential equations (PDEs) to describe dynamically evolving natural systems are appearing in the scientific literature with some regularity in recent years. Often such studies seek to characterize the dynamics of temporal or spatio-temporal phenomena such as invasive species, consumer-resource interactions, community evolution, and resource selection. Specifically, in the spatial setting, data are often available at varying spatial and temporal scales. Additionally, the necessary numerical integration of a PDE may be computationally infeasible over the spatial support of interest. We present an approach to impose computationally advantageous changes of support in statistical implementations of PDE models and demonstrate its utility through simulation using a form of PDE known as “ecological diffusion.” We also apply a statistical ecological diffusion model to a data set involving the spread of mountain pine beetle (Dendroctonus ponderosae) in Idaho, USA.
Equation of State of the Two-Dimensional Hubbard Model.
Cocchi, Eugenio; Miller, Luke A; Drewes, Jan H; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael
2016-04-29
The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0≲U/t≲20 and temperatures, down to k_{B}T/t=0.63(2) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches. PMID:27176527
Equation of State of the Two-Dimensional Hubbard Model
NASA Astrophysics Data System (ADS)
Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H.; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael
2016-04-01
The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲U /t ≲20 and temperatures, down to kBT /t =0.63 (2 ) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.
A Boolean delay equation model of ENSO variability
NASA Astrophysics Data System (ADS)
Saunders, Amira; Ghil, Michael
2001-12-01
Boolean delay equations (BDEs) provide a mathematical framework to formulate and analyze conceptual models of complex multi-component systems. This framework is used here to construct a simple conceptual model for the El-Niño/Southern Oscillation (ENSO) phenomenon. ENSO involves the coupling of atmospheric and oceanic processes that are far from being completely understood. Our BDE model uses Boolean variables to represent key atmospheric and oceanic quantities and equations that involve logical operators to describe their evolution. Two distinct time-delay parameters, one for the local atmosphere-ocean coupling effects and the other for oceanic wave propagation, are introduced. Over a range of physically relevant delay values, this truly minimal model captures two essential features of ENSO’s interannual variability - its regularity and its tendency to phase-lock to the annual cycle. Oscillations with average cycle length that is an integer multiple of the seasonal cycle are prevalent and range from 2 to 7 years. Transition zones - where the average period lengths are noninteger rational multiples of the forcing period - exhibit Devil’s staircases, a signature of the quasi-periodic (QP) route to chaos. Our BDE model thus validates results from previous studies of the interaction of the seasonal cycle with ENSO’s “delayed oscillator”. It gives therewith support to the view that the observed irregularity results predominantly from low-order chaotic processes rather than from stochastic weather noise. Moreover, in the transition zone between the two integer periodicities of 2 and 3 years, a heretofore unsuspected, self-similar “fractal sunburst” pattern emerges in phase-parameter space. This pattern provides a distinct and more complex scenario than the QP route to chaos found in earlier, more detailed ENSO models. Period selection in this 2-3-year transitional region seems to play a key role in ENSO’s irregularity, as well as in the appearance of
ERIC Educational Resources Information Center
Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.
2009-01-01
This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…
Assessments of a Turbulence Model Based on Menter's Modification to Rotta's Two-Equation Model
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.
2013-01-01
The main objective of this paper is to construct a turbulence model with a more reliable second equation simulating length scale. In the present paper, we assess the length scale equation based on Menter s modification to Rotta s two-equation model. Rotta shows that a reliable second equation can be formed in an exact transport equation from the turbulent length scale L and kinetic energy. Rotta s equation is well suited for a term-by-term modeling and shows some interesting features compared to other approaches. The most important difference is that the formulation leads to a natural inclusion of higher order velocity derivatives into the source terms of the scale equation, which has the potential to enhance the capability of Reynolds-averaged Navier-Stokes (RANS) to simulate unsteady flows. The model is implemented in the PAB3D solver with complete formulation, usage methodology, and validation examples to demonstrate its capabilities. The detailed studies include grid convergence. Near-wall and shear flows cases are documented and compared with experimental and Large Eddy Simulation (LES) data. The results from this formulation are as good or better than the well-known SST turbulence model and much better than k-epsilon results. Overall, the study provides useful insights into the model capability in predicting attached and separated flows.
A stochastic differential equation model of diurnal cortisol patterns.
Brown, E N; Meehan, P M; Dempster, A P
2001-03-01
Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems. PMID:11171600
A stochastic differential equation model of diurnal cortisol patterns
NASA Technical Reports Server (NTRS)
Brown, E. N.; Meehan, P. M.; Dempster, A. P.
2001-01-01
Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.
ERIC Educational Resources Information Center
Mooijaart, Ab; Satorra, Albert
2009-01-01
In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of…
NONHOMOGENEOUS TERMS IN THE UNSTEADY FLOW EQUATIONS: MODELING ASPECTS.
Lai, Chintu; Schaffranek, Raymond W.; Baltzer, Robert A.
1987-01-01
A study is in progress to identify the relative significance, effects, and benefits attributable to the use of one-dimensional, unsteady, open-channel, flow-simulation models employing a variety of nonhomogeneous terms in their equation formulations. Nonhomogeneous terms being analyzed include those representing bed slope, frictional resistance, nonprismatic channel geometry, lateral flow, and (surface) wind stress. After an initial theoretical discussion, the results of a set of numerical experiments are presented that demonstrate cause-and-effect relationships and intercomparisons achieved by neglect or improper treatment of important nonhomogeneous terms. Preliminary results of this study are discussed and presented in this paper, both in the form of qualitative considerations and quantitative tabular findings. These results are expected to yield a definitive set of guidelines and suggestions useful to model engineers.
A partial differential equation model of metastasized prostatic cancer.
Friedman, Avner; Jain, Harsh Vardhan
2013-06-01
Biochemically failing metastatic prostate cancer is typically treated with androgen ablation. However, due to the emergence of castration-resistant cells that can survive in low androgen concentrations, such therapy eventually fails. Here, we develop a partial differential equation model of the growth and response to treatment of prostate cancer that has metastasized to the bone. Existence and uniqueness results are derived for the resulting free boundary problem. In particular, existence and uniqueness of solutions for all time are proven for the radially symmetric case. Finally, numerical simulations of a tumor growing in 2-dimensions with radial symmetry are carried in order to evaluate the therapeutic potential of different treatment strategies. These simulations are able to reproduce a variety of clinically observed responses to treatment, and suggest treatment strategies that may result in tumor remission, underscoring our model's potential to make a significant contribution in the field of prostate cancer therapeutics. PMID:23906138
Modeling Dynamic Ductility: An Equation of State for Porous Metals
Colvin, J
2007-07-27
Enhanced heating from shock compression of a porous material can potentially suppress or delay cracking of the material on subsequent expansion. In this paper we quantify the expected enhanced heating in an experiment in which a sector of a thin cylindrical shell is driven from the inside surface by SEMTEX high explosive ({approx}1 {micro}s FWHM pressure pulse with peak pressure {approx}21.5 GPa). We first derive an analytical equation of state (EOS) for porous metals, then discuss the coupling of this EOS with material elastic-plastic response in a 2D hydrocode, and then discuss the modeling of the HE experiment with both fully dense and 10% porous Ta and a Bi/Ta composite. Finally, we compare our modeling with some recent experimental data.
A fractional diffusion equation model for cancer tumor
NASA Astrophysics Data System (ADS)
Iyiola, Olaniyi Samuel; Zaman, F. D.
2014-10-01
In this article, we consider cancer tumor models and investigate the need for fractional order derivative as compared to the classical first order derivative in time. Three different cases of the net killing rate are taken into account including the case where net killing rate of the cancer cells is dependent on the concentration of the cells. At first, we use a relatively new analytical technique called q-Homotopy Analysis Method on the resulting time-fractional partial differential equations to obtain analytical solution in form of convergent series with easily computable components. Our numerical analysis enables us to give some recommendations on the appropriate order (fractional) of derivative in time to be used in modeling cancer tumor.
Controlled Nonlinear Stochastic Delay Equations: Part I: Modeling and Approximations
Kushner, Harold J.
