Modeling Nonlinear Change via Latent Change and Latent Acceleration Frameworks: Examining Velocity and Acceleration of Growth Trajectories

ERIC Educational Resources Information Center

Grimm, Kevin; Zhang, Zhiyong; Hamagami, Fumiaki; Mazzocco, Michele

2013-01-01

We propose the use of the latent change and latent acceleration frameworks for modeling nonlinear growth in structural equation models. Moving to these frameworks allows for the direct identification of "rates of change" and "acceleration" in latent growth curves--information available indirectly through traditional growth…

Algorithmic framework for group analysis of differential equations and its application to generalized Zakharov-Kuznetsov equations

NASA Astrophysics Data System (ADS)

Huang, Ding-jiang; Ivanova, Nataliya M.

2016-02-01

In this paper, we explain in more details the modern treatment of the problem of group classification of (systems of) partial differential equations (PDEs) from the algorithmic point of view. More precisely, we revise the classical Lie algorithm of construction of symmetries of differential equations, describe the group classification algorithm and discuss the process of reduction of (systems of) PDEs to (systems of) equations with smaller number of independent variables in order to construct invariant solutions. The group classification algorithm and reduction process are illustrated by the example of the generalized Zakharov-Kuznetsov (GZK) equations of form ut +(F (u)) xxx +(G (u)) xyy +(H (u)) x = 0. As a result, a complete group classification of the GZK equations is performed and a number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Lie symmetry reductions and exact solutions for two important invariant models, i.e., the classical and modified Zakharov-Kuznetsov equations, are constructed. The algorithmic framework for group analysis of differential equations presented in this paper can also be applied to other nonlinear PDEs.

Formal Derivation of Lotka-Volterra-Haken Amplitude Equations of Task-Related Brain Activity in Multiple, Consecutively Performed Tasks

NASA Astrophysics Data System (ADS)

Frank, T. D.

The Lotka-Volterra-Haken equations have been frequently used in ecology and pattern formation. Recently, the equations have been proposed by several research groups as amplitude equations for task-related patterns of brain activity. In this theoretical study, the focus is on the circular causality aspect of pattern formation systems as formulated within the framework of synergetics. Accordingly, the stable modes of a pattern formation system inhibit the unstable modes, whereas the unstable modes excite the stable modes. Using this circular causality principle it is shown that under certain conditions the Lotka-Volterra-Haken amplitude equations can be derived from a general model of brain activity akin to the Wilson-Cowan model. The model captures the amplitude dynamics for brain activity patterns in experiments involving several consecutively performed multiple-choice tasks. This is explicitly demonstrated for two-choice tasks involving grasping and walking. A comment on the relevance of the theoretical framework for clinical psychology and schizophrenia is given as well.

Overview of the ArbiTER edge plasma eigenvalue code

NASA Astrophysics Data System (ADS)

Baver, Derek; Myra, James; Umansky, Maxim

2011-10-01

The Arbitrary Topology Equation Reader, or ArbiTER, is a flexible eigenvalue solver that is currently under development for plasma physics applications. The ArbiTER code builds on the equation parser framework of the existing 2DX code, extending it to include a topology parser. This will give the code the capability to model problems with complicated geometries (such as multiple X-points and scrape-off layers) or model equations with arbitrary numbers of dimensions (e.g. for kinetic analysis). In the equation parser framework, model equations are not included in the program's source code. Instead, an input file contains instructions for building a matrix from profile functions and elementary differential operators. The program then executes these instructions in a sequential manner. These instructions may also be translated into analytic form, thus giving the code transparency as well as flexibility. We will present an overview of how the ArbiTER code is to work, as well as preliminary results from early versions of this code. Work supported by the U.S. DOE.

A framework to simulate small shallow inland water bodies in semi-arid regions

NASA Astrophysics Data System (ADS)

Abbasi, Ali; Ohene Annor, Frank; van de Giesen, Nick

2017-12-01

In this study, a framework for simulating the flow field and heat transfer processes in small shallow inland water bodies has been developed. As the dynamics and thermal structure of these water bodies are crucial in studying the quality of stored water , and in assessing the heat fluxes from their surfaces as well, the heat transfer and temperature simulations were modeled. The proposed model is able to simulate the full 3-D water flow and heat transfer in the water body by applying complex and time varying boundary conditions. In this model, the continuity, momentum and temperature equations together with the turbulence equations, which comprise the buoyancy effect, have been solved. This model is built on the Reynolds Averaged Navier Stokes (RANS) equations with the widely used Boussinesq approach to solve the turbulence issues of the flow field. Micrometeorological data were obtained from an Automatic Weather Station (AWS) installed on the site and combined with field bathymetric measurements for the model. In the framework developed, a simple, applicable and generalizable approach is proposed for preparing the geometry of small shallow water bodies using coarsely measured bathymetry. All parts of the framework are based on open-source tools, which is essential for developing countries.

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes.

PubMed

Chatterjee, Abhijit; Vlachos, Dionisios G

2007-07-21

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.

Family Environment and Childhood Obesity: A New Framework with Structural Equation Modeling

PubMed Central

Huang, Hui; Wan Mohamed Radzi, Che Wan Jasimah bt; Salarzadeh Jenatabadi, Hashem

2017-01-01

The main purpose of the current article is to introduce a framework of the complexity of childhood obesity based on the family environment. A conceptual model that quantifies the relationships and interactions among parental socioeconomic status, family food security level, child’s food intake and certain aspects of parental feeding behaviour is presented using the structural equation modeling (SEM) concept. Structural models are analysed in terms of the direct and indirect connections among latent and measurement variables that lead to the child weight indicator. To illustrate the accuracy, fit, reliability and validity of the introduced framework, real data collected from 630 families from Urumqi (Xinjiang, China) were considered. The framework includes two categories of data comprising the normal body mass index (BMI) range and obesity data. The comparison analysis between two models provides some evidence that in obesity modeling, obesity data must be extracted from the dataset and analysis must be done separately from the normal BMI range. This study may be helpful for researchers interested in childhood obesity modeling based on family environment. PMID:28208833

Family Environment and Childhood Obesity: A New Framework with Structural Equation Modeling.

PubMed

Huang, Hui; Wan Mohamed Radzi, Che Wan Jasimah Bt; Salarzadeh Jenatabadi, Hashem

2017-02-13

The main purpose of the current article is to introduce a framework of the complexity of childhood obesity based on the family environment. A conceptual model that quantifies the relationships and interactions among parental socioeconomic status, family food security level, child's food intake and certain aspects of parental feeding behaviour is presented using the structural equation modeling (SEM) concept. Structural models are analysed in terms of the direct and indirect connections among latent and measurement variables that lead to the child weight indicator. To illustrate the accuracy, fit, reliability and validity of the introduced framework, real data collected from 630 families from Urumqi (Xinjiang, China) were considered. The framework includes two categories of data comprising the normal body mass index (BMI) range and obesity data. The comparison analysis between two models provides some evidence that in obesity modeling, obesity data must be extracted from the dataset and analysis must be done separately from the normal BMI range. This study may be helpful for researchers interested in childhood obesity modeling based on family environment.

Modeling tree crown dynamics with 3D partial differential equations.

PubMed

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.

A Petascale Non-Hydrostatic Atmospheric Dynamical Core in the HOMME Framework

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

Tufo, Henry

The High-Order Method Modeling Environment (HOMME) is a framework for building scalable, conserva- tive atmospheric models for climate simulation and general atmospheric-modeling applications. Its spatial discretizations are based on Spectral-Element (SE) and Discontinuous Galerkin (DG) methods. These are local methods employing high-order accurate spectral basis-functions that have been shown to perform well on massively parallel supercomputers at any resolution and scale particularly well at high resolutions. HOMME provides the framework upon which the CAM-SE community atmosphere model dynamical-core is constructed. In its current incarnation, CAM-SE employs the hydrostatic primitive-equations (PE) of motion, which limits its resolution to simulations coarser thanmore » 0.1 per grid cell. The primary objective of this project is to remove this resolution limitation by providing HOMME with the capabilities needed to build nonhydrostatic models that solve the compressible Euler/Navier-Stokes equations.« less

Left Ventricular Endocardium Tracking by Fusion of Biomechanical and Deformable Models

PubMed Central

Gu, Jason

2014-01-01

This paper presents a framework for tracking left ventricular (LV) endocardium through 2D echocardiography image sequence. The framework is based on fusion of biomechanical (BM) model of the heart with the parametric deformable model. The BM model constitutive equation consists of passive and active strain energy functions. The deformations of the LV are obtained by solving the constitutive equations using ABAQUS FEM in each frame in the cardiac cycle. The strain energy functions are defined in two user subroutines for active and passive phases. Average fusion technique is used to fuse the BM and deformable model contours. Experimental results are conducted to verify the detected contours and the results are evaluated by comparing themto a created gold standard. The results and the evaluation proved that the framework has the tremendous potential to track and segment the LV through the whole cardiac cycle. PMID:24587814

Multiscale modelling for tokamak pedestals

NASA Astrophysics Data System (ADS)

Abel, I. G.

2018-04-01

Pedestal modelling is crucial to predict the performance of future fusion devices. Current modelling efforts suffer either from a lack of kinetic physics, or an excess of computational complexity. To ameliorate these problems, we take a first-principles multiscale approach to the pedestal. We will present three separate sets of equations, covering the dynamics of edge localised modes (ELMs), the inter-ELM pedestal and pedestal turbulence, respectively. Precisely how these equations should be coupled to each other is covered in detail. This framework is completely self-consistent; it is derived from first principles by means of an asymptotic expansion of the fundamental Vlasov-Landau-Maxwell system in appropriate small parameters. The derivation exploits the narrowness of the pedestal region, the smallness of the thermal gyroradius and the low plasma (the ratio of thermal to magnetic pressures) typical of current pedestal operation to achieve its simplifications. The relationship between this framework and gyrokinetics is analysed, and possibilities to directly match our systems of equations onto multiscale gyrokinetics are explored. A detailed comparison between our model and other models in the literature is performed. Finally, the potential for matching this framework onto an open-field-line region is briefly discussed.

A Two-Stage Approach to Synthesizing Covariance Matrices in Meta-Analytic Structural Equation Modeling

ERIC Educational Resources Information Center

Cheung, Mike W. L.; Chan, Wai

2009-01-01

Structural equation modeling (SEM) is widely used as a statistical framework to test complex models in behavioral and social sciences. When the number of publications increases, there is a need to systematically synthesize them. Methodology of synthesizing findings in the context of SEM is known as meta-analytic SEM (MASEM). Although correlation…

JSEM: A Framework for Identifying and Evaluating Indicators.

ERIC Educational Resources Information Center

Hyman, Jeffrey B.; Leibowitz, Scott G.

2001-01-01

Presents an approach to identifying and evaluating combinations of indicators when the mathematical relationships between the indicators and an endpoint may not be quantified, a limitation common to many ecological assessments. Uses the framework of Structural Equation Modeling (SEM), which combines path analysis with measurement model, to…

Hierarchical Boltzmann simulations and model error estimation

NASA Astrophysics Data System (ADS)

Torrilhon, Manuel; Sarna, Neeraj

2017-08-01

A hierarchical simulation approach for Boltzmann's equation should provide a single numerical framework in which a coarse representation can be used to compute gas flows as accurately and efficiently as in computational fluid dynamics, but a subsequent refinement allows to successively improve the result to the complete Boltzmann result. We use Hermite discretization, or moment equations, for the steady linearized Boltzmann equation for a proof-of-concept of such a framework. All representations of the hierarchy are rotationally invariant and the numerical method is formulated on fully unstructured triangular and quadrilateral meshes using a implicit discontinuous Galerkin formulation. We demonstrate the performance of the numerical method on model problems which in particular highlights the relevance of stability of boundary conditions on curved domains. The hierarchical nature of the method allows also to provide model error estimates by comparing subsequent representations. We present various model errors for a flow through a curved channel with obstacles.

Incorporation of an Energy Equation into a Pulsed Inductive Thruster Performance Model

NASA Technical Reports Server (NTRS)

Polzin, Kurt A.; Reneau, Jarred P.; Sankaran, Kameshwaran

2011-01-01

A model for pulsed inductive plasma acceleration containing an energy equation to account for the various sources and sinks in such devices is presented. The model consists of a set of circuit equations coupled to an equation of motion and energy equation for the plasma. The latter two equations are obtained for the plasma current sheet by treating it as a one-element finite volume, integrating the equations over that volume, and then matching known terms or quantities already calculated in the model to the resulting current sheet-averaged terms in the equations. Calculations showing the time-evolution of the various sources and sinks in the system are presented to demonstrate the efficacy of the model, with two separate resistivity models employed to show an example of how the plasma transport properties can affect the calculation. While neither resistivity model is fully accurate, the demonstration shows that it is possible within this modeling framework to time-accurately update various plasma parameters.

On a model of electromagnetic field propagation in ferroelectric media

NASA Astrophysics Data System (ADS)

Picard, Rainer

2007-04-01

The Maxwell system in an anisotropic, inhomogeneous medium with non-linear memory effect produced by a Maxwell type system for the polarization is investigated under low regularity assumptions on data and domain. The particular form of memory in the system is motivated by a model for electromagnetic wave propagation in ferromagnetic materials suggested by Greenberg, MacCamy and Coffman [J.M. Greenberg, R.C. MacCamy, C.V. Coffman, On the long-time behavior of ferroelectric systems, Phys. D 134 (1999) 362-383]. To avoid unnecessary regularity requirements the problem is approached as a system of space-time operator equation in the framework of extrapolation spaces (Sobolev lattices), a theoretical framework developed in [R. Picard, Evolution equations as space-time operator equations, Math. Anal. Appl. 173 (2) (1993) 436-458; R. Picard, Evolution equations as operator equations in lattices of Hilbert spaces, Glasnik Mat. 35 (2000) 111-136]. A solution theory for a large class of ferromagnetic materials confined to an arbitrary open set (with suitably generalized boundary conditions) is obtained.

A new Eulerian model for viscous and heat conducting compressible flows

NASA Astrophysics Data System (ADS)

Svärd, Magnus

2018-09-01

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the Lagrangian derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely Eulerian framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.

OpenMx: An Open Source Extended Structural Equation Modeling Framework

ERIC Educational Resources Information Center

Boker, Steven; Neale, Michael; Maes, Hermine; Wilde, Michael; Spiegel, Michael; Brick, Timothy; Spies, Jeffrey; Estabrook, Ryne; Kenny, Sarah; Bates, Timothy; Mehta, Paras; Fox, John

2011-01-01

OpenMx is free, full-featured, open source, structural equation modeling (SEM) software. OpenMx runs within the "R" statistical programming environment on Windows, Mac OS-X, and Linux computers. The rationale for developing OpenMx is discussed along with the philosophy behind the user interface. The OpenMx data structures are…

Estimating and Interpreting Latent Variable Interactions: A Tutorial for Applying the Latent Moderated Structural Equations Method

ERIC Educational Resources Information Center

Maslowsky, Julie; Jager, Justin; Hemken, Douglas

2015-01-01

Latent variables are common in psychological research. Research questions involving the interaction of two variables are likewise quite common. Methods for estimating and interpreting interactions between latent variables within a structural equation modeling framework have recently become available. The latent moderated structural equations (LMS)…

An Analytical Framework for Studying Small-Number Effects in Catalytic Reaction Networks: A Probability Generating Function Approach to Chemical Master Equations

PubMed Central

Nakagawa, Masaki; Togashi, Yuichi

2016-01-01

Cell activities primarily depend on chemical reactions, especially those mediated by enzymes, and this has led to these activities being modeled as catalytic reaction networks. Although deterministic ordinary differential equations of concentrations (rate equations) have been widely used for modeling purposes in the field of systems biology, it has been pointed out that these catalytic reaction networks may behave in a way that is qualitatively different from such deterministic representation when the number of molecules for certain chemical species in the system is small. Apart from this, representing these phenomena by simple binary (on/off) systems that omit the quantities would also not be feasible. As recent experiments have revealed the existence of rare chemical species in cells, the importance of being able to model potential small-number phenomena is being recognized. However, most preceding studies were based on numerical simulations, and theoretical frameworks to analyze these phenomena have not been sufficiently developed. Motivated by the small-number issue, this work aimed to develop an analytical framework for the chemical master equation describing the distributional behavior of catalytic reaction networks. For simplicity, we considered networks consisting of two-body catalytic reactions. We used the probability generating function method to obtain the steady-state solutions of the chemical master equation without specifying the parameters. We obtained the time evolution equations of the first- and second-order moments of concentrations, and the steady-state analytical solution of the chemical master equation under certain conditions. These results led to the rank conservation law, the connecting state to the winner-takes-all state, and analysis of 2-molecules M-species systems. A possible interpretation of the theoretical conclusion for actual biochemical pathways is also discussed. PMID:27047384

Modelling vortex-induced fluid-structure interaction.

PubMed

Benaroya, Haym; Gabbai, Rene D

2008-04-13

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid-structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion.Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid-structure interaction models entails-formulating generalized equations of motion, as a superset of the flow-oscillator models; and-developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier-Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.

Simulation of creep effects in framework of a geometrically nonlinear endochronic theory of inelasticity

NASA Astrophysics Data System (ADS)

Zabavnikova, T. A.; Kadashevich, Yu. I.; Pomytkin, S. P.

2018-05-01

A geometric non-linear endochronic theory of inelasticity in tensor parametric form is considered. In the framework of this theory, the creep strains are modelled. The effect of various schemes of applying stresses and changing of material properties on the development of creep strains is studied. The constitutive equations of the model are represented by non-linear systems of ordinary differential equations which are solved in MATLAB environment by implicit difference method. Presented results demonstrate a good qualitative agreement of theoretical data and experimental observations including the description of the tertiary creep and pre-fracture of materials.

Anisotropic neutron stars in R2 gravity

NASA Astrophysics Data System (ADS)

Folomeev, Vladimir

2018-06-01

We consider static neutron stars within the framework of R2 gravity. The neutron fluid is described by three different types of realistic equations of state (soft, moderately stiff, and stiff). Using the observational data on the neutron star mass-radius relation, it is demonstrated that the characteristics of the objects supported by the isotropic fluid agree with the observations only if one uses the soft equation of state. We show that the inclusion of the fluid anisotropy enables one also to employ more stiff equations of state to model configurations that will satisfy the observational constraints sufficiently. Also, using the standard thin accretion disk model, we demonstrate potentially observable differences, which allow us to distinguish the neutron stars constructed within the modified gravity framework from those described in Einstein's general relativity.

Smoking mediates the effect of conscientiousness on mortality: The Veterans Affairs Normative Aging Study

PubMed Central

Turiano, Nicholas A.; Hill, Patrick L.; Roberts, Brent W.; Spiro, Avron; Mroczek, Daniel K.

2013-01-01

This study examined the relationship between conscientiousness and mortality over 18 years and whether smoking behavior mediated this relationship. We utilized data from the Veterans Affairs Normative Aging Study on 1349 men who completed the Goldberg (1992) adjectival markers of the Big Five. Over the 18-year follow-up, 547 (41%) participants died. Through proportional hazards modeling in a structural equation modeling framework, we found that higher levels of conscientiousness significantly predicted longer life, and that this effect was mediated by current smoking status at baseline. Methodologically, we also demonstrate the effectiveness of using a structural equation modeling framework to evaluate mediation when using a censored outcome such as mortality. PMID:23504043

Dubinin-Astakhov model for acetylene adsorption on metal-organic frameworks

NASA Astrophysics Data System (ADS)

Cheng, Peifu; Hu, Yun Hang

2016-07-01

Acetylene (C2H2) is explosive at a pressure above 29 psi, causing a safety issue for its storage and applications. C2H2 adsorption on metal-organic frameworks (MOFs) has been explored to solve the issue. However, a suitable isotherm equation for C2H2 adsorption on various MOFs has not been found. In this paper, it was demonstrated that Dubinin-Astakhov equation can be exploited as a general isotherm model to depict C2H2 adsorption on MOF-5, ZIF-8, HKUST-1, and MIL-53. In contrast, commonly used Langmuir and BET models exhibited their inapplicability for C2H2 adsorption on those MOFs.

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

PubMed Central

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

2015-01-01

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

Features of the Paired Soliton Interactions Within the Framework of the Gardner Equation

NASA Astrophysics Data System (ADS)

Shurgalina, E. G.

2018-02-01

We study the dynamics of the two-soliton interaction within the framework of a completely integrable model, namely, the Gardner equation with negative cubic nonlinearity, which admits the existence of a limiting soliton. The features of the soliton interaction with participation of a thick soliton are demonstrated. Special attention is paid to the nonlinear-interaction influence on the wave-field moments, which determine the skewness and the kurtosis in the theory of turbulence.

A Structural Equation Modeling of EFL Learners' Goal Orientation, Metacognitive Awareness, and Self-Efficacy

ERIC Educational Resources Information Center

Zafarmand, Atefeh; Ghanizadeh, Afsaneh; Akbari, Omid

2014-01-01

This article sets out to examine the relationship between EFL learners' goal orientation, metacognitive awareness and self-efficacy in a single framework. One hundred fifteen EFL students from two universities of Mashhad, a city in north-eastern Iran took part in this study. Structural equation modeling (SEM) was utilized to examine the…

Are Teachers' Approaches to Teaching Responsive to Individual Student Variation? A Two-Level Structural Equation Modeling

ERIC Educational Resources Information Center

Rosário, Pedro; Núñez, José Carlos; Vallejo, Guilermo; Paiva, Olímpia; Valle, António; Fuentes, Sonia; Pinto, Ricardo

2014-01-01

In the framework of teacher's approaches to teaching, this study investigates the relationship between student-related variables (i.e., study time, class absence, domain knowledge, and homework completion), students' approaches to learning, and teachers' approaches to teaching using structural equation modeling (SEM) with two…

Gauge invariance of phenomenological models of the interaction of quantum dissipative systems with electromagnetic fields

NASA Astrophysics Data System (ADS)

Tokman, M. D.

2009-05-01

We discuss specific features of the electrodynamic characteristics of quantum systems within the framework of models that include a phenomenological description of the relaxation processes. As is shown by W. E. Lamb, Jr., R. R. Schlicher, and M. O. Scully [Phys. Rev. A 36, 2763 (1987)], the use of phenomenological relaxation operators, which adequately describe the attenuation of eigenvibrations of a quantum system, may lead to incorrect solutions in the presence of external electromagnetic fields determined by the vector potential for different resonance processes. This incorrectness can be eliminated by giving a gauge-invariant form to the relaxation operator. Lamb, Jr., proposed the corresponding gauge-invariant modification for the Weisskopf-Wigner relaxation operator, which is introduced directly into the Schrödinger equation within the framework of the two-level approximation. In the present paper, this problem is studied for the von Neumann equation supplemented by a relaxation operator. First, we show that the solution of the equation for the density matrix with the relaxation operator correctly obtained “from the first principles” has properties that ensure gauge invariance for the observables. Second, we propose a common recipe for transformation of the phenomenological relaxation operator into the correct (gauge-invariant) form in the density-matrix equations for a multilevel system. Also, we discuss the methods of elimination of other inaccuracies (not related to the gauge-invariance problem) which arise if the electrodynamic response of a dissipative quantum system is calculated within the framework of simplified relaxation models (first of all, the model corresponding to constant relaxation rates of coherences in quantum transitions). Examples illustrating the correctness of the results obtained within the framework of the proposed methods in contrast to inaccuracy of the results of the standard calculation techniques are given.

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

NASA Astrophysics Data System (ADS)

Cara, Javier

2016-05-01

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

Nonequilibrium thermodynamics of the shear-transformation-zone model

NASA Astrophysics Data System (ADS)

Luo, Alan M.; Ã-ttinger, Hans Christian

2014-02-01

The shear-transformation-zone (STZ) model has been applied numerous times to describe the plastic deformation of different types of amorphous systems. We formulate this model within the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) framework, thereby clarifying the thermodynamic structure of the constitutive equations and guaranteeing thermodynamic consistency. We propose natural, physically motivated forms for the building blocks of the GENERIC, which combine to produce a closed set of time evolution equations for the state variables, valid for any choice of free energy. We demonstrate an application of the new GENERIC-based model by choosing a simple form of the free energy. In addition, we present some numerical results and contrast those with the original STZ equations.

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

General Navier–Stokes-like momentum and mass-energy equations

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

Monreal, Jorge, E-mail: jmonreal@mail.usf.edu

2015-03-15

A new system of general Navier–Stokes-like equations is proposed to model electromagnetic flow utilizing analogues of hydrodynamic conservation equations. Such equations are intended to provide a different perspective and, potentially, a better understanding of electromagnetic mass, energy and momentum behaviour. Under such a new framework additional insights into electromagnetism could be gained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors.

A vector-dyadic development of the equations of motion for N-coupled flexible bodies and point masses. [spacecraft trajectories

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1975-01-01

The equations of motion for a system of coupled flexible bodies, rigid bodies, point masses, and symmetric wheels were derived. The equations were cast into a partitioned matrix form in which certain partitions became nontrivial when the effects of flexibility were treated. The equations are shown to contract to the coupled rigid body equations or expand to the coupled flexible body equations all within the same basic framework. Furthermore, the coefficient matrix always has the computationally desirable property of symmetry. Making use of the derived equations, a comparison was made between the equations which described a flexible body model and those which described a rigid body model of the same elastic appendage attached to an arbitrary coupled body system. From the comparison, equivalence relations were developed which defined how the two modeling approaches described identical dynamic effects.

Approach to calculation of mass spectra and two-photon decays of c c¯ mesons in the framework of Bethe-Salpeter equation

NASA Astrophysics Data System (ADS)

Bhatnagar, Shashank; Alemu, Lmenew

2018-02-01

In this work we calculate the mass spectra of charmonium for 1 P ,…,4 P states of 0++ and 1++, for 1 S ,…,5 S states of 0-+, and for 1 S ,…,4 D states of 1- along with the two-photon decay widths of the ground and first excited states of 0++ quarkonia for the process O++→γ γ in the framework of a QCD-motivated Bethe-Salpeter equation (BSE). In this 4 ×4 BSE framework, the coupled Salpeter equations are first shown to decouple for the confining part of the interaction (under the heavy-quark approximation) and are analytically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to mass spectral equations for various quarkonia. The analytic forms of wave functions obtained are used for the calculation of the two-photon decay widths of χc 0. Our results are in reasonable agreement with data (where available) and other models.

Kalman approach to accuracy management for interoperable heterogeneous model abstraction within an HLA-compliant simulation

NASA Astrophysics Data System (ADS)

Leskiw, Donald M.; Zhau, Junmei

2000-06-01

This paper reports on results from an ongoing project to develop methodologies for representing and managing multiple, concurrent levels of detail and enabling high performance computing using parallel arrays within distributed object-based simulation frameworks. At this time we present the methodology for representing and managing multiple, concurrent levels of detail and modeling accuracy by using a representation based on the Kalman approach for estimation. The Kalman System Model equations are used to represent model accuracy, Kalman Measurement Model equations provide transformations between heterogeneous levels of detail, and interoperability among disparate abstractions is provided using a form of the Kalman Update equations.

Field Markup Language: biological field representation in XML.

PubMed

Chang, David; Lovell, Nigel H; Dokos, Socrates

2007-01-01

With an ever increasing number of biological models available on the internet, a standardized modeling framework is required to allow information to be accessed or visualized. Based on the Physiome Modeling Framework, the Field Markup Language (FML) is being developed to describe and exchange field information for biological models. In this paper, we describe the basic features of FML, its supporting application framework and its ability to incorporate CellML models to construct tissue-scale biological models. As a typical application example, we present a spatially-heterogeneous cardiac pacemaker model which utilizes both FML and CellML to describe and solve the underlying equations of electrical activation and propagation.

An Assessment of Peridynamics for Pre and Post Failure Deformation

DTIC Science & Technology

2011-11-01

begin with an overview of the peridynamics equations ; first the micro-elastic and micro-plastic models will be outlined, and then the newer state ...expressed as differential equations . The peridynamics framework was subsequently extended to a state -based approach (2, 7) to facilitate use of common...computing the sums. 2.2.3 Stress and Nodal Forces State -based peridynamics and FE both use the same momentum equation , equation 1, and similar

Bayesian methods for characterizing unknown parameters of material models

DOE PAGES

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

2016-02-04

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian methods for characterizing unknown parameters of material models

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

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Nonlinear and non-Gaussian Bayesian based handwriting beautification

NASA Astrophysics Data System (ADS)

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2013-03-01

A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.

Transport Phenomena During Equiaxed Solidification of Alloys

NASA Technical Reports Server (NTRS)

Beckermann, C.; deGroh, H. C., III

1997-01-01

Recent progress in modeling of transport phenomena during dendritic alloy solidification is reviewed. Starting from the basic theorems of volume averaging, a general multiphase modeling framework is outlined. This framework allows for the incorporation of a variety of microscale phenomena in the macroscopic transport equations. For the case of diffusion dominated solidification, a simplified set of model equations is examined in detail and validated through comparisons with numerous experimental data for both columnar and equiaxed dendritic growth. This provides a critical assessment of the various model assumptions. Models that include melt flow and solid phase transport are also discussed, although their validation is still at an early stage. Several numerical results are presented that illustrate some of the profound effects of convective transport on the final compositional and structural characteristics of a solidified part. Important issues that deserve continuing attention are identified.

Zubarev's Nonequilibrium Statistical Operator Method in the Generalized Statistics of Multiparticle Systems

NASA Astrophysics Data System (ADS)

Glushak, P. A.; Markiv, B. B.; Tokarchuk, M. V.

2018-01-01

We present a generalization of Zubarev's nonequilibrium statistical operator method based on the principle of maximum Renyi entropy. In the framework of this approach, we obtain transport equations for the basic set of parameters of the reduced description of nonequilibrium processes in a classical system of interacting particles using Liouville equations with fractional derivatives. For a classical systems of particles in a medium with a fractal structure, we obtain a non-Markovian diffusion equation with fractional spatial derivatives. For a concrete model of the frequency dependence of a memory function, we obtain generalized Kettano-type diffusion equation with the spatial and temporal fractality taken into account. We present a generalization of nonequilibrium thermofield dynamics in Zubarev's nonequilibrium statistical operator method in the framework of Renyi statistics.

Modeling adsorption of cationic surfactants at air/water interface without using the Gibbs equation.

PubMed

Phan, Chi M; Le, Thu N; Nguyen, Cuong V; Yusa, Shin-ichi

2013-04-16

The Gibbs adsorption equation has been indispensable in predicting the surfactant adsorption at the interfaces, with many applications in industrial and natural processes. This study uses a new theoretical framework to model surfactant adsorption at the air/water interface without the Gibbs equation. The model was applied to two surfactants, C14TAB and C16TAB, to determine the maximum surface excesses. The obtained values demonstrated a fundamental change, which was verified by simulations, in the molecular arrangement at the interface. The new insights, in combination with recent discoveries in the field, expose the limitations of applying the Gibbs adsorption equation to cationic surfactants at the air/water interface.

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

Lue Xing; Sun Kun; Wang Pan

In the framework of Bell-polynomial manipulations, under investigation hereby are three single-field bilinearizable equations: the (1+1)-dimensional shallow water wave model, Boiti-Leon-Manna-Pempinelli model, and (2+1)-dimensional Sawada-Kotera model. Based on the concept of scale invariance, a direct and unifying Bell-polynomial scheme is employed to achieve the Baecklund transformations and Lax pairs associated with those three soliton equations. Note that the Bell-polynomial expressions and Bell-polynomial-typed Baecklund transformations for those three soliton equations can be, respectively, cast into the bilinear equations and bilinear Baecklund transformations with symbolic computation. Consequently, it is also shown that the Bell-polynomial-typed Baecklund transformations can be linearized into the correspondingmore » Lax pairs.« less

Wave propagation problem for a micropolar elastic waveguide

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-04-01

A propagation problem for coupled harmonic waves of translational displacements and microrotations along the axis of a long cylindrical waveguide is discussed at present study. Microrotations modeling is carried out within the linear micropolar elasticity frameworks. The mathematical model of the linear (or even nonlinear) micropolar elasticity is also expanded to a field theory model by variational least action integral and the least action principle. The governing coupled vector differential equations of the linear micropolar elasticity are given. The translational displacements and microrotations in the harmonic coupled wave are decomposed into potential and vortex parts. Calibrating equations providing simplification of the equations for the wave potentials are proposed. The coupled differential equations are then reduced to uncoupled ones and finally to the Helmholtz wave equations. The wave equations solutions for the translational and microrotational waves potentials are obtained for a high-frequency range.

Nonlinear and Dissipation Characteristics of Ocean Surface Waves in Estuarine Environments

DTIC Science & Technology

2013-09-30

developed models while using the general framework of operational wave models. We will conduct robustness tests of the system to determine the...and Guza (1984) model is weakly dispersive, in line with the assumptions behind the Boussinesq equations from which it was derived. The Kaihatu and...interactions across both frequency and directions. This system of equations is solved over a 2D frequency (f) and shore parallel wave number (κ) space. The

Stellar Structure Models of Deformed Neutron Stars

NASA Astrophysics Data System (ADS)

Zubairi, Omair; Wigley, David; Weber, Fridolin

Traditional stellar structure models of non-rotating neutron stars work under the assumption that these stars are perfect spheres. This assumption of perfect spherical symmetry is not correct if the matter inside neutron stars is described by an anisotropic model for the equation of state. Certain classes of neutron stars such as Magnetars and neutron stars which contain color-superconducting quark matter cores are expected to be deformed making them oblong spheroids. In this work, we investigate the stellar structure of these deformed neutron stars by deriving stellar structure equations in the framework of general relativity. Using a non-isotropic equation of state model, we solve these structure equations numerically in two dimensions. We calculate stellar properties such as masses and radii along with pressure profiles and investigate changes from standard spherical models.

