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
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…
Directory of Open Access Journals (Sweden)
Vijay K. Garg
1998-01-01
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.
Handbook of structural equation modeling
Hoyle, Rick H
2012-01-01
The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu
COMPARISON BETWEEN BOUSSINESQ EQUATIONS AND MILD-SLOPE EQUATIONS MODEL
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, the Boussinesq equations and mild-slope equation of wave transformation in near-shore shallow water were introduced and the characteristics of the two forms of equations were compared and analyzed. Meanwhile, a Boussinesq wave model which includes effects of bottom friction, wave breaking and subgrid turbulent mixing is established, slot technique dealing with moving boundary and damping layer dealing with absorbing boundary were established. By adopting empirical nonlinear dispersion relation and including nonlinear term, the mild-slope equation model was modified to take nonlinear effects into account. The two types of models were validated with the experiment results given by Berkhoff and their accuracy was analysed and compared with that of correlated methods.
Thermoviscous Model Equations in Nonlinear Acoustics
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne
Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...
Structural Equation Modeling of Travel Choice Dynamics
Golob, Thomas F.
1988-01-01
This research has two objectives. The first objective is to explore the use of the modeling tool called "latent structural equations" (structural equations with latent variables) in the general field of travel behavior analysis and the more specific field of dynamic analysis of travel behavior. The second objective is to apply a latent structural equation model in order to determine the causal relationships between income, car ownership, and mobility. Many transportation researchers ...
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.
Modelling conjugation with stochastic differential equations.
Philipsen, K R; Christiansen, L E; Hasman, H; Madsen, H
2010-03-07
Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared to the model without plate conjugation. The modelling approach described in this article can be applied generally when modelling dynamical systems.
Modeling helicity dissipation-rate equation
Yokoi, Nobumitsu
2016-01-01
Transport equation of the dissipation rate of turbulent helicity is derived with the aid of a statistical analytical closure theory of inhomogeneous turbulence. It is shown that an assumption on the helicity scaling with an algebraic relationship between the helicity and its dissipation rate leads to the transport equation of the turbulent helicity dissipation rate without resorting to a heuristic modeling.
Structural Equation Modeling of Multivariate Time Series
du Toit, Stephen H. C.; Browne, Michael W.
2007-01-01
The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be…
Stochastic differential equation model to Prendiville processes
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)
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.
Stochastic differential equation model to Prendiville processes
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.
A first course in structural equation modeling
Raykov, Tenko
2012-01-01
In this book, authors Tenko Raykov and George A. Marcoulides introduce students to the basics of structural equation modeling (SEM) through a conceptual, nonmathematical approach. For ease of understanding, the few mathematical formulas presented are used in a conceptual or illustrative nature, rather than a computational one.Featuring examples from EQS, LISREL, and Mplus, A First Course in Structural Equation Modeling is an excellent beginner's guide to learning how to set up input files to fit the most commonly used types of structural equation models with these programs. The basic ideas and methods for conducting SEM are independent of any particular software.Highlights of the Second Edition include: Review of latent change (growth) analysis models at an introductory level Coverage of the popular Mplus program Updated examples of LISREL and EQS A CD that contains all of the text's LISREL, EQS, and Mplus examples.A First Course in Structural Equation Modeling is intended as an introductory book for students...
Partial Differential Equations Modeling and Numerical Simulation
Glowinski, Roland
2008-01-01
This book is dedicated to Olivier Pironneau. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schrödinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this book several experts in this field present their latest results and discuss trends in the numerical analy...
Structural equation modeling methods and applications
Wang, Jichuan
2012-01-01
A reference guide for applications of SEM using Mplus Structural Equation Modeling: Applications Using Mplus is intended as both a teaching resource and a reference guide. Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling (SEM). Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, Mplus, is also featured and provides researchers with a
Stochastic differential equations used to model conjugation
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo
Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can...
Modified Heisenberg Ferromagnet Model and Integrable Equation
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
We investigate some integrable modified Heisenberg ferromagnet models by using the prolongation structure theory. Through associating them with the motion of curve in Minkowski space, the corresponding coupled integrable equations are presented.
Linear causal modeling with structural equations
Mulaik, Stanley A
2009-01-01
Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal
Combat modeling with partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Protopopescu, V.; Santoro, R.T.; Dockery, J.; Cox, R.L.; Barnes, J.M.
1987-11-01
A new analytic model based on coupled nonlinear partial differential equations is proposed to describe the temporal and spatial evolution of opposing forces in combat. Analytic descriptions of combat have been developed previously using relatively simpler models based on ordinary differential equations (.e.g, Lanchester's equations of combat) that capture only the global temporal variation of the forces, but not their spatial movement (advance, retreat, flanking maneuver, etc.). The rationale for analytic models and, particularly, the motivation for the present model are reviewed. A detailed description of this model in terms of the mathematical equations together with the possible and plausible military interpretation are presented. Numerical solutions of the nonlinear differential equation model for a large variety of parameters (battlefield length, initial force ratios, initial spatial distribution of forces, boundary conditions, type of interaction, etc.) are implemented. The computational methods and computer programs are described and the results are given in tabular and graphic form. Where possible, the results are compared with the predictions given by the traditional Lanchester equations. Finally, a PC program is described that uses data downloaded from the mainframe computer for rapid analysis of the various combat scenarios. 11 refs., 10 figs., 5 tabs.
Structural Equation Modeling in Special Education Research.
Moore, Alan D.
1995-01-01
This article suggests the use of structural equation modeling in special education research, to analyze multivariate data from both nonexperimental and experimental research. It combines a structural model linking latent variables and a measurement model linking observed variables with latent variables. (Author/DB)
Multiplicity Control in Structural Equation Modeling
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…
Global identifiability of linear structural equation models
Drton, Mathias; Sullivant, Seth
2010-01-01
Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms. We give a necessary and sufficient condition for global identifiability of the model in terms of a mixed graph encoding the linear structural equations and the correlation structure of the error terms. Global identifiability is understood to mean injectivity of the parametrization of the model and is fundamental in particular for applicability of standard statistical methodology.
Basics of Structural Equation Modeling
Maruyama, Dr Geoffrey M
1997-01-01
With the availability of software programs, such as LISREL, EQS, and AMOS, modeling (SEM) techniques have become a popular tool for formalized presentation of the hypothesized relationships underlying correlational research and test for the plausibility of hypothesizing for a particular data set. Through the use of careful narrative explanation, Maruyama's text describes the logic underlying SEM approaches, describes how SEM approaches relate to techniques like regression and factor analysis, analyzes the strengths and shortcomings of SEM as compared to alternative methodologies, and explores
String Field Equations from Generalized Sigma Model
Energy Technology Data Exchange (ETDEWEB)
Bardakci, K.; Bernardo, L.M.
1997-01-29
We propose a new approach for deriving the string field equations from a general sigma model on the world-sheet. This approach leads to an equation which combines some of the attractive features of both the renormalization group method and the covariant beta function treatment of the massless excitations. It has the advantage of being covariant under a very general set of both local and non-local transformations in the field space. We apply it to the tachyon, massless and first massive level, and show that the resulting field equations reproduce the correct spectrum of a left-right symmetric closed bosonic string.
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.
Modeling and Prediction Using Stochastic Differential Equations
DEFF Research Database (Denmark)
Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp
2016-01-01
Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup...... that describes the variation between subjects. The ODE setup implies that the variation for a single subject is described by a single parameter (or vector), namely the variance (covariance) of the residuals. Furthermore the prediction of the states is given as the solution to the ODEs and hence assumed...... deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs...
Advanced structural equation modeling issues and techniques
Marcoulides, George A
2013-01-01
By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.
Structural Equation Modeling in Rehabilitation Counseling Research
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
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…
The geometry of a vorticity model equation
Escher, Joachim; Wunsch, Marcus
2010-01-01
We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point, with respect to right-invariant metric induced by the homogeneous Sobolev norm $H^{1/2}$ and show the local existence of the geodesics in the extended group of diffeomorphisms of Sobolev class $H^{k}$ with $k\\ge 2$.
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
Principles and practice of structural equation modeling
Kline, Rex B
2015-01-01
Emphasizing concepts and rationale over mathematical minutiae, this is the most widely used, complete, and accessible structural equation modeling (SEM) text. Continuing the tradition of using real data examples from a variety of disciplines, the significantly revised fourth edition incorporates recent developments such as Pearl's graphing theory and the structural causal model (SCM), measurement invariance, and more. Readers gain a comprehensive understanding of all phases of SEM, from data collection and screening to the interpretation and reporting of the results. Learning is enhanced by ex
A limit model for thermoelectric equations
Consiglieri, Luisa
2010-01-01
We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with the Seebeck-Peltier-Thomson cross-effects. Our first purpose is that the existence of a weak solution holds true under minimal assumptions on the data, as in particular convex domains with Lipschitz boundary. The proof is based on a fixed point argument, compactness methods, and existence and regularity theory for elliptic scalar equations. In this process, we prove W^{1,p}-regularity for Neumann problem to an elliptic second order equation in divergence form with discontinuous coefficient by using the potential theory. The second one is to show the existence of a limit model illustrating the asymptotic situation.
Lattice Boltzmann model for nonlinear convection-diffusion equations.
Shi, Baochang; Guo, Zhaoli
2009-01-01
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
Wave equation modelling using Julia programming language
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.
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. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
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.
Meta-analytic structural equation modelling
Jak, Suzanne
2015-01-01
This book explains how to employ MASEM, the combination of meta-analysis (MA) and structural equation modelling (SEM). It shows how by using MASEM, a single model can be tested to explain the relationships between a set of variables in several studies. This book gives an introduction to MASEM, with a focus on the state of the art approach: the two stage approach of Cheung and Cheung & Chan. Both, the fixed and the random approach to MASEM are illustrated with two applications to real data. All steps that have to be taken to perform the analyses are discussed extensively. All data and syntax files are available online, so that readers can imitate all analyses. By using SEM for meta-analysis, this book shows how to benefit from all available information from all available studies, even if few or none of the studies report about all relationships that feature in the full model of interest.
On the Use of Structural Equation Models in Marketing Modeling
Steenkamp, J.E.B.M.; Baumgartner, H.
2000-01-01
We reflect on the role of structural equation modeling (SEM) in marketing modeling and managerial decision making. We discuss some benefits provided by SEM and alert marketing modelers to several recent developments in SEM in three areas: measurement analysis, analysis of cross-sectional data, and a
A first course in differential equations, modeling, and simulation
Smith, Carlos A
2011-01-01
IntroductionAn Introductory ExampleModelingDifferential EquationsForcing FunctionsBook ObjectivesObjects in a Gravitational FieldAn Example Antidifferentiation: Technique for Solving First-Order Ordinary Differential EquationsBack to Section 2-1Another ExampleSeparation of Variables: Technique for Solving First-Order Ordinary Differential Equations Back to Section 2-5Equations, Unknowns, and Degrees of FreedomClassical Solutions of Ordinary Linear Differential EquationsExamples of Differential EquationsDefinition of a Linear Differential EquationIntegrating Factor MethodCharacteristic Equation
Teaching Modeling with Partial Differential Equations: Several Successful Approaches
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…
Teaching Modeling with Partial Differential Equations: Several Successful Approaches
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…
Applying Meta-Analysis to Structural Equation Modeling
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…
Parameter Estimation of Partial Differential Equation Models
Xun, Xiaolei
2013-09-01
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 presence 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 long-range infrared light detection and ranging data. Supplementary materials for this article are available online. © 2013 American Statistical Association.
Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations
Directory of Open Access Journals (Sweden)
Raheleh Jafari
2017-01-01
Full Text Available The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.
Voter Model Perturbations and Reaction Diffusion Equations
Cox, J Theodore; Perkins, Edwin
2011-01-01
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \\ge 3$. Combining this result with properties of the PDE, some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of three systems when the parameters are close to the voter model: (i) a stochastic spatial Lotka-Volterra model of Neuhauser and Pacala, (ii) a model of the evolution of cooperation of Ohtsuki, Hauert, Lieberman, and Nowak, and (iii) a continuous time version of the non-linear voter model of Molofsky, Durrett, Dushoff, Griffeath, and Levin. The first application confirms a conjecture of Cox and Perkins and the second confirms a conjecture of Ohtsuki et al in the ...
The General Linear Model as Structural Equation Modeling
Graham, James M.
2008-01-01
Statistical procedures based on the general linear model (GLM) share much in common with one another, both conceptually and practically. The use of structural equation modeling path diagrams as tools for teaching the GLM as a body of connected statistical procedures is presented. A heuristic data set is used to demonstrate a variety of univariate…
Structural equation models from paths to networks
Westland, J Christopher
2015-01-01
This compact reference surveys the full range of available structural equation modeling (SEM) methodologies. It reviews applications in a broad range of disciplines, particularly in the social sciences where many key concepts are not directly observable. This is the first book to present SEM’s development in its proper historical context–essential to understanding the application, strengths and weaknesses of each particular method. This book also surveys the emerging path and network approaches that complement and enhance SEM, and that will grow in importance in the near future. SEM’s ability to accommodate unobservable theory constructs through latent variables is of significant importance to social scientists. Latent variable theory and application are comprehensively explained, and methods are presented for extending their power, including guidelines for data preparation, sample size calculation, and the special treatment of Likert scale data. Tables of software, methodologies and fit st...
A note on solutions of an equation modelling arterial deformation
Energy Technology Data Exchange (ETDEWEB)
Gordoa, P.R. [Area de Matematica Aplicada, ESCET, Universidad Rey Juan Carlos, C/ Tulipan s/n, 28933 Mostoles, Madrid (Spain)]. E-mail: pilar.gordoa@urjc.es
2007-08-15
The derivation of exact solutions for a partial differential equation modelling arterial deformation in large arteries is considered. Amongst other results, we show that, for any values of the parameters appearing in the equation, solutions in terms of the first Painleve transcendent can be obtained. This is in spite of the non-integrability of the equation. We also establish a connection, via an approximation of the equation under study by the Korteweg-de Vries equation, with the second Painleve equation. Our results thus serve to further demonstrate the wide applicability and importance of the Painleve equations.
Fitting ARMA Time Series by Structural Equation Models.
van Buuren, Stef
1997-01-01
This paper outlines how the stationary ARMA (p,q) model (G. Box and G. Jenkins, 1976) can be specified as a structural equation model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. The method is applied to three problem types. (SLD)
Virtuous organization: A structural equation modeling approach
Directory of Open Access Journals (Sweden)
Majid Zamahani
2013-02-01
Full Text Available For years, the idea of virtue was unfavorable among researchers and virtues were traditionally considered as culture-specific, relativistic and they were supposed to be associated with social conservatism, religious or moral dogmatism, and scientific irrelevance. Virtue and virtuousness have been recently considered seriously among organizational researchers. The proposed study of this paper examines the relationships between leadership, organizational culture, human resource, structure and processes, care for community and virtuous organization. Structural equation modeling is employed to investigate the effects of each variable on other components. The data used in this study consists of questionnaire responses from employees in Payam e Noor University in Yazd province. A total of 250 questionnaires were sent out and a total of 211 valid responses were received. Our results have revealed that all the five variables have positive and significant impacts on virtuous organization. Among the five variables, organizational culture has the most direct impact (0.80 and human resource has the most total impact (0.844 on virtuous organization.
The Kadomtsev{endash}Petviashvili equation as a source of integrable model equations
Energy Technology Data Exchange (ETDEWEB)
Maccari, A. [Technical Institute ``G. Cardano,`` Piazza della Resistenza 1, 00015 Monterotondo Rome (Italy)
1996-12-01
A new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained, by an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev{endash}Petviashvili equation. The integrability property is explicitly demonstrated, by exhibiting the corresponding Lax pair, that is obtained by applying the reduction technique to the Lax pair of the Kadomtsev{endash}Petviashvili equation. This model equation is likely to be of applicative relevance, because it may be considered a consistent approximation of a large class of nonlinear evolution PDEs. {copyright} {ital 1996 American Institute of Physics.}
Introduction to computation and modeling for differential equations
Edsberg, Lennart
2008-01-01
An introduction to scientific computing for differential equationsIntroduction to Computation and Modeling for Differential Equations provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique ""Five-M"" approach: Modeling, Mathematics, Methods, MATLAB, and Multiphysics. This approach facilitates a thorough understanding of h
Microscopic models of traveling wave equations
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.
Rate equation modelling and investigation of quantum cascade detector characteristics
Saha, Sumit; Kumar, Jitendra
2016-10-01
A simple precise transport model has been proposed using rate equation approach for the characterization of a quantum cascade detector. The resonant tunneling transport is incorporated in the rate equation model through a resonant tunneling current density term. All the major scattering processes are included in the rate equation model. The effect of temperature on the quantum cascade detector characteristics has been examined considering the temperature dependent band parameters and the carrier scattering processes. Incorporation of the resonant tunneling process in the rate equation model improves the detector performance appreciably and reproduces the detector characteristics within experimental accuracy.
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
USING STRUCTURAL EQUATION MODELING TO INVESTIGATE RELATIONSHIPS AMONG ECOLOGICAL VARIABLES
This paper gives an introductory account of Structural Equation Modeling (SEM) and demonstrates its application using LISRELmodel utilizing environmental data. Using nine EMAP data variables, we analyzed their correlation matrix with an SEM model. The model characterized...
The Whitham Equation as a Model for Surface Water Waves
Moldabayev, Daulet; Dutykh, Denys
2014-01-01
The Whitham equation was proposed as an alternate model equation for the simplified description of uni-directional wave motion at the surface of an inviscid fluid. As the Whitham equation incorporates the full linear dispersion relation of the water wave problem, it is thought to provide a more faithful description of shorter waves of small amplitude than traditional long wave models such as the KdV equation. In this work, we identify a scaling regime in which the Whitham equation can be derived from the Hamiltonian theory of surface water waves. The Whitham equation is integrated numerically, and it is shown that the equation gives a close approximation of inviscid free surface dynamics as described by the Euler equations. The performance of the Whitham equation as a model for free surface dynamics is also compared to two standard free surface models: the KdV and the BBM equation. It is found that in a wide parameter range of amplitudes and wavelengths, the Whitham equation performs on par with or better tha...
Evaluation of model fit in nonlinear multilevel structural equation modeling
Directory of Open Access Journals (Sweden)
Karin eSchermelleh-Engel
2014-03-01
Full Text Available Evaluating model fit in nonlinear multilevel structural equation models (MSEM presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are nonnormally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of nonnormality, they were not yet investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.
Evaluation of model fit in nonlinear multilevel structural equation modeling.
Schermelleh-Engel, Karin; Kerwer, Martin; Klein, Andreas G
2014-01-01
Evaluating model fit in nonlinear multilevel structural equation models (MSEM) presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are non-normally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of non-normality, they have not yet been investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.
A Bayesian modeling approach for generalized semiparametric structural equation models.
Song, Xin-Yuan; Lu, Zhao-Hua; Cai, Jing-Heng; Ip, Edward Hak-Sing
2013-10-01
In behavioral, biomedical, and psychological studies, structural equation models (SEMs) have been widely used for assessing relationships between latent variables. Regression-type structural models based on parametric functions are often used for such purposes. In many applications, however, parametric SEMs are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable. A different but equally important limitation of traditional parametric SEMs is that they are not designed to handle mixed data types-continuous, count, ordered, and unordered categorical. This paper develops a generalized semiparametric SEM that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables. A structural equation of the proposed SEM is formulated using a series of unspecified smooth functions. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the smooth functions and the unknown parameters. Moreover, we examine the relative benefits of semiparametric modeling over parametric modeling using a Bayesian model-comparison statistic, called the complete deviance information criterion (DIC). The performance of the developed methodology is evaluated using a simulation study. To illustrate the method, we used a data set derived from the National Longitudinal Survey of Youth.
Model equations for simulating flows in multistage turbomachinery
Adamczyk, John J.
1996-01-01
A steady, three dimensional average-passage equation system was derived. The purpose was to simulate multistage turbomachinery flows. These equations describe a steady, viscous flow that is periodic from blade passage to blade passage. Moreover, these equations have a closure problem that is similar to that of the Reynolds-average Navier-Stokes equations. A scaled form of the average-passage equation system could provide an improved mathematical model for simulating the flow in the design and in the off-design conditions of a multistage machine.
Dynamic hysteresis modeling including skin effect using diffusion equation model
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.
Dynamic hysteresis modeling including skin effect using diffusion equation model
Energy Technology Data Exchange (ETDEWEB)
Hamada, Souad, E-mail: souadhamada@yahoo.fr [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Louai, Fatima Zohra, E-mail: fz_louai@yahoo.com [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Nait-Said, Nasreddine, E-mail: n_naitsaid@yahoo.com [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Benabou, Abdelkader, E-mail: Abdelkader.Benabou@univ-lille1.fr [L2EP, Université de Lille1, 59655 Villeneuve d’Ascq (France)
2016-07-15
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
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…
Reporting Monte Carlo Studies in Structural Equation Modeling
Boomsma, Anne
2013-01-01
In structural equation modeling, Monte Carlo simulations have been used increasingly over the last two decades, as an inventory from the journal Structural Equation Modeling illustrates. Reaching out to a broad audience, this article provides guidelines for reporting Monte Carlo studies in that fiel
A practical course in differential equations and mathematical modeling
Ibragimov , Nail H
2009-01-01
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame
Modeling circadian clocks: From equations to oscillations
National Research Council Canada - National Science Library
Gonze, Didier
2011-01-01
... (such as light and temperature) is greatly helped by mathematical modeling. In the present paper we review some mathematical models for circadian clocks, ranging from abstract, phenomenological models to the most detailed molecular models...
Modelling of nonlinear shoaling based on stochastic evolution equations
DEFF Research Database (Denmark)
Kofoed-Hansen, Henrik; Rasmussen, Jørgen Hvenekær
1998-01-01
A one-dimensional stochastic model is derived to simulate the transformation of wave spectra in shallow water including generation of bound sub- and super-harmonics, near-resonant triad wave interaction and wave breaking. Boussinesq type equations with improved linear dispersion characteristics...... are recast into evolution equations for the complex amplitudes, and serve as the underlying deterministic model. Next, a set of evolution equations for the cumulants is derived. By formally introducing the well-known Gaussian closure hypothesis, nonlinear evolution equations for the power spectrum...... and bispectrum are derived. A simple description of depth-induced wave breaking is incorporated in the model equations, assuming that the total rate of dissipation may be distributed in proportion to the spectral energy density on each discrete frequency. The proposed phase-averaged model is compared...
Bayesian structural equation modeling method for hierarchical model validation
Energy Technology Data Exchange (ETDEWEB)
Jiang Xiaomo [Department of Civil and Environmental Engineering, Vanderbilt University, Box 1831-B, Nashville, TN 37235 (United States)], E-mail: xiaomo.jiang@vanderbilt.edu; Mahadevan, Sankaran [Department of Civil and Environmental Engineering, Vanderbilt University, Box 1831-B, Nashville, TN 37235 (United States)], E-mail: sankaran.mahadevan@vanderbilt.edu
2009-04-15
A building block approach to model validation may proceed through various levels, such as material to component to subsystem to system, comparing model predictions with experimental observations at each level. Usually, experimental data becomes scarce as one proceeds from lower to higher levels. This paper presents a structural equation modeling approach to make use of the lower-level data for higher-level model validation under uncertainty, integrating several components: lower-level data, higher-level data, computational model, and latent variables. The method proposed in this paper uses latent variables to model two sets of relationships, namely, the computational model to system-level data, and lower-level data to system-level data. A Bayesian network with Markov chain Monte Carlo simulation is applied to represent the two relationships and to estimate the influencing factors between them. Bayesian hypothesis testing is employed to quantify the confidence in the predictive model at the system level, and the role of lower-level data in the model validation assessment at the system level. The proposed methodology is implemented for hierarchical assessment of three validation problems, using discrete observations and time-series data.
Landscape evolution models: A review of their fundamental equations
Chen, Alex; Darbon, Jérôme; Morel, Jean-Michel
2014-08-01
This paper reviews the main physical laws proposed in landscape evolution models (LEMs). It discusses first the main partial differential equations involved in these models and their variants. These equations govern water runoff, stream incision, regolith-bedrock interaction, hillslope evolution, and sedimentation. A synthesis of existing LEMs is proposed. It proposes three models with growing complexity and with a growing number of components: two-equation models with only two components, governing water and bedrock evolution; three-equation models with three components where water, bedrock, and sediment interact; and finally models with four equations and four interacting components, namely water, bedrock, suspended sediment, and regolith. This analysis is not a mere compilation of existing LEMs. It attempts at giving the simplest and most general physically consistent set of equations, coping with all requirements stated in LEMs and LEM software. Three issues are in particular addressed and hopefully resolved. The first one is a correct formulation of the water transport equation down slopes. A general formulation for this equation is proposed, coping not only with the simplest form computing the drainage area but also with a sound energy dissipation argument associated with the Saint-Venant shallow water equations. The second issue arises from the coexistence of two competing modes, namely the detachment-limited erosion mode on hillslopes, and the transport-limited sediment transport on river beds. The third issue (linked to the second) is the fact that no conservation law is available for material in these two modes. A simple solution proposed to resolve these issues is the introduction, as suggested by several authors, of an additional variable for suspended sediment load in water. With only three variables and three equations, the above-mentioned contradictions seem to be eliminated. Several numerical experiments on real digital elevation models (DEMs
Acoustic Logging Modeling by Refined Biot's Equations
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.
Soluble Boltzmann equations for internal state and Maxwell models
Futcher, E.; Hoare, M.R.; Hendriks, E.M.; Ernst, M.H.
1980-01-01
We consider a class of scalar nonlinear Boltzmann equations describing the evolution of a microcanonical ensemble in which sub-systems exchange internal energy ‘randomly’ in binary interactions. In the continuous variable version these models can equally be interpreted as Boltzmann equations for Ma
Modeling systems containing alkanolamines with the CPA equation of state
DEFF Research Database (Denmark)
Avlund, Ane Søgaard; Kontogeorgis, Georgios; Michelsen, Michael Locht
2008-01-01
An association model, the cubic-plus-association (CPA) equation of state (EoS), is applied for the first time to a class of multifunctional compounds (alkanolamines). Three alkanolamines of practical and scientific significance are considered; monoethanolamine (MEA), diethanolamine (DEA...... studied using the CPA equation of state (alcohols, amines, and glycols)....
Model equation for simulating flows in multistage turbomachinery
Adamczyk, J. J.
1985-01-01
A steady, three-dimensional average-passage equation system is derived for use in simulating multistage turbomachinery flows. These equations describe a steady, viscous flow that is periodic from blade passage to blade passage. From this system of equations, various reduced forms can be derived for use in simulating the three-dimensional flow field within multistage machinery. It is suggested that a properly scaled form of the averaged-passage equation system would provide an improved mathematical model for simulating the flow in multistage machines at design and, in particular, at off-design conditions.