2012-08-15
This two-part paper deals with 'foundational' issues that have not been previously considered in the modeling and numerical optimization of nonlinear stochastic delay systems. There are new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. There are two basic and interconnected themes for these models. The first, dealt with in this part, concerns the definition of admissible control. The classical definition of an admissible control as a nonanticipative relaxed control is inadequate for these models and needs to be extended. This is needed for the convergence proofs of numerical approximations for optimal controls as well as to have a well-defined model. It is shown that the new classes of admissible controls do not enlarge the range of the value functions, is closed (together with the associated paths) under weak convergence, and is approximatable by ordinary controls. The second theme, dealt with in Part II, concerns transportation equation representations, and their role in the development of numerical algorithms with much reduced memory and computational requirements.
Modeling disease transmission near eradication: An equation free approach
NASA Astrophysics Data System (ADS)
Williams, Matthew O.; Proctor, Joshua L.; Kutz, J. Nathan
2015-01-01
Although disease transmission in the near eradication regime is inherently stochastic, deterministic quantities such as the probability of eradication are of interest to policy makers and researchers. Rather than running large ensembles of discrete stochastic simulations over long intervals in time to compute these deterministic quantities, we create a data-driven and deterministic "coarse" model for them using the Equation Free (EF) framework. In lieu of deriving an explicit coarse model, the EF framework approximates any needed information, such as coarse time derivatives, by running short computational experiments. However, the choice of the coarse variables (i.e., the state of the coarse system) is critical if the resulting model is to be accurate. In this manuscript, we propose a set of coarse variables that result in an accurate model in the endemic and near eradication regimes, and demonstrate this on a compartmental model representing the spread of Poliomyelitis. When combined with adaptive time-stepping coarse projective integrators, this approach can yield over a factor of two speedup compared to direct simulation, and due to its lower dimensionality, could be beneficial when conducting systems level tasks such as designing eradication or monitoring campaigns.
Quantifying uncertainty, variability and likelihood for ordinary differential equation models
2010-01-01
Background In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space. Results The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well-known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability. Conclusions While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations. PMID:21029410
Probabilistic delay differential equation modeling of event-related potentials.
Ostwald, Dirk; Starke, Ludger
2016-08-01
"Dynamic causal models" (DCMs) are a promising approach in the analysis of functional neuroimaging data due to their biophysical interpretability and their consolidation of functional-segregative and functional-integrative propositions. In this theoretical note we are concerned with the DCM framework for electroencephalographically recorded event-related potentials (ERP-DCM). Intuitively, ERP-DCM combines deterministic dynamical neural mass models with dipole-based EEG forward models to describe the event-related scalp potential time-series over the entire electrode space. Since its inception, ERP-DCM has been successfully employed to capture the neural underpinnings of a wide range of neurocognitive phenomena. However, in spite of its empirical popularity, the technical literature on ERP-DCM remains somewhat patchy. A number of previous communications have detailed certain aspects of the approach, but no unified and coherent documentation exists. With this technical note, we aim to close this gap and to increase the technical accessibility of ERP-DCM. Specifically, this note makes the following novel contributions: firstly, we provide a unified and coherent review of the mathematical machinery of the latent and forward models constituting ERP-DCM by formulating the approach as a probabilistic latent delay differential equation model. Secondly, we emphasize the probabilistic nature of the model and its variational Bayesian inversion scheme by explicitly deriving the variational free energy function in terms of both the likelihood expectation and variance parameters. Thirdly, we detail and validate the estimation of the model with a special focus on the explicit form of the variational free energy function and introduce a conventional nonlinear optimization scheme for its maximization. Finally, we identify and discuss a number of computational issues which may be addressed in the future development of the approach. PMID:27114057
Fitting Data to Model: Structural Equation Modeling Diagnosis Using Two Scatter Plots
ERIC Educational Resources Information Center
Yuan, Ke-Hai; Hayashi, Kentaro
2010-01-01
This article introduces two simple scatter plots for model diagnosis in structural equation modeling. One plot contrasts a residual-based M-distance of the structural model with the M-distance for the factor score. It contains information on outliers, good leverage observations, bad leverage observations, and normal cases. The other plot contrasts…
Stochastic modeling of driver behavior by Langevin equations
NASA Astrophysics Data System (ADS)
Langner, Michael; Peinke, Joachim
2015-06-01
A procedure based on stochastic Langevin equations is presented and shows how a stochastic model of driver behavior can be estimated directly from given data. The Langevin analysis allows the separation of a given data-set into a stochastic diffusion- and a deterministic drift field. Form the drift field a potential can be derived. In particular the method is here applied on driving data from a simulator. We overcome typical problems like varying sampling rates, low noise levels, low data amounts, inefficient coordinate systems, and non-stationary situations. From the estimation of the drift- and diffusion vector-fields derived from the data, we show different ways how to set up Monte-Carlo simulations for the driver behavior.
Malignant Potential of Gastrointestinal Cancers Assessed by Structural Equation Modeling
Onodera, Kei; Takahashi, Hiroaki; Okahara, Satoshi; Kodaira, Junichi; Oohashi, Hirokazu; Isshiki, Hiroyuki; Kawakami, Kentaro; Yamashita, Kentaro; Shinomura, Yasuhisa; Hosokawa, Masao
2016-01-01
Background Parameters reported in pathologic reviews have been failing to assess exactly the malignant potential of gastrointestinal cancers. We hypothesized that malignant potential could be defined by common latent variables (hypothesis I), but there are substantial differences in the associations between malignant potential and pathologic parameters according to the origin of gastrointestinal cancers (hypothesis II). We shed light on these issues by structural equation modeling. Materials and Methods We conducted a cross-sectional survey of 217 esophageal, 192 gastric, and 175 colorectal cancer patients who consecutively underwent curative surgery for their pathologic stage I cancers at Keiyukai Sapporo Hospital. Latent variables identified by factor analysis and seven conventional pathologic parameters were introduced in the structural equation modeling analysis. Results Because latent variables were disparate except for their number, 'three' in the examined gastrointestinal cancers, the first hypothesis was rejected. Because configural invariance across gastrointestinal cancers was not approved, the second hypothesis was verified. We could trace the three significant paths on the causal graph from latent variables to lymph node metastasis, which were mediated through depth, lymphatic invasion, and matrilysin expression in esophageal cancer, whereas only one significant path could be traced in both gastric and colorectal cancer. Two of the three latent variables were exogenous in esophageal cancer, whereas one factor was exogenous in the other gastrointestinal cancers. Cancer stemness promoted viability in esophageal cancer, but it was suppressed in others. Conclusion These results reflect the malignant potential of esophageal cancer is higher than that of the other gastrointestinal cancers. Such information might contribute to refining clinical treatments for gastrointestinal cancers. PMID:26889682
A Differential Equation Model for the Dynamics of Youth Gambling
Do, Tae Sug; Lee, Young S.
2014-01-01
Objectives We examine the dynamics of gambling among young people aged 16–24 years, how prevalence rates of at-risk gambling and problem gambling change as adolescents enter young adulthood, and prevention and control strategies. Methods A simple epidemiological model is created using ordinary nonlinear differential equations, and a threshold condition that spreads gambling is identified through stability analysis. We estimate all the model parameters using a longitudinal prevalence study by Winters, Stinchfield, and Botzet to run numerical simulations. Parameters to which the system is most sensitive are isolated using sensitivity analysis. Results Problem gambling is endemic among young people, with a steady prevalence of approximately 4–5%. The prevalence of problem gambling is lower in young adults aged 18–24 years than in adolescents aged 16–18 years. At-risk gambling among young adults has increased. The parameters to which the system is most sensitive correspond to primary prevention. Conclusion Prevention and control strategies for gambling should involve school education. A mathematical model that includes the effect of early exposure to gambling would be helpful if a longitudinal study can provide data in the future. PMID:25379374
Iterative solvers for Navier-Stokes equations: Experiments with turbulence model
Page, M.; Garon, A.
1994-12-31
In the framework of developing software for the prediction of flows in hydraulic turbine components, Reynolds averaged Navier-Stokes equations coupled with {kappa}-{omega} two-equation turbulence model are discretized by finite element method. Since the resulting matrices are large, sparse and nonsymmetric, strategies based on CG-type iterative methods must be devised. A segregated solution strategy decouples the momentum equation, the {kappa} transport equation and the {omega} transport equation. These sets of equations must be solved while satisfying constraint equations. Experiments with orthogonal projection method are presented for the imposition of essential boundary conditions in a weak sense.
