Analysis of latency performance of bluetooth low energy (BLE) networks.
Cho, Keuchul; Park, Woojin; Hong, Moonki; Park, Gisu; Cho, Wooseong; Seo, Jihoon; Han, Kijun
2014-12-23
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.
Ayik, S. Joint Inst. for Heavy Ion Research, Oak Ridge, TN ); Ivanov, Y.B.; Russkikh, V.N.; Noerenberg, W. )
1993-01-01
A reduction of the relativistic Boltzmann-Langevin Equation (BLE), to a stochastic two-fluid model is presented, and transport coefficients associated with fluid dynamical variables are extracted. The approach is applied to investigate equilibration in a counter-streaming nuclear system.
Regularized Structural Equation Modeling.
Jacobucci, Ross; Grimm, Kevin J; McArdle, John J
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.
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…
Using modified ballistic limit equations in spacecraft risk assessments
NASA Astrophysics Data System (ADS)
Schonberg, William P.
2016-09-01
The fundamental components of any meteoroid/orbital debris (MOD) risk assessment calculation are environment models, damage response predictor equations, and failure criteria. In the case of a spacecraft operating in low earth orbit, the response predictor equation typically takes the form of a ballistic limit equation (BLE) that defines the threshold particle sizes that cause failure of a spacecraft wall or component. Spacecraft risk assessments often call for BLEs for spacecraft components that do not exist. In such cases, it is a common procedure to use an existing BLE after first equivalencing the actual materials and/or wall thicknesses to the materials that were used in the development of the existing BLE. The question naturally arises regarding how close are the predictions of such an 'adapted BLE' to the response characteristics of the actual materials/wall configurations under high speed projectile impacts. This paper presents the results of a study that compared the predictions of a commonly used BLE when adapted to the Soyuz OM wall configuration against those of a new BLE that was developed specifically for that Soyuz wall configuration. It was found that the critical projectile diameters predicted by the new Soyuz OM wall BLE can exceed those predicted by the adapted use of the existing BLE by as much as 50% of the existing BLE values. Thus, using the adapted version of the existing BLE in this particular case would contribute to a more conservative value of assessed risk. If the same trends were to hold true for other spacecraft wall configurations, then it is also possible that using existing BLEs, even after they have been adjusted for differences in materials, etc., may result in predictions of smaller critical diameters (i.e., increased assessed risk) than would using BLEs purposely developed for actual spacecraft configurations of interest.
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…
Generalized Ordinary Differential Equation Models.
Miao, Hongyu; Wu, Hulin; Xue, Hongqi
2014-10-01
Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method.
Investigation of the kinetic model equations.
Liu, Sha; Zhong, Chengwen
2014-03-01
Currently the Boltzmann equation and its model equations are widely used in numerical predictions for dilute gas flows. The nonlinear integro-differential Boltzmann equation is the fundamental equation in the kinetic theory of dilute monatomic gases. By replacing the nonlinear fivefold collision integral term by a nonlinear relaxation term, its model equations such as the famous Bhatnagar-Gross-Krook (BGK) equation are mathematically simple. Since the computational cost of solving model equations is much less than that of solving the full Boltzmann equation, the model equations are widely used in predicting rarefied flows, multiphase flows, chemical flows, and turbulent flows although their predictions are only qualitatively right for highly nonequilibrium flows in transitional regime. In this paper the differences between the Boltzmann equation and its model equations are investigated aiming at giving guidelines for the further development of kinetic models. By comparing the Boltzmann equation and its model equations using test cases with different nonequilibrium types, two factors (the information held by nonequilibrium moments and the different relaxation rates of high- and low-speed molecules) are found useful for adjusting the behaviors of modeled collision terms in kinetic regime. The usefulness of these two factors are confirmed by a generalized model collision term derived from a mathematical relation between the Boltzmann equation and BGK equation that is also derived in this paper. After the analysis of the difference between the Boltzmann equation and the BGK equation, an attempt at approximating the collision term is proposed.
Spectral Models Based on Boussinesq Equations
2006-10-03
equations assume periodic solutions apriori. This, however, also forces the question of which extended Boussinesq model to use. Various one- equation ... equations of Nwogu (1993), without the traditional reduction to a one- equation model. Optimal numerical techniques to solve this system of equations are...A. and Madsen, P. A. (2004). "Boussinesq evolution equations : numerical efficiency, breaking and amplitude dispersion," Coastal Engineering, 51, 1117
The Specific Analysis of Structural Equation Models.
McDonald, Roderick P
2004-10-01
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 checks identifiability and lists and tests the implied constraints. This approach is complete for Markov models, but has remained incomplete for models with correlated disturbances. Some new algebraic results overcome the limitations of DAG theory and give a specific form of structural equation analysis that checks identifiability, tests the implied constraints, equation by equation, and gives consistent estimators of the parameters in closed form from the equations. At present the method is limited to recursive models subject to exclusion conditions. With further work, specific structural equation modeling may yield a complete alternative to the present, rather unsatisfactory, global covariance structure analysis.
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…
Structural Equation Modeling with Heavy Tailed Distributions
ERIC Educational Resources Information Center
Yuan, Ke-Hai; Bentler, Peter M.; Chan, Wai
2004-01-01
Data in social and behavioral sciences typically possess heavy tails. Structural equation modeling is commonly used in analyzing interrelations among variables of such data. Classical methods for structural equation modeling fit a proposed model to the sample covariance matrix, which can lead to very inefficient parameter estimates. By fitting a…
Discrete Surface Modelling Using Partial Differential Equations.
Xu, Guoliang; Pan, Qing; Bajaj, Chandrajit L
2006-02-01
We use various nonlinear partial differential equations to efficiently solve several surface modelling problems, including surface blending, N-sided hole filling and free-form surface fitting. The nonlinear equations used include two second order flows, two fourth order flows and two sixth order flows. These nonlinear equations are discretized based on discrete differential geometry operators. The proposed approach is simple, efficient and gives very desirable results, for a range of surface models, possibly having sharp creases and corners.
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…
Stochastic differential equation model to Prendiville processes
NASA Astrophysics Data System (ADS)
Granita, Bahar, Arifah
2015-10-01
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.
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.
Quantifying Parsimony in Structural Equation Modeling
ERIC Educational Resources Information Center
Preacher, Kristopher J.
2006-01-01
Fitting propensity (FP) is defined as a model's average ability to fit diverse data patterns, all else being equal. The relevance of FP to model selection is examined in the context of structural equation modeling (SEM). In SEM it is well known that the number of free model parameters influences FP, but other facets of FP are routinely excluded…
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.
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,…
Structural Equation Modeling with Interchangeable Dyads
ERIC Educational Resources Information Center
Olsen, Joseph A.; Kenny, David A.
2006-01-01
Structural equation modeling (SEM) can be adapted in a relatively straightforward fashion to analyze data from interchangeable dyads (i.e., dyads in which the 2 members cannot be differentiated). The authors describe a general strategy for SEM model estimation, comparison, and fit assessment that can be used with either dyad-level or pairwise…
Entropic lattice Boltzmann model for Burgers's equation.
Boghosian, Bruce M; Love, Peter; Yepez, Jeffrey
2004-08-15
Entropic lattice Boltzmann models are discrete-velocity models of hydrodynamics that possess a Lyapunov function. This feature makes them useful as nonlinearly stable numerical methods for integrating hydrodynamic equations. Over the last few years, such models have been successfully developed for the Navier-Stokes equations in two and three dimensions, and have been proposed as a new category of subgrid model of turbulence. In the present work we develop an entropic lattice Boltzmann model for Burgers's equation in one spatial dimension. In addition to its pedagogical value as a simple example of such a model, our result is actually a very effective way to simulate Burgers's equation in one dimension. At moderate to high values of viscosity, we confirm that it exhibits no trace of instability. At very small values of viscosity, however, we report the existence of oscillations of bounded amplitude in the vicinity of the shock, where gradient scale lengths become comparable with the grid size. As the viscosity decreases, the amplitude at which these oscillations saturate tends to increase. This indicates that, in spite of their nonlinear stability, entropic lattice Boltzmann models may become inaccurate when the ratio of gradient scale length to grid spacing becomes too small. Similar inaccuracies may limit the utility of the entropic lattice Boltzmann paradigm as a subgrid model of Navier-Stokes turbulence.
Geometric investigations of a vorticity model equation
NASA Astrophysics Data System (ADS)
Bauer, Martin; Kolev, Boris; Preston, Stephen C.
2016-01-01
This article consists of a detailed geometric study of the one-dimensional vorticity model equation which is a particular case of the generalized Constantin-Lax-Majda equation. Wunsch showed that this equation is the Euler-Arnold equation on Diff (S1) when the latter is endowed with the right-invariant homogeneous H ˙ 1 / 2-metric. In this article we prove that the exponential map of this Riemannian metric is not Fredholm and that the sectional curvature is locally unbounded. Furthermore, we prove a Beale-Kato-Majda-type blow-up criterion, which we then use to demonstrate a link to our non-Fredholmness result. Finally, we extend a blow-up result of Castro-Córdoba to the periodic case and to a much wider class of initial conditions, using a new generalization of an inequality for Hilbert transforms due to Córdoba-Córdoba.
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.
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…
Perez-Diaz de Cerio, David; Hernández, Ángela; Valenzuela, Jose Luis; Valdovinos, Antonio
2017-01-01
The purpose of this paper is to evaluate from a real perspective the performance of Bluetooth Low Energy (BLE) as a technology that enables fast and reliable discovery of a large number of users/devices in a short period of time. The BLE standard specifies a wide range of configurable parameter values that determine the discovery process and need to be set according to the particular application requirements. Many previous works have been addressed to investigate the discovery process through analytical and simulation models, according to the ideal specification of the standard. However, measurements show that additional scanning gaps appear in the scanning process, which reduce the discovery capabilities. These gaps have been identified in all of the analyzed devices and respond to both regular patterns and variable events associated with the decoding process. We have demonstrated that these non-idealities, which are not taken into account in other studies, have a severe impact on the discovery process performance. Extensive performance evaluation for a varying number of devices and feasible parameter combinations has been done by comparing simulations and experimental measurements. This work also includes a simple mathematical model that closely matches both the standard implementation and the different chipset peculiarities for any possible parameter value specified in the standard and for any number of simultaneous advertising devices under scanner coverage. PMID:28273801
Extracting model equations from experimental data
NASA Astrophysics Data System (ADS)
Friedrich, R.; Siegert, S.; Peinke, J.; Lück, St.; Siefert, M.; Lindemann, M.; Raethjen, J.; Deuschl, G.; Pfister, G.
2000-06-01
This letter wants to present a general data-driven method for formulating suitable model equations for nonlinear complex systems. The method is validated in a quantitative way by its application to experimentally found data of a chaotic electric circuit. Furthermore, the results of an analysis of tremor data from patients suffering from Parkinson's disease, from essential tremor, and from normal subjects with physiological tremor are presented, discussed and compared. They allow a distinction between the different forms of tremor.
Functional Difference Equations and an Epidemic Model.
1980-06-09
ADDRESS 12. REPORT DATE AIR FORCE OFFICE OF SCIENTIFIC RESEARC 913 June 9, 1980 BOLLING AIR FORCE BASE , WASHINGTON, D.tI,3. NUMBEROFAGS 14. MONITORING...allowed spatial effects in an S - I model to arrive at the equation t S(t,x) = S(t,x).J B(;x, )S(t+6,0) dAdO in some region f cR. If X is the ordered
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.
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.
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.
Structural equation modeling in environmental risk assessment.
Buncher, C R; Succop, P A; Dietrich, K N
1991-01-01
Environmental epidemiology requires effective models that take individual observations of environmental factors and connect them into meaningful patterns. Single-factor relationships have given way to multivariable analyses; simple additive models have been augmented by multiplicative (logistic) models. Each of these steps has produced greater enlightenment and understanding. Models that allow for factors causing outputs that can affect later outputs with putative causation working at several different time points (e.g., linkage) are not commonly used in the environmental literature. Structural equation models are a class of covariance structure models that have been used extensively in economics/business and social science but are still little used in the realm of biostatistics. Path analysis in genetic studies is one simplified form of this class of models. We have been using these models in a study of the health and development of infants who have been exposed to lead in utero and in the postnatal home environment. These models require as input the directionality of the relationship and then produce fitted models for multiple inputs causing each factor and the opportunity to have outputs serve as input variables into the next phase of the simultaneously fitted model. Some examples of these models from our research are presented to increase familiarity with this class of models. Use of these models can provide insight into the effect of changing an environmental factor when assessing risk. The usual cautions concerning believing a model, believing causation has been proven, and the assumptions that are required for each model are operative. PMID:2050063
Structural equation modeling for observational studies
Grace, J.B.
2008-01-01
Structural equation modeling (SEM) represents a framework for developing and evaluating complex hypotheses about systems. This method of data analysis differs from conventional univariate and multivariate approaches familiar to most biologists in several ways. First, SEMs are multiequational and capable of representing a wide array of complex hypotheses about how system components interrelate. Second, models are typically developed based on theoretical knowledge and designed to represent competing hypotheses about the processes responsible for data structure. Third, SEM is conceptually based on the analysis of covariance relations. Most commonly, solutions are obtained using maximum-likelihood solution procedures, although a variety of solution procedures are used, including Bayesian estimation. Numerous extensions give SEM a very high degree of flexibility in dealing with nonnormal data, categorical responses, latent variables, hierarchical structure, multigroup comparisons, nonlinearities, and other complicating factors. Structural equation modeling allows researchers to address a variety of questions about systems, such as how different processes work in concert, how the influences of perturbations cascade through systems, and about the relative importance of different influences. I present 2 example applications of SEM, one involving interactions among lynx (Lynx pardinus), mongooses (Herpestes ichneumon), and rabbits (Oryctolagus cuniculus), and the second involving anuran species richness. Many wildlife ecologists may find SEM useful for understanding how populations function within their environments. Along with the capability of the methodology comes a need for care in the proper application of SEM.
Structural equation modeling and natural systems
Grace, James B.
2006-01-01
This book, first published in 2006, 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.
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.
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…
Nearshore Modeling using Rotational Boussinesq Equations
NASA Astrophysics Data System (ADS)
Kennedy, A. B.; Zhang, Y.
2012-12-01
There is a strong tradeoff between accuracy and efficiency in phase-resolving modeling of nearshore waves and currents: Boussinesq-type equations are relatively efficient but lack details of interior velocities and are limited in their range of wavenumbers, while full Navier-Stokes solvers are quite accurate but are slow enough to limit their application to small regions. Here, we present details of a new higher order Boussinesq model which includes rotational motions as part of its derivation, and allows for better representations of surf zone properties while retaining reasonable computational cost. Asymptotic rearrangement techniques allow improvement of wave properties up to very large water depths. A novel absorbing-generating sponge layer allows the simple and accurate generation of both linear and nonlinear regular or irregular waves while simultaneously absorbing outgoing waves. We present breaking and nonbreaking examples of nearshore wave transformation, setup and current generation for a variety of tests.
Applying Meta-Analysis to Structural Equation Modeling
ERIC Educational Resources Information Center
Hedges, Larry V.
2016-01-01
Structural equation models play an important role in the social sciences. Consequently, there is an increasing use of meta-analytic methods to combine evidence from studies that estimate the parameters of structural equation models. Two approaches are used to combine evidence from structural equation models: A direct approach that combines…
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 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.
Partial implicitization. [numerical stability of Burger equation model for Navier-Stokes equation
NASA Technical Reports Server (NTRS)
Graves, R. A., Jr.
1973-01-01
The steady-state solution to the full Navier-Stokes equations for complicated flows is generally difficult to obtain. The Burgers (1948) equation is used as a model of the Navier-Stokes equations. The steady-state solution is obtained by a one-step explicit technique resulting from a partial implicitization of the difference equation. Stability analysis shows that the technique is unconditionally stable, and numerical tests show the technique to be accurate.
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.
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.
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…
Mixture Model for Determination of Shock Equation of State
2012-07-25
mixture model for determining the shock equation of state of composite materials is presented. The model is completely flexible allowing for multiple...2) components. Additionally, error propagation analysis for the two component mixture model has been accomplished. The model predicts the equation of state to
Microscopic models of traveling wave equations
NASA Astrophysics Data System (ADS)
Brunet, Eric; Derrida, Bernard
1999-09-01
Reaction-diffusion problems are often described at a macroscopic scale by partial derivative equations of the type of the Fisher or Kolmogorov-Petrovsky-Piscounov equation. These equations have a continuous family of front solutions, each of them corresponding to a different velocity of the front. By simulating systems of size up to N=1016 particles at the microscopic scale, where particles react and diffuse according to some stochastic rules, we show that a single velocity is selected for the front. This velocity converges logarithmically to the solution of the F-KPP equation with minimal velocity when the number N of particles increases. A simple calculation of the effect introduced by the cutoff due to the microscopic scale allows one to understand the origin of the logarithmic correction.
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…
Stochastic two-fluid model for relativistic heavy-ion collisions
Ayik, S. |; Ivanov, Y.B.; Russkikh, V.N.; Noerenberg, W.
1993-04-01
A reduction of the relativistic Boltzmann-Langevin Equation (BLE), to a stochastic two-fluid model is presented, and transport coefficients associated with fluid dynamical variables are extracted. The approach is applied to investigate equilibration in a counter-streaming nuclear system.
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.
Structural equation modeling: building and evaluating causal models: Chapter 8
Grace, James B.; Scheiner, Samuel M.; Schoolmaster, Donald R.
2015-01-01
Scientists frequently wish to study hypotheses about causal relationships, rather than just statistical associations. This chapter addresses the question of how scientists might approach this ambitious task. Here we describe structural equation modeling (SEM), a general modeling framework for the study of causal hypotheses. Our goals are to (a) concisely describe the methodology, (b) illustrate its utility for investigating ecological systems, and (c) provide guidance for its application. Throughout our presentation, we rely on a study of the effects of human activities on wetland ecosystems to make our description of methodology more tangible. We begin by presenting the fundamental principles of SEM, including both its distinguishing characteristics and the requirements for modeling hypotheses about causal networks. We then illustrate SEM procedures and offer guidelines for conducting SEM analyses. Our focus in this presentation is on basic modeling objectives and core techniques. Pointers to additional modeling options are also given.
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…
Modeling some real phenomena by fractional differential equations
NASA Astrophysics Data System (ADS)
Almeida, Ricardo; Bastos, Nuno R. O.; Monteiro, M. Teresa T.
2016-11-01
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters.
A general non-linear multilevel structural equation mixture model
Kelava, Augustin; Brandt, Holger
2014-01-01
In the past 2 decades latent variable modeling has become a standard tool in the social sciences. In the same time period, traditional linear structural equation models have been extended to include non-linear interaction and quadratic effects (e.g., Klein and Moosbrugger, 2000), and multilevel modeling (Rabe-Hesketh et al., 2004). We present a general non-linear multilevel structural equation mixture model (GNM-SEMM) that combines recent semiparametric non-linear structural equation models (Kelava and Nagengast, 2012; Kelava et al., 2014) with multilevel structural equation mixture models (Muthén and Asparouhov, 2009) for clustered and non-normally distributed data. The proposed approach allows for semiparametric relationships at the within and at the between levels. We present examples from the educational science to illustrate different submodels from the general framework. PMID:25101022
Acoustic Logging Modeling by Refined Biot's Equations
NASA Astrophysics Data System (ADS)
Plyushchenkov, Boris D.; Turchaninov, Victor I.
An explicit uniform completely conservative finite difference scheme for the refined Biot's equations is proposed. This system is modified according to the modern theory of dynamic permeability and tortuosity in a fluid-saturated elastic porous media. The approximate local boundary transparency conditions are constructed. The acoustic logging device is simulated by the choice of appropriate boundary conditions on its external surface. This scheme and these conditions are satisfactory for exploring borehole acoustic problems in permeable formations in a real axial-symmetrical situation. The developed approach can be adapted for a nonsymmetric case also.
Excitability in a stochastic differential equation model for calcium puffs.
Rüdiger, S
2014-06-01
Calcium dynamics are essential to a multitude of cellular processes. For many cell types, localized discharges of calcium through small clusters of intracellular channels are building blocks for all spatially extended calcium signals. Because of the large noise amplitude, the validity of noise-approximating model equations for this system has been questioned. Here we revisit the master equations for local calcium release, examine the multiple scales of calcium concentrations in the cluster domain, and derive adapted stochastic differential equations. We show by comparison of discrete and continuous trajectories that the Langevin equations can be made consistent with the master equations even for very small channel numbers. In its deterministic limit, the model reveals that excitability, a dynamical phenomenon observed in many natural systems, is at the core of calcium puffs. The model also predicts a bifurcation from transient to sustained release which may link local and global calcium signals in cells.
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…
Turbulence modeling methods for the compressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Coakley, T. J.
1983-01-01
Turbulence modeling methods for the compressible Navier-Stokes equations, including several zero- and two-equation eddy-viscosity models, are described and applied. Advantages and disadvantages of the models are discussed with respect to mathematical simplicity, conformity with physical theory, and numerical compatibility with methods. A new two-equation model is introduced which shows advantages over other two-equation models with regard to numerical compatibility and the ability to predict low-Reynolds-number transitional phenomena. Calculations of various transonic airfoil flows are compared with experimental results. A new implicit upwind-differencing method is used which enhances numerical stability and accuracy, and leads to rapidly convergent steady-state solutions.
Modeling with Difference Equations: Two Examples.
ERIC Educational Resources Information Center
Wapner, Leonard M.
1984-01-01
Two models are presented that can be understood by students who have completed second-year algebra, as well as by calculus students. The predator-prey population model and the arms race model are included, with a computer program given for each. (MNS)
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…
Partial Least Squares Structural Equation Modeling with R
ERIC Educational Resources Information Center
Ravand, Hamdollah; Baghaei, Purya
2016-01-01
Structural equation modeling (SEM) has become widespread in educational and psychological research. Its flexibility in addressing complex theoretical models and the proper treatment of measurement error has made it the model of choice for many researchers in the social sciences. Nevertheless, the model imposes some daunting assumptions and…
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
Fractal ladder models and power law wave equations.
Kelly, James F; McGough, Robert J
2009-10-01
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.
A physiologically based model for spirometric reference equations in adults.
Brisman, Jonas; Kim, Jeong-Lim; Olin, Anna-Carin; Torén, Kjell; Bake, Björn
2016-01-01
A spirometric reference equation consists of a mathematical model with constants and coefficients optimized to fit a specific data set from healthy individuals. Commonly applied models are selected on statistical rather than physiological considerations. A predetermined model with constants and coefficients optimized to various populations would enable interpretable and interesting comparisons between populations. Lubiński and Gólczewski recently presented a piecewise linear model with constants and coefficients claimed to be physiologically interpretable (Lubiński model). Three questions were addressed: Is the Lubiński model as useful clinically as other models: multiple linear, piecewise polynomial and exponential with splines? Will reference equations based on the Lubiński model and optimized to a Swedish and to a Polish population allow for interpretable comparisons? Are three well-known reference equations clinically useful in the Swedish adult population? A recent Swedish random population sample with high-quality spirometric measurements enabled the present analyses. When optimized to fit the Swedish population sample, the Lubiński model and two other models provided accurate predictive normal values. Interesting differences were demonstrated between the Polish and Swedish populations. The proportion of subjects below lower limit normal was adequate for the piecewise polynomial equations but too low and not clinically useful for the advocated exponential equations with splines. It is concluded that the Lubiński model is clinically as useful as other models, and it adds important value and is recommended for future spirometric reference equations for adults. The advocated exponential equations with splines are not recommended for Swedish adults because of too wide normal limits.
Approaches to Testing Interaction Effects Using Structural Equation Modeling Methodology.
ERIC Educational Resources Information Center
Li, Fuzhong; Harmer, Peter; Duncan, Terry E.; Duncan, Susan C.; Acock, Alan; Boles, Shawn
1998-01-01
Reviews a single indicator approach and multiple indicator approaches that simplify testing interaction effects using structural equation modeling. An illustrative application examines the interactive effect of perceptions of competence and perceptions of autonomy on exercise-intrinsic motivation. (SLD)
ERIC Educational Resources Information Center
Cheung, Mike W.-L.; Cheung, Shu Fai
2016-01-01
Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM.…
Lattice Boltzmann model for the complex Ginzburg-Landau equation.
Zhang, Jianying; Yan, Guangwu
2010-06-01
A lattice Boltzmann model with complex distribution function for the complex Ginzburg-Landau equation (CGLE) is proposed. By using multiscale technique and the Chapman-Enskog expansion on complex variables, we obtain a series of complex partial differential equations. Then, complex equilibrium distribution function and its complex moments are obtained. Based on this model, the rotation and oscillation properties of stable spiral waves and the breaking-up behavior of unstable spiral waves in CGLE are investigated in detail.
Equations of state in a lattice Boltzmann model
NASA Astrophysics Data System (ADS)
Yuan, Peng; Schaefer, Laura
2006-04-01
In this paper we consider the incorporation of various equations of state into the single-component multiphase lattice Boltzmann model. Several cubic equations of state, including the van der Waals, Redlich-Kwong, and Peng-Robinson, as well as a noncubic equation of state (Carnahan-Starling), are incorporated into the lattice Boltzmann model. The details of phase separation in these nonideal single-component systems are presented by comparing the numerical simulation results in terms of density ratios, spurious currents, and temperature ranges. A comparison with a real fluid system, i.e., the properties of saturated water and steam, is also presented.
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.
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
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.
Update to Core reporting practices in structural equation modeling.
Schreiber, James B
2016-07-21
This paper is a technical update to "Core Reporting Practices in Structural Equation Modeling."(1) As such, the content covered in this paper includes, sample size, missing data, specification and identification of models, estimation method choices, fit and residual concerns, nested, alternative, and equivalent models, and unique issues within the SEM family of techniques.
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,…
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)
Hopes and Cautions in Implementing Bayesian Structural Equation Modeling
ERIC Educational Resources Information Center
MacCallum, Robert C.; Edwards, Michael C.; Cai, Li
2012-01-01
Muthen and Asparouhov (2012) have proposed and demonstrated an approach to model specification and estimation in structural equation modeling (SEM) using Bayesian methods. Their contribution builds on previous work in this area by (a) focusing on the translation of conventional SEM models into a Bayesian framework wherein parameters fixed at zero…
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…
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…
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.
Two equation modelling and the pseudo compressibility technique
NASA Technical Reports Server (NTRS)
Steffen, C. J., Jr.
1992-01-01
The primary objective of the Center for Modelling of Turbulence and Transition (CMOTT) is to further the understanding of turbulence theory for engineering applications. One important foundation is the establishment of a data base encompassing the multitude of existing models as well as newly proposed ideas. The research effort described is a precursor to an extended survey of two equation turbulence models in the presence of a separated shear layer. Recently, several authors have examined the performance of two equation models in the context of the backward facing step flow. Conflicting results, however, demand that further attention is necessary to properly understand the behavior and limitations of this popular technique, especially the low Reynolds number formulations. The objective is to validate an incompressible Navier Stokes code for use as a numerical test-bed. In turn, this code will be used for analyzing the performance of several two equation models.
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.
The Causal Foundations of Structural Equation Modeling
2012-02-16
interpretation of SEM as “self-contradictory,” and none of the 11 discussants of his paper were able to detect his error and to articulate the correct...adequacy to serve as a language for causation. Sobel (1996), for example, states that the interpretation of the parameters of SEM model as effects “do...outcome framework, Sobel (2008) asserts that “In general (even in randomized studies), the structural and causal parameters are not equal, implying that
Tropospheric Propagation Modelling with the Parabolic Equation
1990-09-01
raised cosine window to the imaginary part of the square of the refractive index term. From the fust exponential term of (29) it is evident that this...the present implementation of the model, this low pass filtering of spatial frequency is achieved by applying a simple raised cosine window to the...range in thickness from a few metres (these tend to affect propagation above microwave frequencies) up to hundreds of metres (affecting propagation at
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.
Controllability in Hybrid Kinetic Equations Modeling Nonequilibrium Multicellular Systems
Bianca, Carlo
2013-01-01
This paper is concerned with the derivation of hybrid kinetic partial integrodifferential equations that can be proposed for the mathematical modeling of multicellular systems subjected to external force fields and characterized by nonconservative interactions. In order to prevent an uncontrolled time evolution of the moments of the solution, a control operator is introduced which is based on the Gaussian thermostat. Specifically, the analysis shows that the moments are solution of a Riccati-type differential equation. PMID:24191137
Kirchhoff modeling via wave equation datuming
NASA Astrophysics Data System (ADS)
Sullivan, M.
1985-01-01
The acoustic reflection response of a plane wave on a cylindrical surface is calculated from a specialization of the Kirchhoff integral. Computational advantages are obtained by assuming that structural changes occur only along the direction of data collection. Off-line geologic invariance permits an integral to be replaced by a short convolution operator. The restriction to single interface modeling permits implementation of personal computers. Also, the single layer algorithm provides the framework for a multilayer code. Details on implementation, example executions, and program listings are included.
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
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
2016-06-03
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.
Nonautonomous equations of complicated Roessler's model and bifurcation cascades
NASA Astrophysics Data System (ADS)
Sanin, Andrey L.; Bagmanov, Andrey T.