Transformation of equations in analysis of proportionality through referent models
Romay, E O
2006-01-01
In proportionality of objects, samples or populations, usually we work with Z score of proportionality calculated through referent models, instead directly with the variables of the objects in itself. In these studies we have the necessity to transform, the equations that use the variables of the object, in equations that directly use like variables Z score. In the present work a method is developed to transform the parametric equations, in equations in variables Z using like example the studies of human proportionality from the Phantom stratagem of Ross and Wilson.
Meta-analysis a structural equation modeling approach
Cheung, Mike W-L
2015-01-01
Presents a novel approach to conducting meta-analysis using structural equation modeling. Structural equation modeling (SEM) and meta-analysis are two powerful statistical methods in the educational, social, behavioral, and medical sciences. They are often treated as two unrelated topics in the literature. This book presents a unified framework on analyzing meta-analytic data within the SEM framework, and illustrates how to conduct meta-analysis using the metaSEM package in the R statistical environment. Meta-Analysis: A Structural Equation Modeling Approach begins by introducing the impo
Introduction to Structural Equation Modelling Using SPSS and Amos
Blunch, Niels J
2008-01-01
. Introduction to Structural Equation Modelling using SPSS and AMOS is a complete guide to carrying out your own structural equation modelling project. Assuming no previous experience of the subject, and a minimum of mathematical knowledge, this is the ideal guide for those new to structural equation modelling (SEM). Each chapter begins with learning objectives, and ends with a list of the new concepts introduced and questions to open up further discussion. Exercises for each chapter, incuding the necessary data, can be downloaded from the book's website. Helpful real life examples are include
An Overview on R Packages for Structural Equation Modeling
Directory of Open Access Journals (Sweden)
Haibin Qiu
2014-05-01
Full Text Available The aim of this study is to present overview on R packages for structural equation modeling. Structural equation modeling, a statistical technique for testing and estimating causal relations using an amalgamation of statistical data and qualitative causal hypotheses, allow both confirmatory and exploratory modeling, meaning they are matched to both hypothesis testing and theory development. R project or R language, a free and popular programming language and computer software surroundings for statistical computing and graphics, is popularly used among statisticians for developing statistical computer software and data analysis. The major finding is that it is necessary to build excellent and enough structural equation modeling packages for R users to do research. Numerous packages for structural equation modeling of R project are introduced in this study and most of them are enclosed in the Comprehensive R Archive Network task view Psychometrics.
Partial Least Squares Structural Equation Modeling with R
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…
ECONOMETRIC APPROACH TO DIFFERENCE EQUATIONS MODELING OF EXCHANGE RATES CHANGES
Directory of Open Access Journals (Sweden)
Josip Arnerić
2010-12-01
Full Text Available Time series models that are commonly used in econometric modeling are autoregressive stochastic linear models (AR and models of moving averages (MA. Mentioned models by their structure are actually stochastic difference equations. Therefore, the objective of this paper is to estimate difference equations containing stochastic (random component. Estimated models of time series will be used to forecast observed data in the future. Namely, solutions of difference equations are closely related to conditions of stationary time series models. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models and their variants. However, GARCH models will not be analyzed because the purpose of this research is to predict the value of the exchange rate in the levels within conditional mean equation and to determine whether the observed variable has a stable or explosive time path. Based on the estimated difference equation it will be examined whether Croatia is implementing a stable policy of exchange rates.
Dynamic data analysis modeling data with differential equations
Ramsay, James
2017-01-01
This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in...
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
A Framework for Structural Equation Models in General Pedigrees
National Research Council Canada - National Science Library
Morris, Nathan J; Elston, Robert C; Stein, Catherine M
Background/Aims: Structural Equation Modeling (SEM) is an analysis approach that accounts for both the causal relationships between variables and the errors associated with the measurement of these variables...
Modeling the turbulent kinetic energy equation for compressible, homogeneous turbulence
Aupoix, B.; Blaisdell, G. A.; Reynolds, William C.; Zeman, Otto
1990-01-01
The turbulent kinetic energy transport equation, which is the basis of turbulence models, is investigated for homogeneous, compressible turbulence using direct numerical simulations performed at CTR. It is shown that the partition between dilatational and solenoidal modes is very sensitive to initial conditions for isotropic decaying turbulence but not for sheared flows. The importance of the dilatational dissipation and of the pressure-dilatation term is evidenced from simulations and a transport equation is proposed to evaluate the pressure-dilatation term evolution. This transport equation seems to work well for sheared flows but does not account for initial condition sensitivity in isotropic decay. An improved model is proposed.
Modelling AIDS epidemic and treatment with difference equations
Directory of Open Access Journals (Sweden)
Ramani A
2004-01-01
Full Text Available We propose two models for the description of the dynamics of an AIDS epidemic and of the effect of a combined-drugs AIDS treatment based on difference equations. We show that our interacting population model, despite its extreme simplicity, describes adequately the evolution of an AIDS epidemic. A cellular-automaton analogue of the discrete system of equations is presented as well. In the case of drug treatment, we identify two different regimes corresponding to efficient and inefficient medication. The effect of the discreteness of the equations is also studied.
Modelling AIDS epidemic and treatment with difference equations
Directory of Open Access Journals (Sweden)
A. S. Carstea
2004-07-01
Full Text Available We propose two models for the description of the dynamics of an AIDS epidemic and of the effect of a combined-drugs AIDS treatment based on difference equations. We show that our interacting population model, despite its extreme simplicity, describes adequately the evolution of an AIDS epidemic. A cellular-automaton analogue of the discrete system of equations is presented as well. In the case of drug treatment, we identify two different regimes corresponding to efficient and inefficient medication. The effect of the discreteness of the equations is also studied.
CMB Constraints on Reheating Models with Varying Equation of State
de Freitas, Rodolfo C
2015-01-01
The temperature at the end of reheating and the length of this cosmological phase can be bound to the inflationary observables if one considers the cosmological evolution from the time of Hubble crossing until today. There are many examples in the literature where it is made for single-field inflationary models and a constant equation of state during reheating. We adopt two simple varying equation of state parameters during reheating, combine the allowed range of the reheating parameters with the observational limits of the scalar perturbations spectral index and compare the constraints of some inflationary models with the case of a constant equation of state parameter during reheating.
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.…
Finite Feedback Cycling in Structural Equation Models
Hayduk, Leslie A.
2009-01-01
In models containing reciprocal effects, or longer causal loops, the usual effect estimates assume that any effect touching a loop initiates an infinite cycling of effects around that loop. The real world, in contrast, might permit only finite feedback cycles. I use a simple hypothetical model to demonstrate that if the world permits only a few…
Garg, Vijay K.; Ameri, Ali A.
1997-01-01
A three-dimensional Navier-Stokes code has been used to compute the heat transfer coefficient on two film-cooled turbine blades, namely, the VKI rotor with six rows of cooling holes, including three rows on the shower head and the C3X vane with nine rows of holes, including five rows on the shower head. Predictions of heat transfer coefficient at the blade surface using three two-equation turbulence model specifically, Coakley's q-omega model, Chien's k-epsilon model and Wilcox's k-omega model with Menter's modifications, have been compared with the experimental data of Camci and Arts for the VKI rotor, and of Hylton et al. for the C3X vane along with predictions using the Baldwin-Lomar (B-L) model taken from Garg and Gaugler. It is found that for the cases considered here the two equation models predict the blade heat transfer somewhat better than the B-L model except immediately downstream of the film-cooled holes on the suction surface of the VKI rotor, and over most of the suction surface of the C3X vane. However, all two-equation models require 40% more computer core than the B-L model for solution, and while the q-omega and k-epsilon models need 40% more computer time than the B-L model the k-omega model requires at least 65% more time because of the slower rate of convergence. It is found that the heat transfer coefficient exhibit a strong spanwise as well as streamwise variation for both blades and all turbulence models.
NN-πNN equations and the chiral bag model
Afnan, I. R.; Blankleider, B.
1985-12-01
The NN-πNN equations that describe, in a unified framework, pion production in nucleon-nucleon scattering, and pion-deuteron and nucleon-nucleon elastic scattering, have been extended to include the N(939) and Δ(1232) on an equal footing. This extension, motivated by the quark models of hadrons, has the bare N and Δ as three quark states with the same spacial wave function, but different spin isospin states. The final equations, referred to as the BB-πBB equations, are consistent with the chiral bag models to the extent that the πNN, πNΔ, and πΔΔ coupling constants and form factors are related, and can be taken from bag models. The resultant equations satisfy two- and three-body unitarity, and are derived by exposing the lowest unitarity cuts in the n-body Green's function. These equations retain important contributions missing from the NN-πNN equations. For pion production and N-N scattering they include the contribution of backward pions in the NN-->NΔ transition potential, which may overcome the problem of small pp-->πd cross section as predicted by the NN-πNN equations. For π-d elastic scattering they include an additional NΔ-->NΔ tensor force that can influence the tensor polarization.
NN-. pi. NN equations and the chiral bag model
Energy Technology Data Exchange (ETDEWEB)
Afnan, I.R.; Blankleider, B.
1985-12-01
The NN-..pi..NN equations that describe, in a unified framework, pion production in nucleon-nucleon scattering, and pion-deuteron and nucleon-nucleon elastic scattering, have been extended to include the N(939) and ..delta..(1232) on an equal footing. This extension, motivated by the quark models of hadrons, has the bare N and ..delta.. as three quark states with the same spacial wave function, but different spin isospin states. The final equations, referred to as the BB-..pi..BB equations, are consistent with the chiral bag models to the extent that the ..pi..NN, ..pi..N..delta.., and ..pi delta delta.. coupling constants and form factors are related, and can be taken from bag models. The resultant equations satisfy two- and three-body unitarity, and are derived by exposing the lowest unitarity cuts in the n-body Green's function. These equations retain important contributions missing from the NN-..pi..NN equations. For pion production and N-N scattering they include the contribution of backward pions in the NN..-->..N..delta.. transition potential, which may overcome the problem of small pp..--> pi..d cross section as predicted by the NN-..pi..NN equations. For ..pi..-d elastic scattering they include an additional N..delta -->..N..delta.. tensor force that can influence the tensor polarization.
Numerical Comparison of Solutions of Kinetic Model Equations
Directory of Open Access Journals (Sweden)
A. A. Frolova
2015-01-01
Full Text Available The collision integral approximation by different model equations has created a whole new trend in the theory of rarefied gas. One widely used model is the Shakhov model (S-model obtained by expansion of inverse collisions integral in a series of Hermite polynomials up to the third order. Using the same expansion with another value of free parameters leads to a linearized ellipsoidal statistical model (ESL.Both model equations (S and ESL have the same properties, as they give the correct relaxation of non-equilibrium stress tensor components and heat flux vector, the correct Prandtl number at the transition to the hydrodynamic regime and do not guarantee the positivity of the distribution function.The article presents numerical comparison of solutions of Shakhov equation, ESL- model and full Boltzmann equation in the four Riemann problems for molecules of hard spheres.We have considered the expansion of two gas flows, contact discontinuity, the problem of the gas counter-flows and the problem of the shock wave structure. For the numerical solution of the kinetic equations the method of discrete ordinates is used.The comparison shows that solution has a weak sensitivity to the form of collision operator in the problem of expansions of two gas flows and results obtained by the model and the kinetic Boltzmann equations coincide.In the problem of the contact discontinuity the solution of model equations differs from full kinetic solutions at the point of the initial discontinuity. The non-equilibrium stress tensor has the maximum errors, the error of the heat flux is much smaller, and the ESL - model gives the exact value of the extremum of heat flux.In the problems of gas counter-flows and shock wave structure the model equations give significant distortion profiles of heat flux and non-equilibrium stress tensor components in front of the shock waves. This behavior is due to fact that in the models under consideration there is no dependency of the
Differential equations and integrable models the $SU(3)$ case
Dorey, P; Dorey, Patrick; Tateo, Roberto
2000-01-01
We exhibit a relationship between the massless $a_2^{(2)}$ integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schrödinger equation. This forms part of a more general correspondence involving $A_2$-related Bethe ansatz systems and third-order differential equations. A non-linear integral equation for the generalised spectral problem is derived, and some numerical checks are performed. Duality properties are discussed, and a simple variant of the nonlinear equation is suggested as a candidate to describe the finite volume ground state energies of minimal conformal field theories perturbed by the operators $\\phi_{12}$, $\\phi_{21}$ and $\\phi_{15}$. This is checked against previous results obtained using the thermodynamic Bethe ansatz.
Schr\\"odinger-Pauli Equation for the Standard Model Extension CPT-Violating Dirac Equation
Gutierrez, Thomas D
2015-01-01
It is instructive to investigate the non-relativistic limit of the simplest Standard Model Extension (SME) CPT-violating Dirac-like equation but with minimal coupling to the electromagnetic fields. In this limit, it becomes an intuitive Schr\\"odinger-Pauli-like equation. This is comparable to the free particle treatment as explored by Kostelecky and Lane, but this exercise only considers the $a$ and $b$ CPT-violating terms and $\\vec{p}/m$ terms to first order. Several toy systems are discussed.
Transport modelling in coastal waters using stochastic differential equations
Charles, W.M.
2007-01-01
In this thesis, the particle model that takes into account the short term correlation behaviour of pollutants dispersion has been developed. An efficient particle model for sediment transport has been developed. We have modified the existing particle model by adding extra equations for the suspensio
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.
Structural Equation Modeling Diagnostics Using R Package Semdiag and EQS
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…
Hopes and Cautions in Implementing Bayesian Structural Equation Modeling
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…
Parameter Estimates in Differential Equation Models for Population Growth
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,…
Advanced Applications of Structural Equation Modeling in Counseling Psychology Research
Martens, Matthew P.; Haase, Richard F.
2006-01-01
Structural equation modeling (SEM) is a data-analytic technique that allows researchers to test complex theoretical models. Most published applications of SEM involve analyses of cross-sectional recursive (i.e., unidirectional) models, but it is possible for researchers to test more complex designs that involve variables observed at multiple…
A Structural Equation Approach to Models with Spatial Dependence
Oud, J.H.L.; Folmer, H.
2008-01-01
We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it poss
A structural equation approach to models with spatial dependence
Oud, J.H.L.; Folmer, H.
2008-01-01
We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it poss
Residual models for nonlinear partial differential equations
Directory of Open Access Journals (Sweden)
Garry Pantelis
2005-11-01
Full Text Available Residual terms that appear in nonlinear PDEs that are constructed to generate filtered representations of the variables of the fully resolved system are examined by way of a consistency condition. It is shown that certain commonly used empirical gradient models for the residuals fail the test of consistency and therefore cannot be validated as approximations in any reliable sense. An alternate method is presented for computing the residuals. These residual models are independent of free or artificial parameters and there direct link with the functional form of the system of PDEs which describe the fully resolved system are established.
Reverberation Modelling Using a Parabolic Equation Method
2012-10-01
et possiblement des échos de cibles. L’objet du présent contrat est une étude du recours à un modèle à équation parabolique, en particulier le...obtained by the ‘PE method’ were primarily compared to results obtained from a proprietary ray-based model provided by Brooke Numerical Services (BNS... Services . Target echo estimates are also compared to the BNS ray model result. In all cases but one the reference data is plotted as a solid red line
Multiple-relaxation-time model for the correct thermohydrodynamic equations.
Zheng, Lin; Shi, Baochang; Guo, Zhaoli
2008-08-01
A coupling lattice Boltzmann equation (LBE) model with multiple relaxation times is proposed for thermal flows with viscous heat dissipation and compression work. In this model the fixed Prandtl number and the viscous dissipation problems in the energy equation, which exist in most of the LBE models, are successfully overcome. The model is validated by simulating the two-dimensional Couette flow, thermal Poiseuille flow, and the natural convection flow in a square cavity. It is found that the numerical results agree well with the analytical solutions and/or other numerical results.
LATTICE BOLTZMANN EQUATION MODEL IN THE CORIOLIS FIELD
Institute of Scientific and Technical Information of China (English)
FENG SHI-DE; MAO JIANG-YU; ZHANG QIONG
2001-01-01
In a large-scale field of rotational fluid, various unintelligible and surprising dynamic phenomena are produced due to the effect of the Coriolis force. The lattice Boltzmann equation (LBE) model in the Coriolis field is developed based on previous works.[1-4] Geophysical fluid dynamics equations are derived from the model. Numerical simulations have been made on an ideal atmospheric circulation of the Northern Hemisphere by using the model and they reproduce the Rossby wave motion well. Hence the applicability of the model is verified in both theory and experiment.
Development of interfacial area transport equation - modeling and experimental benchmark
Energy Technology Data Exchange (ETDEWEB)
Ishii, M. [Purdue Univ., West Lafayette, Indiana (United States)
2011-07-01
A dynamic treatment of interfacial area concentration has been studied over the last decade by employing the interfacial area transport equation. When coupled with the two-fluid model, the interfacial area transport equation replaces the flow regime dependent correlations for interfacial area concentration and eliminates potential artificial bifurcation or numerical oscillations stemming from these static correlations. An extensive database has been established to evaluate the model under various two-phase flow conditions. These include adiabatic and heated conditions, vertical and horizontal flow orientations, round, rectangular, annulus and 8×8 rod bundle channel geometries, and normal-gravity and simulated reduced-gravity conditions. This paper reviews the current state-of-the-art in the development of the interfacial area transport equation, available experimental databases and 1D and 3D benchmarking work of the interfacial area transport equation. (author)
Model Equations of Shape Memory Effect - Nitinol
Directory of Open Access Journals (Sweden)
Ion Vela
2010-01-01
Full Text Available Even it has been already confirmed that SMA’s have high potential for robotic actuators, actuators included in space robotics, underwater robotics, robotics for logistics, safety, as well as “green robotics” (robotics for the environment, energy conservation, sustainable development or agriculture, the number of applications of SMA-based actuators is still quite small, especially in applications in which their large strains, high specific work output and structural integration potential are useful,. The paper presents a formulated mathematical model calculated for binary SMA (Ni-Ti, helpful to estimate the stress distribution along with the transformation ratio of a SMA active element.
Basic equations of channel model for underground coal gasification
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The underground coal gasification has advantages of zero rubbish, nonpollution, low cost and high safety. According to the characteristics of the gasification, the channel model of chemical fluid mechanics is used to set up the fluid equations and chemical equations by some reasonable suppositions in this paper, which lays a theoretical foundation on requirements of fluid movement rules in the process of underground coal gasification.
QCD Equations of State and the QGP Liquid Model
Letessier, J
2003-01-01
Recent advances in the study of equations of state of thermal lattice Quantum Chromodynamics obtained at non-zero 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.
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.
Quantum-Dot Semiconductor Optical Amplifiers: State Space Model versus Rate Equation Model
Directory of Open Access Journals (Sweden)
Hussein Taleb
2013-01-01
Full Text Available A simple and accurate dynamic model for QD-SOAs is proposed. The proposed model is based on the state space theory, where by eliminating the distance dependence of the rate equation model of the QD-SOA; we derive a state space model for the device. A comparison is made between the rate equation model and the state space model under both steady state and transient regimes. Simulation results demonstrate that the derived state space model not only is much simpler and faster than the rate equation model, but also it is as accurate as the rate equation model.
Mathematical analysis of partial differential equations modeling electrostatic MEMS
Esposito, Pierpaolo; Guo, Yujin
2010-01-01
Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing "electrostatically actuated" MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems-where the stationary MEMS models fit-are a well-developed
Stochastic Differential Equations in Artificial Pancreas Modelling
DEFF Research Database (Denmark)
Duun-Henriksen, Anne Katrine
Type 1 diabetes accounts for approximately 5% of the total diabetes population. It is caused by the destruction of insulin producing β-cells in the pancreas. Various treatment strategies are available today, some of which include advanced technological devices such as an insulin pump and a contin......Type 1 diabetes accounts for approximately 5% of the total diabetes population. It is caused by the destruction of insulin producing β-cells in the pancreas. Various treatment strategies are available today, some of which include advanced technological devices such as an insulin pump...... and a continuous glucose monitor (CGM). Despite these technological advances in the treatment of type 1 diabetes, the disease still poses an enormous and constant challenge for the patients. To obtain tight glucose control the patients are required to assess how much they will eat prior to the meal. They have......, the control algorithm computes the optimal dose adjustment and sends instructions to the insulin pump. To develop control algorithms, mathematical models of the physiological dynamics are needed. They attempt to describe the significant dynamics of the system and hence they approximate the system behavior...
Maximum Likelihood Estimation in Meta-Analytic Structural Equation Modeling
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…
Analyzing Mixed-Dyadic Data Using Structural Equation Models
Peugh, James L.; DiLillo, David; Panuzio, Jillian
2013-01-01
Mixed-dyadic data, collected from distinguishable (nonexchangeable) or indistinguishable (exchangeable) dyads, require statistical analysis techniques that model the variation within dyads and between dyads appropriately. The purpose of this article is to provide a tutorial for performing structural equation modeling analyses of cross-sectional…
Multiplicity Control in Structural Equation Modeling: Incorporating Parameter Dependencies
Smith, Carrie E.; Cribbie, Robert A.
2013-01-01
When structural equation modeling (SEM) analyses are conducted, significance tests for all important model relationships (parameters including factor loadings, covariances, etc.) are typically conducted at a specified nominal Type I error rate ([alpha]). Despite the fact that many significance tests are often conducted in SEM, rarely is…
A Note on Structural Equation Modeling Estimates of Reliability
Yang, Yanyun; Green, Samuel B.
2010-01-01
Reliability can be estimated using structural equation modeling (SEM). Two potential problems with this approach are that estimates may be unstable with small sample sizes and biased with misspecified models. A Monte Carlo study was conducted to investigate the quality of SEM estimates of reliability by themselves and relative to coefficient…
A Structural Equation Model of Expertise in College Physics
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…
A Structural Equation Model for Predicting Business Student Performance
Pomykalski, James J.; Dion, Paul; Brock, James L.
2008-01-01
In this study, the authors developed a structural equation model that accounted for 79% of the variability of a student's final grade point average by using a sample size of 147 students. The model is based on student grades in 4 foundational business courses: introduction to business, macroeconomics, statistics, and using databases. Educators and…
A Bayesian Approach for Analyzing Longitudinal Structural Equation Models
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…
Play Context, Commitment, and Dating Violence: A Structural Equation Model
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 Structural Equation Model of Conceptual Change in Physics
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…
Parallel Evolutionary Modeling for Nonlinear Ordinary Differential Equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
We introduce a new parallel evolutionary algorithm in modeling dynamic systems by nonlinear higher-order ordinary differential equations (NHODEs). The NHODEs models are much more universal than the traditional linear models. In order to accelerate the modeling process, we propose and realize a parallel evolutionary algorithm using distributed CORBA object on the heterogeneous networking. Some numerical experiments show that the new algorithm is feasible and efficient.
Continuous Time Structural Equation Modeling with R Package ctsem
Directory of Open Access Journals (Sweden)
Charles C. Driver
2017-04-01
Full Text Available We introduce ctsem, an R package for continuous time structural equation modeling of panel (N > 1 and time series (N = 1 data, using full information maximum likelihood. Most dynamic models (e.g., cross-lagged panel models in the social and behavioural sciences are discrete time models. An assumption of discrete time models is that time intervals between measurements are equal, and that all subjects were assessed at the same intervals. Violations of this assumption are often ignored due to the difficulty of accounting for varying time intervals, therefore parameter estimates can be biased and the time course of effects becomes ambiguous. By using stochastic differential equations to estimate an underlying continuous process, continuous time models allow for any pattern of measurement occasions. By interfacing to OpenMx, ctsem combines the flexible specification of structural equation models with the enhanced data gathering opportunities and improved estimation of continuous time models. ctsem can estimate relationships over time for multiple latent processes, measured by multiple noisy indicators with varying time intervals between observations. Within and between effects are estimated simultaneously by modeling both observed covariates and unobserved heterogeneity. Exogenous shocks with different shapes, group differences, higher order diffusion effects and oscillating processes can all be simply modeled. We first introduce and define continuous time models, then show how to specify and estimate a range of continuous time models using ctsem.
An evolution equation modeling inversion of tulip flames
Energy Technology Data Exchange (ETDEWEB)
Dold, J.W. [Univ. of Bristol (United Kingdom). School of Mathematics; Joulin, G. [E.N.S.M.A., Poitiers (France). Lab. d`Energetique et de Detonique
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.
Applying meta-analysis to structural equation modeling.
Hedges, Larry V
2016-06-01
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 structural coefficients and an indirect approach that first combines correlation matrices and estimates structural coefficients from the combined correlation matrix. When there is no heterogeneity across studies, direct estimates of structural coefficients from several studies is an appealing approach. Heterogeneity of correlation matrices across studies presents both practical and conceptual problems. An alternative approach to heterogeneity is suggested as an example of how to better handle heterogeneity in this context. Copyright © 2016 John Wiley & Sons, Ltd.
DEFF Research Database (Denmark)
Budtz-Jørgensen, Esben; Keiding, Niels; Grandjean, P.
2003-01-01
observational epidemiology; measurement error; multiple endpoints structural equation models; safety standard......observational epidemiology; measurement error; multiple endpoints structural equation models; safety standard...
XLISP-Stat Tools for Building Generalised Estimating Equation Models
Directory of Open Access Journals (Sweden)
Thomas Lumley
1996-12-01
Full Text Available This paper describes a set of Lisp-Stat tools for building Generalised Estimating Equation models to analyse longitudinal or clustered measurements. The user interface is based on the built-in regression and generalised linear model prototypes, with the addition of object-based error functions, correlation structures and model formula tools. Residual and deletion diagnostic plots are available on the cluster and observation level and use the dynamic graphics capabilities of Lisp-Stat.
Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling.
Ye, Hao; Beamish, Richard J; Glaser, Sarah M; Grant, Sue C H; Hsieh, Chih-Hao; Richards, Laura J; Schnute, Jon T; Sugihara, George
2015-03-31
It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner-recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts.
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.
Langevin equation model of dispersion in the convective boundary layer
Energy Technology Data Exchange (ETDEWEB)
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
Extended master equation models for molecular communication networks
Chou, Chun Tung
2012-01-01
We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signalling molecules, which are diffused over the medium, to the receiver to realise the communication. In order to be able to engineer synthetic molecular communication networks, mathematical models for these networks are required. This paper proposes a new stochastic model for molecular communication networks called reaction-diffusion master equation with exogenous input (RDMEX). The key idea behind RDMEX is to model the transmitters as time sequences specify the emission patterns of signalling molecules, while diffusion in the medium and chemical reactions at the receivers are modelled as Markov processes using master equation. An advantage of RDMEX is that it can readily be used to model molecular communication networks with multiple transmitters and receivers. For the case where the reaction kinetics at the receivers is linear, we show ho...
Gaussian Process Structural Equation Models with Latent Variables
Silva, Ricardo
2010-01-01
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of graphical models known as the structural equation model with latent variables. While linear non-Gaussian variants have been well-studied, inference in nonparametric structural equation models is still underdeveloped. We introduce a sparse Gaussian process parameterization that defines a non-linear structure connecting latent variables, unlike common formulations of Gaussian process latent variable models. An efficient Markov chain Monte Carlo procedure is described. We evaluate the stability of the sampling procedure and the predictive ability of the model compared against the current practice.