Study on the influence of supplying compressed air channels and evicting channels on pneumatical oscillation systems for vibromooshing

NASA Astrophysics Data System (ADS)

Glăvan, D. O.; Radu, I.; Babanatsas, T.; Babanatis Merce, R. M.; Kiss, I.; Gaspar, M. C.

2018-01-01

The paper presents a pneumatic system with two oscillating masses. The system is composed of a cylinder (framework) with mass m1, which has a piston with mass m2 inside. The cylinder (framework system) has one supplying channel for compressed air and one evicting channel for each work chamber (left and right of the piston). Functionality of the piston position comparatively with the cylinder (framework) is possible through the supplying or evicting of compressed air. The variable force that keeps the movement depends on variation of the pressure that is changing depending on the piston position according to the cylinder (framework) and to the section form that is supplying and evicting channels with compressed air. The paper presents the physical model/pattern, the mathematical model/pattern (differential equations) and numerical solution of the differential equations in hypothesis with the section form of supplying and evicting channels with compressed air is rectangular (variation linear) or circular (variation nonlinear).

A discrete model to study reaction-diffusion-mechanics systems.

PubMed

Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

A Discrete Model to Study Reaction-Diffusion-Mechanics Systems

PubMed Central

Weise, Louis D.; Nash, Martyn P.; Panfilov, Alexander V.

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects. PMID:21804911

Poiseuille equation for steady flow of fractal fluid

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2016-07-01

Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

Power-law spatial dispersion from fractional Liouville equation

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

Tarasov, Vasily E.

2013-10-15

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

PetIGA: A framework for high-performance isogeometric analysis

DOE PAGES

Dalcin, Lisandro; Collier, Nathaniel; Vignal, Philippe; ...

2016-05-25

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility ofmore » PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. Lastly, we show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations.« less

Fractal electrodynamics via non-integer dimensional space approach

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-09-01

Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.

A New Biogeochemical Computational Framework Integrated within the Community Land Model

NASA Astrophysics Data System (ADS)

Fang, Y.; Li, H.; Liu, C.; Huang, M.; Leung, L.

2012-12-01

Terrestrial biogeochemical processes, particularly carbon cycle dynamics, have been shown to significantly influence regional and global climate changes. Modeling terrestrial biogeochemical processes within the land component of Earth System Models such as the Community Land model (CLM), however, faces three major challenges: 1) extensive efforts in modifying modeling structures and rewriting computer programs to incorporate biogeochemical processes with increasing complexity, 2) expensive computational cost to solve the governing equations due to numerical stiffness inherited from large variations in the rates of biogeochemical processes, and 3) lack of an efficient framework to systematically evaluate various mathematical representations of biogeochemical processes. To address these challenges, we introduce a new computational framework to incorporate biogeochemical processes into CLM, which consists of a new biogeochemical module with a generic algorithm and reaction database. New and updated biogeochemical processes can be incorporated into CLM without significant code modification. To address the stiffness issue, algorithms and criteria will be developed to identify fast processes, which will be replaced with algebraic equations and decoupled from slow processes. This framework can serve as a generic and user-friendly platform to test out different mechanistic process representations and datasets and gain new insight on the behavior of the terrestrial ecosystems in response to climate change in a systematic way.

Fully Associative, Nonisothermal, Potential-Based Unified Viscoplastic Model for Titanium-Based Matrices

NASA Technical Reports Server (NTRS)

2005-01-01

A number of titanium matrix composite (TMC) systems are currently being investigated for high-temperature air frame and propulsion system applications. As a result, numerous computational methodologies for predicting both deformation and life for this class of materials are under development. An integral part of these methodologies is an accurate and computationally efficient constitutive model for the metallic matrix constituent. Furthermore, because these systems are designed to operate at elevated temperatures, the required constitutive models must account for both time-dependent and time-independent deformations. To accomplish this, the NASA Lewis Research Center is employing a recently developed, complete, potential-based framework. This framework, which utilizes internal state variables, was put forth for the derivation of reversible and irreversible constitutive equations. The framework, and consequently the resulting constitutive model, is termed complete because the existence of the total (integrated) form of the Gibbs complementary free energy and complementary dissipation potentials are assumed a priori. The specific forms selected here for both the Gibbs and complementary dissipation potentials result in a fully associative, multiaxial, nonisothermal, unified viscoplastic model with nonlinear kinematic hardening. This model constitutes one of many models in the Generalized Viscoplasticity with Potential Structure (GVIPS) class of inelastic constitutive equations.

Agent-Based vs. Equation-based Epidemiological Models:A Model Selection Case Study

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

Sukumar, Sreenivas R; Nutaro, James J

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 paradigmmore » to another. We conclude with a discussion of our experience and document future ideas for a model validation framework.« less

Results of EAS characteristics calculations in the framework of the universal hadronic interaction model NEXUS

NASA Astrophysics Data System (ADS)

Kalmykov, N. N.; Ostapchenko, S. S.; Werner, K.

An extensive air shower (EAS) calculation scheme based on cascade equations and some EAS characteristics for energies 1014 -1017 eV are presented. The universal hadronic interaction model NEXUS is employed to provide the necessary data concerning hadron-air collisions. The influence of model assumptions on the longitudinal EAS development is discussed in the framework of the NEXUS and QGSJET models. Applied to EAS simulations, perspectives of combined Monte Carlo and numerical methods are considered.

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

NASA Astrophysics Data System (ADS)

Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

2018-01-01

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics.

PubMed

Holm, Darryl D.

2002-06-01

We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged Lagrangian. This is the Lagrangian averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The glm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for Lagrangian averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.

The Influence of Turbulent Coherent Structure on Suspended Sediment Transport

NASA Astrophysics Data System (ADS)

Huang, S. H.; Tsai, C.

2017-12-01

The anomalous diffusion of turbulent sedimentation has received more and more attention in recent years. With the advent of new instruments and technologies, researchers have found that sediment behavior may deviate from Fickian assumptions when particles are heavier. In particle-laden flow, bursting phenomena affects instantaneous local concentrations, and seems to carry suspended particles for a longer distance. Instead of the pure diffusion process in an analogy to Brownian motion, Levy flight which allows particles to move in response to bursting phenomena is suspected to be more suitable for describing particle movement in turbulence. And the fractional differential equation is a potential candidate to improve the concentration profile. However, stochastic modeling (the Differential Chapmen-Kolmogorov Equation) also provides an alternative mathematical framework to describe system transits between different states through diffusion/the jump processes. Within this framework, the stochastic particle tracking model linked with advection diffusion equation is a powerful tool to simulate particle locations in the flow field. By including the jump process to this model, a more comprehensive description for suspended sediment transport can be provided with a better physical insight. This study also shows the adaptability and expandability of the stochastic particle tracking model for suspended sediment transport modeling.

Experimentally validated multiphysics computational model of focusing and shock wave formation in an electromagnetic lithotripter.

PubMed

Fovargue, Daniel E; Mitran, Sorin; Smith, Nathan B; Sankin, Georgy N; Simmons, Walter N; Zhong, Pei

2013-08-01

A multiphysics computational model of the focusing of an acoustic pulse and subsequent shock wave formation that occurs during extracorporeal shock wave lithotripsy is presented. In the electromagnetic lithotripter modeled in this work the focusing is achieved via a polystyrene acoustic lens. The transition of the acoustic pulse through the solid lens is modeled by the linear elasticity equations and the subsequent shock wave formation in water is modeled by the Euler equations with a Tait equation of state. Both sets of equations are solved simultaneously in subsets of a single computational domain within the BEARCLAW framework which uses a finite-volume Riemann solver approach. This model is first validated against experimental measurements with a standard (or original) lens design. The model is then used to successfully predict the effects of a lens modification in the form of an annular ring cut. A second model which includes a kidney stone simulant in the domain is also presented. Within the stone the linear elasticity equations incorporate a simple damage model.

Experimentally validated multiphysics computational model of focusing and shock wave formation in an electromagnetic lithotripter

PubMed Central

Fovargue, Daniel E.; Mitran, Sorin; Smith, Nathan B.; Sankin, Georgy N.; Simmons, Walter N.; Zhong, Pei

2013-01-01

A multiphysics computational model of the focusing of an acoustic pulse and subsequent shock wave formation that occurs during extracorporeal shock wave lithotripsy is presented. In the electromagnetic lithotripter modeled in this work the focusing is achieved via a polystyrene acoustic lens. The transition of the acoustic pulse through the solid lens is modeled by the linear elasticity equations and the subsequent shock wave formation in water is modeled by the Euler equations with a Tait equation of state. Both sets of equations are solved simultaneously in subsets of a single computational domain within the BEARCLAW framework which uses a finite-volume Riemann solver approach. This model is first validated against experimental measurements with a standard (or original) lens design. The model is then used to successfully predict the effects of a lens modification in the form of an annular ring cut. A second model which includes a kidney stone simulant in the domain is also presented. Within the stone the linear elasticity equations incorporate a simple damage model. PMID:23927200

A hybridized discontinuous Galerkin framework for high-order particle-mesh operator splitting of the incompressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Maljaars, Jakob M.; Labeur, Robert Jan; Möller, Matthias

2018-04-01

A generic particle-mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier-Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an advection operator, and an Eulerian mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to formulate the projections between the Lagrangian particle space and the Eulerian finite element space in terms of local (i.e. cellwise) ℓ2-projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder.

A Framework for Developing Self-Directed Technology Use for Language Learning

ERIC Educational Resources Information Center

Lai, Chun

2013-01-01

Critical to maximizing the potential of technology for learning is enhancing language learners' self-directed use of technology for learning purposes. This study aimed to enhance our understanding of the determinants of self-directed technology use through the construction of a structural equation modelling (SEM) framework of factors and…

Multiscale Simulations of Magnetic Island Coalescence

NASA Technical Reports Server (NTRS)

Dorelli, John C.

2010-01-01

We describe a new interactive parallel Adaptive Mesh Refinement (AMR) framework written in the Python programming language. This new framework, PyAMR, hides the details of parallel AMR data structures and algorithms (e.g., domain decomposition, grid partition, and inter-process communication), allowing the user to focus on the development of algorithms for advancing the solution of a systems of partial differential equations on a single uniform mesh. We demonstrate the use of PyAMR by simulating the pairwise coalescence of magnetic islands using the resistive Hall MHD equations. Techniques for coupling different physics models on different levels of the AMR grid hierarchy are discussed.

Item response theory and structural equation modelling for ordinal data: Describing the relationship between KIDSCREEN and Life-H.

PubMed

Titman, Andrew C; Lancaster, Gillian A; Colver, Allan F

2016-10-01

Both item response theory and structural equation models are useful in the analysis of ordered categorical responses from health assessment questionnaires. We highlight the advantages and disadvantages of the item response theory and structural equation modelling approaches to modelling ordinal data, from within a community health setting. Using data from the SPARCLE project focussing on children with cerebral palsy, this paper investigates the relationship between two ordinal rating scales, the KIDSCREEN, which measures quality-of-life, and Life-H, which measures participation. Practical issues relating to fitting models, such as non-positive definite observed or fitted correlation matrices, and approaches to assessing model fit are discussed. item response theory models allow properties such as the conditional independence of particular domains of a measurement instrument to be assessed. When, as with the SPARCLE data, the latent traits are multidimensional, structural equation models generally provide a much more convenient modelling framework. © The Author(s) 2013.

SPH modeling of fluid-structure interaction

NASA Astrophysics Data System (ADS)

Han, Luhui; Hu, Xiangyu

2018-02-01

This work concerns numerical modeling of fluid-structure interaction (FSI) problems in a uniform smoothed particle hydrodynamics (SPH) framework. It combines a transport-velocity SPH scheme, advancing fluid motions, with a total Lagrangian SPH formulation dealing with the structure deformations. Since both fluid and solid governing equations are solved in SPH framework, while coupling becomes straightforward, the momentum conservation of the FSI system is satisfied strictly. A well-known FSI benchmark test case has been performed to validate the modeling and to demonstrate its potential.

Notes on a General Framework for Observed Score Equating. Research Report. ETS RR-08-59

ERIC Educational Resources Information Center

Moses, Tim; Holland, Paul

2008-01-01

The purpose of this paper is to extend von Davier, Holland, and Thayer's (2004b) framework of kernel equating so that it can incorporate raw data and traditional equipercentile equating methods. One result of this more general framework is that previous equating methodology research can be viewed more comprehensively. Another result is that the…

A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

ERIC Educational Resources Information Center

Chen, Haiwen

2012-01-01

In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

Assessing Vocational Interests in the Basque Country Using Paired Comparison Design

ERIC Educational Resources Information Center

Elosua, Paula

2007-01-01

This article proposes the Thurstonian paired comparison model to assess vocational preferences and uses this approach to evaluate the Realistic, Investigative, Artistic, Social, Enterprise, and Conventional (RIASEC) model in the Basque Country (Spain). First, one unrestricted model is estimated in the Structural Equation Modelling framework using…

Development of an Integrated Modeling Framework for Simulations of Coastal Processes in Deltaic Environments Using High-Performance Computing

DTIC Science & Technology

2008-01-01

exceeds the local water depth. The approximation eliminates the vertical dimension of the elliptic equation that is normally required for the fully non...used for vertical resolution. The shallow water equations (SWE) are a set of non-linear hyperbolic equations. As the equations are derived under...linear standing wave with a wavelength of 10 m in a square 10 m by 10 m basin. The still water depth is 0.5 m. In order to compare with the analytical

Geometric approach to nuclear pasta phases

NASA Astrophysics Data System (ADS)

Kubis, Sebastian; Wójcik, Włodzimierz

2016-12-01

By use of the variational methods and differential geometry in the framework of the liquid drop model we formulate appropriate equilibrium equations for pasta phases with imposed periodicity. The extension of the Young-Laplace equation in the case of charged fluid is obtained. The β equilibrium and virial theorem are also generalized. All equations are shown in gauge invariant form. For the first time, the pasta shape stability analysis is carried out. The proper stability condition in the form of the generalized Jacobi equation is derived. The presented formalism is tested on some particular cases.

Model reduction of multiscale chemical langevin equations: a numerical case study.

PubMed

Sotiropoulos, Vassilios; Contou-Carrere, Marie-Nathalie; Daoutidis, Prodromos; Kaznessis, Yiannis N

2009-01-01

Two very important characteristics of biological reaction networks need to be considered carefully when modeling these systems. First, models must account for the inherent probabilistic nature of systems far from the thermodynamic limit. Often, biological systems cannot be modeled with traditional continuous-deterministic models. Second, models must take into consideration the disparate spectrum of time scales observed in biological phenomena, such as slow transcription events and fast dimerization reactions. In the last decade, significant efforts have been expended on the development of stochastic chemical kinetics models to capture the dynamics of biomolecular systems, and on the development of robust multiscale algorithms, able to handle stiffness. In this paper, the focus is on the dynamics of reaction sets governed by stiff chemical Langevin equations, i.e., stiff stochastic differential equations. These are particularly challenging systems to model, requiring prohibitively small integration step sizes. We describe and illustrate the application of a semianalytical reduction framework for chemical Langevin equations that results in significant gains in computational cost.

PROTO-PLASM: parallel language for adaptive and scalable modelling of biosystems.

PubMed

Bajaj, Chandrajit; DiCarlo, Antonio; Paoluzzi, Alberto

2008-09-13

This paper discusses the design goals and the first developments of PROTO-PLASM, a novel computational environment to produce libraries of executable, combinable and customizable computer models of natural and synthetic biosystems, aiming to provide a supporting framework for predictive understanding of structure and behaviour through multiscale geometric modelling and multiphysics simulations. Admittedly, the PROTO-PLASM platform is still in its infancy. Its computational framework--language, model library, integrated development environment and parallel engine--intends to provide patient-specific computational modelling and simulation of organs and biosystem, exploiting novel functionalities resulting from the symbolic combination of parametrized models of parts at various scales. PROTO-PLASM may define the model equations, but it is currently focused on the symbolic description of model geometry and on the parallel support of simulations. Conversely, CellML and SBML could be viewed as defining the behavioural functions (the model equations) to be used within a PROTO-PLASM program. Here we exemplify the basic functionalities of PROTO-PLASM, by constructing a schematic heart model. We also discuss multiscale issues with reference to the geometric and physical modelling of neuromuscular junctions.

A symbiotic approach to fluid equations and non-linear flux-driven simulations of plasma dynamics

NASA Astrophysics Data System (ADS)

Halpern, Federico

2017-10-01

The fluid framework is ubiquitous in studies of plasma transport and stability. Typical forms of the fluid equations are motivated by analytical work dating several decades ago, before computer simulations were indispensable, and can be, therefore, not optimal for numerical computation. We demonstrate a new first-principles approach to obtaining manifestly consistent, skew-symmetric fluid models, ensuring internal consistency and conservation properties even in discrete form. Mass, kinetic, and internal energy become quadratic (and always positive) invariants of the system. The model lends itself to a robust, straightforward discretization scheme with inherent non-linear stability. A simpler, drift-ordered form of the equations is obtained, and first results of their numerical implementation as a binary framework for bulk-fluid global plasma simulations are demonstrated. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, Theory Program, under Award No. DE-FG02-95ER54309.

Elastic-viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient.

PubMed

Weickenmeier, J; Jabareen, M

2014-11-01

The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic-viscoplastic constitutive equations. The specific elastic-viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic-viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient-the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery. Copyright © 2014 John Wiley & Sons, Ltd.

A Correlation-Based Transition Model using Local Variables. Part 1; Model Formation

NASA Technical Reports Server (NTRS)

Menter, F. R.; Langtry, R. B.; Likki, S. R.; Suzen, Y. B.; Huang, P. G.; Volker, S.

2006-01-01

A new correlation-based transition model has been developed, which is based strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics (CFD) approaches, such as unstructured grids and massive parallel execution. The model is based on two transport equations, one for intermittency and one for the transition onset criteria in terms of momentum thickness Reynolds number. The proposed transport equations do not attempt to model the physics of the transition process (unlike, e.g., turbulence models) but from a framework for the implementation of correlation-based models into general-purpose CFD methods.

Modeling spin magnetization transport in a spatially varying magnetic field

NASA Astrophysics Data System (ADS)

Picone, Rico A. R.; Garbini, Joseph L.; Sidles, John A.

2015-01-01

We present a framework for modeling the transport of any number of globally conserved quantities in any spatial configuration and apply it to obtain a model of magnetization transport for spin-systems that is valid in new regimes (including high-polarization). The framework allows an entropy function to define a model that explicitly respects the laws of thermodynamics. Three facets of the model are explored. First, it is expressed as nonlinear partial differential equations that are valid for the new regime of high dipole-energy and polarization. Second, the nonlinear model is explored in the limit of low dipole-energy (semi-linear), from which is derived a physical parameter characterizing separative magnetization transport (SMT). It is shown that the necessary and sufficient condition for SMT to occur is that the parameter is spatially inhomogeneous. Third, the high spin-temperature (linear) limit is shown to be equivalent to the model of nuclear spin transport of Genack and Redfield (1975) [1]. Differences among the three forms of the model are illustrated by numerical solution with parameters corresponding to a magnetic resonance force microscopy (MRFM) experiment (Degen et al., 2009 [2]; Kuehn et al., 2008 [3]; Sidles et al., 2003 [4]; Dougherty et al., 2000 [5]). A family of analytic, steady-state solutions to the nonlinear equation is derived and shown to be the spin-temperature analog of the Langevin paramagnetic equation and Curie's law. Finally, we analyze the separative quality of magnetization transport, and a steady-state solution for the magnetization is shown to be compatible with Fenske's separative mass transport equation (Fenske, 1932 [6]).

Bayesian Factor Analysis as a Variable Selection Problem: Alternative Priors and Consequences

PubMed Central

Lu, Zhao-Hua; Chow, Sy-Miin; Loken, Eric

2016-01-01

Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, a Bayesian structural equation modeling (BSEM) approach (Muthén & Asparouhov, 2012) has been proposed as a way to explore the presence of cross-loadings in CFA models. We show that the issue of determining factor loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov’s approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike and slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set (Byrne, 2012; Pettegrew & Wolf, 1982) is used to demonstrate our approach. PMID:27314566

Structural Equation Models in a Redundancy Analysis Framework With Covariates.

PubMed

Lovaglio, Pietro Giorgio; Vittadini, Giorgio

2014-01-01

A recent method to specify and fit structural equation modeling in the Redundancy Analysis framework based on so-called Extended Redundancy Analysis (ERA) has been proposed in the literature. In this approach, the relationships between the observed exogenous variables and the observed endogenous variables are moderated by the presence of unobservable composites, estimated as linear combinations of exogenous variables. However, in the presence of direct effects linking exogenous and endogenous variables, or concomitant indicators, the composite scores are estimated by ignoring the presence of the specified direct effects. To fit structural equation models, we propose a new specification and estimation method, called Generalized Redundancy Analysis (GRA), allowing us to specify and fit a variety of relationships among composites, endogenous variables, and external covariates. The proposed methodology extends the ERA method, using a more suitable specification and estimation algorithm, by allowing for covariates that affect endogenous indicators indirectly through the composites and/or directly. To illustrate the advantages of GRA over ERA we propose a simulation study of small samples. Moreover, we propose an application aimed at estimating the impact of formal human capital on the initial earnings of graduates of an Italian university, utilizing a structural model consistent with well-established economic theory.

Nonequilibrium scheme for computing the flux of the convection-diffusion equation in the framework of the lattice Boltzmann method.

PubMed

Chai, Zhenhua; Zhao, T S

2014-07-01

In this paper, we propose a local nonequilibrium scheme for computing the flux of the convection-diffusion equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibrium scheme and the conventional second-order central-difference scheme indicates that, although both schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than the central-difference scheme. In addition, the flux computation rendered by the present scheme also preserves the parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the convection-diffusion equation and in computing the flux.

Investigating Stage-Sequential Growth Mixture Models with Multiphase Longitudinal Data

ERIC Educational Resources Information Center

Kim, Su-Young; Kim, Jee-Seon

2012-01-01

This article investigates three types of stage-sequential growth mixture models in the structural equation modeling framework for the analysis of multiple-phase longitudinal data. These models can be important tools for situations in which a single-phase growth mixture model produces distorted results and can allow researchers to better understand…

The What and Where of Adding Channel Noise to the Hodgkin-Huxley Equations

PubMed Central

Goldwyn, Joshua H.; Shea-Brown, Eric

2011-01-01

Conductance-based equations for electrically active cells form one of the most widely studied mathematical frameworks in computational biology. This framework, as expressed through a set of differential equations by Hodgkin and Huxley, synthesizes the impact of ionic currents on a cell's voltage—and the highly nonlinear impact of that voltage back on the currents themselves—into the rapid push and pull of the action potential. Later studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations or their counterparts. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the equations of Hodgkin-Huxley type. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic equations of Hodgkin-Huxley type as well as to more modern models of ion channel dynamics. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly MATLAB simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html. PMID:22125479

Snow Micro-Structure Model

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

Micah Johnson, Andrew Slaughter

PIKA is a MOOSE-based application for modeling micro-structure evolution of seasonal snow. The model will be useful for environmental, atmospheric, and climate scientists. Possible applications include application to energy balance models, ice sheet modeling, and avalanche forecasting. The model implements physics from published, peer-reviewed articles. The main purpose is to foster university and laboratory collaboration to build a larger multi-scale snow model using MOOSE. The main feature of the code is that it is implemented using the MOOSE framework, thus making features such as multiphysics coupling, adaptive mesh refinement, and parallel scalability native to the application. PIKA implements three equations:more » the phase-field equation for tracking the evolution of the ice-air interface within seasonal snow at the grain-scale; the heat equation for computing the temperature of both the ice and air within the snow; and the mass transport equation for monitoring the diffusion of water vapor in the pore space of the snow.« less

A hybrid model of cell cycle in mammals.

PubMed

Behaegel, Jonathan; Comet, Jean-Paul; Bernot, Gilles; Cornillon, Emilien; Delaunay, Franck

2016-02-01

Time plays an essential role in many biological systems, especially in cell cycle. Many models of biological systems rely on differential equations, but parameter identification is an obstacle to use differential frameworks. In this paper, we present a new hybrid modeling framework that extends René Thomas' discrete modeling. The core idea is to associate with each qualitative state "celerities" allowing us to compute the time spent in each state. This hybrid framework is illustrated by building a 5-variable model of the mammalian cell cycle. Its parameters are determined by applying formal methods on the underlying discrete model and by constraining parameters using timing observations on the cell cycle. This first hybrid model presents the most important known behaviors of the cell cycle, including quiescent phase and endoreplication.

RAS one-equation turbulence model with non-singular eddy-viscosity coefficient

NASA Astrophysics Data System (ADS)

Rahman, M. M.; Agarwal, R. K.; Siikonen, T.

2016-02-01

A simplified consistency formulation for Pk/ε (production to dissipation ratio) is devised to obtain a non-singular Cμ (coefficient of eddy-viscosity) in the explicit algebraic Reynolds stress model of Gatski and Speziale. The coefficient Cμ depends non-linearly on both rotational/irrotational strains and is used in the framework of an improved RAS (Rahman-Agarwal-Siikonen) one-equation turbulence model to calculate a few well-documented turbulent flows, yielding predictions in good agreement with the direct numerical simulation and experimental data. The strain-dependent Cμ assists the RAS model in constructing the coefficients and functions such as to benefit complex flows with non-equilibrium turbulence. Comparisons with the Spalart-Allmaras one-equation model and the shear stress transport k-ω model demonstrate that Cμ improves the response of RAS model to non-equilibrium effects.

A Correlation-Based Transition Model using Local Variables. Part 2; Test Cases and Industrial Applications

NASA Technical Reports Server (NTRS)

Langtry, R. B.; Menter, F. R.; Likki, S. R.; Suzen, Y. B.; Huang, P. G.; Volker, S.

2006-01-01

A new correlation-based transition model has been developed, which is built strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics (CFD) methods using unstructured grids and massive parallel execution. The model is based on two transport equations, one for the intermittency and one for the transition onset criteria in terms of momentum thickness Reynolds number. The proposed transport equations do not attempt to model the physics of the transition process (unlike, e.g., turbulence models), but form a framework for the implementation of correlation-based models into general-purpose CFD methods.

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

Wu, Wei; Wang, Jin, E-mail: jin.wang.1@stonybrook.edu; State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022 Changchun, China and College of Physics, Jilin University, 130021 Changchun

We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic andmore » thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.« less

Quantified choice of root-mean-square errors of approximation for evaluation and power analysis of small differences between structural equation models.

PubMed

Li, Libo; Bentler, Peter M

2011-06-01

MacCallum, Browne, and Cai (2006) proposed a new framework for evaluation and power analysis of small differences between nested structural equation models (SEMs). In their framework, the null and alternative hypotheses for testing a small difference in fit and its related power analyses were defined by some chosen root-mean-square error of approximation (RMSEA) pairs. In this article, we develop a new method that quantifies those chosen RMSEA pairs and allows a quantitative comparison of them. Our method proposes the use of single RMSEA values to replace the choice of RMSEA pairs for model comparison and power analysis, thus avoiding the differential meaning of the chosen RMSEA pairs inherent in the approach of MacCallum et al. (2006). With this choice, the conventional cutoff values in model overall evaluation can directly be transferred and applied to the evaluation and power analysis of model differences. © 2011 American Psychological Association

Multi-dimensional multi-species modeling of transient electrodeposition in LIGA microfabrication.

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

Evans, Gregory Herbert; Chen, Ken Shuang

2004-06-01

This report documents the efforts and accomplishments of the LIGA electrodeposition modeling project which was headed by the ASCI Materials and Physics Modeling Program. A multi-dimensional framework based on GOMA was developed for modeling time-dependent diffusion and migration of multiple charged species in a dilute electrolyte solution with reduction electro-chemical reactions on moving deposition surfaces. By combining the species mass conservation equations with the electroneutrality constraint, a Poisson equation that explicitly describes the electrolyte potential was derived. The set of coupled, nonlinear equations governing species transport, electric potential, velocity, hydrodynamic pressure, and mesh motion were solved in GOMA, using themore » finite-element method and a fully-coupled implicit solution scheme via Newton's method. By treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and by repeatedly performing re-meshing with CUBIT and re-mapping with MAPVAR, the moving deposition surfaces were tracked explicitly from start of deposition until the trenches were filled with metal, thus enabling the computation of local current densities that potentially influence the microstructure and frictional/mechanical properties of the deposit. The multi-dimensional, multi-species, transient computational framework was demonstrated in case studies of two-dimensional nickel electrodeposition in single and multiple trenches, without and with bath stirring or forced flow. Effects of buoyancy-induced convection on deposition were also investigated. To further illustrate its utility, the framework was employed to simulate deposition in microscreen-based LIGA molds. Lastly, future needs for modeling LIGA electrodeposition are discussed.« less

Upwind methods for the Baer–Nunziato equations and higher-order reconstruction using artificial viscosity

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

Fraysse, F., E-mail: francois.fraysse@rs2n.eu; E. T. S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Madrid; Redondo, C.

This article is devoted to the numerical discretisation of the hyperbolic two-phase flow model of Baer and Nunziato. A special attention is paid on the discretisation of intercell flux functions in the framework of Finite Volume and Discontinuous Galerkin approaches, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. Various upwind approximate Riemann solvers have been tested on a bench of discontinuous test cases. New discretisation schemes are proposed in a Discontinuous Galerkin framework following the criterion of Abgrall and the path-conservative formalism. A stabilisation technique based on artificial viscosity is appliedmore » to the high-order Discontinuous Galerkin method and compared against classical TVD-MUSCL Finite Volume flux reconstruction.« less

Geometrothermodynamic model for the evolution of the Universe

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

Gruber, Christine; Quevedo, Hernando, E-mail: christine.gruber@correo.nucleares.unam.mx, E-mail: quevedo@nucleares.unam.mx

Using the formalism of geometrothermodynamics to derive a fundamental thermodynamic equation, we construct a cosmological model in the framework of relativistic cosmology. In a first step, we describe a system without thermodynamic interaction, and show it to be equivalent to the standard ΛCDM paradigm. The second step includes thermodynamic interaction and produces a model consistent with the main features of inflation. With the proposed fundamental equation we are thus able to describe all the known epochs in the evolution of our Universe, starting from the inflationary phase.

Price dynamics of the financial markets using the stochastic differential equation for a potential double well

NASA Astrophysics Data System (ADS)

Lima, L. S.; Miranda, L. L. B.

2018-01-01

We have used the Itô's stochastic differential equation for the double well with additive white noise as a mathematical model for price dynamics of the financial market. We have presented a model which allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents, with respect to the facts of financial markets. We have obtained the mean price in terms of the β parameter that represents the force of the randomness term of the model.

The thermal-wave model: A Schroedinger-like equation for charged particle beam dynamics

NASA Technical Reports Server (NTRS)

Fedele, Renato; Miele, G.

1994-01-01

We review some results on longitudinal beam dynamics obtained in the framework of the Thermal Wave Model (TWM). In this model, which has recently shown the capability to describe both longitudinal and transverse dynamics of charged particle beams, the beam dynamics is ruled by Schroedinger-like equations for the beam wave functions, whose squared modulus is proportional to the beam density profile. Remarkably, the role of the Planck constant is played by a diffractive constant epsilon, the emittance, which has a thermal nature.

Modeling of surface effects in crystalline materials within the framework of gradient crystal plasticity

NASA Astrophysics Data System (ADS)

Peng, Xiang-Long; Husser, Edgar; Huang, Gan-Yun; Bargmann, Swantje

2018-03-01

A finite-deformation gradient crystal plasticity theory is developed, which takes into account the interaction between dislocations and surfaces. The model captures both energetic and dissipative effects for surfaces penetrable by dislocations. By taking advantage of the principle of virtual power, the surface microscopic boundary equations are obtained naturally. Surface equations govern surface yielding and hardening. A thin film under shear deformation serves as a benchmark problem for validation of the proposed model. It is found that both energetic and dissipative surface effects significantly affect the plastic behavior.

Structural Equation Modeling: A Framework for Ocular and Other Medical Sciences Research

PubMed Central

Christ, Sharon L.; Lee, David J.; Lam, Byron L.; Diane, Zheng D.