2003-10-01
The first differential equation of the Rossler model was supplemented by the term that depends explicitly on time. The cosine amplitude defines external action on this dynamical system, and at some value of the amplitude dynamical chaos is possible. Properties of non-autonomous differential equations were investigated by using the standard methods of nonlinear dynamics including the fast Fourier transformation, point maps, phase trajectory projections. The bifurcation cascades were found under variations of the amplitude. The dynamical model presented can be considered as development of the Rossler simple model.
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.
Play Context, Commitment, and Dating Violence: A Structural Equation Model
ERIC Educational Resources Information Center
Gonzalez-Mendez, Rosaura; Hernandez-Cabrera, Juan Andres
2009-01-01
This study develops a structural equation model to describe the effect of two groups of factors (type of commitment and play context) on the violence experienced during intimate partner conflict. After contrasting the model in adolescents and university students, we have confirmed that aggressive play and the simulation of jealousy and anger…
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…
Maximum Likelihood Estimation in Meta-Analytic Structural Equation Modeling
ERIC Educational Resources Information Center
Oort, Frans J.; Jak, Suzanne
2016-01-01
Meta-analytic structural equation modeling (MASEM) involves fitting models to a common population correlation matrix that is estimated on the basis of correlation coefficients that are reported by a number of independent studies. MASEM typically consist of two stages. The method that has been found to perform best in terms of statistical…
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…
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…
On Nonequivalence of Several Procedures of Structural Equation Modeling
ERIC Educational Resources Information Center
Yuan, Ke-Hai; Chan, Wai
2005-01-01
The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are: the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically distribution-free procedure. When data are normally distributed and the model structure…
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…
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…
Structural Equation Modeling of School Violence Data: Methodological Considerations
ERIC Educational Resources Information Center
Mayer, Matthew J.
2004-01-01
Methodological challenges associated with structural equation modeling (SEM) and structured means modeling (SMM) in research on school violence and related topics in the social and behavioral sciences are examined. Problems associated with multiyear implementations of large-scale surveys are discussed. Complex sample designs, part of any…
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…
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.
The Mars Global Surveyor Ka-Band Link Experiment (MGS/KaBLE-II)
NASA Astrophysics Data System (ADS)
Morabito, D.; Butman, S.; Shambayati, S.
1999-01-01
The Mars Global Surveyor (MGS) spacecraft, launched on November 7, 1996, carries an experimental space-to-ground telecommunications link at Ka-band (32 GHz) along with the primary X-band (8.4-GHz) downlink. The signals are simultaneously transmitted from a 1.5-m-diameter parabolic antenna on MGS and received by a beam-waveguide (BWG) research and development (R&D) 34-meter a ntenna located in NASA's Goldstone Deep Space Network (DSN) complex near Barstow, California. This Ka-band link experiment (KaBLE-II) allows the performances of the Ka-band and X-band signals to be compared under nearly identical conditions. The two signals have been regularly tracked during the past 2 years. This article presents carrier-signal-level data (P_c/N_o) for both X-band and Ka-band acquired over a wide range of station elevation angles, weather conditions, and solar elongation angles. The cruise phase of the mission covered the period from launch (November 7, 1996) to Mars orbit capture (September 12, 1997). Since September 12, 1997, MGS has been in orbit around Mars. The measurements confirm that Ka-band could increase data capacity by at least a factor of three (5 dB) as compared with X-band. During May 1998, the solar corona experiment, in which the effects of solar plasma on the X-band and Ka-band links were studied, was conducted. In addition, frequency and difference frequency (f_x - f_(Ka)/3.8), ranging, and telemetry data results are presented. MGS/KaBLE-II measured signal strengths (for 54 percent of the experiments conducted) that were in reasonable agreement with predicted values based on preflight knowledge, and frequency residuals that agreed between bands and whose statistics were consistent with expected noise sources. For passes in which measured signal strengths disagreed with predicted values, the problems were traced to known deficiencies, for example, equipment operating under certain conditions, such as a cold Ka-band solid-state power amplifier (SSPA
Miao, Hongyu; Dykes, Carrie; Demeter, Lisa M; Wu, Hulin
2009-03-01
Many biological processes and systems can be described by a set of differential equation (DE) models. However, literature in statistical inference for DE models is very sparse. We propose statistical estimation, model selection, and multimodel averaging methods for HIV viral fitness experiments in vitro that can be described by a set of nonlinear ordinary differential equations (ODE). The parameter identifiability of the ODE models is also addressed. We apply the proposed methods and techniques to experimental data of viral fitness for HIV-1 mutant 103N. We expect that the proposed modeling and inference approaches for the DE models can be widely used for a variety of biomedical studies.
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
Maximum likelihood estimation in meta-analytic structural equation modeling.
Oort, Frans J; Jak, Suzanne
2016-06-01
Meta-analytic structural equation modeling (MASEM) involves fitting models to a common population correlation matrix that is estimated on the basis of correlation coefficients that are reported by a number of independent studies. MASEM typically consist of two stages. The method that has been found to perform best in terms of statistical properties is the two-stage structural equation modeling, in which maximum likelihood analysis is used to estimate the common correlation matrix in the first stage, and weighted least squares analysis is used to fit structural equation models to the common correlation matrix in the second stage. In the present paper, we propose an alternative method, ML MASEM, that uses ML estimation throughout. In a simulation study, we use both methods and compare chi-square distributions, bias in parameter estimates, false positive rates, and true positive rates. Both methods appear to yield unbiased parameter estimates and false and true positive rates that are close to the expected values. ML MASEM parameter estimates are found to be significantly less bias than two-stage structural equation modeling estimates, but the differences are very small. The choice between the two methods may therefore be based on other fundamental or practical arguments. Copyright © 2016 John Wiley & Sons, Ltd.
Modelling biochemical reaction systems by stochastic differential equations with reflection.
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
2016-05-07
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.
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.
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
Kinetic equations modelling wealth redistribution: A comparison of approaches
NASA Astrophysics Data System (ADS)
Düring, Bertram; Matthes, Daniel; Toscani, Giuseppe
2008-11-01
Kinetic equations modelling the redistribution of wealth in simple market economies is one of the major topics in the field of econophysics. We present a unifying approach to the qualitative study for a large variety of such models, which is based on a moment analysis in the related homogeneous Boltzmann equation, and on the use of suitable metrics for probability measures. In consequence, we are able to classify the most important feature of the steady wealth distribution, namely the fatness of the Pareto tail, and the dynamical stability of the latter in terms of the model parameters. Our results apply, e.g., to the market model with risky investments [S. Cordier, L. Pareschi, and G. Toscani, J. Stat. Phys. 120, 253 (2005)], and to the model with quenched saving propensities [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica A 335, 155 (2004)]. Also, we present results from numerical experiments that confirm the theoretical predictions.
Kinetic equations modelling wealth redistribution: a comparison of approaches.
Düring, Bertram; Matthes, Daniel; Toscani, Giuseppe
2008-11-01
Kinetic equations modelling the redistribution of wealth in simple market economies is one of the major topics in the field of econophysics. We present a unifying approach to the qualitative study for a large variety of such models, which is based on a moment analysis in the related homogeneous Boltzmann equation, and on the use of suitable metrics for probability measures. In consequence, we are able to classify the most important feature of the steady wealth distribution, namely the fatness of the Pareto tail, and the dynamical stability of the latter in terms of the model parameters. Our results apply, e.g., to the market model with risky investments [S. Cordier, L. Pareschi, and G. Toscani, J. Stat. Phys. 120, 253 (2005)], and to the model with quenched saving propensities [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica A 335, 155 (2004)]. Also, we present results from numerical experiments that confirm the theoretical predictions.
Shallow water modeling of Antarctic Bottom Water crossing the equator
NASA Astrophysics Data System (ADS)
Choboter, Paul F.; Swaters, Gordon E.
2004-03-01
The dynamics of abyssal equator-crossing flows are examined by studying simplified models of the flow in the equatorial region in the context of reduced-gravity shallow water theory. A simple "frictional geostrophic" model for one-layer cross-equatorial flow is described, in which geostrophy is replaced at the equator by frictional flow down the pressure gradient. This model is compared via numerical simulations to the one-layer reduced-gravity shallow water model for flow over realistic equatorial Atlantic Ocean bottom topography. It is argued that nonlinear advection is important at key locations where it permits the current to flow against a pressure gradient, a mechanism absent in the frictional geostrophic model and one of the reasons this model predicts less cross-equatorial flow than the shallow water model under similar conditions. Simulations of the shallow water model with an annually varying mass source reproduce the correct amplitude of observed time variability of cross-equatorial flow. The time evolution of volume transport across specific locations suggests that mass is stored in an equatorial basin, which can reduce the amplitude of time dependence of fluid actually proceeding into the Northern Hemisphere as compared to the amount entering the equatorial basin. Observed time series of temperature data at the equator are shown to be consistent with this hypothesis.
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…
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…
Investigating Supervisory Relationships and Therapeutic Alliances Using Structural Equation Modeling
ERIC Educational Resources Information Center
DePue, Mary Kristina; Lambie, Glenn W.; Liu, Ren; Gonzalez, Jessica
2016-01-01
The authors used structural equation modeling to examine the contribution of supervisees' supervisory relationship levels to therapeutic alliance (TA) scores with their clients in practicum. Results showed that supervisory relationship scores positively contributed to the TA. Client and counselor ratings of the TA also differed.
Case-Deletion Diagnostics for Nonlinear Structural Equation Models
ERIC Educational Resources Information Center
Lee, Sik-Yum; Lu, Bin
2003-01-01
In this article, a case-deletion procedure is proposed to detect influential observations in a nonlinear structural equation model. The key idea is to develop the diagnostic measures based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. An one-step pseudo approximation is proposed to reduce the…
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…
Fitting Meta-Analytic Structural Equation Models with Complex Datasets
ERIC Educational Resources Information Center
Wilson, Sandra Jo; Polanin, Joshua R.; Lipsey, Mark W.
2016-01-01
A modification of the first stage of the standard procedure for two-stage meta-analytic structural equation modeling for use with large complex datasets is presented. This modification addresses two common problems that arise in such meta-analyses: (a) primary studies that provide multiple measures of the same construct and (b) the correlation…
Solutions for Missing Data in Structural Equation Modeling
ERIC Educational Resources Information Center
Carter, Rufus Lynn
2006-01-01
Many times in both educational and social science research it is impossible to collect data that is complete. When administering a survey, for example, people may answer some questions and not others. This missing data causes a problem for researchers using structural equation modeling (SEM) techniques for data analyses. Because SEM and…
An Estimating Equations Approach for the LISCOMP Model.
ERIC Educational Resources Information Center
Reboussin, Beth A.; Liang, Kung-Lee
1998-01-01
A quadratic estimating equations approach for the LISCOMP model is proposed that only requires specification of the first two moments. This method is compared with a three-stage generalized least squares approach through a numerical study and application to a study of life events and neurotic illness. (SLD)
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…
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…
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…
Multiple Imputation Strategies for Multiple Group Structural Equation Models
ERIC Educational Resources Information Center
Enders, Craig K.; Gottschall, Amanda C.
2011-01-01
Although structural equation modeling software packages use maximum likelihood estimation by default, there are situations where one might prefer to use multiple imputation to handle missing data rather than maximum likelihood estimation (e.g., when incorporating auxiliary variables). The selection of variables is one of the nuances associated…
In-out intermittency in partial differential equation and ordinary differential equation models.
Covas, Eurico; Tavakol, Reza; Ashwin, Peter; Tworkowski, Andrew; Brooke, John M.
2001-06-01
We find concrete evidence for a recently discovered form of intermittency, referred to as in-out intermittency, in both partial differential equation (PDE) and ordinary differential equation (ODE) models of mean field dynamos. This type of intermittency [introduced in P. Ashwin, E. Covas, and R. Tavakol, Nonlinearity 9, 563 (1999)] occurs in systems with invariant submanifolds and, as opposed to on-off intermittency which can also occur in skew product systems, it requires an absence of skew product structure. By this we mean that the dynamics on the attractor intermittent to the invariant manifold cannot be expressed simply as the dynamics on the invariant subspace forcing the transverse dynamics; the transverse dynamics will alter that tangential to the invariant subspace when one is far enough away from the invariant manifold. Since general systems with invariant submanifolds are not likely to have skew product structure, this type of behavior may be of physical relevance in a variety of dynamical settings. The models employed here to demonstrate in-out intermittency are axisymmetric mean-field dynamo models which are often used to study the observed large-scale magnetic variability in the Sun and solar-type stars. The occurrence of this type of intermittency in such models may be of interest in understanding some aspects of such variabilities. (c) 2001 American Institute of Physics.
Bayesian analysis of structural equation models with dichotomous variables.
Lee, Sik-Yum; Song, Xin-Yuan
2003-10-15
Structural equation modelling has been used extensively in the behavioural and social sciences for studying interrelationships among manifest and latent variables. Recently, its uses have been well recognized in medical research. This paper introduces a Bayesian approach to analysing general structural equation models with dichotomous variables. In the posterior analysis, the observed dichotomous data are augmented with the hypothetical missing values, which involve the latent variables in the model and the unobserved continuous measurements underlying the dichotomous data. An algorithm based on the Gibbs sampler is developed for drawing the parameters values and the hypothetical missing values from the joint posterior distributions. Useful statistics, such as the Bayesian estimates and their standard error estimates, and the highest posterior density intervals, can be obtained from the simulated observations. A posterior predictive p-value is used to test the goodness-of-fit of the posited model. The methodology is applied to a study of hypertensive patient non-adherence to medication.
Model Predictive Control for Nonlinear Parabolic Partial Differential Equations
NASA Astrophysics Data System (ADS)
Hashimoto, Tomoaki; Yoshioka, Yusuke; Ohtsuka, Toshiyuki
In this study, the optimal control problem of nonlinear parabolic partial differential equations (PDEs) is investigated. Optimal control of nonlinear PDEs is an open problem with applications that include fluid, thermal, biological, and chemically-reacting systems. Model predictive control with a fast numerical solution method has been well established to solve the optimal control problem of nonlinear systems described by ordinary differential equations. In this study, we develop a design method of the model predictive control for nonlinear systems described by parabolic PDEs. Our approach is a direct infinite dimensional extension of the model predictive control method for finite-dimensional systems. The objective of this paper is to develop an efficient algorithm for numerically solving the model predictive control problem of nonlinear parabolic PDEs. The effectiveness of the proposed method is verified by numerical simulations.
Nonzero solutions of nonlinear integral equations modeling infectious disease
Williams, L.R.; Leggett, R.W.
1982-01-01
Sufficient conditions to insure the existence of periodic solutions to the nonlinear integral equation, x(t) = ..integral../sup t//sub t-tau/f(s,x(s))ds, are given in terms of simple product and product integral inequalities. The equation can be interpreted as a model for the spread of infectious diseases (e.g., gonorrhea or any of the rhinovirus viruses) if x(t) is the proportion of infectives at time t and f(t,x(t)) is the proportion of new infectives per unit time.
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.
Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
NASA Astrophysics Data System (ADS)
Chen, Hua; Sasakura, Naoki; Sato, Yuki
2017-03-01
The canonical tensor model (CTM) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. The constraint algebra of CTM has a similar structure as that of the Arnowitt-Deser-Misner formalism of general relativity, and it is studied as a discretized model for quantum gravity. In this paper, we analyze the classical equation of motion (EOM) of CTM in a formal continuum limit through a derivative expansion of the tensor of CTM up to the fourth order, and we show that it is the same as the EOM of a coupled system of gravity and a scalar field derived from the Hamilton-Jacobi equation with an appropriate choice of an action. The action contains a scalar field potential of an exponential form, and the system classically respects a dilatational symmetry. We find that the system has a critical dimension, given by six, over which it becomes unstable due to the wrong sign of the scalar kinetic term. In six dimensions, de Sitter spacetime becomes a solution to the EOM, signaling the emergence of a conformal symmetry, while the time evolution of the scale factor is a power law in dimensions below six.
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.
Structural equation modeling in the context of clinical research
2017-01-01
Structural equation modeling (SEM) has been widely used in economics, sociology and behavioral science. However, its use in clinical medicine is quite limited, probably due to technical difficulties. Because SEM is particularly suitable for analysis of complex relationships among observed variables, it must have potential applications to clinical medicine. The article introduces basic ideas of SEM in the context of clinical medicine. A simulated dataset is employed to show how to do model specification, model fit, visualization and assessment of goodness-of-fit. The first example fits a SEM with continuous outcome variable using sem() function, and the second explores the binary outcome variable using lavaan() function. PMID:28361067
Estimating varying coefficients for partial differential equation models.
Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J
2017-01-11
Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data.
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
Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L
2015-01-01
Background There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). Methodology We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δkm=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value of the prediction errors for methadone’s extraction and throughput were less than 2%. Conclusion ODE/PDE modeling of methadone’s hemodialysis is a new approach to study methadone’s removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone’s mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model
Exact solutions of kinetic equations in an autocatalytic growth model.
Jędrak, Jakub
2013-02-01
Kinetic equations are introduced for the transition-metal nanocluster nucleation and growth mechanism, as proposed by Watzky and Finke [J. Am. Chem. Soc. 119, 10382 (1997)]. Equations of this type take the form of Smoluchowski coagulation equations supplemented with the terms responsible for the chemical reactions. In the absence of coagulation, we find complete analytical solutions of the model equations for the autocatalytic rate constant both proportional to the cluster mass, and the mass-independent one. In the former case, ξ(k)=s(k)(ξ(1))[proportionality]ξ(1)(k)/k was obtained, while in the latter, the functional form of s(k)(ξ(1)) is more complicated. In both cases, ξ(1)(t)=h(μ)(M(μ)(t)) is a function of the moments of the mass distribution. Both functions, s(k)(ξ(1)) and h(μ)(M(μ)), depend on the assumed mechanism of autocatalytic growth and monomer production, and not on other chemical reactions present in a system.
The Interface Between Theory and Data in Structural Equation Models
Grace, James B.; Bollen, Kenneth A.
2006-01-01
Structural equation modeling (SEM) holds the promise of providing natural scientists the capacity to evaluate complex multivariate hypotheses about ecological systems. Building on its predecessors, path analysis and factor analysis, SEM allows for the incorporation of both observed and unobserved (latent) variables into theoretically based probabilistic models. In this paper we discuss the interface between theory and data in SEM and the use of an additional variable type, the composite, for representing general concepts. In simple terms, composite variables specify the influences of collections of other variables and can be helpful in modeling general relationships of the sort commonly of interest to ecologists. While long recognized as a potentially important element of SEM, composite variables have received very limited use, in part because of a lack of theoretical consideration, but also because of difficulties that arise in parameter estimation when using conventional solution procedures. In this paper we present a framework for discussing composites and demonstrate how the use of partially reduced form models can help to overcome some of the parameter estimation and evaluation problems associated with models containing composites. Diagnostic procedures for evaluating the most appropriate and effective use of composites are illustrated with an example from the ecological literature. It is argued that an ability to incorporate composite variables into structural equation models may be particularly valuable in the study of natural systems, where concepts are frequently multifaceted and the influences of suites of variables are often of interest.
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
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…
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.
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.
Compact stellar models obeying quadratic equation of state
NASA Astrophysics Data System (ADS)
Bhar, Piyali; Singh, Ksh. Newton; Pant, Neeraj
2016-10-01
In present paper we obtain a new model of compact star by considering quadratic equation of state for the matter distribution and assuming a physically reasonable choice for metric coefficient g_{rr}. The solution is singularity free and well behaved inside the stellar interior. Several features are described analytically as well as graphically. From our analysis we have shown that our model is compatible with the observational data of the compact stars. We have discussed a detail analysis of neutron star PSR J1614-2230 via different graphs after determining all the constant parameters from boundary conditions.
Structural equation models of VMT growth in US urbanised areas.
Ewing, Reid; Hamidi, Shima; Gallivan, Frank; Nelson, Arthur C.; Grace, James B.
2014-01-01
Vehicle miles travelled (VMT) is a primary performance indicator for land use and transportation, bringing with it both positive and negative externalities. This study updates and refines previous work on VMT in urbanised areas, using recent data, additional metrics and structural equation modelling (SEM). In a cross-sectional model for 2010, population, income and freeway capacity are positively related to VMT, while gasoline prices, development density and transit service levels are negatively related. Findings of the cross-sectional model are generally confirmed in a more tightly controlled longitudinal study of changes in VMT between 2000 and 2010, the first model of its kind. The cross-sectional and longitudinal models together, plus the transportation literature generally, give us a basis for generalising across studies to arrive at elasticity values of VMT with respect to different urban variables.
Cause and cure of sloppiness in ordinary differential equation models.
Tönsing, Christian; Timmer, Jens; Kreutz, Clemens
2014-08-01
Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.
Cause and cure of sloppiness in ordinary differential equation models
NASA Astrophysics Data System (ADS)
Tönsing, Christian; Timmer, Jens; Kreutz, Clemens
2014-08-01
Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark 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.
An improved shallow water equation model for water animation
NASA Astrophysics Data System (ADS)
Ai, Mingjing; Du, Anding; Xu, Han; Niu, Jianwei
2017-03-01
In this paper, we proposed a new scheme for simulating water flows under shallow water assumption. The method is an extension of traditional shallow water equations. In contrast to traditional methods, we design a dynamic coordinate system for modeling in order to efficiently simulate water flows. Within this system, we derive our specialized shallow water equations directly from the Navier-Stockes equation. At the same time, we develop an implicit mechanism for solving the advection term and a vector projection operator for solving the external forces acting on water. We also present a two-way coupling method for simulating the interaction between water and rigid solid. The experimental results show that the proposed scheme can achieve a more realistic and accurate water model compared with the traditional methods, especially when the solid surfaces are too steep. Also we demonstrate the efficiency of our method in several scenes, all run at least 50 frames per second on average which allows real-time simulation.
A delay differential equation model of follicle waves in women.
Panza, Nicole M; Wright, Andrew A; Selgrade, James F
2016-01-01
This article presents a mathematical model for hormonal regulation of the menstrual cycle which predicts the occurrence of follicle waves in normally cycling women. Several follicles of ovulatory size that develop sequentially during one menstrual cycle are referred to as follicle waves. The model consists of 13 nonlinear, delay differential equations with 51 parameters. Model simulations exhibit a unique stable periodic cycle and this menstrual cycle accurately approximates blood levels of ovarian and pituitary hormones found in the biological literature. Numerical experiments illustrate that the number of follicle waves corresponds to the number of rises in pituitary follicle stimulating hormone. Modifications of the model equations result in simulations which predict the possibility of two ovulations at different times during the same menstrual cycle and, hence, the occurrence of dizygotic twins via a phenomenon referred to as superfecundation. Sensitive parameters are identified and bifurcations in model behaviour with respect to parameter changes are discussed. Studying follicle waves may be helpful for improving female fertility and for understanding some aspects of female reproductive ageing.
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.
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.
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.
Equation-of-state modeling of mixtures with ionic liquids.
Tsioptsias, Costas; Tsivintzelis, Ioannis; Panayiotou, Costas
2010-05-14
A non-electrolyte equation-of-state model was used to describe the phase behavior of binary systems containing alkyl-methyimidazolium bis(trifluoromethyl-sulfonyl)imide ionic liquids. A methodology is suggested for modeling this phase behavior by using the Non-Random Hydrogen-Bonding (NRHB) model. According to this methodology, the scaling constants of the ionic liquid are calculated using limited available experimental data on liquid densities and Hansen's solubility parameters, while all electrostatic interactions (polar, hydrogen bonding and ionic) are treated as strong specific interactions. Using the aforementioned methodology, the model is applied to describe the vapor-liquid and the liquid-liquid equilibria in mixtures of ionic liquids with various polar or quadrupolar solvents at low and high pressures. In all cases, one temperature-independent binary interaction parameter was used. Accurate correlations were obtained for the majority of the systems, both, for vapor-liquid and liquid-liquid equilibria.
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.
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.
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…
Model equation for strongly focused finite-amplitude sound beams
Kamakura; Ishiwata; Matsuda
2000-06-01
A model equation that describes the propagation of sound beams in a fluid is developed using the oblate spheroidal coordinate system. This spheroidal beam equation (SBE) is a parabolic equation and has a specific application to a theoretical prediction on focused, high-frequency beams from a circular aperture. The aperture angle does not have to be small. The theoretical background is basically along the same analytical lines as the composite method (CM) reported previously [B. Ystad and J. Berntsen, Acustica 82, 698-706 (1996)]. Numerical examples are displayed for the amplitudes of sound pressure along and across the beam axis when sinusoidal waves are radiated from the source with uniform amplitude distribution. The primitive approach to linear field analysis is readily extended to the case where harmonic generation in finite-amplitude sound beams becomes significant due to the inherent nonlinearity of the medium. The theory provides the propagation and beam pattern profiles that differ from the CM solution for each harmonic component.
Cheung, Mike W-L; Cheung, Shu Fai
2016-06-01
Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM. Random-effects models are well known in conventional meta-analysis but are less studied in MASEM. The primary objective of this paper was to address issues related to random-effects models in MASEM. Specifically, we compared two different random-effects models in MASEM-correlation-based MASEM and parameter-based MASEM-and explored their strengths and limitations. Two examples were used to illustrate the similarities and differences between these models. We offered some practical guidelines for choosing between these two models. Future directions for research on random-effects models in MASEM were also discussed. Copyright © 2016 John Wiley & Sons, Ltd.
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
Partial differential equation models in the socio-economic sciences.
Burger, Martin; Caffarelli, Luis; Markowich, Peter A
2014-11-13
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.
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.
Bloch-Redfield equations for modeling light-harvesting complexes.
Jeske, Jan; Ing, David J; Plenio, Martin B; Huelga, Susana F; Cole, Jared H
2015-02-14
We challenge the misconception that Bloch-Redfield equations are a less powerful tool than phenomenological Lindblad equations for modeling exciton transport in photosynthetic complexes. This view predominantly originates from an indiscriminate use of the secular approximation. We provide a detailed description of how to model both coherent oscillations and several types of noise, giving explicit examples. All issues with non-positivity are overcome by a consistent straightforward physical noise model. Herein also lies the strength of the Bloch-Redfield approach because it facilitates the analysis of noise-effects by linking them back to physical parameters of the noise environment. This includes temporal and spatial correlations and the strength and type of interaction between the noise and the system of interest. Finally, we analyze a prototypical dimer system as well as a 7-site Fenna-Matthews-Olson complex in regards to spatial correlation length of the noise, noise strength, temperature, and their connection to the transfer time and transfer probability.
Renormalization group flow equations for chiral nuclear models
NASA Astrophysics Data System (ADS)
Johnson, Andrew Sheriden
1997-10-01
facto use of the hydrodynamic limit fails both qualitatively and quantitatively. These systems require the use of the RG for an understanding beyond that provided by the hydrodynamic continuum limit or mean field theory. Next we discuss the derivation of the exact RG equations and the differential flow equations under various approximations for model field theories containing both bosonic and fermionic degrees of freedom. The RG flow equations for the boson and generalized Yukawa effective potentials to leading order (LO) in the derivative expansion (DE) are derived in detail and compared with previously published results. The derivation of the σ-model flow equations is outlined and the results, which are quite lengthy, are catalogued in an appendix. We present the numerical solution of the LO flow equations for the Yukawa coupled fermions and the σ-model treating the field variables and the momentum scale as independent continuous variables. The results for the flow of the boson and fermion Yukawa couplings are in agreement with those previously published. The results for the σ-model include the calculation of πpi scattering lengths which are an improvement on the old perturbative calculation and essentially in agreement with experiment. (Abstract shortened by UMI.)
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.
Accurate two-equation modelling of falling film flows
NASA Astrophysics Data System (ADS)
Ruyer-Quil, Christian
2015-11-01
The low-dimensional modeling of the wave dynamics of a falling liquid film on an inclined plane is revisited. The advantages and shortcomings of existing modelling approaches: weighted residual method, center-manifold analysis, consistent Saint-Venant approach are discussed and contrasted. A novel formulation of a two-equation consistent model is proposed. The proposed formulation cures the principal limitations of previous approaches: (i) apart from surface tension terms, it admits a conservative form which enables to make use of efficient numerical schemes, (ii) it recovers with less than 1 percent of error the asymptotic speed of solitary waves in the inertial regime found by DNS, (iii) it adequately captures the velocity field under the waves and in particular the wall drag. Research supported by Insitut Universitaire de France.
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.
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.
Modeling ion channel dynamics through reflected stochastic differential equations
NASA Astrophysics Data System (ADS)
Dangerfield, Ciara E.; Kay, David; Burrage, Kevin
2012-05-01
Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the “gold standard,” but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks.
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.
2014-04-01
downstream boundary (when needed) is obtained by extrapolation, taking into account the hyperbolic character of the equation . By separating the...for Developing Reduced Order Models of Reaction-Advection Equations 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT...advection scalar equation is used as a representative equation to investigate the overall approach. Both linear and nonlinear model equations are
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.
How motivation affects academic performance: a structural equation modelling analysis.