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
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.
Non-Grassmann mechanical model of the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Deriglazov, A. A.; Zamudio, G. P.; Castro, P. S. [Department de Matematica, ICE, Universidade Federal de Juiz de Fora, MG (Brazil); Rizzuti, B. F. [ISB, Universidade Federal do Amazonas, Coari-AM (Brazil)
2012-12-15
We construct a new example of the spinning-particle model without Grassmann variables. The spin degrees of freedom are described on the base of an inner anti-de Sitter space. This produces both {Gamma}{sup {mu}} and {Gamma}{sup {mu}{nu}}-matrices in the course of quantization. Canonical quantization of the model implies the Dirac equation. We present the detailed analysis of both the Lagrangian and the Hamiltonian formulations of the model and obtain the general solution to the classical equations of motion. Comparing Zitterbewegung of the spatial coordinate with the evolution of spin, we ask on the possibility of space-time interpretation for the inner space of spin. We enumerate similarities between our analogous model of the Dirac equation and the two-body system subject to confining potential which admits only the elliptic orbits of the order of de Broglie wavelength. The Dirac equation dictates the perpendicularity of the elliptic orbits to the direction of center-of-mass motion.
Building Context with Tumor Growth Modeling Projects in Differential Equations
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…
Multiple Imputation Strategies for Multiple Group Structural Equation Models
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…
On the specification of structural equation models for ecological systems
Grace, James B.; Anderson, T. Michael; Olff, Han; Scheiner, Samuel 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
Investigating Supervisory Relationships and Therapeutic Alliances Using Structural Equation Modeling
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.
Structural Equation Modeling Reporting Practices for Language Assessment
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…
Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
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…
Evaluating Interventions with Multimethod Data: A Structural Equation Modeling Approach
Crayen, Claudia; Geiser, Christian; Scheithauer, Herbert; Eid, Michael
2011-01-01
In many intervention and evaluation studies, outcome variables are assessed using a multimethod approach comparing multiple groups over time. In this article, we show how evaluation data obtained from a complex multitrait-multimethod-multioccasion-multigroup design can be analyzed with structural equation models. In particular, we show how the…
Maximum Likelihood Estimation of Nonlinear Structural Equation Models.
Lee, Sik-Yum; Zhu, Hong-Tu
2002-01-01
Developed an EM type algorithm for maximum likelihood estimation of a general nonlinear structural equation model in which the E-step is completed by a Metropolis-Hastings algorithm. Illustrated the methodology with results from a simulation study and two real examples using data from previous studies. (SLD)
Case-Deletion Diagnostics for Nonlinear Structural Equation Models
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…
Local Influence Analysis of Nonlinear Structural Equation Models
Lee, Sik-Yum; Tang, Nian-Sheng
2004-01-01
By regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm, we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model. The basic building blocks of local influence analysis…
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.
Nonzero solutions of nonlinear integral equations modeling infectious disease
Energy Technology Data Exchange (ETDEWEB)
Williams, L.R. (Indiana Univ., South Bend); 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.
MODELING ORDINARY DIFFERENTIAL EQUATIONS IN MATLAB SIMULINK ®
Ravi Kiran Maddali
2012-01-01
Ordinary differential equations (ODEs) play a vital role in engineering problems. They are used to model continuous dynamical systems as initial and boundary value problems. There are several analytical and numerical methods to solve ODEs. Various numerical methods such as Euler’s method, Runge-Kutta method, etc are so popular in solving these ODEs. MATLAB, the language of technical computation developed by mathworks, is gaining importance both in academic and industry as powerful modeling so...
Structural Identification and Validation in Stochastic Differential Equation based Models
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Carstensen, Jacob; Madsen, Henrik
2011-01-01
Stochastic differential equations (SDEs) for ecosystem modelling have attracted increasing attention during recent years. The modelling has mostly been through simulation based experiments. Estimation of parameters in SDEs is, however, possible by combining Kalman filter and likelihood techniques...... as a function of the state variables and global radiation. Further improvements of both the drift and the diffusion term are achieved by comparing simulated densities and data....
Lattice Boltzmann model for a steady radiative transfer equation.
Yi, Hong-Liang; Yao, Feng-Ju; Tan, He-Ping
2016-08-01
A complete lattice Boltzmann model (LBM) is proposed for the steady radiative transfer equation (RTE). The RTE can be regarded as a pure convection equation with a source term. To derive the expressions for the equilibrium distribution function and the relaxation time, an artificial isotropic diffusion term is introduced to form a convection-diffusion equation. When the dimensionless relaxation time has a value of 0.5, the lattice Boltzmann equation (LBE) is exactly applicable to the original steady RTE. We also perform a multiscale analysis based on the Chapman-Enskog expansion to recover the macroscopic RTE from the mesoscopic LBE. The D2Q9 model is used to solve the LBE, and the numerical results obtained by the LBM are comparable to the results obtained by other methods or analytical solutions, which demonstrates that the proposed model is highly accurate and stable in simulating multidimensional radiative transfer. In addition, we find that the convergence rate of the LBM depends on the transport properties of RTE: for diffusion-dominated RTE with a large optical thickness, the LBM shows a second-order convergence rate in space, while for convection-dominated RTE with a small optical thickness, a lower convergence rate is observed.
Development of a One-Equation Transition/Turbulence Model
Energy Technology Data Exchange (ETDEWEB)
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.
Partial differential equations modeling, analysis and numerical approximation
Le Dret, Hervé
2016-01-01
This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems. .
Short Polymer Modeling using Self-Consistent Integral Equation Method
Kim, Yeongyoon; Park, So Jung; Kim, Jaeup
2014-03-01
Self-consistent field theory (SCFT) is an excellent mean field theoretical tool for predicting the morphologies of polymer based materials. In the standard SCFT, the polymer is modeled as a Gaussian chain which is suitable for a polymer of high molecular weight, but not necessarily for a polymer of low molecular weight. In order to overcome this limitation, Matsen and coworkers have recently developed SCFT of discrete polymer chains in which one polymer is modeled as finite number of beads joined by freely jointed bonds of fixed length. In their model, the diffusion equation of the canonical SCFT is replaced by an iterative integral equation, and the full spectral method is used for the production of the phase diagram of short block copolymers. In this study, for the finite length chain problem, we apply pseudospectral method which is the most efficient numerical scheme to solve the iterative integral equation. We use this new numerical method to investigate two different types of polymer bonds: spring-beads model and freely-jointed chain model. By comparing these results with those of the Gaussian chain model, the influences on the morphologies of diblock copolymer melts due to the chain length and the type of bonds are examined. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (no. 2012R1A1A2043633).
Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
Chen, Hua; Sato, Yuki
2016-01-01
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 ADM formalism of general relativity, and 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 up to the forth order, and 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 s...
Quasi-hydrostatic Primitive Equations for Ocean Global Circulation Models
Institute of Scientific and Technical Information of China (English)
Carine LUCAS; Madalina PETCU; Antoine ROUSSEAU
2010-01-01
Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper.This model,that derives from the full non-hydrostatic model for geophysical fluid dynamics in the zero-limit of the aspect ratio,is more realistic than the classical hydrostatic model,since the traditional approximation that consists in neglecting a part of the Coriolis force is relaxed.After justifying the derivation of the model,the authors provide a rigorous proof of global existence of weak solutions,and well-posedness for strong solutions in dimension three.
Structural Equation Modeling with Mplus Basic Concepts, Applications, and Programming
Byrne, Barbara M
2011-01-01
Modeled after Barbara Byrne's other best-selling structural equation modeling (SEM) books, this practical guide reviews the basic concepts and applications of SEM using Mplus Versions 5 & 6. The author reviews SEM applications based on actual data taken from her own research. Using non-mathematical language, it is written for the novice SEM user. With each application chapter, the author "walks" the reader through all steps involved in testing the SEM model including: an explanation of the issues addressed illustrated and annotated testing of the hypothesized and post hoc models expl
Bloch-Redfield equations for modeling light-harvesting complexes
Jeske, Jan; Plenio, Martin B; Huelga, Susana F; Cole, Jared H
2014-01-01
We challenge the commonly held view 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 the misuse 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 (FMO) complex in regards to spatial correlation length of the noise, noise strength, temperature and their connecti...
Study of a model equation in detonation theory: multidimensional effects
Faria, Luiz M; Rosales, Rodolfo R
2015-01-01
We extend the reactive Burgers equation presented in Kasimov et al. Phys. Rev. Lett., 110 (2013) and Faria et al. SIAM J. Appl. Maths, 74 (2014), to include multidimensional effects. Furthermore, we explain how the model can be rationally justified following the ideas of the asymptotic theory developed in Faria et al. JFM (2015). The proposed model is a forced version of the unsteady small disturbance transonic flow equations. We show that for physically reasonable choices of forcing functions, traveling wave solutions akin to detonation waves exist. It is demonstrated that multidimensional effects play an important role in the stability and dynamics of the traveling waves. Numerical simulations indicate that solutions of the model tend to form multi-dimensional patterns analogous to cells in gaseous detonations.
A stochastic differential equation model for transcriptional regulatory networks
Directory of Open Access Journals (Sweden)
Quirk Michelle D
2007-05-01
Full Text Available Abstract Background This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets. The dynamics of the gene expression level are fitted via a stochastic differential equation model, yielding a set of specific regulators and their contribution. Results We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic differential equation model follows well the dynamic of the gene expression levels. Conclusion When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved models of the transcriptional regulatory networks.
THE DYSON-SCHWINGER EQUATION FOR A MODEL WITH INSTANTONS - THE SCHWINGER MODEL
Adam, C.
1995-01-01
Using the exact path integral solution of the Schwinger model -- a model where instantons are present -- the Dyson-Schwinger equation is shown to hold by explicit computation. It turns out that the Dyson-Schwinger equation separately holds for every instanton sector. This is due to Theta-invariance of the Schwinger model.
Excited TBA equations I: Massive tricritical Ising model
Energy Technology Data Exchange (ETDEWEB)
Pearce, Paul A. E-mail: p.pearce@ms.unimelb.edu.au; Chim, Leung E-mail: leung.chim@dsto.defence.gov.au; Ahn, Changrim E-mail: ahn@dante.ewha.ac.kr
2001-05-14
We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator phi (cursive,open) Greek{sub 1,3} in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A{sub 4} lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m,n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r,s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters {chi}{sub r,s}(q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II.
Constructing stochastic models from deterministic process equations by propensity adjustment
Directory of Open Access Journals (Sweden)
Wu Jialiang
2011-11-01
Full Text Available Abstract Background Gillespie's stochastic simulation algorithm (SSA for chemical reactions admits three kinds of elementary processes, namely, mass action reactions of 0th, 1st or 2nd order. All other types of reaction processes, for instance those containing non-integer kinetic orders or following other types of kinetic laws, are assumed to be convertible to one of the three elementary kinds, so that SSA can validly be applied. However, the conversion to elementary reactions is often difficult, if not impossible. Within deterministic contexts, a strategy of model reduction is often used. Such a reduction simplifies the actual system of reactions by merging or approximating intermediate steps and omitting reactants such as transient complexes. It would be valuable to adopt a similar reduction strategy to stochastic modelling. Indeed, efforts have been devoted to manipulating the chemical master equation (CME in order to achieve a proper propensity function for a reduced stochastic system. However, manipulations of CME are almost always complicated, and successes have been limited to relative simple cases. Results We propose a rather general strategy for converting a deterministic process model into a corresponding stochastic model and characterize the mathematical connections between the two. The deterministic framework is assumed to be a generalized mass action system and the stochastic analogue is in the format of the chemical master equation. The analysis identifies situations: where a direct conversion is valid; where internal noise affecting the system needs to be taken into account; and where the propensity function must be mathematically adjusted. The conversion from deterministic to stochastic models is illustrated with several representative examples, including reversible reactions with feedback controls, Michaelis-Menten enzyme kinetics, a genetic regulatory motif, and stochastic focusing. Conclusions The construction of a stochastic
Generalized latent variable modeling multilevel, longitudinal, and structural equation models
Skrondal, Anders
2004-01-01
METHODOLOGY THE OMNI-PRESENCE OF LATENT VARIABLES Introduction 'True' variable measured with error Hypothetical constructs Unobserved heterogeneity Missing values and counterfactuals Latent responses Generating flexible distributions Combining information Summary MODELING DIFFERENT RESPONSE PROCESSES Introduction Generalized linear models Extensions of generalized linear models Latent response formulation Modeling durations or survival Summary and further reading CLASSICAL LATENT VARIABLE MODELS Introduction Multilevel regression models Factor models and item respons
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
Two-equation modeling of turbulent rotating flows
Cazalbou, Jean-Bernard; Chassaing, Patrick; Dufour, Guillaume; CARBONNEAU, Xavier
2005-01-01
The possibility to take into account the effects of the Coriolis acceleration on turbulence is examined in the framework of two-equation eddy-viscosity models. General results on the physical consistency of such turbulence models are derived from a dynamical-system approach to situations of time-evolving homogeneous turbulence in a rotating frame. Application of this analysis to a (k,epsilon) model fitted with an existing Coriolis correction [J. H. G. Howard, S. V. Patankar, and R. M. Bordynu...
Study of a Model Equation in Detonation Theory
Faria, Luiz
2014-04-24
Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1/2 (u2-uu (0-, t))x=f (x, u (0-, t)), x > 0, t < 0. It describes a detonation shock at x = 0 with the reaction zone in x > 0. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos. © 2014 Society for Industrial and Applied Mathematics.
Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases
Khalil, Nagi; Garzó, Vicente; Santos, Andrés
2014-05-01
The hydrodynamic Burnett equations and the associated transport coefficients are exactly evaluated for generalized inelastic Maxwell models. In those models, the one-particle distribution function obeys the inelastic Boltzmann equation, with a velocity-independent collision rate proportional to the γ power of the temperature. The pressure tensor and the heat flux are obtained to second order in the spatial gradients of the hydrodynamic fields with explicit expressions for all the Burnett transport coefficients as functions of γ, the coefficient of normal restitution, and the dimensionality of the system. Some transport coefficients that are related in a simple way in the elastic limit become decoupled in the inelastic case. As a byproduct, existing results in the literature for three-dimensional elastic systems are recovered, and a generalization to any dimension of the system is given. The structure of the present results is used to estimate the Burnett coefficients for inelastic hard spheres.
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.
Modeling Tree Crown Dynamics with 3D Partial Differential Equations
Directory of Open Access Journals (Sweden)
Robert eBeyer
2014-07-01
Full Text Available 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 towards 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.
Tropospheric Refraction Modeling Using Ray-Tracing and Parabolic Equation
Directory of Open Access Journals (Sweden)
P. Pechac
2005-12-01
Full Text Available Refraction phenomena that occur in the lower atmospheresignificantly influence the performance of wireless communicationsystems. This paper provides an overview of corresponding computationalmethods. Basic properties of the lower atmosphere are mentioned.Practical guidelines for radiowave propagation modeling in the loweratmosphere using ray-tracing and parabolic equation methods are given.In addition, a calculation of angle-of-arrival spectra is introducedfor multipath propagation simulations.
Structural Equation Modeling with Lisrel: An Initial Vision
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Naresh K Malhotra
2014-05-01
Full Text Available LISREL is considered one of the most robust software packages for Structural Equation Modeling with covariance matrices, while it is also considered complex and difficult to use. In this special issue of the Brazilian Journal of Marketing, we aim to present the main functions of LISREL, its features and, through a didactic example, reduce the perceived difficulty of using it. We also provide helpful guidelines to properly using this technique.
Stochastic Differential Equation-Based Flexible Software Reliability Growth Model
Directory of Open Access Journals (Sweden)
P. K. Kapur
2009-01-01
Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.
Extended master equation models for molecular communication networks.
Chou, Chun Tung
2013-06-01
We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signaling molecules, which are diffused over the medium, to the receiver to realize the communication. In order to be able to engineer synthetic molecular communication networks, mathematical models for these networks are required. This paper proposes a new stochastic model for molecular communication networks called reaction-diffusion master equation with exogenous input (RDMEX). The key idea behind RDMEX is to model the transmitters as time series of signaling molecule counts, while diffusion in the medium and chemical reactions at the receivers are modeled as Markov processes using master equation. An advantage of RDMEX is that it can readily be used to model molecular communication networks with multiple transmitters and receivers. For the case where the reaction kinetics at the receivers is linear, we show how RDMEX can be used to determine the mean and covariance of the receiver output signals, and derive closed-form expressions for the mean receiver output signal of the RDMEX model. These closed-form expressions reveal that the output signal of a receiver can be affected by the presence of other receivers. Numerical examples are provided to demonstrate the properties of the model.
Moment equations and dynamics of a household SIS epidemiological model.
Hiebeler, David
2006-08-01
An SIS epidemiological model of individuals partitioned into households is studied, where infections take place either within or between households, the latter generally happening much less frequently. The model is explored using stochastic spatial simulations, as well as mathematical models which consist of an infinite system of ordinary differential equations for the moments of the distribution describing the proportions of individuals who are infectious among households. Various moment-closure approximations are used to truncate the system of ODEs to finite systems of equations. These approximations can sometimes lead to a system of ill-behaved ODEs which predict moments which become negative or unbounded. A reparametrization of the ODEs is then developed, which forces all moments to satisfy necessary constraints. Changing the proportion of contacts within and between households does not change the endemic equilibrium, but does affect the amount of time it takes to approach the fixed point; increasing the proportion of contacts within households slows the spread of the infection toward endemic equilibrium. The system of moment equations does describe this phenomenon, although less accurately in the limit as the proportion of between-household contacts approaches zero. The results indicate that although controlling the movement of individuals does not affect the long-term frequency of an infection with SIS dynamics, it can have a large effect on the time-scale of the dynamics, which may provide an opportunity for other controls such as immunizations to be applied.
Partial Least Squares Structural Equation Modeling with R
Directory of Open Access Journals (Sweden)
Hamdollah Ravand
2016-09-01
Full Text Available 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 restrictions (e.g. normality and relatively large sample sizes that could discourage practitioners from applying the model. Partial least squares SEM (PLS-SEM is a nonparametric technique which makes no distributional assumptions and can be estimated with small sample sizes. In this paper a general introduction to PLS-SEM is given and is compared with conventional SEM. Next, step by step procedures, along with R functions, are presented to estimate the model. A data set is analyzed and the outputs are interpreted
semPLS: Structural Equation Modeling Using Partial Least Squares
Directory of Open Access Journals (Sweden)
Armin Monecke
2012-05-01
Full Text Available Structural equation models (SEM are very popular in many disciplines. The partial least squares (PLS approach to SEM offers an alternative to covariance-based SEM, which is especially suited for situations when data is not normally distributed. PLS path modelling is referred to as soft-modeling-technique with minimum demands regarding mea- surement scales, sample sizes and residual distributions. The semPLS package provides the capability to estimate PLS path models within the R programming environment. Different setups for the estimation of factor scores can be used. Furthermore it contains modular methods for computation of bootstrap confidence intervals, model parameters and several quality indices. Various plot functions help to evaluate the model. The well known mobile phone dataset from marketing research is used to demonstrate the features of the package.
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…
Vertical spectral representation in primitive equation models of the atmosphere
Energy Technology Data Exchange (ETDEWEB)
Mizzi, A.; Tribbia, J. [National Center for Atmospheric Research, Boulder, CO (United States); Curry, J. [Univ. of Colorado, Boulder, CO (United States)
1995-08-01
Attempts to represent the vertical structure in primitive equation models of the atmosphere with the spectral method have been unsuccessful to date. Linear stability analysis showed that small time steps were required for computational stability near the upper boundary with a vertical spectral representation and found it necessary to use an artificial constraint to force temperature to zero when pressure was zero to control the upper-level horizontal velocities. This ad hoc correction is undesirable, and an analysis that shows such a correction is unnecessary is presented. By formulating the model in terms of velocity and geopotential and then using the hydrostatic equation to calculate temperature from geopotential, temperature is necessarily zero when pressure is zero. The authors applied this technique to the dry-adiabatic primitive equations on the equatorial {beta} and tropical f planes. Vertical and horizontal normal modes were used as the spectral basis functions. The vertical modes are based on vertical normal modes, and the horizontal modes are normal modes for the primitive equations on a {beta} or f plane. The results show that the upper-level velocities do not necessarily increase, total energy is conserved, and kinetic energy is bounded. The authors found an upper-level temporal oscillation in the horizontal domain integral of the horizontal velocity components that is related to mass and velocity field imbalances in the initial conditions or introduced during the integration. Through nonlinear normal-mode initialization, the authors effectively removed the initial condition imbalance and reduced the amplitude of this oscillation. It is hypothesized that the vertical spectral representation makes the model more sensitive to initial condition imbalances, or it introduces imbalance during the integration through vertical spectral truncation. 20 refs., 12 figs.
Modeling Inflation Using a Non-Equilibrium Equation of Exchange
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
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.
An integral equation model for warm and hot dense mixtures
Starrett, C E; Daligault, J; Hamel, S
2014-01-01
In Starrett and Saumon [Phys. Rev. E 87, 013104 (2013)] a model for the calculation of electronic and ionic structures of warm and hot dense matter was described and validated. In that model the electronic structure of one "atom" in a plasma is determined using a density functional theory based average-atom (AA) model, and the ionic structure is determined by coupling the AA model to integral equations governing the fluid structure. That model was for plasmas with one nuclear species only. Here we extend it to treat plasmas with many nuclear species, i.e. mixtures, and apply it to a carbon-hydrogen mixture relevant to inertial confinement fusion experiments. Comparison of the predicted electronic and ionic structures with orbital-free and Kohn-Sham molecular dynamics simulations reveals excellent agreement wherever chemical bonding is not significant.
Coarse Analysis of Microscopic Models using Equation-Free Methods
DEFF Research Database (Denmark)
Marschler, Christian
-dimensional models. The goal of this thesis is to investigate such high-dimensional multiscale models and extract relevant low-dimensional information from them. Recently developed mathematical tools allow to reach this goal: a combination of so-called equation-free methods with numerical bifurcation analysis....... Applications include the learning behavior in the barn owl’s auditory system, traffic jam formation in an optimal velocity model for circular car traffic and oscillating behavior of pedestrian groups in a counter-flow through a corridor with narrow door. The methods do not only quantify interesting properties...... factor for the complexity of models, e.g., in real-time applications. With the increasing amount of data generated by computer simulations a challenge is to extract valuable information from the models in order to help scientists and managers in a decision-making process. Although the dynamics...
Structural Equation Modeling: Theory and Applications in Forest Management
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Tzeng Yih Lam
2012-01-01
Full Text Available Forest ecosystem dynamics are driven by a complex array of simultaneous cause-and-effect relationships. Understanding this complex web requires specialized analytical techniques such as Structural Equation Modeling (SEM. The SEM framework and implementation steps are outlined in this study, and we then demonstrate the technique by application to overstory-understory relationships in mature Douglas-fir forests in the northwestern USA. A SEM model was formulated with (1 a path model representing the effects of successively higher layers of vegetation on late-seral herbs through processes such as light attenuation and (2 a measurement model accounting for measurement errors. The fitted SEM model suggested a direct negative effect of light attenuation on late-seral herbs cover but a direct positive effect of northern aspect. Moreover, many processes have indirect effects mediated through midstory vegetation. SEM is recommended as a forest management tool for designing silvicultural treatments and systems for attaining complex arrays of management objectives.
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.
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.
Calculus for cognitive scientists partial differential equation models
Peterson, James K
2016-01-01
This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics. A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.
An improved shallow water equation model for water animation
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.
Application of Stochastic Partial Differential Equations to Reservoir Property Modelling
Potsepaev, R.
2010-09-06
Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.
Generalized elastic model yields a fractional Langevin equation description.
Taloni, Alessandro; Chechkin, Aleksei; Klafter, Joseph
2010-04-23
Starting from a generalized elastic model which accounts for the stochastic motion of several physical systems such as membranes, (semi)flexible polymers, and fluctuating interfaces among others, we derive the fractional Langevin equation (FLE) for a probe particle in such systems, in the case of thermal initial conditions. We show that this FLE is the only one fulfilling the fluctuation-dissipation relation within a new family of fractional Brownian motion equations. The FLE for the time-dependent fluctuations of the donor-acceptor distance in a protein is shown to be recovered. When the system starts from nonthermal conditions, the corresponding FLE, which does not fulfill the fluctuation-dissipation relation, is derived.
Correlations in a generalized elastic model: fractional Langevin equation approach.
Taloni, Alessandro; Chechkin, Aleksei; Klafter, Joseph
2010-12-01
The generalized elastic model (GEM) provides the evolution equation which governs the stochastic motion of several many-body systems in nature, such as polymers, membranes, and growing interfaces. On the other hand a probe (tracer) particle in these systems performs a fractional Brownian motion due to the spatial interactions with the other system's components. The tracer's anomalous dynamics can be described by a fractional Langevin equation (FLE) with a space-time correlated noise. We demonstrate that the description given in terms of GEM coincides with that furnished by the relative FLE, by showing that the correlation functions of the stochastic field obtained within the FLE framework agree with the corresponding quantities calculated from the GEM. Furthermore we show that the Fox H -function formalism appears to be very convenient to describe the correlation properties within the FLE approach.
Two-equation turbulence modeling for 3-D hypersonic flows
Bardina, J. E.; Coakley, T. J.; Marvin, J. G.
1992-01-01
An investigation to verify, incorporate and develop two-equation turbulence models for three-dimensional high speed flows is presented. The current design effort of hypersonic vehicles has led to an intensive study of turbulence models for compressible hypersonic flows. This research complements an extensive review of experimental data and the current development of 2D turbulence models. The review of experimental data on 2D and 3D flows includes complex hypersonic flows with pressure profiles, skin friction, wall heat transfer, and turbulence statistics data. In a parallel effort, turbulence models for high speed flows have been tested against flat plate boundary layers, and are being tested against the 2D database. In the present paper, we present the results of 3D Navier-Stokes numerical simulations with an improved k-omega two-equation turbulence model against experimental data and empirical correlations of an adiabatic flat plate boundary layer, a cold wall flat plate boundary layer, and a 3D database flow, the interaction of an oblique shock wave and a thick turbulent boundary layer with a free stream Mach number = 8.18 and Reynolds number = 5 x 10 to the 6th.
Scale invariant cosmology II: model equations and properties
Maeder, Andre
2016-01-01
We want to establish the basic properties of a scale invariant cosmology, that also accounts for the hypothesis of scale invariance of the empty space at large scales. We write the basic analytical properties of the scale invariant cosmological models. The hypothesis of scale invariance of the empty space at large scale brings interesting simplifications in the scale invariant equations for cosmology. There is one new term, depending on the scale factor of the scale invariant cosmology, that opposes to gravity and favours an accelerated expansion. We first consider a zero-density model and find an accelerated expansion, going like t square. In models with matter present, the displacements due to the new term make a significant contribution Omega_l to the energy-density of the Universe, satisfying an equation of the form Omega_m + Omega_k + Omega_l = 1. Unlike the Friedman's models, there is a whole family of flat models (k=0) with different density parameters Omega_m smaller than 1. We examine the basic relat...