2017-01-01

Structural equation modeling (SEM) is a modeling framework that encompasses many types of statistical models and can accommodate a variety of estimation and testing methods. SEM has been used primarily in social sciences but is increasingly used in epidemiology, public health, and the medical sciences. SEM provides many advantages for the analysis of survey and clinical data, including the ability to model latent constructs that may not be directly observable. Another major feature is simultaneous estimation of parameters in systems of equations that may include mediated relationships, correlated dependent variables, and in some instances feedback relationships. SEM allows for the specification of theoretically holistic models because multiple and varied relationships may be estimated together in the same model. SEM has recently expanded by adding generalized linear modeling capabilities that include the simultaneous estimation of parameters of different functional form for outcomes with different distributions in the same model. Therefore, mortality modeling and other relevant health outcomes may be evaluated. Random effects estimation using latent variables has been advanced in the SEM literature and software. In addition, SEM software has increased estimation options. Therefore, modern SEM is quite general and includes model types frequently used by health researchers, including generalized linear modeling, mixed effects linear modeling, and population average modeling. This article does not present any new information. It is meant as an introduction to SEM and its uses in ocular and other health research. PMID:24467557

Managing complexity in simulations of land surface and near-surface processes

DOE PAGES

Coon, Ethan T.; Moulton, J. David; Painter, Scott L.

2016-01-12

Increasing computing power and the growing role of simulation in Earth systems science have led to an increase in the number and complexity of processes in modern simulators. We present a multiphysics framework that specifies interfaces for coupled processes and automates weak and strong coupling strategies to manage this complexity. Process management is enabled by viewing the system of equations as a tree, where individual equations are associated with leaf nodes and coupling strategies with internal nodes. A dynamically generated dependency graph connects a variable to its dependencies, streamlining and automating model evaluation, easing model development, and ensuring models aremore » modular and flexible. Additionally, the dependency graph is used to ensure that data requirements are consistent between all processes in a given simulation. Here we discuss the design and implementation of these concepts within the Arcos framework, and demonstrate their use for verification testing and hypothesis evaluation in numerical experiments.« less

Modeling of active transmembrane transport in a mixture theory framework.

PubMed

Ateshian, Gerard A; Morrison, Barclay; Hung, Clark T

2010-05-01

This study formulates governing equations for active transport across semi-permeable membranes within the framework of the theory of mixtures. In mixture theory, which models the interactions of any number of fluid and solid constituents, a supply term appears in the conservation of linear momentum to describe momentum exchanges among the constituents. In past applications, this momentum supply was used to model frictional interactions only, thereby describing passive transport processes. In this study, it is shown that active transport processes, which impart momentum to solutes or solvent, may also be incorporated in this term. By projecting the equation of conservation of linear momentum along the normal to the membrane, a jump condition is formulated for the mechano-electrochemical potential of fluid constituents which is generally applicable to nonequilibrium processes involving active transport. The resulting relations are simple and easy to use, and address an important need in the membrane transport literature.

Full thermomechanical coupling in modelling of micropolar thermoelasticity

NASA Astrophysics Data System (ADS)

Murashkin, E. V.; Radayev, Y. N.

2018-04-01

The present paper is devoted to plane harmonic waves of displacements and microrotations propagating in fully coupled thermoelastic continua. The analysis is carried out in the framework of linear conventional thermoelastic micropolar continuum model. The reduced energy balance equation and the special form of the Helmholtz free energy are discussed. The constitutive constants providing fully coupling of equations of motion and heat conduction are considered. The dispersion equation is derived and analysed in the form bi-cubic and bi-quadratic polynoms product. The equation are analyzed by the computer algebra system Mathematica. Algebraic forms expressed by complex multivalued square and cubic radicals are obtained for wavenumbers of transverse and longitudinal waves. The exact forms of wavenumbers of a plane harmonic coupled thermoelastic waves are computed.

Anyons in an electromagnetic field and the Bargmann-Michel-Telegdi equation

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

Ghosh, S.

1995-05-15

The Lagrangian model for anyons, presented earlier, is extended to include interactions with an external, homogeneous electromagnetic field. Explicit electric and magnetic moment terms for the anyon are introduced in the Lagrangian. The (2+1)-dimensional Bargmann-Michel-Telegdi equation as well as the correct value (2) of the gyromagnetic ratio is rederived, in the Hamiltonian framework.

A Model of Metacognition, Achievement Goal Orientation, Learning Style and Self-Efficacy

ERIC Educational Resources Information Center

Coutinho, Savia A.; Neuman, George

2008-01-01

Structural equation modelling was used to test a model integrating achievement goal orientation, learning style, self-efficacy and metacognition into a single framework that explained and predicted variation in performance. Self-efficacy was the strongest predictor of performance. Metacognition was a weak predictor of performance. Deep processing…

Hypersurface Homogeneous Cosmological Model in Modified Theory of Gravitation

NASA Astrophysics Data System (ADS)

Katore, S. D.; Hatkar, S. P.; Baxi, R. J.

2016-12-01

We study a hypersurface homogeneous space-time in the framework of the f (R, T) theory of gravitation in the presence of a perfect fluid. Exact solutions of field equations are obtained for exponential and power law volumetric expansions. We also solve the field equations by assuming the proportionality relation between the shear scalar (σ ) and the expansion scalar (θ ). It is observed that in the exponential model, the universe approaches isotropy at large time (late universe). The investigated model is notably accelerating and expanding. The physical and geometrical properties of the investigated model are also discussed.

Hydrodynamics of bacterial colonies: A model

NASA Astrophysics Data System (ADS)

Lega, J.; Passot, T.

2003-03-01

We propose a hydrodynamic model for the evolution of bacterial colonies growing on soft agar plates. This model consists of reaction-diffusion equations for the concentrations of nutrients, water, and bacteria, coupled to a single hydrodynamic equation for the velocity field of the bacteria-water mixture. It captures the dynamics inside the colony as well as on its boundary and allows us to identify a mechanism for collective motion towards fresh nutrients, which, in its modeling aspects, is similar to classical chemotaxis. As shown in numerical simulations, our model reproduces both usual colony shapes and typical hydrodynamic motions, such as the whirls and jets recently observed in wet colonies of Bacillus subtilis. The approach presented here could be extended to different experimental situations and provides a general framework for the use of advection-reaction-diffusion equations in modeling bacterial colonies.

A trajectory generation framework for modeling spacecraft entry in MDAO

NASA Astrophysics Data System (ADS)

D`Souza, Sarah N.; Sarigul-Klijn, Nesrin

2016-04-01

In this paper a novel trajectory generation framework was developed that optimizes trajectory event conditions for use in a Generalized Entry Guidance algorithm. The framework was developed to be adaptable via the use of high fidelity equations of motion and drag based analytical bank profiles. Within this framework, a novel technique was implemented that resolved the sensitivity of the bank profile to atmospheric non-linearities. The framework's adaptability was established by running two different entry bank conditions. Each case yielded a reference trajectory and set of transition event conditions that are flight feasible and implementable in a Generalized Entry Guidance algorithm.

Development of an Adaptive Framework for Management of Military Operations in Arid/Semi-Arid Regions to Minimize Watershed and Instream Impacts from Non-Point Pollution

DTIC Science & Technology

2007-12-01

equivalent TMDL Total Maximum Daily Load USLE Universal Soil Loss Equation VTM Virtual Transect Model WEPP Water Erosion Prediction Project WMS Web...models, which do not reproduce the large storm dominance of sediment yield (e.g., Universal Soil Loss Equation [ USLE ]/RUSLE) significantly underestimate...technology is the USLE /RUSLE soil erosion prediction technology. The USLE (Wischmeier and Smith 1978) is the simplest and historically most widely

Superspace and global stability in general relativity

NASA Astrophysics Data System (ADS)

Gurzadyan, A. V.; Kocharyan, A. A.

A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalized Jacobi equation reformulated for pseudo-Riemannian manifolds. We give a direct formalism for dynamical analysis in the superspace, the requisite equation pertinent for stability analysis of the universe by means of generalized covariant and Fermi derivative is derived. Then, the relevant definitions and formulae are retrieved for cosmological models with a scalar field.

Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations.

PubMed

Meffin, Hamish; Tahayori, Bahman; Grayden, David B; Burkitt, Anthony N

2012-12-01

Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace's equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite's membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

From microscopic taxation and redistribution models to macroscopic income distributions

NASA Astrophysics Data System (ADS)

Bertotti, Maria Letizia; Modanese, Giovanni

2011-10-01

We present here a general framework, expressed by a system of nonlinear differential equations, suitable for the modeling of taxation and redistribution in a closed society. This framework allows one to describe the evolution of income distribution over the population and to explain the emergence of collective features based on knowledge of the individual interactions. By making different choices of the framework parameters, we construct different models, whose long-time behavior is then investigated. Asymptotic stationary distributions are found, which enjoy similar properties as those observed in empirical distributions. In particular, they exhibit power law tails of Pareto type and their Lorenz curves and Gini indices are consistent with some real world ones.

Phase field approaches of bone remodeling based on TIP

NASA Astrophysics Data System (ADS)

Ganghoffer, Jean-François; Rahouadj, Rachid; Boisse, Julien; Forest, Samuel

2016-01-01

The process of bone remodeling includes a cycle of repair, renewal, and optimization. This adaptation process, in response to variations in external loads and chemical driving factors, involves three main types of bone cells: osteoclasts, which remove the old pre-existing bone; osteoblasts, which form the new bone in a second phase; osteocytes, which are sensing cells embedded into the bone matrix, trigger the aforementioned sequence of events. The remodeling process involves mineralization of the bone in the diffuse interface separating the marrow, which contains all specialized cells, from the newly formed bone. The main objective advocated in this contribution is the setting up of a modeling and simulation framework relying on the phase field method to capture the evolution of the diffuse interface between the new bone and the marrow at the scale of individual trabeculae. The phase field describes the degree of mineralization of this diffuse interface; it varies continuously between the lower value (no mineral) and unity (fully mineralized phase, e.g. new bone), allowing the consideration of a diffuse moving interface. The modeling framework is the theory of continuous media, for which field equations for the mechanical, chemical, and interfacial phenomena are written, based on the thermodynamics of irreversible processes. Additional models for the cellular activity are formulated to describe the coupling of the cell activity responsible for bone production/resorption to the kinetics of the internal variables. Kinetic equations for the internal variables are obtained from a pseudo-potential of dissipation. The combination of the balance equations for the microforce associated to the phase field and the kinetic equations lead to the Ginzburg-Landau equation satisfied by the phase field with a source term accounting for the dissipative microforce. Simulations illustrating the proposed framework are performed in a one-dimensional situation showing the evolution of the diffuse interface separating new bone from marrow.

Energy exchange analysis in droplet dynamics via the Navier-Stokes-Cahn-Hilliard model

NASA Astrophysics Data System (ADS)

Espath, L. F. R.; Sarmiento, A. F.; Vignal, P.; Varga, B. O. N.; Cortes, A. M. A.; Dalcin, L.; Calo, V. M.

2016-06-01

We develop the energy budget equation of the coupled Navier-Stokes-Cahn-Hilliard (NSCH) system. We use the NSCH equations to model the dynamics of liquid droplets in a liquid continuum. Buoyancy effects are accounted for through the Boussinesq assumption. We physically interpret each quantity involved in the energy exchange to further insight into the model. Highly resolved simulations involving density-driven flows and merging of droplets allow us to analyze these energy budgets. In particular, we focus on the energy exchanges when droplets merge, and describe flow features relevant to this phenomenon. By comparing our numerical simulations to analytical predictions and experimental results available in the literature, we conclude that modeling droplet dynamics within the framework of NSCH equations is a sensible approach worth further research.

Regionally Adaptable Ground Motion Prediction Equation (GMPE) from Empirical Models of Fourier and Duration of Ground Motion

NASA Astrophysics Data System (ADS)

Bora, Sanjay; Scherbaum, Frank; Kuehn, Nicolas; Stafford, Peter; Edwards, Benjamin

2016-04-01

The current practice of deriving empirical ground motion prediction equations (GMPEs) involves using ground motions recorded at multiple sites. However, in applications like site-specific (e.g., critical facility) hazard ground motions obtained from the GMPEs are need to be adjusted/corrected to a particular site/site-condition under investigation. This study presents a complete framework for developing a response spectral GMPE, within which the issue of adjustment of ground motions is addressed in a manner consistent with the linear system framework. The present approach is a two-step process in which the first step consists of deriving two separate empirical models, one for Fourier amplitude spectra (FAS) and the other for a random vibration theory (RVT) optimized duration (Drvto) of ground motion. In the second step the two models are combined within the RVT framework to obtain full response spectral amplitudes. Additionally, the framework also involves a stochastic model based extrapolation of individual Fourier spectra to extend the useable frequency limit of the empirically derived FAS model. The stochastic model parameters were determined by inverting the Fourier spectral data using an approach similar to the one as described in Edwards and Faeh (2013). Comparison of median predicted response spectra from present approach with those from other regional GMPEs indicates that the present approach can also be used as a stand-alone model. The dataset used for the presented analysis is a subset of the recently compiled database RESORCE-2012 across Europe, the Middle East and the Mediterranean region.

Phase-field modeling of isothermal quasi-incompressible multicomponent liquids

NASA Astrophysics Data System (ADS)

Tóth, Gyula I.

2016-09-01

In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional) and (ii) can influence nonequilibrium pattern formation significantly.

A Comparative Investigation of TPB and Altruism Frameworks for an Empirically Based Communication Approach to Enhance Paper Recycling

ERIC Educational Resources Information Center

Chaisamrej, Rungrat; Zimmerman, Rick S.

2014-01-01

This research compared the ability of the theory of planned behavior (TPB) and the altruism framework (AM) to predict paper-recycling behavior. It was comprised of formative research and a major survey. Data collected from 628 undergraduate students in Thailand were analyzed using structural equation modeling. Results showed that TPB was superior…

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

PubMed

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

2018-06-01

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

Challenges in soil erosion research and prediction model development

USDA-ARS?s Scientific Manuscript database

Quantification of soil erosion has been traditionally considered as a surface hydrologic process with equations for soil detachment and sediment transport derived from the mechanics and hydraulics of the rainfall and surface flow. Under the current erosion modeling framework, the soil has a constant...

The ACTIVE conceptual framework as a structural equation model.

PubMed

Gross, Alden L; Payne, Brennan R; Casanova, Ramon; Davoudzadeh, Pega; Dzierzewski, Joseph M; Farias, Sarah; Giovannetti, Tania; Ip, Edward H; Marsiske, Michael; Rebok, George W; Schaie, K Warner; Thomas, Kelsey; Willis, Sherry; Jones, Richard N

2018-01-01

Background/Study Context: Conceptual frameworks are analytic models at a high level of abstraction. Their operationalization can inform randomized trial design and sample size considerations. The Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE) conceptual framework was empirically tested using structural equation modeling (N=2,802). ACTIVE was guided by a conceptual framework for cognitive training in which proximal cognitive abilities (memory, inductive reasoning, speed of processing) mediate treatment-related improvement in primary outcomes (everyday problem-solving, difficulty with activities of daily living, everyday speed, driving difficulty), which in turn lead to improved secondary outcomes (health-related quality of life, health service utilization, mobility). Measurement models for each proximal, primary, and secondary outcome were developed and tested using baseline data. Each construct was then combined in one model to evaluate fit (RMSEA, CFI, normalized residuals of each indicator). To expand the conceptual model and potentially inform future trials, evidence of modification of structural model parameters was evaluated by age, years of education, sex, race, and self-rated health status. Preconceived measurement models for memory, reasoning, speed of processing, everyday problem-solving, instrumental activities of daily living (IADL) difficulty, everyday speed, driving difficulty, and health-related quality of life each fit well to the data (all RMSEA < .05; all CFI > .95). Fit of the full model was excellent (RMSEA = .038; CFI = .924). In contrast with previous findings from ACTIVE regarding who benefits from training, interaction testing revealed associations between proximal abilities and primary outcomes are stronger on average by nonwhite race, worse health, older age, and less education (p < .005). Empirical data confirm the hypothesized ACTIVE conceptual model. Findings suggest that the types of people who show intervention effects on cognitive performance potentially may be different from those with the greatest chance of transfer to real-world activities.

Methods for compressible multiphase flows and their applications

NASA Astrophysics Data System (ADS)

Kim, H.; Choe, Y.; Kim, H.; Min, D.; Kim, C.

2018-06-01

This paper presents an efficient and robust numerical framework to deal with multiphase real-fluid flows and their broad spectrum of engineering applications. A homogeneous mixture model incorporated with a real-fluid equation of state and a phase change model is considered to calculate complex multiphase problems. As robust and accurate numerical methods to handle multiphase shocks and phase interfaces over a wide range of flow speeds, the AUSMPW+_N and RoeM_N schemes with a system preconditioning method are presented. These methods are assessed by extensive validation problems with various types of equation of state and phase change models. Representative realistic multiphase phenomena, including the flow inside a thermal vapor compressor, pressurization in a cryogenic tank, and unsteady cavitating flow around a wedge, are then investigated as application problems. With appropriate physical modeling followed by robust and accurate numerical treatments, compressible multiphase flow physics such as phase changes, shock discontinuities, and their interactions are well captured, confirming the suitability of the proposed numerical framework to wide engineering applications.

Evolutionary prisoner's dilemma games coevolving on adaptive networks.

PubMed

Lee, Hsuan-Wei; Malik, Nishant; Mucha, Peter J

2018-02-01

We study a model for switching strategies in the Prisoner's Dilemma game on adaptive networks of player pairings that coevolve as players attempt to maximize their return. We use a node-based strategy model wherein each player follows one strategy at a time (cooperate or defect) across all of its neighbors, changing that strategy and possibly changing partners in response to local changes in the network of player pairing and in the strategies used by connected partners. We compare and contrast numerical simulations with existing pair approximation differential equations for describing this system, as well as more accurate equations developed here using the framework of approximate master equations. We explore the parameter space of the model, demonstrating the relatively high accuracy of the approximate master equations for describing the system observations made from simulations. We study two variations of this partner-switching model to investigate the system evolution, predict stationary states, and compare the total utilities and other qualitative differences between these two model variants.

Frequentist Model Averaging in Structural Equation Modelling.

PubMed

Jin, Shaobo; Ankargren, Sebastian

2018-06-04

Model selection from a set of candidate models plays an important role in many structural equation modelling applications. However, traditional model selection methods introduce extra randomness that is not accounted for by post-model selection inference. In the current study, we propose a model averaging technique within the frequentist statistical framework. Instead of selecting an optimal model, the contributions of all candidate models are acknowledged. Valid confidence intervals and a [Formula: see text] test statistic are proposed. A simulation study shows that the proposed method is able to produce a robust mean-squared error, a better coverage probability, and a better goodness-of-fit test compared to model selection. It is an interesting compromise between model selection and the full model.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

NASA Astrophysics Data System (ADS)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

Analysis of Flame Deflector Spray Nozzles in Rocket Engine Test Stands

NASA Technical Reports Server (NTRS)

Sachdev, Jai S.; Ahuja, Vineet; Hosangadi, Ashvin; Allgood, Daniel C.

2010-01-01

The development of a unified tightly coupled multi-phase computational framework is described for the analysis and design of cooling spray nozzle configurations on the flame deflector in rocket engine test stands. An Eulerian formulation is used to model the disperse phase and is coupled to the gas-phase equations through momentum and heat transfer as well as phase change. The phase change formulation is modeled according to a modified form of the Hertz-Knudsen equation. Various simple test cases are presented to verify the validity of the numerical framework. The ability of the methodology to accurately predict the temperature load on the flame deflector is demonstrated though application to an actual sub-scale test facility. The CFD simulation was able to reproduce the result of the test-firing, showing that the spray nozzle configuration provided insufficient amount of cooling.

Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems

NASA Astrophysics Data System (ADS)

Williams, Rube B.

2004-02-01

Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.

Numerical modelling in biosciences using delay differential equations

NASA Astrophysics Data System (ADS)

Bocharov, Gennadii A.; Rihan, Fathalla A.

2000-12-01

Our principal purposes here are (i) to consider, from the perspective of applied mathematics, models of phenomena in the biosciences that are based on delay differential equations and for which numerical approaches are a major tool in understanding their dynamics, (ii) to review the application of numerical techniques to investigate these models. We show that there are prima facie reasons for using such models: (i) they have a richer mathematical framework (compared with ordinary differential equations) for the analysis of biosystem dynamics, (ii) they display better consistency with the nature of certain biological processes and predictive results. We analyze both the qualitative and quantitative role that delays play in basic time-lag models proposed in population dynamics, epidemiology, physiology, immunology, neural networks and cell kinetics. We then indicate suitable computational techniques for the numerical treatment of mathematical problems emerging in the biosciences, comparing them with those implemented by the bio-modellers.

BioMog: A Computational Framework for the De Novo Generation or Modification of Essential Biomass Components

PubMed Central

Tervo, Christopher J.; Reed, Jennifer L.

2013-01-01

The success of genome-scale metabolic modeling is contingent on a model's ability to accurately predict growth and metabolic behaviors. To date, little focus has been directed towards developing systematic methods of proposing, modifying and interrogating an organism's biomass requirements that are used in constraint-based models. To address this gap, the biomass modification and generation (BioMog) framework was created and used to generate lists of biomass components de novo, as well as to modify predefined biomass component lists, for models of Escherichia coli (iJO1366) and of Shewanella oneidensis (iSO783) from high-throughput growth phenotype and fitness datasets. BioMog's de novo biomass component lists included, either implicitly or explicitly, up to seventy percent of the components included in the predefined biomass equations, and the resulting de novo biomass equations outperformed the predefined biomass equations at qualitatively predicting mutant growth phenotypes by up to five percent. Additionally, the BioMog procedure can quantify how many experiments support or refute a particular metabolite's essentiality to a cell, and it facilitates the determination of inconsistent experiments and inaccurate reaction and/or gene to reaction associations. To further interrogate metabolite essentiality, the BioMog framework includes an experiment generation algorithm that allows for the design of experiments to test whether a metabolite is essential. Using BioMog, we correct experimental results relating to the essentiality of thyA gene in E. coli, as well as perform knockout experiments supporting the essentiality of protoheme. With these capabilities, BioMog can be a valuable resource for analyzing growth phenotyping data and component of a model developer's toolbox. PMID:24339916

Stochastic modelling of non-stationary financial assets

NASA Astrophysics Data System (ADS)

Estevens, Joana; Rocha, Paulo; Boto, João P.; Lind, Pedro G.

2017-11-01

We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic variables in other research fields, namely, biology, medicine, and geology.

On the thermodynamic framework of generalized coupled thermoelastic-viscoplastic-damage modeling

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Saleeb, A. F.

1991-01-01

A complete potential based framework using internal state variables is put forth for the derivation of reversible and irreversible constitutive equations. In this framework, the existence of the total (integrated) form of either the (Helmholtz) free energy or the (Gibbs) complementary free energy are assumed a priori. Two options for describing the flow and evolutionary equations are described, wherein option one (the fully coupled form) is shown to be over restrictive while the second option (the decoupled form) provides significant flexibility. As a consequence of the decoupled form, a new operator, i.e., the Compliance operator, is defined which provides a link between the assumed Gibb's and complementary dissipation potential and ensures a number of desirable numerical features, for example the symmetry of the resulting consistent tangent stiffness matrix. An important conclusion reached, is that although many theories in the literature do not conform to the general potential framework outlined, it is still possible in some cases, by slight modifications of the used forms, to restore the complete potential structure.

Equation-free multiscale computation: algorithms and applications.

PubMed

Kevrekidis, Ioannis G; Samaey, Giovanni

2009-01-01

In traditional physicochemical modeling, one derives evolution equations at the (macroscopic, coarse) scale of interest; these are used to perform a variety of tasks (simulation, bifurcation analysis, optimization) using an arsenal of analytical and numerical techniques. For many complex systems, however, although one observes evolution at a macroscopic scale of interest, accurate models are only given at a more detailed (fine-scale, microscopic) level of description (e.g., lattice Boltzmann, kinetic Monte Carlo, molecular dynamics). Here, we review a framework for computer-aided multiscale analysis, which enables macroscopic computational tasks (over extended spatiotemporal scales) using only appropriately initialized microscopic simulation on short time and length scales. The methodology bypasses the derivation of macroscopic evolution equations when these equations conceptually exist but are not available in closed form-hence the term equation-free. We selectively discuss basic algorithms and underlying principles and illustrate the approach through representative applications. We also discuss potential difficulties and outline areas for future research.

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

NASA Astrophysics Data System (ADS)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

2007-10-01

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

A general science-based framework for dynamical spatio-temporal models

USGS Publications Warehouse

Wikle, C.K.; Hooten, M.B.

2010-01-01

Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially-explicit processes that evolve over time. Correspondingly, in recent years there has been a significant amount of research on new statistical methodology for such models. Although descriptive models that approach the problem from the second-order (covariance) perspective are important, and innovative work is being done in this regard, many real-world processes are dynamic, and it can be more efficient in some cases to characterize the associated spatio-temporal dependence by the use of dynamical models. The chief challenge with the specification of such dynamical models has been related to the curse of dimensionality. Even in fairly simple linear, first-order Markovian, Gaussian error settings, statistical models are often over parameterized. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters. In addition, this framework has allowed for the specification of science based parameterizations (and associated prior distributions) in which classes of deterministic dynamical models (e. g., partial differential equations (PDEs), integro-difference equations (IDEs), matrix models, and agent-based models) are used to guide specific parameterizations. Most of the focus for the application of such models in statistics has been in the linear case. The problems mentioned above with linear dynamic models are compounded in the case of nonlinear models. In this sense, the need for coherent and sensible model parameterizations is not only helpful, it is essential. Here, we present an overview of a framework for incorporating scientific information to motivate dynamical spatio-temporal models. First, we illustrate the methodology with the linear case. We then develop a general nonlinear spatio-temporal framework that we call general quadratic nonlinearity and demonstrate that it accommodates many different classes of scientific-based parameterizations as special cases. The model is presented in a hierarchical Bayesian framework and is illustrated with examples from ecology and oceanography. ?? 2010 Sociedad de Estad??stica e Investigaci??n Operativa.

Printer model for dot-on-dot halftone screens

NASA Astrophysics Data System (ADS)

Balasubramanian, Raja

1995-04-01

A printer model is described for dot-on-dot halftone screens. For a given input CMYK signal, the model predicts the resulting spectral reflectance of the printed patch. The model is derived in two steps. First, the C, M, Y, K dot growth functions are determined which relate the input digital value to the actual dot area coverages of the colorants. Next, the reflectance of a patch is predicted as a weighted combination of the reflectances of the four solid C, M, Y, K patches and their various overlays. This approach is analogous to the Neugebauer model, with the random mixing equations being replaced by dot-on-dot mixing equations. A Yule-Neilsen correction factor is incorporated to account for light scattering within the paper. The dot area functions and Yule-Neilsen parameter are chosen to optimize the fit to a set of training data. The model is also extended to a cellular framework, requiring additional measurements. The model is tested with a four color xerographic printer employing a line-on-line halftone screen. CIE L*a*b* errors are obtained between measurements and model predictions. The Yule-Neilsen factor significantly decreases the model error. Accuracy is also increased with the use of a cellular framework.

Viscoelastic tides: models for use in Celestial Mechanics

NASA Astrophysics Data System (ADS)

Ragazzo, C.; Ruiz, L. S.

2017-05-01

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

Numerical Coupling and Simulation of Point-Mass System with the Turbulent Fluid Flow

NASA Astrophysics Data System (ADS)

Gao, Zheng

A computational framework that combines the Eulerian description of the turbulence field with a Lagrangian point-mass ensemble is proposed in this dissertation. Depending on the Reynolds number, the turbulence field is simulated using Direct Numerical Simulation (DNS) or eddy viscosity model. In the meanwhile, the particle system, such as spring-mass system and cloud droplets, are modeled using the ordinary differential system, which is stiff and hence poses a challenge to the stability of the entire system. This computational framework is applied to the numerical study of parachute deceleration and cloud microphysics. These two distinct problems can be uniformly modeled with Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs), and numerically solved in the same framework. For the parachute simulation, a novel porosity model is proposed to simulate the porous effects of the parachute canopy. This model is easy to implement with the projection method and is able to reproduce Darcy's law observed in the experiment. Moreover, the impacts of using different versions of k-epsilon turbulence model in the parachute simulation have been investigated and conclude that the standard and Re-Normalisation Group (RNG) model may overestimate the turbulence effects when Reynolds number is small while the Realizable model has a consistent performance with both large and small Reynolds number. For another application, cloud microphysics, the cloud entrainment-mixing problem is studied in the same numerical framework. Three sets of DNS are carried out with both decaying and forced turbulence. The numerical result suggests a new way parameterize the cloud mixing degree using the dynamical measures. The numerical experiments also verify the negative relationship between the droplets number concentration and the vorticity field. The results imply that the gravity has fewer impacts on the forced turbulence than the decaying turbulence. In summary, the proposed framework can be used to solve a physics problem that involves turbulence field and point-mass system, and therefore has a broad application.

Coupled Thermo-Hydro-Mechanical Numerical Framework for Simulating Unconventional Formations

NASA Astrophysics Data System (ADS)

Garipov, T. T.; White, J. A.; Lapene, A.; Tchelepi, H.

2016-12-01

Unconventional deposits are found in all world oil provinces. Modeling these systems is challenging, however, due to complex thermo-hydro-mechanical processes that govern their behavior. As a motivating example, we consider in situ thermal processing of oil shale deposits. When oil shale is heated to sufficient temperatures, kerogen can be converted to oil and gas products over a relatively short timespan. This phase change dramatically impact both the mechanical and hydrologic properties of the rock, leading to strongly coupled THMC interactions. Here, we present a numerical framework for simulating tightly-coupled chemistry, geomechanics, and multiphase flow within a reservoir simulator (the AD-GPRS General Purpose Research Simulator). We model changes in constitutive behavior of the rock using a thermoplasticity model that accounts for microstructural evolution. The multi-component, multiphase flow and transport processes of both mass and heat are modeled at the macroscopic (e.g., Darcy) scale. The phase compositions and properties are described by a cubic equation of state; Arrhenius-type chemical reactions are used to represent kerogen conversion. The system of partial differential equations is discretized using a combination of finite-volumes and finite-elements, respectively, for the flow and mechanics problems. Fully implicit and sequentially implicit method are used to solve resulting nonlinear problem. The proposed framework is verified against available analytical and numerical benchmark cases. We demonstrate the efficiency, performance, and capabilities of the proposed simulation framework by analyzing near well deformation in an oil shale formation.

Establishing an Explanatory Model for Mathematics Identity

ERIC Educational Resources Information Center

Cribbs, Jennifer D.; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M.

2015-01-01

This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence…

A General Approach to Causal Mediation Analysis

ERIC Educational Resources Information Center

Imai, Kosuke; Keele, Luke; Tingley, Dustin

2010-01-01

Traditionally in the social sciences, causal mediation analysis has been formulated, understood, and implemented within the framework of linear structural equation models. We argue and demonstrate that this is problematic for 3 reasons: the lack of a general definition of causal mediation effects independent of a particular statistical model, the…

A Framework for Designing Optimal Spacecraft Formations

DTIC Science & Technology

2002-09-01

to the Hill- Clohessy - Wiltshire equations were reproduced. For an example using elliptical reference orbits, Reference 17 outlines a solution with...2001. 15. Clohessy , W.H. and Wiltshire , R. S., “Terminal Guidance System for Satellite Rendezvous,” Journal of the Aerospace Sciences, Vol.27, No...Hill- Clohessy -Wiltshire15 (C-W) equations were chosen as the first model specifically because the solutions were known. This allowed a validation

Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Oleschko, K.; Khrennikov, A.

2017-10-01

This paper is about a novel mathematical framework to model transport (of, e.g., fluid or gas) through networks of capillaries. This framework takes into account the tree structure of the networks of capillaries. (Roughly speaking, we use the tree-like system of coordinates.) As is well known, tree-geometry can be topologically described as the geometry of an ultrametric space, i.e., a metric space in which the metric satisfies the strong triangle inequality: in each triangle, the third side is less than or equal to the maximum of two other sides. Thus transport (e.g., of oil or emulsion of oil and water in porous media, or blood and air in biological organisms) through networks of capillaries can be mathematically modelled as ultrametric diffusion. Such modelling was performed in a series of recently published papers of the authors. However, the process of transport through capillaries can be only approximately described by the linear diffusion, because the concentration of, e.g., oil droplets, in a capillary can essentially modify the dynamics. Therefore nonlinear dynamical equations provide a more adequate model of transport in a network of capillaries. We consider a nonlinear ultrametric diffusion equation with quadratic nonlinearity - to model transport in such a network. Here, as in the linear case, we apply the theory of ultrametric wavelets. The paper also contains a simple introduction to theory of ultrametric spaces and analysis on them.

Four-fluid MHD Simulations of the Plasma and Neutral Gas Environment of Comet Churyumov-Gerasimenko Near Perihelion

NASA Astrophysics Data System (ADS)

Huang, Z.; Toth, G.; Gombosi, T.; Jia, X.; Rubin, M.; Fougere, N.; Tenishev, V.; Combi, M.; Bieler, A.; Hansen, K.; Shou, Y.; Altwegg, K.

2015-10-01

We develop a 3-D four fluid model to study the plasma environment of comet Churyumov- Gerasimenko (CG), which is the target of the Rosetta mission. Our model is based on BATS-R-US within the SWMF (Space Weather Modeling Framework) that solves the governing multifluid MHD equations and and the Euler equations for the neutral gas fluid. These equations describe the behavior and interactions of the cometary heavy ions, the solar wind protons, the electrons, and the neutrals. This model incorporates mass loading processes, including photo and electron impact ionization, furthermore taken into account are charge exchange, dissociative ion-electron recombination, as well as collisional interactions between different fluids. We simulate the near nucleus plasma and neutral gas environment with a realistic shape model of CG near perihelion and compare our simulation results with Rosetta observations.