Kusurkar, R A; Ten Cate, Th J; Vos, C M P; Westers, P; Croiset, G
2013-03-01
Few studies in medical education have studied effect of quality of motivation on performance. Self-Determination Theory based on quality of motivation differentiates between Autonomous Motivation (AM) that originates within an individual and Controlled Motivation (CM) that originates from external sources. To determine whether Relative Autonomous Motivation (RAM, a measure of the balance between AM and CM) affects academic performance through good study strategy and higher study effort and compare this model between subgroups: males and females; students selected via two different systems namely qualitative and weighted lottery selection. Data on motivation, study strategy and effort was collected from 383 medical students of VU University Medical Center Amsterdam and their academic performance results were obtained from the student administration. Structural Equation Modelling analysis technique was used to test a hypothesized model in which high RAM would positively affect Good Study Strategy (GSS) and study effort, which in turn would positively affect academic performance in the form of grade point averages. This model fit well with the data, Chi square = 1.095, df = 3, p = 0.778, RMSEA model fit = 0.000. This model also fitted well for all tested subgroups of students. Differences were found in the strength of relationships between the variables for the different subgroups as expected. In conclusion, RAM positively correlated with academic performance through deep strategy towards study and higher study effort. This model seems valid in medical education in subgroups such as males, females, students selected by qualitative and weighted lottery selection.
Sensitivity of Material Response Calculations to the Equation of State Model
equation of state model. Three equation of state models, all...sources. The sensitivity of the calculated material response to the choice of equation of state model is characterized in terms of the generated impulse...and the peak propagating stress at the time the radiation source is cut off. For the calculations presented in this report, the three equation of state models are in fairly good
ERIC Educational Resources Information Center
Macho, Siegfried; Ledermann, Thomas
2011-01-01
The phantom model approach for estimating, testing, and comparing specific effects within structural equation models (SEMs) is presented. The rationale underlying this novel method consists in representing the specific effect to be assessed as a total effect within a separate latent variable model, the phantom model that is added to the main…
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…
On the specification of structural equation models for ecological systems
Grace, J.B.; Michael, Anderson T.; Han, O.; Scheiner, S.M.
2010-01-01
The use of structural equation modeling (SEM) is often motivated by its utility for investigating complex networks of relationships, but also because of its promise as a means of representing theoretical concepts using latent variables. In this paper, we discuss characteristics of ecological theory and some of the challenges for proper specification of theoretical ideas in structural equation models (SE models). In our presentation, we describe some of the requirements for classical latent variable models in which observed variables (indicators) are interpreted as the effects of underlying causes. We also describe alternative model specifications in which indicators are interpreted as having causal influences on the theoretical concepts. We suggest that this latter nonclassical specification (which involves another variable type-the composite) will often be appropriate for ecological studies because of the multifaceted nature of our theoretical concepts. In this paper, we employ the use of meta-models to aid the translation of theory into SE models and also to facilitate our ability to relate results back to our theories. We demonstrate our approach by showing how a synthetic theory of grassland biodiversity can be evaluated using SEM and data from a coastal grassland. In this example, the theory focuses on the responses of species richness to abiotic stress and disturbance, both directly and through intervening effects on community biomass. Models examined include both those based on classical forms (where each concept is represented using a single latent variable) and also ones in which the concepts are recognized to be multifaceted and modeled as such. To address the challenge of matching SE models with the conceptual level of our theory, two approaches are illustrated, compositing and aggregation. Both approaches are shown to have merits, with the former being preferable for cases where the multiple facets of a concept have widely differing effects in the
Symmetry structure of a wave equation on some classes of Bianchi cosmological models
NASA Astrophysics Data System (ADS)
Jamal, S.; Kara, A. H.; Narain, R.; Shabbir, G.
2015-04-01
Nonlinear wave equations are constructed on certain Bianchi models and a symmetry analysis of these equations are performed to construct some exact solutions. Conservation laws of the respective wave equations are also obtained by the application of Noether's theorem. We show how a knowledge of these contributes to the reduction of the wave equation on this manifold.
Robust transformation with applications to structural equation modelling.
Yuan, K H; Chan, W; Bentler, P M
2000-05-01
Data sets in social and behavioural sciences are seldom normal. Influential cases or outliers can lead to inappropriate solutions and problematic conclusions in structural equation modelling. By giving a proper weight to each case, the influence of outliers on a robust procedure can be minimized. We propose using a robust procedure as a transformation technique, generating a new data matrix that can be analysed by a variety of multivariate methods. Mardia's multivariate skewness and kurtosis statistics are used to measure the effect of the transformation in achieving approximate normality. Since the transformation makes the data approximately normal, applying a classical normal theory based procedure to the transformed data gives more efficient parameter estimates. Three procedures for parameter evaluation and model testing are discussed. Six examples illustrate the various aspects with the robust transformation.
Critical examination of two-equation turbulence closure models
NASA Technical Reports Server (NTRS)
Chambers, T. L.; Wilcox, D. C.
1976-01-01
Comparison of the Jones-Launder, Ng-Spalding, Saffman-Wilcox, and Wilcox-Traci two-equation turbulence models has been conducted. It was shown that the Saffman-Wilcox and Wilcox-Traci dissipation-rate formulations admit straightforward integration through the viscous sublayer, whereas integration through the viscous sublayer is a more difficult issue with the Jones-Launder dissipation-function and the Ng-Spalding length-scale formulations. Numerical computations were conducted in which the models were applied to four equilibrium boundary layer flows including adverse, zero, and favorable pressure gradients. Computations of zero pressure gradient flow over a convex wall composed the final part of the comparison.
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 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.
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.
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.
ERIC Educational Resources Information Center
Fan, Xitao; Wang, Lin; Thompson, Bruce
1999-01-01
A Monte Carlo simulation study investigated the effects on 10 structural equation modeling fit indexes of sample size, estimation method, and model specification. Some fit indexes did not appear to be comparable, and it was apparent that estimation method strongly influenced almost all fit indexes examined, especially for misspecified models. (SLD)
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…
Differential equation dynamical system based assessment model in GNSS interoperability
NASA Astrophysics Data System (ADS)
Han, Tao; Lu, XiaoChun; Wang, Xue; Rao, YongNan; Zou, DeCai; Yang, JianFei; Wu, YangYang
2011-06-01
With the development of Global Navigation Satellite System (GNSS), the idea of GNSS interoperability is born and has become the focus of study in the field of satellite navigation. The popularity for GNSS to augment the interoperability with the existing ones necessitates the study of the assessment algorithm of this idea. In this paper, an assessment algorithm for interoperability comprehensive benefits based on the differential equation dynamical system is discussed. There are two important aspects in GNSS that interoperability will affect: one is the performance advancement; the other one is the cost of adopting interoperability. While researching the complex relationship between the performance and cost, we found this relationship is similar as what between prey and predator in biomathematics, so the Lotka-Volterra model used to depict the prey-predator relationship is a felicitous tool. After building a differential dynamical model, we analyze the existence and stability of the positive equilibrium in the model. Then a Cost-Effective Function of GNSS is constructed based on the positive equilibrium, which is employed to assess the interoperability, qualitatively and quantitatively. Finally, the paper demonstrates the significance of the model and its application by citing a numerical example.
Maxwell's equations-based dynamic laser-tissue interaction model.
Ahmed, Elharith M; Barrera, Frederick J; Early, Edward A; Denton, Michael L; Clark, C D; Sardar, Dhiraj K
2013-12-01
Since its invention in the early 1960s, the laser has been used as a tool for surgical, therapeutic, and diagnostic purposes. To achieve maximum effectiveness with the greatest margin of safety it is important to understand the mechanisms of light propagation through tissue and how that light affects living cells. Lasers with novel output characteristics for medical and military applications are too often implemented prior to proper evaluation with respect to tissue optical properties and human safety. Therefore, advances in computational models that describe light propagation and the cellular responses to laser exposure, without the use of animal models, are of considerable interest. Here, a physics-based laser-tissue interaction model was developed to predict the dynamic changes in the spatial and temporal temperature rise during laser exposure to biological tissues. Unlike conventional models, the new approach is grounded on the rigorous electromagnetic theory that accounts for wave interference, polarization, and nonlinearity in propagation using a Maxwell's equations-based technique.
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.
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.
Structural equation modeling of personality disorders and pathological personality traits.
South, Susan C; Jarnecke, Amber M
2017-04-01
Structural equation modeling (SEM) is a family of related statistical techniques that lend themselves to understanding the complex relationships among variables that differ among individuals in the population. SEM techniques have become increasingly popular in the study of personality disorders (PDs) and maladaptive personality traits. The current article takes a critical look at the ways in which SEM techniques have been used in the study of PDs, PD symptoms, and pathological personality traits. By far the most common use of SEM in the study of PDs has been to examine the latent structure of these constructs, with an overwhelming bulk of the evidence in favor of a dimensional, as opposed to categorical, conceptualization. Other common uses of SEM in this area are factor models that examine the joint multivariate space of PDs, maladaptive personality traits, and psychopathology. Relatively underused, however, are observed or latent variable path models. We review the strengths and weaknesses of the work done to date, focusing on ways that these SEM studies have been either theoretically and/or statistically sound. Finally, we offer suggestions for future research examining PDs with SEM techniques. (PsycINFO Database Record
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
The Noble-Abel Equation of State: Thermodynamic Derivations for Ballistics Modelling
2005-11-01
equation of state for propellant gases at the high densities and temperatures experienced in guns. Most computational fluid dynamics-based ballistics models, however, require additional thermodynamic functions which...derived from the equation of state . This note presents
A model for closing the inviscid form of the average-passage equation system
NASA Technical Reports Server (NTRS)
Adamczyk, J. J.; Mulac, R. A.; Celestina, M. L.
1985-01-01
A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented.
A model for closing the inviscid form of the average-passage equation system
NASA Technical Reports Server (NTRS)
Adamczyk, J. J.; Mulac, R. A.; Celestina, M. L.
1986-01-01
A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented.
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
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.
Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Matinelli, L.
1994-01-01
The steady state solution of the system of equations consisting of the full Navier-Stokes equations and two turbulence equations has been obtained using a multigrid strategy of 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 turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positivity. 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, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.
2009-10-07
relative velocity of colliding molecules, and b and ε are geometric impact parameters. The Boltzmann equation is a nonlinear integro - differential equation ...Space and Velocity Discretization to Model Kinetic Equations (PREPRINT) 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Alexander...Galerkin discretization is proposed for the Bhatnagar-Gross-Krook model kinetic equation . This approach allows for a high order polynomial approximation of
Fitting meta-analytic structural equation models with complex datasets.
Wilson, Sandra Jo; Polanin, Joshua R; Lipsey, Mark W
2016-06-01
A modification of the first stage of the standard procedure for two-stage meta-analytic structural equation modeling for use with large complex datasets is presented. This modification addresses two common problems that arise in such meta-analyses: (a) primary studies that provide multiple measures of the same construct and (b) the correlation coefficients that exhibit substantial heterogeneity, some of which obscures the relationships between the constructs of interest or undermines the comparability of the correlations across the cells. One component of this approach is a three-level random effects model capable of synthesizing a pooled correlation matrix with dependent correlation coefficients. Another component is a meta-regression that can be used to generate covariate-adjusted correlation coefficients that reduce the influence of selected unevenly distributed moderator variables. A non-technical presentation of these techniques is given, along with an illustration of the procedures with a meta-analytic dataset. Copyright © 2016 John Wiley & Sons, Ltd.
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.
Bursting processes in plasmas and relevant nonlinear model equations
Basu, B.; Coppi, B.
1995-01-01
Important intrinsic plasma instabilities manifest themselves in the form of periodic bursts of fluctuations rather than as a state of stationary fluctuations, which a conventional application of quasilinear theory would lead to expect. A set of coupled nonlinear equations for the time evolution of the fluctuation amplitude and of the driving factor of the relevant instability is shown to have the features necessary to reproduce the variety of bursts that are observed experimentally. These are the periodicity, the duration, and the shape of the bursts, special consideration being given to the excitation of modes by high-energy particle populations in thermalized plasmas and to a model for the transition from a bursting state to one of stationary fluctuations. A model is introduced that is relevant to the case where the spatial dependence of the mode amplitude is important. The application of the given analysis to the bursty wave emissions observed in space is discussed. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Equivalence and Differences between Structural Equation Modeling and State-Space Modeling Techniques
ERIC Educational Resources Information Center
Chow, Sy-Miin; Ho, Moon-ho R.; Hamaker, Ellen L.; Dolan, Conor V.
2010-01-01
State-space modeling techniques have been compared to structural equation modeling (SEM) techniques in various contexts but their unique strengths have often been overshadowed by their similarities to SEM. In this article, we provide a comprehensive discussion of these 2 approaches' similarities and differences through analytic comparisons and…
Using the Friedman Method of Ranks for Model Comparison in Structural Equation Modeling.
ERIC Educational Resources Information Center
Rigdon, Edward E.
1999-01-01
Explores the use of the Friedman method of ranks (H. Friedman, 1937) as an inferential procedure for evaluating competing models in structural-equation modeling. Describes the attractive features of this approach, but raises important issues regarding the lack of independence of observations and the power of the test. (SLD)
Evaluating Small Sample Approaches for Model Test Statistics in Structural Equation Modeling
ERIC Educational Resources Information Center
Nevitt, Jonathan; Hancock, Gregory R.
2004-01-01
Through Monte Carlo simulation, small sample methods for evaluating overall data-model fit in structural equation modeling were explored. Type I error behavior and power were examined using maximum likelihood (ML), Satorra-Bentler scaled and adjusted (SB; Satorra & Bentler, 1988, 1994), residual-based (Browne, 1984), and asymptotically…
ERIC Educational Resources Information Center
Butner, Jonathan; Amazeen, Polemnia G.; Mulvey, Genna M.
2005-01-01
The authors present a dynamical multilevel model that captures changes over time in the bidirectional, potentially asymmetric influence of 2 cyclical processes. S. M. Boker and J. Graham's (1998) differential structural equation modeling approach was expanded to the case of a nonlinear coupled oscillator that is common in bimanual coordination…
Development of a parallel implicit solver of fluid modeling equations for gas discharges
NASA Astrophysics Data System (ADS)
Hung, Chieh-Tsan; Chiu, Yuan-Ming; Hwang, Feng-Nan; Wu, Jong-Shinn
2011-01-01
A parallel fully implicit PETSc-based fluid modeling equations solver for simulating gas discharges is developed. Fluid modeling equations include: the neutral species continuity equation, the charged species continuity equation with drift-diffusion approximation for mass fluxes, the electron energy density equation, and Poisson's equation for electrostatic potential. Except for Poisson's equation, all model equations are discretized by the fully implicit backward Euler method as a time integrator, and finite differences with the Scharfetter-Gummel scheme for mass fluxes on the spatial domain. At each time step, the resulting large sparse algebraic nonlinear system is solved by the Newton-Krylov-Schwarz algorithm. A 2D-GEC RF discharge is used as a benchmark to validate our solver by comparing the numerical results with both the published experimental data and the theoretical prediction. The parallel performance of the solver is investigated.
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…
ERIC Educational Resources Information Center
Kozan, Kadir
2016-01-01
The present study investigated the relationships among teaching, cognitive, and social presence through several structural equation models to see which model would better fit the data. To this end, the present study employed and compared several different structural equation models because different models could fit the data equally well. Among…
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…
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.
Battery Life Estimator (BLE) Data Analysis Software v. 1.2
Thomas, Edward; Bloom, Ira; Battaglia, Vincent; & Christopherson, Jon
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 an 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
A model for closing the inviscid form of the average passage equation system
NASA Technical Reports Server (NTRS)
Adamczyk, John J.; Mulac, R. A.; Celestina, M. L.
1996-01-01
A mathematical model for closing or mathematically completing the system of equations is proposed. The model describes the time average flow field through the blade passages of multistage turbomachinery. These average-passage equation systems govern a conceptual model useful in turbomachinery aerodynamic design and analysis. The closure model was developed to insure a consistency between these equations and the axisymmetric through-flow equations. The closure model was incorporated into a calculation code for use in the simulation of the flow field about a high-speed counter rotating propeller and a high-speed fan stage.
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.
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.
Master equation simulations of a model of a thermochemical system.
Kawczyński, Andrzej L; Nowakowski, Bogdan
2003-09-01
Master equation approach is used to study the influence of fluctuations on the dynamics of a model thermochemical system. For appropriate values of parameters, the deterministic description of the system gives the subcritical or supercritical Hopf bifurcations. For small systems (containing 100 000 particles) close to the supercritical Hopf bifurcation, the stochastic trajectories obtained from numerical simulations do not allow to distinguish between damped oscillations around a stable focus and sustained oscillations around a small stable limit cycle. This uncertainty disappears if the number of particles in the system is increased (up to 1 000 000). Close to subcritical Hopf bifurcation the stochastic trajectory of the system jumps from the basin of attraction of a stable focus to the basin of attraction of a stable limit cycle. In this case the time dependencies of temperature and concentration of reactant in the system are apparently similar to intermittent chaotic oscillations. The mean first passage time for the transitions from the stable focus to the stable limit cycle show the characteristic exponential dependence on the number of particles. This passage time depends very strongly on the bifurcation parameter (reaction heat), which determines the distance between the stable focus and an unstable limit cycle.
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.
Modeling asymmetric cavity collapse with plasma equations of state.
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.
Structural equation modeling of pesticide poisoning, depression, safety, and injury.
Beseler, Cheryl L; Stallones, Lorann
2013-01-01
The role of pesticide poisoning in risk of injuries may operate through a link between pesticide-induced depressive symptoms and reduced engagement in safety behaviors. The authors conducted structural equation modeling of cross-sectional data to examine the pattern of associations between pesticide poisoning, depressive symptoms, safety knowledge, safety behaviors, and injury. Interviews of 1637 Colorado farm operators and their spouses from 964 farms were conducted during 1993-1997. Pesticide poisoning was assessed based on a history of ever having been poisoned. The Center for Epidemiologic Studies-Depression scale was used to assess depressive symptoms. Safety knowledge and safety behaviors were assessed using ten items for each latent variable. Outcomes were safety behaviors and injuries. A total of 154 injuries occurred among 1604 individuals with complete data. Pesticide poisoning, financial problems, health, and age predicted negative affect/somatic depressive symptoms with similar effect sizes; sex did not. Depression was more strongly associated with safety behavior than was safety knowledge. Two safety behaviors were significantly associated with an increased risk of injury. This study emphasizes the importance of financial problems and health on depression, and provides further evidence for the link between neurological effects of past pesticide poisoning on risk-taking behaviors and injury.
Chaotic attractors in tumor growth and decay: a differential equation model.
Harney, Michael; Yim, Wen-sau
2015-01-01
Tumorigenesis can be modeled as a system of chaotic nonlinear differential equations. A simulation of the system is realized by converting the differential equations to difference equations. The results of the simulation show that an increase in glucose in the presence of low oxygen levels decreases tumor growth.
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…
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…
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…
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
Background-Error Correlation Model Based on the Implicit Solution of a Diffusion Equation
2010-01-01
1 Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation Matthew J. Carrier* and Hans Ngodock...4. TITLE AND SUBTITLE Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation 5a. CONTRACT NUMBER 5b. GRANT...2001), which sought to model error correlations based on the explicit solution of a generalized diffusion equation. The implicit solution is
Delayed uncoupled continuous-time random walks do not provide a model for the telegraph equation.
Rukolaine, S A; Samsonov, A M
2012-02-01
It has been alleged in several papers that the so-called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since the telegraph equation describes phenomena with finite propagation speed, while the velocity of the motion of particles in the DCTRWs is infinite. In this paper we investigate the accuracy of the approximations to the DCTRWs provided by the telegraph equation. We show that the diffusion equation, being the correct limit of the DCTRWs, gives better approximations in L(2) norm to the DCTRWs than the telegraph equation. We conclude, therefore, that first, the DCTRWs do not provide any correct microscopic interpretation of the one-dimensional telegraph equation, and second, the kinetic (exact) model of the telegraph equation is different from the model based on the DCTRWs.
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
An asymptotic model in acoustics: acoustic drift equations.
Vladimirov, Vladimir A; Ilin, Konstantin
2013-11-01
A rigorous asymptotic procedure with the Mach number as a small parameter is used to derive the equations of mean flows which coexist and are affected by the background acoustic waves in the limit of very high Reynolds number.
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…
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)
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…
Xiao, Yanni; Miao, Hongyu; Tang, Sanyi; Wu, Hulin
2013-06-30
We review mathematical modeling and related statistical issues of HIV dynamics primarily in response to antiretroviral drug therapy in this article. We start from a basic model of virus infection and then review a number of more advanced models with consideration of pharmacokinetic factors, adherence and drug resistance. Specifically, we illustrate how mathematical models can be developed and parameterized to understand the effects of long-term treatment and different treatment strategies on disease progression. In addition, we discuss a variety of parameter estimation methods for differential equation models that are applicable to either within- or between-host viral dynamics.
Xiao, Yanni; Miao, Hongyu; Tang, Sanyi; Wu, Hulin
2014-01-01
Summary We review mathematical modeling and related statistical issues of HIV dynamics primarily in response to antiretroviral drug therapy in this article. We start from a basic model of virus infection and then review a number of more advanced models with considering, e.g., pharmacokinetic factors, adherence and drug resistance. Specifically, we illustrate how mathematical models can be developed and parameterized to understand effects of long-term treatment and different treatment strategies on disease progression. In addition, we discuss a variety of parameter estimation methods for differential equation models that are applicable to either within- or between-host viral dynamics. PMID:23603208
Fixed- and random-effects meta-analytic structural equation modeling: examples and analyses in R.
Cheung, Mike W-L
2014-03-01
Meta-analytic structural equation modeling (MASEM) combines the ideas of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Cheung and Chan (Psychological Methods 10:40-64, 2005b, Structural Equation Modeling 16:28-53, 2009) proposed a two-stage structural equation modeling (TSSEM) approach to conducting MASEM that was based on a fixed-effects model by assuming that all studies have the same population correlation or covariance matrices. The main objective of this article is to extend the TSSEM approach to a random-effects model by the inclusion of study-specific random effects. Another objective is to demonstrate the procedures with two examples using the metaSEM package implemented in the R statistical environment. Issues related to and future directions for MASEM are discussed.
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
Optimal harvesting for a predator-prey agent-based model using difference equations.
Oremland, Matthew; Laubenbacher, Reinhard
2015-03-01
In this paper, a method known as Pareto optimization is applied in the solution of a multi-objective optimization problem. The system in question is an agent-based model (ABM) wherein global dynamics emerge from local interactions. A system of discrete mathematical equations is formulated in order to capture the dynamics of the ABM; while the original model is built up analytically from the rules of the model, the paper shows how minor changes to the ABM rule set can have a substantial effect on model dynamics. To address this issue, we introduce parameters into the equation model that track such changes. The equation model is amenable to mathematical theory—we show how stability analysis can be performed and validated using ABM data. We then reduce the equation model to a simpler version and implement changes to allow controls from the ABM to be tested using the equations. Cohen's weighted κ is proposed as a measure of similarity between the equation model and the ABM, particularly with respect to the optimization problem. The reduced equation model is used to solve a multi-objective optimization problem via a technique known as Pareto optimization, a heuristic evolutionary algorithm. Results show that the equation model is a good fit for ABM data; Pareto optimization provides a suite of solutions to the multi-objective optimization problem that can be implemented directly in the ABM.
A near-wall two-equation model for turbulent heat fluxes
NASA Technical Reports Server (NTRS)
Sommer, T. P.; So, R. M. C.; Lai, Y. G.
1992-01-01
A near-wall two-equation model for turbulent heat fluxes is derived from the temperature variance and its dissipation-rate equations and the assumption of gradient transport. Only incompressible flows with non-buoyant heat transfer are considered. The near-wall asymptotics of each term in the exact equations are examined and used to derive near-wall correction functions that render the modeled equations consistent with these behavior. Thus modeled, the equations are used to calculate fully-developed pipe and channel flows with heat transfer. It is found that the proposed two-equation model yields asymptotically correct near-wall behavior for the normal heat flux, the temperature variance and its near-wall budget and correct limiting wall values for these properties compared to direct simulation data and measurements obtained under different wall boundary conditions.
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.
2014-03-01
method to the numerical solution of nonlinear and variable coefficient wave equations ,” SIAM, vol. 15, no. 2, pp. 423, Apr. 1973. [3] D. Lee and S. T...DIFFERENT IMPLEMENTATION OPTIONS FOR DENSITY DISCONTINUITY IN SPLIT– STEP FOURIER PARABOLIC EQUATION MODELS by Matthew D. Owens March 2014...FOR DENSITY DISCONTINUITY IN SPLIT–STEP FOURIER PARABOLIC EQUATION MODELS 5. FUNDING NUMBERS 6. AUTHOR(S) Matthew D. Owens 7. PERFORMING
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.
A Comparison of Solutions of Two Model Equations for Long Waves.
1983-02-01
focused on solutions of (A) and (B) that correspond to the initial condition that u(x,0) is a given function. Equation (A) is the Korteweg -de Vries...waves on the surface of water, two models have received particular attention. One is the equation of Korteweg and de Vries (1895) ( equation (A) or the...channel is the equation proposed by Korteweg and de Vries (1895), 3 1:’il nt * nx + 7 nnx + F n + . l= O. (la) In this equation n - n(x,t) represents
Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models
NASA Astrophysics Data System (ADS)
Ferialdi, L.
2017-02-01
We provide the exact non-Markovian master equation for a two-level system interacting with a thermal bosonic bath, and we write the solution of such a master equation in terms of the Bloch vector. We show that previous approximated results are particular limits of our exact master equation. We generalize these results to more complex systems involving an arbitrary number of two-level systems coupled to different thermal baths, providing the exact master equations also for these systems. As an example of this general case we derive the master equation for the Jaynes-Cummings model.
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…
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.
Numerical method based on the lattice Boltzmann model for the Fisher equation.
Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng
2008-06-01
In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.
Ledermann, Thomas; Kenny, David A
2017-02-06
Multilevel modeling (MLM) and structural equation modeling (SEM) are the dominant methods for the analysis of dyadic data. Both methods are extensively reviewed for the widely used actor-partner interdependence model and the dyadic growth curve model, as well as other less frequently adopted models, including the common fate model and the mutual influence model. For each method, we discuss the analysis of distinguishable and indistinguishable members, the treatment of missing data, the standardization of effects, and tests of mediation. Even though there has been some blending of the 2 methods, each method has its own advantages and disadvantages, thus both should be in the toolbox of dyadic researchers. (PsycINFO Database Record
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.
Modeling biological gradient formation: combining partial differential equations and Petri nets.
Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J
2016-01-01
Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.
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 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.
NASA Technical Reports Server (NTRS)
Golden, R. L.; Badhwar, G. D.; Stephens, S. A.
1975-01-01
The continuity equation for cosmic ray propagation is used to derive a set of linear equations interrelating the fluxes of multiply charged nuclei as observed at any particular part of the galaxy. The derivation leads to model independent definitions for cosmic ray storage time, mean density of target nuclei and effective mass traversed. The set of equations form a common framework for comparisons of theories and observations. As an illustration, it is shown that there exists a large class of propagation models which give the same result as the exponential path length model. The formalism is shown to accommodate dynamic as well as equilibrium models of production and propagation.
Figaro, S; Avril, J P; Brouers, F; Ouensanga, A; Gaspard, S
2009-01-30
Adsorption kinetic of molasses wastewaters after anaerobic digestion (MSWD) and melanoidin respectively on activated carbon was studied at different pH. The kinetic parameters could be determined using classical kinetic equations and a recently published fractal kinetic equation. A linear form of this equation can also be used to fit adsorption data. Even with lower correlation coefficients the fractal kinetic equation gives lower normalized standard deviation values than the pseudo-second order model generally used to fit adsorption kinetic data, indicating that the fractal kinetic model is much more accurate for describing the kinetic adsorption data than the pseudo-second order kinetic model.
Bogomol'nyi equations and solutions for Einstein-Yang-Mills-dilaton-σ models
NASA Astrophysics Data System (ADS)
Braden, H. W.; Varela, V.
1998-12-01
We derive Bogomol'nyi equations for an Einstein-Yang-Mills-dilaton-σ model on a static spacetime, showing that the Einstein equations are satisfied if and only if the associated (conformally scaled) three-metric is flat. These are precisely the static metrics for which super-covariantly constant spinors exist. We study some general properties of these equations and then consider the problem of obtaining axially symmetric solutions for the gauge group SU(2).
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.
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.
Macho, Siegfried; Ledermann, Thomas
2011-03-01
The phantom model approach for estimating, testing, and comparing specific effects within structural equation models (SEMs) is presented. The rationale underlying this novel method consists in representing the specific effect to be assessed as a total effect within a separate latent variable model, the phantom model that is added to the main model. The following favorable features characterize the method: (a) It enables the estimation, testing, and comparison of arbitrary specific effects for recursive and nonrecursive models with latent and manifest variables; (b) it enables the bootstrapping of confidence intervals; and (c) it can be applied with all standard SEM programs permitting latent variables, the specification of equality constraints, and the bootstrapping of total effects. These features along with the fact that no manipulation of matrices and formulas is required make the approach particularly suitable for applied researchers. The method is illustrated by means of 3 examples with real data sets.
2009-10-01
Beattie - Bridgeman Virial expansion The above equations are suitable for moderate pressures and are usually based on either empirical constants...CR 2010-013 October 2009 A Review of Equation of State Models, Chemical Equilibrium Calculations and CERV Code Requirements for SHS Detonation...Defence R&D Canada. A Review of Equation of State Models, Chemical Equilibrium Calculations and CERV Code Requirements for SHS Detonation
NASA Technical Reports Server (NTRS)
Sislian, J. P.