Modeling rapid mass movements using the shallow water equations
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S. Hergarten
2014-11-01
Full Text Available 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
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-based model for the stock market
Xavier, Paloma O. C.; Atman, A. P. F.; de Magalhães, A. R. Bosco
2017-09-01
We propose a stock market model which is investigated in the forms of difference and differential equations whose variables correspond to the demand or supply of each agent and to the price. In the model, agents are driven by the behavior of their trust contact network as well by fundamental analysis. By means of the deterministic version of the model, the connection between such drive mechanisms and the price is analyzed: imitation behavior promotes market instability, finitude of resources is associated to stock index stability, and high sensitivity to the fair price provokes price oscillations. Long-range correlations in the price temporal series and heavy-tailed distribution of returns are observed for the version of the model which considers different proposals for stochasticity of microeconomic and macroeconomic origins.
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.
Using of Structural Equation Modeling Techniques in Cognitive Levels Validation
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Natalija Curkovic
2012-10-01
Full Text Available When constructing knowledge tests, cognitive level is usually one of the dimensions comprising the test specifications with each item assigned to measure a particular level. Recently used taxonomies of the cognitive levels most often represent some modification of the original Bloom’s taxonomy. There are many concerns in current literature about existence of predefined cognitive levels. The aim of this article is to investigate can structural equation modeling techniques confirm existence of different cognitive levels. For the purpose of the research, a Croatian final high-school Mathematics exam was used (N = 9626. Confirmatory factor analysis and structural regression modeling were used to test three different models. Structural equation modeling techniques did not support existence of different cognitive levels in this case. There is more than one possible explanation for that finding. Some other techniques that take into account nonlinear behaviour of the items as well as qualitative techniques might be more useful for the purpose of the cognitive levels validation. Furthermore, it seems that cognitive levels were not efficient descriptors of the items and so improvements are needed in describing the cognitive skills measured by items.
Modeling Dynamic Functional Neuroimaging Data Using Structural Equation Modeling
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.
Short guide to direct gravitational field modelling with Hotine's equations
Sebera, Josef; Wagner, Carl A.; Bezděk, Aleš; Klokočník, Jaroslav
2013-03-01
This paper presents a unified approach to the least squares spherical harmonic analysis of the acceleration vector and Eötvös tensor (gravitational gradients) in an arbitrary orientation. The Jacobian matrices are based on Hotine's equations that hold in the Earth-fixed Cartesian frame and do not need any derivatives of the associated Legendre functions. The implementation was confirmed through closed-loop tests in which the simulated input is inverted in the least square sense using the rotated Hotine's equations. The precision achieved is at the level of rounding error with RMS about 10^{-12}{-}10^{-14} m in terms of the height anomaly. The second validation of the linear model is done with help from the standard ellipsoidal correction for the gravity disturbance that can be computed with an analytic expression as well as with the rotated equations. Although the analytic expression for this correction is only of a limited accuracy at the submillimeter level, it was used for an independent validation. Finally, the equivalent of the ellipsoidal correction, called the effect of the normal, has been numerically obtained also for other gravitational functionals and some of their combinations. Most of the numerical investigations are provided up to spherical harmonic degree 70, with degree 80 for the computation time comparison using real GRACE data. The relevant Matlab source codes for the design matrices are provided.
Partial differential equation models in the socio-economic sciences
Burger, Martin
2014-10-06
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.
New equation of state models for hydrodynamic applications
Young, David A.; Barbee, Troy W.; Rogers, Forrest J.
1998-07-01
Two new theoretical methods for computing the equation of state of hot, dense matter are discussed. The ab initio phonon theory gives a first-principles calculation of lattice frequencies, which can be used to compare theory and experiment for isothermal and shock compression of solids. The ACTEX dense plasma theory has been improved to allow it to be compared directly with ultrahigh pressure shock data on low-Z materials. The comparisons with experiment are good, suggesting that these models will be useful in generating global EOS tables for hydrodynamic simulations.
New equation of state model for hydrodynamic applications
Energy Technology Data Exchange (ETDEWEB)
Young, D.A.; Barbee, T.W. III; Rogers, F.J.
1997-07-01
Two new theoretical methods for computing the equation of state of hot, dense matter are discussed.The ab initio phonon theory gives a first-principles calculation of lattice frequencies, which can be used to compare theory and experiment for isothermal and shock compression of solids. The ACTEX dense plasma theory has been improved to allow it to be compared directly with ultrahigh pressure shock data on low-Z materials. The comparisons with experiment are good, suggesting that these models will be useful in generating global EOS tables for hydrodynamic simulations.
New equation of state models for hydrodynamic applications
Energy Technology Data Exchange (ETDEWEB)
Young, D.A.; Barbee, T.W. III; Rogers, F.J. [Physics Department, Lawrence Livermore National Laboratory, Livermore, California 94551 (United States)
1998-07-01
Two new theoretical methods for computing the equation of state of hot, dense matter are discussed. The ab initio phonon theory gives a first-principles calculation of lattice frequencies, which can be used to compare theory and experiment for isothermal and shock compression of solids. The ACTEX dense plasma theory has been improved to allow it to be compared directly with ultrahigh pressure shock data on low-Z materials. The comparisons with experiment are good, suggesting that these models will be useful in generating global EOS tables for hydrodynamic simulations. {copyright} {ital 1998 American Institute of Physics.}
Equation oriented method for Rectisol wash modeling and analysis☆
Institute of Scientific and Technical Information of China (English)
Ning Gao; Chi Zhai; Wei Sun; Xingyu Zhang
2015-01-01
Rectisol process is more efficient in comparison with other physical or chemical absorption methods for gas pu-rification. To implement a real time simulation of Rectisol process, thermodynamic model and simulation strat-egy are needed. In this paper, a method of modified statistical associated fluid theory with perturbation theory is used to predict thermodynamic behavior of process. As Rectisol process is a highly heat-integrated process with many loops, a method of equation oriented strategy, sequential quadratic programming, is used as the solver and the process converges perfectly. Then analyses are conducted with this simulator.
A mathematical model on fractional Lotka-Volterra equations.
Das, S; Gupta, P K
2011-05-21
The article presents the solutions of Lotka-Volterra equations of fractional-order time derivatives with the help of analytical method of nonlinear problem called the homotopy perturbation method (HPM). By using initial values, the explicit solutions of predator and prey populations for different particular cases have been derived. The numerical solutions show that only a few iterations are needed to obtain accurate approximate solutions. The method performs extremely well in terms of efficiency and simplicity to solve this historical biological model. Copyright © 2011 Elsevier Ltd. All rights reserved.
Integrable Cosmological Models From Higher Dimensional Einstein Equations
Sano, M; Sano, Masakazu; Suzuki, Hisao
2007-01-01
We consider the cosmological models for the higher dimensional spacetime which includes the curvatures of our space as well as the curvatures of the internal space. We find that the condition for the integrability of the cosmological equations is that the total space-time dimensions are D=10 or D=11 which is exactly the conditions for superstrings or M-theory. We obtain analytic solutions with generic initial conditions in the four dimensional Einstein frame and study the accelerating universe when both our space and the internal space have negative curvatures.
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.
FLEXIBILITY ANALYSIS IN AN INFORMATION ECONOMY: STRUCTURAL EQUATION MODELING
Directory of Open Access Journals (Sweden)
Ricardo da Silva
2006-11-01
Full Text Available This paper analyzes the new concept of flexibility in organizations – of relevance both at micro and macro level. Information Economy (IE modern function is specifically analyzed. The purpose of this paper is not limited to the study of information economy flexibility, but extends its focus to other areas of organization and economic studies, having as reference the proposed model. Although not covering all aspects regarding objectives and hypotheses, results obtained demonstrate that subsequent studies can lead to success experiences, since the models presented are: stability in relation to the deviations presented in the resulting equations; values that are very close to what is desirable for adjustment indexes, factorial loads, t-values, extracted variances and reliability; as well as other necessary aspects for the application of the technique. The approach focuses the analysis of information economy flexibility based on structural equations modeling to serve as reference for the development of adaptation phenomenon studies in relation to structures, strategies and organizational processes, against the environmental dynamics contemporary society is faced with.
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.
MODELING ORDINARY DIFFERENTIAL EQUATIONS IN MATLAB SIMULINK ®
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Ravi Kiran Maddali
2012-07-01
Full Text Available Ordinary differential equations (ODEs play a vital role in engineering problems. They are used to model continuous dynamical systems as initial and boundary value problems. There are several analytical and numerical methods to solve ODEs. Various numerical methods such as Euler’s method, Runge-Kutta method, etc are so popular in solving these ODEs. MATLAB, the language of technical computation developed by mathworks, is gaining importance both in academic and industry as powerful modeling software. SIMULINK®,is a tool in MATLAB for simulating both continuous and discrete dynamical systems. In SIMULINK®, we can simulate the behavior of a system by representing the system in terms of a block diagram with interconnections between the blocks and there by simulate its behavior over certain period of time. The study of ODEs has variety of applications in disciplines like aerospace, electronics, communication, medicine, finance, economics, and physiology. In this article, the technique of modeling and simulation of first order differential equations in SIMULINK, which can be further extended to higher order systems, is discussed.
Stochastic differential equation model for cerebellar granule cell excitability.
Saarinen, Antti; Linne, Marja-Leena; Yli-Harja, Olli
2008-02-29
Neurons in the brain express intrinsic dynamic behavior which is known to be stochastic in nature. A crucial question in building models of neuronal excitability is how to be able to mimic the dynamic behavior of the biological counterpart accurately and how to perform simulations in the fastest possible way. The well-established Hodgkin-Huxley formalism has formed to a large extent the basis for building biophysically and anatomically detailed models of neurons. However, the deterministic Hodgkin-Huxley formalism does not take into account the stochastic behavior of voltage-dependent ion channels. Ion channel stochasticity is shown to be important in adjusting the transmembrane voltage dynamics at or close to the threshold of action potential firing, at the very least in small neurons. In order to achieve a better understanding of the dynamic behavior of a neuron, a new modeling and simulation approach based on stochastic differential equations and Brownian motion is developed. The basis of the work is a deterministic one-compartmental multi-conductance model of the cerebellar granule cell. This model includes six different types of voltage-dependent conductances described by Hodgkin-Huxley formalism and simple calcium dynamics. A new model for the granule cell is developed by incorporating stochasticity inherently present in the ion channel function into the gating variables of conductances. With the new stochastic model, the irregular electrophysiological activity of an in vitro granule cell is reproduced accurately, with the same parameter values for which the membrane potential of the original deterministic model exhibits regular behavior. The irregular electrophysiological activity includes experimentally observed random subthreshold oscillations, occasional spontaneous spikes, and clusters of action potentials. As a conclusion, the new stochastic differential equation model of the cerebellar granule cell excitability is found to expand the range of dynamics
Simulating sympathetic detonation using the hydrodynamic models and constitutive equations
Energy Technology Data Exchange (ETDEWEB)
Kim, Bo Hoon; Kim, Min Sung; Yoh, Jack J. [Dept. of Mechanical and Aerospace Engineering, Seoul National University, Seoul (Korea, Republic of); Sun, Tae Boo [Hanwha Corporation Defense Rand D Center, Daejeon (Korea, Republic of)
2016-12-15
A Sympathetic detonation (SD) is a detonation of an explosive charge by a nearby explosion. Most of times it is unintended while the impact of blast fragments or strong shock waves from the initiating donor explosive is the cause of SD. We investigate the SD of a cylindrical explosive charge (64 % RDX, 20 % Al, 16 % HTPB) contained in a steel casing. The constitutive relations for high explosive are obtained from a thermo-chemical code that provides the size effect data without the rate stick data typically used for building the rate law and equation of state. A full size SD test of eight pallet-packaged artillery shells is performed that provides the pressure data while the hydrodynamic model with proper constitutive relations for reactive materials and the fragmentation model for steel casing is conducted to replicate the experimental findings. The work presents a novel effort to accurately model and reproduce the sympathetic detonation event with a reduced experimental effort.
Differential equations models for interacting wild and transgenic mosquito populations.
Li, Jia
2008-07-01
We formulate and study continuous-time models, based on systems of ordinary differential equations, for interacting wild and transgenic mosquito populations. We assume that the mosquito mating rate is either constant, proportional to total mosquito population size, or has a Holling-II-type functional form. The focus is on the model with the Holling-II-type functional mating rate that incorporates Allee effects, in order to account for mating difficulty when the size of the total mosquito populations is small. We investigate the existence and stability of both boundary and positive equilibria. We show that the Holling-II-type model is the more realistic and, by means of numerical simulations, that it exhibits richer dynamics.
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
2016-04-01
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.
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.
The example of modeling of logistics processes using differential equations
Ryczyński, Jacek
2017-07-01
The article describes the use of differential calculus to determine the form of differential equations family of curves. Form of differential equations obtained by eliminating the parameters of the equations describing the different family of curves. Elimination of the parameters has been performed several times by differentiation starting equations. Received appropriate form of differential equations for the case of family circles, family of curves of the second degree and the families of the logistic function.
Ramlall, Indranarain
2016-01-01
This book explains in a rigorous, concise and practical manner all the vital components embedded in structural equation modelling. Focusing on R and stata to implement and perform various structural equation models.
A stochastic differential equation model of diurnal cortisol patterns
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.
Temperature characteristics of quantum dot devices: Rate vs. Master Equation Models
DEFF Research Database (Denmark)
Berg, Tommy Winther; Bischoff, Svend; Magnúsdóttir, Ingibjörg;
2001-01-01
The change of transparency current with temperature for quantum dot devices depends strongly on whether a rate or master equation model is used. The master equation model successfully explains experimental observations of negative characteristic temperatures.......The change of transparency current with temperature for quantum dot devices depends strongly on whether a rate or master equation model is used. The master equation model successfully explains experimental observations of negative characteristic temperatures....
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
Reduction of static field equation of Faddeev model to first order PDE
Energy Technology Data Exchange (ETDEWEB)
Hirayama, Minoru [Department of Mathematics and Physics, Shanghai University of Electric Power, Pinglian road 2103, Shanghai 200090 (China); Shi Changguang [Department of Mathematics and Physics, Shanghai University of Electric Power, Pinglian road 2103, Shanghai 200090 (China)], E-mail: shichangguang@shiep.edu.cn
2007-09-06
A method to solve the static field equation of the Faddeev model is presented. For a special combination of the concerned field, we adopt a form which is compatible with the field equation and involves two arbitrary complex functions. As a result, the static field equation is reduced to a set of first order partial differential equations.
A fractional diffusion equation model for cancer tumor
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.
Explicit estimating equations for semiparametric generalized linear latent variable models
Ma, Yanyuan
2010-07-05
We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n consistency and asymptotic normality. We explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies. The advantage of our estimators over the existing likelihood approach is also shown via numerical comparison. We employ the method to analyse a real data example from economics. © 2010 Royal Statistical Society.
2003-01-01
An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized...
Structural Equation Modeling for Analyzing Erythrocyte Fatty Acids in Framingham
Directory of Open Access Journals (Sweden)
James V. Pottala
2014-01-01
Full Text Available Research has shown that several types of erythrocyte fatty acids (i.e., omega-3, omega-6, and trans are associated with risk for cardiovascular diseases. However, there are complex metabolic and dietary relations among fatty acids, which induce correlations that are typically ignored when using them as risk predictors. A latent variable approach could summarize these complex relations into a few latent variable scores for use in statistical models. Twenty-two red blood cell (RBC fatty acids were measured in Framingham (N = 3196. The correlation matrix of the fatty acids was modeled using structural equation modeling; the model was tested for goodness-of-fit and gender invariance. Thirteen fatty acids were summarized by three latent variables, and gender invariance was rejected so separate models were developed for men and women. A score was developed for the polyunsaturated fatty acid (PUFA latent variable, which explained about 30% of the variance in the data. The PUFA score included loadings in opposing directions among three omega-3 and three omega-6 fatty acids, and incorporated the biosynthetic and dietary relations among them. Whether the PUFA factor score can improve the performance of risk prediction in cardiovascular diseases remains to be tested.
Quantifying uncertainty, variability and likelihood for ordinary differential equation models
LENUS (Irish Health Repository)
Weisse, Andrea Y
2010-10-28
Abstract Background In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space. Results The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well-known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability. Conclusions While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations.
New Exact Solutions for New Model Nonlinear Partial Differential Equation
Directory of Open Access Journals (Sweden)
A. Maher
2013-01-01
Full Text Available In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II and modified Padé-II equation. The mapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined Padé-II and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions, and elliptic functions.
Model Identification Using Stochastic Differential Equation Grey-Box Models in Diabetes
DEFF Research Database (Denmark)
Duun-Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard
2013-01-01
BACKGROUND: The acceptance of virtual preclinical testing of control algorithms is growing and thus also the need for robust and reliable models. Models based on ordinary differential equations (ODEs) can rarely be validated with standard statistical tools. Stochastic differential equations (SDEs......) offer the possibility of building models that can be validated statistically and that are capable of predicting not only a realistic trajectory, but also the uncertainty of the prediction. In an SDE, the prediction error is split into two noise terms. This separation ensures that the errors...... are uncorrelated and provides the possibility to pinpoint model deficiencies. METHODS: An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters...
Partial differential equations in action from modelling to theory
Salsa, Sandro
2016-01-01
The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear bo...
Partial differential equations in action from modelling to theory
Salsa, Sandro
2015-01-01
The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear bo...
Partial Differential Equations of an Epidemic Model with Spatial Diffusion
Directory of Open Access Journals (Sweden)
El Mehdi Lotfi
2014-01-01
Full Text Available The aim of this paper is to study the dynamics of a reaction-diffusion SIR epidemic model with specific nonlinear incidence rate. The global existence, positivity, and boundedness of solutions for a reaction-diffusion system with homogeneous Neumann boundary conditions are proved. The local stability of the disease-free equilibrium and endemic equilibrium is obtained via characteristic equations. By means of Lyapunov functional, the global stability of both equilibria is investigated. More precisely, our results show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than or equal to unity, which leads to the eradication of disease from population. When the basic reproduction number is greater than unity, then disease-free equilibrium becomes unstable and the endemic equilibrium is globally asymptotically stable; in this case the disease persists in the population. Numerical simulations are presented to illustrate our theoretical results.
Analisis Loyalitas Pelanggan Industri Jasa Pengiriman Menggunakan Structural Equation Modeling
Directory of Open Access Journals (Sweden)
Sarika Zuhri
2017-01-01
Full Text Available Customer loyalty is important for both product and service industries. A loyal customer keeps using the company’s product and services. For a shipping service company, retaining existing customers in order to remain faithful will certainly be very crucial. This study was to determine relationship between variables affecting customer loyalty at PT. Pos Indonesia-Banda Aceh, a shipping service industry. The research used Structural Equation Modeling (SEM and with samples of 153 questionnaires obtained through a non-probability sampling technique. By using AMOS software, it can be concluded that the perceived quality does affect customer satisfaction, perceived value has influence on the customer satisfaction, the customer satisfaction is influential to trust and the trust itself has positive influence on customer loyalty.
A performance measurement using balanced scorecard and structural equation modeling
Directory of Open Access Journals (Sweden)
Rosha Makvandi
2014-02-01
Full Text Available During the past few years, balanced scorecard (BSC has been widely used as a promising method for performance measurement. BSC studies organizations in terms of four perspectives including customer, internal processes, learning and growth and financial figures. This paper presents a hybrid of BSC and structural equation modeling (SEM to measure the performance of an Iranian university in province of Alborz, Iran. The proposed study of this paper uses this conceptual method, designs a questionnaire and distributes it among some university students and professors. Using SEM technique, the survey analyzes the data and the results indicate that the university did poorly in terms of all four perspectives. The survey extracts necessary target improvement by presenting necessary attributes for performance improvement.
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.
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
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…
Iterative solvers for Navier-Stokes equations: Experiments with turbulence model
Energy Technology Data Exchange (ETDEWEB)
Page, M. [IREQ - Institut de Recherche d`Hydro-Quebec, Varennes (Canada); Garon, A. [Ecole Polytechnique de Montreal (Canada)
1994-12-31
In the framework of developing software for the prediction of flows in hydraulic turbine components, Reynolds averaged Navier-Stokes equations coupled with {kappa}-{omega} two-equation turbulence model are discretized by finite element method. Since the resulting matrices are large, sparse and nonsymmetric, strategies based on CG-type iterative methods must be devised. A segregated solution strategy decouples the momentum equation, the {kappa} transport equation and the {omega} transport equation. These sets of equations must be solved while satisfying constraint equations. Experiments with orthogonal projection method are presented for the imposition of essential boundary conditions in a weak sense.
Using structural equation modeling for network meta-analysis.
Tu, Yu-Kang; Wu, Yun-Chun
2017-07-14
Network meta-analysis overcomes the limitations of traditional pair-wise meta-analysis by incorporating all available evidence into a general statistical framework for simultaneous comparisons of several treatments. Currently, network meta-analyses are undertaken either within the Bayesian hierarchical linear models or frequentist generalized linear mixed models. Structural equation modeling (SEM) is a statistical method originally developed for modeling causal relations among observed and latent variables. As random effect is explicitly modeled as a latent variable in SEM, it is very flexible for analysts to specify complex random effect structure and to make linear and nonlinear constraints on parameters. The aim of this article is to show how to undertake a network meta-analysis within the statistical framework of SEM. We used an example dataset to demonstrate the standard fixed and random effect network meta-analysis models can be easily implemented in SEM. It contains results of 26 studies that directly compared three treatment groups A, B and C for prevention of first bleeding in patients with liver cirrhosis. We also showed that a new approach to network meta-analysis based on the technique of unrestricted weighted least squares (UWLS) method can also be undertaken using SEM. For both the fixed and random effect network meta-analysis, SEM yielded similar coefficients and confidence intervals to those reported in the previous literature. The point estimates of two UWLS models were identical to those in the fixed effect model but the confidence intervals were greater. This is consistent with results from the traditional pairwise meta-analyses. Comparing to UWLS model with common variance adjusted factor, UWLS model with unique variance adjusted factor has greater confidence intervals when the heterogeneity was larger in the pairwise comparison. The UWLS model with unique variance adjusted factor reflects the difference in heterogeneity within each comparison
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
A model for closing the inviscid form of the average-passage equation system
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.
The issue of statistical power for overall model fit in evaluating structural equation models
Directory of Open Access Journals (Sweden)
Richard HERMIDA
2015-06-01
Full Text Available Statistical power is an important concept for psychological research. However, examining the power of a structural equation model (SEM is rare in practice. This article provides an accessible review of the concept of statistical power for the Root Mean Square Error of Approximation (RMSEA index of overall model fit in structural equation modeling. By way of example, we examine the current state of power in the literature by reviewing studies in top Industrial-Organizational (I/O Psychology journals using SEMs. Results indicate that in many studies, power is very low, which implies acceptance of invalid models. Additionally, we examined methodological situations which may have an influence on statistical power of SEMs. Results showed that power varies significantly as a function of model type and whether or not the model is the main model for the study. Finally, results indicated that power is significantly related to model fit statistics used in evaluating SEMs. The results from this quantitative review imply that researchers should be more vigilant with respect to power in structural equation modeling. We therefore conclude by offering methodological best practices to increase confidence in the interpretation of structural equation modeling results with respect to statistical power issues.
Agent-Based vs. Equation-based Epidemiological Models:A Model Selection Case Study
Energy Technology Data Exchange (ETDEWEB)
Sukumar, Sreenivas R [ORNL; Nutaro, James J [ORNL
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.
Basic equations of the quasiparticle-phonon nuclear model for odd spherical nuclei
Energy Technology Data Exchange (ETDEWEB)
Vdovin, A.I.; Tien Khoa, D.; Voronov, V.V.
1986-02-01
This paper obtains, in general form, the system of basic equations of the quasiparticle-phonon nuclear model for odd spherical nuclei. The equations take into account the anharmonicity of the vibrations of the even-even core and the corrections made necessary by the Pauli principle. It is shown that the system of equations contains all the variants of approximate equations of the quasiparticle-phonon model that are widely used in calculations.
Distributed-order diffusion equations and multifractality: Models and solutions
Sandev, Trifce; Chechkin, Aleksei V.; Korabel, Nickolay; Kantz, Holger; Sokolov, Igor M.; Metzler, Ralf
2015-10-01
We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided.
Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order
Energy Technology Data Exchange (ETDEWEB)
Favalli, Andrea, E-mail: afavalli@lanl.gov [Safeguards Science & Technology Group,Non-proliferation and Nuclear Engineering Division, Los Alamos National Laboratory, MS E540, Los Alamos, NM 87545 (United States); Croft, Stephen [Safeguards & Security Technology, Nuclear Security and Isotope Technology Division, Oak Ridge National Laboratory, One Bethel Valley Road, PO Box 2008, MS-6166, Oak Ridge, TN 37831-6166 (United States); Santi, Peter [Safeguards Science & Technology Group,Non-proliferation and Nuclear Engineering Division, Los Alamos National Laboratory, MS E540, Los Alamos, NM 87545 (United States)
2015-09-21
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 5{sup th} 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.
POD/DEIM Nonlinear model order reduction of an ADI implicit shallow water equations model
Stefanescu, Razvan
2012-01-01
In the present paper we consider a 2-D shallow-water equations (SWE) model on a $\\beta$-plane solved using an alternating direction fully implicit (ADI) finite-difference scheme on a rectangular domain. The scheme was shown to be unconditionally stable for the linearized equations. The discretization yields a number of nonlinear systems of algebraic equations. We then use a proper orthogonal decomposition (POD) to reduce the dimension of the SWE model. Due to the model nonlinearities, the computational complexity of the reduced model still depends on the number of variables of the full shallow - water equations model. By employing the discrete empirical interpolation method (DEIM) we reduce the computational complexity of the reduced order model due to its depending on the nonlinear full dimension model and regain the full model reduction expected from the POD model. To emphasize the CPU gain in performance due to use of POD/DEIM, we also propose testing an explicit Euler finite difference scheme (EE) as an a...
Linearization models for parabolic dynamical systems via Abel's functional equation
Elin, Mark; Reich, Simeon; Shoikhet, David
2009-01-01
We study linearization models for continuous one-parameter semigroups of parabolic type. In particular, we introduce new limit schemes to obtain solutions of Abel's functional equation and to study asymptotic behavior of such semigroups. The crucial point is that these solutions are univalent functions convex in one direction. In a parallel direction, we find analytic conditions which determine certain geometric properties of those functions, such as the location of their images in either a half-plane or a strip, and their containing either a half-plane or a strip. In the context of semigroup theory these geometric questions may be interpreted as follows: is a given one-parameter continuous semigroup either an outer or an inner conjugate of a group of automorphisms? In other words, the problem is finding a fractional linear model of the semigroup which is defined by a group of automorphisms of the open unit disk. Our results enable us to establish some new important analytic and geometric characteristics of t...
The Trauma Outcome Process Assessment Model: A Structural Equation Model Examination of Adjustment
Borja, Susan E.; Callahan, Jennifer L.