Estimating unknown input parameters when implementing the NGA ground-motion prediction equations in engineering practice

USGS Publications Warehouse

Kaklamanos, James; Baise, Laurie G.; Boore, David M.

2011-01-01

The ground-motion prediction equations (GMPEs) developed as part of the Next Generation Attenuation of Ground Motions (NGA-West) project in 2008 are becoming widely used in seismic hazard analyses. However, these new models are considerably more complicated than previous GMPEs, and they require several more input parameters. When employing the NGA models, users routinely face situations in which some of the required input parameters are unknown. In this paper, we present a framework for estimating the unknown source, path, and site parameters when implementing the NGA models in engineering practice, and we derive geometrically-based equations relating the three distance measures found in the NGA models. Our intent is for the content of this paper not only to make the NGA models more accessible, but also to help with the implementation of other present or future GMPEs.

Diffusion Coefficients from Molecular Dynamics Simulations in Binary and Ternary Mixtures

NASA Astrophysics Data System (ADS)

Liu, Xin; Schnell, Sondre K.; Simon, Jean-Marc; Krüger, Peter; Bedeaux, Dick; Kjelstrup, Signe; Bardow, André; Vlugt, Thijs J. H.

2013-07-01

Multicomponent diffusion in liquids is ubiquitous in (bio)chemical processes. It has gained considerable and increasing interest as it is often the rate limiting step in a process. In this paper, we review methods for calculating diffusion coefficients from molecular simulation and predictive engineering models. The main achievements of our research during the past years can be summarized as follows: (1) we introduced a consistent method for computing Fick diffusion coefficients using equilibrium molecular dynamics simulations; (2) we developed a multicomponent Darken equation for the description of the concentration dependence of Maxwell-Stefan diffusivities. In the case of infinite dilution, the multicomponent Darken equation provides an expression for [InlineEquation not available: see fulltext.] which can be used to parametrize the generalized Vignes equation; and (3) a predictive model for self-diffusivities was proposed for the parametrization of the multicomponent Darken equation. This equation accurately describes the concentration dependence of self-diffusivities in weakly associating systems. With these methods, a sound framework for the prediction of mutual diffusion in liquids is achieved.

A stochastic differential equation model of diurnal cortisol patterns

NASA Technical Reports Server (NTRS)

Brown, E. N.; Meehan, P. M.; Dempster, A. P.

2001-01-01

Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.

From Physics Model to Results: An Optimizing Framework for Cross-Architecture Code Generation

DOE PAGES

Blazewicz, Marek; Hinder, Ian; Koppelman, David M.; ...

2013-01-01

Starting from a high-level problem description in terms of partial differential equations using abstract tensor notation, the Chemora framework discretizes, optimizes, and generates complete high performance codes for a wide range of compute architectures. Chemora extends the capabilities of Cactus, facilitating the usage of large-scale CPU/GPU systems in an efficient manner for complex applications, without low-level code tuning. Chemora achieves parallelism through MPI and multi-threading, combining OpenMP and CUDA. Optimizations include high-level code transformations, efficient loop traversal strategies, dynamically selected data and instruction cache usage strategies, and JIT compilation of GPU code tailored to the problem characteristics. The discretization ismore » based on higher-order finite differences on multi-block domains. Chemora's capabilities are demonstrated by simulations of black hole collisions. This problem provides an acid test of the framework, as the Einstein equations contain hundreds of variables and thousands of terms.« less

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.

PubMed

Gomez, Christophe; Hartung, Niklas

2018-01-01

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

A Catchment-Based Land Surface Model for GCMs and the Framework for its Evaluation

NASA Technical Reports Server (NTRS)

Ducharen, A.; Koster, R. D.; Suarez, M. J.; Kumar, P.

1998-01-01

A new GCM-scale land surface modeling strategy that explicitly accounts for subgrid soil moisture variability and its effects on evaporation and runoff is now being explored. In a break from traditional modeling strategies, the continental surface is disaggregated into a mosaic of hydrological catchments, with boundaries that are not dictated by a regular grid but by topography. Within each catchment, the variability of soil moisture is deduced from TOP-MODEL equations with a special treatment of the unsaturated zone. This paper gives an overview of this new approach and presents the general framework for its off-line evaluation over North-America.

Framework for analyzing ecological trait-based models in multidimensional niche spaces

NASA Astrophysics Data System (ADS)

Biancalani, Tommaso; DeVille, Lee; Goldenfeld, Nigel

2015-05-01

We develop a theoretical framework for analyzing ecological models with a multidimensional niche space. Our approach relies on the fact that ecological niches are described by sequences of symbols, which allows us to include multiple phenotypic traits. Ecological drivers, such as competitive exclusion, are modeled by introducing the Hamming distance between two sequences. We show that a suitable transform diagonalizes the community interaction matrix of these models, making it possible to predict the conditions for niche differentiation and, close to the instability onset, the asymptotically long time population distributions of niches. We exemplify our method using the Lotka-Volterra equations with an exponential competition kernel.

Computational fluid dynamics modeling of laminar, transitional, and turbulent flows with sensitivity to streamline curvature and rotational effects

NASA Astrophysics Data System (ADS)

Chitta, Varun

Modeling of complex flows involving the combined effects of flow transition and streamline curvature using two advanced turbulence models, one in the Reynolds-averaged Navier-Stokes (RANS) category and the other in the hybrid RANS-Large eddy simulation (LES) category is considered in this research effort. In the first part of the research, a new scalar eddy-viscosity model (EVM) is proposed, designed to exhibit physically correct responses to flow transition, streamline curvature, and system rotation effects. The four equation model developed herein is a curvature-sensitized version of a commercially available three-equation transition-sensitive model. The physical effects of rotation and curvature (RC) enter the model through the added transport equation, analogous to a transverse turbulent velocity scale. The eddy-viscosity has been redefined such that the proposed model is constrained to reduce to the original transition-sensitive model definition in nonrotating flows or in regions with negligible RC effects. In the second part of the research, the developed four-equation model is combined with a LES technique using a new hybrid modeling framework, dynamic hybrid RANS-LES. The new framework is highly generalized, allowing coupling of any desired LES model with any given RANS model and addresses several deficiencies inherent in most current hybrid models. In the present research effort, the DHRL model comprises of the proposed four-equation model for RANS component and the MILES scheme for LES component. Both the models were implemented into a commercial computational fluid dynamics (CFD) solver and tested on a number of engineering and generic flow problems. Results from both the RANS and hybrid models show successful resolution of the combined effects of transition and curvature with reasonable engineering accuracy, and for only a small increase in computational cost. In addition, results from the hybrid model indicate significant levels of turbulent fluctuations in the flowfield, improved accuracy compared to RANS models predictions, and are obtained at a significant reduction of computational cost compared to full LES models. The results suggest that the advanced turbulence modeling techniques presented in this research effort have potential as practical tools for solving low/high Re flows over blunt/curved bodies for the prediction of transition and RC effects.

Automated numerical simulation of biological pattern formation based on visual feedback simulation framework

PubMed Central

Sun, Mingzhu; Xu, Hui; Zeng, Xingjuan; Zhao, Xin

2017-01-01

There are various fantastic biological phenomena in biological pattern formation. Mathematical modeling using reaction-diffusion partial differential equation systems is employed to study the mechanism of pattern formation. However, model parameter selection is both difficult and time consuming. In this paper, a visual feedback simulation framework is proposed to calculate the parameters of a mathematical model automatically based on the basic principle of feedback control. In the simulation framework, the simulation results are visualized, and the image features are extracted as the system feedback. Then, the unknown model parameters are obtained by comparing the image features of the simulation image and the target biological pattern. Considering two typical applications, the visual feedback simulation framework is applied to fulfill pattern formation simulations for vascular mesenchymal cells and lung development. In the simulation framework, the spot, stripe, labyrinthine patterns of vascular mesenchymal cells, the normal branching pattern and the branching pattern lacking side branching for lung branching are obtained in a finite number of iterations. The simulation results indicate that it is easy to achieve the simulation targets, especially when the simulation patterns are sensitive to the model parameters. Moreover, this simulation framework can expand to other types of biological pattern formation. PMID:28225811

Automated numerical simulation of biological pattern formation based on visual feedback simulation framework.

PubMed

Sun, Mingzhu; Xu, Hui; Zeng, Xingjuan; Zhao, Xin

2017-01-01

There are various fantastic biological phenomena in biological pattern formation. Mathematical modeling using reaction-diffusion partial differential equation systems is employed to study the mechanism of pattern formation. However, model parameter selection is both difficult and time consuming. In this paper, a visual feedback simulation framework is proposed to calculate the parameters of a mathematical model automatically based on the basic principle of feedback control. In the simulation framework, the simulation results are visualized, and the image features are extracted as the system feedback. Then, the unknown model parameters are obtained by comparing the image features of the simulation image and the target biological pattern. Considering two typical applications, the visual feedback simulation framework is applied to fulfill pattern formation simulations for vascular mesenchymal cells and lung development. In the simulation framework, the spot, stripe, labyrinthine patterns of vascular mesenchymal cells, the normal branching pattern and the branching pattern lacking side branching for lung branching are obtained in a finite number of iterations. The simulation results indicate that it is easy to achieve the simulation targets, especially when the simulation patterns are sensitive to the model parameters. Moreover, this simulation framework can expand to other types of biological pattern formation.

GLOFRIM v1.0 - A globally applicable computational framework for integrated hydrological-hydrodynamic modelling

NASA Astrophysics Data System (ADS)

Hoch, Jannis M.; Neal, Jeffrey C.; Baart, Fedor; van Beek, Rens; Winsemius, Hessel C.; Bates, Paul D.; Bierkens, Marc F. P.

2017-10-01

We here present GLOFRIM, a globally applicable computational framework for integrated hydrological-hydrodynamic modelling. GLOFRIM facilitates spatially explicit coupling of hydrodynamic and hydrologic models and caters for an ensemble of models to be coupled. It currently encompasses the global hydrological model PCR-GLOBWB as well as the hydrodynamic models Delft3D Flexible Mesh (DFM; solving the full shallow-water equations and allowing for spatially flexible meshing) and LISFLOOD-FP (LFP; solving the local inertia equations and running on regular grids). The main advantages of the framework are its open and free access, its global applicability, its versatility, and its extensibility with other hydrological or hydrodynamic models. Before applying GLOFRIM to an actual test case, we benchmarked both DFM and LFP for a synthetic test case. Results show that for sub-critical flow conditions, discharge response to the same input signal is near-identical for both models, which agrees with previous studies. We subsequently applied the framework to the Amazon River basin to not only test the framework thoroughly, but also to perform a first-ever benchmark of flexible and regular grids on a large-scale. Both DFM and LFP produce comparable results in terms of simulated discharge with LFP exhibiting slightly higher accuracy as expressed by a Kling-Gupta efficiency of 0.82 compared to 0.76 for DFM. However, benchmarking inundation extent between DFM and LFP over the entire study area, a critical success index of 0.46 was obtained, indicating that the models disagree as often as they agree. Differences between models in both simulated discharge and inundation extent are to a large extent attributable to the gridding techniques employed. In fact, the results show that both the numerical scheme of the inundation model and the gridding technique can contribute to deviations in simulated inundation extent as we control for model forcing and boundary conditions. This study shows that the presented computational framework is robust and widely applicable. GLOFRIM is designed as open access and easily extendable, and thus we hope that other large-scale hydrological and hydrodynamic models will be added. Eventually, more locally relevant processes would be captured and more robust model inter-comparison, benchmarking, and ensemble simulations of flood hazard on a large scale would be allowed for.

Signature modelling and radiometric rendering equations in infrared scene simulation systems

NASA Astrophysics Data System (ADS)

Willers, Cornelius J.; Willers, Maria S.; Lapierre, Fabian

2011-11-01

The development and optimisation of modern infrared systems necessitates the use of simulation systems to create radiometrically realistic representations (e.g. images) of infrared scenes. Such simulation systems are used in signature prediction, the development of surveillance and missile sensors, signal/image processing algorithm development and aircraft self-protection countermeasure system development and evaluation. Even the most cursory investigation reveals a multitude of factors affecting the infrared signatures of realworld objects. Factors such as spectral emissivity, spatial/volumetric radiance distribution, specular reflection, reflected direct sunlight, reflected ambient light, atmospheric degradation and more, all affect the presentation of an object's instantaneous signature. The signature is furthermore dynamically varying as a result of internal and external influences on the object, resulting from the heat balance comprising insolation, internal heat sources, aerodynamic heating (airborne objects), conduction, convection and radiation. In order to accurately render the object's signature in a computer simulation, the rendering equations must therefore account for all the elements of the signature. In this overview paper, the signature models, rendering equations and application frameworks of three infrared simulation systems are reviewed and compared. The paper first considers the problem of infrared scene simulation in a framework for simulation validation. This approach provides concise definitions and a convenient context for considering signature models and subsequent computer implementation. The primary radiometric requirements for an infrared scene simulator are presented next. The signature models and rendering equations implemented in OSMOSIS (Belgian Royal Military Academy), DIRSIG (Rochester Institute of Technology) and OSSIM (CSIR & Denel Dynamics) are reviewed. In spite of these three simulation systems' different application focus areas, their underlying physics-based approach is similar. The commonalities and differences between the different systems are investigated, in the context of their somewhat different application areas. The application of an infrared scene simulation system towards the development of imaging missiles and missile countermeasures are briefly described. Flowing from the review of the available models and equations, recommendations are made to further enhance and improve the signature models and rendering equations in infrared scene simulators.

Assessing Tsunami Vulnerabilities of Geographies with Shallow Water Equations

NASA Technical Reports Server (NTRS)

Aras, Rifat; Shen, Yuzhong

2012-01-01

Tsunami preparedness is crucial for saving human lives in case of disasters that involve massive water movement. In this work, we develop a framework for visual assessment of tsunami preparedness of geographies. Shallow water equations (also called Saint Venant equations) are a set of hyperbolic partial differential equations that are derived by depth-integrating the Navier-Stokes equations and provide a great abstraction of water masses that have lower depths compared to their free surface area. Our specific contribution in this study is to use Microsoft's XNA Game Studio to import underwater and shore line geographies, create different tsunami scenarios, and visualize the propagation of the waves and their impact on the shore line geography. Most importantly, we utilized the computational power of graphical processing units (GPUs) as HLSL based shader files and delegated all of the heavy computations to the GPU. Finally, we also conducted a validation study, in which we have tested our model against a controlled shallow water experiment. We believe that such a framework with an easy to use interface that is based on readily available software libraries, which are widely available and easily distributable, would encourage not only researchers, but also educators to showcase ideas.

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

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

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE PAGES

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

2016-07-26

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Central role of the observable electric potential in transport equations.

PubMed

Garrido, J; Compañ, V; López, M L

2001-07-01

Nonequilibrium systems are usually studied in the framework of transport equations that involve the true electric potential (TEP), a nonobservable variable. Nevertheless another electric potential, the observable electric potential (OEP), may be defined to construct a useful set of transport equations. In this paper several basic characteristics of the OEP are deduced and emphasized: (i) the OEP distribution depends on thermodynamic state of the solution, (ii) the observable equations have a reference value for all other transport equations, (iii) the bridge that connects the OEP with a certain TEP is usually defined by the ion activity coefficient, (iv) the electric charge density is a nonobservable variable, and (v) the OEP formulation constitutes a natural model for studying the fluxes in membrane systems.

A zero-equation turbulence model for two-dimensional hybrid Hall thruster simulations

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

Cappelli, Mark A., E-mail: cap@stanford.edu; Young, Christopher V.; Cha, Eunsun

2015-11-15

We present a model for electron transport across the magnetic field of a Hall thruster and integrate this model into 2-D hybrid particle-in-cell simulations. The model is based on a simple scaling of the turbulent electron energy dissipation rate and the assumption that this dissipation results in Ohmic heating. Implementing the model into 2-D hybrid simulations is straightforward and leverages the existing framework for solving the electron fluid equations. The model recovers the axial variation in the mobility seen in experiments, predicting the generation of a transport barrier which anchors the region of plasma acceleration. The predicted xenon neutral andmore » ion velocities are found to be in good agreement with laser-induced fluorescence measurements.« less

Is Directivity Still Effective in a PSHA Framework?

NASA Astrophysics Data System (ADS)

Spagnuolo, E.; Herrero, A.; Cultrera, G.

2008-12-01

Source rupture parameters, like directivity, modulate the energy release causing variations in the radiated signal amplitude. Thus they affect the empirical predictive equations and as a consequence the seismic hazard assessment. Classical probabilistic hazard evaluations, e.g. Cornell (1968), use very simple predictive equations only based on magnitude and distance which do not account for variables concerning the rupture process. However nowadays, a few predictive equations (e.g. Somerville 1997, Spudich and Chiou 2008) take into account for rupture directivity. Also few implementations have been made in a PSHA framework (e.g. Convertito et al. 2006, Rowshandel 2006). In practice, these new empirical predictive models incorporate quantitatively the rupture propagation effects through the introduction of variables like rake, azimuth, rupture velocity and laterality. The contribution of all these variables is summarized in corrective factors derived from measuring differences between the real data and the predicted ones Therefore, it's possible to keep the older computation, making use of a simple predictive model, and besides, to incorporate the directivity effect through the corrective factors. Any single supplementary variable meaning a new integral in the parametric space. However the difficulty consists of the constraints on parameter distribution functions. We present the preliminary result for ad hoc distributions (Gaussian, uniform distributions) in order to test the impact of incorporating directivity into PSHA models. We demonstrate that incorporating directivity in PSHA by means of the new predictive equations may lead to strong percentage variations in the hazard assessment.

A Hierarchical Learning Control Framework for an Aerial Manipulation System

NASA Astrophysics Data System (ADS)

Ma, Le; Chi, yanxun; Li, Jiapeng; Li, Zhongsheng; Ding, Yalei; Liu, Lixing

2017-07-01

A hierarchical learning control framework for an aerial manipulation system is proposed. Firstly, the mechanical design of aerial manipulation system is introduced and analyzed, and the kinematics and the dynamics based on Newton-Euler equation are modeled. Secondly, the framework of hierarchical learning for this system is presented, in which flight platform and manipulator are controlled by different controller respectively. The RBF (Radial Basis Function) neural networks are employed to estimate parameters and control. The Simulation and experiment demonstrate that the methods proposed effective and advanced.

A Modified Robinson-Stokes equation for describing the thermodynamic properties of aqueous solutions of 1-1 electrolytes

NASA Astrophysics Data System (ADS)

Rudakov, A. M.; Sergievskii, V. V.

2008-05-01

Equations relating osmotic, mean ionic activity, and water activity coefficients to electrolyte concentrations in binary aqueous solutions were substantiated within the framework of cluster concepts. The model includes the contribution to solution nonideality of electrostatic interactions in terms of the Debye-Hückel theory along with hydration and association of salts via relations containing hydration and association numbers in the standard states. According to the description of data on 54 aqueous solutions of 1-1 electrolytes, this model should be given preference compared with the most extensively used NRTL, NRTL-NRF, Wilson, and Pitzer models.

A Four-parameter Budyko Equation for Mean Annual Water Balance

NASA Astrophysics Data System (ADS)

Tang, Y.; Wang, D.

2016-12-01

In this study, a four-parameter Budyko equation for long-term water balance at watershed scale is derived based on the proportionality relationships of the two-stage partitioning of precipitation. The four-parameter Budyko equation provides a practical solution to balance model simplicity and representation of dominated hydrologic processes. Under the four-parameter Budyko framework, the key hydrologic processes related to the lower bound of Budyko curve are determined, that is, the lower bound is corresponding to the situation when surface runoff and initial evaporation not competing with base flow generation are zero. The derived model is applied to 166 MOPEX watersheds in United States, and the dominant controlling factors on each parameter are determined. Then, four statistical models are proposed to predict the four model parameters based on the dominant controlling factors, e.g., saturated hydraulic conductivity, fraction of sand, time period between two storms, watershed slope, and Normalized Difference Vegetation Index. This study shows a potential application of the four-parameter Budyko equation to constrain land-surface parameterizations in ungauged watersheds or general circulation models.

Numerical simulation of solitary waves on deep water with constant vorticity

NASA Astrophysics Data System (ADS)

Dosaev, A. S.; Shishina, M. I.; Troitskaya, Yu I.

2018-01-01

Characteristics of solitary deep water waves on a flow with constant vorticity are investigated by numerical simulation within the framework of fully nonlinear equations of motion (Euler equations) using the method of surface-tracking conformal coordinates. To ensure that solutions observed are stable, soliton formation as a result of disintegration of an initial pulse-like disturbance is modeled. Evidence is obtained that solitary waves with height above a certain threshold are unstable.

Guidelines for a graph-theoretic implementation of structural equation modeling

USGS Publications Warehouse

Grace, James B.; Schoolmaster, Donald R.; Guntenspergen, Glenn R.; Little, Amanda M.; Mitchell, Brian R.; Miller, Kathryn M.; Schweiger, E. William

2012-01-01

Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for an updated definition of the SEM process that subsumes the historical matrix approach under a graph-theory implementation. The implementation is also designed to permit complex specifications and to be compatible with various estimation methods. Finally, they are meant to foster the use of probabilistic reasoning in both retrospective and prospective considerations of the quantitative implications of the results.

A Path Analysis of a Randomized "Promotora de Salud" Cardiovascular Disease-Prevention Trial among At-Risk Hispanic Adults

ERIC Educational Resources Information Center

de Heer, Hendrik Dirk; Balcazar, Hector G.; Castro, Felipe; Schulz, Leslie

2012-01-01

This study assessed effectiveness of an educational community intervention taught by "promotoras de salud" in reducing cardiovascular disease (CVD) risk among Hispanics using a structural equation modeling (SEM) approach. Model development was guided by a social ecological framework proposing CVD risk reduction through improvement of…

Higher Education as an Extended Duration Service: An Investigation of the Determinants of Vietnamese Overseas Student Loyalty

ERIC Educational Resources Information Center

Pham, Hiep-Hung; Lai, Sue Ling

2016-01-01

Regarding higher education as a type of extended duration service, this article proposes a framework considering adjusted expectation, disconfirmation, satisfaction, and commitment in a conceptual model to explain international student loyalty. Employing a structure equation model to the sample data collected from 252 Vietnam overseas students…

Explaining Scientists' Plans for International Mobility from a Life Course Perspective

ERIC Educational Resources Information Center

Netz, Nicolai; Jaksztat, Steffen

2017-01-01

We identify factors influencing young scientists' plans for research stays abroad by embedding theories of social inequality, educational decision making, and migration into a life course framework. We test the developed model of international academic mobility by calculating a structural equation model using data from an online survey of…

Four-fluid MHD Simulations of the Plasma and Neutral Gas Environment of Comet Churyumov-Gerasimenko Near Perihelio

NASA Astrophysics Data System (ADS)

Huang, Z.; Toth, G.; Gombosi, T. I.; Jia, X.; Rubin, M.; Hansen, K. C.; Fougere, N.; Bieler, A. M.; Shou, Y.; Altwegg, K.; Combi, M. R.; Tenishev, V.

2015-12-01

The neutral and plasma environment is critical in understanding the interaction of comet Churyumov-Gerasimenko (CG), the target of the Rosetta mission, and the solar wind. To serve this need and support the Rosetta mission, we develop a 3-D four fluid model, which is based on BATS-R-US within the SWMF (Space Weather Modeling Framework) that solves the governing multi-fluid MHD equations and the Euler equations for the neutral gas fluid. These equations describe the behavior and interactions of the cometary heavy ions, the solar wind protons, the electrons, and the neutrals. This model incorporates different mass loading processes, including photo and electron impact ionization, charge exchange, dissociative ion-electron recombination, and collisional interactions between different fluids. We simulate the near nucleus plasma and neutral gas environment near perihelion with a realistic shape model of CG and compare our simulation results with Rosetta observations.

Multiscale Concrete Modeling of Aging Degradation

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

Hammi, Yousseff; Gullett, Philipp; Horstemeyer, Mark F.

In this work a numerical finite element framework is implemented to enable the integration of coupled multiscale and multiphysics transport processes. A User Element subroutine (UEL) in Abaqus is used to simultaneously solve stress equilibrium, heat conduction, and multiple diffusion equations for 2D and 3D linear and quadratic elements. Transport processes in concrete structures and their degradation mechanisms are presented along with the discretization of the governing equations. The multiphysics modeling framework is theoretically extended to the linear elastic fracture mechanics (LEFM) by introducing the eXtended Finite Element Method (XFEM) and based on the XFEM user element implementation of Ginermore » et al. [2009]. A damage model that takes into account the damage contribution from the different degradation mechanisms is theoretically developed. The total contribution of damage is forwarded to a Multi-Stage Fatigue (MSF) model to enable the assessment of the fatigue life and the deterioration of reinforced concrete structures in a nuclear power plant. Finally, two examples are presented to illustrate the developed multiphysics user element implementation and the XFEM implementation of Giner et al. [2009].« less

Equation-free modeling unravels the behavior of complex ecological systems

USGS Publications Warehouse

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.

Boundary control of bidomain equations with state-dependent switching source functions in the ionic model

NASA Astrophysics Data System (ADS)

Chamakuri, Nagaiah; Engwer, Christian; Kunisch, Karl

2014-09-01

Optimal control for cardiac electrophysiology based on the bidomain equations in conjunction with the Fenton-Karma ionic model is considered. This generic ventricular model approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potentials. However, it is challenging due to the appearance of state-dependent discontinuities in the source terms. A computational framework for the numerical realization of optimal control problems is presented. Essential ingredients are a shape calculus based treatment of the sensitivities of the discontinuous source terms and a marching cubes algorithm to track iso-surface of excitation wavefronts. Numerical results exhibit successful defibrillation by applying an optimally controlled extracellular stimulus.

Well-posedness and decay for the dissipative system modeling electro-hydrodynamics in negative Besov spaces

NASA Astrophysics Data System (ADS)

Zhao, Jihong; Liu, Qiao

2017-07-01

In Guo and Wang (2012) [10], Y. Guo and Y. Wang developed a general new energy method for proving the optimal time decay rates of the solutions to dissipative equations. In this paper, we generalize this method in the framework of homogeneous Besov spaces. Moreover, we apply this method to a model arising from electro-hydrodynamics, which is a strongly coupled system of the Navier-Stokes equations and the Poisson-Nernst-Planck equations through charge transport and external forcing terms. We show that some weighted negative Besov norms of solutions are preserved along time evolution, and obtain the optimal time decay rates of the higher-order spatial derivatives of solutions by the Fourier splitting approach and the interpolation techniques.

Student Background, School Climate, School Disorder, and Student Achievement: An Empirical Study of New York City's Middle Schools

ERIC Educational Resources Information Center

Chen, Greg; Weikart, Lynne A.

2008-01-01

This study develops and tests a school disorder and student achievement model based upon the school climate framework. The model was fitted to 212 New York City middle schools using the Structural Equations Modeling Analysis method. The analysis shows that the model fits the data well based upon test statistics and goodness of fit indices. The…

A unified framework for heat and mass transport at the atomic scale

NASA Astrophysics Data System (ADS)

Ponga, Mauricio; Sun, Dingyi

2018-04-01

We present a unified framework to simulate heat and mass transport in systems of particles. The proposed framework is based on kinematic mean field theory and uses a phenomenological master equation to compute effective transport rates between particles without the need to evaluate operators. We exploit this advantage and apply the model to simulate transport phenomena at the nanoscale. We demonstrate that, when calibrated to experimentally-measured transport coefficients, the model can accurately predict transient and steady state temperature and concentration profiles even in scenarios where the length of the device is comparable to the mean free path of the carriers. Through several example applications, we demonstrate the validity of our model for all classes of materials, including ones that, until now, would have been outside the domain of computational feasibility.

On braneworld inverse power-law inflation

NASA Astrophysics Data System (ADS)

Es-Sobbahi, H.; Nach, M.

2018-04-01

In the framework of the braneworld Randall-Sundrum type II model, we investigate an inflationary scalar model in the high-energy regime. In this regime, the slow-roll parameters and the perturbation spectrum of the model are derived. The corresponding results are dealt with according to the known observational data. Then the solutions to the equations of motion on the brane are given.

Modeling disease transmission near eradication: An equation free approach

NASA Astrophysics Data System (ADS)

Williams, Matthew O.; Proctor, Joshua L.; Kutz, J. Nathan

2015-01-01

Although disease transmission in the near eradication regime is inherently stochastic, deterministic quantities such as the probability of eradication are of interest to policy makers and researchers. Rather than running large ensembles of discrete stochastic simulations over long intervals in time to compute these deterministic quantities, we create a data-driven and deterministic "coarse" model for them using the Equation Free (EF) framework. In lieu of deriving an explicit coarse model, the EF framework approximates any needed information, such as coarse time derivatives, by running short computational experiments. However, the choice of the coarse variables (i.e., the state of the coarse system) is critical if the resulting model is to be accurate. In this manuscript, we propose a set of coarse variables that result in an accurate model in the endemic and near eradication regimes, and demonstrate this on a compartmental model representing the spread of Poliomyelitis. When combined with adaptive time-stepping coarse projective integrators, this approach can yield over a factor of two speedup compared to direct simulation, and due to its lower dimensionality, could be beneficial when conducting systems level tasks such as designing eradication or monitoring campaigns.

An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations

PubMed Central

Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.

2016-01-01

We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach. PMID:28316360

Influence of geometry variations on the gravitational focusing of timelike geodesic congruences

NASA Astrophysics Data System (ADS)

Seriu, Masafumi

2015-10-01

We derive a set of equations describing the linear response of the convergence properties of a geodesic congruence to arbitrary geometry variations. It is a combination of equations describing the deviations from the standard Raychaudhuri-type equations due to the geodesic shifts and an equation describing the geodesic shifts due to the geometry variations. In this framework, the geometry variations, which can be chosen arbitrarily, serve as probes to investigate the gravitational contraction processes from various angles. We apply the obtained framework to the case of conformal geometry variations, characterized by an arbitrary function f (x ), and see that the formulas get simplified to a great extent. We investigate the response of the convergence properties of geodesics in the latest phase of gravitational contractions by restricting the class of conformal geometry variations to the one satisfying the strong energy condition. We then find out that in the final stage, f and D .D f control the overall contraction behavior and that the contraction rate gets larger when f is negative and |f | is so large as to overwhelm |D .D f |. (Here D .D is the Laplacian operator on the spatial hypersurfaces orthogonal to the geodesic congruence in concern.) To get more concrete insights, we also apply the framework to the time-reversed Friedmann-Robertson-Walker model as the simplest case of the singularity formations.

Analyzing latent state-trait and multiple-indicator latent growth curve models as multilevel structural equation models

PubMed Central

Geiser, Christian; Bishop, Jacob; Lockhart, Ginger; Shiffman, Saul; Grenard, Jerry L.

2013-01-01

Latent state-trait (LST) and latent growth curve (LGC) models are frequently used in the analysis of longitudinal data. Although it is well-known that standard single-indicator LGC models can be analyzed within either the structural equation modeling (SEM) or multilevel (ML; hierarchical linear modeling) frameworks, few researchers realize that LST and multivariate LGC models, which use multiple indicators at each time point, can also be specified as ML models. In the present paper, we demonstrate that using the ML-SEM rather than the SL-SEM framework to estimate the parameters of these models can be practical when the study involves (1) a large number of time points, (2) individually-varying times of observation, (3) unequally spaced time intervals, and/or (4) incomplete data. Despite the practical advantages of the ML-SEM approach under these circumstances, there are also some limitations that researchers should consider. We present an application to an ecological momentary assessment study (N = 158 youths with an average of 23.49 observations of positive mood per person) using the software Mplus (Muthén and Muthén, 1998–2012) and discuss advantages and disadvantages of using the ML-SEM approach to estimate the parameters of LST and multiple-indicator LGC models. PMID:24416023

Covariant approach of perturbations in Lovelock type brane gravity

NASA Astrophysics Data System (ADS)

Bagatella-Flores, Norma; Campuzano, Cuauhtemoc; Cruz, Miguel; Rojas, Efraín

2016-12-01

We develop a covariant scheme to describe the dynamics of small perturbations on Lovelock type extended objects propagating in a flat Minkowski spacetime. The higher-dimensional analogue of the Jacobi equation in this theory becomes a wave type equation for a scalar field Φ . Whithin this framework, we analyse the stability of membranes with a de Sitter geometry where we find that the Jacobi equation specializes to a Klein-Gordon (KG) equation for Φ possessing a tachyonic mass. This shows that, to some extent, these types of extended objects share the symmetries of the Dirac-Nambu-Goto (DNG) action which is by no means coincidental because the DNG model is the simplest included in this type of gravity.