Using structural equation modeling to investigate relationships among ecological variables
Malaeb, Z.A.; Kevin, Summers J.; Pugesek, B.H.
2000-01-01
Structural equation modeling is an advanced multivariate statistical process with which a researcher can construct theoretical concepts, test their measurement reliability, hypothesize and test a theory about their relationships, take into account measurement errors, and consider both direct and indirect effects of variables on one another. Latent variables are theoretical concepts that unite phenomena under a single term, e.g., ecosystem health, environmental condition, and pollution (Bollen, 1989). Latent variables are not measured directly but can be expressed in terms of one or more directly measurable variables called indicators. For some researchers, defining, constructing, and examining the validity of latent variables may be the end task of itself. For others, testing hypothesized relationships of latent variables may be of interest. We analyzed the correlation matrix of eleven environmental variables from the U.S. Environmental Protection Agency's (USEPA) Environmental Monitoring and Assessment Program for Estuaries (EMAP-E) using methods of structural equation modeling. We hypothesized and tested a conceptual model to characterize the interdependencies between four latent variables-sediment contamination, natural variability, biodiversity, and growth potential. In particular, we were interested in measuring the direct, indirect, and total effects of sediment contamination and natural variability on biodiversity and growth potential. The model fit the data well and accounted for 81% of the variability in biodiversity and 69% of the variability in growth potential. It revealed a positive total effect of natural variability on growth potential that otherwise would have been judged negative had we not considered indirect effects. That is, natural variability had a negative direct effect on growth potential of magnitude -0.3251 and a positive indirect effect mediated through biodiversity of magnitude 0.4509, yielding a net positive total effect of 0
Damping models in the truncated derivative nonlinear Schroedinger equation
Sanchez-Arriaga, G.; Sanmartin, J. R.; Elaskar, S. A.
2007-08-15
Four-dimensional flow in the phase space of three amplitudes of circularly polarized Alfven waves and one relative phase, resulting from a resonant three-wave truncation of the derivative nonlinear Schroedinger equation, has been analyzed; wave 1 is linearly unstable with growth rate {gamma}, and waves 2 and 3 are stable with damping {gamma}{sub 2} and {gamma}{sub 3}, respectively. The dependence of gross dynamical features on the damping model (as characterized by the relation between damping and wave-vector ratios, {gamma}{sub 2}/{gamma}{sub 3}, k{sub 2}/k{sub 3}), and the polarization of the waves, is discussed; two damping models, Landau ({gamma}{proportional_to}k) and resistive ({gamma}{proportional_to}k{sup 2}), are studied in depth. Very complex dynamics, such as multiple blue sky catastrophes and chaotic attractors arising from Feigenbaum sequences, and explosive bifurcations involving Intermittency-I chaos, are shown to be associated with the existence and loss of stability of certain fixed point P of the flow. Independently of the damping model, P may only exist for {gamma}<2({gamma}{sub 2}+{gamma}{sub 3})/3, as against flow contraction just requiring {gamma}<{gamma}{sub 2}+{gamma}{sub 3}. In the case of right-hand (RH) polarization, point P may exist for all models other than Landau damping; for the resistive model, P may exist for RH polarization only if {gamma}<({gamma}{sub 2}+{gamma}{sub 3})/2.
Agent-Based vs. Equation-based Epidemiological Models:A Model Selection Case Study
Sukumar, Sreenivas R; Nutaro, James J
2012-01-01
This paper is motivated by the need to design model validation strategies for epidemiological disease-spread models. We consider both agent-based and equation-based models of pandemic disease spread and study the nuances and complexities one has to consider from the perspective of model validation. For this purpose, we instantiate an equation based model and an agent based model of the 1918 Spanish flu and we leverage data published in the literature for our case- study. We present our observations from the perspective of each implementation and discuss the application of model-selection criteria to compare the risk in choosing one modeling paradigm to another. We conclude with a discussion of our experience and document future ideas for a model validation framework.
Bayesian Estimation and Uncertainty Quantification in Differential Equation Models
NASA Astrophysics Data System (ADS)
Bhaumik, Prithwish
In engineering, physics, biomedical sciences, pharmacokinetics and pharmacodynamics (PKPD) and many other fields the regression function is often specified as solution of a system of ordinary differential equations (ODEs) given by. dƒtheta(t) / dt = F(t), ƒtheta(, t),theta), t ∈ [0, 1]; here F is a known appropriately smooth vector valued function. Our interest lies in estimating theta from the noisy data. A two-step approach to solve this problem consists of the first step fitting the data nonparametrically, and the second step estimating the parameter by minimizing the distance between the nonparametrically estimated derivative and the derivative suggested by the system of ODEs. In Chapter 2 we consider a Bayesian analog of the two step approach by putting a finite random series prior on the regression function using B-spline basis. We establish a Bernstein-von Mises theorem for the posterior distribution of the parameter of interest induced from that on the regression function with the n --1/2 contraction rate. Although this approach is computationally fast, the Bayes estimator is not asymptotically efficient. This can be remedied by directly considering the distance between the function in the nonparametric model and a Runge-Kutta (RK4) approximate solution of the ODE while inducing the posterior distribution on the parameter as done in Chapter 3. We also study the asymptotic properties of a direct Bayesian method obtained from the approximate likelihood obtained by the RK4 method in Chapter 3. Chapters 4 and 5 contain the extensions of the methods discussed so far for higher order ODE's and partial differential equations (PDE's) respectively. We have mentioned the scopes of some future works in Chapter 6.
A Study of Two-Equation Turbulence Models on the Elliptic Streamline Flow
NASA Technical Reports Server (NTRS)
Blaisdell, Gregory A.; Qin, Jim H.; Shariff, Karim; Rai, Man Mohan (Technical Monitor)
1995-01-01
Several two-equation turbulence models are compared to data from direct numerical simulations (DNS) of the homogeneous elliptic streamline flow, which combines rotation and strain. The models considered include standard two-equation models and models with corrections for rotational effects. Most of the rotational corrections modify the dissipation rate equation to account for the reduced dissipation rate in rotating turbulent flows, however, the DNS data shows that the production term in the turbulent kinetic energy equation is not modeled correctly by these models. Nonlinear relations for the Reynolds stresses are considered as a means of modifying the production term. Implications for the modeling of turbulent vortices will be discussed.
Jing, Yun; Xiang, Ning
2010-04-01
In this paper, the accuracy and efficiency of the previously discussed one-dimensional transport equation models [Y. Jing et al., J. Acoust. Soc. Am. 127, 2312-2322 (2010)] are examined both numerically and experimentally. The finite element method is employed to solve the equations. Artificial diffusion is applied in the numerical implementation to suppress oscillations of the solution. The transport equation models are then compared with the ray-tracing based method for different scenarios. In general, they are in good agreement, and the transport equation models are substantially less time consuming. In addition, the two-group model is found to yield more accurate results than the one-group model for the tested cases. Lastly, acoustic experimental results obtained from a 1:10 long room scale-model are used to verify the transport equation models. The results suggest that the transport equation models are able to accurately model the sound field in a long space. PMID:20370014
Hyperbolicity of the Nonlinear Models of Maxwell's Equations
NASA Astrophysics Data System (ADS)
Serre, Denis
. We consider the class of nonlinear models of electromagnetism that has been described by Coleman & Dill [7]. A model is completely determined by its energy density W(B,D). Viewing the electromagnetic field (B,D) as a 3×2 matrix, we show that polyconvexity of W implies the local well-posedness of the Cauchy problem within smooth functions of class Hs with s>1+d/2. The method follows that designed by Dafermos in his book [9] in the context of nonlinear elasticity. We use the fact that B×D is a (vectorial, non-convex) entropy, and we enlarge the system from 6 to 9 equations. The resulting system admits an entropy (actually the energy) that is convex. Since the energy conservation law does not derive from the system of conservation laws itself (Faraday's and Ampère's laws), but also needs the compatibility relations divB=divD=0 (the latter may be relaxed in order to take into account electric charges), the energy density is not an entropy in the classical sense. Thus the system cannot be symmetrized, strictly speaking. However, we show that the structure is close enough to symmetrizability, so that the standard estimates still hold true.