2009-01-01
This investigation sought to operationalize a comprehensive theoretical model, the Trauma Outcome Process Assessment, and test it empirically with structural equation modeling. The Trauma Outcome Process Assessment reflects a robust body of research and incorporates known ecological factors (e.g., family dynamics, social support) to explain…
Equivalence and Differences between Structural Equation Modeling and State-Space Modeling Techniques
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…
Equivalence and differences between structural equation modeling and state-space modeling techniques
Chow, Sy-Miin; Ho, Moon-ho R.; Hamaker, E.L.; Dolan, C.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
Eid, Michael; Nussbeck, Fridtjof W.; Geiser, Christian; Cole, David A.; Gollwitzer, Mario; Lischetzke, Tanja
2008-01-01
The question as to which structural equation model should be selected when multitrait-multimethod (MTMM) data are analyzed is of interest to many researchers. In the past, attempts to find a well-fitting model have often been data-driven and highly arbitrary. In the present article, the authors argue that the measurement design (type of methods…
Strategic Competence as a Fourth-Order Factor Model: A Structural Equation Modeling Approach
Phakiti, Aek
2008-01-01
This article reports on an empirical study that tests a fourth-order factor model of strategic competence through the use of structural equation modeling (SEM). The study examines the hierarchical relationship of strategic competence to (a) strategic knowledge of cognitive and metacognitive strategy use in general (i.e., trait) and (b) strategic…
Equivalence and Differences between Structural Equation Modeling and State-Space Modeling Techniques
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…
Viscosity modeling for ionic liquid solutions by Eyring-Wilson equation
Directory of Open Access Journals (Sweden)
He Yang-Chun
2012-01-01
Full Text Available A semi-theoretical model based on the classical Eyring’s mixture viscosity equation and the Wilson activity coefficient equation is presented for correlating the viscosity of ionic liquids with solvent systems. The accuracy of the proposed model was verified by comparing calculated and experimental viscosity values from literatures for 49mixtures with total 1560 data points. The results show that the equation similar to the Wilson activity coefficient equation can be well applied to describe the non-ideal term in the Eyring’s mixture viscosity equation. The model has a relatively simple mathematical form and can be easily incorporated into process simulation software.
Automated computational modelling for complicated partial differential equations
Ølgaard, K.B.
2013-01-01
In engineering, physical phenomena are often described mathematically by partial differential equations (PDEs), and a commonly used method to solve these equations is the finite element method (FEM). Implementing a solver based on this method for a given PDE in a computer program written in source c
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…
Multigrid solution of incompressible turbulent flows by using two-equation turbulence models
Energy Technology Data Exchange (ETDEWEB)
Zheng, X.; Liu, C. [Front Range Scientific Computations, Inc., Denver, CO (United States); Sung, C.H. [David Taylor Model Basin, Bethesda, MD (United States)
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.
Comparing Entrepreneurship Intention: A Multigroup Structural Equation Modeling Approach
Directory of Open Access Journals (Sweden)
Sabrina O. Sihombing
2012-04-01
Full Text Available Unemployment is one of the main social and economic problems that many countries face nowadays. One strategic way to overcome this problem is by fostering entrepreneurship spirit especially for unem-ployment graduates. Entrepreneurship is becoming an alternative Job for students after they graduate. This is because entrepreneurship of fers major benefits, such as setting up one’s own business and the pos sibility of having significant financial rewards than working for others. Entrepreneurship is then offered by many universities. This research applies the theory of planned behavior (TPB by incorporating attitude toward success as an antecedent variable of the attitude to examine students’ intention to become an entrepreneur. The objective of this research is to compare entrepreneurship intention between business students and non-business students. A self-administered questionnaire was used to collect data for this study. Questionnaires were distributed to respondents by applying the drop-off/pick-up method. A number of 294 by questionnaires were used in the analysis. Data were analyzed by using structural equation modeling. Two out of four hypotheses were confirmed. These hypotheses are the relationship between the attitude toward becoming an entrepreneur and the intention to try becoming an entrepreneur, and the relationship perceived behavioral control and intention to try becoming an entrepreneur. This paper also provides a discussion and offers directions for future research.
Comparing Entrepreneurship Intention: A Multigroup Structural Equation Modeling Approach
Directory of Open Access Journals (Sweden)
Sabrina O. Sihombing
2012-04-01
Full Text Available Unemployment is one of the main social and economic problems that many countries face nowadays. One strategic way to overcome this problem is by fostering entrepreneurship spirit especially for unem ployment graduates. Entrepreneurship is becoming an alternative Job for students after they graduate. This is because entrepreneurship of-fers major benefits, such as setting up one’s own business and the pos-sibility of having significant financial rewards than working for others. Entrepreneurship is then offered by many universities. This research applies the theory of planned behavior (TPB by incorporating attitude toward success as an antecedent variable of the attitude to examine students’ intention to become an entrepreneur. The objective of this research is to compare entrepreneurship intention between business students and non-business students. A self-administered questionnaire was used to collect data for this study. Questionnaires were distributed to respondents by applying the drop-off/pick-up method. A number of 294 by questionnaires were used in the analysis. Data were analyzed by using structural equation modeling. Two out of four hypotheses were confirmed. These hypotheses are the relationship between the attitude toward becoming an entrepreneur and the intention to try becoming an entrepreneur, and the relationship perceived behavioral control and intention to try becoming an entrepreneur. This paper also provides a discussion and offers directions for future research.
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.
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.
Identifiability of Gaussian Structural Equation Models with Same Error Variances
Peters, Jonas
2012-01-01
We consider structural equation models (SEMs) in which variables can be written as a function of their parents and noise terms (the latter are assumed to be jointly independent). Corresponding to each SEM, there is a directed acyclic graph (DAG) G_0 describing the relationships between the variables. In Gaussian SEMs with linear functions, the graph can be identified from the joint distribution only up to Markov equivalence classes (assuming faithfulness). It has been shown, however, that this constitutes an exceptional case. In the case of linear functions and non-Gaussian noise, the DAG becomes identifiable. Apart from few exceptions the same is true for non-linear functions and arbitrarily distributed additive noise. In this work, we prove identifiability for a third modification: if we require all noise variables to have the same variances, again, the DAG can be recovered from the joint Gaussian distribution. Our result can be applied to the problem of causal inference. If the data follow a Gaussian SEM w...
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.
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.
A model for closing the inviscid form of the average passage equation system
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.
A model for closing the inviscid form of the average passage equation system
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.
Notes on TQFT Wire Models and Coherence Equations for SU(3 Triangular Cells
Directory of Open Access Journals (Sweden)
Robert Coquereaux
2010-12-01
Full Text Available After a summary of the TQFT wire model formalism we bridge the gap from Kuperberg equations for SU(3 spiders to Ocneanu coherence equations for systems of triangular cells on fusion graphs that describe modules associated with the fusion category of SU(3 at level k. We show how to solve these equations in a number of examples.
A Note on Two-Equation Closure Modelling of Canopy Flow
DEFF Research Database (Denmark)
Sogachev, Andrey
2009-01-01
The note presents a rational approach to modelling the source/sink due to vegetation or buoyancy effects that appear in the turbulent kinetic energy, E, equation and a supplementary equation for a length-scale determining variable, φ, when two-equation closure is applied to canopy and atmospheric...
A Note on Two-Equation Closure Modelling of Canopy Flow
DEFF Research Database (Denmark)
Sogachev, Andrey
2009-01-01
The note presents a rational approach to modelling the source/sink due to vegetation or buoyancy effects that appear in the turbulent kinetic energy, E, equation and a supplementary equation for a length-scale determining variable, φ, when two-equation closure is applied to canopy and atmospheric...
Notes on TQFT wire models and coherence equations for SU(3) triangular cells
Coquereaux, R; Schieber, G
2010-01-01
After a summary of the TQFT wire model formalism we bridge the gap from Kuperberg equations for SU(3) spiders to Ocneanu coherence equations for systems of triangular cells on fusion graphs that describe modules associated with the fusion category of SU(3) at level k. We show how to solve these equations in a number of examples.
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Meleshko, Sergey V [School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000 (Thailand); Rudenko, Oleg V, E-mail: nib@bth.se, E-mail: sergey@math.sut.ac.th, E-mail: rudenko@acs366.phys.msu.ru [Department of Physics, Moscow State University, 119991 Moscow (Russian Federation)
2011-08-05
The paper deals with an evolutionary integro-differential equation describing nonlinear waves. A particular choice of the kernel in the integral leads to well-known equations such as the Khokhlov-Zabolotskaya equation, the Kadomtsev-Petviashvili equation and others. Since the solutions of these equations describe many physical phenomena, the analysis of the general model studied in this paper is important. One of the methods for obtaining solutions of differential equations is provided by the Lie group analysis. However, this method is not applicable to integro-differential equations. Therefore, we discuss new approaches developed in modern group analysis and apply them to the general model considered in this paper. Reduced equations and exact solutions are also presented.
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
Exploration of POD-Galerkin Techniques for Developing Reduced Order Models of the Euler Equations
2015-07-01
Models of the Euler Equations 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Mundis, N., Edoh, A. and Sankaran...for describing combustion response to specific excitations using Euler equations as a continued work from a previous studies using a reaction...eigen-bases. For purposes of this study, a linearized version of the Euler equations is employed. The knowledge obtained from previous scalar equation
Liu, Pengfei; Duan, Huilong
2012-01-01
The objectives of this study are to model the endocardiac radiofrequency (RF) ablation procedure and to employ the Hyperbolic Bioheat Equation (HBE), which takes the thermal wave behaviour into account, comparing the results with those obtained using the common Pennes Bioheat Equation (BE) method. A complex model is created to cover particular endocardiac physical and geometry environment. Finite Element Method (FEM) is adopted to study the model with both BE and HBE methods. Different convection coefficients and voltages are applied to simulate different conditions. Lesion size, max temperature and specified position temperature are selected as criteria to evaluate the simulated results. The study found that during ablation, the lesion size difference ratio can reach 20% in some periods. The difference is obvious and cannot be neglected.
National Research Council Canada - National Science Library
Hyeon Woo LEE
2011-01-01
AN APPLICATION OF LATENT VARIABL AN APPLICATION OF LATENT VARIABLE STRUCTURAL EQUATION MODELING FOR EXPERIMENTAL RESEARCH IN EDUCATIONAL TECHNOLOGY As the technology-enriched learning environments...
TBA equations for excited states in the O(3) and O(4) nonlinear $\\sigma$-model
Balog, J.; Hegedus, A
2003-01-01
TBA integral equations are proposed for 1-particle states in the sausage- and SS-models and their $\\sigma$-model limits. Combined with the ground state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear $\\sigma$-model and the results are compared to 3-loop perturbation theory and Monte Carlo data.
Song, Xin-Yuan; Lee, Sik-Yum
2006-01-01
Structural equation models are widely appreciated in social-psychological research and other behavioral research to model relations between latent constructs and manifest variables and to control for measurement error. Most applications of SEMs are based on fully observed continuous normal data and models with a linear structural equation.…
Song, Xin-Yuan; Lee, Sik-Yum
2008-01-01
Structural equation models are widely appreciated in behavioral, social, and psychological research to model relations between latent constructs and manifest variables, and to control for measurement errors. Most applications of structural equation models are based on fully observed data that are independently distributed. However, hierarchical…
Langevin equation with fluctuating diffusivity: A two-state model.
Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji
2016-07-01
Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.
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.
A hybrid moment equation approach to gas-grain chemical modeling
Du, Fujun
2011-01-01
[Context] The stochasticity of grain chemistry requires special care in modeling. Previously methods based on the modified rate equation, the master equation, the moment equation, and Monte Carlo simulations have been used. [Aims] We attempt to develop a systematic and efficient way to model the gas-grain chemistry with a large reaction network as accurately as possible. [Methods] We present a hybrid moment equation approach which is a general and automatic method where the generating function is used to generate the moment equations. For large reaction networks, the moment equation is cut off at the second order, and a switch scheme is used when the average population of certain species reaches 1. For small networks, the third order moments can also be utilized to achieve a higher accuracy. [Results] For physical conditions in which the surface reactions are important, our method provides a major improvement over the rate equation approach, when benchmarked against the rigorous Monte Carlo results. For eithe...
MODELLING OF SHORT DURATION RAINFALL (SDR INTENSITY EQUATIONS FOR ERZURUM
Directory of Open Access Journals (Sweden)
Serkan ŞENOCAK
2007-01-01
Full Text Available The scope of this study is to develop a rainfall intensity-duration-frequency (IDF equation for some return periods at Erzurum rainfall station. The maximum annual rainfall values for 5, 10, 15, 30 and 60 minutes are statistically analyzed for the period 1956 – 2004 by using some statistical distributions such as the Generalized Extreme Values (GEV, Gumbel, Normal, Two-parameter Lognormal, Three-parameter Lognormal, Gamma, Pearson type III and Log-Pearson type III distributions. ?2 goodness-of-fit test was used to choose the best statistical distribution among all distributions. IDF equation constants and coefficients of correlation (R for each emprical functions are calculated using nonlinear estimation method for each return periods (T = 2, 5, 10, 25, 50, 75 and 100 years. The most suitable IDF equation is observed that ( B max i (t = A/ t + C , except for T=100 years, because of the highest coefficients of correlation.
Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models
Directory of Open Access Journals (Sweden)
Narcisa Apreutesei
2014-05-01
Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.
Exact Shock Solution of a Coupled System of Delay Differential Equations: A Car-Following Model
Tutiya, Yohei; Kanai, Masahiro
2007-08-01
In this letter, we present exact shock solutions of a coupled system of delay differential equations, which was introduced as a traffic-flow model called car-following model. We use the Hirota method, originally developed in order to solve soliton equations. The relevant delay differential equations have been known to allow exact solutions expressed by elliptic functions with periodic boundary conditions. In the present work, however, shock solutions are obtained with open boundaries, representing the stationary propagation of a traffic jam.
A Lattice Boltzmann Model and Simulation of KdV-Burgers Equation
Institute of Scientific and Technical Information of China (English)
ZHANGChao-Ying; TANHui-Li; LIUMu-Ren; KONGLing-Jiang
2004-01-01
A lattice Boltzmann model of KdV-Burgers equation is derived by using the single-relaxation form of the lattice Boltzmann equation. With the present model, we simulate the traveling-wave solutions, the solitary-wave solutions, and the sock-wave solutions of KdV-Burgers equation, and calculate the decay factor and the wavelength of the sock-wave solution, which has exponential decay. The numerical results agree with the analytical solutions quite well.
A New Lattice Boltzmann Model for KdV-Burgers Equation
Institute of Scientific and Technical Information of China (English)
MA Chang-Feng
2005-01-01
@@ A new lattice Boltzmann model with amending-function for KdV-Burgers equation, ut +uux - αuxx +βuxxx = 0,is presented by using the single-relaxation form of the lattice Boltzmann equation. Applying the proposed model,we simulate the solutions ofa kind of KdV-Burgers equations, and the numerical results agree with the analytical solutions quite well.
Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models
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.
An analytic equation of state for Ising-like models
Energy Technology Data Exchange (ETDEWEB)
O' Connor, Denjoe [School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); Santiago, J A [Centro de Investigacion Avanzada en IngenierIa Industrial. Universidad Autonoma del Estado de Hidalgo, Pachuca 42184 (Mexico); Stephens, C R [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, Mexico DF 04510 (Mexico)
2007-02-02
Using an environmentally friendly renormalization we derive, from an underlying field theory representation, a formal expression for the equation of state, y = f(x), that exhibits all desired asymptotic and analyticity properties in the three limits x {yields} 0, x {yields} {infinity} and x {yields} -1. The only necessary inputs are the Wilson functions {gamma}{sub {lambda}}, {gamma}{sub {psi}} and {gamma}{sub {phi}{sup 2}}, associated with a renormalization of the transverse vertex functions. These Wilson functions exhibit a crossover between the Wilson-Fisher fixed point and the fixed point that controls the coexistence curve. Restricting to the case N = 1, we derive a one-loop equation of state for 2 < d < 4 naturally parameterized by a ratio of nonlinear scaling fields. For d = 3 we show that a non-parameterized analytic form can be deduced. Various asymptotic amplitudes are calculated directly from the equation of state in all three asymptotic limits of interest and comparison made with known results. By positing a scaling form for the equation of state inspired by the one-loop result, but adjusted to fit the known values of the critical exponents, we obtain better agreement with known asymptotic amplitudes.
Optimal prediction for moment models: Crescendo diffusion and reordered equations
Seibold, Benjamin
2009-01-01
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to study moment closure generally within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, e.g. $P_N$, diffusion, and diffusion correction closures. In addition, the formalism gives rise to new parabolic systems, the reordered $P_N$ equations, that are similar to the simplified $P_N$ equations. Furthermore, we propose a modification to existing closures. Although simple and with no extra cost, this newly derived...
Optimal prediction for moment models: crescendo diffusion and reordered equations
Seibold, Benjamin; Frank, Martin
2009-12-01
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to generally study the moment closure within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, such as P N , diffusion, and diffusion correction closures. In addition, the formalism gives rise to new parabolic systems, the reordered P N equations, that are similar to the simplified P N equations. Furthermore, we propose a modification to existing closures. Although simple and with no extra cost, this newly derived crescendo diffusion yields better approximations in numerical tests.
Structure analysis of solution to equations of quasi 3-D accretion disk model
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper we discuss the problems contained in the solution to the equations of quasi 3-D accretion disk model, and point out that the angular momentum equation should not be integrated directly. Finally, we develop a criterion of the existence of a disconnected solution to this model.
Coombes, S.; Venkov, N.A.; Shiau, L.; Bojak, I.; Liley, D.T.; Laing, C.R.
2007-01-01
Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal dela
A physical five-equation model for compressible two-fluid flow, and its numerical treatment
Kreeft, J.J.; Koren, B.
2009-01-01
A novel five-equation model for inviscid, non-heat-conducting, compressible two-fluid flow is derived, together with an appropriate numerical method. The model uses flow equations based on conservation laws and exchange laws only. The two fluids exchange momentum and energy, for which source terms a
Meta-Analytic Structural Equation Modeling (MASEM): Comparison of the Multivariate Methods
Zhang, Ying
2011-01-01
Meta-analytic Structural Equation Modeling (MASEM) has drawn interest from many researchers recently. In doing MASEM, researchers usually first synthesize correlation matrices across studies using meta-analysis techniques and then analyze the pooled correlation matrix using structural equation modeling techniques. Several multivariate methods of…
Maximum Likelihood Analysis of Nonlinear Structural Equation Models with Dichotomous Variables
Song, Xin-Yuan; Lee, Sik-Yum
2005-01-01
In this article, a maximum likelihood approach is developed to analyze structural equation models with dichotomous variables that are common in behavioral, psychological and social research. To assess nonlinear causal effects among the latent variables, the structural equation in the model is defined by a nonlinear function. The basic idea of the…
Equation-of-state model for shock compression of hot dense matter
Pain, J C
2007-01-01
A quantum equation-of-state model is presented and applied to the calculation of high-pressure shock Hugoniot curves beyond the asymptotic fourfold density, close to the maximum compression where quantum effects play a role. An analytical estimate for the maximum attainable compression is proposed. It gives a good agreement with the equation-of-state model.
Is it appropriate to model turbidity currents with the Three-Equation Model?
Hu, Peng; He, Zhiguo
2015-01-01
The Three-Equation Model (TEM) was developed in the 1980s to model turbidity currents (TCs) and has been widely used ever since. However, its physical justification was questioned because self-accelerating TCs simulated with the steady TEM seemed to violate the turbulent kinetic energy balance. This violation was considered as a result of very strong sediment erosion that consumes more turbulent kinetic energy than is produced. To confine bed erosion and thus remedy this issue, the Four-Equation Model (FEM) was introduced by assuming a proportionality between the bed shear stress and the turbulent kinetic energy. Here we analytically proof that self-accelerating TCs simulated with the original steady TEM actually never violate the turbulent kinetic energy balance, provided that the bed drag coefficient is not unrealistically low. We find that stronger bed erosion, surprisingly, leads to more production of turbulent kinetic energy due to conversion of potential energy of eroded material into kinetic energy of ...
Dynamic modeling of dual-arm cooperating manipulators based on Udwadia–Kalaba equation
Directory of Open Access Journals (Sweden)
Jia Liu
2016-07-01
Full Text Available Dual-arm cooperating manipulators subject to a certain constraint brought about by the desired trajectory and geometric constraint show high nonlinearity and coupling in their dynamic characteristic. Therefore, it is hard to build dynamical equation with traditional Lagrange equation. The Udwadia–Kalaba equation presents a new idea of dynamic modeling of multi-body systems. However, the dynamic modeling of the unconstrained systems still depends on the traditional Lagrange equation and is quite tedious for dual-arm cooperating manipulators. A generalized dynamical equation of multi-link planar manipulators is thus presented and proven to make modeling conveniently. The constraint relationship is established from a new perspective, and the dynamical equation of dual-arm cooperating manipulator subject to the desired trajectory is acquired with the Udwadia–Kalaba equation. The simple approach overcomes the disadvantage of obtaining dynamical equation from traditional Lagrange equation by Lagrange multiplier. The simulation results of varying law of the joint angles and the motion path of the bar prove that the dynamical equation established by this method conforms to reality.
A Parabolic Equation Approach to Modeling Acousto-Gravity Waves for Local Helioseismology
Del Bene, Kevin; Lingevitch, Joseph; Doschek, George
2016-08-01
A wide-angle parabolic-wave-equation algorithm is developed and validated for local-helioseismic wave propagation. The parabolic equation is derived from a factorization of the linearized acousto-gravity wave equation. We apply the parabolic-wave equation to modeling acoustic propagation in a plane-parallel waveguide with physical properties derived from helioseismic data. The wavenumber power spectrum and wave-packet arrival-time structure for receivers in the photosphere with separation up to 30° is computed, and good agreement is demonstrated with measured values and a reference spectral model.
A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers
Schüler, L.; Suciu, N.; Knabner, P.; Attinger, S.
2016-10-01
Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.
Development and validation of skinfold-thickness prediction equations with a 4-compartment model.
Peterson, Matthew J; Czerwinski, Stefan A; Siervogel, Roger M
2003-05-01
Skinfold-thickness measurements are commonly obtained for the indirect assessment of body composition. We developed new skinfold-thickness equations by using a 4-compartment model as the reference. Additionally, we compared our new equations with the Durnin and Womersley and Jackson and Pollock skinfold-thickness equations to evaluate each equation's validity and precision. Data from 681 healthy, white adults were used. Percentage body fat (%BF) values were calculated by using the 4-compartment model. The cohort was then divided into validation and cross-validation groups. Equations were developed by using regression analyses and the 4-compartment model. All equations were then tested by using the cross-validation group. Tests for accuracy included mean differences, R(2), and Bland-Altman plots. Precision was evaluated by comparing root mean squared errors. Our new equations' estimated means for %BF in men and women (22.7% and 32.6%, respectively) were closest to the corresponding 4-compartment values (22.8% and 32.8%). The Durnin and Womersley equation means in men and women (20.0% and 31.0%, respectively) and the Jackson and Pollock mean in women (26.2%) underestimated %BF. All equations showed a tendency toward underestimation in subjects with higher %BF. Bland-Altman plots showed limited agreement between Durnin and Wormersley, Jackson and Pollock, and the 4-compartment model. Precision was similar among all the equations. We developed accurate and precise skinfold-thickness equations by using a 4-compartment model as the method of reference. Additionally, we found that the skinfold-thickness equations frequently used by clinicians and practitioners underestimate %BF.
Logic functions and equations binary models for computer science
Posthoff, Christian
2004-01-01
Logic functions and equations are (some of) the most important concepts of Computer Science with many applications such as Binary Arithmetics, Coding, Complexity, Logic Design, Programming, Computer Architecture and Artificial Intelligence. They are very often studied in a minimum way prior to or together with their respective applications. Based on our long-time teaching experience, a comprehensive presentation of these concepts is given, especially emphasising a thorough understanding as well as numerical and computer-based solution methods. Any applications and examples from all the respective areas are given that can be dealt with in a unified way. They offer a broad understanding of the recent developments in Computer Science and are directly applicable in professional life. Logic Functions and Equations is highly recommended for a one- or two-semester course in many Computer Science or computer Science-oriented programmes. It allows students an easy high-level access to these methods and enables sophist...
Nonaligned shocks for discrete velocity models of the Boltzmann equation
Directory of Open Access Journals (Sweden)
J. M. Greenberg
1991-05-01
Full Text Available At the conclusion of I. Bonzani's presentation on the existence of structured shock solutions to the six-velocity, planar, discrete Boltzmann equation (with binary and triple collisions, Greenberg asked whether such solutions were possible in directions e(α=(cosα ,sinα when α was not one of the particle flow directions. This question generated a spirited discussion but the question was still open at the conclusion of the conference. In this note the author will provide a partial resolution to the question raised above. Using formal perturbation arguments he will produce approximate solutions to the equation considered by Bonzani which represent traveling waves propagating in any direction e(α=(cosα ,sinα.
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
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.
A stochastic particle system modeling the Carleman equation
Energy Technology Data Exchange (ETDEWEB)
Caprino, S.; De Masi, A.; Presutti, E.; Pulvirenti, M. (Universita dell' Aquila (Italy))
1989-05-01
Two species of Brownian particles on the unit circle are considered; both have diffusion coefficient {sigma} > 0 but different velocities (drift), 1 for one species and {minus}1 for the other. During the evolution the particles randomly change their velocity: if two particles have the same velocity and are at distance {<=} {var epsilon} ({var epsilon} being a positive parameter), they both may simultaneously flip their velocity according to a poisson process of a given intensity. The analogue of the Boltzmann-Grad limit is studied when {var epsilon} goes to zero and the total number of particles increases like {var epsilon}{sup {minus}1}. In such a limit propagation of chaos and convergence to a limiting kinetic equation are proven globally in time, under suitable assumptions on the initial state. If, furthermore, {sigma} depends on {var epsilon} and suitably vanishes when {var epsilon} goes to zero, then the limiting kinetic equation (for the density of the two species of particles) is the Carleman equation.
Transition study of 3D aerodynamic configures using improved transport equations modeling
Directory of Open Access Journals (Sweden)
Xu Jiakuan
2016-08-01
Full Text Available As boundary layer transition plays an important role in aerodynamic drag prediction, the proposal and study of transition prediction methods simulating the complex flow phenomena are prerequisite for aerodynamic design. In this paper, with the application of the linear stability theory based on amplification factor transport transition equations on the two-equation shear stress transport (SST eddy-viscosity model, a new method, the SST-NTS-NCF model, is yielded. The new amplification factor transport equation for the crossflow instability induced transition is proposed to add to the NTS equation proposed by Coder, which simulates Tollmien–Schlichting wave transition. The turbulent kinetic energy equation is modified by introducing a new source term that simulates the transition process without the intermittency factor equation. Finally, coupled with these two amplification factor transport equations and SST turbulence model, a four-equation transition turbulence model is built. Comparisons between predictions using the new model and wind-tunnel experiments of NACA64(2A015, NLF(2-0415 and ONERA-D infinite swept wing and ONERA-M6 swept wing validate the predictive quality of the new SST-NTS-NCF model.