1978-01-01
The full Navier-Stokes time-dependent, compressible, turbulent, mean-flow equations in mass-averaged variables for plane or axisymmetric flow are presented. The equations are derived in a body-oriented, orthogonal, curvilinear coordinate system. Turbulence is modelled by a system of two equations for mass-averaged turbulent kinetic energy and dissipation rate proposed. These equations are rederived and some new features are discussed. A system of second order boundary layer equations is then derived which includes the effects of longitudinal curvature and the normal pressure gradient. The Wilcox and Chambers approach is used in considering effects of streamline curvature on turbulence phenomena in turbulent boundary layer type flows. Their two-equation turbulence model with curvature terms are rederived for the cases considered in the present report. The derived system equations serves as a basis for an investigation of problems where streamline curvature is of the order of the characteristic length in the longitudinal direction.
Structural Equation Modeling of Paired-Comparison and Ranking Data
ERIC Educational Resources Information Center
Maydeu-Olivares, Albert; Bockenholt, Ulf
2005-01-01
L. L. Thurstone's (1927) model provides a powerful framework for modeling individual differences in choice behavior. An overview of Thurstonian models for comparative data is provided, including the classical Case V and Case III models as well as more general choice models with unrestricted and factor-analytic covariance structures. A flow chart…
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.
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.
A note on the Dirichlet problem for model complex partial differential equations
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Karaca, Bahriye
2016-08-01
Complex model partial differential equations of arbitrary order are considered. The uniqueness of the Dirichlet problem is studied. It is proved that the Dirichlet problem for higher order of complex partial differential equations with one complex variable has infinitely many solutions.
Invariance principle and model reduction for the Fokker-Planck equation
NASA Astrophysics Data System (ADS)
Karlin, I. V.
2016-11-01
The principle of dynamic invariance is applied to obtain closed moment equations from the Fokker-Planck kinetic equation. The analysis is carried out to explicit formulae for computation of the lowest eigenvalue and of the corresponding eigenfunction for arbitrary potentials. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.
NASA Astrophysics Data System (ADS)
Mann, R. F.; Amphlett, J. C.; Peppley, B. A.; Thurgood, C. P.
Proton exchange membrane (PEM) fuel cells have been under development for many years and appear to be the potential solution for many electricity supply applications. Modelling and computer simulation of PEM fuel cells have been equally active areas of work as a means of developing better understanding of cell and stack operation, facilitating design improvements and supporting system simulation studies. In general, fuel cell models must be capable of predicting values of the activation polarization at both the anode and the cathode. Since the magnitude of an activation polarization for a particular electrode depends on the inverse of the chemical (or electrochemical) reaction rate at that electrode, reaction rate expressions are normally required for each electrode. The reaction rate is commonly expressed as an 'exchange current density', typical symbol i 0, and mechanistic expressions to predict i 0 are, therefore, components of an ideal model. Most expressions for i 0 are based on the Butler-Volmer (B-V) equation or on more approximate equations derived from the B-V equation. Many publications use one of these B-V equations without a critical determination of the applicability or accuracy of the particular equation being used. The present paper examines these questions and makes some recommendations regarding the applicability of each equation in the 'B-V family of equations'. In addition, terminology and symbols have been modified, where possible, to make modelling based on B-V equations more easily understood and applied by those without an extensive background in electrochemistry.
The Noble-Abel Equation of State: Thermodynamic Derivations for Ballistic Modelling
2005-11-01
reasonably accurate equation of state for propellant gases at the high densities and temperature experienced in guns. Most computational fluid dynamics-base...ballistics models, however, require additional thermodynamic functions which must be derived form the equation of state . This note presents the
QCD equations of state and the quark-gluon plasma liquid model
NASA Astrophysics Data System (ADS)
Letessier, Jean; Rafelski, Johann
2003-03-01
Recent advances in the study of equations of state of thermal lattice quantum chromodynamics obtained at nonzero baryon density allow validation of the quark-gluon plasma (QGP) liquid model equations of state (EOS). We study here the properties of the QGP-EOS near to the phase transformation boundary at finite baryon density and show a close agreement with the lattice results.
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…
A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics
ERIC Educational Resources Information Center
Spayd, Kimberly; Puckett, James
2016-01-01
This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical…
Solitons of the Kadomtsev-Petviashvili equation based on lattice Boltzmann model
NASA Astrophysics Data System (ADS)
Wang, Huimin
2017-01-01
In this paper, a lattice Boltzmann model for the Kadomtsev-Petviashvili equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales are obtained. Due to the asymmetry in x direction and y direction of the equation, the moments of the equilibrium distribution function are selected are asymmetric. The numerical results demonstrate the lattice Boltzmann method is an effective method to simulate the solitons of the Kadomtsev-Petviashvili equation.
The Dissipation Rate Transport Equation and Subgrid-Scale Models in Rotating Turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Ye, Zhou
1997-01-01
The dissipation rate transport equation remains the most uncertain part of turbulence modeling. The difficulties arc increased when external agencies like rotation prevent straightforward dimensional analysis from determining the correct form of the modelled equation. In this work, the dissipation rate transport equation and subgrid scale models for rotating turbulence are derived from an analytical statistical theory of rotating turbulence. In the strong rotation limit, the theory predicts a turbulent steady state in which the inertial range energy spectrum scales as k(sup -2) and the turbulent time scale is the inverse rotation rate. This scaling has been derived previously by heuristic arguments.
HuBLE-UK, the Hudson Bay Lithospheric Experiment: Insights into the formation of the Canadian Shield
NASA Astrophysics Data System (ADS)
Bastow, I. D.; Kendall, J.; Helffrich, G.; Wookey, J.; Thompson, D.; Eaton, D.; Snyder, D.
2008-12-01
Hudson Bay lies in the Precambrian core of North America, which is comprised of the Canadian Shield and contiguous platform regions. The region is underlain by one of the largest lithospheric keels on Earth; it is also the site of one of the largest negative geoid anomalies. We have deployed 10 broadband seismic stations in the northern part of the bay that complement the existing POLARIS, CHASME and CNSN network stations in the region. Here we present preliminary SKS shear wave splitting analyses and independent tomographic inversion of P- and S-wave travel-time data in order to: 1) understand better the origin and evolution of the Hudson Bay cratonic interior basins; 2) to illuminate possible relationships between the lithospheric keel, sub-lithospheric mantle flow and formation of the Hudson Bay basin; 3) to improve understanding of postglacial isostatic rebound; 4) to map the lithospheric structure of the Trans-Hudson orogen in a region characterized by extreme salient-reentrant geometry, possibly analogous to the western syntaxis of the Himalayan front. SKS delay times vary from 0.5-1.2s, which indicate a lithospheric-scale anisotropic layer up to 150km thick. However, SKS fast directions and preliminary tomographic images do not relate simply to the structural trends of the Trans Hudson Orogen and neighboring Archean terranes. Our work complements ongoing HuBLE studies that focus on receiver function analyses, dispersion analysis of teleseismic Rayleigh waves, and applications of ambient noise tomography that extract more information about lithospheric structure of the Hudson Bay basin.
Simulations of diffusion-reaction equations with implications to turbulent combustion modeling
NASA Technical Reports Server (NTRS)
Girimaji, Sharath S.
1993-01-01
An enhanced diffusion-reaction reaction system (DRS) is proposed as a statistical model for the evolution of multiple scalars undergoing mixing and reaction in an isotropic turbulence field. The DRS model is close enough to the scalar equations in a reacting flow that other statistical models of turbulent mixing that decouple the velocity field from scalar mixing and reaction (e.g. mapping closure model, assumed-pdf models) cannot distinguish the model equations from the original equations. Numerical simulations of DRS are performed for three scalars evolving from non-premixed initial conditions. A simple one-step reversible reaction is considered. The data from the simulations are used (1) to study the effect of chemical conversion on the evolution of scalar statistics, and (2) to evaluate other models (mapping-closure model, assumed multivariate beta-pdf model).
A Novel Approach to Modeling of Hydrogeologic Systems Using Fuzzy Differential Equations
NASA Astrophysics Data System (ADS)
Faybishenko, B. A.
2003-12-01
The many simultaneously occurring processes in unsaturated-saturated heterogeneous soils and fractured rocks can cause field observations to become imprecise and incomplete. Consequently, the results of predictions using deterministic and stochastic mathematical models are often uncertain, vague or "fuzzy." One of the alternative approaches to modeling hydrogeologic systems is the application of a fuzzy-systems approach, which is already widely used in such fields as engineering, physics, chemistry, and biology. After presenting a hydrogeologic system as a fuzzy system, the author presents a fuzzy form of Darcy's equation. Based on this equation, second-order fuzzy partial differential equations of the elliptic type (analogous to the Laplace equation) and the parabolic type (analogous to the Richards equation) are derived. These equations are then approximated as fuzzy-difference equations and solved using the basic principles of fuzzy arithmetic. The solutions for the fuzzy-difference equations take the form of fuzzy membership functions for each observation point (node). The author gives examples of the solutions of these equations for flow in unsaturated and saturated media and then compares them with those obtained using deterministic and stochastic methods.
Bypass Transitional Flow Calculations Using a Navier-Stokes Solver and Two-Equation Models
NASA Technical Reports Server (NTRS)
Liuo, William W.; Shih, Tsan-Hsing; Povinelli, L. A. (Technical Monitor)
2000-01-01
Bypass transitional flows over a flat plate were simulated using a Navier-Stokes solver and two equation models. A new model for the bypass transition, which occurs in cases with high free stream turbulence intensity (TI), is described. The new transition model is developed by including an intermittency correction function to an existing two-equation turbulence model. The advantages of using Navier-Stokes equations, as opposed to boundary-layer equations, in bypass transition simulations are also illustrated. The results for two test flows over a flat plate with different levels of free stream turbulence intensity are reported. Comparisons with the experimental measurements show that the new model can capture very well both the onset and the length of bypass transition.
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…
Fitting data to model: structural equation modeling diagnosis using two scatter plots.
Yuan, Ke-Hai; Hayashi, Kentaro
2010-12-01
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 the residual-based M-distance with the quantile of a chi distribution. It allows the researcher to visually identify clusters of potential outliers. The article further studies the effect of the potential outliers on the overall model evaluation when they are removed according to the order of the clusters exhibited in the plot. Suggestions are provided on determining the outlier status of outstanding cases in real data analysis. Recommendations are also made on the choice of robust methods and maximum likelihood following outlier removal.
A Hierarchical Latent Stochastic Differential Equation Model for Affective Dynamics
ERIC Educational Resources Information Center
Oravecz, Zita; Tuerlinckx, Francis; Vandekerckhove, Joachim
2011-01-01
In this article a continuous-time stochastic model (the Ornstein-Uhlenbeck process) is presented to model the perpetually altering states of the core affect, which is a 2-dimensional concept underlying all our affective experiences. The process model that we propose can account for the temporal changes in core affect on the latent level. The key…
A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models
NASA Technical Reports Server (NTRS)
Morrison, Joseph H.
1992-01-01
This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.
Adiabatic limit in Abelian Higgs model with application to Seiberg-Witten equations
NASA Astrophysics Data System (ADS)
Sergeev, A.
2017-03-01
In this paper we deal with the (2 + 1)-dimensional Higgs model governed by the Ginzburg-Landau Lagrangian. The static solutions of this model, called otherwise vortices, are described by the theorem of Taubes. This theorem gives, in particular, an explicit description of the moduli space of vortices (with respect to gauge transforms). However, much less is known about the moduli space of dynamical solutions. A description of slowly moving solutions may be given in terms of the adiabatic limit. In this limit the dynamical Ginzburg-Landau equations reduce to the adiabatic equation coinciding with the Euler equation for geodesics on the moduli space of vortices with respect to the Riemannian metric (called T-metric) determined by the kinetic energy of the model. A similar adiabatic limit procedure can be used to describe approximately solutions of the Seiberg-Witten equations on 4-dimensional symplectic manifolds. In this case the geodesics of T-metric are replaced by the pseudoholomorphic curves while the solutions of Seiberg-Witten equations reduce to the families of vortices defined in the normal planes to the limiting pseudoholomorphic curve. Such families should satisfy a nonlinear ∂-equation which can be considered as a complex analogue of the adiabatic equation. Respectively, the arising pseudoholomorphic curves may be considered as complex analogues of adiabatic geodesics in (2 + 1)-dimensional case. In this sense the Seiberg-Witten model may be treated as a (2 + 1)-dimensional analogue of the (2 + 1)-dimensional Abelian Higgs model2.
A model of the nerve impulse using two first-order differential equations
NASA Astrophysics Data System (ADS)
Hindmarsh, J. L.; Rose, R. M.
1982-03-01
The Hodgkin-Huxley model1 of the nerve impulse consists of four coupled nonlinear differential equations, six functions and seven constants. Because of the complexity of these equations and the necessity for numerical solution, it is difficult to use them in simulations of interactions in small neural networks. Thus, it would be useful to have a second-order differential equation which predicted correctly properties such as the frequency-current relationship. Fitzhugh2 introduced a second-order model of the nerve impulse, but his equations predict an action potential duration which is similar to the inter-spike interval3 and they do not give a reasonable frequency-current relationship. To develop a second-order model having few parameters but which does not have these disadvantages, we have generalized the second-order Fitzhugh equations2, and based the form of the functions in the new equations on voltage-clamp data obtained from a snail neurone. We report here an unexpected property of the resulting equations-the x and y null clines in the phase plane lie close together when the phase point is on the recovery side of the phase plane. The resulting slow movement along the phase path gives a long inter-spike interval, a property not shown clearly by previous models2,4. The model also predicts the linearity of the frequency-current relationship, and may be useful for studying detailed interactions in networks containing small numbers of neurones.
Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J
2015-03-01
We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a "full" model. We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso. We show the resulting method, here called the LSA method, to be an (asymptotically) oracle model selection method. The finite sample performance of the proposed LSA method is investigated with Monte Carlo simulations, in which we examine the percentage of selecting true ODE models, the efficiency of the parameter estimation compared to simply using the full and true models, and coverage probabilities of the estimated confidence intervals for ODE parameters, all of which have satisfactory performances. Our method is also demonstrated by selecting the best predator-prey ODE to model a lynx and hare population dynamical system among some well-known and biologically interpretable ODE models.
Liang, Hua; Wu, Hulin
2008-12-01
Differential equation (DE) models are widely used in many scientific fields that include engineering, physics and biomedical sciences. The so-called "forward problem", the problem of simulations and predictions of state variables for given parameter values in the DE models, has been extensively studied by mathematicians, physicists, engineers and other scientists. However, the "inverse problem", the problem of parameter estimation based on the measurements of output variables, has not been well explored using modern statistical methods, although some least squares-based approaches have been proposed and studied. In this paper, we propose parameter estimation methods for ordinary differential equation models (ODE) based on the local smoothing approach and a pseudo-least squares (PsLS) principle under a framework of measurement error in regression models. The asymptotic properties of the proposed PsLS estimator are established. We also compare the PsLS method to the corresponding SIMEX method and evaluate their finite sample performances via simulation studies. We illustrate the proposed approach using an application example from an HIV dynamic study.
ERIC Educational Resources Information Center
Kim, Minkee; Song, Jinwoong
2010-01-01
Many models in science education have tried to clarify the causal relationships of affective variables on student performance, by presenting theoretical models, exploratory SEM (structural equation models), and confirmatory SEM. Based on the literature, the recent AS-TI-CU model scrutinised the most robust stimuli of conceptual understanding (CU):…
Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces
NASA Technical Reports Server (NTRS)
Wang, Chi R.
2005-01-01
This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one-equation
Fast and accurate calculation of dilute quantum gas using Uehling-Uhlenbeck model equation
NASA Astrophysics Data System (ADS)
Yano, Ryosuke
2017-02-01
The Uehling-Uhlenbeck (U-U) model equation is studied for the fast and accurate calculation of a dilute quantum gas. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U-U model equation. DSMC analysis based on the U-U model equation is expected to enable the thermalization to be accurately obtained using a small number of sample particles and the dilute quantum gas dynamics to be calculated in a practical time. Finally, the applicability of DSMC analysis based on the U-U model equation to the fast and accurate calculation of a dilute quantum gas is confirmed by calculating the viscosity coefficient of a Bose gas on the basis of the Green-Kubo expression and the shock layer of a dilute Bose gas around a cylinder.
Modeling neck linker of kinesin motor movement with MRSR stochastic differential equation
NASA Astrophysics Data System (ADS)
Razali, Wan Qashishah Akmal Wan; Ramli, Siti Norafidah Mohd; Radiman, Shahidan
2016-11-01
Stochastic differential equation has a significant role in a range of biological areas including molecular motor like kinesin motor. Mean-reverting square root (MRSR) stochastic differential equation is commonly used in economics and finance areas. In this study, we use the MRSR stochastic differential equation to model neck linker motion of kinesin motor by considering the possibilities of rightward direction and occasionally in the leftward direction of kinesin movements. This neck linker docking model of kinesin motor incorporates the conformational change in the chemical kinetics and the tethered diffusion of the free head of kinesin motor. Here, we demonstrate this model by using Hookean spring method which referred to the stiffness model of neck linker. The motion of kinesin motor seems to be well described to move in unidirectional way with volatile behavior based on MRSR rather than common stochastic differential equation [DOI 10.1007/s11538-011-9697-6].
Equation-free modeling unravels the behavior of complex ecological systems
DeAngelis, Donald L.; Yurek, Simeon
2015-01-01
Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.
Kwan, Joyce L Y; Chan, Wai
2011-09-01
We propose a two-stage method for comparing standardized coefficients in structural equation modeling (SEM). At stage 1, we transform the original model of interest into the standardized model by model reparameterization, so that the model parameters appearing in the standardized model are equivalent to the standardized parameters of the original model. At stage 2, we impose appropriate linear equality constraints on the standardized model and use a likelihood ratio test to make statistical inferences about the equality of standardized coefficients. Unlike other existing methods for comparing standardized coefficients, the proposed method does not require specific modeling features (e.g., specification of nonlinear constraints), which are available only in certain SEM software programs. Moreover, this method allows researchers to compare two or more standardized coefficients simultaneously in a standard and convenient way. Three real examples are given to illustrate the proposed method, using EQS, a popular SEM software program. Results show that the proposed method performs satisfactorily for testing the equality of standardized coefficients.
Kaur, A; Takhar, P S; Smith, D M; Mann, J E; Brashears, M M
2008-10-01
A fractional differential equations (FDEs)-based theory involving 1- and 2-term equations was developed to predict the nonlinear survival and growth curves of foodborne pathogens. It is interesting to note that the solution of 1-term FDE leads to the Weibull model. Nonlinear regression (Gauss-Newton method) was performed to calculate the parameters of the 1-term and 2-term FDEs. The experimental inactivation data of Salmonella cocktail in ground turkey breast, ground turkey thigh, and pork shoulder; and cocktail of Salmonella, E. coli, and Listeria monocytogenes in ground beef exposed at isothermal cooking conditions of 50 to 66 degrees C were used for validation. To evaluate the performance of 2-term FDE in predicting the growth curves-growth of Salmonella typhimurium, Salmonella Enteritidis, and background flora in ground pork and boneless pork chops; and E. coli O157:H7 in ground beef in the temperature range of 22.2 to 4.4 degrees C were chosen. A program was written in Matlab to predict the model parameters and survival and growth curves. Two-term FDE was more successful in describing the complex shapes of microbial survival and growth curves as compared to the linear and Weibull models. Predicted curves of 2-term FDE had higher magnitudes of R(2) (0.89 to 0.99) and lower magnitudes of root mean square error (0.0182 to 0.5461) for all experimental cases in comparison to the linear and Weibull models. This model was capable of predicting the tails in survival curves, which was not possible using Weibull and linear models. The developed model can be used for other foodborne pathogens in a variety of food products to study the destruction and growth behavior.
Approximation of Quantum Stochastic Differential Equations for Input-Output Model Reduction
2016-02-25
Papers published in non peer-reviewed journals: " Algorithms and software for quantum engineering," H. Mabuchi and R. Balu, Review Management Board...Approximation of Quantum Stochastic Differential Equations for Input-Output Model Reduction We have completed a short program of theoretical research...on dimensional reduction and approximation of models based on quantum stochastic differential equations. Our primary results lie in the area of
Testing for Structural Change by D-Methods in Switching Simultaneous Equations Models.
1982-02-01
TEST CHART NATIONAL BURLAU (IF STANOAROS-613-A PROFESSIONAL PAPER 342 / February 1982 TESTING FOR STRUCTURAL CHANGE BY D- METHODS IN SWITCHING...BY D- METHODS IN SWITCHING SIMULTANEOUS EQUATIONS MODELS Lung-Fei Lee c. Maddala DTIC ACCESSION Feb 2NOTICE 1.RE RT IDENTIFYING INORMATIO.-."--- T...PROFESSIONAL PAPER 34. February 1982 TESTING FOR STRUCTURAL CHANGE BY D- METHODS IN SWITCHING SIMULTANEOUS EQUATIONS MODELS Lung-Fei Lee G. S. Maddala R
Testing strong factorial invariance using three-level structural equation modeling.
Jak, Suzanne
2014-01-01
Within structural equation modeling, the most prevalent model to investigate measurement bias is the multigroup model. Equal factor loadings and intercepts across groups in a multigroup model represent strong factorial invariance (absence of measurement bias) across groups. Although this approach is possible in principle, it is hardly practical when the number of groups is large or when the group size is relatively small. Jak et al. (2013) showed how strong factorial invariance across large numbers of groups can be tested in a multilevel structural equation modeling framework, by treating group as a random instead of a fixed variable. In the present study, this model is extended for use with three-level data. The proposed method is illustrated with an investigation of strong factorial invariance across 156 school classes and 50 schools in a Dutch dyscalculia test, using three-level structural equation modeling.
Equations for the kinetic modeling of supersonically flowing electrically excited lasers
NASA Technical Reports Server (NTRS)
Lind, R. C.
1973-01-01
The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration-vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is then discussed.
Computation of Separated and Unsteady Flows with One- and Two-Equation Turbulence Models
NASA Technical Reports Server (NTRS)
Ekaterinaris, John A.; Menter, Florian R.
1994-01-01
The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. The two-equation turbulence models are discretized in space with an upwind-biased, second order accurate total variation diminishing scheme. One and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading edge and where natural transition was allowed to occur naturally are considered. The more recently developed field-equation turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are obtained. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading edge transitional flow region in order to capture the correct physical mechanism that leads to dynamic stall.
Developing Itô stochastic differential equation models for neuronal signal transduction pathways.
Manninen, Tiina; Linne, Marja-Leena; Ruohonen, Keijo
2006-08-01
Mathematical modeling and simulation of dynamic biochemical systems are receiving considerable attention due to the increasing availability of experimental knowledge of complex intracellular functions. In addition to deterministic approaches, several stochastic approaches have been developed for simulating the time-series behavior of biochemical systems. The problem with stochastic approaches, however, is the larger computational time compared to deterministic approaches. It is therefore necessary to study alternative ways to incorporate stochasticity and to seek approaches that reduce the computational time needed for simulations, yet preserve the characteristic behavior of the system in question. In this work, we develop a computational framework based on the Itô stochastic differential equations for neuronal signal transduction networks. There are several different ways to incorporate stochasticity into deterministic differential equation models and to obtain Itô stochastic differential equations. Two of the developed models are found most suitable for stochastic modeling of neuronal signal transduction. The best models give stable responses which means that the variances of the responses with time are not increasing and negative concentrations are avoided. We also make a comparative analysis of different kinds of stochastic approaches, that is the Itô stochastic differential equations, the chemical Langevin equation, and the Gillespie stochastic simulation algorithm. Different kinds of stochastic approaches can be used to produce similar responses for the neuronal protein kinase C signal transduction pathway. The fine details of the responses vary slightly, depending on the approach and the parameter values. However, when simulating great numbers of chemical species, the Gillespie algorithm is computationally several orders of magnitude slower than the Itô stochastic differential equations and the chemical Langevin equation. Furthermore, the chemical
Integrating occupancy models and structural equation models to understand species occurrence
Joseph, Maxwell B.; Preston, Daniel L.; Johnson, Pieter T. J.
2016-01-01
Understanding the drivers of species occurrence is a fundamental goal in basic and applied ecology. Occupancy models have emerged as a popular approach for inferring species occurrence because they account for problems associated with imperfect detection in field surveys. Current models, however, are limited because they assume covariates are independent (i.e., indirect effects do not occur). Here, we combined structural equation and occupancy models to investigate complex influences on species occurrence while accounting for imperfect detection. These two methods are inherently compatible because they both provide means to make inference on latent or unobserved quantities based on observed data. Our models evaluated the direct and indirect roles of cattle grazing, water chemistry, vegetation, nonnative fishes, and pond permanence on the occurrence of six pond-breeding amphibians, two of which are threatened: the California tiger salamander (Ambystoma californiense), and the California red-legged frog (Rana draytonii). While cattle had strong effects on pond vegetation and water chemistry, their overall effects on amphibian occurrence were small compared to the consistently negative effects of nonnative fish. Fish strongly reduced occurrence probabilities for four of five native amphibians, including both species of conservation concern. These results could help to identify drivers of amphibian declines and to prioritize strategies for amphibian conservation. More generally, this approach facilitates a more mechanistic representation of ideas about the causes of species distributions in space and time. As shown here, occupancy modeling and structural equation modeling are readily combined, and bring rich sets of techniques that may provide unique theoretical and applied insights into basic ecological questions. PMID:27197402
A near-wall four-equation turbulence model for compressible boundary layers
NASA Technical Reports Server (NTRS)
Sommer, T. P.; So, R. M. C.; Zhang, H. S.
1992-01-01
A near-wall four-equation turbulence model is developed for the calculation of high-speed compressible turbulent boundary layers. The four equations used are the k-epsilon equations and the theta(exp 2)-epsilon(sub theta) equations. These equations are used to define the turbulent diffusivities for momentum and heat fluxes, thus allowing the assumption of dynamic similarity between momentum and heat transport to be relaxed. The Favre-averaged equations of motion are solved in conjunction with the four transport equations. Calculations are compared with measurements and with another model's predictions where the assumption of the constant turbulent Prandtl number is invoked. Compressible flat plate turbulent boundary layers with both adiabatic and constant temperature wall boundary conditions are considered. Results for the range of low Mach numbers and temperature ratios investigated are essentially the same as those obtained using an identical near-wall k-epsilon model. In general, the numerical predictions are in very good agreement with measurements and there are significant improvements in the predictions of mean flow properties at high Mach numbers.
Mean-field message-passing equations in the Hopfield model and its generalizations
NASA Astrophysics Data System (ADS)
Mézard, Marc
2017-02-01
Motivated by recent progress in using restricted Boltzmann machines as preprocessing algorithms for deep neural network, we revisit the mean-field equations [belief-propagation and Thouless-Anderson Palmer (TAP) equations] in the best understood of such machines, namely the Hopfield model of neural networks, and we explicit how they can be used as iterative message-passing algorithms, providing a fast method to compute the local polarizations of neurons. In the "retrieval phase", where neurons polarize in the direction of one memorized pattern, we point out a major difference between the belief propagation and TAP equations: The set of belief propagation equations depends on the pattern which is retrieved, while one can use a unique set of TAP equations. This makes the latter method much better suited for applications in the learning process of restricted Boltzmann machines. In the case where the patterns memorized in the Hopfield model are not independent, but are correlated through a combinatorial structure, we show that the TAP equations have to be modified. This modification can be seen either as an alteration of the reaction term in TAP equations or, more interestingly, as the consequence of message passing on a graphical model with several hidden layers, where the number of hidden layers depends on the depth of the correlations in the memorized patterns. This layered structure is actually necessary when one deals with more general restricted Boltzmann machines.
Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
NASA Astrophysics Data System (ADS)
Tseytlin, A. A.; Wulff, L.
2016-06-01
We determine the constraints imposed on the 10d target superspace geometry by the requirement of classical kappa-symmetry of the Green-Schwarz superstring. In the type I case we find that the background must satisfy a generalization of type I supergravity equations. These equations depend on an arbitrary vector X a and imply the one-loop scale invariance of the GS sigma model. In the special case when X a is the gradient of a scalar ϕ (dilaton) one recovers the standard type I equations equivalent to the 2d Weyl invariance conditions of the superstring sigma model. In the type II case we find a generalized version of the 10d supergravity equations the bosonic part of which was introduced in arXiv:1511.05795. These equations depend on two vectors X a and K a subject to 1st order differential relations (with the equations in the NS-NS sector depending only on the combination X a = X a + K a ). In the special case of K a = 0 one finds that X a = ∂ a ϕ and thus obtains the standard type II supergravity equations. New generalized solutions are found if K a is chosen to be a Killing vector (and thus they exist only if the metric admits an isometry). Non-trivial solutions of the generalized equations describe K-isometric backgrounds that can be mapped by T-duality to type II supergravity solutions with dilaton containing a linear isometry-breaking term. Examples of such backgrounds appeared recently in the context of integrable η-deformations of AdS n × S n sigma models. The classical kappa-symmetry thus does not, in general, imply the 2d Weyl invariance conditions for the GS sigma model (equivalent to type II supergravity equations) but only weaker scale invariance type conditions.
Women's Path into Science and Engineering Majors: A Structural Equation Model
ERIC Educational Resources Information Center
Camp, Amanda G.; Gilleland, Diane; Pearson, Carolyn; Vander Putten, Jim
2009-01-01
The intent of this study was to investigate the adequacy of Weidman's (1985, 1989) theoretical undergraduate socialization model as an empirical-based causal model pertaining to women's career path choice into a science or engineering (SE) major via structural equation modeling. Data were obtained from the Beginning Postsecondary Students…
Embedding IRT in Structural Equation Models: A Comparison with Regression Based on IRT Scores
ERIC Educational Resources Information Center
Lu, Irene R. R.; Thomas, D. Roland; Zumbo, Bruno D.