Ages estimated from a diffusion equation model for scarp degradation
Colman, Steven M.; Watson, K.E.N.
1983-01-01
The diffusion equation derived from the continuity equation for hillslopes is applied to scarp erosion in unconsolidated materials. Solutions to this equation allow direct calculation of the product of the rate coefficient and the age of the scarp from measurements of scarp morphology. Where the rate coefficient can be estimated or can be derived from scarps of known age, this method allows direct calculation of unknown ages of scarps.
Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Martinelli, L.
1991-01-01
The system of equations consisting of the full Navier-Stokes equations and two turbulence equations was solved for in the steady state using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time stepping scheme with a stability bound local time step, while the turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positively. Low Reynolds number modifications to the original two equation model are incorporated in a manner which results in well behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved for, initializing all quantities with uniform freestream values, and resulting in rapid and uniform convergence rates for the flow and turbulence equations.
The Trauma Outcome Process Assessment Model: A Structural Equation Model Examination of Adjustment
ERIC Educational Resources Information Center
Borja, Susan E.; Callahan, Jennifer L.
2009-01-01
This investigation sought to operationalize a comprehensive theoretical model, the Trauma Outcome Process Assessment, and test it empirically with structural equation modeling. The Trauma Outcome Process Assessment reflects a robust body of research and incorporates known ecological factors (e.g., family dynamics, social support) to explain…
A Comparison of Equating Methods under the Graded Response Model.
ERIC Educational Resources Information Center
Cohen, Allan S.; Kim, Seock-Ho
Equating tests from different calibrations under item response theory (IRT) requires calculation of the slope and intercept of the appropriate linear transformation. Two methods have been proposed recently for equating graded response items under IRT, a test characteristic curve method and a minimum chi-square method. These two methods are…
POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model
NASA Astrophysics Data System (ADS)
Ştefănescu, R.; Navon, I. M.
2013-03-01
In the present paper we consider a 2-D shallow-water equations (SWE) model on a β-plane solved using an alternating direction fully implicit (ADI) finite-difference scheme on a rectangular domain. The scheme was shown to be unconditionally stable for the linearized equations. The discretization yields a number of nonlinear systems of algebraic equations. We then use a proper orthogonal decomposition (POD) to reduce the dimension of the SWE model. Due to the model nonlinearities, the computational complexity of the reduced model still depends on the number of variables of the full shallow - water equations model. By employing the discrete empirical interpolation method (DEIM) we reduce the computational complexity of the reduced order model due to its depending on the nonlinear full dimension model and regain the full model reduction expected from the POD model. To emphasize the CPU gain in performance due to use of POD/DEIM, we also propose testing an explicit Euler finite difference scheme (EE) as an alternative to the ADI implicit scheme for solving the swallow water equations model. We then proceed to assess the efficiency of POD/DEIM as a function of number of spatial discretization points, time steps, and POD basis functions. As was expected, our numerical experiments showed that the CPU time performances of POD/DEIM schemes are proportional to the number of mesh points. Once the number of spatial discretization points exceeded 10000 and for 90 DEIM interpolation points, the CPU time decreased by a factor of 10 in case of POD/DEIM implicit SWE scheme and by a factor of 15 for the POD/DEIM explicit SWE scheme in comparison with the corresponding POD SWE schemes. Moreover, our numerical tests revealed that if the number of points selected by DEIM algorithm reached 50, the approximation errors due to POD/DEIM and POD reduced systems have the same orders of magnitude, thus supporting the theoretical results existing in the literature.
Evaluation of Structural Equation Mixture Models: Parameter Estimates and Correct Class Assignment
ERIC Educational Resources Information Center
Tueller, Stephen; Lubke, Gitta
2010-01-01
Structural equation mixture models (SEMMs) are latent class models that permit the estimation of a structural equation model within each class. Fitting SEMMs is illustrated using data from 1 wave of the Notre Dame Longitudinal Study of Aging. Based on the model used in the illustration, SEMM parameter estimation and correct class assignment are…
The Role of Sign in Students' Modeling of Scalar Equations
NASA Astrophysics Data System (ADS)
Hayes, Kate; Wittmann, Michael C.
2010-04-01
Helping students set up equations is one of the major goals of teaching a course in physics that contains elements of problem solving. Students must take the stories we present, interpret them, and turn them into physics; from there, they must turn that physical, idealized story into mathematics. How they do so and what problems lie along the way are a major source of difficulty for us as instructors. In this paper, we consider just one such difficulty, getting the plus and minus signs correct when setting a net force equal to mass times acceleration. Even in such simple equations, we find that students make common errors in how they connect the mathematics and the physics. Specifically, we have seen college physics students use physical and mathematical reasoning inconsistently when determining signs of terms in equations. The problem seems to lie in how a vector equation gets interpreted into a scalar equation (whose form depends on one's choice of coordinate system).
Regularized lattice Boltzmann model for a class of convection-diffusion equations.
Wang, Lei; Shi, Baochang; Chai, Zhenhua
2015-10-01
In this paper, a regularized lattice Boltzmann model for a class of nonlinear convection-diffusion equations with variable coefficients is proposed. The main idea of the present model is to introduce a set of precollision distribution functions that are defined only in terms of macroscopic moments. The Chapman-Enskog analysis shows that the nonlinear convection-diffusion equations can be recovered correctly. Numerical tests, including Fokker-Planck equations, Buckley-Leverett equation with discontinuous initial function, nonlinear convection-diffusion equation with anisotropic diffusion, are carried out to validate the present model, and the results show that the present model is more accurate than some available lattice Boltzmann models. It is also demonstrated that the present model is more stable than the traditional single-relaxation-time model for the nonlinear convection-diffusion equations. PMID:26565368
Kamaruzzaman, Syahrul Nizam; Egbu, C O; Zawawi, Emma Marinie Ahmad; Karim, Saipol Bari Abd; Woon, Chen Jia
2015-05-01
It is accepted that occupants who are more satisfied with their workplace's building internal environment are more productive. The main objective of the study was to measure the occupants' level of satisfaction and the perceived importance of the design or refurbishment on office conditions. The study also attempted to determine the factors affecting the occupants' satisfaction with their building or office conditions. Post-occupancy evaluations were conducted using a structured questionnaire developed by the Built Environment Research Group at the University of Manchester, UK. Our questionnaires incorporate 22 factors relating to the internal environment and rate these in terms of "user satisfaction" and "degree of importance." The questions were modified to reflect the specific setting of the study and take into consideration the local conditions and climate in Malaysia. The overall mean satisfaction of the occupants toward their office environment was 5.35. The results were measured by a single item of overall liking of office conditions in general. Occupants were more satisfied with their state of health in the workplace, but they were extremely dissatisfied with the distance away from a window. The factor analysis divided the variables into three groups, namely intrusion, air quality, and office appearance. Structural equation modeling (SEM) was then used to determine which factor had the most significant influence on occupants' satisfaction: appearance. The findings from the study suggest that continuous improvement in aspects of the building's appearance needs to be supported with effective and comprehensive maintenance to sustain the occupants' satisfaction. PMID:25864077
Three-dimensional parabolic equation modeling of mesoscale eddy deflection.