Spectral Elements Analysis for Viscoelastic Fluids at High Weissenberg Number Using Logarithmic conformation Tensor Model

NASA Astrophysics Data System (ADS)

Jafari, Azadeh; Deville, Michel O.; Fiétier, Nicolas

2008-09-01

This study discusses the capability of the constitutive laws for the matrix logarithm of the conformation tensor (LCT model) within the framework of the spectral elements method. The high Weissenberg number problems (HWNP) usually produce a lack of convergence of the numerical algorithms. Even though the question whether the HWNP is a purely numerical problem or rather a breakdown of the constitutive law of the model has remained somewhat of a mystery, it has been recognized that the selection of an appropriate constitutive equation constitutes a very crucial step although implementing a suitable numerical technique is still important for successful discrete modeling of non-Newtonian flows. The LCT model formulation of the viscoelastic equations originally suggested by Fattal and Kupferman is applied for 2-dimensional (2D) FENE-CR model. The Planar Poiseuille flow is considered as a benchmark problem to test this representation at high Weissenberg number. The numerical results are compared with numerical solution of the standard constitutive equation.

Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization

NASA Astrophysics Data System (ADS)

Espejo, Elio; Winkler, Michael

2018-04-01

The interplay of chemotaxis, convection and reaction terms is studied in the particular framework of a refined model for coral broadcast spawning, consisting of three equations describing the population densities of unfertilized sperms and eggs and the concentration of a chemical released by the latter, coupled to the incompressible Navier-Stokes equations. Under mild assumptions on the initial data, global existence of classical solutions to an associated initial-boundary value problem in bounded planar domains is established. Moreover, all these solutions are shown to approach a spatially homogeneous equilibrium in the large time limit.

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation.

PubMed

Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

2014-11-25

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.

Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs

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

Liao, Qifeng, E-mail: liaoqf@shanghaitech.edu.cn; Lin, Guang, E-mail: guanglin@purdue.edu

2016-07-15

In this paper we present a reduced basis ANOVA approach for partial deferential equations (PDEs) with random inputs. The ANOVA method combined with stochastic collocation methods provides model reduction in high-dimensional parameter space through decomposing high-dimensional inputs into unions of low-dimensional inputs. In this work, to further reduce the computational cost, we investigate spatial low-rank structures in the ANOVA-collocation method, and develop efficient spatial model reduction techniques using hierarchically generated reduced bases. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

Proposed framework for thermomechanical life modeling of metal matrix composites

NASA Technical Reports Server (NTRS)

Halford, Gary R.; Lerch, Bradley A.; Saltsman, James F.

1993-01-01

The framework of a mechanics of materials model is proposed for thermomechanical fatigue (TMF) life prediction of unidirectional, continuous-fiber metal matrix composites (MMC's). Axially loaded MMC test samples are analyzed as structural components whose fatigue lives are governed by local stress-strain conditions resulting from combined interactions of the matrix, interfacial layer, and fiber constituents. The metallic matrix is identified as the vehicle for tracking fatigue crack initiation and propagation. The proposed framework has three major elements. First, TMF flow and failure characteristics of in situ matrix material are approximated from tests of unreinforced matrix material, and matrix TMF life prediction equations are numerically calibrated. The macrocrack initiation fatigue life of the matrix material is divided into microcrack initiation and microcrack propagation phases. Second, the influencing factors created by the presence of fibers and interfaces are analyzed, characterized, and documented in equation form. Some of the influences act on the microcrack initiation portion of the matrix fatigue life, others on the microcrack propagation life, while some affect both. Influencing factors include coefficient of thermal expansion mismatch strains, residual (mean) stresses, multiaxial stress states, off-axis fibers, internal stress concentrations, multiple initiation sites, nonuniform fiber spacing, fiber debonding, interfacial layers and cracking, fractured fibers, fiber deflections of crack fronts, fiber bridging of matrix cracks, and internal oxidation along internal interfaces. Equations exist for some, but not all, of the currently identified influencing factors. The third element is the inclusion of overriding influences such as maximum tensile strain limits of brittle fibers that could cause local fractures and ensuing catastrophic failure of surrounding matrix material. Some experimental data exist for assessing the plausibility of the proposed framework.

Boundary conditions estimation on a road network using compressed sensing.

DOT National Transportation Integrated Search

2016-02-01

This report presents a new boundary condition estimation framework for transportation networks in which : the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a : Hamilton-Jacobi equation, we pose th...

The ACTIVE conceptual framework as a structural equation model

PubMed Central

Gross, Alden L.; Payne, Brennan R.; Casanova, Ramon; Davoudzadeh, Pega; Dzierzewski, Joseph M.; Farias, Sarah; Giovannetti, Tania; Ip, Edward H.; Marsiske, Michael; Rebok, George W.; Schaie, K. Warner; Thomas, Kelsey; Willis, Sherry; Jones, Richard N.

2018-01-01

Background/Study Context Conceptual frameworks are analytic models at a high level of abstraction. Their operationalization can inform randomized trial design and sample size considerations. Methods The Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE) conceptual framework was empirically tested using structural equation modeling (N=2,802). ACTIVE was guided by a conceptual framework for cognitive training in which proximal cognitive abilities (memory, inductive reasoning, speed of processing) mediate treatment-related improvement in primary outcomes (everyday problem-solving, difficulty with activities of daily living, everyday speed, driving difficulty), which in turn lead to improved secondary outcomes (health-related quality of life, health service utilization, mobility). Measurement models for each proximal, primary, and secondary outcome were developed and tested using baseline data. Each construct was then combined in one model to evaluate fit (RMSEA, CFI, normalized residuals of each indicator). To expand the conceptual model and potentially inform future trials, evidence of modification of structural model parameters was evaluated by age, years of education, sex, race, and self-rated health status. Results Preconceived measurement models for memory, reasoning, speed of processing, everyday problem-solving, instrumental activities of daily living (IADL) difficulty, everyday speed, driving difficulty, and health-related quality of life each fit well to the data (all RMSEA < .05; all CFI > .95). Fit of the full model was excellent (RMSEA = .038; CFI = .924). In contrast with previous findings from ACTIVE regarding who benefits from training, interaction testing revealed associations between proximal abilities and primary outcomes are stronger on average by nonwhite race, worse health, older age, and less education (p < .005). Conclusions Empirical data confirm the hypothesized ACTIVE conceptual model. Findings suggest that the types of people who show intervention effects on cognitive performance potentially may be different from those with the greatest chance of transfer to real-world activities. PMID:29303475

Approximations of thermoelastic and viscoelastic control systems

NASA Technical Reports Server (NTRS)

Burns, J. A.; Liu, Z. Y.; Miller, R. E.

1990-01-01

Well-posed models and computational algorithms are developed and analyzed for control of a class of partial differential equations that describe the motions of thermo-viscoelastic structures. An abstract (state space) framework and a general well-posedness result are presented that can be applied to a large class of thermo-elastic and thermo-viscoelastic models. This state space framework is used in the development of a computational scheme to be used in the solution of a linear quadratic regulator (LQR) control problem. A detailed convergence proof is provided for the viscoelastic model and several numerical results are presented to illustrate the theory and to analyze problems for which the theory is incomplete.

Quantum cluster theory for the polarizable continuum model. I. The CCSD level with analytical first and second derivatives.

PubMed

Cammi, R

2009-10-28

We present a general formulation of the coupled-cluster (CC) theory for a molecular solute described within the framework of the polarizable continuum model (PCM). The PCM-CC theory is derived in its complete form, called PTDE scheme, in which the correlated electronic density is used to have a self-consistent reaction field, and in an approximate form, called PTE scheme, in which the PCM-CC equations are solved assuming the fixed Hartree-Fock solvent reaction field. Explicit forms for the PCM-CC-PTDE equations are derived at the single and double (CCSD) excitation level of the cluster operator. At the same level, explicit equations for the analytical first derivatives of the PCM basic energy functional are presented, and analytical second derivatives are also discussed. The corresponding PCM-CCSD-PTE equations are given as a special case of the full theory.

Radiative transfer equation accounting for rotational Raman scattering and its solution by the discrete-ordinates method

NASA Astrophysics Data System (ADS)

Rozanov, Vladimir V.; Vountas, Marco

2014-01-01

Rotational Raman scattering of solar light in Earth's atmosphere leads to the filling-in of Fraunhofer and telluric lines observed in the reflected spectrum. The phenomenological derivation of the inelastic radiative transfer equation including rotational Raman scattering is presented. The different forms of the approximate radiative transfer equation with first-order rotational Raman scattering terms are obtained employing the Cabannes, Rayleigh, and Cabannes-Rayleigh scattering models. The solution of these equations is considered in the framework of the discrete-ordinates method using rigorous and approximate approaches to derive particular integrals. An alternative forward-adjoint technique is suggested as well. A detailed description of the model including the exact spectral matching and a binning scheme that significantly speeds up the calculations is given. The considered solution techniques are implemented in the radiative transfer software package SCIATRAN and a specified benchmark setup is presented to enable readers to compare with own results transparently.

Existence and stability of periodic solutions of quasi-linear Korteweg — de Vries equation

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Kolesov, A. Yu; Preobrazhenskaia, M. M.

2017-01-01

We consider the scalar nonlinear differential-difference equation with two delays, which models electrical activity of a neuron. Under some additional suppositions for this equation well known method of quasi-normal forms can be applied. Its essence lies in the formal normalization of the Poincare - Dulac obtaining quasi-normal form and the subsequent application of the theorems of conformity. In this case, the result of the application of quasi-normal forms is a countable system of differential-difference equations, which can be turned into a boundary value problem of the Korteweg - de Vries equation. The investigation of this boundary value problem allows us to draw a conclusion about the behaviour of the original equation. Namely, for a suitable choice of parameters in the framework of this equation is implemented buffer phenomenon consisting in the presence of the bifurcation mechanism for the birth of an arbitrarily large number of stable cycles.

Modeling formalisms in Systems Biology

PubMed Central

2011-01-01

Systems Biology has taken advantage of computational tools and high-throughput experimental data to model several biological processes. These include signaling, gene regulatory, and metabolic networks. However, most of these models are specific to each kind of network. Their interconnection demands a whole-cell modeling framework for a complete understanding of cellular systems. We describe the features required by an integrated framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms that have been used in Systems Biology including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, differential equations, rule-based models, interacting state machines, cellular automata, and agent-based models. We compare the features provided by different formalisms, and discuss recent approaches in the integration of these formalisms, as well as possible directions for the future. PMID:22141422

Essential equivalence of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) and steepest-entropy-ascent models of dissipation for nonequilibrium thermodynamics.

PubMed

Montefusco, Alberto; Consonni, Francesco; Beretta, Gian Paolo

2015-04-01

By reformulating the steepest-entropy-ascent (SEA) dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry, we compare it with the primitive formulation of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) model and discuss the main technical differences of the two approaches. In both dynamical models the description of dissipation is of the "entropy-gradient" type. SEA focuses only on the dissipative, i.e., entropy generating, component of the time evolution, chooses a sub-Riemannian metric tensor as dissipative structure, and uses the local entropy density field as potential. GENERIC emphasizes the coupling between the dissipative and nondissipative components of the time evolution, chooses two compatible degenerate structures (Poisson and degenerate co-Riemannian), and uses the global energy and entropy functionals as potentials. As an illustration, we rewrite the known GENERIC formulation of the Boltzmann equation in terms of the square root of the distribution function adopted by the SEA formulation. We then provide a formal proof that in more general frameworks, whenever all degeneracies in the GENERIC framework are related to conservation laws, the SEA and GENERIC models of the dissipative component of the dynamics are essentially interchangeable, provided of course they assume the same kinematics. As part of the discussion, we note that equipping the dissipative structure of GENERIC with the Leibniz identity makes it automatically SEA on metric leaves.

A Non-Incompressible Non-Boussinesq (NINB) framework for studying atmospheric turbulence

NASA Astrophysics Data System (ADS)

Yan, C.; Archer, C. L.; Xie, S.; Ghaisas, N.

2015-12-01

The incompressible assumption is widely used for studying the turbulent atmospheric boundary layer (ABL) and is generally accepted when the Mach number < ~0.3 (velocity < ~100 m/s). Since the tips of modern wind turbine blades can reach and exceed this threshold, neglecting air compressibility will introduce errors. In addition, if air incompressibility does not hold, then the Boussinesq approximation, by which air density is treated as a constant except in the gravity term of the Navier-Stokes equation, is also invalidated. Here, we propose a new theoretical framework, called NINB for Non-Incompressible Non-Boussinesq, in which air is not considered incompressible and air density is treated as a non-turbulent 4D variable. First, the NINB mass, momentum, and energy conservation equations are developed using Reynolds averaging. Second, numerical simulations of the NINB equations, coupled with a k-epsilon turbulence model, are performed with the finite-volume method. Wind turbines are modeled with the actuator-line model using SOWFA (Software for Offshore/onshore Wind Farm Applications). Third, NINB results are compared with the traditional incompressible buoyant simulations performed by SOWFA with the same set up. The results show differences between NINB and traditional simulations in the neutral atmosphere with a wind turbine. The largest differences in wind speed (up to 1 m/s), turbulent kinetic energy (~10%), dissipation rate (~5%), and shear stress (~10%) occur near the turbine tip region. The power generation differences are 5-15% (depending on setup). These preliminary results suggest that compressibility effects are non-negligible around wind turbines and should be taken into account when forecasting wind power. Since only a few extra terms are introduced, the NINB framework may be an alternative to the traditional incompressible Boussinesq framework for studying the turbulent ABL in general (i.e., without turbines) in the absence of shock waves.

Unraveling the Relationships between Ecosystems and Human Wellbeing in Spain

PubMed Central

Santos-Martín, Fernando; Martín-López, Berta; García-Llorente, Marina; Aguado, Mateo; Benayas, Javier; Montes, Carlos

2013-01-01

National ecosystem assessments provide evidence on the status and trends of biodiversity, ecosystem conditions, and the delivery of ecosystem services to society. I this study, we analyze the complex relationships established between ecosystems and human systems in Spain through the combination of Driver-Pressure-State-Impact-Response framework and structural equation models. Firstly, to operationalize the framework, we selected 53 national scale indicators that provide accurate, long-term information on each of the components. Secondly, structural equation models were performed to understand the relationships among the components of the framework. Trend indicators have shown an overall progressive biodiversity loss, trade-offs between provisioning and cultural services associated with urban areas vs. regulating and cultural services associated with rural areas, a decoupling effect between material and non-material dimensions of human wellbeing, a rapid growing trend of conservation responses in recent years and a constant growing linear trend of direct or indirect drivers of change. Results also show that all the components analyzed in the model are strongly related. On one hand, the model shows that biodiversity erosion negatively affect the supply of regulating services, while it is positively related with the increase of provisioning service delivery. On the other hand, the most important relationship found in the model is the effect of pressures on biodiversity loss, indicating that response options for conserving nature cannot counteract the effect of the drivers of change. These results suggest that there is an insufficient institutional response to address the underlying causes (indirect drivers of change) of biodiversity loos in Spain. We conclude that more structural changes are required in the Spanish institutional framework to reach 2020 biodiversity conservation international targets. PMID:24039894

Unraveling the relationships between ecosystems and human wellbeing in Spain.

PubMed

Santos-Martín, Fernando; Martín-López, Berta; García-Llorente, Marina; Aguado, Mateo; Benayas, Javier; Montes, Carlos

2013-01-01

National ecosystem assessments provide evidence on the status and trends of biodiversity, ecosystem conditions, and the delivery of ecosystem services to society. I this study, we analyze the complex relationships established between ecosystems and human systems in Spain through the combination of Driver-Pressure-State-Impact-Response framework and structural equation models. Firstly, to operationalize the framework, we selected 53 national scale indicators that provide accurate, long-term information on each of the components. Secondly, structural equation models were performed to understand the relationships among the components of the framework. Trend indicators have shown an overall progressive biodiversity loss, trade-offs between provisioning and cultural services associated with urban areas vs. regulating and cultural services associated with rural areas, a decoupling effect between material and non-material dimensions of human wellbeing, a rapid growing trend of conservation responses in recent years and a constant growing linear trend of direct or indirect drivers of change. Results also show that all the components analyzed in the model are strongly related. On one hand, the model shows that biodiversity erosion negatively affect the supply of regulating services, while it is positively related with the increase of provisioning service delivery. On the other hand, the most important relationship found in the model is the effect of pressures on biodiversity loss, indicating that response options for conserving nature cannot counteract the effect of the drivers of change. These results suggest that there is an insufficient institutional response to address the underlying causes (indirect drivers of change) of biodiversity loos in Spain. We conclude that more structural changes are required in the Spanish institutional framework to reach 2020 biodiversity conservation international targets.

Modelling Bathymetric Control of Near Coastal Wave Climate: Report 3

DTIC Science & Technology

1992-02-01

complexity would occur if we were to make the full set of restrictions appropriate to the parabolic approximation of the KP equation ( Kadomtsev ... Kadomtsev , B.B. and Petviashvili , V.I., 1970, "On the stability of solitary waves in weakly dispersing media", Soy. Phys. Dokl., 15, 539-541. 24 Kirby...bar theory. Theory for Small Amplitude Bars The theory which provides the framework for analysis here is given by an extended mild-slope equation

Bulk scalar field in brane-worlds with induced gravity inspired by the L(R) term

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

Heydari-Fard, M.; Sepangi, H.R., E-mail: heydarifard@qom.ac.ir, E-mail: hr-sepangi@sbu.ac.ir

2009-01-15

We obtain the effective field equations in a brane-world scenario within the framework of a DGP model where the action on the brane is an arbitrary function of the Ricci scalar, L(R), and the bulk action includes a scalar field in the matter Lagrangian. We obtain the Friedmann equations and acceleration conditions in the presence of the bulk scalar field for the R{sup n} term in four-dimensional gravity.

Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.

PubMed

Ullah, M; Schmidt, H; Cho, K H; Wolkenhauer, O

2006-03-01

The analysis of complex biochemical networks is conducted in two popular conceptual frameworks for modelling. The deterministic approach requires the solution of ordinary differential equations (ODEs, reaction rate equations) with concentrations as continuous state variables. The stochastic approach involves the simulation of differential-difference equations (chemical master equations, CMEs) with probabilities as variables. This is to generate counts of molecules for chemical species as realisations of random variables drawn from the probability distribution described by the CMEs. Although there are numerous tools available, many of them free, the modelling and simulation environment MATLAB is widely used in the physical and engineering sciences. We describe a collection of MATLAB functions to construct and solve ODEs for deterministic simulation and to implement realisations of CMEs for stochastic simulation using advanced MATLAB coding (Release 14). The program was successfully applied to pathway models from the literature for both cases. The results were compared to implementations using alternative tools for dynamic modelling and simulation of biochemical networks. The aim is to provide a concise set of MATLAB functions that encourage the experimentation with systems biology models. All the script files are available from www.sbi.uni-rostock.de/ publications_matlab-paper.html.

A patient-specific aortic valve model based on moving resistive immersed implicit surfaces.

PubMed

Fedele, Marco; Faggiano, Elena; Dedè, Luca; Quarteroni, Alfio

2017-10-01

In this paper, we propose a full computational framework to simulate the hemodynamics in the aorta including the valve. Closed and open valve surfaces, as well as the lumen aorta, are reconstructed directly from medical images using new ad hoc algorithms, allowing a patient-specific simulation. The fluid dynamics problem that accounts from the movement of the valve is solved by a new 3D-0D fluid-structure interaction model in which the valve surface is implicitly represented through level set functions, yielding, in the Navier-Stokes equations, a resistive penalization term enforcing the blood to adhere to the valve leaflets. The dynamics of the valve between its closed and open position is modeled using a reduced geometric 0D model. At the discrete level, a finite element formulation is used and the SUPG stabilization is extended to include the resistive term in the Navier-Stokes equations. Then, after time discretization, the 3D fluid and 0D valve models are coupled through a staggered approach. This computational framework, applied to a patient-specific geometry and data, allows to simulate the movement of the valve, the sharp pressure jump occurring across the leaflets, and the blood flow pattern inside the aorta.

Isostable reduction with applications to time-dependent partial differential equations.

PubMed

Wilson, Dan; Moehlis, Jeff

2016-07-01

Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

Applications of General Systems Theory to the Development of an Adjustable Tutorial Software Machine.

ERIC Educational Resources Information Center

Vos, Hans J.

1994-01-01

Describes the construction of a model of computer-assisted instruction using a qualitative block diagram based on general systems theory (GST) as a framework. Subject matter representation is discussed, and appendices include system variables and system equations of the GST model, as well as an example of developing flexible courseware. (Contains…

A Structural Equation Model of the Writing Process in Typically-Developing Sixth Grade Children

ERIC Educational Resources Information Center

Koutsoftas, Anthony D.; Gray, Shelley

2013-01-01

The purpose of this study was to evaluate how sixth grade children planned, translated, and revised written narrative stories using a task reflecting current instructional and assessment practices. A modified version of the Hayes and Flower (1980) writing process model was used as the theoretical framework for the study. Two hundred one…

On the Interface of Probabilistic and PDE Methods in a Multifactor Term Structure Theory

ERIC Educational Resources Information Center

Mamon, Rogemar S.

2004-01-01

Within the general framework of a multifactor term structure model, the fundamental partial differential equation (PDE) satisfied by a default-free zero-coupon bond price is derived via a martingale-oriented approach. Using this PDE, a result characterizing a model belonging to an exponential affine class is established using only a system of…

Improved Representation of the Self-Perception Profile for Children through Bifactor Exploratory Structural Equation Modeling

ERIC Educational Resources Information Center

Arens, A. Katrin; Morin, Alexandre J. S.

2017-01-01

This study illustrates an integrative psychometric framework to investigate two sources of construct-relevant multidimensionality in answers to the Self-Perception Profile for Children (SPPC). Using a sample of 2,353 German students attending Grades 3 to 6, we contrasted: (a) first-order versus hierarchical and bifactor models to investigate…

Hierarchical models for informing general biomass equations with felled tree data

Treesearch

Brian J. Clough; Matthew B. Russell; Christopher W. Woodall; Grant M. Domke; Philip J. Radtke

2015-01-01

We present a hierarchical framework that uses a large multispecies felled tree database to inform a set of general models for predicting tree foliage biomass, with accompanying uncertainty, within the FIA database. Results suggest significant prediction uncertainty for individual trees and reveal higher errors when predicting foliage biomass for larger trees and for...

A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis

ERIC Educational Resources Information Center

Edwards, Michael C.

2010-01-01

Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…

Using Multigroup Confirmatory Factor Analysis to Test Measurement Invariance in Raters: A Clinical Skills Examination Application

ERIC Educational Resources Information Center

Kahraman, Nilufer; Brown, Crystal B.

2015-01-01

Psychometric models based on structural equation modeling framework are commonly used in many multiple-choice test settings to assess measurement invariance of test items across examinee subpopulations. The premise of the current article is that they may also be useful in the context of performance assessment tests to test measurement invariance…

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

DOE PAGES

Hagos, Samson; Feng, Zhe; Plant, Robert S.; ...

2018-02-20

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. Finally, in addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.« less

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

NASA Astrophysics Data System (ADS)

Hagos, Samson; Feng, Zhe; Plant, Robert S.; Houze, Robert A.; Xiao, Heng

2018-02-01

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii) the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. In addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

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

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. Finally, in addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.« less

Subjective Values of Quality of Life Dimensions in Elderly People. A SEM Preference Model Approach

ERIC Educational Resources Information Center

Elosua, Paula

2011-01-01

This article proposes a Thurstonian model in the framework of Structural Equation Modelling (SEM) to assess preferences among quality of life dimensions for the elderly. Data were gathered by a paired comparison design in a sample comprised of 323 people aged from 65 to 94 years old. Five dimensions of quality of life were evaluated: Health,…

A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations

NASA Astrophysics Data System (ADS)

Hsieh, Chang-Yu; Cao, Jianshu

2018-01-01

We extend a standard stochastic theory to study open quantum systems coupled to a generic quantum environment. We exemplify the general framework by studying a two-level quantum system coupled bilinearly to the three fundamental classes of non-interacting particles: bosons, fermions, and spins. In this unified stochastic approach, the generalized stochastic Liouville equation (SLE) formally captures the exact quantum dissipations when noise variables with appropriate statistics for different bath models are applied. Anharmonic effects of a non-Gaussian bath are precisely encoded in the bath multi-time correlation functions that noise variables have to satisfy. Starting from the SLE, we devise a family of generalized hierarchical equations by averaging out the noise variables and expand bath multi-time correlation functions in a complete basis of orthonormal functions. The general hierarchical equations constitute systems of linear equations that provide numerically exact simulations of quantum dynamics. For bosonic bath models, our general hierarchical equation of motion reduces exactly to an extended version of hierarchical equation of motion which allows efficient simulation for arbitrary spectral densities and temperature regimes. Similar efficiency and flexibility can be achieved for the fermionic bath models within our formalism. The spin bath models can be simulated with two complementary approaches in the present formalism. (I) They can be viewed as an example of non-Gaussian bath models and be directly handled with the general hierarchical equation approach given their multi-time correlation functions. (II) Alternatively, each bath spin can be first mapped onto a pair of fermions and be treated as fermionic environments within the present formalism.

Statistical methods for incomplete data: Some results on model misspecification.

PubMed

McIsaac, Michael; Cook, R J

2017-02-01

Inverse probability weighted estimating equations and multiple imputation are two of the most studied frameworks for dealing with incomplete data in clinical and epidemiological research. We examine the limiting behaviour of estimators arising from inverse probability weighted estimating equations, augmented inverse probability weighted estimating equations and multiple imputation when the requisite auxiliary models are misspecified. We compute limiting values for settings involving binary responses and covariates and illustrate the effects of model misspecification using simulations based on data from a breast cancer clinical trial. We demonstrate that, even when both auxiliary models are misspecified, the asymptotic biases of double-robust augmented inverse probability weighted estimators are often smaller than the asymptotic biases of estimators arising from complete-case analyses, inverse probability weighting or multiple imputation. We further demonstrate that use of inverse probability weighting or multiple imputation with slightly misspecified auxiliary models can actually result in greater asymptotic bias than the use of naïve, complete case analyses. These asymptotic results are shown to be consistent with empirical results from simulation studies.

Detecting Unobserved Heterogeneity in the Relationship between Subjective Well-Being and Satisfaction in Various Domains of Life Using the REBUS-PLS Path Modelling Approach: A Case Study

ERIC Educational Resources Information Center

Zanin, Luca

2013-01-01

In this article, we propose a model to estimate the direct and indirect effects of the relationship between subjective well-being and satisfaction in various domains of life using a partial least squares path modelling approach in a structural equation model framework. A drawback of these models is that they assume homogeneous behaviour over the…

Five-equation and robust three-equation methods for solution verification of large eddy simulation

NASA Astrophysics Data System (ADS)

Dutta, Rabijit; Xing, Tao

2018-02-01

This study evaluates the recently developed general framework for solution verification methods for large eddy simulation (LES) using implicitly filtered LES of periodic channel flows at friction Reynolds number of 395 on eight systematically refined grids. The seven-equation method shows that the coupling error based on Hypothesis I is much smaller as compared with the numerical and modeling errors and therefore can be neglected. The authors recommend five-equation method based on Hypothesis II, which shows a monotonic convergence behavior of the predicted numerical benchmark ( S C ), and provides realistic error estimates without the need of fixing the orders of accuracy for either numerical or modeling errors. Based on the results from seven-equation and five-equation methods, less expensive three and four-equation methods for practical LES applications were derived. It was found that the new three-equation method is robust as it can be applied to any convergence types and reasonably predict the error trends. It was also observed that the numerical and modeling errors usually have opposite signs, which suggests error cancellation play an essential role in LES. When Reynolds averaged Navier-Stokes (RANS) based error estimation method is applied, it shows significant error in the prediction of S C on coarse meshes. However, it predicts reasonable S C when the grids resolve at least 80% of the total turbulent kinetic energy.

Search algorithm complexity modeling with application to image alignment and matching

NASA Astrophysics Data System (ADS)

DelMarco, Stephen

2014-05-01

Search algorithm complexity modeling, in the form of penetration rate estimation, provides a useful way to estimate search efficiency in application domains which involve searching over a hypothesis space of reference templates or models, as in model-based object recognition, automatic target recognition, and biometric recognition. The penetration rate quantifies the expected portion of the database that must be searched, and is useful for estimating search algorithm computational requirements. In this paper we perform mathematical modeling to derive general equations for penetration rate estimates that are applicable to a wide range of recognition problems. We extend previous penetration rate analyses to use more general probabilistic modeling assumptions. In particular we provide penetration rate equations within the framework of a model-based image alignment application domain in which a prioritized hierarchical grid search is used to rank subspace bins based on matching probability. We derive general equations, and provide special cases based on simplifying assumptions. We show how previously-derived penetration rate equations are special cases of the general formulation. We apply the analysis to model-based logo image alignment in which a hierarchical grid search is used over a geometric misalignment transform hypothesis space. We present numerical results validating the modeling assumptions and derived formulation.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size.

PubMed

Schwalger, Tilo; Deger, Moritz; Gerstner, Wulfram

2017-04-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

A framework for scalable parameter estimation of gene circuit models using structural information.

PubMed

Kuwahara, Hiroyuki; Fan, Ming; Wang, Suojin; Gao, Xin

2013-07-01

Systematic and scalable parameter estimation is a key to construct complex gene regulatory models and to ultimately facilitate an integrative systems biology approach to quantitatively understand the molecular mechanisms underpinning gene regulation. Here, we report a novel framework for efficient and scalable parameter estimation that focuses specifically on modeling of gene circuits. Exploiting the structure commonly found in gene circuit models, this framework decomposes a system of coupled rate equations into individual ones and efficiently integrates them separately to reconstruct the mean time evolution of the gene products. The accuracy of the parameter estimates is refined by iteratively increasing the accuracy of numerical integration using the model structure. As a case study, we applied our framework to four gene circuit models with complex dynamics based on three synthetic datasets and one time series microarray data set. We compared our framework to three state-of-the-art parameter estimation methods and found that our approach consistently generated higher quality parameter solutions efficiently. Although many general-purpose parameter estimation methods have been applied for modeling of gene circuits, our results suggest that the use of more tailored approaches to use domain-specific information may be a key to reverse engineering of complex biological systems. http://sfb.kaust.edu.sa/Pages/Software.aspx. Supplementary data are available at Bioinformatics online.

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

DOE PAGES

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

2017-11-09

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

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

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Full three-body problem in effective-field-theory models of gravity

NASA Astrophysics Data System (ADS)

Battista, Emmanuele; Esposito, Giampiero

2014-10-01

Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian potential is replaced by a more general central potential which depends on the mutual separations of the three bodies. The general form of the equations of motion is written down, and they are studied when the interaction potential reduces to the quantum-corrected central potential considered recently in the literature. A recursive algorithm is found for solving the associated variational equations, which describe small departures from given periodic solutions of the equations of motion. Our scheme involves repeated application of a 2×2 matrix of first-order linear differential operators.

Seismic waves in a self-gravitating planet

NASA Astrophysics Data System (ADS)

Brazda, Katharina; de Hoop, Maarten V.; Hörmann, Günther

2013-04-01

The elastic-gravitational equations describe the propagation of seismic waves including the effect of self-gravitation. We rigorously derive and analyze this system of partial differential equations and boundary conditions for a general, uniformly rotating, elastic, but aspherical, inhomogeneous, and anisotropic, fluid-solid earth model, under minimal assumptions concerning the smoothness of material parameters and geometry. For this purpose we first establish a consistent mathematical formulation of the low regularity planetary model within the framework of nonlinear continuum mechanics. Using calculus of variations in a Sobolev space setting, we then show how the weak form of the linearized elastic-gravitational equations directly arises from Hamilton's principle of stationary action. Finally we prove existence and uniqueness of weak solutions by the method of energy estimates and discuss additional regularity properties.

Enhancing a socio-hydrological modelling framework through field observations: a case study in India

NASA Astrophysics Data System (ADS)

den Besten, Nadja; Pande, Saket; Savenije, Huub H. G.

2016-04-01

Recently a smallholder socio-hydrological modelling framework was proposed and deployed to understand the underlying dynamics of Agrarian Crisis in Maharashtra state of India. It was found that cotton and sugarcane smallholders whom lack irrigation and storage techniques are most susceptible to distress. This study further expands the application of the modelling framework to other crops that are abundant in the state of Maharashtra, such as Paddy, Jowar and Soyabean to assess whether the conclusions on the possible causes behind smallholder distress still hold. Further, a fieldwork will be undertaken in March 2016 in the district of Pune. During the fieldwork 50 smallholders will be interviewed in which socio-hydrological assumptions on hydrology and capital equations and corresponding closure relationships, incorporated the current model, will be put to test. Besides the assumptions, the questionnaires will be used to better understand the hydrological reality of the farm holders, in terms of water usage and storage capacity. In combination with historical records on the smallholders' socio-economic data acquired over the last thirty years available through several NGOs in the region, socio-hydrological realism of the modelling framework will be enhanced. The preliminary outcomes of a desktop study show the possibilities of a water-centric modelling framework in understanding the constraints on smallholder farming. The results and methods described can be a first step guiding following research on the modelling framework: a start in testing the framework in multiple rural locations around the globe.