2005-01-01
This article reviews the problems associated with using item response theory (IRT)-based latent variable scores for analytical modeling, discusses the connection between IRT and structural equation modeling (SEM)-based latent regression modeling for discrete data, and compares regression parameter estimates obtained using predicted IRT scores and…
ERIC Educational Resources Information Center
Kim, Young-Mi; Neff, James Alan
2010-01-01
A model incorporating the direct and indirect effects of parental monitoring on adolescent alcohol use was evaluated by applying structural equation modeling (SEM) techniques to data on 4,765 tenth-graders in the 2001 Monitoring the Future Study. Analyses indicated good fit of hypothesized measurement and structural models. Analyses supported both…
A Graphical Method for Assessing the Identification of Linear Structural Equation Models
ERIC Educational Resources Information Center
Eusebi, Paolo
2008-01-01
A graphical method is presented for assessing the state of identifiability of the parameters in a linear structural equation model based on the associated directed graph. We do not restrict attention to recursive models. In the recent literature, methods based on graphical models have been presented as a useful tool for assessing the state of…
ERIC Educational Resources Information Center
Dawson, Thomas E.
This paper describes structural equation modeling (SEM) in comparison with another overarching analysis within the general linear model (GLM) analytic family: canonical correlation analysis. The uninitiated reader can gain an understanding of SEM's basic tenets and applications. Latent constructs discovered via a measurement model are explored and…
Derivation of a two-term infiltration equation from the Green Ampt model
NASA Astrophysics Data System (ADS)
Swartzendruber, D.
2000-09-01
For a uniform and infinitely deep soil at constant initial volumetric soil water content θn, the soil surface is subjected instantaneously to a ponded-water head that increases with the square root of time t1/2 after the initial ponding of water. An integration procedure is used in a rigorous derivation of the one-dimensional Green-Ampt flux equation. The resulting ordinary differential equation is solved exactly to yield the two-term infiltration equation wherein the coefficient of t is the sated hydraulic conductivity, but the ponded-head t1/2 function must be the same as the one found earlier by a different but exact mathematical derivation. The present findings reveal and describe this previously unknown kinship between the Green-Ampt infiltration model and the two-term infiltration equation, and underscore in still another way the serious limitations of the two-term equation.
NASA Technical Reports Server (NTRS)
Fortenbaugh, R. L.
1980-01-01
Equations incorporated in a VATOL six degree of freedom off-line digital simulation program and data for the Vought SF-121 VATOL aircraft concept which served as the baseline for the development of this program are presented. The equations and data are intended to facilitate the development of a piloted VATOL simulation. The equation presentation format is to state the equations which define a particular model segment. Listings of constants required to quantify the model segment, input variables required to exercise the model segment, and output variables required by other model segments are included. In several instances a series of input or output variables are followed by a section number in parentheses which identifies the model segment of origination or termination of those variables.
Wireless Fading Channel Models: From Classical to Stochastic Differential Equations
Olama, Mohammed M; Djouadi, Seddik M; Charalambous, Prof. Charalambos
2010-01-01
The wireless communications channel constitutes the basic physical link between the transmitter and the receiver antennas. Its modeling has been and continues to be a tantalizing issue, while being one of the most fundamental components based on which transmitters and receivers are designed and optimized. The ultimate performance limits of any communication system are determined by the channel it operates in. Realistic channel models are thus of utmost importance for system design and testing. In addition to exponential power path-loss, wireless channels suffer from stochastic short term fading (STF) due to multipath, and stochastic long term fading (LTF) due to shadowing depending on the geographical area. STF corresponds to severe signal envelope fluctuations, and occurs in densely built-up areas filled with lots of objects like buildings, vehicles, etc. On the other hand, LTF corresponds to less severe mean signal envelope fluctuations, and occurs in sparsely populated or suburban areas. In general, LTF and STF are considered as superimposed and may be treated separately. Ossanna was the pioneer to characterize the statistical properties of the signal received by a mobile user, in terms of interference of incident and reflected waves. His model was better suited for describing fading occurring mainly in suburban areas (LTF environments). It is described by the average power loss due to distance and power loss due to reflection of signals from surfaces, which when measured in dB's give rise to normal distributions, and this implies that the channel attenuation coefficient is log-normally distributed. Furthermore, in mobile communications, the LTF channel models are also characterized by their special correlation characteristics which have been reported. Clarke introduced the first comprehensive scattering model describing STF occurring mainly in urban areas. An easy way to simulate Clarke's model using a computer simulation is described. This model was later
An H Theorem for Boltzmann's Equation for the Yard-Sale Model of Asset Exchange
NASA Astrophysics Data System (ADS)
Boghosian, Bruce M.; Johnson, Merek; Marcq, Jeremy A.
2015-12-01
In recent work (Boghosian, Phys Rev E 89:042804-042825, 2014; Boghosian, Int J Mod Phys 25:1441008-1441015, 2014), Boltzmann and Fokker-Planck equations were derived for the "Yard-Sale Model" of asset exchange. For the version of the model without redistribution, it was conjectured, based on numerical evidence, that the time-asymptotic state of the model was oligarchy—complete concentration of wealth by a single individual. In this work, we prove that conjecture by demonstrating that the Gini coefficient, a measure of inequality commonly used by economists, is an H function of both the Boltzmann and Fokker-Planck equations for the model.
Kururi, Nana; Tozato, Fusae; Lee, Bumsuk; Kazama, Hiroko; Katsuyama, Shiori; Takahashi, Maiko; Abe, Yumiko; Matsui, Hiroki; Tokita, Yoshiharu; Saitoh, Takayuki; Kanaizumi, Shiomi; Makino, Takatoshi; Shinozaki, Hiromitsu; Yamaji, Takehiko; Watanabe, Hideomi
2016-01-01
The mandatory interprofessional education (IPE) programme at Gunma University, Japan, was initiated in 1999. A questionnaire of 10 items to assess the students' understanding of the IPE training programme has been distributed since then, and the factor analysis of the responses revealed that it was categorised into four subscales, i.e. "professional identity", "structure and function of training facilities", "teamwork and collaboration", and "role and responsibilities", and suggested that these may take into account the development of IPE programme with clinical training. The purpose of this study was to examine the professional identity acquisition process (PIAP) model in IPE using structural equation modelling (SEM). Overall, 1,581 respondents of a possible 1,809 students from the departments of nursing, laboratory sciences, physical therapy, and occupational therapy completed the questionnaire. The SEM technique was utilised to construct a PIAP model on the relationships among four factors. The original PIAP model showed that "professional identity" was predicted by two factors, namely "role and responsibilities" and "teamwork and collaboration". These two factors were predicted by the factor "structure and function of training facilities". The same structure was observed in nursing and physical therapy students' PIAP models, but it was not completely the same in laboratory sciences and occupational therapy students' PIAP models. A parallel but not isolated curriculum on expertise unique to the profession, which may help to understand their professional identity in combination with learning the collaboration, may be necessary.
Teacher Change Beliefs: Validating a Scale with Structural Equation Modelling
ERIC Educational Resources Information Center
Kin, Tai Mei; Abdull Kareem, Omar; Nordin, Mohamad Sahari; Wai Bing, Khuan
2015-01-01
The objectives of the study were to validate a substantiated Teacher Change Beliefs Model (TCBM) and an instrument to identify critical components of teacher change beliefs (TCB) in Malaysian secondary schools. Five different pilot test approaches were applied to ensure the validity and reliability of the instrument. A total of 936 teachers from…
A Structural Equation Model for ICT Usage in Higher Education
ERIC Educational Resources Information Center
Usluel, Yasemin Kocak; Askar, Petek; Bas, Turgay
2008-01-01
This study focuses on Information and Communication Technologies (ICT) usage, which is the indicator of diffusion. A model composed of the variables which can explain ICT usage in Turkish higher education is established and tested within the study. The two dimensions of ICT usage are considered: instructional and managerial. The data collected…
On Sensitivity of Structural Equation Modeling to Latent Relationship Misspecifications.
ERIC Educational Resources Information Center
Raykov, Tenko
2000-01-01
Provides counterexamples where the covariance matrix provides crucial information about consequential model misspecifications and cautions researchers about overinterpreting the conclusion of D. Rogosa and J. Willett (1985) that the covariance matrix is a severe summary of longitudinal data that may discard crucial information about growth. (SLD)
Application of Structural Equation Models to Quality of Life
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan; Skevington, Suzanne; Hao, Yua-Tao
2005-01-01
Quality of life (QOL) has become an important concept for health care. As QOL is a multidimensional concept that is best evaluated by a number of latent constructs, it is well recognized that latent variable models, such as exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) are useful tools for analyzing QOL data. Recently,…
Numerical integration of the master equation in some models of stochastic epidemiology.
Jenkinson, Garrett; Goutsias, John
2012-01-01
The processes by which disease spreads in a population of individuals are inherently stochastic. The master equation has proven to be a useful tool for modeling such processes. Unfortunately, solving the master equation analytically is possible only in limited cases (e.g., when the model is linear), and thus numerical procedures or approximation methods must be employed. Available approximation methods, such as the system size expansion method of van Kampen, may fail to provide reliable solutions, whereas current numerical approaches can induce appreciable computational cost. In this paper, we propose a new numerical technique for solving the master equation. Our method is based on a more informative stochastic process than the population process commonly used in the literature. By exploiting the structure of the master equation governing this process, we develop a novel technique for calculating the exact solution of the master equation--up to a desired precision--in certain models of stochastic epidemiology. We demonstrate the potential of our method by solving the master equation associated with the stochastic SIR epidemic model. MATLAB software that implements the methods discussed in this paper is freely available as Supporting Information S1.
Anisotropic Elastic Resonance Scattering model for the Neutron Transport equation
Mohamed Ouisloumen; Abderrafi M. Ougouag; Shadi Z. Ghrayeb
2014-11-24
The resonance scattering transfer cross-section has been reformulated to account for anisotropic scattering in the center-of-mass of the neutron-nucleus system. The main innovation over previous implementations is the relaxation of the ubiquitous assumption of isotropic scattering in the center-of-mass and the actual effective use of scattering angle distributions from evaluated nuclear data files in the computation of the angular moments of the resonant scattering kernels. The formulas for the high order anisotropic moments in the laboratory system are also derived. A multi-group numerical formulation is derived and implemented into a module incorporated within the NJOY nuclear data processing code. An ultra-fine energy mesh cross section library was generated using these new theoretical models and then was used for fuel assembly calculations with the PARAGON lattice physics code. The results obtained indicate a strong effect of this new model on reactivity, multi-group fluxes and isotopic inventory during depletion.
Eikonal solutions to optical model coupled-channel equations
NASA Technical Reports Server (NTRS)
Cucinotta, Francis A.; Khandelwal, Govind S.; Maung, Khin M.; Townsend, Lawrence W.; Wilson, John W.
1988-01-01
Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel scattering amplitudes. Analytic solutions are obtained for the second-order optical potential for elastic scattering. A numerical comparison is made between the first and second order optical model solutions for elastic and inelastic scattering of H-1 and He-4 on C-12. The effects of bound-state excitations on total and reaction cross sections are also estimated.
On the solutions of a model equation for shallow water waves of moderate amplitude
NASA Astrophysics Data System (ADS)
Mi, Yongsheng; Mu, Chunlai
This paper is concerned with the Cauchy problem of a model equation for shallow water waves of moderate amplitude, which was proposed by A. Constantin and D. Lannes [The hydrodynamical relevance of the Camassa-Holmand Degasperis-Procesi equations, Arch. Ration. Mech. Anal. 192 (2009) 165-186]. First, the local well-posedness of the model equation is obtained in Besov spaces Bp,rs, p,r∈[1,∞], s>max{3/2,1+1/p} (which generalize the Sobolev spaces Hs) by using Littlewood-Paley decomposition and transport equation theory. Second, the local well-posedness in critical case (with s=3/2, p=2, r=1) is considered. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time. Finally, persistence properties on strong solutions are also investigated.
The SMM model as a boundary value problem using the discrete diffusion equation.
Campbell, Joel
2007-12-01
A generalized single-step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.
The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation
NASA Technical Reports Server (NTRS)
Campbell, Joel
2007-01-01
A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.
Exploring Factor Model Parameters across Continuous Variables with Local Structural Equation Models.
Hildebrandt, Andrea; Lüdtke, Oliver; Robitzsch, Alexander; Sommer, Christopher; Wilhelm, Oliver
2016-01-01
Using an empirical data set, we investigated variation in factor model parameters across a continuous moderator variable and demonstrated three modeling approaches: multiple-group mean and covariance structure (MGMCS) analyses, local structural equation modeling (LSEM), and moderated factor analysis (MFA). We focused on how to study variation in factor model parameters as a function of continuous variables such as age, socioeconomic status, ability levels, acculturation, and so forth. Specifically, we formalized the LSEM approach in detail as compared with previous work and investigated its statistical properties with an analytical derivation and a simulation study. We also provide code for the easy implementation of LSEM. The illustration of methods was based on cross-sectional cognitive ability data from individuals ranging in age from 4 to 23 years. Variations in factor loadings across age were examined with regard to the age differentiation hypothesis. LSEM and MFA converged with respect to the conclusions. When there was a broad age range within groups and varying relations between the indicator variables and the common factor across age, MGMCS produced distorted parameter estimates. We discuss the pros of LSEM compared with MFA and recommend using the two tools as complementary approaches for investigating moderation in factor model parameters.
ANALYSIS OF TWO-PHASE FLOW MODELS WITH TWO MOMENTUM EQUATIONS.
KROSHILIN,A.E.KROSHILIN,V.E.KOHUT,P.
2004-03-15
An analysis of the standard system of differential equations describing multi-speed flows of multi-phase media is performed. It is proved that the Cauchy problem, as posed in most best-estimate thermal-hydraulic codes, results in unstable solutions and potentially unreliable description of many physical phenomena. A system of equations, free from instability effects, is developed allowing more rigorous numerical modeling.
Finite-difference models of ordinary differential equations - Influence of denominator functions
NASA Technical Reports Server (NTRS)
Mickens, Ronald E.; Smith, Arthur
1990-01-01
This paper discusses the influence on the solutions of finite-difference schemes of using a variety of denominator functions in the discrete modeling of the derivative for any ordinary differential equation. The results obtained are a consequence of using a generalized definition of the first derivative. A particular example of the linear decay equation is used to illustrate in detail the various solution possibilities that can occur.
The Wheeler-DeWitt Equation in Filćhenkov Model: The Lie Algebraic Approach
NASA Astrophysics Data System (ADS)
Panahi, H.; Zarrinkamar, S.; Baradaran, M.
2016-11-01
The Wheeler-DeWitt equation in Filćhenkov model with terms related to strings, dust, relativistic matter, bosons and fermions, and ultra stiff matter is solved in a quasi-exact analytical manner via the Lie algebraic approach. In the calculations, using the representation theory of sl(2), the general (N+1)-dimensional matrix equation is constructed whose determinant yields the solutions of the problem.
Entropic Lattice Boltzmann Model for Burger’s Equation
2004-05-28
invariant multi- speed entropic lattice Boltzmann models. Physica D. (In the press.) (doi:10.1016/j.physd. 2004.01.018.) Chen, H., Kandasamy , S ., Orszag, S ...61102F 6. AUTHOR( S ) 5d. PROJECT NUMBER B. M. Boghosian*, P. Love*, and J. Yepez 230 So. TASK NUMBER 0T f. WORK UNIT NUMBER Bi 7. PERFORMING...ORGANIZATION NAME( S ) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT Air Force Research Laboratory/VSBYA NUMBER 29 Randolph Road Hanscom AFB MA 01731-3010
A near-wall two-equation model for compressible turbulent flows
NASA Technical Reports Server (NTRS)
Zhang, H. S.; So, R. M. C.; Speziale, C. G.; Lai, Y. G.
1992-01-01
A near-wall two-equation turbulence model of the k-epsilon type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K-omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers, provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper.
Advances in modeling the pressure correlation terms in the second moment equations
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Shabbir, Aamir; Lumley, John L.
1991-01-01
In developing turbulence models, various model constraints were proposed in an attempt to make the model equations more general (or universal). The most recent of these are the realizability principle, the linearity principle, the rapid distortion theory, and the material indifference principle. Several issues are discussed concerning these principles and special attention is payed to the realizability principle. Realizability (defined as the requirement of non-negative energy and Schwarz' inequality between any fluctuating quantities) is the basic physical and mathematical principle that any modeled equation should obey. Hence, it is the most universal, important and also the minimal requirement for a model equation to prevent it from producing unphysical results. The principle of realizability is described in detail, the realizability conditions are derived for various turbulence models, and the model forms are proposed for the pressure correlation terms in the second moment equations. Detailed comparisons of various turbulence models with experiments and direct numerical simulations are presented. As a special case of turbulence, the two dimensional two-component turbulence modeling is also discussed.
A near-wall two-equation model for compressible turbulent flows
NASA Technical Reports Server (NTRS)
Zhang, H. S.; So, R. M. C.; Speziale, C. G.; Lai, Y. G.
1991-01-01
A near-wall two-equation turbulence model of the K - epsilon type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K - omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers, provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper.
Meffin, Hamish; Tahayori, Bahman; Grayden, David B; Burkitt, Anthony N
2012-12-01
Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace's equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite's membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.
Validating SESAME Equations of State for Use in Hydrocode Models of Small Solar System Bodies
NASA Astrophysics Data System (ADS)
Catherine, Plesko; Ferguson, Jim; Gisler, Galen R.; Weaver, Robert P.
2014-11-01
Hydrodynamic models of small solar system body impacts, collisions, and hazard mitigation require material-specific equations of state (EOS's) in order to close the system of equations that comprise the model and accurately predict the response of such objects to shocks and other hydrodynamic phenomena. Current models approximate meteoritic and cometary materials using Earth-analogue EOS's, e.g., quartz, dunite, hydrated tuff, water ice, and numerical convolutions of analog EOS's. Earth-analogues are used because the formulation of a comprehensive equation of state requires a large amount of experimental data that is destructive to the often rare samples. Analogue EOS's can, however, perform very differently from the original material under shock loading. Some experimental data has become available over time for various meteorite types. Here we compare the available shock data for meteoritic materials to analogue EOS's available in the public Los Alamos National Laboratory SESAME EOS database to explore the applicability and limitations of these models.
Lopez, L F; Coutinho, F A
2000-03-01
In this paper, we show that the positive solution of a nonlinear integral equation which appears in classical SIR epidemiological models is unique. The demonstration of this fact is necessary to justify the correctness of any approximate or numerical solution. The SIR epidemiological model is used only for simplicity. In fact, the methods used can be easily extended to prove the existence and uniqueness of the more involved integral equations that appear when more biological realities are considered. Thus the inclusion of a latent class (SLIR models) and models incorporating variability in the infectiousness with duration of the infection and spatial distribution lead to integral equations to which the results derived in this paper apply immediately.
NASA Astrophysics Data System (ADS)
Srokowski, T.
2001-09-01
The kangaroo process (KP) is characterized by various forms of covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential, and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some results appear to be incompatible with requirements of the fluctuation-dissipation theorem because probability distributions change when the process is inserted into the equation. We demonstrate how one can construct a model of noise free of that difficulty. This form of the KP is especially suitable for physical applications.
Rupšys, P.
2015-10-28
A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE.
Issues in multi-item scale testing and development using structural equation models.
McQuitty, Shaun; Bishop, James W
2006-01-01
Employing a structural equation model to evaluate a measurement scale can be challenging, especially for a multidimensional scale that contains many items. We describe two issues that can contribute to the poor fit of such models: the statistical power associated with the test of a large measurement scale; and the degree of correlation between items and factors within the scale. These issues are not well understood, so our purpose is to explain them at an applied level, clarify their practical implications for tests of measurement scales and other large structural equation models, and discuss potential strategies for addressing them.
NASA Astrophysics Data System (ADS)
Rupšys, P.
2015-10-01
A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE.
Review of Integrated Noise Model (INM) Equations and Processes
NASA Technical Reports Server (NTRS)
Shepherd, Kevin P. (Technical Monitor); Forsyth, David W.; Gulding, John; DiPardo, Joseph
2003-01-01
The FAA's Integrated Noise Model (INM) relies on the methods of the SAE AIR-1845 'Procedure for the Calculation of Airplane Noise in the Vicinity of Airports' issued in 1986. Simplifying assumptions for aerodynamics and noise calculation were made in the SAE standard and the INM based on the limited computing power commonly available then. The key objectives of this study are 1) to test some of those assumptions against Boeing source data, and 2) to automate the manufacturer's methods of data development to enable the maintenance of a consistent INM database over time. These new automated tools were used to generate INM database submissions for six airplane types :737-700 (CFM56-7 24K), 767-400ER (CF6-80C2BF), 777-300 (Trent 892), 717-200 (BR7 15), 757-300 (RR535E4B), and the 737-800 (CFM56-7 26K).
Finite difference modeling of Biot's poroelastic equations atseismic frequencies
Masson, Y.J.; Pride, S.R.; Nihei, K.T.
2006-02-24
Across the seismic band of frequencies (loosely defined as<10 kHz), a seismic wave propagating through a porous material willcreate flow in the pore space that is laminar; that is, in thislow-frequency "seismic limit," the development of viscous boundary layersin the pores need not be modeled. An explicit time steppingstaggered-grid finite difference scheme is presented for solving Biot'sequations of poroelasticity in this low-frequency limit. A key part ofthis work is the establishment of rigorous stability conditions. It isdemonstrated that over a wide range of porous material properties typicalof sedimentary rock and despite the presenceof fluid pressure diffusion(Biot slow waves), the usual Courant condition governs the stability asif the problem involved purely elastic waves. The accuracy of the methodis demonstrated by comparing to exact analytical solutions for both fastcompressional waves and slow waves. Additional numerical modelingexamples are also presented.
Gaseous microflow modeling using the Fokker-Planck equation
NASA Astrophysics Data System (ADS)
Singh, S. K.; Thantanapally, Chakradhar; Ansumali, Santosh
2016-12-01
We present a comparative study of gaseous microflow systems using the recently introduced Fokker-Planck approach and other methods such as: direct simulation Monte Carlo, lattice Boltzmann, and variational solution of Boltzmann-BGK. We show that this Fokker-Plank approach performs efficiently at intermediate values of Knudsen number, a region where direct simulation Monte Carlo becomes expensive and lattice Boltzmann becomes inaccurate. We also investigate the effectiveness of a recently proposed Fokker-Planck model in simulations of heat transfer, as a function of relevant parameters such as the Prandtl, Knudsen numbers. Furthermore, we present simulation of shock wave as a function of Mach number in transonic regime. Our results suggest that the performance of the Fokker-Planck approach is superior to that of the other methods in transition regime for rarefied gas flow and transonic regime for shock wave.
NASA Astrophysics Data System (ADS)
Cole, James B.
2014-09-01
The finite difference time domain (FDTD) algorithm is a popular tool for photonics design and simulations, but it also can yield deep insights into the fundamental nature of light and - more speculatively - into the discretization and connectivity and geometry of space-time. The CFL stability limit in FDTD can be interpreted as a limit on the speed of light. It depends not only on the dimensionality of space-time, but also on its connectivity. Thus the speed of light not only tells us something about the dimensionality of space-time but also about its connectivity. The computational molecule in conventional 2-D FDTD is (х +/- h,y)-(x,+/- y h)-(x-y), where h= triangle x = triangle y . It yields the CFL stability limit ctriangle/h<= t/h 1 √2 . Including diagonal nodes (x+/- h, y +/- h) in the computational molecule changes the connectivity of the space and changes the CFL limit. The FDTD model also predicts precursor signals (which physically exist). The Green's function of the FDTD model, which differs from that of the wave equation, may tell us something about underlying periodicities in space-time. It may be possible to experimentally observe effects of space-time discretization and connectivity in optics experiments.
Hoyle, Rick H; Gottfredson, Nisha C
2015-10-01
When the goal of prevention research is to capture in statistical models some measure of the dynamic complexity in structures and processes implicated in problem behavior and its prevention, approaches such as multilevel modeling (MLM) and structural equation modeling (SEM) are indicated. Yet the assumptions that must be satisfied if these approaches are to be used responsibly raise concerns regarding their use in prevention research involving smaller samples. In this article, we discuss in nontechnical terms the role of sample size in MLM and SEM and present findings from the latest simulation work on the performance of each approach at sample sizes typical of prevention research. For each statistical approach, we draw from extant simulation studies to establish lower bounds for sample size (e.g., MLM can be applied with as few as ten groups comprising ten members with normally distributed data, restricted maximum likelihood estimation, and a focus on fixed effects; sample sizes as small as N = 50 can produce reliable SEM results with normally distributed data and at least three reliable indicators per factor) and suggest strategies for making the best use of the modeling approach when N is near the lower bound.
Hoyle, Rick H.; Gottfredson, Nisha C.
2014-01-01
When the goal of prevention research is to capture in statistical models some measure of the dynamic complexity in structures and processes implicated in problem behavior and its prevention, approaches such as multilevel modeling (MLM) and structural equation modeling (SEM) are indicated. Yet the assumptions that must be satisfied if these approaches are to be used responsibly raise concerns regarding their use in prevention research involving smaller samples. In this manuscript we discuss in nontechnical terms the role of sample size in MLM and SEM and present findings from the latest simulation work on the performance of each approach at sample sizes typical of prevention research. For each statistical approach, we draw from extant simulation studies to establish lower bounds for sample size (e.g., MLM can be applied with as few as 10 groups comprising 10 members with normally distributed data, restricted maximum likelihood estimation, and a focus on fixed effects; sample sizes as small as N = 50 can produce reliable SEM results with normally distributed data and at least three reliable indicators per factor) and suggest strategies for making the best use of the modeling approach when N is near the lower bound. PMID:24752569
ERIC Educational Resources Information Center
Elrod, Terry; Haubl, Gerald; Tipps, Steven W.
2012-01-01
Recent research reflects a growing awareness of the value of using structural equation models to analyze repeated measures data. However, such data, particularly in the presence of covariates, often lead to models that either fit the data poorly, are exceedingly general and hard to interpret, or are specified in a manner that is highly data…
Matrix Solution of Coupled Differential Equations and Looped Car Following Models
ERIC Educational Resources Information Center
McCartney, Mark
2008-01-01
A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…
Technology Transfer Automated Retrieval System (TEKTRAN)
Soil erodibility is a key factor for estimating soil erosion using physically based models. In this study, a new parameterization approach for estimating erodibility was developed for the Rangeland Hydrology and Erosion Model (RHEM). The approach uses empirical equations that were developed by apply...
A new three-equation model for the CO{sub 2} laser
Stanghini, M.; Basso, M.; Genesio, R.; Tesi, A.; Meucci, R.; Ciofini, M.
1996-07-01
Three rate equations describing the single-mode CO{sub 2} laser dynamics are derived by applying the theory of linear filters to an improved four-level model. The model is studied in the case of periodic modulations of the losses and compared with the outcome of an experiment, revealing a good agreement.
ERIC Educational Resources Information Center
Karadag, Engin; Kilicoglu, Gökhan; Yilmaz, Derya
2014-01-01
The purpose of this study is to explain constructed theoretical models that organizational cynicism perceptions of primary school teachers affect school culture and academic achievement, by using structural equation modeling. With the assumption that there is a cause-effect relationship between three main variables, the study was constructed with…
A Demonstration of a Systematic Item-Reduction Approach Using Structural Equation Modeling
ERIC Educational Resources Information Center
Larwin, Karen; Harvey, Milton
2012-01-01
Establishing model parsimony is an important component of structural equation modeling (SEM). Unfortunately, little attention has been given to developing systematic procedures to accomplish this goal. To this end, the current study introduces an innovative application of the jackknife approach first presented in Rensvold and Cheung (1999). Unlike…
Residuals and the Residual-Based Statistic for Testing Goodness of Fit of Structural Equation Models
ERIC Educational Resources Information Center
Foldnes, Njal; Foss, Tron; Olsson, Ulf Henning
2012-01-01
The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…
ERIC Educational Resources Information Center
Leth-Steensen, Craig; Gallitto, Elena
2016-01-01
A large number of approaches have been proposed for estimating and testing the significance of indirect effects in mediation models. In this study, four sets of Monte Carlo simulations involving full latent variable structural equation models were run in order to contrast the effectiveness of the currently popular bias-corrected bootstrapping…
ERIC Educational Resources Information Center
Thompson, Bruce
A general linear model (GLM) framework is used to suggest that structure coefficients ought to be interpreted in structural equation modeling confirmatory factor analysis (CFA) studies in which factors are correlated. The computation of structure coefficients in explanatory factor analysis and CFA is explained. Two heuristic data sets are used to…
Keep Your Distance! Using Second-Order Ordinary Differential Equations to Model Traffic Flow
ERIC Educational Resources Information Center
McCartney, Mark
2004-01-01
A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted. The model can be used as an application of solution techniques taught at first-year undergraduate level and as a motivator to encourage…
ERIC Educational Resources Information Center
Cheung, Mike W. L.; Chan, Wai
2009-01-01
Structural equation modeling (SEM) is widely used as a statistical framework to test complex models in behavioral and social sciences. When the number of publications increases, there is a need to systematically synthesize them. Methodology of synthesizing findings in the context of SEM is known as meta-analytic SEM (MASEM). Although correlation…
ERIC Educational Resources Information Center
Green, Samuel B.; Yang, Yanyun
2009-01-01
A method is presented for estimating reliability using structural equation modeling (SEM) that allows for nonlinearity between factors and item scores. Assuming the focus is on consistency of summed item scores, this method for estimating reliability is preferred to those based on linear SEM models and to the most commonly reported estimate of…
Approximations to the Distributions of Fit Indexes for Misspecified Structural Equation Models.