Heaney, Kevin D; Campbell, Richard L
2016-02-01
The impact of mesoscale oceanography, including ocean fronts and eddies, on global scale low-frequency acoustics is examined using a fully three-dimensional parabolic equation model. The narrowband acoustic signal, for frequencies from 2 to 16 Hz, is simulated from a seismic event on the Kerguellen Plateau in the South Indian Ocean to an array of receivers south of Ascension Island in the South Atlantic, a distance of 9100 km. The path was chosen for its relevance to seismic detections from the HA10 Ascension Island station of the International Monitoring System, for its lack of bathymetric interaction, and for the dynamic oceanography encountered as the sound passes the Cape of Good Hope. The acoustic field was propagated through two years (1992 and 1993) of the eddy-permitting ocean state estimation ECCO2 (Estimating the Circulation and Climate of the Ocean, Phase II) system. The range of deflection of the back-azimuth was 1.8° with a root-mean-square of 0.34°. The refraction due to mesoscale oceanography could therefore have significant impacts upon localization of distant low-frequency sources, such as seismic or nuclear test events. PMID:26936572
Modeling asymmetric cavity collapse with plasma equations of state
NASA Astrophysics Data System (ADS)
Tully, Brett; Hawker, Nicholas; Ventikos, Yiannis
2016-05-01
We explore the effect that equation of state (EOS) thermodynamics has on shock-driven cavity-collapse processes. We account for full, multidimensional, unsteady hydrodynamics and incorporate a range of relevant EOSs (polytropic, QEOS-type, and SESAME). In doing so, we show that simplified analytic EOSs, like ideal gas, capture certain critical parameters of the collapse such as velocity of the main transverse jet and pressure at jet strike, while also providing a good representation of overall trends. However, more sophisticated EOSs yield different and more relevant estimates of temperature and density, especially for higher incident shock strengths. We model incident shocks ranging from 0.1 to 1000 GPa, the latter being of interest in investigating the warm dense matter regime for which experimental and theoretical EOS data are difficult to obtain. At certain shock strengths, there is a factor of two difference in predicted density between QEOS-type and SESAME EOS, indicating cavity collapse as an experimental method for exploring EOS in this range.
Is racism dead? Comparing (expressive) means and (structural equation) models.
Leach, C W; Peng, T R; Volckens, J
2000-09-01
Much scholarship suggests that racism--belief in out-group inferiority--is unrelated to contemporary attitudes. Purportedly, a new form of racism, one which relies upon a belief in cultural difference, has become a more acceptable basis for such attitudes. The authors argue that an appropriate empirical assessment of racism (both 'old' and 'new') depends upon (1) clear conceptualization and operationalization, and (2) attention to both mean-level expression and explanatory value in structural equation models. This study assessed the endorsement of racism and belief in cultural difference as well as their association with a measure of general attitude in a secondary analysis of parallel representative surveys of attitudes toward different ethnic out-groups in France, The Netherlands, Western Germany and Britain (N = 3242; see Reif & Melich, 1991). For six of the seven out-group targets, racism was strongly related to ethnic majority attitudes, despite low mean-level endorsement. In a pattern consistent with a 'new', indirect racism, the relationship between British racism and attitudes toward Afro-Caribbeans was mediated by belief in cultural difference. PMID:11041013
Multigrid solution of incompressible turbulent flows by using two-equation turbulence models
Zheng, X.; Liu, C.; Sung, C.H.
1996-12-31
Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.
Factors of home dream recall: a structural equation model.
Schredl, Michael; Wittmann, Lutz; Ciric, Petra; Götz, Simon
2003-06-01
Previous research has indicated that personality factors such as openness to experience, creativity, visual memory, attitude toward dreams, and sleep behavior is related to home dream recall frequency (DRF). However, a study investigating all areas simultaneously within one sample in order to determine the percentage of variance explained by all variables and to take intercorrelations between the influencing factors into account has not been performed till now. The present study with 444 participants fills this gap. Using several indicators for each of the variables mentioned above, a structural equation model was tested. Although the model fit was satisfying, the four factors which were significantly related to DRF: personality (openness to experience, thin boundaries, absorption), creativity, nocturnal awakenings, and attitude toward dreams, explained only 8.4% of the total variance. As this value is considerably lower than those of studies investigating a single influencing factor and using similar measurement instruments in similar samples, one might speculate about possible expectancy effects in these previous studies, an effect which has been demonstrated for DRF in the laboratory setting. In addition, the small percentage of explained variance of each single factors (<3%) may indicate that other, in this study unmeasured, variables such as sleep duration (state aspect), introspection, and cognitive functioning immediately upon awakening (sleep inertia) show substantial covariance with the interindividual differences in DRF. Future studies should focus on longitudinal aspects in order to differentiate between state versus trait factors (although methodologic issues, e.g. the effect of the measurement technique on DRF itself, have to be clarified) and investigate additional variables which might be associated with DRF (see above). PMID:12753350
Habitat fragmentation and reproductive success: a structural equation modelling approach.
Le Tortorec, Eric; Helle, Samuli; Käyhkö, Niina; Suorsa, Petri; Huhta, Esa; Hakkarainen, Harri
2013-09-01
1. There is great interest on the effects of habitat fragmentation, whereby habitat is lost and the spatial configuration of remaining habitat patches is altered, on individual breeding performance. However, we still lack consensus of how this important process affects reproductive success, and whether its effects are mainly due to reduced fecundity or nestling survival. 2. The main reason for this may be the way that habitat fragmentation has been previously modelled. Studies have treated habitat loss and altered spatial configuration as two independent processes instead of as one hierarchical and interdependent process, and therefore have not been able to consider the relative direct and indirect effects of habitat loss and altered spatial configuration. 3. We investigated how habitat (i.e. old forest) fragmentation, caused by intense forest harvesting at the territory and landscape scales, is associated with the number of fledged offspring of an area-sensitive passerine, the Eurasian treecreeper (Certhia familiaris). We used structural equation modelling (SEM) to examine the complex hierarchical associations between habitat loss and altered spatial configuration on the number of fledged offspring, by controlling for individual condition and weather conditions during incubation. 4. Against generally held expectations, treecreeper reproductive success did not show a significant association with habitat fragmentation measured at the territory scale. Instead, our analyses suggested that an increasing amount of habitat at the landscape scale caused a significant increase in nest predation rates, leading to reduced reproductive success. This effect operated directly on nest predation rates, instead of acting indirectly through altered spatial configuration. 5. Because habitat amount and configuration are inherently strongly collinear, particularly when multiple scales are considered, our study demonstrates the usefulness of a SEM approach for hierarchical partitioning
Modelling with Difference Equations Supported by GeoGebra: Exploring the Kepler Problem
ERIC Educational Resources Information Center
Kovacs, Zoltan
2010-01-01
The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…
Bayesian Analysis of Structural Equation Models with Nonlinear Covariates and Latent Variables
ERIC Educational Resources Information Center
Song, Xin-Yuan; Lee, Sik-Yum
2006-01-01
In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the…
Informed Conjecturing of Solutions for Differential Equations in a Modeling Context
ERIC Educational Resources Information Center
Winkel, Brian
2015-01-01
We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…
Duan, Aiguo; Zhang, Jianguo; Zhang, Xiongqing; He, Caiyun
2015-01-01
In this study, seven popular equations, including 3-parameter Weibull, 2-parameter Weibull, Gompertz, Logistic, Mitscherlich, Korf and R distribution, were used to model stand diameter distributions for exploring the relationship between the equations’ inflection point attributes and model accuracy. A database comprised of 146 diameter frequency distributions of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) plantations was used to demonstrate model fitting and comparison. Results showed that the inflection points of the stand diameter cumulative percentage distribution ranged from 0.4 to 0.6, showing a 1/2 close rule. The equation’s inflection point attribute was strongly related to its model accuracy. Equation with an inflection point showed much higher accuracy than that without an inflection point. The larger the effective inflection point interval of the fitting curve of the equation was, and the closer the inflection point was to 0.5 for the equations with fixed inflection points, the higher the equation’s accuracy was. It could be found that the equation’s inflection point had close relationship with skewness of diameter distribution and stand age, stand density, which provided a scientific basis for model selection of a stand diameter distribution for Chinese fir plantations and other tree species. PMID:26016995
Modeling Multibody Stage Separation Dynamics Using Constraint Force Equation Methodology
NASA Technical Reports Server (NTRS)
Tartabini, Paul V.; Roithmayr, Carlos M.; Toniolo, Matthew D.; Karlgaard, Christopher D.; Pamadi, Bandu N.
2011-01-01
This paper discusses the application of the constraint force equation methodology and its implementation for multibody separation problems using three specially designed test cases. The first test case involves two rigid bodies connected by a fixed joint, the second case involves two rigid bodies connected with a universal joint, and the third test case is that of Mach 7 separation of the X-43A vehicle. For the first two cases, the solutions obtained using the constraint force equation method compare well with those obtained using industry- standard benchmark codes. For the X-43A case, the constraint force equation solutions show reasonable agreement with the flight-test data. Use of the constraint force equation method facilitates the analysis of stage separation in end-to-end simulations of launch vehicle trajectories
Exactly Solvable Wormhole and Cosmological Models with a Barotropic Equation of State
NASA Astrophysics Data System (ADS)
Kuhfittig, P. K. F.