Transition study of 3D aerodynamic configures using improved transport equations modeling
Institute of Scientific and Technical Information of China (English)
Xu Jiakuan; Bai Junqiang; Zhang Yang; Qiao Lei
2016-01-01
As boundary layer transition plays an important role in aerodynamic drag prediction, the proposal and study of transition prediction methods simulating the complex flow phenomena are prerequisite for aerodynamic design. In this paper, with the application of the linear stability theory based on amplification factor transport transition equations on the two-equation shear stress transport (SST) eddy-viscosity model, a new method, the SST-NTS-NCF model, is yielded. The new amplification factor transport equation for the crossflow instability induced transition is proposed to add to the NTS equation proposed by Coder, which simulates Tollmien–Schlichting wave tran-sition. The turbulent kinetic energy equation is modified by introducing a new source term that sim-ulates the transition process without the intermittency factor equation. Finally, coupled with these two amplification factor transport equations and SST turbulence model, a four-equation transition turbulence model is built. Comparisons between predictions using the new model and wind-tunnel experiments of NACA64(2)A015, NLF(2)-0415 and ONERA-D infinite swept wing and ONERA-M6 swept wing validate the predictive quality of the new SST-NTS-NCF model.
Institute of Scientific and Technical Information of China (English)
Hua Huang; Mao Sun
2012-01-01
The forward flight of a model butterfly was studied by simulation using the equations of motion coupled with the Navier-Stokes equations.The model butterfly moved under the action of aerodynamic and gravitational forces,where the aerodynamic forces were generated by flapping wings which moved with the body,allowing the body oscillations of the model butterfly to be simulated.The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the upstroke.In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward,giving the weight-supporting vertical force and a small negative horizontal force,whilst in the upstroke,the body angle is large and the relatively small aerodynamic force points forward and slightly downward,giving a positive horizontal force which overcomes the body drag and the negative horizontal force generated in the downstroke.(2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects.(3) The body-massspecific power of the model butterfly is 33.3 W/kg,not very different from that of many other insects,e.g.,fruitflies and dragonflies.
The Hill equation: a review of its capabilities in pharmacological modelling.
Goutelle, Sylvain; Maurin, Michel; Rougier, Florent; Barbaut, Xavier; Bourguignon, Laurent; Ducher, Michel; Maire, Pascal
2008-12-01
The Hill equation was first introduced by A.V. Hill to describe the equilibrium relationship between oxygen tension and the saturation of haemoglobin. In pharmacology, the Hill equation has been extensively used to analyse quantitative drug-receptor relationships. Many pharmacokinetic-pharmacodynamic models have used the Hill equation to describe nonlinear drug dose-response relationships. Although the Hill equation is widely used, its many properties are not all well known. This article aims at reviewing the various properties of the Hill equation. The descriptive aspects of the Hill equation, in particular mathematical and graphical properties, are examined, and related to Hill's original work. The mechanistic aspect of the Hill equation, involving a strong connection with the Guldberg and Waage law of mass action, is also described. Finally, a probabilistic view of the Hill equation is examined. Here, we provide some new calculation results, such as Fisher information and Shannon entropy, and we introduce multivariate probabilistic Hill equations. The main features and potential applications of this probabilistic approach are also discussed. Thus, within the same formalism, the Hill equation has many different properties which can be of great interest for those interested in mathematical modelling in pharmacology and biosciences.
Index-aware model order reduction methods applications to differential-algebraic equations
Banagaaya, N; Schilders, W H A
2016-01-01
The main aim of this book is to discuss model order reduction (MOR) methods for differential-algebraic equations (DAEs) with linear coefficients that make use of splitting techniques before applying model order reduction. The splitting produces a system of ordinary differential equations (ODE) and a system of algebraic equations, which are then reduced separately. For the reduction of the ODE system, conventional MOR methods can be used, whereas for the reduction of the algebraic systems new methods are discussed. The discussion focuses on the index-aware model order reduction method (IMOR) and its variations, methods for which the so-called index of the original model is automatically preserved after reduction.
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.
A higher order lattice BGK model for simulating some nonlinear partial differential equations
Institute of Scientific and Technical Information of China (English)
LAI HuiLin; MA ChangFeng
2009-01-01
In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux+βunux-γuxx+δuxxx= F(U). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.
A higher order lattice BGK model for simulating some nonlinear partial differential equations
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux + βunux - γuxx + δuxxx = F(u). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.
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.
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. Mathematical Education, State Islamic University of Sultan Syarif Kasim Riau, 28293 Indonesia and Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor (Malaysia); Bahar, A. [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor Malaysia and UTM Center for Industrial and Applied Mathematics (UTM-CIAM) (Malaysia)
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.
Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models
Hisakado, M
1998-01-01
We consider the hungry Volterra hierarchy from the view point of the multi boson KP hierarchy. We construct the hungry Volterra equation as the ``fractional '' BT. We also study the relations between the (discrete time) hungry Volterra equation and two matrix models. From this point of view we study the reduction from (discrete time) 2d Toda lattice to the (discrete time) hungry Volterra equation.
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.
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
Duane, G. S.; Selten, F.
2016-12-01
Different models of climate and weather commonly give projections/predictions that differ widely in their details. While averaging of model outputs almost always improves results, nonlinearity implies that further improvement can be obtained from model interaction in run time, as has already been demonstrated with toy systems of ODEs and idealized quasigeostrophic models. In the supermodeling scheme, models effectively assimilate data from one another and partially synchronize with one another. Spread among models is manifest as a spread in possible inter-model connection coefficients, so that the models effectively "agree to disagree". Here, we construct a supermodel formed from variants of the SPEEDO model, a primitive-equation atmospheric model (SPEEDY) coupled to ocean and land. A suite of atmospheric models, coupled to the same ocean and land, is chosen to represent typical differences among climate models by varying model parameters. Connections are introduced between all pairs of corresponding independent variables at synoptic-scale intervals. Strengths of the inter-atmospheric connections can be considered to represent inverse inter-model observation error. Connection strengths are adapted based on an established procedure that extends the dynamical equations of a pair of synchronizing systems to synchronize parameters as well. The procedure is applied to synchronize the suite of SPEEDO models with another SPEEDO model regarded as "truth", adapting the inter-model connections along the way. The supermodel with trained connections gives marginally lower error in all fields than any weighted combination of the separate model outputs when used in "weather-prediction mode", i.e. with constant nudging to truth. Stronger results are obtained if a supermodel is used to predict the formation of coherent structures or the frequency of such. Partially synchronized SPEEDO models give a better representation of the blocked-zonal index cycle than does a weighted average
Generalized isothermal models with strange equation of state
Indian Academy of Sciences (India)
S D Maharaj; S Thirukkanesh
2009-03-01
We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein–Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.
ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION
MARKOWICH, P. A.
2009-10-01
We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results. © 2009 World Scientific Publishing Company.
Technical Note: Alternative in-stream denitrification equation for the INCA-N model
Etheridge, J. R.; Birgand, F.; Burchell, M. R., II; Lepistö, A.; Rankinen, K.; Granlund, K.
2014-04-01
The Integrated Catchment model for Nitrogen (INCA-N) is a semi-distributed, process based model that has been used to model the impacts of land use, climate, and land management changes on hydrology and nitrogen loading. An observed problem with the INCA-N model is reproducing low nitrate-nitrogen concentrations during the summer growing season in some catchments. In this study, the current equation used to simulate the rate of in-stream denitrification was replaced with an alternate equation that uses a mass transfer coefficient and the stream bottom area. The results of simulating in-stream denitrification using the two different methods were compared for a one year simulation period of the Yläneenjoki catchment in Finland. The alternate equation (Nash-Sutcliffe efficiency = 0.61) simulated concentrations during the periods of the growing season with the lowest flow that were closer to the observed concentrations than the current equation (Nash-Sutcliffe efficiency = 0.60), but the results were mixed during other portions of the year. The results of the calibration and validation of the model using the two equations show that the alternate equation will simulate lower nitrate-nitrogen concentrations during the growing season when compared to the current equation, but promote investigation into other errors in the model that may be causing inaccuracies in the modeled concentrations.
Incorporation of an Energy Equation into a Pulsed Inductive Thruster Performance Model
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.
Energy Technology Data Exchange (ETDEWEB)
Gregoire, O
2008-07-01
In order to simulate nuclear reactor cores, we presently use the 4 equation model implemented within FLICA4 code. This model is complemented with 2 algebraic closures for thermal disequilibrium and relative velocity between phases. Using such closures, means an 'a priori' knowledge of flows calculated in order to ensure that modelling assumptions apply. In order to improve the degree of universality to our macroscopic modelling, we propose in the report to derive a more general 6 equation model (balance equations for mass, momentum and enthalpy for each phase) for 2-phase flows. We apply the up-scaling procedure (Whitaker, 1999) classically used in porous media analysis to the statistically averaged equations (Aniel-Buchheit et al., 2003). By doing this, we apply the double-averaging procedure (Pedras and De Lemos, 2001 and Pinson et al. 2006): statistical and spatial averages. Then, using weighted averages (analogous to Favre's average) we extend the spatial averaging concept to variable density and 2-phase flows. This approach allows the global recovering of the structure of the systems of equations implemented in industrial codes. Supplementary contributions, such as dispersion, are also highlighted. Mechanical and thermal exchanges between solids and fluid are formally derived. Then, thanks to realistic simplifying assumptions, we show how it is possible to derive the original 4 equation model from the full 6 equation model. (author)
1988-01-22
all simultaneously. ANALOGIES ENTRE DIGITATIONS VISQUEUSES ET CROISSANCE DENDRI TIQUE Yves COUDER(*) When, between two narrowly spaced glass plates, a...consider viscoelastic fluids which obey an Oldroyd type constitutive equation with retardation time. For the mixed Cauchy problem with homogeneous...visco61astiques d6crits par une 1oi de comportement do type Oldroyd avec temps de retard . On montre, pour le probl~me de Cauchy mixte avec conditions
A mathematical model for phase separation: A generalized Cahn-Hilliard equation
Berti, Alessia; 10.1002/mma.1432
2011-01-01
In this paper we present a mathematical model to describe the phenomenon of phase separation, which is modelled as space regions where an order parameter changes smoothly. The model proposed, including thermal and mixing effects, is deduced for an incompressible fluid, so the resulting differential system couples a generalized Cahn-Hilliard equation with the Navier-Stokes equation. Its consistency with the second law of thermodynamics in the classical Clausius-Duhem form is finally proved.
Stochastic partial differential equations a modeling, white noise functional approach
Holden, Helge; Ubøe, Jan; Zhang, Tusheng
1996-01-01
This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in r...
Weakly coupled heat bath models for Gibbs-like invariant states in nonlinear wave equations
J. Bajars (Janis); J.E. Frank (Jason); B.J. Leimkuhler (Ben)
2013-01-01
textabstractThermal bath coupling mechanisms as utilized in molecular dynamics are applied to partial differential equation models. Working from a semi-discrete (Fourier mode) formulation for the Burgers–Hopf or Korteweg–de Vries equation, we introduce auxiliary variables and stochastic
A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics
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…
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.
Simplified TBA equations of the AdS5 × S5 mirror model
Arutyunov, G.E.; Frolov, S.
2009-01-01
We use the recently found integral representation for the dressing phase in the kinematic region of the mirror theory to simplify the TBA equations for the AdS5 × S5 mirror model. The resulting set of equations provides an efficient starting point for both analytic and numerical studies.
QCD equations of state and the quark-gluon plasma liquid model
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.
Invariance principle and model reduction for the Fokker-Planck equation
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'.
A note on the Dirichlet problem for model complex partial differential equations
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.
Similarity Reduction and Integrability for the Nonlinear Wave Equations from EPM Model
Institute of Scientific and Technical Information of China (English)
YAN ZhenYa
2001-01-01
Four types of similarity reductions are obtained for the nonlinear wave equation arising in the elasto-plasticmicrostructure model by using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou. As a result, the nonlinear wave equation is not integrable.``
River water quality model no. 1 (RWQM1): II. Biochemical process equations
DEFF Research Database (Denmark)
Reichert, P.; Borchardt, D.; Henze, Mogens
2001-01-01
In this paper, biochemical process equations are presented as a basis for water quality modelling in rivers under aerobic and anoxic conditions. These equations are not new, but they summarise parts of the development over the past 75 years. The primary goals of the presentation are to stimulate ...
Modeling of the Equation of State for 0 < ρ/ρ0 < 1010
Prut, V. V.
2016-09-01
An approximation of the equation of state of matter in nonrelativistic and relativistic regions is considered. The cold component is determined in the limit v → 0 by the properties of an ideal homogeneous degenerate relativistic electron gas, and under normal conditions, by four experimental parameters: the specific volume, the binding energy, the bulk compression modulus, and the parameter -(∂lnB/∂lnv). Results are confirmed and illustrated by the experimental equation of state for iron in the region up to p ≈ 3 Mbar. A comparison of the model equation of state and the classical equation of state of an ideal homogeneous degenerate electron gas is given.
Lattice Boltzmann Model for The Volume-Averaged Navier-Stokes Equations
Zhang, Jingfeng; Ouyang, Jie
2014-01-01
A numerical method, based on discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged Navier-Stokes equations can be recovered from the lattice Boltzmann equation in the limit of small Mach number by the Chapman-Enskog analysis and Taylor expansion. Due to its advantages such as explicit solver and inherent parallelism, the method appears to be more competitive with traditional numerical techniques. Numerical simulations show that the proposed model can accurately reproduce both the linear and nonlinear drag effects of porosity in the fluid flow through porous media.
A Novel Approach to Modeling of Hydrogeologic Systems Using Fuzzy Differential Equations
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.
Directory of Open Access Journals (Sweden)
Yaodeng Chen
2014-01-01
Full Text Available There are two different approaches on how to formulate adjoint numerical model (ANM. Aiming at the disputes arising from the construction methods of ANM, the differences between nonlinear shallow water equation and its adjoint equation are analyzed; the hyperbolicity and homogeneity of the adjoint equation are discussed. Then, based on unstructured meshes and finite volume method, a new adjoint model was advanced by getting numerical model of the adjoint equations directly. Using a gradient check, the correctness of the adjoint model was verified. The results of twin experiments to invert the bottom friction coefficient (Manning’s roughness coefficient indicate that the adjoint model can extract the observation information and produce good quality inversion. The reason of disputes about construction methods of ANM is also discussed in the paper.
A data storage model for novel partial differential equation descretizations.
Energy Technology Data Exchange (ETDEWEB)
Doyle, Wendy S.K.; Thompson, David C.; Pebay, Philippe Pierre
2007-04-01
The purpose of this report is to define a standard interface for storing and retrieving novel, non-traditional partial differential equation (PDE) discretizations. Although it focuses specifically on finite elements where state is associated with edges and faces of volumetric elements rather than nodes and the elements themselves (as implemented in ALEGRA), the proposed interface should be general enough to accommodate most discretizations, including hp-adaptive finite elements and even mimetic techniques that define fields over arbitrary polyhedra. This report reviews the representation of edge and face elements as implemented by ALEGRA. It then specifies a convention for storing these elements in EXODUS files by extending the EXODUS API to include edge and face blocks in addition to element blocks. Finally, it presents several techniques for rendering edge and face elements using VTK and ParaView, including the use of VTK's generic dataset interface for interpolating values interior to edges and faces.
Retinex Poisson Equation: a Model for Color Perception
Directory of Open Access Journals (Sweden)
Nicola Limare
2011-04-01
Full Text Available In 1964 Edwin H. Land formulated the Retinex theory, the first attempt to simulate and explain how the human visual system perceives color. Unfortunately, the Retinex Land-McCann original algorithm is both complex and not fully specified. Indeed, this algorithm computes at each pixel an average of a very large set of paths on the image. For this reason, Retinex has received several interpretations and implementations which, among other aims, attempt to tune down its excessive complexity. But, Morel et al. have shown that the original Retinex algorithm can be formalized as a (discrete partial differential equation. This article describes the PDE-Retinex, a fast implementation of the Land-McCann original theory using only two DFT’s.
A Hierarchical Latent Stochastic Differential Equation Model for Affective Dynamics
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…
Adiabatic limit in Abelian Higgs model with application to Seiberg-Witten equations
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.
Ferron, Bruno; Mercier, Herle; Treguier, Anne-marie
2000-01-01
This paper investigates the dynamics of the Antarctic Bottom Water (AABW) flow through the Romanche Fracture Zone (RFZ) in a primitive equation model with a high horizontal and vertical resolution. Two examples of Rows over simple bathymetries show that a reduced gravity model captures the essential dynamics of the primitive equation model. The reduced gravity model is then used as a tool to identify what are the bathymetric structures (sills, narrows) that mostly constrain the AABW flow thro...
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
Modelling the heat dynamics of a building using stochastic differential equations
DEFF Research Database (Denmark)
Andersen, Klaus Kaae; Madsen, Henrik; Hansen, Lars Henrik
2000-01-01
estimation and model validation, while physical knowledge is used in forming the model structure. The suggested lumped parameter model is thus based on thermodynamics and formulated as a system of stochastic differential equations. Due to the continuous time formulation the parameters of the model...
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.
DEFF Research Database (Denmark)
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode
2009-01-01
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......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(l)) (2005) 109-141; C.W. Tornoe, R.V Overgaard, H. Agerso, 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...
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.
Modeling neck linker of kinesin motor movement with MRSR stochastic differential equation
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].
Regularity criterion to some liquid crystal models and the Landau-Lifshitz equations in R3
Institute of Scientific and Technical Information of China (English)
FAN JiShan; GUO BoLing
2008-01-01
We consider the regularity problem under the critical condition to some liquid crystal models and the Landau-Lifshitz equations.The Serrin type reularity criteria are obtained in the terms of the Besov spaces.
Calculating the renormalisation group equations of a SUSY model with Susyno
Fonseca, Renato M
2011-01-01
Susyno is a Mathematica package dedicated to the computation of the 2-loop renormalisation group equations of a supersymmetric model based on any gauge group (the only exception being multiple U(1) groups) and for any field content.
Half-trek criterion for generic identifiability of linear structural equation models
Foygel, Rina; Drton, Mathias
2011-01-01
A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations among noise terms. We study parameter identifiability in these models, that is, we ask for conditions that ensure that the edge coefficients and correlations appearing in a linear structural equation model can be uniquely recovered from the covariance matrix of the associated normal distribution. We treat the case of generic identifiability, where unique recovery is possible for almost every choice of parameters. We give a new graphical criterion that is sufficient for generic identifiability. It improves criteria from prior work and does not require the directed part of the graph to be acyclic. We also develop a related necessary condition and examine the "gap" between sufficient and necessary conditions through sim...
Trimming Behavior of H_2-Loaded Silica Fiber Modeled by Rate Equations
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Photosensitivity behavior of H2-loaded silica fiber was modeled by rate equations for activated particles. The theoretical deductions give a close explanation to experimental phenomena on post-exposure growth in fiber gratings.
Fast and accurate calculation of dilute quantum gas using Uehling-Uhlenbeck model equation
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.
CSIR Research Space (South Africa)
Kim, S
2008-03-01
Full Text Available Motivated by a large multilevel survey conducted by the US Veterans Health Administration (VHA), we propose a structural equations model which involves a set of latent variables to capture dependence between different responses, a set of facility...
Regularity criterion to some liquid crystal models and the Landau-Lifshitz equations in R~3
Institute of Scientific and Technical Information of China (English)
2008-01-01
We consider the regularity problem under the critical condition to some liquid crystal models and the Landau-Lifshitz equations. The Serrin type reularity criteria are obtained in the terms of the Besov spaces.
Two-Dimensional Saddle Point Equation of Ginzburg-Landau Hamiltonian for the Diluted Ising Model
Institute of Scientific and Technical Information of China (English)
WU Xin-Tian
2006-01-01
@@ The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approximation.
Analytical solution of Boussinesq equations as a model of wave generation
Wiryanto, L. H.; Mungkasi, S.
2016-02-01
When a uniform stream on an open channel is disturbed by existing of a bump at the bottom of the channel, the surface boundary forms waves growing splitting and propagating. The model of the wave generation can be a forced Korteweg de Vries (fKdV) equation or Boussinesq-type equations. In case the governing equations are approximated from steady problem, the fKdV equation is obtained. The model gives two solutions representing solitary-like wave, with different amplitude. However, phyically there is only one profile generated from that process. Which solution is occured, we confirm from unsteady model. The Boussinesq equations are proposed to determine the stabil solution of the fKdV equation. From the linear and steady model, its solution is developed to determine the analytical solution of the unsteady equations, so that it can explain the physical phenomena, i.e. the process of the wave generation, wave splitting and wave propagation. The solution can also determine the amplitude and wave speed of the waves.
A unified lattice Boltzmann model for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Chai Zhenhua [State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074 (China); Shi Baochang [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)], E-mail: sbchust@126.com; Zheng Lin [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)
2008-05-15
In this paper, a unified and novel lattice Boltzmann model is proposed for solving nonlinear partial differential equation that has the form DU{sub t} + {alpha}UU{sub x} + {beta}U{sup n}U{sub x} - {gamma}U{sub xx} + {delta} U{sub xxx} = F(x,t). Numerical results agree well with the analytical solutions and results derived by existing literature, which indicates the present model is satisfactory and efficient on solving nonlinear partial differential equations.
Well-posedness of the limiting equation of a noisy consensus model in opinion dynamics
Chazelle, Bernard; Jiu, Quansen; Li, Qianxiao; Wang, Chu
2017-07-01
This paper establishes the global well-posedness of the nonlinear Fokker-Planck equation for a noisy version of the Hegselmann-Krause model. The equation captures the mean-field behavior of a classic multiagent system for opinion dynamics. We prove the global existence, uniqueness, nonnegativity and regularity of the weak solution. We also exhibit a global stability condition, which delineates a forbidden region for consensus formation. This is the first nonlinear stability result derived for the Hegselmann-Krause model.
Pakal: A Three-dimensional Model to Solve the Radiative Transfer Equation
De la Luz, Victor; Lara, Alejandro; Mendoza-Torres, J. E.; Selhorst, Caius L.
2011-01-01
We present a new numerical model called "Pakal" intended to solve the radiative transfer equation in a three-dimensional (3D) geometry, using the approximation for a locally plane-parallel atmosphere. Pakal uses pre-calculated radial profiles of density and temperature (based on hydrostatic, hydrodynamic, or MHD models) to compute the emission from 3D source structures with high spatial resolution. Then, Pakal solves the radiative transfer equation in a set of (3D) ray paths, going from the s...
Numerical Solution of Fractional Diffusion Equation Model for Freezing in Finite Media
Directory of Open Access Journals (Sweden)
R. S. Damor
2013-01-01
Full Text Available Phase change problems play very important role in engineering sciences including casting of nuclear waste materials, vivo freezing of biological tissues, solar collectors and so forth. In present paper, we propose fractional diffusion equation model for alloy solidification. A transient heat transfer analysis is carried out to study the anomalous diffusion. Finite difference method is used to solve the fractional differential equation model. The temperature profiles, the motion of interface, and interface velocity have been evaluated for space fractional diffusion equation.
On the form of the power equation for modeling solar chimney power plant systems
Fathi, Nima; Vorobieff, Peter
2015-01-01
Recently several mathematical models of a solar chimney power plant were derived, studied for a variety of boundary conditions, and compared against CFD calculations. The importance of these analyses is about the accuracy of the derived pressure drop and output power equation for solar chimney power plant systems (SCPPS). We examine the assumptions underlying the derivation and present reasons to believe that some of the derived equations, specifically the power equation in this model, may require a correction to be applicable in more realistic conditions. The analytical resutls are compared against the available experimental data from the Manzanares power plant.
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.
Testing strong factorial invariance using three-level structural equation modeling
Directory of Open Access Journals (Sweden)
Suzanne eJak
2014-07-01
Full Text Available 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, Oort and Dolan (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.
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.
2015-06-01
HIGHER-ORDER TREATMENTS OF BOUNDARY CONDITIONS IN SPLIT-STEP FOURIER PARABOLIC EQUATION MODELS by Savas Erdim June 2015 Thesis Advisor...CONDITIONS IN SPLIT-STEP FOURIER PARABOLIC EQUATION MODELS 5. FUNDING NUMBERS 6. AUTHOR(S) Savas Erdim 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES... Parabolic equation models solved using the split-step Fourier (SSF) algorithm, such as the Monterey Miami Parabolic Equation model, are commonly used
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
Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit
Matsuya, Keisuke; Kanai, Masahiro
2015-01-01
We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time version of the delayed optimal-velocity model; in the continuum limit, we recover the delay differential equation for this model and the exact solutions as well. We then work in the ultra-discrete limit, obtaining a delay cellular-automaton model, which successfully inherits the solutions. Also the dispersion relation ...
Discrete Boltzmann model of shallow water equations with polynomial equilibria
Meng, Jianping; Emerson, David R; Peng, Yong; Zhang, Jianmin
2016-01-01
A hierarchy of discrete Boltzmann model is proposed for simulating shallow water flows. By using the Hermite expansion and Gauss-Hermite quadrature, the conservation laws are automatically satisfied without extra effort. Moreover, the expansion order and quadrature can be chosen flexibly according to the problem for striking the balance of accuracy and efficiency. The models are then tested using the classical one-dimensional dam-breaking problem, and successes are found for both supercritical and subcritical flows.
Levy-Bencheton, D; Terras, V
2015-01-01
We pursue our study of the antiperiodic dynamical 6-vertex model using Sklyanin's separation of variables approach, allowing in the model new possible global shifts of the dynamical parameter. We show in particular that the spectrum and eigenstates of the antiperiodic transfer matrix are completely characterized by a system of discrete equations. We prove the existence of different reformulations of this characterization in terms of functional equations of Baxter's type. We notably consider the homogeneous functional $T$-$Q$ equation which is the continuous analog of the aforementioned discrete system and show, in the case of a model with an even number of sites, that the complete spectrum and eigenstates of the antiperiodic transfer matrix can equivalently be described in terms of a particular class of its $Q$-solutions, hence leading to a complete system of Bethe equations. Finally, we compute the form factors of local operators for which we obtain determinant representations in finite volume.
Numerical Models of Higher-Order Boussinesq Equations and Comparisons with Laboratory Measurement
Institute of Scientific and Technical Information of China (English)
邹志利; 张晓莉
2001-01-01
Nonlinear water wave propagation passing a submerged shelf is studied experimentally and numerically. The applicability of two different wave propagation models has been investigated. One is higher-order Boussinesq equationsderived by Zou (1999) and the other is the classic Boussinesq equations. Physical experiments are conducted, three differ-ent front slopes (1:10, 1:5 and 1:2) of the shelf are set up in the experiment and their effects on wave propagation are in-vestigated. Comparisons of numerical results with test data are made, the model of higher-order Boussinesq equationsagrees much better with the measurements than the model of the classical Boussinesq equations. The results show thatthe higher-order Boussinesq equations can also be applied to the steeper slope case although the mild slope assumption isemployed in the derivation of the higher order terms of higher order Boussinesq equations.