ERIC Educational Resources Information Center
Ogasawara, Haruhiko
2001-01-01
Derives approximations to the distributions of goodness-of-fit indexes in structural equation modeling with the assumption of multivariate normality and slight misspecification of models. Also derives an approximation to the asymptotic covariance matrix for the fit indexes by using the delta method and develops approximations to the densities of…
ERIC Educational Resources Information Center
In'nami, Yo; Koizumi, Rie
2010-01-01
Because structural equation models are widely used in testing and assessment, investigation into the accuracy of such models may help raise awareness of the value of reanalysis or replication. We focused on second language testing and learning studies and examined: (a) To what extent is information necessary for replication provided by authors?…
ERIC Educational Resources Information Center
Gonzalez-Pienda, Julio Antonio; Nunez, Jose Carlos; Gonzalez-Pumariega, Soledad; Alvarez, Luis; Roces, Cristina; Garcia, Marta
2002-01-01
Used the structural equation model approach to test a model hypothesizing the influence of parental involvement on students' academic aptitudes, self-concept, and causal attributions, as well as the influence of these variables on academic achievement. Results for 261 adolescents aged 12 to 18 years suggest that cognitive-affective variables are…
Relativistic compact anisotropic charged stellar models with Chaplygin equation of state
NASA Astrophysics Data System (ADS)
Bhar, Piyali; Murad, Mohammad Hassan
2016-10-01
This paper presents a new model of static spherically symmetric relativistic charged stellar objects with locally anisotropic matter distribution together with the Chaplygin equation of state. The interior spacetime has been matched continuously to the exterior Reissner-Nordström geometry. Different physical properties of the stellar model have been investigated, analyzed, and presented graphically.
ERIC Educational Resources Information Center
Wang, Jing-Ru; Chen, Shin-Feng
2014-01-01
This study used a Chinese-language version of the Index of Science Reading Awareness (ISRA) to investigate metacognitive awareness and the Reading Comprehension of Science Test (RCST) to explore comprehension of science text by Taiwanese students. Structural equation modeling (SEM) results confirmed the validity of the underlying models of…
Introduction of the Notion of Differential Equations by Modelling Based Teaching
ERIC Educational Resources Information Center
Budinski, Natalija; Takaci, Djurdjica
2011-01-01
This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…
Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data
ERIC Educational Resources Information Center
Lee, Sik-Yum
2006-01-01
A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…
Fixed-Effects Meta-Analyses as Multiple-Group Structural Equation Models
ERIC Educational Resources Information Center
Cheung, Mike W. -L.
2010-01-01
Meta-analysis is the statistical analysis of a collection of analysis results from individual studies, conducted for the purpose of integrating the findings. Structural equation modeling (SEM), on the other hand, is a multivariate technique for testing hypothetical models with latent and observed variables. This article shows that fixed-effects…
An Examination of Statistical Power in Multigroup Dynamic Structural Equation Models
ERIC Educational Resources Information Center
Prindle, John J.; McArdle, John J.
2012-01-01
This study used statistical simulation to calculate differential statistical power in dynamic structural equation models with groups (as in McArdle & Prindle, 2008). Patterns of between-group differences were simulated to provide insight into how model parameters influence power approximations. Chi-square and root mean square error of…
A moist Boussinesq shallow water equations set for testing atmospheric models
Zerroukat, M. Allen, T.
2015-06-01
The shallow water equations have long been used as an initial test for numerical methods applied to atmospheric models with the test suite of Williamson et al. being used extensively for validating new schemes and assessing their accuracy. However the lack of physics forcing within this simplified framework often requires numerical techniques to be reworked when applied to fully three dimensional models. In this paper a novel two-dimensional shallow water equations system that retains moist processes is derived. This system is derived from three-dimensional Boussinesq approximation of the hydrostatic Euler equations where, unlike the classical shallow water set, we allow the density to vary slightly with temperature. This results in extra (or buoyancy) terms for the momentum equations, through which a two-way moist-physics dynamics feedback is achieved. The temperature and moisture variables are advected as separate tracers with sources that interact with the mean-flow through a simplified yet realistic bulk moist-thermodynamic phase-change model. This moist shallow water system provides a unique tool to assess the usually complex and highly non-linear dynamics–physics interactions in atmospheric models in a simple yet realistic way. The full non-linear shallow water equations are solved numerically on several case studies and the results suggest quite realistic interaction between the dynamics and physics and in particular the generation of cloud and rain. - Highlights: • Novel shallow water equations which retains moist processes are derived from the three-dimensional hydrostatic Boussinesq equations. • The new shallow water set can be seen as a more general one, where the classical equations are a special case of these equations. • This moist shallow water system naturally allows a feedback mechanism from the moist physics increments to the momentum via buoyancy. • Like full models, temperature and moistures are advected as tracers that interact
Noise modeling from high-permeability shields using Kirchhoff equations
Sandin, Henrik J; Volegov, Petr L; Espy, Michelle A; Matlashov, Andrei N; Savukov, Igor M; Schultz, Larry J
2010-01-01
Progress in the development of high-sensitivity magnetic-field measurements has stimulated interest in understanding magnetic noise of conductive materials, especially of magnetic shields (DC or rf) based on high-permeability materials and/or high-conductivity materials. For example, SQUIDs and atomic magnetometers have been used in many experiments with mu-metal shields, and additionally SQUID systems frequently have rf shielding based on thin conductive materials. Typical existing approaches to modeling noise only work with simple shield and sensor geometries while common experimental setups today consist of multiple sensor systems arbitrary shapes and complex shield geometries. With complex sensor arrays used in, for example, MEG and Ultra Low Field MRI studies the knowledge of the noise correlation between sensors is as important as the knowledge of the noise itself. This is crucial for incorporating efficient noise cancelation schemes for the system. We developed an approach that allows us to calculate the Johnson noise for any geometrically shaped shield and multiple sensor systems. The approach uses a fraction of the processing power of other approaches and with a multiple sensor system our approach not only calculates the noise for each sensor but it also calculates the noise correlation matrix between sensors. Here we will show the algorithm and examples where it can be implemented.
Tao, Youshan; Guo, Qian; Aihara, Kazuyuki
2014-10-01
Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.
Coefficients of an analytical aerosol forcing equation determined with a Monte-Carlo radiation model
NASA Astrophysics Data System (ADS)
Hassan, Taufiq; Moosmüller, H.; Chung, Chul E.
2015-10-01
Simple analytical equations for global-average direct aerosol radiative forcing are useful to quickly estimate aerosol forcing changes as function of key atmosphere, surface and aerosol parameters. The surface and atmosphere parameters in these analytical equations are the globally uniform atmospheric transmittance and surface albedo, and have so far been estimated from simplified observations under untested assumptions. In the present study, we take the state-of-the-art analytical equation and write the aerosol forcing as a linear function of the single scattering albedo (SSA) and replace the average upscatter fraction with the asymmetry parameter (ASY). Then we determine the surface and atmosphere parameter values of this equation using the output from the global MACR (Monte-Carlo Aerosol Cloud Radiation) model, as well as testing the validity of the equation. The MACR model incorporated spatio-temporally varying observations for surface albedo, cloud optical depth, water vapor, stratosphere column ozone, etc., instead of assuming as in the analytical equation that the atmosphere and surface parameters are globally uniform, and should thus be viewed as providing realistic radiation simulations. The modified analytical equation needs globally uniform aerosol parameters that consist of AOD (Aerosol Optical Depth), SSA, and ASY. The MACR model is run here with the same globally uniform aerosol parameters. The MACR model is also run without cloud to test the cloud effect. In both cloudy and cloud-free runs, the equation fits in the model output well whether SSA or ASY varies. This means the equation is an excellent approximation for the atmospheric radiation. On the other hand, the determined parameter values are somewhat realistic for the cloud-free runs but unrealistic for the cloudy runs. The global atmospheric transmittance, one of the determined parameters, is found to be around 0.74 in case of the cloud-free conditions and around 1.03 with cloud. The surface
Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state
NASA Astrophysics Data System (ADS)
Sharov, G. S.
2016-06-01
Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter H(z) and cosmic microwave background constraints are described with different cosmological models. We compare the ΛCDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale rs(zd). Among the considered models the best value of χ2 is achieved for the model with quadratic equation of state, but it has 2 additional parameters in comparison with the ΛCDM and therefore is not favored by the Akaike information criterion.
NASA Technical Reports Server (NTRS)
Gnoffo, Peter A.; Gupta, Roop N.; Shinn, Judy L.
1989-01-01
The conservation equations for simulating hypersonic flows in thermal and chemical nonequilibrium and details of the associated physical models are presented. These details include the curve fits used for defining thermodynamic properties of the 11 species air model, curve fits for collision cross sections, expressions for transport properties, the chemical kinetics models, and the vibrational and electronic energy relaxation models. The expressions are formulated in the context of either a two or three temperature model. Greater emphasis is placed on the two temperature model in which it is assumed that the translational and rotational energy models are in equilibrium at the translational temperature, T, and the vibrational, electronic, and electron translational energy modes are in equilibrium at the vibrational temperature, T sub v. The eigenvalues and eigenvectors associated with the Jacobian of the flux vector are also presented in order to accommodate the upwind based numerical solutions of the complete equation set.
A new form of the elliptic relaxation equation to account for wall effects in RANS modeling
NASA Astrophysics Data System (ADS)
Manceau, Rémi; Hanjalić, Kemal
2000-09-01
Different methods for improving the behavior in the logarithmic layer of the elliptic relaxation equation, which enable the extension of Reynolds stress models or eddy viscosity models down to the wall, are tested in a channel flow at Reτ=590 and compared with direct numerical simulation (DNS) data. First, a priori tests are performed in order to confirm the improvement predicted by the theory, either with the Rotta+IP (isotropization of production) model or the Speziale-Sarkar-Gatski (SSG) model as the source term of the elliptic relaxation equation. The best form of the model is then used for full simulations, in Durbin second moment closure or in the frame of the v2¯-f model. It is shown that the results can be significantly improved, in particular by using a formulation based on the refinement of the modeling of the two-point correlations involved in the redistribution term.
A Multi-Fidelity Surrogate Model for Handling Real Gas Equations of State
NASA Astrophysics Data System (ADS)
Ouellet, Frederick; Park, Chanyoung; Rollin, Bertrand; Balachandar, S."bala"
2016-11-01
The explosive dispersal of particles is an example of a complex multiphase and multi-species fluid flow problem. This problem has many engineering applications including particle-laden explosives. In these flows, the detonation products of the explosive cannot be treated as a perfect gas so a real gas equation of state is used to close the governing equations (unlike air, which uses the ideal gas equation for closure). As the products expand outward from the detonation point, they mix with ambient air and create a mixing region where both of the state equations must be satisfied. One of the more accurate, yet computationally expensive, methods to deal with this is a scheme that iterates between the two equations of state until pressure and thermal equilibrium are achieved inside of each computational cell. This work strives to create a multi-fidelity surrogate model of this process. We then study the performance of the model with respect to the iterative method by performing both gas-only and particle laden flow simulations using an Eulerian-Lagrangian approach with a finite volume code. Specifically, the model's (i) computational speed, (ii) memory requirements and (iii) computational accuracy are analyzed to show the benefits of this novel modeling approach. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA00023.
A single-equation study of US petroleum consumption: The role of model specificiation
Jones, C.T. )
1993-04-01
The price responsiveness of US petroleum consumption began to attract a great deal of attention following the unexpected and substantial oil price increases of 1973-74. There have been a number of large, multi-equation econometric studies of US energy demand since then which have focused primarily on estimating short run and long run price and income elasticities of individual energy resources (coal, oil, natural gas electricity) for various consumer sectors (residential, industrial, commercial). Following these early multi-equation studies there have been several single-equation studies of aggregate US petroleum consumption. When choosing an economic model specification for a single-equation study of aggregate US petroleum consumption, an easily estimated model that will provide unbiased price and income elasticity estimates and yield accurate forecasts is needed. Using Hendry's general-to-simple specification search technique and annual data to obtain a restricted, data-acceptable simplification of a general ADL model yielded GNP and short run price elasticities near the consensus estimates, but a long run price elasticity substantially smaller than existing estimates. Comparisons with three other seemingly acceptable simple-to-general models showed that popular model specifications often involve untested, unacceptable parameter restrictions. These models may also demonstrate poorer forecasting performance. Based on results, the general-to-simple approach appears to offer a more accurate methodology for generating superior forecast models of petroleum consumption and other energy use patterns.
Molecular drag model based on differential reduction of the Kruger-Shapiro equations
NASA Astrophysics Data System (ADS)
Helmer, J. C.; Levi, G.
2002-07-01
The history of the method of differential probability in molecular flow is reviewed, beginning with the little known derivation by D. Santeler (5th Annual Symposium on Space Environmental Simulation, Arnold Air Force Station, TN, May, 1964), based on the equation of C. W. Oatley [Br. J. Appl. Phys. 8, 15 (1957)]. This method contains the aperture correction within the theory, without phenomenological assumptions. A new equation of this type, for molecular pumping, is derived by differential reduction of the Kruger-Shapiro equations. A simple solution of the differential equations yields results of good accuracy for engineering use. The physical characteristics of molecular pumping are clarified by describing the pressure distribution within the pumping tube as if it were a conductance. By this method the calculated performance of a model pump is shown to be in satisfactory agreement with a Clausing-type solution from a previous publication. copyright 2002 American Vacuum Society.
A pseudospectral solution of a Fokker-Planck equation to model isomerization reactions
NASA Astrophysics Data System (ADS)
Shizgal, Bernie D.
2016-11-01
A Fokker-Planck equation is used to model a reactive system with two stable states. The barrier of the potential that separates the states is controlled with a parameter, ɛ, that alters the height of the barrier that separates the two states of the system. The rate of transitions between the two states, equivalently the rate of reaction, can be treated with a transition state theory as for a large class of chemical reactions. The Fokker-Planck equation is solved with a pseudospectral method based on nonclassical basis polynomials. The time dependent solution is expressed in terms of the eigenvalues and eigenfunctions of the linear Fokker-Planck operator. This eigenvalue problem can be written as the solution of a Schrödinger equation with a potential function defined by the drift and diffusion coefficients in the Fokker-Planck equation.
Contribution to modeling the viscosity Arrhenius-type equation for saturated pure fluids
NASA Astrophysics Data System (ADS)
Tian, Jianxiang; Zhang, Laibin
2016-09-01
Recently, Haj-Kacem et al. proposed an equation modeling the relationship between the two parameters of viscosity Arrhenius-type equations [Fluid Phase Equilibria 383, 11 (2014)]. The authors found that the two parameters are dependent upon each other in an exponential function form. In this paper, we reconsidered their ideas and calculated the two parameter values for 49 saturated pure fluids by using the experimental data in the NIST WebBook. Our conclusion is different with the ones of Haj-Kacem et al. We found that (the linearity shown by) the Arrhenius equation stands strongly only in low temperature range and that the two parameters of the Arrhenius equation are independent upon each other in the whole temperature range from the triple point to the critical point.
Discontinuous Galerkin method for Krauseʼs consensus models and pressureless Euler equations
NASA Astrophysics Data System (ADS)
Yang, Yang; Wei, Dongming; Shu, Chi-Wang
2013-11-01
In this paper, we apply discontinuous Galerkin (DG) methods to solve two model equations: Krause's consensus models and pressureless Euler equations. These two models are used to describe the collisions of particles, and the distributions can be identified as density functions. If the particles are placed at a single point, then the density function turns out to be a δ-function and is difficult to be well approximated numerically. In this paper, we use DG method to approximate such a singularity and demonstrate the good performance of the scheme. Since the density functions are always positive, we apply a positivity-preserving limiter to them. Moreover, for pressureless Euler equations, the velocity satisfies the maximum principle. We also construct special limiters to fulfill this requirement.
Chiu, Weisheng; Rodriguez, Fernando M; Won, Doyeon
2016-10-01
This study examines the factor structure of the shortened version of the Leadership Scale for Sport, through a survey of 201 collegiate swimmers at National Collegiate Athletic Association Division II and III institutions, using both exploratory structural equation modeling and confirmatory factor analysis. Both exploratory structural equation modeling and confirmatory factor analysis showed that a five-factor solution fit the data adequately. The sizes of factor loadings on target factors substantially differed between the confirmatory factor analysis and exploratory structural equation modeling solutions. In addition, the inter-correlations between factors of the Leadership Scale for Sport and the correlations with athletes' satisfaction were found to be inflated in the confirmatory factor analysis solution. Overall, the findings provide evidence of the factorial validity of the shortened Leadership Scale for Sport.
Modeling of human movement monitoring using Bluetooth Low Energy technology.
Mokhtari, G; Zhang, Q; Karunanithi, M
2015-01-01
Bluetooth Low Energy (BLE) is a wireless communication technology which can be used to monitor human movements. In this monitoring system, a BLE signal scanner scans signal strength of BLE tags carried by people, to thus infer human movement patterns within its monitoring zone. However to the extent of our knowledge one main aspect of this monitoring system which has not yet been thoroughly investigated in literature is how to build a sound theoretical model, based on tunable BLE communication parameters such as scanning time interval and advertising time interval, to enable the study and design of effective and efficient movement monitoring systems. In this paper, we proposed and developed a statistical model based on Monte-Carlo simulation, which can be utilized to assess impacts of BLE technology parameters in terms of latency and efficiency, on a movement monitoring system, and can thus benefit a more efficient system design.
Lee, Sik-Yum; Song, Xin-Yuan
2004-05-01
Missing data are very common in behavioural and psychological research. In this paper, we develop a Bayesian approach in the context of a general nonlinear structural equation model with missing continuous and ordinal categorical data. In the development, the missing data are treated as latent quantities, and provision for the incompleteness of the data is made by a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm. We show by means of a simulation study that the Bayesian estimates are accurate. A Bayesian model comparison procedure based on the Bayes factor and path sampling is proposed. The required observations from the posterior distribution for computing the Bayes factor are simulated by the hybrid algorithm in Bayesian estimation. Our simulation results indicate that the correct model is selected more frequently when the incomplete records are used in the analysis than when they are ignored. The methodology is further illustrated with a real data set from a study concerned with an AIDS preventative intervention for Filipina sex workers.
Modeling languages for biochemical network simulation: reaction vs equation based approaches.
Wiechert, Wolfgang; Noack, Stephan; Elsheikh, Atya
2010-01-01
Biochemical network modeling and simulation is an essential task in any systems biology project. The systems biology markup language (SBML) was established as a standardized model exchange language for mechanistic models. A specific strength of SBML is that numerous tools for formulating, processing, simulation and analysis of models are freely available. Interestingly, in the field of multidisciplinary simulation, the problem of model exchange between different simulation tools occurred much earlier. Several general modeling languages like Modelica have been developed in the 1990s. Modelica enables an equation based modular specification of arbitrary hierarchical differential algebraic equation models. Moreover, libraries for special application domains can be rapidly developed. This contribution compares the reaction based approach of SBML with the equation based approach of Modelica and explains the specific strengths of both tools. Several biological examples illustrating essential SBML and Modelica concepts are given. The chosen criteria for tool comparison are flexibility for constraint specification, different modeling flavors, hierarchical, modular and multidisciplinary modeling. Additionally, support for spatially distributed systems, event handling and network analysis features is discussed. As a major result it is shown that the choice of the modeling tool has a strong impact on the expressivity of the specified models but also strongly depends on the requirements of the application context.
Wu, Liejun; Chen, Maoxue; Chen, Yongli; Li, Qing X.
2013-01-01
Gas holdup time (tM) is a basic parameter in isothermal gas chromatography (GC). Determination and evaluation of tM and retention behaviors of n-alkanes under isothermal GC conditions have been extensively studied since the 1950s, but still remains unresolved. The difference equation (DE) model [J. Chromatogr. A 1260:215–223] reveals retention behaviors of n-alkanes excluding tM, while the quadratic equation (QE) model [J. Chromatogr. A 1260:224–231] including tM is suitable for applications. In the present study, tM values were calculated with the QE model, which is referred to as tMT, evaluated and compared with other three typical nonlinear models. The QE model gives an accurate estimation of tM in isothermal GC. The tMT values are highly accurate, stable, and easy to calculate and use. There is only one tMT value at each GC condition. The proper classification of tM values can clarify their disagreement and facilitate GC retention data standardization for which tMT values are promising reference tM values. PMID:23726077
The universal characteristics of a thermodynamic model to conform to the Gibbs-Duhem equation
Tao, Dong-Ping
2016-01-01
In a multi-component homogeneous system, the relationship between partial molar and molar quantity (RPMQ) is proved to be an equivalent relation of the Gibbs-Duhem equation. The universal characteristics of a thermodynamic model to conform to the Gibbs-Duhem equation are inferred from the RPMQ. Based on the inference, an asymmetric regular solution model is suggested to deal with those systems that exhibit strong negative deviation, strong positive deviation, and both strong positive and negative deviation from ideality. PMID:27762329
NASA Astrophysics Data System (ADS)
Jin, Liang; Bauer, Helmut F.
1991-09-01
Kane's dynamical model of flexible multibody space systems with tree structure is developed in this paper. The system topology is restricted to a tree configuration which is defined as an arbitrary set of flexible and rigid bodies connected by hinges characterizing relative translations and rotations of two adjoining bodies. The relative translational velocities, angular velocities, and the differential of model coordinates are selected as the generalized velocities. The motion equations of minimum dimension are derived via Kane's method. The resulting equations are suitable for automatic generation and computer simulation.
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik
2009-06-01
The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.
RAS one-equation turbulence model with non-singular eddy-viscosity coefficient
NASA Astrophysics Data System (ADS)
Rahman, M. M.; Agarwal, R. K.; Siikonen, T.
2016-02-01
A simplified consistency formulation for Pk/ε (production to dissipation ratio) is devised to obtain a non-singular Cμ (coefficient of eddy-viscosity) in the explicit algebraic Reynolds stress model of Gatski and Speziale. The coefficient Cμ depends non-linearly on both rotational/irrotational strains and is used in the framework of an improved RAS (Rahman-Agarwal-Siikonen) one-equation turbulence model to calculate a few well-documented turbulent flows, yielding predictions in good agreement with the direct numerical simulation and experimental data. The strain-dependent Cμ assists the RAS model in constructing the coefficients and functions such as to benefit complex flows with non-equilibrium turbulence. Comparisons with the Spalart-Allmaras one-equation model and the shear stress transport k-ω model demonstrate that Cμ improves the response of RAS model to non-equilibrium effects.
Equation-based languages – A new paradigm for building energy modeling, simulation and optimization
Wetter, Michael; Bonvini, Marco; Nouidui, Thierry S.
2016-04-01
Most of the state-of-the-art building simulation programs implement models in imperative programming languages. This complicates modeling and excludes the use of certain efficient methods for simulation and optimization. In contrast, equation-based modeling languages declare relations among variables, thereby allowing the use of computer algebra to enable much simpler schematic modeling and to generate efficient code for simulation and optimization. We contrast the two approaches in this paper. We explain how such manipulations support new use cases. In the first of two examples, we couple models of the electrical grid, multiple buildings, HVAC systems and controllers to test a controller that adjusts building room temperatures and PV inverter reactive power to maintain power quality. In the second example, we contrast the computing time for solving an optimal control problem for a room-level model predictive controller with and without symbolic manipulations. As a result, exploiting the equation-based language led to 2, 200 times faster solution
Variational Derivation of Dissipative Equations
NASA Astrophysics Data System (ADS)
Sogo, Kiyoshi
2017-03-01
A new variational principle is formulated to derive various dissipative equations. Model equations considered are the damping equation, Bloch equation, diffusion equation, Fokker-Planck equation, Kramers equation and Smoluchowski equation. Each equation and its time reversal equation are simultaneously obtained in our variational principle.
ERIC Educational Resources Information Center
Deboeck, Pascal R.; Boker, Steven M.; Bergeman, C. S.
2008-01-01
Among the many methods available for modeling intraindividual time series, differential equation modeling has several advantages that make it promising for applications to psychological data. One interesting differential equation model is that of the damped linear oscillator (DLO), which can be used to model variables that have a tendency to…
a Radiative Transfer Equation/phase Function Approach to Vegetation Canopy Reflectance Modeling
NASA Astrophysics Data System (ADS)
Randolph, Marion Herbert
Vegetation canopy reflectance models currently in use differ considerably in their treatment of the radiation scattering problem, and it is this fundamental difference which stimulated this investigation of the radiative transfer equation/phase function approach. The primary objective of this thesis is the development of vegetation canopy phase functions which describe the probability of radiation scattering within a canopy in terms of its biological and physical characteristics. In this thesis a technique based upon quadrature formulae is used to numerically generate a variety of vegetation canopy phase functions. Based upon leaf inclination distribution functions, phase functions are generated for plagiophile, extremophile, erectophile, spherical, planophile, blue grama (Bouteloua gracilis), and soybean canopies. The vegetation canopy phase functions generated are symmetric with respect to the incident and exitant angles, and hence satisfy the principle of reciprocity. The remaining terms in the radiative transfer equation are also derived in terms of canopy geometry and optical properties to complete the development of the radiative transfer equation/phase function description for vegetation canopy reflectance modeling. In order to test the radiative transfer equation/phase function approach the iterative discrete ordinates method for solving the radiative transfer equation is implemented. In comparison with field data, the approach tends to underestimate the visible reflectance and overestimate infrared reflectance. The approach does compare well, however, with other extant canopy reflectance models; for example, it agrees to within ten to fifteen percent of the Suits model (Suits, 1972). Sensitivity analysis indicates that canopy geometry may influence reflectance as much as 100 percent for a given wavelength. Optical thickness produces little change in reflectance after a depth of 2.5 (Leaf area index of 4.0) is reached, and reflectance generally increases
Acoustic Field Associated with Parabolized Stability Equation Models in Turbulent Jets
2013-05-01
discusses linear models of these wavepackets for supersonic turbulent jets based on Parabolized Stability Equations ( PSE ). In the past, results of...comparisons of the PSE models with near-field pressure fields from LES, filtered by means of Proper Orthogonal Decomposition (POD), demonstrate acceptable...fidelity of the model. Finally, the acoustic far-field associated with the PSE wavepackets is computed using a Kirchhoff surface method, capturing
Kershaw closures for linear transport equations in slab geometry I: Model derivation
NASA Astrophysics Data System (ADS)
Schneider, Florian
2016-10-01
This paper provides a new class of moment models for linear kinetic equations in slab geometry. These models can be evaluated cheaply while preserving the important realizability property, that is the fact that the underlying closure is non-negative. Several comparisons with the (expensive) state-of-the-art minimum-entropy models are made, showing the similarity in approximation quality of the two classes.
Complete Galilean-Invariant Lattice BGK Models for the Navier-Stokes Equation
NASA Technical Reports Server (NTRS)
Qian, Yue-Hong; Zhou, Ye
1998-01-01
Galilean invariance has been an important issue in lattice-based hydrodynamics models. Previous models concentrated on the nonlinear advection term. In this paper, we take into account the nonlinear response effect in a systematic way. Using the Chapman-Enskog expansion up to second order, complete Galilean invariant lattice BGK models in one dimension (theta = 3) and two dimensions (theta = 1) for the Navier-Stokes equation have been obtained.
KdV-Burgers equation in the modified continuum model considering anticipation effect
NASA Astrophysics Data System (ADS)
Liu, Huaqing; Zheng, Pengjun; Zhu, Keqiang; Ge, Hongxia
2015-11-01
The new continuum model mentioned in this paper is developed based on optimal velocity car-following model, which takes the drivers' anticipation effect into account. The critical condition for traffic flow is derived, and nonlinear analysis shows density waves occur in traffic flow because of the small disturbance. Near the neutral stability line, the KdV-Burgers equation is derived and one of the solutions is given. Numerical simulation is carried out to show the local cluster described by the model.
Implementation of a two-equation k-omega turbulence model in NPARC
NASA Technical Reports Server (NTRS)
Yoder, Dennis A.; Georgiadis, Nicholas J.; Orkwis, Paul D.
1996-01-01
The implementation of a two-equation k-omega turbulence model into the NPARC flow solver is described. Motivation for the selection of this model is given, major code modifications are outlined, new imputs to the code are described, and results are presented for several validation cases: an incompressible flow over a smooth flat plate, a subsonic diffuser flow, and a shock-induced separated flow. Comparison of results with the k-epsilon model indicate that the k-omega model predicts simple flows equally well whereas, for adverse pressure gradient flows, the k-omega model outperforms the other turbulence models in NPARC.
A New Equation Solver for Modeling Turbulent Flow in Coupled Matrix-Conduit Flow Models.