An exact solution of the Einstein field equations given the barotropic equation of state $p=\\omega\\rho$ yields two possible models: (1) if $\\omega <-1$, we obtain the most general possible anisotropic model for wormholes supported by phantom energy and (2) if $\\omega >0$, we obtain a model for galactic rotation curves. Here the equation of state represents a perfect fluid which may include dark matter. These results illustrate the power and usefulness of exact solutions.
NASA Astrophysics Data System (ADS)
Kuraz, Michal
2016-06-01
This paper presents pseudo-deterministic catchment runoff model based on the Richards equation model [1] - the governing equation for the subsurface flow. The subsurface flow in a catchment is described here by two-dimensional variably saturated flow (unsaturated and saturated). The governing equation is the Richards equation with a slight modification of the time derivative term as considered e.g. by Neuman [2]. The nonlinear nature of this problem appears in unsaturated zone only, however the delineation of the saturated zone boundary is a nonlinear computationally expensive issue. The simple one-dimensional Boussinesq equation was used here as a rough estimator of the saturated zone boundary. With this estimate the dd-adaptivity algorithm (see Kuraz et al. [4, 5, 6]) could always start with an optimal subdomain split, so it is now possible to avoid solutions of huge systems of linear equations in the initial iteration level of our Richards equation based runoff model.
Applications of Multilevel Structural Equation Modeling to Cross-Cultural Research
ERIC Educational Resources Information Center
Cheung, Mike W.-L.; Au, Kevin
2005-01-01
Multilevel structural equation modeling (MSEM) has been proposed as an extension to structural equation modeling for analyzing data with nested structure. We have begun to see a few applications in cross-cultural research in which MSEM fits well as the statistical model. However, given that cross-cultural studies can only afford collecting data…
ERIC Educational Resources Information Center
Song, Xin-Yuan; Lee, Sik-Yum
2008-01-01
Structural equation models are widely appreciated in behavioral, social, and psychological research to model relations between latent constructs and manifest variables, and to control for measurement errors. Most applications of structural equation models are based on fully observed data that are independently distributed. However, hierarchical…
Langevin equation with fluctuating diffusivity: A two-state model
NASA Astrophysics Data System (ADS)
Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji
2016-07-01
Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.
Langevin equation with fluctuating diffusivity: A two-state model.
Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji
2016-07-01
Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool. PMID:27575079
Effect of the Number of Variables on Measures of Fit in Structural Equation Modeling.
ERIC Educational Resources Information Center
Kenny, David A.; McCoach, D. Betsy
2003-01-01
Used three approaches to understand the effect of the number of variables in the model on model fit in structural equation modeling through computer simulation. Developed a simple formula for the theoretical value of the comparative fit index. (SLD)
Exploring Term Dependences in Probabilistic Information Retrieval Model.
ERIC Educational Resources Information Center
Cho, Bong-Hyun; Lee, Changki; Lee, Gary Geunbae
2003-01-01
Describes a theoretic process to apply Bahadur-Lazarsfeld expansion (BLE) to general probabilistic models and the state-of-the-art 2-Poisson model. Through experiments on two standard document collections, one in Korean and one in English, it is demonstrated that incorporation of term dependences using BLE significantly contributes to performance…
Evaluating Small Sample Approaches for Model Test Statistics in Structural Equation Modeling.
ERIC Educational Resources Information Center
Nevitt, Jonathan
Structural equation modeling (SEM) attempts to remove the negative influence of measurement error and allows for investigation of relationships at the level of the underlying constructs of interest. SEM has been regarded as a "large sample" technique since its inception. Recent developments in SEM, some of which are currently available in popular…
ERIC Educational Resources Information Center
Bechger, Timo M.; Maris, Gunter
2004-01-01
This paper is about the structural equation modelling of quantitative measures that are obtained from a multiple facet design. A facet is simply a set consisting of a finite number of elements. It is assumed that measures are obtained by combining each element of each facet. Methods and traits are two such facets, and a multitrait-multimethod…
The Cusp Catastrophe Model as Cross-Sectional and Longitudinal Mixture Structural Equation Models
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
Is the Langevin phase equation an efficient model for oscillating neurons?
NASA Astrophysics Data System (ADS)
Ota, Keisuke; Tsunoda, Takamasa; Omori, Toshiaki; Watanabe, Shigeo; Miyakawa, Hiroyoshi; Okada, Masato; Aonishi, Toru
2009-12-01
The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.
Bianchi type-I cosmological model with quadratic equation of state
NASA Astrophysics Data System (ADS)
Reddy, D. R. K.; Adhav, K. S.; Purandare, M. A.
2015-05-01
Bianchi type-I cosmological model containing perfect fluid with quadratic equation of state has been studied in general theory of relativity. The general solutions of the Einstein's field equations for Bianchi type-I space-time have been obtained under the assumption of quadratic equation of state (EoS) p= αρ 2- ρ, where α is constant and strictly α≠0. The physical and geometrical aspects of the model are discussed.
On the basic equations for the second-order modeling of compressible turbulence
NASA Technical Reports Server (NTRS)
Liou, W. W.; Shih, T.-H.
1991-01-01
Equations for the mean and turbulent quantities for compressible turbulent flows are derived. Both the conventional Reynolds average and the mass-weighted, Favre average were employed to decompose the flow variable into a mean and a turbulent quality. These equations are to be used later in developing second order Reynolds stress models for high speed compressible flows. A few recent advances in modeling some of the terms in the equations due to compressibility effects are also summarized.
The Role of Sign in Students' Modeling of Scalar Equations
ERIC Educational Resources Information Center
Hayes, Kate; Wittmann, Michael C.
2010-01-01
Helping students set up equations is one of the major goals of teaching a course in physics that contains elements of problem solving. Students must take the stories we present, interpret them, and turn them into physics; from there, they must turn that physical, idealized story into mathematics. How they do so and what problems lie along the way…
Meta-Analytic Structural Equation Modeling (MASEM): Comparison of the Multivariate Methods
ERIC Educational Resources Information Center
Zhang, Ying
2011-01-01
Meta-analytic Structural Equation Modeling (MASEM) has drawn interest from many researchers recently. In doing MASEM, researchers usually first synthesize correlation matrices across studies using meta-analysis techniques and then analyze the pooled correlation matrix using structural equation modeling techniques. Several multivariate methods of…
ERIC Educational Resources Information Center
Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang
2006-01-01
This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…
NASA Astrophysics Data System (ADS)
Caglar, Mehmet Umut; Pal, Ranadip
2011-03-01
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 cell level data and probabilistic - nonlinear nature of interactions. Several models widely used to analyze and simulate these types of nonlinear interactions. Stochastic Master Equation (SME) models give probabilistic nature of the interactions in a detailed manner, with a high calculation cost. On the other hand Probabilistic Boolean Network (PBN) models give a coarse scale picture of the stochastic processes, with a less calculation cost. Differential Equation (DE) models give the time evolution of mean values of processes in a highly cost effective way. The understanding of the relations between the predictions of these models is important to understand the reliability of the simulations of genetic regulatory networks. In this work the success of the mapping between SME, PBN and DE models is analyzed and the accuracy and affectivity of the control policies generated by using PBN and DE models is compared.
Delay equation models for populations that experience competition at immature life stages
NASA Astrophysics Data System (ADS)
Gourley, Stephen A.; Liu, Rongsong
2015-09-01
We consider stage-structured population models of intra- and inter-specific competition at immature life stages. A prototype delay model is derived for a single species that experiences larval competition. Its solutions are bounded for any birth function. Other ways of modelling the birth rate can lead to nonlinear integral equations. In some situations the technique of reducing an age-structured model to a system of delay equations applies. In the case of immature competition the delay equations cannot always be written down explicitly because their right hand sides depend on the solutions of the nonlinear ordinary differential equations that arise when one solves the nonlinear age-structured equations that determine the maturation rates in terms of the birth rates. This situation arises in the case of competition between two strains or species. However, in our two-strain competition model, vital properties of those right hand sides can be indirectly inferred using monotone systems theory.