Finite difference modeling of sinking stage curved beam based on revised Vlasov equations
Institute of Scientific and Technical Information of China (English)
张磊; 朱真才; 沈刚; 曹国华
2015-01-01
For the static analysis of the sinking stage curved beam, a finite difference model was presented based on the proposed revised Vlasov equations. First, revised Vlasov equations for thin-walled curved beams with closed sections were deduced considering the shear strain on the mid-surface of the cross-section. Then, the finite difference formulation of revised Vlasov equations was implemented with the parabolic interpolation based on Taylor series. At last, the finite difference model was built by substituting geometry and boundary conditions of the sinking stage curved beam into the finite difference formulation. The validity of present work is confirmed by the published literature and ANSYS simulation results. It can be concluded that revised Vlasov equations are more accurate than the original one in the analysis of thin-walled beams with closed sections, and that present finite difference model is applicable in the evaluation of the sinking stage curved beam.
A near-wall four-equation turbulence model for compressible boundary layers
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.
A new type numerical model foraction balance equation in simulating nearshore waves
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Several current used wave numerical models are briefly described, the computing techniques of the source terms, numerical wave generation and boundary conditions in the action balance equation model are discussed. Not only the quadruplet wave-wave interactions, but also the triad wave-wave interactions are included in the model, so that nearshore waves could be simulated reasonably. The model is compared with the Boussinesq equation and the mild slope equation. The model is applied to calculating the distribu-tions of wave height and wave period field in the Haian Bay area and to simulating the influences of the unsteady current and water level variation on the wave field. Finally, the de-veloping tendency of the model is discussed.
Constitutive Equation Models of Hot-Compressed T122 Heat Resistant Steel
Institute of Scientific and Technical Information of China (English)
CA0Jin-rong; LIUZheng—dong; CHENGShi—chang; YANGGang; XIEJian-xin
2012-01-01
Based on dislocation reaction theory and Avrami equation, a constitutive equation model was developed to describe dynamic recovery and dynamic recrystallization during hot deformation of T122 heat resistant steel, which have taken the effect of dynamic strain aging into account. Uniaxial hot compression test had been carried out over a wide range of strain rate （0.01 to 10 s-1 ） and temperature （900 to 1 200 ~C） with the help of Gleeble 3500. Obtained experimental data was applied to determine the material parameters in proposed constitutive equations of T122 steel, by using the non-linear least square regress optimization method. The calculated constitutive equations are quantita- tively in good agreement with experimentally measured curves and microstructure observation. It shows that propose constitutive equation T122 steel is able to be used to predict flow stress of T122 steel during hot deformation in aus- tenite temperature scope.
A Surface Tension Model for Liquid Mixtures Based on NRTL Equation
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the excess Gibbs free energy, a two-parameter surface tension equation is derived. The feasibility of the new equation has been tested in terms of 124 binary and 16 multicomponent systems(13-ternary and 3-quaternary) with absolute relative deviations of 0.59% and 1.55% respectively. This model is also predictive for the temperature dependence of surface tension of liquid mixtures. It is shown that, with good accuracy, this equation is simple and reliable for practical use.
Modelling pathways to Rubisco degradation: a structural equation network modelling approach.
Directory of Open Access Journals (Sweden)
Catherine Tétard-Jones
Full Text Available 'Omics analysis (transcriptomics, proteomics quantifies changes in gene/protein expression, providing a snapshot of changes in biochemical pathways over time. Although tools such as modelling that are needed to investigate the relationships between genes/proteins already exist, they are rarely utilised. We consider the potential for using Structural Equation Modelling to investigate protein-protein interactions in a proposed Rubisco protein degradation pathway using previously published data from 2D electrophoresis and mass spectrometry proteome analysis. These informed the development of a prior model that hypothesised a pathway of Rubisco Large Subunit and Small Subunit degradation, producing both primary and secondary degradation products. While some of the putative pathways were confirmed by the modelling approach, the model also demonstrated features that had not been originally hypothesised. We used Bayesian analysis based on Markov Chain Monte Carlo simulation to generate output statistics suggesting that the model had replicated the variation in the observed data due to protein-protein interactions. This study represents an early step in the development of approaches that seek to enable the full utilisation of information regarding the dynamics of biochemical pathways contained within proteomics data. As these approaches gain attention, they will guide the design and conduct of experiments that enable 'Omics modelling to become a common place practice within molecular biology.
Wen, Zhonglin; Marsh, Herbert W.; Hau, Kit-Tai
2010-01-01
Standardized parameter estimates are routinely used to summarize the results of multiple regression models of manifest variables and structural equation models of latent variables, because they facilitate interpretation. Although the typical standardization of interaction terms is not appropriate for multiple regression models, straightforward…
The efficient global primitive equation climate model SPEEDO V2.0
Severijns, C.A.; Hazeleger, W.
2010-01-01
The efficient primitive-equation coupled atmosphere-ocean model SPEEDO V2.0 is presented. The model includes an interactive sea-ice and land component. SPEEDO is a global earth system model of intermediate complexity. It has a horizontal resolution of T30 (triangular truncation at wave number 30) an
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…
The efficient global primitive equation climate model SPEEDO V2.0
Severijns, C.A.; Hazeleger, W.
2010-01-01
The efficient primitive-equation coupled atmosphere-ocean model SPEEDO V2.0 is presented. The model includes an interactive sea-ice and land component. SPEEDO is a global earth system model of intermediate complexity. It has a horizontal resolution of T30 (triangular truncation at wave number 30) an
Women's Path into Science and Engineering Majors: A Structural Equation Model
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…
A new differential equations-based model for nonlinear history-dependent magnetic behaviour
Aktaa, J
2000-01-01
The paper presents a new kind of numerical model describing nonlinear magnetic behaviour. The model is formulated as a set of differential equations taking into account history dependence phenomena like the magnetisation hysteresis as well as saturation effects. The capability of the model is demonstrated carrying out comparisons between measurements and calculations.
Wireless Fading Channel Models: From Classical to Stochastic Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Olama, Mohammed M [ORNL; Djouadi, Seddik M [ORNL; Charalambous, Prof. Charalambos [University of Cyprus
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
A Boussinesq Equation-Based Model for Nearshore Wave Breaking
Institute of Scientific and Technical Information of China (English)
余建星; 张伟; 王广东; 杨树清
2004-01-01
Based on the wave breaking model by Li and Wang (1999), this work is to apply Dally' s analytical solution to the wave-height decay irstead of the empirical and semi-empirical hypotheses of wave-height distribution within the wave breaking zone. This enhances the applicability of the model. Computational results of shoaling, location of wave breaking, wave-height decay after wave breaking, set-down and set-up for incident regular waves are shown to have good agreement with experimental and field data.
Differential Equations Related to the Williams-Bjerknes Tumour Model
Indian Academy of Sciences (India)
F Martinez; A R Villena
2000-08-01
We investigate an initial value problem which is closely related to the Williams-Bjerknes tumour model for a cancer which spreads through an epithelial basal layer modeled on ⊂ 2. The solution of this problem is a family =(()), where each () could be considered as an approximation to the probability that the cell situated at is cancerous at time . We prove that this problem has a unique solution, it is defined on [0, + ∞], and, for some relevant situations, lim → ∞ ()=1 for all ∈ . Moreover, we study the expected number of cancerous cells at time .
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.
A Structural Equation Model for ICT Usage in Higher Education
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…
Highly covariant quantum lattice gas model of the Dirac equation
Yepez, Jeffrey
2011-01-01
We revisit the quantum lattice gas model of a spinor quantum field theory-the smallest scale particle dynamics is partitioned into unitary collide and stream operations. The construction is covariant (on all scales down to a small length {\\ell} and small time {\\tau} = c {\\ell}) with respect to Lorentz transformations. The mass m and momentum p of the modeled Dirac particle depend on {\\ell} according to newfound relations m = mo cos (2{\\pi}{\\ell}/{\\lambda}) and p = (h/2{\\pi}{\\ell}) sin(2{\\pi}{\\ell}/{\\lambda}), respectively, where {\\lambda} is the Compton wavelength of the modeled particle. These relations represent departures from a relativistically invariant mass and the de Broglie relation-when taken as quantifying numerical errors the model is physically accurate when {\\ell} {\\ll} {\\lambda}. Calculating the vacuum energy in the special case of a massless spinor field, we find that it vanishes (or can have a small positive value) for a sufficiently large wave number cutoff. This is a marked departure from th...
Relation Between Chiral Susceptibility and Solutions of Gap Equation in Nambu--Jona-Lasinio Model
Zhao, Y; Liu, Y; Yuan, W; Chang, Lei; Liu, Yu-xin; Yuan, Wei; Zhao, Yue
2006-01-01
We study the solutions of the gap equation, the thermodynamic potential and the chiral susceptibility in and beyond the chiral limit at finite chemical potential in the Nambu--Jona-Lasinio (NJL) model. We give an explicit relation between the chiral susceptibility and the thermodynamic potential in the NJL model. We find that the chiral susceptibility is a quantity being able to represent the furcation of the solutions of the gap equation and the concavo-convexity of the thermodynamic potential in NJL model. It indicates that the chiral susceptibility can identify the stable state and the possibility of the chiral phase transition in NJL model.
An H Theorem for Boltzmann's Equation for the Yard-Sale Model of Asset Exchange
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.
DEFF Research Database (Denmark)
Jørgensen, Bo Hoffmann
2003-01-01
by Ayotte and Taylor (1995) and in the work of Beljaars et al. (1987). Unlike the previous models, the present work uses general orthogonal coordinates. Strong conservation form of the model equations is employedto allow a robust and consistent numerical procedure. An invariant tensor form of the model...... equations is utilized expressing the flow variables in a transformed coordinate system in which they are horizontally homogeneous. The model utilizes the k - emodel with limited mixing length by Apsley and Castro (1997). This turbulence closure reflects the fact that the atmosphere is only neutral up...
An Improved Nearshore Wave Breaking Model Based on the Fully Nonlinear Boussinesq Equations
Institute of Scientific and Technical Information of China (English)
LI Shao-wu; LI Chun-ying; SHI Zhong; GU Han-bin
2005-01-01
This paper aims to propose an improved numerical model for wave breaking in the nearshore region based on the fully nonlinear form of Boussinesq equations. The model uses the κ equation turbulence scheme to determine the eddy viscosity in the Boussinesq equations. To calculate the turbulence production term in the equation, a new formula is derived based on the concept of surface roller. By use of this formula, the turbulence production in the one-equation turbulence scheme is directly related to the difference between the water particle velocity and the wave celerity. The model is verified by Hansen and Svendsen's experimental data (1979) in terms of wave height and setup and setdown. The comparison between the model and experimental results of wave height and setup and setdown shows satisfactory agreement. The modeled turbulence energy decreases as waves attenuate in the surf zone. The modeled production term peaks at the breaking point and decreases as waves propagate shoreward. It is also suggested that both convection and diffusion play their important roles in the transport of turbulence energy immediately after wave breaking. When waves approach to the shoreline, the production and dissipation of turbulence energy are almost balanced. By use of the slot technique for the simulation of the movable shoreline boundary, wave runup in the swash zone is well simulated by the present model.
Numerical integration of the master equation in some models of stochastic epidemiology.
Directory of Open Access Journals (Sweden)
Garrett Jenkinson
Full Text Available 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.
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.
Is it appropriate to model turbidity currents with the three-equation model?
Hu, Peng; Pähtz, Thomas; He, Zhiguo
2015-07-01
The three-equation model (TEM) was developed in the 1980s to model turbidity currents (TCs) and has been widely used ever since. However, its physical justification was questioned because self-accelerating TCs simulated with the steady TEM seemed to violate the turbulent kinetic energy balance. This violation was considered as a result of very strong sediment erosion that consumes more turbulent kinetic energy than is produced. To confine bed erosion and thus remedy this issue, the four-equation model (FEM) was introduced by assuming a proportionality between the bed shear stress and the turbulent kinetic energy. Here we analytically proof that self-accelerating TCs simulated with the original steady TEM actually never violate the turbulent kinetic energy balance, provided that the bed drag coefficient is not unrealistically low. We find that stronger bed erosion, surprisingly, leads to more production of turbulent kinetic energy due to conversion of potential energy of eroded material into kinetic energy of the current. Furthermore, we analytically show that, for asymptotically supercritical flow conditions, the original steady TEM always produces self-accelerating TCs if the upstream boundary conditions ("ignition" values) are chosen appropriately, while it never does so for asymptotically subcritical flow conditions. We numerically show that our novel method to obtain the ignition values even works for Richardson numbers very near to unity. Our study also includes a comparison of the TEM and FEM closures for the bed shear stress to simulation data of a coupled Large Eddy and Discrete Element Model of sediment transport in water, which suggests that the TEM closure might be more realistic than the FEM closure.
SNSequate: Standard and Nonstandard Statistical Models and Methods for Test Equating
Directory of Open Access Journals (Sweden)
Jorge González
2014-09-01
Full Text Available Equating is a family of statistical models and methods that are used to adjust scores on two or more versions of a test, so that the scores from different tests may be used interchangeably. In this paper we present the R package SNSequate which implements both standard and nonstandard statistical models and methods for test equating. The package construction was motivated by the need of having a modular, simple, yet comprehensive, and general software that carries out traditional and new equating methods. SNSequate currently implements the traditional mean, linear and equipercentile equating methods, as well as the mean-mean, mean-sigma, Haebara and Stocking-Lord item response theory linking methods. It also supports the newest methods such as local equating, kernel equating, and item response theory parameter linking methods based on asymmetric item characteristic functions. Practical examples are given to illustrate the capabilities of the software. A list of other programs for equating is presented, highlighting the main differences between them. Future directions for the package are also discussed.
Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
Wulff, L
2016-01-01
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 \\phi (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=\\d_a \\phi and thus obtains the standard type II supergravity equat...
Quality of peas modelled by a structural equation system
DEFF Research Database (Denmark)
Bech, Anne C.; Juhl, Hans Jørn; Martens, Magni
2000-01-01
The quality of peas has been studied in a joint project between a pea producing company in Denmark and several research institutions. The study included quality from a consumer point of view based on market research and quality from more internal company points of view based on measurement...... in a PLS structural model with the Total Food Quality Model as starting point. The results show that texture and flavour do have approximately the same effect on consumers' perception of overall quality. Quality development goals for plant breeders would be to optimse perceived flavour directly...... by increasing the amount of sugars and more indirectly by improving the perception of colour through darker and less yellow peas. Perceived texture can be optimised by focusing on selected texture measurements. Udgivelsesdato: JUL...
Quality of peas modelled by a structural equation system
DEFF Research Database (Denmark)
Bech, Anne C.; Juhl, Hans Jørn; Martens, Magni
2000-01-01
The quality of peas has been studied in a joint project between a pea producing company in Denmark and several research institutions. The study included quality from a consumer point of view based on market research and quality from more internal company points of view based on measurement...... expressed by consumers as a function of the objective measurements of quality, eg the physical/chemical variables? (3) Which of the measured objective variables are most important for further product development? In the paper we describe consumer evaluations as a function of physical/chemical variables...... in a PLS structural model with the Total Food Quality Model as starting point. The results show that texture and flavour do have approximately the same effect on consumers' perception of overall quality. Quality development goals for plant breeders would be to optimse perceived flavour directly...
Eikonal solutions to optical model coupled-channel equations
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.
Integrodifferential equations and delay models in population dynamics
Cushing, Jim M
1977-01-01
These notes are, for the most part, the result of a course I taught at the University of Arizona during the Spring of 1977. Their main purpose is to inves tigate the effect that delays (of Volterra integral type) have when placed in the differential models of mathematical ecology, as far as stability of equilibria and the nature of oscillations of species densities are concerned. A secondary pur pose of the course out of which they evolved was to give students an (at least elementary) introduction to some mathematical modeling in ecology as well as to some purely mathematical subjects, such as stability theory for integrodifferentia1 systems, bifurcation theory, and some simple topics in perturbation theory. The choice of topics of course reflects my personal interests; and while these notes were not meant to exhaust the topics covered, I think they and the list of refer ences come close to covering the literature to date, as far as integrodifferentia1 models in ecology are concerned. I would like to th...
A new approach to model CW CO$_2$ laser using rate equations
Indian Academy of Sciences (India)
UTPAL NUNDY; SUNIL DAGA; MANOJ KUMAR
2016-12-01
Two popular methods to analyse the operation of CW CO$_2$ lasers use the temperature model and the rate equation model. Among the two, the latter model directly calculates the population densities in the various vibrational levels connected with the lasing action, and provides a clearer illustration of the processes involved. Rate equation models used earlier grouped a number of vibration levels together, on the basis of normal modes of vibrations of CO$_2$. However, such grouping has an inherent disadvantage as it requires that theselevels be in thermal equilibrium. Here we report a new approach for modelling CW CO$_2$ lasers wherein the relevant vibration levels are identified and independently treated. They are connected with each other through theprocesses of excitation, relaxation and radiative transitions. We use the universally accepted rate coefficients to describe these processes. The other distinguishing feature of our model is the methodology adopted for carryingout the calculations. For instance, the CW case being a steady state, all the rate equations are thus equated to zero. In the prior works, researchers derived analytical expressions for the vibration level population densities, thatbecomes quite a tedious task with increasing number of levels. Grouping of the vibration levels helped in restricting the number of equations and this facilitated the derivation of these analytical expressions. We show that insteady state, these rate equations form a set of linear algebric equations. Instead of deriving analytical expressions, these can be elegantly solved using the matrix method. The population inversion calculated in this manner alongwith the relaxation rate of the upper laser level determines the output power of the laser. We have applied the model to an experimental CW laser reported in literature. Our results match the experimentally reported power.
Energy Technology Data Exchange (ETDEWEB)
Besnard, D. (Los Alamos National Lab., NM (United States) CEA Centre d' Etudes de Limeil, 94 - Villeneuve-Saint-Georges (France)); Harlow, F.H.; Rauenzahn, R.M.; Zemach, C. (Los Alamos National Lab., NM (United States))
1992-06-01
This study gives an updated account of our current ability to describe multimaterial compressible turbulent flows by means of a one-point transport model. Evolution equations are developed for a number of second-order correlations of turbulent data, and approximations of the gradient type are applied to additional correlations to close the system of equations. The principal fields of interest are the one- point Reynolds tensor for variable-density flow, the turbulent energy dissipation rate, and correlations for density-velocity and density- density fluctuations. This single-field description of turbulent flows is compared in some detail to two-field flow equations for nonturbulent, highly dispersed flow with separate variables for each field. This comparison suggests means for improved modeling of some correlations not subjected to evolution equations.
Modelling with the master equation solution methods and applications in social and natural sciences
Haag, Günter
2017-01-01
This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples. Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences. The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author’s extensive teaching and research experience...
An Equation of State for Fluids by Applying the Tower—Well Potential Model
Institute of Scientific and Technical Information of China (English)
ZengXiangdong; ShangDemin; 等
1994-01-01
A simple theoretical equation of state is derived by applying the Tower-well potential model about the molecular distribution based on the generalized van der Waals partition function.It needs only three molecular parameters which have distince physical meanings,The resulting equation of state predicts rapther well the vapor pressures,saturated liquid volumes,saturated vapor volumes and PVT thermodynamic properties of polar and structureally complex molecules over a wide temperature and pressure range.
The Wheeler-DeWitt Equation in Filćhenkov Model: The Lie Algebraic Approach
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.
The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation
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.
A Generic Length-scale Equation For Second-order Turbulence Models of Oceanic Boundary Layers
Umlauf, L.; Burchard, H.
A generic transport equation for a generalized length-scale in second-order turbulence closure models for geophysical boundary layers is suggested. This variable consists of the products of powers of the turbulent kinetic energy, k, and the integral length-scale, l. The new approach generalizes traditional second-order models used in geophysical boundary layer modelling, e.g. the Mellor-Yamada model and the k- model, which, however, can be recovered as special cases. It is demonstrated how this new model can be calibrated with measurements in some typical geophysical boundary layer flows. As an example, the generic model is applied to the uppermost oceanic boundary layer directly influenced by the effects of breaking surface waves. Recent measurements show that in this layer the classical law of the wall is invalid, since there turbulence is dominated by turbulent transport of TKE from above, and not by shear-production. A widely accepted approach to describe the wave-affected layer with a one-equation turbulence model was suggested by Craig and Banner (1994). Here, some deficien- cies of their solutions are pointed out and a generalization of their ideas for the case of two-equation models is suggested. Direct comparison with very recently obtained measurements of the dissipation rate, , in the wave-affected boundary layer with com- puted results clearly demonstrate that only the generic two-equation model yields cor- rect predictions for the profiles of and the turbulent length scale, l. Also, the pre- dicted velocity profiles in the wave-affected layer, important e.g. for the interpretation of surface drifter experiments, are reproduced correctly only by the generic model. Implementation and computational costs of the generic model are comparable with traditonal two-equation models.
A near-wall two-equation model for compressible turbulent flows
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.
Modeling Sodium Iodide Detector Response Using Parametric Equations
2013-03-22
and the source are kept in a constant geometry using a thin wooden plank . Both are moved back as a unit in 10 cm increments...using a thin wooden plank . Both are moved back as a unit in 10 cm increments. Similar to the MCNP model, the source and detector remained in a...simulated particles Error % Max Backscatter 0 9.29E‐04 1% 100% 10 3.86E‐04 2% 42% 20 1.98E‐04 2% 21% 30 1.16E‐04 3% 13% 40 8.01E
Gaseous microflow modeling using the Fokker-Planck equation
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.
Energy Technology Data Exchange (ETDEWEB)
Rupšys, P. [Aleksandras Stulginskis University, Studenų g. 11, Akademija, Kaunas district, LT – 53361 Lithuania (Lithuania)
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.
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.
Causal Analysis of Religious Violence, a Structural Equation Modeling Approach
Directory of Open Access Journals (Sweden)
M Munajat
2015-12-01
[Penelitian ini berusaha mengkaji sebab kekerasan keagamaan dengan menggunakan pendekatan Model Persamaan Struktur (SEM. Penelitian kuantitatif terdahulu dalam bidang gerakan sosial dan kekerasan politik menunjukkan bahwa setidaknya ada tiga faktor yang diduga kuat menjadi penyebab kekerasan kolektif, seperti kekerasan agama, yaitu: 1 semakin fundamentalis seseorang, maka ia akan semakin cenderung menyetujui pernggunaan cara kekerasan, 2 semakin rendah kepercayaan seseorang terhadap pemerintah, maka ia akan semakin menyetujui penggunaan kekerasan, 3 berbeda dengan pendapat ke-dua, hanya orang yang rendah kepercayaanya kepada pemerintah, namun mempunyai semangat politik tinggi, yang akan menyetujui penggunaan cara-cara kekerasan. Berdasarkan pada data yang diambil dari 343 responden dari para aktivis, Front Pembela Islam, Muhammadiyah dan Nahdlatul Ulama, penelitian ini mengkonfirmasi bahwa semakin fundamentalis seseorang, maka ia akan semakin cenderung menyetujui kekerasan, terlepas dari afiliasi organisasi mereka. Namun demikian, penelitian ini tidak mendukung hubungan antara kepercayaan terhadap pemerintah dan kekerasan. Demikian juga, hubungan antara kekerasan dan interaksi antara kepercayaan pemerintah dan semangat politik tidak dapat dibuktikan dari data dalam penelitian ini. Oleh karena itu, penelitian ini menyimpulkan bahwa fundamentalisme, sebagai salah satu bentuk keagamaan, merupakan faktor yang sangat penting dalam menjelaskan kekerasan keagamaan.
Noise Modeling From Conductive Shields Using Kirchhoff Equations.
Sandin, Henrik J; Volegov, Petr L; Espy, Michelle A; Matlashov, Andrei N; Savukov, Igor M; Schultz, Larry J
2010-10-01
Progress in the development of high-sensitivity magnetic-field measurements has stimulated interest in understanding the magnetic noise of conductive materials, especially of magnetic shields 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 radio frequency 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 with complex shield geometries. With complex sensor arrays used in, for example, MEG and Ultra Low Field MRI studies, knowledge of the noise correlation between sensors is as important as 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 arbitrary shaped shields and multiple sensor systems. The approach is efficient enough to be able to run on a single PC system and return results on a minute scale. With a multiple sensor system our approach calculates not only the noise for each sensor but also the noise correlation matrix between sensors. Here we will show how the algorithm can be implemented.
Prescriptive Statements and Educational Practice: What Can Structural Equation Modeling (SEM) Offer?
Martin, Andrew J.
2011-01-01
Longitudinal structural equation modeling (SEM) can be a basis for making prescriptive statements on educational practice and offers yields over "traditional" statistical techniques under the general linear model. The extent to which prescriptive statements can be made will rely on the appropriate accommodation of key elements of research design,…
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…
Vertical Equating: An Empirical Study of the Consistency of Thurstone and Rasch Model Approaches.
Schratz, Mary K.
To explore the appropriateness of the Rasch model for the vertical equating of a multi-level, multi-form achievement test series, both the Rasch model and the traditional Thurstone procedures were applied to the Listening Comprehension subtest scores of the Stanford Achievement Test. Two adjacent levels of these tests were administered in 1981 to…
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...
Dijkstra, T.K.; Henseler, J.
2011-01-01
The recent advent of nonlinear structural equation models with indices poses a new challenge to the measurement of scientific constructs. We discuss, exemplify and add to a family of statistical methods aimed at creating linear indices, and compare their suitability in a complex path model with line
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…
Baldwin, Beatrice
LISREL-type structural equation modeling is a powerful statistical technique that seems appropriate for social science variables which are complex and difficult to measure. The literature on the specification, estimation, and testing of such models is voluminous. The greatest proportion of this literature, however, focuses on the technical aspects…
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Directory of Open Access Journals (Sweden)
Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
A Demonstration of a Systematic Item-Reduction Approach Using Structural Equation Modeling
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…
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…
Matrix Solution of Coupled Differential Equations and Looped Car Following Models
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…
Maximum Likelihood Analysis of a Two-Level Nonlinear Structural Equation Model with Fixed Covariates
Lee, Sik-Yum; Song, Xin-Yuan
2005-01-01
In this article, a maximum likelihood (ML) approach for analyzing a rather general two-level structural equation model is developed for hierarchically structured data that are very common in educational and/or behavioral research. The proposed two-level model can accommodate nonlinear causal relations among latent variables as well as effects…
Standards-Based Evaluation and Teacher Career Satisfaction: A Structural Equation Modeling Analysis
Conley, Sharon; Muncey, Donna E.; You, Sukkyung
2005-01-01
Structural equation modeling was used to assess the plausibility of a conceptual model specifying hypothesized linkages among perceptions of characteristics of standards-based evaluation, work environment mediators, and career satisfaction and other outcomes. Four comprehensive high schools located in two neighboring counties in southern…
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…
Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data
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…
An iterative construction of solutions of the TAP equations for the Sherrington-Kirkpatrick model
Bolthausen, Erwin
2012-01-01
We propose an iterative construction of solutions of the Thouless-Anderson-Palmer-equations for the Sherrington-Kirpatrick model. The iterative scheme is proved to converge exactly up to the de Almayda-Thouless-line. No results on the SK-model itself are derived.