Self-Assembled Magnetic Surface Swimmers: Theoretical Model

NASA Astrophysics Data System (ADS)

Aranson, Igor; Belkin, Maxim; Snezhko, Alexey

2009-03-01

The mechanisms of self-propulsion of living microorganisms are a fascinating phenomenon attracting enormous attention in the physics community. A new type of self-assembled micro-swimmers, magnetic snakes, is an excellent tool to model locomotion in a simple table-top experiment. The snakes self-assemble from a dispersion of magnetic microparticles suspended on the liquid-air interface and subjected to an alternating magnetic field. Formation and dynamics of these swimmers are captured in the framework of theoretical model coupling paradigm equation for the amplitude of surface waves, conservation law for the density of particles, and the Navier-Stokes equation for hydrodynamic flows. The results of continuum modeling are supported by hybrid molecular dynamics simulations of magnetic particles floating on the surface of fluid.

Plane Symmetric Dark Energy Models in the Form of Wet Dark Fluid in f ( R, T) Gravity

NASA Astrophysics Data System (ADS)

Chirde, V. R.; Shekh, S. H.

2016-06-01

In this paper, we have investigated the plane symmetric space-time with wet dark fluid (WDF), which is a candidate for dark energy, in the framework of f ( R, T) gravity Harko et al. 2011, Phys. Rev. D, 84, 024020), where R and T denote the Ricci scalar and the trace of the energy-momentum tensor respectively. We have used the equation of state in the form of WDF for the dark energy component of the Universe. It is modeled on the equation of state p = ω( ρ - ρ ∗). The exact solutions to the corresponding field equations are obtained for power-law and exponential volumetric expansion. The geometrical and physical parameters for both the models are studied. Also, we have discussed the well-known astrophysical phenomena, namely the look-back time, proper distance, the luminosity distance and angular diameter distance with red shift.

Generalized two-temperature model for coupled phonon-magnon diffusion.

PubMed

Liao, Bolin; Zhou, Jiawei; Chen, Gang

2014-07-11

We generalize the two-temperature model [Sanders and Walton, Phys. Rev. B 15, 1489 (1977)] for coupled phonon-magnon diffusion to include the effect of the concurrent magnetization flow, with a particular emphasis on the thermal consequence of the magnon flow driven by a nonuniform magnetic field. Working within the framework of the Boltzmann transport equation, we derive the constitutive equations for coupled phonon-magnon transport driven by gradients of both temperature and external magnetic fields, and the corresponding conservation laws. Our equations reduce to the original Sanders-Walton two-temperature model under a uniform external field, but predict a new magnon cooling effect driven by a nonuniform magnetic field in a homogeneous single-domain ferromagnet. We estimate the magnitude of the cooling effect in an yttrium iron garnet, and show it is within current experimental reach. With properly optimized materials, the predicted cooling effect can potentially supplement the conventional magnetocaloric effect in cryogenic applications in the future.

Piezo-Phototronic Effect in a Quantum Well Structure.

PubMed

Huang, Xin; Du, Chunhua; Zhou, Yongli; Jiang, Chunyan; Pu, Xiong; Liu, Wei; Hu, Weiguo; Chen, Hong; Wang, Zhong Lin

2016-05-24

With enhancements in the performance of optoelectronic devices, the field of piezo-phototronics has attracted much attention, and several theoretical works have been reported based on semiclassical models. At present, the feature size of optoelectronic devices are rapidly shrinking toward several tens of nanometers, which results in the quantum confinement effect. Starting from the basic piezoelectricity equation, Schrödinger equation, Poisson equation, and Fermi's golden rule, a self-consistent theoretical model is proposed to study the piezo-phototronic effect in the framework of perturbation theory in quantum mechanics. The validity and universality of this model are well-proven with photoluminescence measurements in a single GaN/InGaN quantum well and multiple GaN/InGaN quantum wells. This study provides important insight into the working principle of nanoscale piezo-phototronic devices as well as guidance for the future device design.

Online Updating of Statistical Inference in the Big Data Setting.

PubMed

Schifano, Elizabeth D; Wu, Jing; Wang, Chun; Yan, Jun; Chen, Ming-Hui

2016-01-01

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.

A flamelet model for transcritical LOx/GCH4 flames

NASA Astrophysics Data System (ADS)

Müller, Hagen; Pfitzner, Michael

2017-03-01

This work presents a numerical framework to efficiently simulate methane combustion at supercritical pressures. A LES flamelet approach is adapted to account for real-gas thermodynamics effects which are a prominent feature of flames at near-critical injection conditions. The thermodynamics model is based on the Peng-Robinson equation of state (PR-EoS) in conjunction with a novel volume-translation method to correct deficiencies in the transcritical regime. The resulting formulation is more accurate than standard cubic EoSs without deteriorating their good computational performance. To consistently account for pressure and strain fluctuations in the flamelet model, an additional enthalpy equation is solved along with the transport equations for mixture fraction and mixture fraction variance. The method is validated against available experimental data for a laboratory scale LOx/GCH4 flame at conditions that resemble those in liquid-propellant rocket engines. The LES result is in good agreement with the measured OH* radiation.

Morphing Continuum Theory: A First Order Approximation to the Balance Laws

NASA Astrophysics Data System (ADS)

Wonnell, Louis; Cheikh, Mohamad Ibrahim; Chen, James

2017-11-01

Morphing Continuum Theory is constructed under the framework of Rational Continuum Mechanics (RCM) for fluid flows with inner structure. This multiscale theory has been successfully emplyed to model turbulent flows. The framework of RCM ensures the mathematical rigor of MCT, but contains new material constants related to the inner structure. The physical meanings of these material constants have yet to be determined. Here, a linear deviation from the zeroth-order Boltzmann-Curtiss distribution function is derived. When applied to the Boltzmann-Curtiss equation, a first-order approximation of the MCT governing equations is obtained. The integral equations are then related to the appropriate material constants found in the heat flux, Cauchy stress, and moment stress terms in the governing equations. These new material properties associated with the inner structure of the fluid are compared with the corresponding integrals, and a clearer physical interpretation of these coefficients emerges. The physical meanings of these material properties is determined by analyzing previous results obtained from numerical simulations of MCT for compressible and incompressible flows. The implications for the physics underlying the MCT governing equations will also be discussed. This material is based upon work supported by the Air Force Office of Scientific Research under Award Number FA9550-17-1-0154.

Predicting change in epistemological beliefs, reflective thinking and learning styles: a longitudinal study.

PubMed

Phan, Huy P

2008-03-01

Although extensive research has examined epistemological beliefs, reflective thinking and learning approaches, very few studies have looked at these three theoretical frameworks in their totality. This research tested two separate structural models of epistemological beliefs, learning approaches, reflective thinking and academic performance among tertiary students over a period of 12 months. Participants were first-year Arts (N=616; 271 females, 345 males) and second-year Mathematics (N=581; 241 females, 341 males) university students. Students' epistemological beliefs were measured with the Schommer epistemological questionnaire (EQ, Schommer, 1990). Reflective thinking was measured with the reflective thinking questionnaire (RTQ, Kember et al., 2000). Student learning approaches were measured with the revised study process questionnaire (R-SPQ-2F, Biggs, Kember, & Leung, 2001). LISREL 8 was used to test two structural equation models - the cross-lag model and the causal-mediating model. In the cross-lag model involving Arts students, structural equation modelling showed that epistemological beliefs influenced student learning approaches rather than the contrary. In the causal-mediating model involving Mathematics students, the results indicate that both epistemological beliefs and learning approaches predicted reflective thinking and academic performance. Furthermore, learning approaches mediated the effect of epistemological beliefs on reflective thinking and academic performance. Results of this study are significant as they integrated the three theoretical frameworks within the one study.

General framework for fluctuating dynamic density functional theory

NASA Astrophysics Data System (ADS)

Durán-Olivencia, Miguel A.; Yatsyshin, Peter; Goddard, Benjamin D.; Kalliadasis, Serafim

2017-12-01

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.

Development of a restricted state space stochastic differential equation model for bacterial growth in rich media.

PubMed

Møller, Jan Kloppenborg; Bergmann, Kirsten Riber; Christiansen, Lasse Engbo; Madsen, Henrik

2012-07-21

In the present study, bacterial growth in a rich media is analysed in a Stochastic Differential Equation (SDE) framework. It is demonstrated that the SDE formulation and smoothened state estimates provide a systematic framework for data driven model improvements, using random walk hidden states. Bacterial growth is limited by the available substrate and the inclusion of diffusion must obey this natural restriction. By inclusion of a modified logistic diffusion term it is possible to introduce a diffusion term flexible enough to capture both the growth phase and the stationary phase, while concentration is restricted to the natural state space (substrate and bacteria non-negative). The case considered is the growth of Salmonella and Enterococcus in a rich media. It is found that a hidden state is necessary to capture the lag phase of growth, and that a flexible logistic diffusion term is needed to capture the random behaviour of the growth model. Further, it is concluded that the Monod effect is not needed to capture the dynamics of bacterial growth in the data presented. Copyright © 2012 Elsevier Ltd. All rights reserved.

Toward Improved Fidelity of Thermal Explosion Simulations

NASA Astrophysics Data System (ADS)

Nichols, Albert; Becker, Richard; Burnham, Alan; Howard, W. Michael; Knap, Jarek; Wemhoff, Aaron

2009-06-01

We present results of an improved thermal/chemical/mechanical model of HMX based explosives like LX04 and LX10 for thermal cook-off. The original HMX model and analysis scheme were developed by Yoh et.al. for use in the ALE3D modeling framework. The improvements were concentrated in four areas. First, we added porosity to the chemical material model framework in ALE3D used to model HMX explosive formulations to handle the roughly 2% porosity in solid explosives. Second, we improved the HMX reaction network, which included the addition of a reactive phase change model base on work by Henson et.al. Third, we added early decomposition gas species to the CHEETAH material database to improve equations of state for gaseous intermediates and products. Finally, we improved the implicit mechanics module in ALE3D to more naturally handle the long time scales associated with thermal cookoff. The application of the resulting framework to the analysis of the Scaled Thermal Explosion (STEX) experiments will be discussed.

An object-oriented framework for distributed hydrologic and geomorphic modeling using triangulated irregular networks

NASA Astrophysics Data System (ADS)

Tucker, Gregory E.; Lancaster, Stephen T.; Gasparini, Nicole M.; Bras, Rafael L.; Rybarczyk, Scott M.

2001-10-01

We describe a new set of data structures and algorithms for dynamic terrain modeling using a triangulated irregular network (TINs). The framework provides an efficient method for storing, accessing, and updating a Delaunay triangulation and its associated Voronoi diagram. The basic data structure consists of three interconnected data objects: triangles, nodes, and directed edges. Encapsulating each of these geometric elements within a data object makes it possible to essentially decouple the TIN representation from the modeling applications that make use of it. Both the triangulation and its corresponding Voronoi diagram can be rapidly retrieved or updated, making these methods well suited to adaptive remeshing schemes. We develop a set of algorithms for defining drainage networks and identifying closed depressions (e.g., lakes) for hydrologic and geomorphic modeling applications. We also outline simple numerical algorithms for solving network routing and 2D transport equations within the TIN framework. The methods are illustrated with two example applications, a landscape evolution model and a distributed rainfall-runoff model.

Automatising the analysis of stochastic biochemical time-series

PubMed Central

2015-01-01

Background Mathematical and computational modelling of biochemical systems has seen a lot of effort devoted to the definition and implementation of high-performance mechanistic simulation frameworks. Within these frameworks it is possible to analyse complex models under a variety of configurations, eventually selecting the best setting of, e.g., parameters for a target system. Motivation This operational pipeline relies on the ability to interpret the predictions of a model, often represented as simulation time-series. Thus, an efficient data analysis pipeline is crucial to automatise time-series analyses, bearing in mind that errors in this phase might mislead the modeller's conclusions. Results For this reason we have developed an intuitive framework-independent Python tool to automate analyses common to a variety of modelling approaches. These include assessment of useful non-trivial statistics for simulation ensembles, e.g., estimation of master equations. Intuitive and domain-independent batch scripts will allow the researcher to automatically prepare reports, thus speeding up the usual model-definition, testing and refinement pipeline. PMID:26051821

Behaviour of charged collapsing fluids after hydrostatic equilibrium in R^n gravity

NASA Astrophysics Data System (ADS)

Kausar, Hafiza Rizwana

2017-06-01

The purpose of this paper is to study the transport equation and its coupling with the Maxwell equation in the framework of R^n gravity. Using Müller-Israel-Stewart theory for the conduction of dissipative fluids, we analyze the temperature, heat flux, viscosity and thermal conductivity in the scenario of relaxation time. All these thermodynamical variables appear in the form of a single factor whose influence is discussed on the evolution of relativistic model for the heat conducting collapsing star.

An Open Source Framework for Coupled Hydro-Hydrogeo-Chemical Systems in Catchment Research

NASA Astrophysics Data System (ADS)

Delfs, J.; Sachse, A.; Gayler, S.; Grathwohl, P.; He, W.; Jang, E.; Kalbacher, T.; Klein, C.; Kolditz, O.; Maier, U.; Priesack, E.; Rink, K.; Selle, B.; Shao, H.; Singh, A. K.; Streck, T.; Sun, Y.; Wang, W.; Walther, M.

2013-12-01

This poster presents an open-source framework designed to assist water scientists in the study of catchment hydraulic functions with associated chemical processes, e.g. contaminant degradation, plant nutrient turnover. The model successfully calculates the feedbacks between surface water, subsurface water and air in standard benchmarks. In specific model applications to heterogeneous catchments, subsurface water is driven by density variations and runs through double porous media. Software codes of water science are tightly coupled by iteration, namely the Storm Water Management Model (SWMM) for urban runoff, Expert-N for simulating water fluxes and nutrient turnover in agricultural and forested soils, and OpenGeoSys (OGS) for groundwater. The coupled model calculates flow of hydrostatic shallow water over the land surface with finite volume and difference methods. The flow equations for water in the porous subsurface are discretized in space with finite elements. Chemical components are transferred through 1D, 2D or 3D watershed representations with advection-dispersion solvers or, as an alternative, random walk particle tracking. A transport solver can be in sequence with a chemical solver, e.g. PHREEQ-C, BRNS, additionally. Besides coupled partial differential equations, the concept of hydrological response units is employed in simulations at regional scale with scarce data availability. In this case, a conceptual hydrological model, specifically the Jena Adaptable Modeling System (JAMS), passes groundwater recharge through a software interface into OGS, which solves the partial differential equations of groundwater flow. Most components of the modeling framework are open source and can be modified for individual purposes. Applications range from temperate climate regions in Germany (Ammer catchment and Hessian Ried) to arid regions in the Middle East (Oman and Dead See). Some of the presented examples originate from intensively monitored research sites of the WESS research centre and the monitoring initiative TERENO. Other examples originate from the IWAS project on integrated water resources management. The model applications are primarily concerned with groundwater resources, which are endangered by overexploitation, intrusion of saltwater, and nitrate loads.

Sensitivity of Dynamical Systems to Banach Space Parameters

DTIC Science & Technology

2005-02-13

We consider general nonlinear dynamical systems in a Banach space with dependence on parameters in a second Banach space. An abstract theoretical ... framework for sensitivity equations is developed. An application to measure dependent delay differential systems arising in a class of HIV models is presented.

Cultural Beliefs and Instructional Intentions: Do Experiences in Teacher Education Institutions Matter?

ERIC Educational Resources Information Center

Kumar, Revathy; Lauermann, Fani

2018-01-01

This cross-sectional study examines associations between preservice teachers' experiences in teacher education (n = 2,129), their beliefs about culturally diverse students, and their endorsed instructional practices within social reconstructionist and achievement goal theory frameworks. Structural equation modeling confirmed significant…

Multiple model cardinalized probability hypothesis density filter

NASA Astrophysics Data System (ADS)

Georgescu, Ramona; Willett, Peter

2011-09-01

The Probability Hypothesis Density (PHD) filter propagates the first-moment approximation to the multi-target Bayesian posterior distribution while the Cardinalized PHD (CPHD) filter propagates both the posterior likelihood of (an unlabeled) target state and the posterior probability mass function of the number of targets. Extensions of the PHD filter to the multiple model (MM) framework have been published and were implemented either with a Sequential Monte Carlo or a Gaussian Mixture approach. In this work, we introduce the multiple model version of the more elaborate CPHD filter. We present the derivation of the prediction and update steps of the MMCPHD particularized for the case of two target motion models and proceed to show that in the case of a single model, the new MMCPHD equations reduce to the original CPHD equations.

A unified framework for mesh refinement in random and physical space

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

Li, Jing; Stinis, Panos

In recent work we have shown how an accurate reduced model can be utilized to perform mesh renement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity from the large to the small scales of the solution. Since this is not always available, we present in the current work a framework which shares the merits and basic idea of the previous approach but does not require an explicit knowledge of a reduced model. Moreover, the current framework can be applied for renement in both randommore » and physical space. In this manuscript we focus on the application to random space mesh renement. We study examples of increasing difficulty (from ordinary to partial differential equations) which demonstrate the effciency and versatility of our approach. We also provide some results from the application of the new framework to physical space mesh refinement.« less

Development of One-Group and Two-Group Interfacial Area Transport Equation

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

Ishii, M.; Kim, S.

A dynamic approach employing the interfacial area transport equation is presented to replace the static flow regime dependent correlations for the interfacial area concentration. The current study derives the transport equations for the bubble number, volume, and interfacial area concentration. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, both one-group and two-group interfacial area transport equations are developed along with the necessary constitutive relations. The framework for the complicated source and sink terms in the two-group transport equation is also presented by identifying the major intragroup and intergroup bubble interaction mechanisms. In view ofmore » evaluating the theoretical model, the one-group interfacial area transport equation is benchmarked based on the available data obtained in a wide range of air-water bubbly flow in round tubes of various diameters. In general, the results show good agreement within the measurement error of {+-}10%.« less

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

NASA Astrophysics Data System (ADS)

Zalaletdinov, R. M.

1998-04-01

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

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

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

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Modelling biochemical reaction systems by stochastic differential equations with reflection.

PubMed

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. Copyright © 2016 Elsevier Ltd. All rights reserved.

A Cross-Cultural Analysis of Personality Structure Through the Lens of the HEXACO Model.

PubMed

Ion, Andrei; Iliescu, Dragos; Aldhafri, Said; Rana, Neeti; Ratanadilok, Kattiya; Widyanti, Ari; Nedelcea, Cătălin

2017-01-01

Across 5 different samples, totaling more than 1,600 participants from India, Indonesia, Oman, Romania, and Thailand, the authors address the question of cross-cultural replicability of a personality structure, while exploring the utility of exploratory structural equation modeling (ESEM) as a data analysis technique in cross-cultural personality research. Personality was measured with an alternative, non-Five-Factor Model (FFM) personality framework, provided by the HEXACO-PI (Lee & Ashton, 2004 ). The results show that the HEXACO framework was replicated in some of the investigated cultures. The ESEM data analysis technique proved to be especially useful in investigating the between-group measurement equivalence of broad personality measures across different cultures.

Structural Equation Model Approach to the Use of Response Times for Improving Estimation in Item Response Models

ERIC Educational Resources Information Center

Sen, Rohini

2012-01-01

In the last five decades, research on the uses of response time has extended into the field of psychometrics (Schnikpe & Scrams, 1999; van der Linden, 2006; van der Linden, 2007), where interest has centered around the usefulness of response time information in item calibration and person measurement within an item response theory. framework.…

Analysis of the Relations among the Components of Technological Pedagogical and Content Knowledge (TPACK): A Structural Equation Model

ERIC Educational Resources Information Center

Celik, Ismail; Sahin, Ismail; Akturk, Ahmet Oguz

2014-01-01

In the current study, the model of technological pedagogical and content knowledge (TPACK) is used as the theoretical framework in the process of data collection and interpretation of the results. This study analyzes the perceptions of 744 undergraduate students regarding their TPACK levels measured by responses to a survey developed by Sahin…

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation

PubMed Central

Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

2014-01-01

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design. PMID:25404761

A computational study of the discretization error in the solution of the Spencer-Lewis equation by doubling applied to the upwind finite-difference approximation

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

Nelson, P.; Seth, D.L.; Ray, A.K.

A detailed and systematic study of the nature of the discretization error associated with the upwind finite-difference method is presented. A basic model problem has been identified and based upon the results for this problem, a basic hypothesis regarding the accuracy of the computational solution of the Spencer-Lewis equation is formulated. The basic hypothesis is then tested under various systematic single complexifications of the basic model problem. The results of these tests provide the framework of the refined hypothesis presented in the concluding comments. 27 refs., 3 figs., 14 tabs.

Quantum cluster variational method and message passing algorithms revisited

NASA Astrophysics Data System (ADS)

Domínguez, E.; Mulet, Roberto

2018-02-01

We present a general framework to study quantum disordered systems in the context of the Kikuchi's cluster variational method (CVM). The method relies in the solution of message passing-like equations for single instances or in the iterative solution of complex population dynamic algorithms for an average case scenario. We first show how a standard application of the Kikuchi's CVM can be easily translated to message passing equations for specific instances of the disordered system. We then present an "ad hoc" extension of these equations to a population dynamic algorithm representing an average case scenario. At the Bethe level, these equations are equivalent to the dynamic population equations that can be derived from a proper cavity ansatz. However, at the plaquette approximation, the interpretation is more subtle and we discuss it taking also into account previous results in classical disordered models. Moreover, we develop a formalism to properly deal with the average case scenario using a replica-symmetric ansatz within this CVM for quantum disordered systems. Finally, we present and discuss numerical solutions of the different approximations for the quantum transverse Ising model and the quantum random field Ising model in two-dimensional lattices.

Hidden physics models: Machine learning of nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Raissi, Maziar; Karniadakis, George Em

2018-03-01

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

Theoretical Foundation of Copernicus: A Unified System for Trajectory Design and Optimization

NASA Technical Reports Server (NTRS)

Ocampo, Cesar; Senent, Juan S.; Williams, Jacob

2010-01-01

The fundamental methods are described for the general spacecraft trajectory design and optimization software system called Copernicus. The methods rely on a unified framework that is used to model, design, and optimize spacecraft trajectories that may operate in complex gravitational force fields, use multiple propulsion systems, and involve multiple spacecraft. The trajectory model, with its associated equations of motion and maneuver models, are discussed.

Stochastic Individual-Based Modeling of Bacterial Growth and Division Using Flow Cytometry.

PubMed

García, Míriam R; Vázquez, José A; Teixeira, Isabel G; Alonso, Antonio A

2017-01-01

A realistic description of the variability in bacterial growth and division is critical to produce reliable predictions of safety risks along the food chain. Individual-based modeling of bacteria provides the theoretical framework to deal with this variability, but it requires information about the individual behavior of bacteria inside populations. In this work, we overcome this problem by estimating the individual behavior of bacteria from population statistics obtained with flow cytometry. For this objective, a stochastic individual-based modeling framework is defined based on standard assumptions during division and exponential growth. The unknown single-cell parameters required for running the individual-based modeling simulations, such as cell size growth rate, are estimated from the flow cytometry data. Instead of using directly the individual-based model, we make use of a modified Fokker-Plank equation. This only equation simulates the population statistics in function of the unknown single-cell parameters. We test the validity of the approach by modeling the growth and division of Pediococcus acidilactici within the exponential phase. Estimations reveal the statistics of cell growth and division using only data from flow cytometry at a given time. From the relationship between the mother and daughter volumes, we also predict that P. acidilactici divide into two successive parallel planes.

GNuMe: A Galerkin-based Numerical Modeliing Environment for modeling geophysical fluid dynamics applications ranging from the Atmosphere to the Ocean

NASA Astrophysics Data System (ADS)

Giraldo, Francis; Abdi, Daniel; Kopera, Michal

2017-04-01

We have built a Galerkin-based Numerical Modeling Environment (GNuMe) for non hydrostatic atmospheric and ocean processes. GNuMe uses continuous Galerkin and Discontinuous Galerkin (CG/DG) discetizations as well as non-conforming adaptive mesh refinement (AMR), along with advanced time-integration methods that exploits both CG/DG and AMR capabilities. GNuMe currently solves the compressible and incompressible Navier-Stokes equations, the shallow water equations (with wetting and drying), and work is underway for inclusion of other types of equations. Moreover, GNuMe can run in both 2D and 3D modes on any type of accelerator hardware such as Nvidia GPUs and Intel KNL, and on standard X86 cores. In this talk, we shall present representative solutions obtained with GNuMe and will discuss where we think such a modeling framework could fit within standard Earth Systems Models. For further information on GNuMe please visit: http://frankgiraldo.wixsite.com/mysite/gnume.

Development of Response Spectral Ground Motion Prediction Equations from Empirical Models for Fourier Spectra and Duration of Ground Motion

NASA Astrophysics Data System (ADS)

Bora, S. S.; Scherbaum, F.; Kuehn, N. M.; Stafford, P.; Edwards, B.

2014-12-01

In a probabilistic seismic hazard assessment (PSHA) framework, it still remains a challenge to adjust ground motion prediction equations (GMPEs) for application in different seismological environments. In this context, this study presents a complete framework for the development of a response spectral GMPE easily adjustable to different seismological conditions; and which does not suffer from the technical problems associated with the adjustment in response spectral domain. Essentially, the approach consists of an empirical FAS (Fourier Amplitude Spectrum) model and a duration model for ground motion which are combined within the random vibration theory (RVT) framework to obtain the full response spectral ordinates. Additionally, FAS corresponding to individual acceleration records are extrapolated beyond the frequency range defined by the data using the stochastic FAS model, obtained by inversion as described in Edwards & Faeh, (2013). To that end, an empirical model for a duration, which is tuned to optimize the fit between RVT based and observed response spectral ordinate, at each oscillator frequency is derived. Although, the main motive of the presented approach was to address the adjustability issues of response spectral GMPEs; comparison, of median predicted response spectra with the other regional models indicate that presented approach can also be used as a stand-alone model. Besides that, a significantly lower aleatory variability (σ<0.5 in log units) in comparison to other regional models, at shorter periods brands it to a potentially viable alternative to the classical regression (on response spectral ordinates) based GMPEs for seismic hazard studies in the near future. The dataset used for the presented analysis is a subset of the recently compiled database RESORCE-2012 across Europe, Middle East and the Mediterranean region.

Methods for integrating moderation and mediation: a general analytical framework using moderated path analysis.

PubMed

Edwards, Jeffrey R; Lambert, Lisa Schurer

2007-03-01

Studies that combine moderation and mediation are prevalent in basic and applied psychology research. Typically, these studies are framed in terms of moderated mediation or mediated moderation, both of which involve similar analytical approaches. Unfortunately, these approaches have important shortcomings that conceal the nature of the moderated and the mediated effects under investigation. This article presents a general analytical framework for combining moderation and mediation that integrates moderated regression analysis and path analysis. This framework clarifies how moderator variables influence the paths that constitute the direct, indirect, and total effects of mediated models. The authors empirically illustrate this framework and give step-by-step instructions for estimation and interpretation. They summarize the advantages of their framework over current approaches, explain how it subsumes moderated mediation and mediated moderation, and describe how it can accommodate additional moderator and mediator variables, curvilinear relationships, and structural equation models with latent variables. (c) 2007 APA, all rights reserved.

IT vendor selection model by using structural equation model & analytical hierarchy process

NASA Astrophysics Data System (ADS)

Maitra, Sarit; Dominic, P. D. D.

2012-11-01

Selecting and evaluating the right vendors is imperative for an organization's global marketplace competitiveness. Improper selection and evaluation of potential vendors can dwarf an organization's supply chain performance. Numerous studies have demonstrated that firms consider multiple criteria when selecting key vendors. This research intends to develop a new hybrid model for vendor selection process with better decision making. The new proposed model provides a suitable tool for assisting decision makers and managers to make the right decisions and select the most suitable vendor. This paper proposes a Hybrid model based on Structural Equation Model (SEM) and Analytical Hierarchy Process (AHP) for long-term strategic vendor selection problems. The five steps framework of the model has been designed after the thorough literature study. The proposed hybrid model will be applied using a real life case study to assess its effectiveness. In addition, What-if analysis technique will be used for model validation purpose.

Moderation and Mediation in Structural Equation Modeling: Applications for Early Intervention Research

ERIC Educational Resources Information Center

Hopwood, Christopher J.

2007-01-01

Second-generation early intervention research typically involves the specification of multivariate relations between interventions, outcomes, and other variables. Moderation and mediation involve variables or sets of variables that influence relations between interventions and outcomes. Following the framework of Baron and Kenny's (1986) seminal…

A moist Boussinesq shallow water equations set for testing atmospheric models

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

Zerroukat, M., E-mail: mohamed.zerroukat@metoffice.gov.uk; Allen, T.

The shallow water equations have long been used as an initial test for numerical methods applied to atmospheric models with the test suite of Williamson et al. being used extensively for validating new schemes and assessing their accuracy. However the lack of physics forcing within this simplified framework often requires numerical techniques to be reworked when applied to fully three dimensional models. In this paper a novel two-dimensional shallow water equations system that retains moist processes is derived. This system is derived from three-dimensional Boussinesq approximation of the hydrostatic Euler equations where, unlike the classical shallow water set, we allowmore » the density to vary slightly with temperature. This results in extra (or buoyancy) terms for the momentum equations, through which a two-way moist-physics dynamics feedback is achieved. The temperature and moisture variables are advected as separate tracers with sources that interact with the mean-flow through a simplified yet realistic bulk moist-thermodynamic phase-change model. This moist shallow water system provides a unique tool to assess the usually complex and highly non-linear dynamics–physics interactions in atmospheric models in a simple yet realistic way. The full non-linear shallow water equations are solved numerically on several case studies and the results suggest quite realistic interaction between the dynamics and physics and in particular the generation of cloud and rain. - Highlights: • Novel shallow water equations which retains moist processes are derived from the three-dimensional hydrostatic Boussinesq equations. • The new shallow water set can be seen as a more general one, where the classical equations are a special case of these equations. • This moist shallow water system naturally allows a feedback mechanism from the moist physics increments to the momentum via buoyancy. • Like full models, temperature and moistures are advected as tracers that interact through a simplified yet realistic phase-change model. • This model is a unique tool to test numerical methods for atmospheric models, and physics–dynamics coupling, in a very realistic and simple way.« less

Multiphysics modeling of non-linear laser-matter interactions for optically active semiconductors

NASA Astrophysics Data System (ADS)

Kraczek, Brent; Kanp, Jaroslaw

Development of photonic devices for sensors and communications devices has been significantly enhanced by computational modeling. We present a new computational method for modelling laser propagation in optically-active semiconductors within the paraxial wave approximation (PWA). Light propagation is modeled using the Streamline-upwind/Petrov-Galerkin finite element method (FEM). Material response enters through the non-linear polarization, which serves as the right-hand side of the FEM calculation. Maxwell's equations for classical light propagation within the PWA can be written solely in terms of the electric field, producing a wave equation that is a form of the advection-diffusion-reaction equations (ADREs). This allows adaptation of the computational machinery developed for solving ADREs in fluid dynamics to light-propagation modeling. The non-linear polarization is incorporated using a flexible framework to enable the use of multiple methods for carrier-carrier interactions (e.g. relaxation-time-based or Monte Carlo) to enter through the non-linear polarization, as appropriate to the material type. We demonstrate using a simple carrier-carrier model approximating the response of GaN. Supported by ARL Materials Enterprise.

BPS counting for knots and combinatorics on words

NASA Astrophysics Data System (ADS)

Kucharski, Piotr; Sułkowski, Piotr

2016-11-01

We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded in the form of such difference equations, and whose generating functions (Hilbert-Poincaré series) are solutions to those equations and reproduce generating series that encode BPS invariants. Furthermore, BPS invariants in question are expressed in terms of Lyndon words in an appropriate language, thereby relating counting of BPS states to the branch of mathematics referred to as combinatorics on words. We illustrate these results in the framework of colored extremal knot polynomials: among others we determine dual quantum extremal A-polynomials for various knots, present associated combinatorial models, find corresponding BPS invariants (extremal Labastida-Mariño-Ooguri-Vafa invariants) and discuss their integrality.

A generalized threshold model for computing bed load grain size distribution

NASA Astrophysics Data System (ADS)

Recking, Alain

2016-12-01

For morphodynamic studies, it is important to compute not only the transported volumes of bed load, but also the size of the transported material. A few bed load equations compute fractional transport (i.e., both the volume and grain size distribution), but many equations compute only the bulk transport (a volume) with no consideration of the transported grain sizes. To fill this gap, a method is proposed to compute the bed load grain size distribution separately to the bed load flux. The method is called the Generalized Threshold Model (GTM), because it extends the flow competence method for threshold of motion of the largest transported grain size to the full bed surface grain size distribution. This was achieved by replacing dimensional diameters with their size indices in the standard hiding function, which offers a useful framework for computation, carried out for each indices considered in the range [1, 100]. New functions are also proposed to account for partial transport. The method is very simple to implement and is sufficiently flexible to be tested in many environments. In addition to being a good complement to standard bulk bed load equations, it could also serve as a framework to assist in analyzing the physics of bed load transport in future research.