IT vendor selection model by using structural equation model & analytical hierarchy process
NASA Astrophysics Data System (ADS)
Maitra, Sarit; Dominic, P. D. D.
2012-11-01
Selecting and evaluating the right vendors is imperative for an organization's global marketplace competitiveness. Improper selection and evaluation of potential vendors can dwarf an organization's supply chain performance. Numerous studies have demonstrated that firms consider multiple criteria when selecting key vendors. This research intends to develop a new hybrid model for vendor selection process with better decision making. The new proposed model provides a suitable tool for assisting decision makers and managers to make the right decisions and select the most suitable vendor. This paper proposes a Hybrid model based on Structural Equation Model (SEM) and Analytical Hierarchy Process (AHP) for long-term strategic vendor selection problems. The five steps framework of the model has been designed after the thorough literature study. The proposed hybrid model will be applied using a real life case study to assess its effectiveness. In addition, What-if analysis technique will be used for model validation purpose.
ERIC Educational Resources Information Center
Raines-Eudy, Ruth
2000-01-01
Demonstrates empirically a structural equation modeling technique for group comparison of reliability and validity. Data, which are from a study of 495 mothers' attitudes toward pregnancy, have a one-factor measurement model and three sets of subpopulation comparisons. (SLD)
Clausius relation and Friedmann equation in FRW universe model
Cao, Qiao-Jun; Chen, Yi-Xin; Shao, Kai-Nan E-mail: yxchen@zimp.zju.edu.cn
2010-05-01
It has been shown that Friedmann equation of FRW universe can be derived from the first law of thermodynamics in Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, scalar-tensor gravity and f(R) gravity. Moreover, it was pointed out that the temperature of the apparent horizon can be obtained using the tunneling formalism for the corresponding observers defined by Kodama vector. In this article, we find that the energy flux through the apparent horizon can be determined by using the Kodama vector. This implies the fact that the Clausius relation and the first law of thermodynamics associated with the apparent horizon in FRW universe is relative to the Kodama observers. We illustrate the derivation of Friedmann equation, and also extend the study to the cases of Hořava-Lifshitz gravity and IR modified Hořava-Lifshitz gravity.
A Parabolic Equation Approach to Modeling Acousto-Gravity Waves for Local Helioseismology
NASA Astrophysics Data System (ADS)
Del Bene, Kevin; Lingevitch, Joseph; Doschek, George
2016-08-01
A wide-angle parabolic-wave-equation algorithm is developed and validated for local-helioseismic wave propagation. The parabolic equation is derived from a factorization of the linearized acousto-gravity wave equation. We apply the parabolic-wave equation to modeling acoustic propagation in a plane-parallel waveguide with physical properties derived from helioseismic data. The wavenumber power spectrum and wave-packet arrival-time structure for receivers in the photosphere with separation up to 30° is computed, and good agreement is demonstrated with measured values and a reference spectral model.
A Parabolic Equation Approach to Modeling Acousto-Gravity Waves for Local Helioseismology
NASA Astrophysics Data System (ADS)
Del Bene, Kevin; Lingevitch, Joseph; Doschek, George
2016-07-01
A wide-angle parabolic-wave-equation algorithm is developed and validated for local-helioseismic wave propagation. The parabolic equation is derived from a factorization of the linearized acousto-gravity wave equation. We apply the parabolic-wave equation to modeling acoustic propagation in a plane-parallel waveguide with physical properties derived from helioseismic data. The wavenumber power spectrum and wave-packet arrival-time structure for receivers in the photosphere with separation up to 30° is computed, and good agreement is demonstrated with measured values and a reference spectral model.
Battery Life Estimator (BLE) Data Analysis Software v. 1.2
Energy Science and Technology Software Center (ESTSC)
2010-02-24
The purpose of this software is estimate the useable life of rechargeable batteries (e.g., lithium-ion). The software employs a generalized statistical approach to model cell data in the context of accelerated aging experiments. The cell performance is modeled in two parts. The first part consists of a deterministic degradation model which models the average cell behavior. The second part relates to the statistical variation in performance of the cells (error model). Experimental data from anmore » accelerated aging experiment will be input from an Excel worksheet. The software will then query the user for a specific model form (within the generalized model framework). Model parameters will be estimated by the software using various statistical methodologies. Average cell life will be predicted using the estimated model parameters. The uncertainty in the estimated cell life will also be computed using bootstrap simulations. This software can be used in several modes: 1) fit only, 2) fit and simulation, and 3) simulation only« less
NASA Astrophysics Data System (ADS)
Huang, Hua; Sun, Mao
2012-12-01
The forward flight of a model butterfly was studied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body oscillations of the model butterfly to be simulated. The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the upstroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small negative horizontal force, whilst in the upstroke, the body angle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizontal force which overcomes the body drag and the negative horizontal force generated in the downstroke. (2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. (3) The body-massspecific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies.
The lattice Boltzmann model for the second-order Benjamin-Ono equations
NASA Astrophysics Data System (ADS)
Lai, Huilin; Ma, Changfeng
2010-04-01
In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin-Ono equation. With the Taylor expansion and the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations.
Primitive-Equation-Based Low-Order Models with Seasonal Cycle. Part I: Model Construction.
NASA Astrophysics Data System (ADS)
Achatz, Ulrich; Opsteegh, J. D.
2003-02-01
In a continuation of previous investigations on deterministic reduced atmosphere models with compact state space representation, two main modifications are introduced. First, primitive equation dynamics is used to describe the nonlinear interactions between resolved scales. Second, the seasonal cycle in its main aspects is incorporated. Stability considerations lead to a gridpoint formulation of the basic equations in the dynamical core. A total energy metric consistent with the equations can be derived, provided surface pressure is treated as constant in time. Using this metric, a reduction in the number of degrees of freedom is achieved by a projection onto three-dimensional empirical orthogonal functions (EOFs), each of them encompassing simultaneously all prognostic variables (winds and temperature). The impact of unresolved scales and not explicitly described physical processes is incorporated via an empirical linear parameterization. The basis patterns having been determined from 3 sigma levels from a GCM dataset, it is found that, in spite of the presence of a seasonal cycle, at most 500 are needed for describing 90% of the variance produced by the GCM. If compared to previous low-order models with quasigeostrophic dynamics, the reduced models exhibit at this and lower-order truncations, a considerably enhanced capability to predict GCM tendencies. An analysis of the dynamical impact of the empirical parameterization is given, hinting at an important role in controlling the seasonally dependent storm track dynamics.
A one-equation turbulence transport model for high Reynolds number wall-bounded flows
NASA Technical Reports Server (NTRS)
Baldwin, Barrett S.; Barth, Timothy J.
1990-01-01
A one-equation turbulence model that avoids the need for an algebraic length scale is derived from a simplified form of the standard k-epsilon model equations. After calibration based on well established properties of the flow over a flat plate, predictions of several other flows are compared with experiment. The preliminary results presented indicate that the model has predictive and numerical properties of sufficient interest to merit further investigation and refinement. The one-equation model is also analyzed numerically and robust solution methods are presented.
A one-equation turbulence transport model for high Reynolds number wall-bounded flows
NASA Technical Reports Server (NTRS)
Baldwin, Barrett S.; Barth, Timothy J.
1991-01-01
A one-equation turbulence model that avoids the need for an algebraic length scale is derived from a simplified form of the standard-k-epsilon model equations. After calibration based on well established properties of the flow over a flat plate, predictions of several other flows are compared with experiment. The preliminary results presented indicate that the model has predictive and numerical properties of sufficient interest to merit further investigation and refinement. The one-equation model is also analyzed numerically and robust solution methods are presented.
Modeling the dissipation-rate equation with the aid of direct simulation data
NASA Technical Reports Server (NTRS)
Rodi, W.; Mansour, N. N.