Hubinger, Bernhard; Birk, Steffen; Hergarten, Stefan
2016-07-01
Karst aquifers represent dual flow systems consisting of a highly conductive conduit system embedded in a less permeable rock matrix. Hybrid models iteratively coupling both flow systems generally consume much time, especially because of the nonlinearity of turbulent conduit flow. To reduce calculation times compared to those of existing approaches, a new iterative equation solver for the conduit system is developed based on an approximated Newton-Raphson expression and a Gauß-Seidel or successive over-relaxation scheme with a single iteration step at the innermost level. It is implemented and tested in the research code CAVE but should be easily adaptable to similar models such as the Conduit Flow Process for MODFLOW-2005. It substantially reduces the computational effort as demonstrated by steady-state benchmark scenarios as well as by transient karst genesis simulations. Water balance errors are found to be acceptable in most of the test cases. However, the performance and accuracy may deteriorate under unfavorable conditions such as sudden, strong changes of the flow field at some stages of the karst genesis simulations.
Parabolic equation modeling of high frequency acoustic transmission with an evolving sea surface.
Senne, J; Song, A; Badiey, M; Smith, K B
2012-09-01
The present paper examines the temporal evolution of acoustic fields by modeling forward propagation subject to sea surface dynamics with time scales of less than a second to tens of seconds. A time-evolving rough sea surface model is combined with a rough surface formulation of a parabolic equation model for predicting time-varying acoustic fields. Surface waves are generated from surface wave spectra, and stepped in time using a Runge-Kutta integration technique applied to linear evolution equations. This evolving, range-dependent surface information is combined with other environmental parameters and input to the acoustic model, giving an approximation of the time-varying acoustic field. The wide-angle parabolic equation model manages the rough sea surfaces by molding them into the boundary conditions for calculations of the near-surface acoustic field. This merged acoustic model is validated using concurrently-collected acoustic and environmental information, including surface wave spectra. Data to model comparisons demonstrate that the model is able to approximate the ensemble-averaged acoustic intensity at ranges of about a kilometer for acoustic signals of around 15 kHz. Furthermore, the model is shown to capture variations due to surface fluctuations occurring over time scales of less than a second to tens of seconds.
Heat Transfer on a Film-Cooled Rotating Blade Using a Two Equation Turbulence Model
NASA Technical Reports Server (NTRS)
Garg, Vijay K.
1998-01-01
A three-dimensional Navier-Stokes code has been used to compare the heat transfer coefficient on a film-cooled, rotating turbine blade. The blade chosen is the ACE rotor with five rows containing 93 film cooling holes covering the entire span. This is the only film-cooled rotating blade over which experimental data is available for comparison. Over 2.278 million grid points are used to compute the flow over the blade including the tip clearance region, using Coakley's q-omega turbulence model. Results are also compared with those obtained by Garg and Abhari (1997) using the zero-equation Baldwin-Lomax (B-L) model. A reasonably good comparison with the experimental data is obtained on the suction surface for both the turbulence models. At the leading edge, the B-L model yields a better comparison than the q-omega model. On the pressure surface, however, the comparison between the experimental data and the prediction from either turbulence model is poor. A potential reason for the discrepancy on the pressure surface could be the presence of unsteady effects due to stator-rotor interaction in the experiments which are not modeled in the present computations. Prediction using the two-equation model is in general poorer than that using the zero-equation model, while the former requires at least 40% more computational resources.
2008-01-01
Equation sets and test casesq F.X. Giraldo a,*, M. Restelli b aDepartment of Applied Mathematics, Naval Postgraduate School, 833 Dyer Road, Monterey, CA...93943, USA bMOX–Modellistica e Calcolo Scientifico, Dipartimento di Matematica , ‘‘F. Brioschi”, Politecnico di Milano, via Bonardi 9 20133 Milano...are of importance in nonhydrostatic mesoscale atmospheric modeling. We study three different forms of the governing equations using seven test cases
A method for solving stochastic equations by reduced order models and local approximations
Grigoriu, M.
2012-08-01
A method is proposed for solving equations with random entries, referred to as stochastic equations (SEs). The method is based on two recent developments. The first approximates the response surface giving the solution of a stochastic equation as a function of its random parameters by a finite set of hyperplanes tangent to it at expansion points selected by geometrical arguments. The second approximates the vector of random parameters in the definition of a stochastic equation by a simple random vector, referred to as stochastic reduced order model (SROM), and uses it to construct a SROM for the solution of this equation. The proposed method is a direct extension of these two methods. It uses SROMs to select expansion points, rather than selecting these points by geometrical considerations, and represents the solution by linear and/or higher order local approximations. The implementation and the performance of the method are illustrated by numerical examples involving random eigenvalue problems and stochastic algebraic/differential equations. The method is conceptually simple, non-intrusive, efficient relative to classical Monte Carlo simulation, accurate, and guaranteed to converge to the exact solution.
Equation of state and transition temperatures in the quark-hadron hybrid model
NASA Astrophysics Data System (ADS)
Miyahara, Akihisa; Torigoe, Yuhei; Kouno, Hiroaki; Yahiro, Masanobu
2016-07-01
We analyze the equation of state of 2 +1 flavor lattice QCD at zero baryon density by constructing a simple quark-hadron hybrid model that has both quark and hadron components simultaneously. We calculate the hadron and quark contributions separately and parameterize those to match with lattice QCD data. Lattice data on the equation of state are decomposed into hadron and quark components by using the model. The transition temperature is defined by the temperature at which the hadron component is equal to the quark one in the equation of state. The transition temperature thus obtained is about 215 MeV; this is somewhat higher than the chiral and the deconfinement pseudocritical temperatures defined by the temperature at which the susceptibility or the absolute value of the derivative of the order parameter with respect to temperature becomes maximum.
Navarro, Juan M; Escolano, José; Cobos, Maximo; López, José J
2013-03-01
The diffusion equation model was used for room acoustic simulations to predict the sound pressure level and the reverberation time. The technical literature states that the diffusion equation method accurately models the late portion of the room impulse response if the energy is sufficiently scattered. This work provides conclusions on the validity of the diffusion equation model for rooms with homogeneous dimensions in relation to the scattering coefficients of the boundaries. A systematic evaluation was conducted out to determine the ranges of the absorption and scattering coefficient values that result in low noticeable differences between the predictions from a geometrical acoustic model and those from the diffusion equation model.
Yang-Mills equation for the nuclear geometrical collective model connexion
NASA Astrophysics Data System (ADS)
Sparks, N.; Rosensteel, G.
2017-01-01
The Bohr-Mottelson collective model of rotations and quadrupole vibrations is a foundational model in nuclear structure physics. A modern formulation using differential geometry of bundles builds on this legacy collective model to allow a deformation-dependent interaction between rotational and vortical degrees of freedom. The interaction is described by the bundle connexion. This article reports the Yang-Mills equation for the connexion. For a class of solutions to the Yang-Mills equation, the differential geometric collective model attains agreement between experiment and theory for the moments of inertia of deformed isotopes. More generally, the differential geometric framework applies to models of emergent phenomena in which two interacting sets of degrees of freedom must be unified.
Stability analysis for a delay differential equations model of a hydraulic turbine speed governor
NASA Astrophysics Data System (ADS)
Halanay, Andrei; Safta, Carmen A.; Dragoi, Constantin; Piraianu, Vlad F.
2017-01-01
The paper aims to study the dynamic behavior of a speed governor for a hydraulic turbine using a mathematical model. The nonlinear mathematical model proposed consists in a system of delay differential equations (DDE) to be compared with already established mathematical models of ordinary differential equations (ODE). A new kind of nonlinearity is introduced as a time delay. The delays can characterize different running conditions of the speed governor. For example, it is considered that spool displacement of hydraulic amplifier might be blocked due to oil impurities in the oil supply system and so the hydraulic amplifier has a time delay in comparison to the time control. Numerical simulations are presented in a comparative manner. A stability analysis of the hydraulic control system is performed, too. Conclusions of the dynamic behavior using the DDE model of a hydraulic turbine speed governor are useful in modeling and controlling hydropower plants.
Ruess, Jakob
2015-12-28
Many stochastic models of biochemical reaction networks contain some chemical species for which the number of molecules that are present in the system can only be finite (for instance due to conservation laws), but also other species that can be present in arbitrarily large amounts. The prime example of such networks are models of gene expression, which typically contain a small and finite number of possible states for the promoter but an infinite number of possible states for the amount of mRNA and protein. One of the main approaches to analyze such models is through the use of equations for the time evolution of moments of the chemical species. Recently, a new approach based on conditional moments of the species with infinite state space given all the different possible states of the finite species has been proposed. It was argued that this approach allows one to capture more details about the full underlying probability distribution with a smaller number of equations. Here, I show that the result that less moments provide more information can only stem from an unnecessarily complicated description of the system in the classical formulation. The foundation of this argument will be the derivation of moment equations that describe the complete probability distribution over the finite state space but only low-order moments over the infinite state space. I will show that the number of equations that is needed is always less than what was previously claimed and always less than the number of conditional moment equations up to the same order. To support these arguments, a symbolic algorithm is provided that can be used to derive minimal systems of unconditional moment equations for models with partially finite state space.
Buenzli, Pascal R
2016-01-01
Several biological tissues undergo changes in their geometry and in their bulk material properties by modelling and remodelling processes. Modelling synthesises tissue in some regions and removes tissue in others. Remodelling overwrites old tissue material properties with newly formed, immature tissue properties. As a result, tissues are made up of different "patches", i.e., adjacent tissue regions of different ages and different material properties, within evolving boundaries. In this paper, generalised equations governing the spatio-temporal evolution of such tissues are developed within the continuum model. These equations take into account nonconservative, discontinuous surface mass balance due to creation and destruction of material at moving interfaces, and bulk balance due to tissue maturation. These equations make it possible to model patchy tissue states and their evolution without explicitly maintaining a record of when/where resorption and formation processes occurred. The time evolution of spatially averaged tissue properties is derived systematically by integration. These spatially-averaged equations cannot be written in closed form as they retain traces that tissue destruction is localised at tissue boundaries. The formalism developed in this paper is applied to bone tissues, which exhibit strong material heterogeneities due to their slow mineralisation and remodelling processes. Evolution equations are proposed in particular for osteocyte density and bone mineral density. Effective average equations for bone mineral density (BMD) and tissue mineral density (TMD) are derived using a mean-field approximation. The error made by this approximation when remodelling patchy tissue is investigated. The specific signatures of the time evolution of BMD or TMD during remodelling events are exhibited. These signatures may provide a way to detect remodelling events at lower, unseen spatial resolutions from microCT scans.
Buenzli, Pascal R.
2016-01-01
Several biological tissues undergo changes in their geometry and in their bulk material properties by modelling and remodelling processes. Modelling synthesises tissue in some regions and removes tissue in others. Remodelling overwrites old tissue material properties with newly formed, immature tissue properties. As a result, tissues are made up of different “patches”, i.e., adjacent tissue regions of different ages and different material properties, within evolving boundaries. In this paper, generalised equations governing the spatio-temporal evolution of such tissues are developed within the continuum model. These equations take into account nonconservative, discontinuous surface mass balance due to creation and destruction of material at moving interfaces, and bulk balance due to tissue maturation. These equations make it possible to model patchy tissue states and their evolution without explicitly maintaining a record of when/where resorption and formation processes occurred. The time evolution of spatially averaged tissue properties is derived systematically by integration. These spatially-averaged equations cannot be written in closed form as they retain traces that tissue destruction is localised at tissue boundaries. The formalism developed in this paper is applied to bone tissues, which exhibit strong material heterogeneities due to their slow mineralisation and remodelling processes. Evolution equations are proposed in particular for osteocyte density and bone mineral density. Effective average equations for bone mineral density (BMD) and tissue mineral density (TMD) are derived using a mean-field approximation. The error made by this approximation when remodelling patchy tissue is investigated. The specific signatures of the time evolution of BMD or TMD during remodelling events are exhibited. These signatures may provide a way to detect remodelling events at lower, unseen spatial resolutions from microCT scans. PMID:27043309
NASA Technical Reports Server (NTRS)
Goldberg, Robert K.; Stouffer, Donald C.
1998-01-01
Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.
ERIC Educational Resources Information Center
Xie, Qin; Andrews, Stephen
2013-01-01
This study introduces Expectancy-value motivation theory to explain the paths of influences from perceptions of test design and uses to test preparation as a special case of washback on learning. Based on this theory, two conceptual models were proposed and tested via Structural Equation Modeling. Data collection involved over 870 test takers of…
ERIC Educational Resources Information Center
Lei, Pui-Wa; Dunbar, Stephen B.
2004-01-01
The primary purpose of this study was to examine relative performance of 2 power estimation methods in structural equation modeling. Sample size, alpha level, type of manifest variable, type of specification errors, and size of correlation between constructs were manipulated. Type 1 error rate of the model chi-square test, empirical critical…
Wharton, A. M. Kumar Shaw, Pankaj; Janaki, M. S.; Sekar Iyengar, A. N.
2014-02-15
In the last few years, third order explicit autonomous differential equations, known as jerk equations, have generated great interest as they show features of regular and chaotic motion. In this paper, we have modelled chaotic electrostatic ion cyclotron oscillations using a third order nonlinear ordinary differential equation (ODE) and investigated its nonlinear dynamical properties. The nonlinear ODE has been derived for a plasma system from a two fluid model in the presence of a source term, under the influence of an external magnetic field, which is perpendicular to the direction of the wave vector. It is seen that the equation does not require an external forcing term to obtain chaotic behaviour. The stability of the solutions of the equation has been investigated analytically as well as numerically, and the bifurcation diagram obtained shows a number of interesting phenomena for various regimes of parameters. The coexisting attractors as well as their corresponding basins are shown and the phase space portraits at different conditions are obtained numerically and shown here. The results obtained here are in agreement with preliminary experiments conducted for a similar configuration of a plasma system.
Modeling water table fluctuations by means of a stochastic differential equation
NASA Astrophysics Data System (ADS)
Bierkens, Marc F. P.
1998-10-01
The combined system of soil-water and shallow groundwater is modeled with simple mass balance equations assuming equilibrium soil moisture conditions. This results in an ordinary but nonlinear differential equation of water table depth at a single location. If errors in model inputs, errors due to model assumptions and parameter uncertainty are lumped and modeled as a wide band noise process, a stochastic differential equation (SDE) results. A solution for the stationary probability density function is given through use of the Fokker-Planck equation. For the nonstationary case, where the model inputs are given as daily time series, sample functions of water table depth, soil saturation, and drainage discharge can be simulated by numerically solving the SDE. These sample functions can be used for designing drainage systems and to perform risk analyses. The parameters and noise statistics of the SDE are calibrated on time series of water table depths by embedding the SDE in a Kaiman filter algorithm and using the filter innovations in a filter-type maximum likelihood criterion. The stochastic model is calibrated and validated at two locations: a peat soil with a very shallow water table and a loamy sand soil with a moderately shallow water table. It is shown in both cases that sample functions simulated with the SDE are able to reproduce a wide range of statistics of water table depth. Despite its unrealistic assumption of constant inputs, the stationary solution derived from the Fokker-Planck equation gives good results for the peat soil, most likely because the characteristic response time of the water table is very small.
ERIC Educational Resources Information Center
Celik, Eyup; Arici, Neslihan
2014-01-01
This study aimed to predict the effects of levels of sexual awareness, sexual courage, and sexual self-disclosure on sexual embarrassment. Data was collected from 336 married individuals, who have students in the Sultangazi District of Istanbul. According to the structural equation model (SEM), sexual self-disclosure, directly, and sexual courage…
NASA Technical Reports Server (NTRS)
Taylor, Lawrence W., Jr.; Rajiyah, H.
1991-01-01
Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.
ERIC Educational Resources Information Center
Wolf, Erika J.; Harrington, Kelly M.; Clark, Shaunna L.; Miller, Mark W.
2013-01-01
Determining sample size requirements for structural equation modeling (SEM) is a challenge often faced by investigators, peer reviewers, and grant writers. Recent years have seen a large increase in SEMs in the behavioral science literature, but consideration of sample size requirements for applied SEMs often relies on outdated rules-of-thumb.…
Bias and Efficiency in Structural Equation Modeling: Maximum Likelihood versus Robust Methods
ERIC Educational Resources Information Center
Zhong, Xiaoling; Yuan, Ke-Hai
2011-01-01
In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…
ERIC Educational Resources Information Center
Bollen, Kenneth A.; Maydeu-Olivares, Albert
2007-01-01
This paper presents a new polychoric instrumental variable (PIV) estimator to use in structural equation models (SEMs) with categorical observed variables. The PIV estimator is a generalization of Bollen's (Psychometrika 61:109-121, 1996) 2SLS/IV estimator for continuous variables to categorical endogenous variables. We derive the PIV estimator…
Spiritual Leadership and Organizational Culture: A Study of Structural Equation Modeling
ERIC Educational Resources Information Center
Karadag, Engin
2009-01-01
The aim of this study is to test the spiritual leadership behaviors of school principles in a structural equation model. The study is designed to test causality with the assumption that causality exists between the two variables. In this study, spiritual leadership behavior of managers is treated as the independent variable whereas the…
Asymptotic Standard Errors of Observed-Score Equating with Polytomous IRT Models
ERIC Educational Resources Information Center
Andersson, Björn
2016-01-01
In observed-score equipercentile equating, the goal is to make scores on two scales or tests measuring the same construct comparable by matching the percentiles of the respective score distributions. If the tests consist of different items with multiple categories for each item, a suitable model for the responses is a polytomous item response…
ERIC Educational Resources Information Center
Moses, Tim; Holland, Paul W.
2010-01-01
In this study, eight statistical strategies were evaluated for selecting the parameterizations of loglinear models for smoothing the bivariate test score distributions used in nonequivalent groups with anchor test (NEAT) equating. Four of the strategies were based on significance tests of chi-square statistics (Likelihood Ratio, Pearson,…
ERIC Educational Resources Information Center
Marsh, Herbert W.; Muthen, Bengt; Asparouhov, Tihomir; Ludtke, Oliver; Robitzsch, Alexander; Morin, Alexandre J. S.; Trautwein, Ulrich
2009-01-01
This study is a methodological-substantive synergy, demonstrating the power and flexibility of exploratory structural equation modeling (ESEM) methods that integrate confirmatory and exploratory factor analyses (CFA and EFA), as applied to substantively important questions based on multidimentional students' evaluations of university teaching…
An Extension of IRT-Based Equating to the Dichotomous Testlet Response Theory Model
ERIC Educational Resources Information Center
Tao, Wei; Cao, Yi
2016-01-01
Current procedures for equating number-correct scores using traditional item response theory (IRT) methods assume local independence. However, when tests are constructed using testlets, one concern is the violation of the local item independence assumption. The testlet response theory (TRT) model is one way to accommodate local item dependence.…
ERIC Educational Resources Information Center
Raykov, Tenko; Marcoulides, George A.
2006-01-01
A structural equation modeling approach to scale reliability evaluation can be employed to estimate generalizability theory indexes in settings where sampling of subjects and conditions is carried out. In one- and two-facet crossed designs, it is demonstrated how this method can be used to obtain estimates of relative generalizability…
Model Selection for Equating Testlet-Based Tests in the NEAT Design: An Empirical Study
ERIC Educational Resources Information Center
He, Wei; Li, Feifei; Wolfe, Edward W.; Mao, Xia
2012-01-01
For those tests solely composed of testlets, local item independency assumption tends to be violated. This study, by using empirical data from a large-scale state assessment program, was interested in investigates the effects of using different models on equating results under the non-equivalent group anchor-test (NEAT) design. Specifically, the…
ERIC Educational Resources Information Center
Sideridis, Georgios; Simos, Panagiotis; Papanicolaou, Andrew; Fletcher, Jack
2014-01-01
The present study assessed the impact of sample size on the power and fit of structural equation modeling applied to functional brain connectivity hypotheses. The data consisted of time-constrained minimum norm estimates of regional brain activity during performance of a reading task obtained with magnetoencephalography. Power analysis was first…
Mathematical Modeling with a "CAS" in an Introductory Course of Differential Equations.
ERIC Educational Resources Information Center
Balderas Puga, Angel
In this paper are described some features of the intensive use of math software, primarily Derive, in the context of modeling in an introductory university course in differential equations. Different aspects are detailed: changes in the curriculum that includes not only course contents, but also the sequence of introduction to various topics and…
ERIC Educational Resources Information Center
Schluchter, Mark D.
2008-01-01
In behavioral research, interest is often in examining the degree to which the effect of an independent variable X on an outcome Y is mediated by an intermediary or mediator variable M. This article illustrates how generalized estimating equations (GEE) modeling can be used to estimate the indirect or mediated effect, defined as the amount by…
ERIC Educational Resources Information Center
Rowland, David R.; Jovanoski, Zlatko
2004-01-01
A study of first-year undergraduate students' interpretational difficulties with first-order ordinary differential equations (ODEs) in modelling contexts was conducted using a diagnostic quiz, exam questions and follow-up interviews. These investigations indicate that when thinking about such ODEs, many students muddle thinking about the function…
Anti-Transgender Prejudice: A Structural Equation Model of Associated Constructs
ERIC Educational Resources Information Center
Tebbe, Esther N.; Moradi, Bonnie
2012-01-01
This study aimed to identify theoretically relevant key correlates of anti-transgender prejudice. Specifically, structural equation modeling was used to test the unique relations of anti-lesbian, gay, and bisexual (LGB) prejudice; traditional gender role attitudes; need for closure; and social dominance orientation with anti-transgender prejudice.…
ERIC Educational Resources Information Center
Zhang, Dongbo
2012-01-01
Using structural equation modeling analysis, this study examined the contribution of vocabulary and grammatical knowledge to second language reading comprehension among 190 advanced Chinese English as a foreign language learners. Vocabulary knowledge was measured in both breadth (Vocabulary Levels Test) and depth (Word Associates Test);…
Accurate integral equation theory for the central force model of liquid water and ionic solutions
NASA Astrophysics Data System (ADS)
Ichiye, Toshiko; Haymet, A. D. J.
1988-10-01
The atom-atom pair correlation functions and thermodynamics of the central force model of water, introduced by Lemberg, Stillinger, and Rahman, have been calculated accurately by an integral equation method which incorporates two new developments. First, a rapid new scheme has been used to solve the Ornstein-Zernike equation. This scheme combines the renormalization methods of Allnatt, and Rossky and Friedman with an extension of the trigonometric basis-set solution of Labik and co-workers. Second, by adding approximate ``bridge'' functions to the hypernetted-chain (HNC) integral equation, we have obtained predictions for liquid water in which the hydrogen bond length and number are in good agreement with ``exact'' computer simulations of the same model force laws. In addition, for dilute ionic solutions, the ion-oxygen and ion-hydrogen coordination numbers display both the physically correct stoichiometry and good agreement with earlier simulations. These results represent a measurable improvement over both a previous HNC solution of the central force model and the ex-RISM integral equation solutions for the TIPS and other rigid molecule models of water.
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan; Cai, Jing-Heng
2010-01-01
Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software…
ERIC Educational Resources Information Center
Winkel, Brian
2012-01-01
We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)
ERIC Educational Resources Information Center
Chen, Wei; Wang, Long; Zhang, Xing-Li; Shi, Jian-Nong
2012-01-01
The objective of this study was to investigate the impact of trauma exposure on the posttraumatic stress symptomatology (PTSS) of children who resided near the epicenter of the 2008 Wenchuan earthquake. The mechanisms of this impact were explored via structural equation models with self-esteem and coping strategies included as mediators. The…
A Structural Equation Modelling of the Academic Self-Concept Scale
ERIC Educational Resources Information Center
Matovu, Musa
2014-01-01
The study aimed at validating the academic self-concept scale by Liu and Wang (2005) in measuring academic self-concept among university students. Structural equation modelling was used to validate the scale which was composed of two subscales; academic confidence and academic effort. The study was conducted on university students; males and…
ERIC Educational Resources Information Center
Horzum, Mehmet Baris; Kaymak, Zeliha Demir; Gungoren, Ozlem Canan
2015-01-01
The relationship between online learning readiness, academic motivations, and perceived learning was investigated via structural equation modeling in the research. The population of the research consisted of 750 students who studied using the online learning programs of Sakarya University. 420 of the students who volunteered for the research and…
A New Look at the Big Five Factor Structure through Exploratory Structural Equation Modeling
ERIC Educational Resources Information Center
Marsh, Herbert W.; Ludtke, Oliver; Muthen, Bengt; Asparouhov, Tihomir; Morin, Alexandre J. S.; Trautwein, Ulrich; Nagengast, Benjamin
2010-01-01
NEO instruments are widely used to assess Big Five personality factors, but confirmatory factor analyses (CFAs) conducted at the item level do not support their a priori structure due, in part, to the overly restrictive CFA assumptions. We demonstrate that exploratory structural equation modeling (ESEM), an integration of CFA and exploratory…
Bayesian Structural Equation Modeling: A More Flexible Representation of Substantive Theory
ERIC Educational Resources Information Center
Muthen, Bengt; Asparouhov, Tihomir
2012-01-01
This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed…
ERIC Educational Resources Information Center
Budsankom, Prayoonsri; Sawangboon, Tatsirin; Damrongpanit, Suntorapot; Chuensirimongkol, Jariya
2015-01-01
The purpose of the research is to develop and identify the validity of factors affecting higher order thinking skills (HOTS) of students. The thinking skills can be divided into three types: analytical, critical, and creative thinking. This analysis is done by applying the meta-analytic structural equation modeling (MASEM) based on a database of…
ERIC Educational Resources Information Center
Klein, Andreas G.; Muthen, Bengt O.
2007-01-01
In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly…
ERIC Educational Resources Information Center
Okech, David
2012-01-01
Objectives: Using baseline and second wave data, the study evaluated the measurement and structural properties of parenting stress, personal mastery, and economic strain with N = 381 lower income parents who decided to join and those who did not join in a child development savings account program. Methods: Structural equation modeling mean and…
ERIC Educational Resources Information Center
Steed, Teneka C.
2013-01-01
Evaluating the psychometric properties of a newly developed instrument is critical to understanding how well an instrument measures what it intends to measure, and ensuring proposed use and interpretation of questionnaire scores are valid. The current study uses Structural Equation Modeling (SEM) techniques to examine the factorial structure and…
A Structural Equation Modelling Approach for Massive Blended Synchronous Teacher Training
ERIC Educational Resources Information Center
Kannan, Kalpana; Narayanan, Krishnan
2015-01-01
This paper presents a structural equation modelling (SEM) approach for blended synchronous teacher training workshop. It examines the relationship among various factors that influence the Satisfaction (SAT) of participating teachers. Data were collected with the help of a questionnaire from about 500 engineering college teachers. These teachers…
ERIC Educational Resources Information Center
Caro, Daniel H.; Sandoval-Hernández, Andrés; Lüdtke, Oliver
2014-01-01
The article employs exploratory structural equation modeling (ESEM) to evaluate constructs of economic, cultural, and social capital in international large-scale assessment (LSA) data from the Progress in International Reading Literacy Study (PIRLS) 2006 and the Programme for International Student Assessment (PISA) 2009. ESEM integrates the…
ERIC Educational Resources Information Center
Enders, Craig K.; Bandalos, Deborah L.
2001-01-01
Used Monte Carlo simulation to examine the performance of four missing data methods in structural equation models: (1)full information maximum likelihood (FIML); (2) listwise deletion; (3) pairwise deletion; and (4) similar response pattern imputation. Results show that FIML estimation is superior across all conditions of the design. (SLD)
Reporting Structural Equation Modeling and Confirmatory Factor Analysis Results: A Review
ERIC Educational Resources Information Center
Schreiber, James B.; Nora, Amaury; Stage, Frances K.; Barlow, Elizabeth A.; King, Jamie
2006-01-01
The authors provide a basic set of guidelines and recommendations for information that should be included in any manuscript that has confirmatory factor analysis or structural equation modeling as the primary statistical analysis technique. The authors provide an introduction to both techniques, along with sample analyses, recommendations for…
Meta-Analytic Structural Equation Modeling: A Two-Stage Approach
ERIC Educational Resources Information Center
Cheung, Mike W. L.; Chan, Wai
2005-01-01
To synthesize studies that use structural equation modeling (SEM), researchers usually use Pearson correlations (univariate r), Fisher z scores (univariate z), or generalized least squares (GLS) to combine the correlation matrices. The pooled correlation matrix is then analyzed by the use of SEM. Questionable inferences may occur for these ad hoc…
OpenMx: An Open Source Extended Structural Equation Modeling Framework
ERIC Educational Resources Information Center
Boker, Steven; Neale, Michael; Maes, Hermine; Wilde, Michael; Spiegel, Michael; Brick, Timothy; Spies, Jeffrey; Estabrook, Ryne; Kenny, Sarah; Bates, Timothy; Mehta, Paras; Fox, John
2011-01-01
OpenMx is free, full-featured, open source, structural equation modeling (SEM) software. OpenMx runs within the "R" statistical programming environment on Windows, Mac OS-X, and Linux computers. The rationale for developing OpenMx is discussed along with the philosophy behind the user interface. The OpenMx data structures are…
Teacher's Corner: Structural Equation Modeling with the Sem Package in R
ERIC Educational Resources Information Center
Fox, John
2006-01-01
R is free, open-source, cooperatively developed software that implements the S statistical programming language and computing environment. The current capabilities of R are extensive, and it is in wide use, especially among statisticians. The sem package provides basic structural equation modeling facilities in R, including the ability to fit…
Application of Exploratory Structural Equation Modeling to Evaluate the Academic Motivation Scale
ERIC Educational Resources Information Center
Guay, Frédéric; Morin, Alexandre J. S.; Litalien, David; Valois, Pierre; Vallerand, Robert J.