Multi-flexible-body analysis for application to wind turbine control design

NASA Astrophysics Data System (ADS)

Lee, Donghoon

The objective of the present research is to build a theoretical and computational framework for the aeroelastic analysis of flexible rotating systems, more specifically with special application to a wind turbine control design. The methodology is based on the integration of Kane's approach for the analysis of the multi-rigid-body subsystem and a mixed finite element method for the analysis of the flexible-body subsystem. The combined analysis is then strongly coupled with an aerodynamic model based on Blade Element Momentum theory for inflow model. The unified framework from the analysis of subsystems is represented as, in a symbolic manner, a set of nonlinear ordinary differential equations with time-variant, periodic coefficients, which describe the aeroelastic behavior of whole system. The framework can be directly applied to control design due to its symbolic characteristics. The solution procedures for the equations are presented for the study of nonlinear simulation, periodic steady-state solution, and Floquet stability of the linearized system about the steady-state solution. Finally the linear periodic system equation can be obtained with both system and control matrices as explicit functions of time, which can be directly applicable to control design. The structural model is validated by comparison of its results with those from software, some of which is commercial. The stability of the linearized system about periodic steady-state solution is different from that obtained about a constant steady-state solution, which have been conventional in the field of wind turbine dynamics. Parametric studies are performed on a wind turbine model with various pitch angles, precone angles, and rotor speeds. Combined with composite material, their effects on wind turbine aeroelastic stability are investigated. Finally it is suggested that the aeroelastic stability analysis and control design for the whole system is crucial for the design of wind turbines, and the present research breaks new ground in the ability to treat the issue.

Model of dissolution in the framework of tissue engineering and drug delivery.

PubMed

Sanz-Herrera, J A; Soria, L; Reina-Romo, E; Torres, Y; Boccaccini, A R

2018-05-22

Dissolution phenomena are ubiquitously present in biomaterials in many different fields. Despite the advantages of simulation-based design of biomaterials in medical applications, additional efforts are needed to derive reliable models which describe the process of dissolution. A phenomenologically based model, available for simulation of dissolution in biomaterials, is introduced in this paper. The model turns into a set of reaction-diffusion equations implemented in a finite element numerical framework. First, a parametric analysis is conducted in order to explore the role of model parameters on the overall dissolution process. Then, the model is calibrated and validated versus a straightforward but rigorous experimental setup. Results show that the mathematical model macroscopically reproduces the main physicochemical phenomena that take place in the tests, corroborating its usefulness for design of biomaterials in the tissue engineering and drug delivery research areas.

Multi-Dimensional Quantum Effect Simulation Using a Density-Gradient Model and Script-Level Programming Techniques

NASA Technical Reports Server (NTRS)

Rafferty, Connor S.; Biegel, Bryan A.; Yu, Zhi-Ping; Ancona, Mario G.; Bude, J.; Dutton, Robert W.; Saini, Subhash (Technical Monitor)

1998-01-01

A density-gradient (DG) model is used to calculate quantum-mechanical corrections to classical carrier transport in MOS (Metal Oxide Semiconductor) inversion/accumulation layers. The model is compared to measured data and to a fully self-consistent coupled Schrodinger and Poisson equation (SCSP) solver. Good agreement is demonstrated for MOS capacitors with gate oxide as thin as 21 A. It is then applied to study carrier distribution in ultra short MOSFETs (Metal Oxide Semiconductor Field Effect Transistor) with surface roughness. This work represents the first implementation of the DG formulation on multidimensional unstructured meshes. It was enabled by a powerful scripting approach which provides an easy-to-use and flexible framework for solving the fourth-order PDEs (Partial Differential Equation) of the DG model.

X-ray Raman scattering from molecules and solids in the framework of the Mahan-Nozières-De Dominicis model

NASA Astrophysics Data System (ADS)

Privalov, Timofei; Gel'mukhanov, Faris; Ågren, Hans

2001-10-01

We have developed a formulation of resonant x-ray Raman scattering of molecules and solids based on the Mahan-Nozières-De Dominicis model. A key step in the formulation is given by a reduction of the Keldysh-Dyson equations for the Green's function to a set of linear algebraic equations. This gave way for a tractable scheme that can be used to analyze the resonant x-ray scattering in the whole time domain. The formalism is used to investigate the role of core-hole relaxation, interference, band filling, detuning, and size of the scattering target. Numerical applications are performed with a one-dimensional tight-binding model.

Contact interaction of thin-walled elements with an elastic layer and an infinite circular cylinder under torsion

NASA Astrophysics Data System (ADS)

Kanetsyan, E. G.; Mkrtchyan, M. S.; Mkhitaryan, S. M.

2018-04-01

We consider a class of contact torsion problems on interaction of thin-walled elements shaped as an elastic thin washer – a flat circular plate of small height – with an elastic layer, in particular, with a half-space, and on interaction of thin cylindrical shells with a solid elastic cylinder, infinite in both directions. The governing equations of the physical models of elastic thin washers and thin circular cylindrical shells under torsion are derived from the exact equations of mathematical theory of elasticity using the Hankel and Fourier transforms. Within the framework of the accepted physical models, the solution of the contact problem between an elastic washer and an elastic layer is reduced to solving the Fredholm integral equation of the first kind with a kernel representable as a sum of the Weber–Sonin integral and some integral regular kernel, while solving the contact problem between a cylindrical shell and solid cylinder is reduced to a singular integral equation (SIE). An effective method for solving the governing integral equations of these problems are specified.

Electromagnetic field computation at fractal dimensions

NASA Astrophysics Data System (ADS)

Zubair, M.; Ang, Y. S.; Ang, L. K.

According to Mandelbrot's work on fractals, many objects are in fractional dimensions that the traditional calculus or differential equations are not sufficient. Thus fractional models solving the relevant differential equations are critical to understand the physical dynamics of such objects. In this work, we develop computational electromagnetics or Maxwell equations in fractional dimensions. For a given degree of imperfection, impurity, roughness, anisotropy or inhomogeneity, we consider the complicated object can be formulated into a fractional dimensional continuous object characterized by an effective fractional dimension D, which can be calculated from a self-developed algorithm. With this non-integer value of D, we develop the computational methods to design and analyze the EM scattering problems involving rough surfaces or irregularities in an efficient framework. The fractional electromagnetic based model can be extended to other key differential equations such as Schrodinger or Dirac equations, which will be useful for design of novel 2D materials stacked up in complicated device configuration for applications in electronics and photonics. This work is supported by Singapore Temasek Laboratories (TL) Seed Grant (IGDS S16 02 05 1).

Multi-physics simulations of space weather

NASA Astrophysics Data System (ADS)

Gombosi, Tamas; Toth, Gabor; Sokolov, Igor; de Zeeuw, Darren; van der Holst, Bart; Cohen, Ofer; Glocer, Alex; Manchester, Ward, IV; Ridley, Aaron

Presently magnetohydrodynamic (MHD) models represent the "workhorse" technology for simulating the space environment from the solar corona to the ionosphere. While these models are very successful in describing many important phenomena, they are based on a low-order moment approximation of the phase-space distribution function. In the last decade our group at the Center for Space Environment Modeling (CSEM) has developed the Space Weather Modeling Framework (SWMF) that efficiently couples together different models describing the interacting regions of the space environment. Many of these domain models (such as the global solar corona, the inner heliosphere or the global magnetosphere) are based on MHD and are represented by our multiphysics code, BATS-R-US. BATS-R-US can solve the equations of "standard" ideal MHD, but it can also go beyond this first approximation. It can solve resistive MHD, Hall MHD, semi-relativistic MHD (that keeps the displacement current), multispecies (different ion species have different continuity equations) and multifluid (all ion species have separate continuity, momentum and energy equations) MHD. Recently we added two-fluid Hall MHD (solving the electron and ion energy equations separately) and are working on extended magnetohydrodynamics with anisotropic pressures. This talk will show the effects of added physics and compare space weather simulation results to "standard" ideal MHD.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

PubMed Central

Gerstner, Wulfram

2017-01-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. PMID:28422957

Food waste behaviour at the household level: A conceptual framework.

PubMed

Abdelradi, Fadi

2018-01-01

One-third of the world produced food is wasted according to FAO (2011). The aim of this paper is to have an in-depth analysis of consumers' behaviours regarding food waste in Egypt. A conceptual framework is developed that brings many factors considered in the recent literature in one model to be tested using structural equation modeling. Results indicate that the incorporated factors were found statistically significant. Additionally, the individual's perception about food waste was related with food quantities wasted at the household level. The findings suggest considering these factors when developing new policies and campaigns for food waste reduction. Copyright © 2017 Elsevier Ltd. All rights reserved.

Prediction of Complex Aerodynamic Flows with Explicit Algebraic Stress Models

NASA Technical Reports Server (NTRS)

Abid, Ridha; Morrison, Joseph H.; Gatski, Thomas B.; Speziale, Charles G.

1996-01-01

An explicit algebraic stress equation, developed by Gatski and Speziale, is used in the framework of K-epsilon formulation to predict complex aerodynamic turbulent flows. The nonequilibrium effects are modeled through coefficients that depend nonlinearly on both rotational and irrotational strains. The proposed model was implemented in the ISAAC Navier-Stokes code. Comparisons with the experimental data are presented which clearly demonstrate that explicit algebraic stress models can predict the correct response to nonequilibrium flow.

Modeling mass transfer and reaction of dilute solutes in a ternary phase system by the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Fu, Yu-Hang; Bai, Lin; Luo, Kai-Hong; Jin, Yong; Cheng, Yi

2017-04-01

In this work, we propose a general approach for modeling mass transfer and reaction of dilute solute(s) in incompressible three-phase flows by introducing a collision operator in lattice Boltzmann (LB) method. An LB equation was used to simulate the solute dynamics among three different fluids, in which the newly expanded collision operator was used to depict the interface behavior of dilute solute(s). The multiscale analysis showed that the presented model can recover the macroscopic transport equations derived from the Maxwell-Stefan equation for dilute solutes in three-phase systems. Compared with the analytical equation of state of solute and dynamic behavior, these results are proven to constitute a generalized framework to simulate solute distributions in three-phase flows, including compound soluble in one phase, compound adsorbed on single-interface, compound in two phases, and solute soluble in three phases. Moreover, numerical simulations of benchmark cases, such as phase decomposition, multilayered planar interfaces, and liquid lens, were performed to test the stability and efficiency of the model. Finally, the multiphase mass transfer and reaction in Janus droplet transport in a straight microchannel were well reproduced.

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

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

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The approach used follows the non-equilibrium statistical mechanical approach through a master equation. The aim is to represent the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and mass flux is a non-linear function of convective cell area, mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated mass flux variability under diurnally varying forcing. Besides its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to be capable of providing alternative, non-equilibrium, closure formulations for spectral mass flux parameterizations.« less

Comparison of methods for the analysis of relatively simple mediation models.

PubMed

Rijnhart, Judith J M; Twisk, Jos W R; Chinapaw, Mai J M; de Boer, Michiel R; Heymans, Martijn W

2017-09-01

Statistical mediation analysis is an often used method in trials, to unravel the pathways underlying the effect of an intervention on a particular outcome variable. Throughout the years, several methods have been proposed, such as ordinary least square (OLS) regression, structural equation modeling (SEM), and the potential outcomes framework. Most applied researchers do not know that these methods are mathematically equivalent when applied to mediation models with a continuous mediator and outcome variable. Therefore, the aim of this paper was to demonstrate the similarities between OLS regression, SEM, and the potential outcomes framework in three mediation models: 1) a crude model, 2) a confounder-adjusted model, and 3) a model with an interaction term for exposure-mediator interaction. Secondary data analysis of a randomized controlled trial that included 546 schoolchildren. In our data example, the mediator and outcome variable were both continuous. We compared the estimates of the total, direct and indirect effects, proportion mediated, and 95% confidence intervals (CIs) for the indirect effect across OLS regression, SEM, and the potential outcomes framework. OLS regression, SEM, and the potential outcomes framework yielded the same effect estimates in the crude mediation model, the confounder-adjusted mediation model, and the mediation model with an interaction term for exposure-mediator interaction. Since OLS regression, SEM, and the potential outcomes framework yield the same results in three mediation models with a continuous mediator and outcome variable, researchers can continue using the method that is most convenient to them.

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

PubMed

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

2010-02-01

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

Artificial neural network methods in quantum mechanics

NASA Astrophysics Data System (ADS)

Lagaris, I. E.; Likas, A.; Fotiadis, D. I.

1997-08-01

In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for differential and integrodifferential operators, using ANNs. We start by considering the Schrödinger equation for the Morse potential that has an analytically known solution, to test the accuracy of the method. We then proceed with the Schrödinger and the Dirac equations for a muonic atom, as well as with a nonlocal Schrödinger integrodifferential equation that models the n + α system in the framework of the resonating group method. In two dimensions we consider the well-studied Henon-Heiles Hamiltonian and in three dimensions the model problem of three coupled anharmonic oscillators. The method in all of the treated cases proved to be highly accurate, robust and efficient. Hence it is a promising tool for tackling problems of higher complexity and dimensionality.

Preschool Interactive Peer Play Mediates Problem Behavior and Learning for Low-Income Children

ERIC Educational Resources Information Center

Bulotsky-Shearer, Rebecca J.; Bell, Elizabeth R.; Romero, Sandy L.; Carter, Tracy M.

2012-01-01

The study employed a developmental, ecological, and resiliency framework to examine whether interactive peer play competencies mediated associations between teacher reported problem behavior and learning outcomes for a representative sample of urban low-income children (N = 507 across 46 Head Start classrooms). Structural equation models provided…

Cognitive Processes in University Learning: A Developmental Framework Using Structural Equation Modelling

ERIC Educational Resources Information Center

Phan, Huy P.

2011-01-01

Background: Both achievement goals and study processing strategies theories have been shown to contribute to the prediction of students' academic performance. Existing research studies (Fenollar, Roman, & Cuestas, 2007; Liem, Lau, & Nie, 2008; Simons, Dewitte, & Lens, 2004) amalgamating these two theoretical orientations in different causal models…

Students' Levels of Explanations, Models, and Misconceptions in Basic Quantum Chemistry: A Phenomenographic Study

ERIC Educational Resources Information Center

Stefani, Christina; Tsaparlis, Georgios

2009-01-01

We investigated students' knowledge constructions of basic quantum chemistry concepts, namely atomic orbitals, the Schrodinger equation, molecular orbitals, hybridization, and chemical bonding. Ausubel's theory of meaningful learning provided the theoretical framework and phenomenography the method of analysis. The semi-structured interview with…

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution - Part 1: theoretical development

NASA Astrophysics Data System (ADS)

Dib, Alain; Kavvas, M. Levent

2018-03-01

The Saint-Venant equations are commonly used as the governing equations to solve for modeling the spatially varied unsteady flow in open channels. The presence of uncertainties in the channel or flow parameters renders these equations stochastic, thus requiring their solution in a stochastic framework in order to quantify the ensemble behavior and the variability of the process. While the Monte Carlo approach can be used for such a solution, its computational expense and its large number of simulations act to its disadvantage. This study proposes, explains, and derives a new methodology for solving the stochastic Saint-Venant equations in only one shot, without the need for a large number of simulations. The proposed methodology is derived by developing the nonlocal Lagrangian-Eulerian Fokker-Planck equation of the characteristic form of the stochastic Saint-Venant equations for an open-channel flow process, with an uncertain roughness coefficient. A numerical method for its solution is subsequently devised. The application and validation of this methodology are provided in a companion paper, in which the statistical results computed by the proposed methodology are compared against the results obtained by the Monte Carlo approach.

A constrained robust least squares approach for contaminant release history identification

NASA Astrophysics Data System (ADS)

Sun, Alexander Y.; Painter, Scott L.; Wittmeyer, Gordon W.

2006-04-01

Contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty. Model uncertainty was rarely considered in the previous studies. In this work, a robust framework for solving contaminant source recovery problems is introduced. The contaminant source identification problem is first cast into one of solving uncertain linear equations, where the response matrix is constructed using a superposition technique. The formulation presented here is general and is applicable to any porous media flow and transport solvers. The robust least squares (RLS) estimator, which originated in the field of robust identification, directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data. In this work, a new variant of RLS, the constrained robust least squares (CRLS), is formulated for solving uncertain linear equations. CRLS allows for additional constraints, such as nonnegativity, to be imposed. The performance of CRLS is demonstrated through one- and two-dimensional test problems. When the system is ill-conditioned and uncertain, it is found that CRLS gave much better performance than its classical counterpart, the nonnegative least squares. The source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications.

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

NASA Technical Reports Server (NTRS)

Carton De Wiart, Corentin; Diosady, Laslo T.; Garai, Anirban; Burgess, Nicholas; Blonigan, Patrick; Ekelschot, Dirk; Murman, Scott M.

2018-01-01

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

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

NASA Astrophysics Data System (ADS)

Shaw, Jeremy A.; Daescu, Dacian N.

2017-08-01

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

Using Instrumental Variable (IV) Tests to Evaluate Model Specification in Latent Variable Structural Equation Models*

PubMed Central

Kirby, James B.; Bollen, Kenneth A.

2009-01-01

Structural Equation Modeling with latent variables (SEM) is a powerful tool for social and behavioral scientists, combining many of the strengths of psychometrics and econometrics into a single framework. The most common estimator for SEM is the full-information maximum likelihood estimator (ML), but there is continuing interest in limited information estimators because of their distributional robustness and their greater resistance to structural specification errors. However, the literature discussing model fit for limited information estimators for latent variable models is sparse compared to that for full information estimators. We address this shortcoming by providing several specification tests based on the 2SLS estimator for latent variable structural equation models developed by Bollen (1996). We explain how these tests can be used to not only identify a misspecified model, but to help diagnose the source of misspecification within a model. We present and discuss results from a Monte Carlo experiment designed to evaluate the finite sample properties of these tests. Our findings suggest that the 2SLS tests successfully identify most misspecified models, even those with modest misspecification, and that they provide researchers with information that can help diagnose the source of misspecification. PMID:20419054

Minimal string theories and integrable hierarchies

NASA Astrophysics Data System (ADS)

Iyer, Ramakrishnan

Well-defined, non-perturbative formulations of the physics of string theories in specific minimal or superminimal model backgrounds can be obtained by solving matrix models in the double scaling limit. They provide us with the first examples of completely solvable string theories. Despite being relatively simple compared to higher dimensional critical string theories, they furnish non-perturbative descriptions of interesting physical phenomena such as geometrical transitions between D-branes and fluxes, tachyon condensation and holography. The physics of these theories in the minimal model backgrounds is succinctly encoded in a non-linear differential equation known as the string equation, along with an associated hierarchy of integrable partial differential equations (PDEs). The bosonic string in (2,2m-1) conformal minimal model backgrounds and the type 0A string in (2,4 m) superconformal minimal model backgrounds have the Korteweg-de Vries system, while type 0B in (2,4m) backgrounds has the Zakharov-Shabat system. The integrable PDE hierarchy governs flows between backgrounds with different m. In this thesis, we explore this interesting connection between minimal string theories and integrable hierarchies further. We uncover the remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain minimal string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We find that there are several other string-like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several other string-like special points arise and are connected. In some cases, the framework endows the theories with a non-perturbative definition for the first time. Notably, we discover that the Painleve IV equation plays a key role in organizing the string theory physics, joining its siblings, Painleve I and II, whose roles have previously been identified in this minimal string context. We then present evidence that the conjectured type II theories have smooth non-perturbative solutions, connecting two perturbative asymptotic regimes, in a 't Hooft limit. Our technique also demonstrates evidence for new minimal string theories that are not apparent in a perturbative analysis.

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth.

PubMed

Lv, Qiming; Schneider, Manuel K; Pitchford, Jonathan W

2008-08-01

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.

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

USGS Publications Warehouse

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

2015-01-01

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

RadVel: General toolkit for modeling Radial Velocities

NASA Astrophysics Data System (ADS)

Fulton, Benjamin J.; Petigura, Erik A.; Blunt, Sarah; Sinukoff, Evan

2018-01-01

RadVel models Keplerian orbits in radial velocity (RV) time series. The code is written in Python with a fast Kepler's equation solver written in C. It provides a framework for fitting RVs using maximum a posteriori optimization and computing robust confidence intervals by sampling the posterior probability density via Markov Chain Monte Carlo (MCMC). RadVel can perform Bayesian model comparison and produces publication quality plots and LaTeX tables.

Examining the Moderating Effect of Individual-Level Cultural Values on Users' Acceptance of E-Learning in Developing Countries: A Structural Equation Modeling of an Extended Technology Acceptance Model

ERIC Educational Resources Information Center

Tarhini, Ali; Hone, Kate; Liu, Xiaohui; Tarhini, Takwa

2017-01-01

In this study, we examine the effects of individual-level culture on the adoption and acceptance of e-learning tools by students in Lebanon using a theoretical framework based on the Technology Acceptance Model (TAM). To overcome possible limitations of using TAM in developing countries, we extend TAM to include "subjective norms" (SN)…

A resilient and efficient CFD framework: Statistical learning tools for multi-fidelity and heterogeneous information fusion

NASA Astrophysics Data System (ADS)

Lee, Seungjoon; Kevrekidis, Ioannis G.; Karniadakis, George Em

2017-09-01

Exascale-level simulations require fault-resilient algorithms that are robust against repeated and expected software and/or hardware failures during computations, which may render the simulation results unsatisfactory. If each processor can share some global information about the simulation from a coarse, limited accuracy but relatively costless auxiliary simulator we can effectively fill-in the missing spatial data at the required times by a statistical learning technique - multi-level Gaussian process regression, on the fly; this has been demonstrated in previous work [1]. Based on the previous work, we also employ another (nonlinear) statistical learning technique, Diffusion Maps, that detects computational redundancy in time and hence accelerate the simulation by projective time integration, giving the overall computation a "patch dynamics" flavor. Furthermore, we are now able to perform information fusion with multi-fidelity and heterogeneous data (including stochastic data). Finally, we set the foundations of a new framework in CFD, called patch simulation, that combines information fusion techniques from, in principle, multiple fidelity and resolution simulations (and even experiments) with a new adaptive timestep refinement technique. We present two benchmark problems (the heat equation and the Navier-Stokes equations) to demonstrate the new capability that statistical learning tools can bring to traditional scientific computing algorithms. For each problem, we rely on heterogeneous and multi-fidelity data, either from a coarse simulation of the same equation or from a stochastic, particle-based, more "microscopic" simulation. We consider, as such "auxiliary" models, a Monte Carlo random walk for the heat equation and a dissipative particle dynamics (DPD) model for the Navier-Stokes equations. More broadly, in this paper we demonstrate the symbiotic and synergistic combination of statistical learning, domain decomposition, and scientific computing in exascale simulations.

A nonlinear autoregressive Volterra model of the Hodgkin-Huxley equations.

PubMed

Eikenberry, Steffen E; Marmarelis, Vasilis Z

2013-02-01

We propose a new variant of Volterra-type model with a nonlinear auto-regressive (NAR) component that is a suitable framework for describing the process of AP generation by the neuron membrane potential, and we apply it to input-output data generated by the Hodgkin-Huxley (H-H) equations. Volterra models use a functional series expansion to describe the input-output relation for most nonlinear dynamic systems, and are applicable to a wide range of physiologic systems. It is difficult, however, to apply the Volterra methodology to the H-H model because is characterized by distinct subthreshold and suprathreshold dynamics. When threshold is crossed, an autonomous action potential (AP) is generated, the output becomes temporarily decoupled from the input, and the standard Volterra model fails. Therefore, in our framework, whenever membrane potential exceeds some threshold, it is taken as a second input to a dual-input Volterra model. This model correctly predicts membrane voltage deflection both within the subthreshold region and during APs. Moreover, the model naturally generates a post-AP afterpotential and refractory period. It is known that the H-H model converges to a limit cycle in response to a constant current injection. This behavior is correctly predicted by the proposed model, while the standard Volterra model is incapable of generating such limit cycle behavior. The inclusion of cross-kernels, which describe the nonlinear interactions between the exogenous and autoregressive inputs, is found to be absolutely necessary. The proposed model is general, non-parametric, and data-derived.

An Object-Oriented Finite Element Framework for Multiphysics Phase Field Simulations

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

Michael R Tonks; Derek R Gaston; Paul C Millett

2012-01-01

The phase field approach is a powerful and popular method for modeling microstructure evolution. In this work, advanced numerical tools are used to create a phase field framework that facilitates rapid model development. This framework, called MARMOT, is based on Idaho National Laboratory's finite element Multiphysics Object-Oriented Simulation Environment. In MARMOT, the system of phase field partial differential equations (PDEs) are solved simultaneously with PDEs describing additional physics, such as solid mechanics and heat conduction, using the Jacobian-Free Newton Krylov Method. An object-oriented architecture is created by taking advantage of commonalities in phase fields models to facilitate development of newmore » models with very little written code. In addition, MARMOT provides access to mesh and time step adaptivity, reducing the cost for performing simulations with large disparities in both spatial and temporal scales. In this work, phase separation simulations are used to show the numerical performance of MARMOT. Deformation-induced grain growth and void growth simulations are included to demonstrate the muliphysics capability.« less

Gassmann Theory Applies to Nanoporous Media

NASA Astrophysics Data System (ADS)

Gor, Gennady Y.; Gurevich, Boris

2018-01-01

Recent progress in extraction of unconventional hydrocarbon resources has ignited the interest in the studies of nanoporous media. Since many thermodynamic and mechanical properties of nanoscale solids and fluids differ from the analogous bulk materials, it is not obvious whether wave propagation in nanoporous media can be described using the same framework as in macroporous media. Here we test the validity of Gassmann equation using two published sets of ultrasonic measurements for a model nanoporous medium, Vycor glass, saturated with two different fluids, argon, and n-hexane. Predictions of the Gassmann theory depend on the bulk and shear moduli of the dry samples, which are known from ultrasonic measurements and the bulk moduli of the solid and fluid constituents. The solid bulk modulus can be estimated from adsorption-induced deformation or from elastic effective medium theory. The fluid modulus can be calculated according to the Tait-Murnaghan equation at the solvation pressure in the pore. Substitution of these parameters into the Gassmann equation provides predictions consistent with measured data. Our findings set up a theoretical framework for investigation of fluid-saturated nanoporous media using ultrasonic elastic wave propagation.

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

Gevorkyan, A. S., E-mail: g-ashot@sci.am; Sahakyan, V. V.

We study the classical 1D Heisenberg spin glasses in the framework of nearest-neighboring model. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from the first principles of classical mechanics lead to ℕℙ hard problem, that however in the limit of the statistical equilibrium can be calculated by ℙ algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.

The mechanics of solids in the plastically-deformable state

NASA Technical Reports Server (NTRS)

Mises, R. V.

1986-01-01

The mechanics of continua, which is based on the general stress model of Cauchy, up to the present has almost exclusively been applied to liquid and solid elastic bodies. Saint-Venant has developed a theory for the plastic or remaining form changes of solids, but it does not give the required number of equations for determining motion. A complete set of equations of motion for plastic deformable bodies is derived. This is done within the framework of Cauch mechanics. And it is supported by certain experimental facts which characterize the range of applications.

Correspondence between discrete and continuous models of excitable media: trigger waves

NASA Technical Reports Server (NTRS)

Chernyak, Y. B.; Feldman, A. B.; Cohen, R. J.

1997-01-01

We present a theoretical framework for relating continuous partial differential equation (PDE) models of excitable media to discrete cellular automata (CA) models on a randomized lattice. These relations establish a quantitative link between the CA model and the specific physical system under study. We derive expressions for the CA model's plane wave speed, critical curvature, and effective diffusion constant in terms of the model's internal parameters (the interaction radius, excitation threshold, and time step). We then equate these expressions to the corresponding quantities obtained from solution of the PDEs (for a fixed excitability). This yields a set of coupled equations with a unique solution for the required CA parameter values. Here we restrict our analysis to "trigger" wave solutions obtained in the limiting case of a two-dimensional excitable medium with no recovery processes. We tested the correspondence between our CA model and two PDE models (the FitzHugh-Nagumo medium and a medium with a "sawtooth" nonlinear reaction source) and found good agreement with the numerical solutions of the PDEs. Our results suggest that the behavior of trigger waves is actually controlled by a small number of parameters.

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

PubMed

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

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

A stochastic model for the normal tissue complication probability (NTCP) and applicationss.

PubMed

Stocks, Theresa; Hillen, Thomas; Gong, Jiafen; Burger, Martin

2017-12-11

The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth-death process to define an organ-specific and patient-specific NTCP. We emphasize an asymptotic simplification which relates the NTCP to the solution of a logistic differential equation. This framework is based on simple modelling assumptions and it prepares a framework for the use of the NTCP model in clinical practice. As example, we consider side effects of prostate cancer brachytherapy such as increase in urinal frequency, urinal retention and acute rectal dysfunction. © The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Lagrangian averaging, nonlinear waves, and shock regularization

NASA Astrophysics Data System (ADS)

Bhat, Harish S.

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

On the use of internal state variables in thermoviscoplastic constitutive equations

NASA Technical Reports Server (NTRS)

Allen, D. H.; Beek, J. M.

1985-01-01

The general theory of internal state variables are reviewed to apply it to inelastic metals in use in high temperature environments. In this process, certain constraints and clarifications will be made regarding internal state variables. It is shown that the Helmholtz free energy can be utilized to construct constitutive equations which are appropriate for metallic superalloys. Internal state variables are shown to represent locally averaged measures of dislocation arrangement, dislocation density, and intergranular fracture. The internal state variable model is demonstrated to be a suitable framework for comparison of several currently proposed models for metals and can therefore be used to exhibit history dependence, nonlinearity, and rate as well as temperature sensitivity.

Rank-preserving regression: a more robust rank regression model against outliers.

PubMed

Chen, Tian; Kowalski, Jeanne; Chen, Rui; Wu, Pan; Zhang, Hui; Feng, Changyong; Tu, Xin M

2016-08-30

Mean-based semi-parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models. Unfortunately, such models are quite sensitive to outlying observations. The Wilcoxon-score-based rank regression (RR) provides more robust estimates over generalized estimating equations against outliers. However, the RR and its extensions do not sufficiently address missing data arising in longitudinal studies. In this paper, we propose a new approach to address outliers under a different framework based on the functional response models. This functional-response-model-based alternative not only addresses limitations of the RR and its extensions for longitudinal data, but, with its rank-preserving property, even provides more robust estimates than these alternatives. The proposed approach is illustrated with both real and simulated data. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Development and Application of Compatible Discretizations of Maxwell's Equations

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

White, D; Koning, J; Rieben, R

We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we havemore » designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve.« less

Large Eddy Simulation (LES) of Particle-Laden Temporal Mixing Layers

NASA Technical Reports Server (NTRS)

Bellan, Josette; Radhakrishnan, Senthilkumaran

2012-01-01

High-fidelity models of plume-regolith interaction are difficult to develop because of the widely disparate flow conditions that exist in this process. The gas in the core of a rocket plume can often be modeled as a time-dependent, high-temperature, turbulent, reacting continuum flow. However, due to the vacuum conditions on the lunar surface, the mean molecular path in the outer parts of the plume is too long for the continuum assumption to remain valid. Molecular methods are better suited to model this region of the flow. Finally, granular and multiphase flow models must be employed to describe the dust and debris that are displaced from the surface, as well as how a crater is formed in the regolith. At present, standard commercial CFD (computational fluid dynamics) software is not capable of coupling each of these flow regimes to provide an accurate representation of this flow process, necessitating the development of custom software. This software solves the fluid-flow-governing equations in an Eulerian framework, coupled with the particle transport equations that are solved in a Lagrangian framework. It uses a fourth-order explicit Runge-Kutta scheme for temporal integration, an eighth-order central finite differencing scheme for spatial discretization. The non-linear terms in the governing equations are recast in cubic skew symmetric form to reduce aliasing error. The second derivative viscous terms are computed using eighth-order narrow stencils that provide better diffusion for the highest resolved wave numbers. A fourth-order Lagrange interpolation procedure is used to obtain gas-phase variable values at the particle locations.

Using structural equation modeling for network meta-analysis.

PubMed

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. SEM provides a very flexible framework for univariate and multivariate meta-analysis, and its potential as a powerful tool for advanced meta-analysis is still to be explored.

A generalized Poisson solver for first-principles device simulations

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

Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost, E-mail: joost.vandevondele@mat.ethz.ch; Brück, Sascha

2016-01-28

Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative methodmore » in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.« less

Four-fluid MHD Simulations of the Plasma and Neutral Gas Environment of Comet 67P/Churyumov-Gerasimenko Near Perihelion

NASA Astrophysics Data System (ADS)

Huang, Zhenguang; Toth, Gabor; Gombosi, Tamas; Jia, Xianzhe; Rubin, Martin; Fougere, Nicolas; Tenishev, Valeriy; Combi, Michael; Bieler, Andre; Hansen, Kenneth; Shou, Yinsi; Altwegg, Kathrin

2016-04-01

The neutral and plasma environment is critical in understanding the interaction of the solar wind and comet 67P/Churyumov-Gerasimenko (CG), the target of the European Space Agency's Rosetta mission. In this study, we have developed a 3-D four-fluid model, which is based on BATS-R-US (Block-Adaptive Tree Solarwind Roe-type Upwind Scheme) within SWMF (Space Weather Modeling Framework) that solves the governing multi-fluid MHD equations and the Euler equations for the neutral gas fluid. These equations describe the behavior and interactions of the cometary heavy ions, the solar wind protons, the electrons, and the neutrals. We simulated the plasma and neutral gas environment of comet CG with SHAP5 model near perihelion and we showed that the plasma environment in the inner coma region have some new features: magnetic reconnection in the tail region, a magnetic pile-up region on the nightside, and nucleus directed plasma flow inside the nightside reconnection region.