1992-01-01
The epsilon-budget was computed from the direct simulation data (DNS) of Kim (1990) for developed channel flow at Re(tau) = 395. The relative magnitude of the terms in the epsilon-equation is shown with the aid of scaling arguments, and the parameter governing this magnitude is established. The modeling of the terms in the equation is then addressed in the context of eddy-viscosity k-epsilon models. Some existing models for the sum of all source and sink terms in the epsilon-equation are tested against DNS data, and an improved model is proposed on the basis of these data.
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.
1988-01-01
An LU implicit multigrid algorithm is developed to calculate 3-D compressible viscous flows. This scheme solves the full 3-D Reynolds-Averaged Navier-Stokes equation with a two-equation kappa-epsilon model of turbulence. The flow equations are integrated by an efficient, diagonally inverted, LU implicit multigrid scheme while the kappa-epsilon equations are solved, uncoupled from the flow equations, by a block LU implicit algorithm. The flow equations are solved within the framework of the multigrid method using a four-grid level W-cycle, while the kappa-epsilon equations are iterated only on the finest grid. This treatment of the Reynolds-Averaged Navier-Stokes equations proves to be an efficient method for calculating 3-D compressible viscous flows.
The Hill equation: a review of its capabilities in pharmacological modelling.
Goutelle, Sylvain; Maurin, Michel; Rougier, Florent; Barbaut, Xavier; Bourguignon, Laurent; Ducher, Michel; Maire, Pascal
2008-12-01
The Hill equation was first introduced by A.V. Hill to describe the equilibrium relationship between oxygen tension and the saturation of haemoglobin. In pharmacology, the Hill equation has been extensively used to analyse quantitative drug-receptor relationships. Many pharmacokinetic-pharmacodynamic models have used the Hill equation to describe nonlinear drug dose-response relationships. Although the Hill equation is widely used, its many properties are not all well known. This article aims at reviewing the various properties of the Hill equation. The descriptive aspects of the Hill equation, in particular mathematical and graphical properties, are examined, and related to Hill's original work. The mechanistic aspect of the Hill equation, involving a strong connection with the Guldberg and Waage law of mass action, is also described. Finally, a probabilistic view of the Hill equation is examined. Here, we provide some new calculation results, such as Fisher information and Shannon entropy, and we introduce multivariate probabilistic Hill equations. The main features and potential applications of this probabilistic approach are also discussed. Thus, within the same formalism, the Hill equation has many different properties which can be of great interest for those interested in mathematical modelling in pharmacology and biosciences. PMID:19049668
Granita; Bahar, A.
2015-03-09
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.
NASA Astrophysics Data System (ADS)
Granita, Bahar, A.
2015-03-01
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.
NASA Technical Reports Server (NTRS)
Thormann, Wolfgang; Mosher, Richard A.
1985-01-01
The general equations which describe the electrophoretic transport of components in solution are restated using Newman's general concept of mobilities. A concise derivation of the moving boundary equation and the regulating function from the continuity equation is presented. Various other regulating principles across moving and stationary boundaries are also discussed, which permits a review of the features and interrelationships of the electrophoretic models based on electromigration only. The effect of considering an interactive (dissociating) solvent on the mathematical treatment is discussed.
Population Uncertainty in Model Ecosystem: Analysis by Stochastic Differential Equation
NASA Astrophysics Data System (ADS)
Morita, Satoru; Tainaka, Kei-ichi; Nagata, Hiroyasu; Yoshimura, Jin
2008-09-01
Perturbation experiments are carried out by the numerical simulations of a contact process and its mean-field version. Here, the mortality rate increases or decreases suddenly. It is known that fluctuation enhancement (FE) occurs after perturbation, where FE indicates population uncertainty. In the present paper, we develop a new theory of stochastic differential equation. The agreement between the theory and the mean-field simulation is almost perfect. This theory enables us to find a much stronger FE than that reported previously. We discuss the population uncertainty in the recovering process of endangered species.
The Issue of Isopower in Power Analysis for Tests of Structural Equation Models
ERIC Educational Resources Information Center
MacCallum, Robert; Lee, Taehun; Browne, Michael W.
2010-01-01
Two general frameworks have been proposed for evaluating statistical power of tests of model fit in structural equation modeling (SEM). Under the Satorra-Saris (1985) approach, to evaluate the power of the test of fit of Model A, a Model B, within which A is nested, is specified as the alternative hypothesis and considered as the true model. We…
Technical Note: Alternative in-stream denitrification equation for the INCA-N model
NASA Astrophysics Data System (ADS)
Etheridge, J. R.; Birgand, F.; Burchell, M. R., II; Lepistö, A.; Rankinen, K.; Granlund, K.
2014-04-01
The Integrated Catchment model for Nitrogen (INCA-N) is a semi-distributed, process based model that has been used to model the impacts of land use, climate, and land management changes on hydrology and nitrogen loading. An observed problem with the INCA-N model is reproducing low nitrate-nitrogen concentrations during the summer growing season in some catchments. In this study, the current equation used to simulate the rate of in-stream denitrification was replaced with an alternate equation that uses a mass transfer coefficient and the stream bottom area. The results of simulating in-stream denitrification using the two different methods were compared for a one year simulation period of the Yläneenjoki catchment in Finland. The alternate equation (Nash-Sutcliffe efficiency = 0.61) simulated concentrations during the periods of the growing season with the lowest flow that were closer to the observed concentrations than the current equation (Nash-Sutcliffe efficiency = 0.60), but the results were mixed during other portions of the year. The results of the calibration and validation of the model using the two equations show that the alternate equation will simulate lower nitrate-nitrogen concentrations during the growing season when compared to the current equation, but promote investigation into other errors in the model that may be causing inaccuracies in the modeled concentrations.
Incorporation of an Energy Equation into a Pulsed Inductive Thruster Performance Model
NASA Technical Reports Server (NTRS)
Polzin, Kurt A.; Reneau, Jarred P.; Sankaran, Kameshwaran
2011-01-01
A model for pulsed inductive plasma acceleration containing an energy equation to account for the various sources and sinks in such devices is presented. The model consists of a set of circuit equations coupled to an equation of motion and energy equation for the plasma. The latter two equations are obtained for the plasma current sheet by treating it as a one-element finite volume, integrating the equations over that volume, and then matching known terms or quantities already calculated in the model to the resulting current sheet-averaged terms in the equations. Calculations showing the time-evolution of the various sources and sinks in the system are presented to demonstrate the efficacy of the model, with two separate resistivity models employed to show an example of how the plasma transport properties can affect the calculation. While neither resistivity model is fully accurate, the demonstration shows that it is possible within this modeling framework to time-accurately update various plasma parameters.
Applicability of equations of state for modeling helium systems
NASA Astrophysics Data System (ADS)
Thomas, Rijo Jacob; Dutta, Rohan; Ghosh, Parthasarathi; Chowdhury, Kanchan
2012-07-01
Proper design of helium systems with large number of components and involved configurations such as helium liquefiers/refrigerators requires the use of tools like process simulators. The accuracy of the simulation results, to a great extent, depends on the accuracy of property data. For computation of thermodynamic properties of helium, the 32-parameter MBWR equation of state proposed by McCarty and Arp [1] is widely used. However, it is computationally involved, makes the simulation process more time-consuming and sometimes leads to computational difficulties such as numerical oscillations, divergence in solution especially, when the process operates over a wide thermodynamic region and is constituted of many components. Substituting MBWR EOS by simpler equations of state (EOS(s)) at selected thermodynamic planes, where the simpler EOS(s) have the similar accuracy as that of MBWR EOS may enhance ease of computation. In the present paper, the methodology to implement this concept has been elucidated with examples of steady state and dynamic simulation of helium liquefier/refrigerator based on Collins cycle. The above concept can be applied to thermodynamic analysis of other process cycles where computation of fluid property is involved.
A Comparison of Two Methods of Test Equating in the Rasch Model.
ERIC Educational Resources Information Center
Smith, Richard M.; Kramer, Gene A.
1992-01-01
The common item equating method (weighted and unweighted) and the one-step missing data calibration method used with Rasch measurement models were compared using data from six equivalent forms of a perceptual ability test administered as part of the Dental Admission Test. Results suggest little difference among the equating methods. (SLD)
Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices
ERIC Educational Resources Information Center
Deboeck, Pascal R.; Boker, Steven M.
2010-01-01
Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for…