2015-01-01
In this research, the authors examined the construct validity of scores of the Academic Motivation Scale using exploratory structural equation modeling. Study 1 and Study 2 involved 1,416 college students and 4,498 high school students, respectively. First, results of both studies indicated that the factor structure tested with exploratory…
ERIC Educational Resources Information Center
Santos-George, Arlene A.
2012-01-01
This dissertation empirically tested Tinto's student integration theory through structural equation modeling using a national sample of 2,847 first-time entering community college students. Tinto theorized that the more academically and socially integrated a student is to the college environment, the more likely the student will persist through…
Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes
ERIC Educational Resources Information Center
Steele, Joel S.; Ferrer, Emilio
2011-01-01
We examine emotion self-regulation and coregulation in romantic couples using daily self-reports of positive and negative affect. We fit these data using a damped linear oscillator model specified as a latent differential equation to investigate affect dynamics at the individual level and coupled influences for the 2 partners in each couple.…
ERIC Educational Resources Information Center
Simsek, Gulhayat Golbasi; Noyan, Fatma
2009-01-01
Social sciences research often entails the analysis of data with a multilevel structure. An example of multilevel data is containing measurement on university students nested within instructors. This paper concentrates on multilevel analysis of structural equation modeling with educational data. Data used in this study were gathered from 17647…
ERIC Educational Resources Information Center
Sahin, Elvan; Ertepinar, Hamide; Teksoz, Gaye
2012-01-01
The purpose of this study is to construct a structural equation model to examine the links among attitudes, values, and behaviors pertaining to sustainability, participation in outdoor recreation as well as gender and tendency to follow mass media for university students. The data were collected by on-line administration of a survey to 958…
Structural Equation Modeling in Language Testing and Learning Research: A Review
ERIC Educational Resources Information Center
In'nami, Yo; Koizumi, Rie
2011-01-01
Despite the recent increase of structural equation modeling (SEM) in language testing and learning research and Kunnan's (1998) call for the proper use of SEM to produce useful findings, there seem to be no reviews about how SEM is applied in these areas or about the extent to which the current application accords with appropriate practices. To…
Canonical Correlation Analysis and Structural Equation Modeling: What Do They Have in Common?
ERIC Educational Resources Information Center
Fan, Xitao
1997-01-01
The relationship between structural equation modeling (SEM) and canonical correlation analysis (CCA) is illustrated. The representation of CCA in SEM may provide interpretive information not available from conventional CCA. Hierarchically, the relationship suggests that SEM is a more general analytic approach. (SLD)
ERIC Educational Resources Information Center
Li, Spencer D.
2011-01-01
Mediation analysis in child and adolescent development research is possible using large secondary data sets. This article provides an overview of two statistical methods commonly used to test mediated effects in secondary analysis: multiple regression and structural equation modeling (SEM). Two empirical studies are presented to illustrate the…
Maximum Likelihood Estimation of Nonlinear Structural Equation Models with Ignorable Missing Data
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan; Lee, John C. K.
2003-01-01
The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models…
Use of Item Parceling in Structural Equation Modeling with Missing Data
ERIC Educational Resources Information Center
Orcan, Fatih
2013-01-01
Parceling is referred to as a procedure for computing sums or average scores across multiple items. Parcels instead of individual items are then used as indicators of latent factors in the structural equation modeling analysis (Bandalos 2002, 2008; Little et al., 2002; Yang, Nay, & Hoyle, 2010). Item parceling may be applied to alleviate some…
A Robust Bayesian Approach for Structural Equation Models with Missing Data
ERIC Educational Resources Information Center
Lee, Sik-Yum; Xia, Ye-Mao
2008-01-01
In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear…
Does Method of Handling Missing Data Affect Results of a Structural Equation Model?
ERIC Educational Resources Information Center
Witta, E. Lea
The influence of method of handling missing data on estimates produced by a structural equation model of the effects of part-time work on high-school student achievement was investigated. Missing data methods studied were listwise deletion, pairwise deletion, the expectation maximization (EM) algorithm, regression, and response pattern. The 26…
Analysis of Structural Equation Model with Ignorable Missing Continuous and Polytomous Data.
ERIC Educational Resources Information Center
Song, Xin-Yuan; Lee, Sik-Yum
2002-01-01
Developed a Bayesian approach for structural equation models with ignorable missing continuous and polytomous data that obtains joint Bayesian estimates of thresholds, structural parameters, and latent factor scores simultaneously. Illustrated the approach through analysis of a real data set of 20 patterns of condom use in the Philippines. (SLD)
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan; Tang, Nian-Sheng
2007-01-01
The analysis of interaction among latent variables has received much attention. This article introduces a Bayesian approach to analyze a general structural equation model that accommodates the general nonlinear terms of latent variables and covariates. This approach produces a Bayesian estimate that has the same statistical optimal properties as a…
ERIC Educational Resources Information Center
Zafarmand, Atefeh; Ghanizadeh, Afsaneh; Akbari, Omid
2014-01-01
This article sets out to examine the relationship between EFL learners' goal orientation, metacognitive awareness and self-efficacy in a single framework. One hundred fifteen EFL students from two universities of Mashhad, a city in north-eastern Iran took part in this study. Structural equation modeling (SEM) was utilized to examine the…
Structural Equation Modeling in Assessing Students' Understanding of the State Changes of Matter
ERIC Educational Resources Information Center
Stamovlasis, Dimitrios; Tsitsipis, Georgios; Papageorgiou, George
2012-01-01
In this study, structural equation modeling (SEM) is applied to an instrument assessing students' understanding of the particulate nature of matter, the collective properties and physical changes, such as melting, evaporation, boiling and condensation. The structural relationships among particular groups of items were investigated. In addition,…
A Double-Structure Structural Equation Model for Three-Mode Data
ERIC Educational Resources Information Center
Gonzalez, Jorge; De Boeck, Paul; Tuerlinckx, Francis
2008-01-01
Structural equation models are commonly used to analyze 2-mode data sets, in which a set of objects is measured on a set of variables. The underlying structure within the object mode is evaluated using latent variables, which are measured by indicators coming from the variable mode. Additionally, when the objects are measured under different…
NASA Astrophysics Data System (ADS)
Taylor, Lawrence W., Jr.; Rajiyah, H.
Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.
An Application of Structural Equation Modeling for Developing Good Teaching Characteristics Ontology
ERIC Educational Resources Information Center
Phiakoksong, Somjin; Niwattanakul, Suphakit; Angskun, Thara
2013-01-01
Ontology is a knowledge representation technique which aims to make knowledge explicit by defining the core concepts and their relationships. The Structural Equation Modeling (SEM) is a statistical technique which aims to explore the core factors from empirical data and estimates the relationship between these factors. This article presents an…
Ballistic Limit Equation for Single Wall Titanium
NASA Technical Reports Server (NTRS)
Ratliff, J. M.; Christiansen, Eric L.; Bryant, C.
2009-01-01
Hypervelocity impact tests and hydrocode simulations were used to determine the ballistic limit equation (BLE) for perforation of a titanium wall, as a function of wall thickness. Two titanium alloys were considered, and separate BLEs were derived for each. Tested wall thicknesses ranged from 0.5mm to 2.0mm. The single-wall damage equation of Cour-Palais [ref. 1] was used to analyze the Ti wall's shielding effectiveness. It was concluded that the Cour-Palais single-wall equation produced a non-conservative prediction of the ballistic limit for the Ti shield. The inaccurate prediction was not a particularly surprising result; the Cour-Palais single-wall BLE contains shield material properties as parameters, but it was formulated only from tests of different aluminum alloys. Single-wall Ti shield tests were run (thicknesses of 2.0 mm, 1.5 mm, 1.0 mm, and 0.5 mm) on Ti 15-3-3-3 material custom cut from rod stock. Hypervelocity impact (HVI) tests were used to establish the failure threshold empirically, using the additional constraint that the damage scales with impact energy, as was indicated by hydrocode simulations. The criterion for shield failure was defined as no detached spall from the shield back surface during HVI. Based on the test results, which confirmed an approximately energy-dependent shield effectiveness, the Cour-Palais equation was modified.
Review of Ballistic Limit Equations for Composite Structure Walls of Satellites
NASA Astrophysics Data System (ADS)
Schaefer, Frank K.*; Schneider, E.; Lambert, M.
2004-08-01
In this paper a review of existing ballistic limit equations for CFRP (Carbon Fibre Reinforced Plastics) structure walls of satellites is given, and two new ballistic limit equations are presented. The predictive capabilities of the equations are compared to a set of experimental hypervelocity impact test data of CFRP plates and CFRP honeycomb sandwich panels (satellite structure wall) from ENVISAT, AXAF, and a generic technology program. In the literature, three ballistic limit equations for sandwich panels (SP) made from CFRP face-sheets and Al- honeycomb (H/C) core were found and analyzed (Frost's approach, Approach using Christiansen's Whipple shield Ballistic Limit Equation (BLE), and Taylor's approach). Furthermore, in this paper, a new ballistic limit equation was proposed for CFRP H/C SP (Modified ESA Triple Wall Equation) and for composite panels (plates) with and without MLI attached to the surface. The amount of impact data on CFRP structure walls of satellites found in the literature was rather scarce. The new BLE for CFRP plates makes good predictions to the available set of test data. For the BLE for CFRP H/C SP, it was found that Frost's approach and application of Christiansen's BLE to CFRP H/C SP lead to an overprediction of the ballistic limit diameters for ENVISAT structure walls and the samples of the generic technology program. Taylor's approach and the newly designed MET ballistic limit equation have both yielded good predictions for all samples except for the AXAF samples that had rather thin-walled face-sheets and a thin Al H/C core: for these samples the predictions were conservative. Thus, for use in risk analysis tools for satellites (e. g. ESA's ESABASE/DEBRIS tool or NASA's BUMPER code), it is recommended to use either the MET or Taylor equation.
NASA Trapezoidal Wing Simulation Using Stress-w and One- and Two-Equation Turbulence Models
NASA Technical Reports Server (NTRS)
Rodio, J. J.; Xiao, X; Hassan, H. A.; Rumsey, C. L.
2014-01-01
The Wilcox 2006 stress-omega model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley code CFL3D and used to study a variety of 2-D and 3-D configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than experiment, similar to results of a two-equation model.
Implementation of Advanced Two Equation Turbulence Models in the USM3D Unstructured Flow Solver
NASA Technical Reports Server (NTRS)
Wang, Qun-Zhen; Massey, Steven J.; Abdol-Hamid, Khaled S.
2000-01-01
USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flow. We have implemented two modified versions of the original Jones and Launder k-epsilon "two-equation" turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for three flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those from direct numerical simulation, empirical formulae, theoretical results, and the existing Spalart-Allmaras one-equation model.
Bayesian inference using two-stage Laplace approximation for differential equation models
NASA Astrophysics Data System (ADS)
Dass, Sarat C.; Lee, Jaeyong; Lee, Kyoungjae
2016-11-01
We consider the problem of Bayesian inference for parameters in non-linear regression models whereby the underlying unknown response functions are formed by a set of differential equations. Bayesian methods of inference for unknown parameters rely primarily on the posterior obtained by Bayes rule. For differential equation models, analytic and closed forms for the posterior are not available and one has to resort to approximations. We propose a two-stage Laplace expansion to approximate the marginal likelihood, and hence, the posterior, to obtain an approximate closed form solution. For large sample sizes, the method of inference borrows from non-linear regression theory for maximum likelihood estimates, and is therefore, consistent. Our approach is exact in the limit and does not need the specification of an additional penalty parameter. Examples in this paper include the exponential model and SIR (Susceptible-Infected-Recovered) disease spread model.
Parametric reduced models for the nonlinear Schrödinger equation.
Harlim, John; Li, Xiantao
2015-05-01
Reduced models for the (defocusing) nonlinear Schrödinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced parametric models are obtained by employing a rational approximation and a colored-noise approximation, respectively, on the memory terms and the random noise of a generalized Langevin equation that is derived from the standard Mori-Zwanzig formalism. The parameters in the resulting reduced models are inferred from noisy observations with a recently developed ensemble Kalman filter-based parametrization method. The forecasting skill across different temperature regimes are verified by comparing the moments up to order four, a two-time correlation function statistics, and marginal densities of the coarse-grained variables.
NASA Technical Reports Server (NTRS)
Wang, Qun-Zhen; Massey, Steven J.; Abdol-Hamid, Khaled S.; Frink, Neal T.
1999-01-01
USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flows. We have implemented two modified versions of the original Jones and Launder k-epsilon two-equation turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for two flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those of empirical formulae, theoretical results and the existing Spalart-Allmaras one-equation model.
Modeling of delays in PKPD: classical approaches and a tutorial for delay differential equations.
Koch, Gilbert; Krzyzanski, Wojciech; Pérez-Ruixo, Juan Jose; Schropp, Johannes
2014-08-01
In pharmacokinetics/pharmacodynamics (PKPD) the measured response is often delayed relative to drug administration, individuals in a population have a certain lifespan until they maturate or the change of biomarkers does not immediately affects the primary endpoint. The classical approach in PKPD is to apply transit compartment models (TCM) based on ordinary differential equations to handle such delays. However, an alternative approach to deal with delays are delay differential equations (DDE). DDEs feature additional flexibility and properties, realize more complex dynamics and can complementary be used together with TCMs. We introduce several delay based PKPD models and investigate mathematical properties of general DDE based models, which serve as subunits in order to build larger PKPD models. Finally, we review current PKPD software with respect to the implementation of DDEs for PKPD analysis.
Virial coefficients and equation of state of the penetrable sphere model.
Viererblová, Linda; Kolafa, Jirí; Labík, Stanislav; Malijevský, Anatol
2010-01-07
We study the penetrable sphere (alias square mound) model in the fluid phase by means of the virial expansion, molecular dynamics simulations, and Ornstein-Zernike integral equation. The virial coefficients up to B(8) are expressed as polynomials in the Boltzmann factor with the coefficients calculated by a Monte Carlo integration. New data for pressure and internal energy are obtained by molecular dynamics simulations with attention paid to finite-size errors and properties of the Andersen thermostat. The data and virial coefficients are correlated by a formula for the Helmholtz free energy. We also propose a new closure for the Ornstein-Zernike equation and test several other closures.
Dillenseger, Jean-Louis; Esneault, Simon; Garnier, Carole
2008-01-01
This paper describes a modeling method of the tissue temperature evolution over time in hyperthermia. More precisely, this approach is used to simulate the hepatocellular carcinoma curative treatment by a percutaneous high intensity ultrasound surgery. The tissue temperature evolution over time is classically described by Pennes' bioheat transfer equation which is generally solved by a finite difference method. In this paper we will present a method where the bioheat transfer equation can be algebraically solved after a Fourier transformation over the space coordinates. The implementation and boundary conditions of this method will be shown and compared with the finite difference method.
Dillenseger, Jean-Louis; Esneault, Simon; Garnier, Carole
2008-01-01
This paper describes a modeling method of the tissue temperature evolution over time in hyperthermia. More precisely, this approach is used to simulate the hepatocellular carcinoma curative treatment by a percutaneous high intensity ultrasound surgery. The tissue temperature evolution over time is classically described by Pennes’ bioheat transfer equation which is generally solved by a finite difference method. In this paper we will present a method where the bioheat transfer equation can be algebraically solved after a Fourier transformation over the space coordinates. The implementation and boundary conditions of this method will be shown and compared with the finite difference method. PMID:19163220
Rate-equation model for multi-mode semiconductor lasers with spatial hole burning.
Lenstra, Daan; Yousefi, Mirvais
2014-04-07
We present a set of rate equations for the modal amplitudes and carrier-inversion moments that describe the deterministic multi-mode dynamics of a semiconductor laser due to spatial hole burning. Mutual interactions among the lasing modes, induced by high- frequency modulations of the carrier distribution, are included by carrier-inversion moments for which rate equations are given as well. We derive the Bogatov effect of asymmetric gain suppression in semiconductor lasers and illustrate the potential of the model for a two and three-mode laser by numerical and analytical methods.
An equation-of-state for methane for modeling hydrogen attack in ferritic steels
NASA Astrophysics Data System (ADS)
Odette, G. R.; Vagarali, S. S.
1982-02-01
A statistical mechanical-based high temperature and high pressure equation-of-state for methane has been developed using the McQuarrie and Katz formulation based on Leonard-Jones (n, 6) intermolecular potential. Fugacity coefficients for methane have been estimated, and it is shown that for plain carbon steels during hydrogen attack the methane pressures are considerably lower than the fugacities and fall into a physically meaningful range (≤2500 MPa). Further, simple, but reasonably accurate, expressions for both the equation-of-state and fugacity coefficient have been developed for the purpose of modeling hydrogen attack kinetics in ferritic steels.
Using spline-enhanced ordinary differential equations for PK/PD model development.
Wang, Yi; Eskridge, Kent; Zhang, Shunpu; Wang, Dong
2008-10-01
A spline-enhanced ordinary differential equation (ODE) method is proposed for developing a proper parametric kinetic ODE model and is shown to be a useful approach to PK/PD model development. The new method differs substantially from a previously proposed model development approach using a stochastic differential equation (SDE)-based method. In the SDE-based method, a Gaussian diffusion term is introduced into an ODE to quantify the system noise. In our proposed method, we assume an ODE system with form dx/dt = A(t)x + B(t) where B(t) is a nonparametric function vector that is estimated using penalized splines. B(t) is used to construct a quantitative measure of model uncertainty useful for finding the proper model structure for a given data set. By means of two examples with simulated data, we demonstrate that the spline-enhanced ODE method can provide model diagnostics and serve as a basis for systematic model development similar to the SDE-based method. We compare and highlight the differences between the SDE-based and the spline-enhanced ODE methods of model development. We conclude that the spline-enhanced ODE method can be useful for PK/PD modeling since it is based on a relatively uncomplicated estimation algorithm which can be implemented with readily available software, provides numerically stable, robust estimation for many models, is distribution-free and allows for identification and accommodation of model deficiencies due to model misspecification.
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization. PMID:27243005
A Tutorial on RxODE: Simulating Differential Equation Pharmacometric Models in R.
Wang, W; Hallow, K M; James, D A
2016-01-01
This tutorial presents the application of an R package, RxODE, that facilitates quick, efficient simulations of ordinary differential equation models completely within R. Its application is illustrated through simulation of design decision effects on an adaptive dosing regimen. The package provides an efficient, versatile way to specify dosing scenarios and to perform simulation with variability with minimal custom coding. Models can be directly translated to Rshiny applications to facilitate interactive, real-time evaluation/iteration on simulation scenarios.
Towards understanding of near wall behavior in two-equation models for supersonic flows
NASA Astrophysics Data System (ADS)
Lakshmipathy, Sunil; Arasanipalai, Sriram; Girimaji, Sharath
2008-11-01
The standard two-equation models over-predict the turbulent viscosity and turbulent kinetic energy in the near wall region for supersonic flows. There are several approaches to tune the model behavior to agree with experimental values. In the present approach we modify Cμ along the lines of Durbin stagnation point correction. The influence of the turbulent Prandtl numbers - σk, σɛ, σφ-- are also examined.
A Parameter Sensitivity Methodology in the Context of HIV Delay Equation Models
2002-08-07
1988), 71–90. [18] KAMINA, A ., MAKUCH , R. W., AND ZHAO, H. Stochastic modeling of early HIV-1 population dynamics. Mathematical Biosciences 170... A PARAMETER SENSITIVITY METHODOLOGY IN THE CONTEXT OF HIV DELAY EQUATION MODELS H. T. Banks1 and D. M. Bortz Center for Research in Scientific...Computation Box 8205, North Carolina State University Raleigh, NC 27695-8205 ABSTRACT. A sensitivity methodology for nonlinear delay systems arising in one
Properties of Linear Integral Equations Related to the Six-Vertex Model with Disorder Parameter
NASA Astrophysics Data System (ADS)
Boos, Hermann; Göhmann, Frank
2011-10-01
One of the key steps in recent work on the correlation functions of the XXZ chain was to regularize the underlying six-vertex model by a disorder parameter α. For the regularized model it was shown that all static correlation functions are polynomials in only two functions. It was further shown that these two functions can be written as contour integrals involving the solutions of a certain type of linear and non-linear integral equations. The linear integral equations depend parametrically on α and generalize linear integral equations known from the study of the bulk thermodynamic properties of the model. In this note we consider the generalized dressed charge and a generalized magnetization density. We express the generalized dressed charge as a linear combination of two quotients of Q-functions, the solutions of Baxter's t-Q-equation. With this result we give a new proof of a lemma on the asymptotics of the generalized magnetization density as a function of the spectral parameter.
Thomaseth, K
1994-02-14
Software is presented for automatic generation of first-order ordinary differential equations (ODE) that arise from lumped parameter representations of metabolic and pharmacokinetic systems. The definition of system structures is accomplished by fractional transfer rates between state variables, together with input/output equations and initial conditions of state variables. General non-linear mathematical expressions can be assigned to all structure definition items. The software parses and interprets the system definitions and generates symbolically the mathematical expression of the model's set of ODE. In addition, symbolic derivatives of state equations are determined with respect to model parameters, state variables and external inputs. These derivatives represent the constituents of systems of sensitivity-differential and adjoint-differential equations that arise in identification and optimal control problems. Finally, output routines generate source code that, once compiled and linked to simulation programs, allows efficient numerical integration of the system of ODE. This software has been developed in PROLOG on Macintosh computers and has been extensively used with the programming environment MATLAB. Possible applications of this software include model building, sensitivity analysis, identification, optimal experiment design and numerical solution of optimal control problems.
NASA Astrophysics Data System (ADS)
Paparella, F.; Oliveri, F.
2009-04-01
The interplay of advection, reaction and diffusion terms in ADR equations is a rather difficult one to be modeled numerically. The kind of spurious oscillations that is usually harmless for non-reacting scalars is often amplified without bounds by reaction terms. Furthermore, in most biogeochimical applications, such as mesoscale or global-scale plankton modeling, the diffusive fluxes may be smaller than the numerical ones. Inspired by the particle-mesh methods used by cosmologists, we propose to discretize on a grid only the diffusive term of the equation, and solve the advection-reaction terms as ordinary differential equations along the characteristic lines. Diffusion happens by letting the concentration field carried by each particle to relax towards the diffusive field known on the grid, without redistributing the particles. This method, in the limit of vanishing diffusivity and for a fixed mesh size, recovers the advection-reaction solution with no numerical diffusion. We show some example numerical solutions of the ADR equations stemming from a simple predator-prey model.
Approximate-master-equation approach for the Kinouchi-Copelli neural model on networks.
Wang, Chong-Yang; Wu, Zhi-Xi; Chen, Michael Z Q
2017-01-01
In this work, we use the approximate-master-equation approach to study the dynamics of the Kinouchi-Copelli neural model on various networks. By categorizing each neuron in terms of its state and also the states of its neighbors, we are able to uncover how the coupled system evolves with respective to time by directly solving a set of ordinary differential equations. In particular, we can easily calculate the statistical properties of the time evolution of the network instantaneous response, the network response curve, the dynamic range, and the critical point in the framework of the approximate-master-equation approach. The possible usage of the proposed theoretical approach to other spreading phenomena is briefly discussed.
Pretend model of traveling wave solution of two-dimensional K-dV equation
NASA Astrophysics Data System (ADS)
Karim, Md Rezaul; Alim, Md Abdul; Andallah, Laek Sazzad
2013-11-01
Traveling wave resolution of Korteweg-de Vries (K-dV) solitary and numerical estimation of analytic solutions have been studied in this paper for imaginary concept. Pretend model of traveling wave deals with giant waves or series of waves created by an undersea earthquake, volcanic eruption or landslide. The concept of traveling wave is frequently used by mariners and in coastal, ocean and naval engineering. We have found some exact traveling wave solutions with relevant physical parameters using new auxiliary equation method introduced by Pang et al. (Appl. Math. Mech-Engl. Ed 31(7):929-936, 2010). We have solved the imaginary part of exact traveling wave equations analytically, and numerical results of time-dependent wave solutions have been presented graphically. This procedure has a potential to be used in more complex system for other types of K-dV equations.
Approximate-master-equation approach for the Kinouchi-Copelli neural model on networks
NASA Astrophysics Data System (ADS)
Wang, Chong-Yang; Wu, Zhi-Xi; Chen, Michael Z. Q.
2017-01-01
In this work, we use the approximate-master-equation approach to study the dynamics of the Kinouchi-Copelli neural model on various networks. By categorizing each neuron in terms of its state and also the states of its neighbors, we are able to uncover how the coupled system evolves with respective to time by directly solving a set of ordinary differential equations. In particular, we can easily calculate the statistical properties of the time evolution of the network instantaneous response, the network response curve, the dynamic range, and the critical point in the framework of the approximate-master-equation approach. The possible usage of the proposed theoretical approach to other spreading phenomena is briefly discussed.
NASA Astrophysics Data System (ADS)
Khan, Irfan; Costeux, Stephane; Adrian, David; Cristancho, Diego
2013-11-01
Due to environmental regulations carbon-dioxide (CO2) is increasingly being used to replace traditional blowing agents in thermoplastic foams. CO2 is dissolved in the polymer matrix under supercritical conditions. In order to predict the effect of process parameters on foam properties using numerical modeling, the P-V-T relationship of the blowing agents should accurately be represented at the supercritical state. Previous studies in the area of foam modeling have all used ideal gas equation of state to predict the behavior of the blowing agent. In this work the Peng-Robinson equation of state is being used to model the blowing agent during its diffusion into the growing bubble. The model is based on the popular ``Influence Volume Approach,'' which assumes a growing boundary layer with depleted blowing agent surrounds each bubble. Classical nucleation theory is used to predict the rate of nucleation of bubbles. By solving the mass balance, momentum balance and species conservation equations for each bubble, the model is capable of predicting average bubble size, bubble size distribution and bulk porosity. The effect of the improved model on the bubble growth and foam properties are discussed.
Unified Einstein-Virasoro Master Equation in the General Non-Linear Sigma Model
Boer, J. de; Halpern, M.B.
1996-06-05
The Virasoro master equation (VME) describes the general affine-Virasoro construction $T=L^abJ_aJ_b+iD^a \\dif J_a$ in the operator algebra of the WZW model, where $L^ab$ is the inverse inertia tensor and $D^a $ is the improvement vector. In this paper, we generalize this construction to find the general (one-loop) Virasoro construction in the operator algebra of the general non-linear sigma model. The result is a unified Einstein-Virasoro master equation which couples the spacetime spin-two field $L^ab$ to the background fields of the sigma model. For a particular solution $L_G^ab$, the unified system reduces to the canonical stress tensors and conventional Einstein equations of the sigma model, and the system reduces to the general affine-Virasoro construction and the VME when the sigma model is taken to be the WZW action. More generally, the unified system describes a space of conformal field theories which is presumably much larger than the sum of the general affine-Virasoro construction and the sigma model with its canonical stress tensors. We also discuss a number of algebraic and geometrical properties of the system, including its relation to an unsolved problem in the theory of $G$-structures on manifolds with torsion.
Structural models and surface equation of state for pulmonary surfactant monolayers.
Zeng, Zuoxiang; Li, Dan; Xue, Weilan; Sun, Li
2007-12-01
A simple surface equation of state is proposed to describe pi-A isotherms of pulmonary surfactant monolayers. The monolayer is considered as undergoing three characteristic states during the compression: the disordered liquid-expanded (LE) state, the ordered liquid-condensed (LC) state and the collapse state. Structural models of pure protein (SP-B and SP-C) monolayer are proposed to interpret the behavior characteristics of monolayer in the states. The area, ALC, is defined as an instantaneous LC-state area when the monolayer is under the complete LC state. The area, At, is defined as a transition area from the ordered LC state to the collapse state. And the collapse pressure, pi(max), is defined as the maximum surface pressure that the monolayer can bear before collapse. The ideal equation of state is revised by ALC, At and pi(max), and a new equation of state is obtained, which is applicable for pure components of pulmonary surfactant. The theoretical pi-A isotherms described by the equation of state are compared with the experimental ones for SP-B, SP-C, DPPC and DPPG, and good agreements are obtained. The equation of state is generalized to protein-lipid binary mixtures by introducing mixing rules. The predicted pi-A isotherms agree with the experimental ones for various pulmonary surfactant components and the average deviation is about 9.2%.
Health belief structural equation model predicting sleep behavior of employed college students.
Knowlden, Adam P; Sharma, Manoj
2014-01-01
Adequate sleep comprising 7 to 8 hours per day is vital for health and effective functioning for all adults. The purpose of this study was to specify a health belief model to measure and predict the sleep behavior of employed college students. A 52-item instrument was developed with acceptable validity and reliability. A cross-sectional, convenience sample of 188 students was recruited for this study. Structural equation modeling was used to build models. The health belief model explained 34% of the variance in sleep behavior, with perceived severity, perceived barriers, cues to action, and self-efficacy identified as significant predictors.
NASA Astrophysics Data System (ADS)
Kudryashov, Nikolay A.; Volkov, Alexandr K.
2017-01-01
We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the Fermi-Pasta-Ulam model. We use the potential of interaction between neighbouring masses with both quadratic and cubic terms. The equation is derived using the continuous limit. Unlike the previous works, we take into account higher order terms in the Taylor series expansions. We investigate the equation using the Painlevé approach. We show that the equation does not pass the Painlevé test and can not be integrated by the inverse scattering transform. We use the logistic function method and the Laurent expansion method to find travelling wave solutions of the fifth-order equation. We use the pseudospectral method for the numerical simulation of wave processes, described by the equation.