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…
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.
Algebraic Stress Model with RNG ε-Equation for Simulating Confined Strongly Swirling Turbulent Flows
Institute of Scientific and Technical Information of China (English)
Xu Jiangrong; Yao Qiang; Cao Xingyu; Cen Kefa
2001-01-01
Strongly swirl flow simulation are still under developing. In this paper, ε equation based on the Renormalization Group theory is used into algebraic stress model. Standard k-ε model, algebraic stress model by Jiang Zhang[5]and present model (RNG-ASM) are applied simultaneously to simulating the confined strongly swirling flow.The Simulating results by RNG-ASM model are compared to the results by other two model, it is shown that the predictions by this model display reasonable agreement with experimental data, and lead to greater improvement than Zhang's ASM turbulence model[5].
2015-01-01
Objectives The aim of this study was to examine the relationships among maternal and infant characteristics, breastfeeding techniques, and exclusive breastfeeding initiation in different modes of birth using structural equation modeling approaches. Methods We examined a hypothetical model based on integrating concepts of a breastfeeding decision-making model, a breastfeeding initiation model, and a social cognitive theory among 952 mother-infant dyads. The LATCH breastfeeding assessment tool ...
Chen, Yongpin P; Jiang, Li Jun; Meng, Min; Wu, Yu Mao; Chew, Weng Cho
2016-01-01
A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum mechanics, a unified Maxwell-Schrodinger system is derived by the variational principle. The coupled system is well-posed and symplectic, which ensures energy conserving property during the time evolution. However, due to the disparity of wavelengths of EM waves and that of electron waves, a numerical implementation of the finite-difference time-domain (FDTD) method to the multiscale coupled system is extremely challenging. To overcome this difficulty, a reduced eigenmode expansion technique is first applied to represent the wave function of the particle. Then, a set of ordinary differential equations (ODEs) governing the time evolution of the slowly-varying expansion coefficients are derived to replace the original Schrodinger equation. Finally, Maxwell's equations represented b...
Contribution to modeling the viscosity Arrhenius-type equation for saturated pure fluids
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.
Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model
Directory of Open Access Journals (Sweden)
Nikola V. Georgiev
2003-01-01
Full Text Available An analytic time series in the form of numerical solution (in an appropriate finite time interval of the Hodgkin-Huxley current clamped (HHCC system of four differential equations, well known in the neurophysiology as an exact empirical model of excitation of a giant axon of Loligo, is presented. Then we search for a second-order differential equation of generalized Fitzhugh-Nagumo (GFN type, having as a solution the given single component (action potential of the numerical solution. The given time series is used as a basis for reconstructing orders, powers, and coefficients of the polynomial right-hand sides of GFN equation approximately governing the process of action potential. For this purpose, a new geometrical method for determining phase space dimension of the unknown dynamical system (GFN equation and a specific modification of least squares method for identifying unknown coefficients are developed and applied.
The time-dependent Ginzburg-Landau equation for the two-velocity difference model
Institute of Scientific and Technical Information of China (English)
Wu Shu-zhen; Cheng Rong-Jun; Ge Hong-xia
2011-01-01
A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow.Based on the two-velocity difference model,the time-dependent Ginzburg-Landau(TDGL)equation under certain condition is derived to describe the traffic flow near the critical point through the nonlinear analytical method.The corresponding two solutions,the uniform and the kink solutions,are given.The coexisting curve,spinodal line and critical point are obtained by the first and second derivatives of the thermodynamic potential.The modified Kortewegde Vries(mKdV)equation around the critical point is derived by using the reductive perturbation method and its kink-antikink solution is also obtained.The relation between the TDGL equation and the mKdV equation is shown.The simulation result is consistent with the nonlinear analytical result.
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. [1] 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.
A Multi-Fidelity Surrogate Model for Handling Real Gas Equations of State
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.
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.
Equations and their physical interpretation in numerical modeling of heavy metals in fluvial rivers
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on the previous work on the transport-transformation of heavy metal pollutants in fluvial rivers, this paper presented the formulation of a two-dimensional model to describe heavy metal transport-transformation in fluvial rivers by considering basic principles of environmental chemistry, hydraulics, mechanics of sediment transport and recent developments along with three very simplified test cases. The model consists of water flow governing equations, sediment transport governing equations, transport-transformation equation of heavy metal pollutants, and convection-diffusion equations of adsorption-desorption kinetics of particulate heavy metal concentrations on suspended load, bed load and bed sediment. The heavy metal transport-transformation equation is basically a mass balance equation, which demonstrates how sediment transport affects transport-transformation of heavy metals in fluvial rivers. The convection-diffusion equations of adsorption-desorption kinetics of heavy metals, being an extension of batch reactor experimental results and a major advancement of the previous work, take both physical transport, i.e. convection and diffusion and chemical reactions, i.e. adsorption-desorption into account. Effects of sediment transport on heavy metal transport-transformation were clarified through three examples. Specifically, the transport-transformation of heavy metals in a steady, uniform and equilibrium sediment-laden flow was calculated by applying this model, and results were shown to be rational. Both theoretical analysis and numerical simulation indicated that the transport-transformation of heavy metals in sediment-laden flows with clay-enriched riverbed possesses not only the generality of common tracer pollutants, but also characteristics of transport-transformation induced by sediment motion. Future work will be conducted to present validation/application of the model with available data.
Spiral-defect chaos: Swift-Hohenberg model versus Boussinesq equations.
Schmitz, Rainer; Pesch, Werner; Zimmermann, Walter
2002-03-01
Spiral-defect chaos (SDC) in Rayleigh-Bénard convection is a well-established spatio-temporal complex pattern, which competes with stationary rolls near the onset of convection. The characteristic properties of SDC are accurately described on the basis of the standard three-dimensional Boussinesq equations. As a much simpler and attractive two-dimensional model for SDC generalized Swift-Hohenberg (SH) equations have been extensively used in the literature from the early beginning. Here, we show that the description of SDC by SH models has to be considered with care, especially regarding its long-time dynamics. For parameters used in previous SH simulations, SDC occurs only as a transient in contrast to the experiments and the rigorous solutions of the Boussinesq equations. The small-scale structure of the vorticity field at the spiral cores, which might be crucial for persistent SDC, is presumably not perfectly captured in the SH model.
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.
The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
Energy Technology Data Exchange (ETDEWEB)
Gurau, Razvan, E-mail: rgurau@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, ON N2L 2Y5, Waterloo (Canada)
2012-12-01
Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D-ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.
Solution of the 5D Einstein equations in a dilaton background model
de Paula, W; Forkel, H; Beyer, M
2008-01-01
We obtain an explicit solution of the 5d Einstein equations in a dilaton background model. We demonstrate that for each metric ansatz that only depends on the extra coordinate, it is possible to uniquely determine the dilaton field and its potential consistently with the 5d Einstein equation. In this holographic dual model of QCD, conformal symmetry of the Anti-de-Sitter metric near the 4d boundary is broken by a term that leads to an area law for the Wilson loop. We verify that confinement of the string modes dual to mesons follows from the metric background and the corresponding dilaton solution of the gravity-dilaton coupled equations. In addition, we show that the meson Regge trajectories constrain the metric and corresponding dilaton background within the area law requirement. We can also incorporate asymptotic freedom in the gravity background within the model.
A simple and accurate model for Love wave based sensors: Dispersion equation and mass sensitivity
Directory of Open Access Journals (Sweden)
Jiansheng Liu
2014-07-01
Full Text Available Dispersion equation is an important tool for analyzing propagation properties of acoustic waves in layered structures. For Love wave (LW sensors, the dispersion equation with an isotropic-considered substrate is too rough to get accurate solutions; the full dispersion equation with a piezoelectric-considered substrate is too complicated to get simple and practical expressions for optimizing LW-based sensors. In this work, a dispersion equation is introduced for Love waves in a layered structure with an anisotropic-considered substrate and an isotropic guiding layer; an intuitive expression for mass sensitivity is also derived based on the dispersion equation. The new equations are in simple forms similar to the previously reported simplified model with an isotropic substrate. By introducing the Maxwell-Weichert model, these equations are also applicable to the LW device incorporating a viscoelastic guiding layer; the mass velocity sensitivity and the mass propagation loss sensitivity are obtained from the real part and the imaginary part of the complex mass sensitivity, respectively. With Love waves in an elastic SiO2 layer on an ST-90°X quartz structure, for example, comparisons are carried out between the velocities and normalized sensitivities calculated by using different dispersion equations and corresponding mass sensitivities. Numerical results of the method presented in this work are very close to those of the method with a piezoelectric-considered substrate. Another numerical calculation is carried out for the case of a LW sensor with a viscoelastic guiding layer. If the viscosity of the layer is not too big, the effect on the real part of the velocity and the mass velocity sensitivity is relatively small; the propagation loss and the mass loss sensitivity are proportional to the viscosity of the guiding layer.
Directory of Open Access Journals (Sweden)
Hashem Salarzadeh Jenatabadi
2016-11-01
Full Text Available There are many factors which could influence the sustainability of airlines. The main purpose of this study is to introduce a framework for a financial sustainability index and model it based on structural equation modeling (SEM with maximum likelihood and Bayesian predictors. The introduced framework includes economic performance, operational performance, cost performance, and financial performance. Based on both Bayesian SEM (Bayesian-SEM and Classical SEM (Classical-SEM, it was found that economic performance with both operational performance and cost performance are significantly related to the financial performance index. The four mathematical indices employed are root mean square error, coefficient of determination, mean absolute error, and mean absolute percentage error to compare the efficiency of Bayesian-SEM and Classical-SEM in predicting the airline financial performance. The outputs confirmed that the framework with Bayesian prediction delivered a good fit with the data, although the framework predicted with a Classical-SEM approach did not prepare a well-fitting model. The reasons for this discrepancy between Classical and Bayesian predictions, as well as the potential advantages and caveats with the application of Bayesian approach in airline sustainability studies, are debated.
Structural equation models for meta-analysis in environmental risk assessment
DEFF Research Database (Denmark)
Budtz-Jørgensen, Esben; Debes, Frodi; Weihe, Pal;
2010-01-01
The potential of structural equation models for combining information from different studies in environmental epidemiology is explored. For illustration we synthesize data from two birth cohorts assessing the effects of prenatal exposure to methylmercury on childhood cognitive performance. One...... cohort was the largest by far, but a smaller cohort included superior assessment of the PCB exposure which has been considered an important confounder when estimating the mercury effect. The data were analyzed by specification of a structural equation model for each cohort. Information was then pooled...
Lee, Sik-Yum
2012-01-01
This book provides clear instructions to researchers on how to apply Structural Equation Models (SEMs) for analyzing the inter relationships between observed and latent variables. Basic and Advanced Bayesian Structural Equation Modeling introduces basic and advanced SEMs for analyzing various kinds of complex data, such as ordered and unordered categorical data, multilevel data, mixture data, longitudinal data, highly non-normal data, as well as some of their combinations. In addition, Bayesian semiparametric SEMs to capture the true distribution of explanatory latent variables are introduce
Strange matter equation of state in the quark mass-density-dependent model
Energy Technology Data Exchange (ETDEWEB)
Benvenuto, O.G. (Facultad de Ciencias Astronomicas y Geofisicas, Universidad Nacional de La Plata, Paseo del Bosque S/N, 1900 La Plata (Argentina)); Lugones, G. (Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata (Argentina))
1995-02-15
We study the properties and stability of strange matter at [ital T]=0 in the quark mass-density-dependent model for noninteracting quarks. We found a wide stability window'' for the values of the parameters ([ital C],[ital M][sub [ital s]0]) and the resulting equation of state at low densities is stiffer than that of the MIT bag model. At high densities it tends to the ultrarelativistic behavior expected because of the asymptotic freedom of quarks. The density of zero pressure is near the one predicted by the bag model and [ital not] shifted away as stated before; nevertheless, at these densities the velocity of sound is [approx]50% larger in this model than in the bag model. We have integrated the equations of stellar structure for strange stars with the present equation of state. We found that the mass-radius relation is very much the same as in the bag model, although it extends to more massive objects, due to the stiffening of the equation of state at low densities.
A new LES model derived from generalized Navier-Stokes equations with nonlinear viscosity
Rodríguez, José M
2015-01-01
Large Eddy Simulation (LES) is a very useful tool when simulating turbulent flows if we are only interested in its "larger" scales. One of the possible ways to derive the LES equations is to apply a filter operator to the Navier-Stokes equations, obtaining a new equation governing the behavior of the filtered velocity. This approach introduces in the equations the so called subgrid-scale tensor, that must be expressed in terms of the filtered velocity to close the problem. One of the most popular models is that proposed by Smagorinsky, where the subgrid-scale tensor is modeled by introducing an eddy viscosity. In this work, we shall propose a new approximation to this problem by applying the filter, not to the Navier-Stokes equations, but to a generalized version of them with nonlinear viscosity. That is, we shall introduce a nonlinear viscosity, not as a procedure to close the subgrid-scale tensor, but as part of the model itself (see below). Consequently, we shall need a different method to close the subgri...
Ginzburg-Landau equation as a heuristic model for generating rogue waves
Lechuga, Antonio
2016-04-01
Envelope equations have many applications in the study of physical systems. Particularly interesting is the case 0f surface water waves. In steady conditions, laboratory experiments are carried out for multiple purposes either for researches or for practical problems. In both cases envelope equations are useful for understanding qualitative and quantitative results. The Ginzburg-Landau equation provides an excellent model for systems of that kind with remarkable patterns. Taking into account the above paragraph the main aim of our work is to generate waves in a water tank with almost a symmetric spectrum according to Akhmediev (2011) and thus, to produce a succession of rogue waves. The envelope of these waves gives us some patterns whose model is a type of Ginzburg-Landau equation, Danilov et al (1988). From a heuristic point of view the link between the experiment and the model is achieved. Further, the next step consists of changing generating parameters on the water tank and also the coefficients of the Ginzburg-Landau equation, Lechuga (2013) in order to reach a sufficient good approach.
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.
a Radiative Transfer Equation/phase Function Approach to Vegetation Canopy Reflectance Modeling
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
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…
Investigating market efficiency through a forecasting model based on differential equations
de Resende, Charlene C.; Pereira, Adriano C. M.; Cardoso, Rodrigo T. N.; de Magalhães, A. R. Bosco
2017-05-01
A new differential equation based model for stock price trend forecast is proposed as a tool to investigate efficiency in an emerging market. Its predictive power showed statistically to be higher than the one of a completely random model, signaling towards the presence of arbitrage opportunities. Conditions for accuracy to be enhanced are investigated, and application of the model as part of a trading strategy is discussed.
Modeling of the subgrid-scale term of the filtered magnetic field transport equation
Balarac, Guillaume; Kosovichev, Alexander; Brugière, Olivier; Wray, Alan; Mansour, Nagi
2010-01-01
Accurate subgrid-scale turbulence models are needed to perform realistic numerical magnetohydrodynamic (MHD) simulations of the subsurface flows of the Sun. To perform large-eddy simulations (LES) of turbulent MHD flows, three unknown terms have to be modeled. As a first step, this work proposes to use a priori tests to measure the accuracy of various models proposed to predict the SGS term appearing in the transport equation of the filtered magnetic field. It is proposed to evaluate the SGS ...
Kershaw closures for linear transport equations in slab geometry I: Model derivation
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.
KdV-Burgers equation in the modified continuum model considering anticipation effect
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.
Characteristics of quantum dash laser under the rate equation model framework
Khan, Mohammed Zahed Mustafa
2010-09-01
The authors present a numerical model to study the carrier dynamics of InAs/InP quantum dash (QDash) lasers. The model is based on single-state rate equations, which incorporates both, the homogeneous and the inhomogeneous broadening of lasing spectra. The numerical technique also considers the unique features of the QDash gain medium. This model has been applied successfully to analyze the laser spectra of QDash laser. ©2010 IEEE.
Measurement of the Equation of State of the Two-Dimensional Hubbard Model
Miller, Luke; Cocchi, Eugenio; Drewes, Jan; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Koehl, Michael
2016-05-01
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 constitute benchmarks for state-of-the-art theoretical approaches.
Institute of Scientific and Technical Information of China (English)
XU JingBo; ZOU XuBo; GAO XiaoChun; FU Jian
2002-01-01
By making use of the dynamical algebraic approach, we study the two-mode Raman coupled model governed by the Milburn equation and find the exact solution of the Milburn equation without diffusion approximation. The exact solution is then used to discuss the influence of intrinsic decoherence on the revivals of atomic inversion, oscillation of the photon number distribution and squeezing of radiation field in the whole ranges of the decoherence parameter γ.
Accuracy Assessment for Cad Modeling of Freeform Surface Described by Equation
Directory of Open Access Journals (Sweden)
Golba Grzegorz
2015-06-01
Full Text Available This paper presents the results of comparative analysis of modeling accuracy the freeform surface constructed by using a variety of algorithms for surface modeling. Also determined the accuracy of mapping the theoretical freeform surface described by mathematical equation. To model surface objects used: SolidWorks 2012, CATIA v5 and Geomagic Studio 12. During the design process of CAD models were used: profile curves, fitting parametric surface and polygonal mesh. To assess the accuracy of the CAD models used Geomagic Qualify 12. On the basis of analyse defined the scope of application of each modeling techniques depending on the nature of the constructed object.
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.
Heat Transfer on a Film-Cooled Rotating Blade Using a Two Equation Turbulence Model
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.
Equation of state and transition temperatures in the quark-hadron hybrid model
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.
Institute of Scientific and Technical Information of China (English)
Jian-Wan Ding; Li-Ping Chen; Fan-Li Zhou
2006-01-01
Object-oriented modeling with declarative equation based languages often unconsciously leads to structural inconsistencies. Component-based debugging is a new structural analysis approach that addresses this problem by analyzing the structure of each component in a model to separately locate faulty components. The analysis procedure is performed recursively based on the depth-first rule. It first generates fictitious equations for a component to establish a debugging environment, and then detects structural defects by using graph theoretical approaches to analyzing the structure of the system of equations resulting from the component. The proposed method can automatically locate components that cause the structural inconsistencies, and show the user detailed error messages. This information can be a great help in finding and localizing structural inconsistencies, and in some cases pinpoints them immediately.
Indian Academy of Sciences (India)
Surendra P Verma
2000-03-01
This paper presents error propagation equations for modeling of radiogenic isotopes during mixing of two components or end-members. These equations can be used to estimate errors on an isotopic ratio in the mixture of two components, as a function of the analytical errors or the total errors of geological field sampling and analytical errors. Two typical cases (``Small errors'' and ``Large errors'') are illustrated for mixing of Sr isotopes. Similar examples can be formulated for the other radiogenic isotopic ratios. Actual isotopic data for sediment and basalt samples from the Cocos plate are also included to further illustrate the use of these equations. The isotopic compositions of the predicted mixtures can be used to constrain the origin of magmas in the central part of the Mexican Volcanic Belt. These examples show the need of high quality experimental data for them to be useful in geochemical modeling of magmatic processes.
Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
Energy Technology Data Exchange (ETDEWEB)
Tseytlin, A.A.; Wulff, L. [Blackett Laboratory, Imperial College,London SW7 2AZ (United Kingdom)
2016-06-29
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{sub a} and imply the one-loop scale invariance of the GS sigma model. In the special case when X{sub 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 http://arxiv.org/abs/1511.05795. These equations depend on two vectors X{sub a} and K{sub a} subject to 1st order differential relations (with the equations in the NS-NS sector depending only on the combination X{sub a}=X{sub a}+K{sub a}). In the special case of K{sub a}=0 one finds that X{sub a}=∂{sub a}ϕ and thus obtains the standard type II supergravity equations. New generalized solutions are found if K{sub 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{sub n}×S{sup 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.
THE CONTENT MODEL AND THE EQUATIONS OF MOTION OF ELECTRIC VEHICLE
Directory of Open Access Journals (Sweden)
K. O. Soroka
2015-06-01
Full Text Available Purpose. The calculation methods improvement of the electric vehicle curve movement and the cost of electricity with the aim of performance and accuracy of calculations improving are considered in the paper. Methodology. The method is based upon the general principles of mathematical simulation, when a conceptual model of problem domain is created and then a mathematic model is formulated according to the conceptual model. Development of an improved conceptual model of electric vehicles motion is proposed and a corresponding mathematical model is studied. Findings. The authors proposed model in which the vehicle considers as a system of interacting point-like particles with defined interactions under the influence of external forces. As a mathematical model the Euler-Lagrange equation of the second kind is used. Conservative and dissipative forces affecting the system dynamics are considered. Equations for calculating motion of electric vehicles with taking into account the energy consumption are proposed. Originality. In the paper the conceptual model of motion for electric vehicles with distributed masses has been developed as a system of interacting point-like particles. In the easiest case the system has only one degree of freedom. The mathematical model is based on Lagrange equations. The shown approach allows a detailed and physically based description of the electric vehicles dynamics. The derived motion equations for public electric transport are substantially more precise than the equations recommended in textbooks and the reference documentation. The motion equations and energy consumption calculations for transportation of one passenger with a trolleybus are developed. It is shown that the energy consumption depends on the data of vehicle and can increase when the manload is above the certain level. Practical value. The authors received the equations of motion and labour costs in the calculations focused on the use of computer methods
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.
Ruess, Jakob
2015-12-01
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.
A Fokker-Planck Model of the Boltzmann Equation with Correct Prandtl Number for Polyatomic Gases
Mathiaud, J.; Mieussens, L.
2017-09-01
We propose an extension of the Fokker-Planck model of the Boltzmann equation to get a correct Prandtl number in the Compressible Navier-Stokes asymptotics for polyatomic gases. This is obtained by replacing the diffusion coefficient (which is the equilibrium temperature) by a non diagonal temperature tensor, like the Ellipsoidal-Statistical model is obtained from the Bathnagar-Gross-Krook model of the Boltzmann equation, and by adding a diffusion term for the internal energy. Our model is proved to satisfy the properties of conservation and a H-theorem. A Chapman-Enskog analysis shows how to compute the transport coefficients of our model. Some numerical tests are performed to illustrate that a correct Prandtl number can be obtained.
Modelling of gastrocnemius muscle using Hills equation in COMSOL Multiphysics 4.0a
Directory of Open Access Journals (Sweden)
S.Vivekanandan
2012-05-01
Full Text Available This paper summarizes the force generated by gastrocnemius muscle for the analysis of muscoskeletal simulation in human locomotion using Hills muscle model. Biomechanics of Hills equation describes the study of physical phenomenon by means of mathematical model that relates force and muscle length with the help of a partial differential equation. To calculate maximum fatigue in the muscle and to discriminate strained muscle from the normal one FEM based modelling was done in COMSOL Multiphysics 4.0a. The model parameters were evaluated using similar in vitro experiments performed on frogs gastrocnemius muscle. The biomechanical model was then incorporated into human body for the purpose of predicting force - length response for all the four phases of gait cycle. Evaluating the response for gait cycle will enable the physiotherapist to obtain clues for muscle weakness and fatigue in a rehabilitation program
Institute of Scientific and Technical Information of China (English)
Pascale KULISA; Cédric DANO
2006-01-01
Three linear two-equation turbulence models k- ε, k- ω and k- 1 and a non-linear k- l model are used for aerodynamic and thermal turbine flow prediction. The pressure profile in the wake and the heat transfer coefficient on the blade are compared with experimental data. Good agreement is obtained with the linear k- l model. No significant modifications are observed with the non-linear model. The balance of transport equation terms in the blade wake is also presented. Linear and non-linear k- l models are evaluated to predict the threedimensional vortices characterising the turbine flows. The simulations show that the passage vortex is the main origin of the losses.
A non-local evolution equation model of cell-cell adhesion in higher dimensional space.
Dyson, Janet; Gourley, Stephen A; Webb, Glenn F
2013-01-01
A model for cell-cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell-cell adhesion, J. Theor. Biol. 243 (2006), pp. 98-113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments.
A Fokker-Planck Model of the Boltzmann Equation with Correct Prandtl Number for Polyatomic Gases
Mathiaud, J.; Mieussens, L.
2017-07-01
We propose an extension of the Fokker-Planck model of the Boltzmann equation to get a correct Prandtl number in the Compressible Navier-Stokes asymptotics for polyatomic gases. This is obtained by replacing the diffusion coefficient (which is the equilibrium temperature) by a non diagonal temperature tensor, like the Ellipsoidal-Statistical model is obtained from the Bathnagar-Gross-Krook model of the Boltzmann equation, and by adding a diffusion term for the internal energy. Our model is proved to satisfy the properties of conservation and a H-theorem. A Chapman-Enskog analysis shows how to compute the transport coefficients of our model. Some numerical tests are performed to illustrate that a correct Prandtl number can be obtained.
Yang-Mills equation for the nuclear geometrical collective model connexion
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.
Langevin equation for the extended Rayleigh model with an asymmetric bath.
Plyukhin, Alexander V; Schofield, Jeremy
2004-02-01
In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The nonlinear Langevin equation for the motion of the piston is derived from first principles for the case when the thermodynamic parameters and/or the molecular masses of gas particles on the left and right sides of the piston are different. Microscopic expressions involving time correlation functions of the force between bath particles and the piston are obtained for all parameters appearing in the nonlinear Langevin equation. It is demonstrated that the equation has stationary solutions corresponding to directional fluctuation-induced drift in the absence of systematic forces. In the case of ideal gases interacting with the piston via a quadratic repulsive potential, the model is exactly solvable and explicit expressions for the kinetic coefficients in the nonlinear Langevin equation are derived. The transient solution of the nonlinear Langevin equation is analyzed perturbatively and it is demonstrated that previously obtained results for systems with the hard-wall interaction are recovered.
Maassen, Jesse; Lundstrom, Mark
2016-03-01
Understanding ballistic phonon transport effects in transient thermoreflectance experiments and explaining the observed deviations from classical theory remains a challenge. Diffusion equations are simple and computationally efficient but are widely believed to break down when the characteristic length scale is similar or less than the phonon mean-free-path. Building on our prior work, we demonstrate how well-known diffusion equations, namely, the hyperbolic heat equation and the Cattaneo equation, can be used to model ballistic phonon effects in frequency-dependent periodic steady-state thermal transport. Our analytical solutions are found to compare excellently to rigorous numerical results of the phonon Boltzmann transport equation. The correct physical boundary conditions can be different from those traditionally used and are paramount for accurately capturing ballistic effects. To illustrate the technique, we consider a simple model problem using two different, commonly used heating conditions. We demonstrate how this framework can easily handle detailed material properties, by considering the case of bulk silicon using a full phonon dispersion and mean-free-path distribution. This physically transparent approach provides clear insights into the nonequilibrium physics of quasi-ballistic phonon transport and its impact on thermal transport properties.
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.
Modeling water table fluctuations by means of a stochastic differential equation
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.