The Bethe ansatz

NASA Astrophysics Data System (ADS)

Levkovich-Maslyuk, Fedor

2016-08-01

We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based on the exact S-matrix. Then we illustrate this method in several concrete theories. The first case we study is the SU(2) chiral Gross-Neveu model. We derive the Bethe equations via algebraic Bethe ansatz, solving in the process the Heisenberg XXX spin chain. We discuss this famous spin chain model in some detail, covering in particular the coordinate Bethe ansatz, some properties of Bethe states, and the classical scaling limit leading to finite-gap equations. Then we proceed to the more involved SU(3) chiral Gross-Neveu model and derive the Bethe equations using nested algebraic Bethe ansatz to solve the arising SU(3) spin chain. Finally we show how a method similar to the Bethe ansatz works in a completely different setting, namely for the 1D oscillator in quantum mechanics.

Ruijsenaars-Schneider three-body models with N = 2 supersymmetry

NASA Astrophysics Data System (ADS)

Galajinsky, Anton

2018-04-01

The Ruijsenaars-Schneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. Surprisingly enough, their supersymmetric generalizations escaped attention. In this work, N = 2 supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider three-body models are constructed within the framework of the Hamiltonian formalism. It is also known that the rational model can be described by the geodesic equations associated with a metric connection. We demonstrate that the hyperbolic systems are linked to non-metric connections.

Differential renormalization-group generators for static and dynamic critical phenomena

NASA Astrophysics Data System (ADS)

Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

1992-09-01

The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

Modeling of high pressure arc-discharge with a fully-implicit Navier-Stokes stabilized finite element flow solver

NASA Astrophysics Data System (ADS)

Sahai, A.; Mansour, N. N.; Lopez, B.; Panesi, M.

2017-05-01

This work addresses the modeling of high pressure electric discharge in an arc-heated wind tunnel. The combined numerical solution of Poisson’s equation, radiative transfer equations, and the set of Favre-averaged thermochemical nonequilibrium Navier-Stokes equations allows for the determination of the electric, radiation, and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles with the Chapman-Enskog method. A multi-temperature formulation is used to account for thermal non-equilibrium. Finally, the turbulence closure of the flow equations is obtained by means of the Spalart-Allmaras model, which requires the solution of an additional scalar transport equation. A Streamline upwind Petrov-Galerkin stabilized finite element formulation is employed to solve the Navier-Stokes equation. The electric field equation is solved using the standard Galerkin formulation. A stable formulation for the radiative transfer equations is obtained using the least-squares finite element method. The developed simulation framework has been applied to investigate turbulent plasma flows in the 20 MW Aerodynamic Heating Facility at NASA Ames Research Center. The current model is able to predict the process of energy addition and re-distribution due to Joule heating and thermal radiation, resulting in a hot central core surrounded by colder flow. The use of an unsteady three-dimensional treatment also allows the asymmetry due to a dynamic electric arc attachment point in the cathode chamber to be captured accurately. The current work paves the way for detailed estimation of operating characteristics for arc-heated wind tunnels which are critical in testing thermal protection systems.

Cosmic ray air shower characteristics in the framework of the parton-based Gribov-Regge model NEXUS

NASA Astrophysics Data System (ADS)

Bossard, G.; Drescher, H. J.; Kalmykov, N. N.; Ostapchenko, S.; Pavlov, A. I.; Pierog, T.; Vishnevskaya, E. A.; Werner, K.

2001-03-01

The purpose of this paper is twofold: first we want to introduce a new type of hadronic interaction model (NEXUS), which has a much more solid theoretical basis than, for example, presently used models such as QGSJET and VENUS, and ensures therefore a much more reliable extrapolation towards high energies. Secondly, we want to promote an extensive air shower (EAS) calculation scheme, based on cascade equations rather than explicit Monte Carlo simulations, which is very accurate in calculations of main EAS characteristics and extremely fast concerning computing time. We employ the NEXUS model to provide the necessary data on particle production in hadron-air collisions and present the average EAS characteristics for energies 1014-1017 eV. The experimental data of the CASA-BLANCA group are analyzed in the framework of the new model.

Steepest entropy ascent quantum thermodynamic model of electron and phonon transport

NASA Astrophysics Data System (ADS)

Li, Guanchen; von Spakovsky, Michael R.; Hin, Celine

2018-01-01

An advanced nonequilibrium thermodynamic model for electron and phonon transport is formulated based on the steepest-entropy-ascent quantum thermodynamics framework. This framework, based on the principle of steepest entropy ascent (or the equivalent maximum entropy production principle), inherently satisfies the laws of thermodynamics and mechanics and is applicable at all temporal and spatial scales even in the far-from-equilibrium realm. Specifically, the model is proven to recover the Boltzmann transport equations in the near-equilibrium limit and the two-temperature model of electron-phonon coupling when no dispersion is assumed. The heat and mass transport at a temperature discontinuity across a homogeneous interface where the dispersion and coupling of electron and phonon transport are both considered are then modeled. Local nonequilibrium system evolution and nonquasiequilibrium interactions are predicted and the results discussed.

Three-dimensional finite elements for the analysis of soil contamination using a multiple-porosity approach

NASA Astrophysics Data System (ADS)

El-Zein, Abbas; Carter, John P.; Airey, David W.

2006-06-01

A three-dimensional finite-element model of contaminant migration in fissured clays or contaminated sand which includes multiple sources of non-equilibrium processes is proposed. The conceptual framework can accommodate a regular network of fissures in 1D, 2D or 3D and immobile solutions in the macro-pores of aggregated topsoils, as well as non-equilibrium sorption. A Galerkin weighted-residual statement for the three-dimensional form of the equations in the Laplace domain is formulated. Equations are discretized using linear and quadratic prism elements. The system of algebraic equations is solved in the Laplace domain and solution is inverted to the time domain numerically. The model is validated and its scope is illustrated through the analysis of three problems: a waste repository deeply buried in fissured clay, a storage tank leaking into sand and a sanitary landfill leaching into fissured clay over a sand aquifer.

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

Pereira, S.H.; Pinho, A.S.S.; Silva, J.M. Hoff da

In this work the exact Friedmann-Robertson-Walker equations for an Elko spinor field coupled to gravity in an Einstein-Cartan framework are presented. The torsion functions coupling the Elko field spin-connection to gravity can be exactly solved and the FRW equations for the system assume a relatively simple form. In the limit of a slowly varying Elko spinor field there is a relevant contribution to the field equations acting exactly as a time varying cosmological model Λ( t )=Λ{sub *}+3β H {sup 2}, where Λ{sub *} and β are constants. Observational data using distance luminosity from magnitudes of supernovae constraint the parametersmore » Ω {sub m} and β, which leads to a lower limit to the Elko mass. Such model mimics, then, the effects of a dark energy fluid, here sourced by the Elko spinor field. The density perturbations in the linear regime were also studied in the pseudo-Newtonian formalism.« less

Observational constraints on variable equation of state parameters of dark matter and dark energy after Planck

NASA Astrophysics Data System (ADS)

Kumar, Suresh; Xu, Lixin

2014-10-01

In this paper, we study a cosmological model in general relativity within the framework of spatially flat Friedmann-Robertson-Walker space-time filled with ordinary matter (baryonic), radiation, dark matter and dark energy, where the latter two components are described by Chevallier-Polarski-Linder equation of state parameters. We utilize the observational data sets from SNLS3, BAO and Planck + WMAP9 + WiggleZ measurements of matter power spectrum to constrain the model parameters. We find that the current observational data offer tight constraints on the equation of state parameter of dark matter. We consider the perturbations and study the behavior of dark matter by observing its effects on CMB and matter power spectra. We find that the current observational data favor the cold dark matter scenario with the cosmological constant type dark energy at the present epoch.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

A continuum mechanics constitutive framework for transverse isotropic soft tissues

NASA Astrophysics Data System (ADS)

Garcia-Gonzalez, D.; Jérusalem, A.; Garzon-Hernandez, S.; Zaera, R.; Arias, A.

2018-03-01

In this work, a continuum constitutive framework for the mechanical modelling of soft tissues that incorporates strain rate and temperature dependencies as well as the transverse isotropy arising from fibres embedded into a soft matrix is developed. The constitutive formulation is based on a Helmholtz free energy function decoupled into the contribution of a viscous-hyperelastic matrix and the contribution of fibres introducing dispersion dependent transverse isotropy. The proposed framework considers finite deformation kinematics, is thermodynamically consistent and allows for the particularisation of the energy potentials and flow equations of each constitutive branch. In this regard, the approach developed herein provides the basis on which specific constitutive models can be potentially formulated for a wide variety of soft tissues. To illustrate this versatility, the constitutive framework is particularised here for animal and human white matter and skin, for which constitutive models are provided. In both cases, different energy functions are considered: Neo-Hookean, Gent and Ogden. Finally, the ability of the approach at capturing the experimental behaviour of the two soft tissues is confirmed.

Nonlinearity Domination in Hassellmann Equation as a Reason for Alternative Framework of its Numerical Simulation

DTIC Science & Technology

2014-09-30

nonlinear Schrodinger equation. It is well known that dark solitons are exact solutions of such equation. In the present paper it has been shown that gray...Reason for Alternative Framework of its Numerical Simulation Vladimir Zakharov, Andrei Pushkarev Waves and Solitons LLC 1719 W. Marlette Ave...situation; study of the implications of modulational instability on solitons , rogue waves and air-surface interaction. APPROACH Numerical methods

A new approach for turbulent simulations in complex geometries

NASA Astrophysics Data System (ADS)

Israel, Daniel M.

Historically turbulence modeling has been sharply divided into Reynolds averaged Navier-Stokes (RANS), in which all the turbulent scales of motion are modeled, and large-eddy simulation (LES), in which only a portion of the turbulent spectrum is modeled. In recent years there have been numerous attempts to couple these two approaches either by patching RANS and LES calculations together (zonal methods) or by blending the two sets of equations. In order to create a proper bridging model, that is, a single set of equations which captures both RANS and LES like behavior, it is necessary to place both RANS and LES in a more general framework. The goal of the current work is threefold: to provide such a framework, to demonstrate how the Flow Simulation Methodology (FSM) fits into this framework, and to evaluate the strengths and weaknesses of the current version of the FSM. To do this, first a set of filtered Navier-Stokes (FNS) equations are introduced in terms of an arbitrary generalized filter. Additional exact equations are given for the second order moments and the generalized subfilter dissipation rate tensor. This is followed by a discussion of the role of implicit and explicit filters in turbulence modeling. The FSM is then described with particular attention to its role as a bridging model. In order to evaluate the method a specific implementation of the FSM approach is proposed. Simulations are presented using this model for the case of a separating flow over a "hump" with and without flow control. Careful attention is paid to error estimation, and, in particular, how using flow statistics and time series affects the error analysis. Both mean flow and Reynolds stress profiles are presented, as well as the phase averaged turbulent structures and wall pressure spectra. Using the phase averaged data it is possible to examine how the FSM partitions the energy between the coherent resolved scale motions, the random resolved scale fluctuations, and the subfilter quantities. The method proves to be qualitatively successful at reproducing large turbulent structures. However, like other hybrid methods, it has difficulty in the region where the model behavior transitions from RANS to LES. Consequently the phase averaged structures reproduce the experiments quite well, and the forcing does significantly reduce the length of the separated region. Nevertheless, the recirculation length is significantly too large for all the cases. Overall the current results demonstrate the promise of bridging models in general and the FSM in particular. However, current bridging techniques are still in their infancy. There is still important progress to be made and it is hoped that this work points out the more important avenues for exploration.

Stochastic effects in a discretized kinetic model of economic exchange

NASA Astrophysics Data System (ADS)

Bertotti, M. L.; Chattopadhyay, A. K.; Modanese, G.

2017-04-01

Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker-Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.

Constitutive modeling and structural analysis considering simultaneous phase transformation and plastic yield in shape memory alloys

NASA Astrophysics Data System (ADS)

Hartl, D. J.; Lagoudas, D. C.

2009-10-01

The new developments summarized in this work represent both theoretical and experimental investigations of the effects of plastic strain generation in shape memory alloys (SMAs). Based on the results of SMA experimental characterization described in the literature and additional testing described in this work, a new 3D constitutive model is proposed. This phenomenological model captures both the conventional shape memory effects of pseudoelasticity and thermal strain recovery, and additionally considers the initiation and evolution of plastic strains. The model is numerically implemented in a finite element framework using a return mapping algorithm to solve the constitutive equations at each material point. This combination of theory and implementation is unique in its ability to capture the simultaneous evolution of recoverable transformation strains and irrecoverable plastic strains. The consideration of isotropic and kinematic plastic hardening allows the derivation of a theoretical framework capturing the interactions between irrecoverable plastic strain and recoverable strain due to martensitic transformation. Further, the numerical integration of the constitutive equations is formulated such that objectivity is maintained for SMA structures undergoing moderate strains and large displacements. The implemented model has been used to perform 3D analysis of SMA structural components under uniaxial and bending loads, including a case of local buckling behavior. Experimentally validated results considering simultaneous transformation and plasticity in a bending member are provided, illustrating the predictive accuracy of the model and its implementation.

Building Relationships between Business Schools and Students: An Empirical Investigation into Student Retention

ERIC Educational Resources Information Center

Adidam, Phani Tej; Bingi, R. Prasad; Sindhav, Birud

2004-01-01

This study uses the relationship marketing theory of commitment and trust as a framework to investigate the issue of student retention in business schools. Structural equation modeling was used to examine relationships specified by Morgan and Hunt's (1994) theory of relationship marketing. Students' commitment to the business schools were…

A Hierarchical Approach to Examine Personal and School Effect on Teacher Motivation

ERIC Educational Resources Information Center

Wei, Yi-En

2012-01-01

In order to depict a better picture of teacher motivation, the researcher developed the theoretical framework based on Deci and Ryan's (1985) self-determination theory (SDT) and examined factors affecting teachers' autonomous motivation at both the personal and school level. Several multilevel structural equation models (ML-SEM) were…

The Rural Context and Post-Secondary School Enrollment: An Ecological Systems Approach

ERIC Educational Resources Information Center

Demi, Mary Ann; Coleman-Jensen, Alisha; Snyder, Anastasia R.

2010-01-01

This study uses an ecological systems framework to examine how indicators of individual, family, and school contexts are associated with post-secondary educational enrollment among a sample of rural youth. Structural equation modeling allows us to examine both direct and indirect effects of these contexts on school enrollment. Unique elements of…

Factors Influencing Students' Adoption of E-Learning: A Structural Equation Modeling Approach

ERIC Educational Resources Information Center

Tarhini, Ali; Masa'deh, Ra'ed; Al-Busaidi, Kamla Ali; Mohammed, Ashraf Bany; Maqableh, Mahmoud

2017-01-01

Purpose: This research aims to examine the factors that may hinder or enable the adoption of e-learning systems by university students. Design/methodology/approach: A conceptual framework was developed through extending the unified theory of acceptance and use of technology (performance expectancy, effort expectancy, hedonic motivation, habit,…

Faculty Agency: Departmental Contexts That Matter in Faculty Careers

ERIC Educational Resources Information Center

Campbell, Corbin M.; O'Meara, KerryAnn

2014-01-01

In a modern context of constrained resources and high demands, faculty exert agency to strategically navigate their careers (Baez 2000a; Neumann et al. 2006). Guided by the O'Meara et al. (2011) framework on agency in faculty professional lives, this study used Structural Equation Modeling to investigate which departmental factors…

State Aid and Student Performance: A Supply-Demand Analysis

ERIC Educational Resources Information Center

Kinnucan, Henry W.; Zheng, Yuqing; Brehmer, Gerald

2006-01-01

Using a supply-demand framework, a six-equation model is specified to generate hypotheses about the relationship between state aid and student performance. Theory predicts that an increase in state or federal aid provides an incentive to decrease local funding, but that the disincentive associated with increased state aid is moderated when federal…

Breathing pulses in the damped-soliton model for nerves

NASA Astrophysics Data System (ADS)

Fongang Achu, G.; Moukam Kakmeni, F. M.; Dikande, A. M.

2018-01-01

Unlike the Hodgkin-Huxley picture in which the nerve impulse results from ion exchanges across the cell membrane through ion-gate channels, in the so-called soliton model the impulse is seen as an electromechanical process related to thermodynamical phenomena accompanying the generation of the action potential. In this work, account is taken of the effects of damping on the nerve impulse propagation, within the framework of the soliton model. Applying the reductive perturbation expansion on the resulting KdV-Burgers equation, a damped nonlinear Schrödinger equation is derived and shown to admit breathing-type solitary wave solutions. Under specific constraints, these breathing pulse solitons become self-trapped structures in which the damping is balanced by nonlinearity such that the pulse amplitude remains unchanged even in the presence of damping.

Phase noise suppression for coherent optical block transmission systems: a unified framework.

PubMed

Yang, Chuanchuan; Yang, Feng; Wang, Ziyu

2011-08-29

A unified framework for phase noise suppression is proposed in this paper, which could be applied in any coherent optical block transmission systems, including coherent optical orthogonal frequency-division multiplexing (CO-OFDM), coherent optical single-carrier frequency-domain equalization block transmission (CO-SCFDE), etc. Based on adaptive modeling of phase noise, unified observation equations for different coherent optical block transmission systems are constructed, which lead to unified phase noise estimation and suppression. Numerical results demonstrate that the proposal is powerful in mitigating laser phase noise.

Advanced computational simulations of water waves interacting with wave energy converters

NASA Astrophysics Data System (ADS)

Pathak, Ashish; Freniere, Cole; Raessi, Mehdi

2017-03-01

Wave energy converter (WEC) devices harness the renewable ocean wave energy and convert it into useful forms of energy, e.g. mechanical or electrical. This paper presents an advanced 3D computational framework to study the interaction between water waves and WEC devices. The computational tool solves the full Navier-Stokes equations and considers all important effects impacting the device performance. To enable large-scale simulations in fast turnaround times, the computational solver was developed in an MPI parallel framework. A fast multigrid preconditioned solver is introduced to solve the computationally expensive pressure Poisson equation. The computational solver was applied to two surface-piercing WEC geometries: bottom-hinged cylinder and flap. Their numerically simulated response was validated against experimental data. Additional simulations were conducted to investigate the applicability of Froude scaling in predicting full-scale WEC response from the model experiments.

Control volume based hydrocephalus research; analysis of human data

NASA Astrophysics Data System (ADS)

Cohen, Benjamin; Wei, Timothy; Voorhees, Abram; Madsen, Joseph; Anor, Tomer

2010-11-01

Hydrocephalus is a neuropathophysiological disorder primarily diagnosed by increased cerebrospinal fluid volume and pressure within the brain. To date, utilization of clinical measurements have been limited to understanding of the relative amplitude and timing of flow, volume and pressure waveforms; qualitative approaches without a clear framework for meaningful quantitative comparison. Pressure volume models and electric circuit analogs enforce volume conservation principles in terms of pressure. Control volume analysis, through the integral mass and momentum conservation equations, ensures that pressure and volume are accounted for using first principles fluid physics. This approach is able to directly incorporate the diverse measurements obtained by clinicians into a simple, direct and robust mechanics based framework. Clinical data obtained for analysis are discussed along with data processing techniques used to extract terms in the conservation equation. Control volume analysis provides a non-invasive, physics-based approach to extracting pressure information from magnetic resonance velocity data that cannot be measured directly by pressure instrumentation.

First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2016-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media.

PubMed

Mishchenko, Michael I; Dlugach, Janna M; Yurkin, Maxim A; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R Lee; Travis, Larry D; Yang, Ping; Zakharova, Nadezhda T

2016-05-16

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ , or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

PubMed Central

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2018-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies. PMID:29657355

Wavelet neural networks: a practical guide.

PubMed

Alexandridis, Antonios K; Zapranis, Achilleas D

2013-06-01

Wavelet networks (WNs) are a new class of networks which have been used with great success in a wide range of applications. However a general accepted framework for applying WNs is missing from the literature. In this study, we present a complete statistical model identification framework in order to apply WNs in various applications. The following subjects were thoroughly examined: the structure of a WN, training methods, initialization algorithms, variable significance and variable selection algorithms, model selection methods and finally methods to construct confidence and prediction intervals. In addition the complexity of each algorithm is discussed. Our proposed framework was tested in two simulated cases, in one chaotic time series described by the Mackey-Glass equation and in three real datasets described by daily temperatures in Berlin, daily wind speeds in New York and breast cancer classification. Our results have shown that the proposed algorithms produce stable and robust results indicating that our proposed framework can be applied in various applications. Copyright © 2013 Elsevier Ltd. All rights reserved.

A Stochastic Framework for Evaluating Seizure Prediction Algorithms Using Hidden Markov Models

PubMed Central

Wong, Stephen; Gardner, Andrew B.; Krieger, Abba M.; Litt, Brian

2007-01-01

Responsive, implantable stimulation devices to treat epilepsy are now in clinical trials. New evidence suggests that these devices may be more effective when they deliver therapy before seizure onset. Despite years of effort, prospective seizure prediction, which could improve device performance, remains elusive. In large part, this is explained by lack of agreement on a statistical framework for modeling seizure generation and a method for validating algorithm performance. We present a novel stochastic framework based on a three-state hidden Markov model (HMM) (representing interictal, preictal, and seizure states) with the feature that periods of increased seizure probability can transition back to the interictal state. This notion reflects clinical experience and may enhance interpretation of published seizure prediction studies. Our model accommodates clipped EEG segments and formalizes intuitive notions regarding statistical validation. We derive equations for type I and type II errors as a function of the number of seizures, duration of interictal data, and prediction horizon length and we demonstrate the model’s utility with a novel seizure detection algorithm that appeared to predicted seizure onset. We propose this framework as a vital tool for designing and validating prediction algorithms and for facilitating collaborative research in this area. PMID:17021032

A classical regression framework for mediation analysis: fitting one model to estimate mediation effects.

PubMed

Saunders, Christina T; Blume, Jeffrey D

2017-10-26

Mediation analysis explores the degree to which an exposure's effect on an outcome is diverted through a mediating variable. We describe a classical regression framework for conducting mediation analyses in which estimates of causal mediation effects and their variance are obtained from the fit of a single regression model. The vector of changes in exposure pathway coefficients, which we named the essential mediation components (EMCs), is used to estimate standard causal mediation effects. Because these effects are often simple functions of the EMCs, an analytical expression for their model-based variance follows directly. Given this formula, it is instructive to revisit the performance of routinely used variance approximations (e.g., delta method and resampling methods). Requiring the fit of only one model reduces the computation time required for complex mediation analyses and permits the use of a rich suite of regression tools that are not easily implemented on a system of three equations, as would be required in the Baron-Kenny framework. Using data from the BRAIN-ICU study, we provide examples to illustrate the advantages of this framework and compare it with the existing approaches. © The Author 2017. Published by Oxford University Press.

Nonlinearity analysis of measurement model for vision-based optical navigation system

NASA Astrophysics Data System (ADS)

Li, Jianguo; Cui, Hutao; Tian, Yang

2015-02-01

In the autonomous optical navigation system based on line-of-sight vector observation, nonlinearity of measurement model is highly correlated with the navigation performance. By quantitatively calculating the degree of nonlinearity of the focal plane model and the unit vector model, this paper focuses on determining which optical measurement model performs better. Firstly, measurement equations and measurement noise statistics of these two line-of-sight measurement models are established based on perspective projection co-linearity equation. Then the nonlinear effects of measurement model on the filter performance are analyzed within the framework of the Extended Kalman filter, also the degrees of nonlinearity of two measurement models are compared using the curvature measure theory from differential geometry. Finally, a simulation of star-tracker-based attitude determination is presented to confirm the superiority of the unit vector measurement model. Simulation results show that the magnitude of curvature nonlinearity measurement is consistent with the filter performance, and the unit vector measurement model yields higher estimation precision and faster convergence properties.

Refined Models for an Analysis of Internal and External Buckling Modes of a Monolayer in a Layered Composite

NASA Astrophysics Data System (ADS)

Paimushin, V. N.

2017-11-01

For an analysis of internal and external buckling modes of a monolayer inside or at the periphery of a layered composite, refined geometrically nonlinear equations are constructed. They are based on modeling the monolayer as a thin plate interacting with binder layers at the points of boundary surfaces. The binder layer is modeled as a transversely soft foundation. It is assumed the foundations, previously compressed in the transverse direction (the first loading stage), have zero displacements of its external boundary surfaces at the second loading stage, but the contact interaction of the plate with foundations occurs without slippage or delamination. The deformation of the plate at a medium flexure is described by geometrically nonlinear relations of the classical plate theory based on the Kirchhoff-Love hypothesis (the first variant) or the refined Timoshenko model with account of the transverse shear and compression (the second variant). The foundation is described by linearized 3D equations of elasticity theory, which are simplified within the framework of the model of a transversely soft layer. Integrating the linearized equations along the transverse coordinate and satisfying the kinematic joining conditions of the plate with foundations, with account of their initial compression in the thickness direction, a system of 2D geometrically nonlinear equations and appropriate boundary conditions are derived. These equations describe the contact interaction between elements of the deformable system. The relations obtained are simplified for the case of a symmetric stacking sequence.

An outline of cellular automaton universe via cosmological KdV equation

NASA Astrophysics Data System (ADS)

Christianto, V.; Smarandache, F.; Umniyati, Y.

2018-03-01

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework. This paper can be considered as our second attempt towards such a complete description of the Universe based on soliton wave solution of cosmological KdV equation. Then we advance further this KdV equation by virtue of Cellular Automaton method to solve the PDEs. We submit wholeheartedly Robert Kuruczs hypothesis that Big Bang should be replaced with a finite cellular automaton universe with no expansion [4][5]. Nonetheless, we are fully aware that our model is far from being complete, but it appears the proposed cellular automaton model of the Universe is very close in spirit to what Konrad Zuse envisaged long time ago. It is our hope that the new proposed method can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details.

The ABC model: a non-hydrostatic toy model for use in convective-scale data assimilation investigations

NASA Astrophysics Data System (ADS)

Petrie, Ruth Elizabeth; Bannister, Ross Noel; Priestley Cullen, Michael John

2017-12-01

In developing methods for convective-scale data assimilation (DA), it is necessary to consider the full range of motions governed by the compressible Navier-Stokes equations (including non-hydrostatic and ageostrophic flow). These equations describe motion on a wide range of timescales with non-linear coupling. For the purpose of developing new DA techniques that suit the convective-scale problem, it is helpful to use so-called toy models that are easy to run and contain the same types of motion as the full equation set. Such a model needs to permit hydrostatic and geostrophic balance at large scales but allow imbalance at small scales, and in particular, it needs to exhibit intermittent convection-like behaviour. Existing toy models are not always sufficient for investigating these issues. A simplified system of intermediate complexity derived from the Euler equations is presented, which supports dispersive gravity and acoustic modes. In this system, the separation of timescales can be greatly reduced by changing the physical parameters. Unlike in existing toy models, this allows the acoustic modes to be treated explicitly and hence inexpensively. In addition, the non-linear coupling induced by the equation of state is simplified. This means that the gravity and acoustic modes are less coupled than in conventional models. A vertical slice formulation is used which contains only dry dynamics. The model is shown to give physically reasonable results, and convective behaviour is generated by localised compressible effects. This model provides an affordable and flexible framework within which some of the complex issues of convective-scale DA can later be investigated. The model is called the ABC model after the three tunable parameters introduced: A (the pure gravity wave frequency), B (the modulation of the divergent term in the continuity equation), and C (defining the compressibility).

Generalised and Fractional Langevin Equations-Implications for Energy Balance Models

NASA Astrophysics Data System (ADS)

Watkins, N. W.; Chapman, S. C.; Chechkin, A.; Ford, I.; Klages, R.; Stainforth, D. A.

2017-12-01

Energy Balance Models (EBMs) have a long heritage in climate science, including their use in modelling anomalies in global mean temperature. Many types of EBM have now been studied, and this presentation concerns the stochastic EBMs, which allow direct treatment of climate fluctuations and noise. Some recent stochastic EBMs (e.g. [1]) map on to Langevin's original form of his equation, with temperature anomaly replacing velocity, and other corresponding replacements being made. Considerable sophistication has now been reached in the application of multivariate stochastic Langevin modelling in many areas of climate. Our work is complementary in intent and investigates the Mori-Kubo "Generalised Langevin Equation" (GLE) which incorporates non-Markovian noise and response in a univariate framework, as a tool for modelling GMT [2]. We show how, if it is present, long memory simplifies the GLE to a fractional Langevin equation (FLE). Evidence for long range memory in global temperature, and the success of fractional Gaussian noise in its prediction [5] has already motivated investigation of a power law response model [3,4,5]. We go beyond this work to ask whether an EBM of FLE-type exists, and what its solutions would be. [l] Padilla et al, J. Climate (2011); [2] Watkins, GRL (2013); [3] Rypdal, JGR (2012); [4] Rypdal and Rypdal, J. Climate (2014); [5] Lovejoy et al, ESDD (2015).

Singularity-free dynamic equations of spacecraft-manipulator systems

NASA Astrophysics Data System (ADS)

From, Pål J.; Ytterstad Pettersen, Kristin; Gravdahl, Jan T.

2011-12-01

In this paper we derive the singularity-free dynamic equations of spacecraft-manipulator systems using a minimal representation. Spacecraft are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange's equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of a spacecraft is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the dynamic properties of free-floating and free-flying spacecraft-manipulator systems and we show how to calculate the inertia and Coriolis matrices in such a way that this can be implemented for simulation and control purposes without extensive knowledge of the mathematical background. This paper represents the first detailed study of modeling of spacecraft-manipulator systems with a focus on a singularity free formulation using the proposed framework.

Hybrid modeling in biochemical systems theory by means of functional petri nets.

PubMed

Wu, Jialiang; Voit, Eberhard

2009-02-01

Many biological systems are genuinely hybrids consisting of interacting discrete and continuous components and processes that often operate at different time scales. It is therefore desirable to create modeling frameworks capable of combining differently structured processes and permitting their analysis over multiple time horizons. During the past 40 years, Biochemical Systems Theory (BST) has been a very successful approach to elucidating metabolic, gene regulatory, and signaling systems. However, its foundation in ordinary differential equations has precluded BST from directly addressing problems containing switches, delays, and stochastic effects. In this study, we extend BST to hybrid modeling within the framework of Hybrid Functional Petri Nets (HFPN). First, we show how the canonical GMA and S-system models in BST can be directly implemented in a standard Petri Net framework. In a second step we demonstrate how to account for different types of time delays as well as for discrete, stochastic, and switching effects. Using representative test cases, we validate the hybrid modeling approach through comparative analyses and simulations with other approaches and highlight the feasibility, quality, and efficiency of the hybrid method.

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

NASA Technical Reports Server (NTRS)

Buttrill, Carey S.

1989-01-01

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems

NASA Astrophysics Data System (ADS)

Thüroff, Florian; Weber, Christoph A.; Frey, Erwin

2014-10-01

Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system's dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system's ordered state nematic, despite purely polar interactions on the level of single particles.

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

ERIC Educational Resources Information Center

Lee, Eunjung

2013-01-01

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

Multi-Fluid Simulations of a Coupled Ionosphere-Magnetosphere System

NASA Astrophysics Data System (ADS)

Gombosi, T. I.; Glocer, A.; Toth, G.; Ridley, A. J.; Sokolov, I. V.; de Zeeuw, D. L.

2008-05-01

In the last decade we have developed the Space Weather Modeling Framework (SWMF) that efficiently couples together different models describing the interacting regions of the space environment. Many of these domain models (such as the global solar corona, the inner heliosphere or the global magnetosphere) are based on MHD and are represented by our multiphysics code, BATS-R-US. BATS-R-US can solve the equations of "standard" ideal MHD, but it can also go beyond this first approximation. It can solve resistive MHD, Hall MHD, semi-relativistic MHD (that keeps the displacement current), multispecies (different ion species have different continuity equations) and multifluid (all ion species have separate continuity, momentum and energy equations) MHD. Recently we added two-fluid Hall MHD (solving the electron and ion energy equations separately) and are working on an extended magnetohydrodynamics model with anisotropic pressures. Ionosheric outflow can be a significant contributor to the plasma population of the magnetosphere during active geomagnetic conditions. This talk will present preliminary results of our simulations when we couple a new field- aligned multi-fluid polar wind code to the Ionosphere Electrodynamics (IE), and Global Magnetosphere (GM) components of the SWMF. We use multi-species and multi-fluid MHD to track the resulting plasma composition in the magnetosphere.

Time-local equation for exact time-dependent optimized effective potential in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Liao, Sheng-Lun; Ho, Tak-San; Rabitz, Herschel; Chu, Shih-I.

2017-04-01

Solving and analyzing the exact time-dependent optimized effective potential (TDOEP) integral equation has been a longstanding challenge due to its highly nonlinear and nonlocal nature. To meet the challenge, we derive an exact time-local TDOEP equation that admits a unique real-time solution in terms of time-dependent Kohn-Sham orbitals and effective memory orbitals. For illustration, the dipole evolution dynamics of a one-dimension-model chain of hydrogen atoms is numerically evaluated and examined to demonstrate the utility of the proposed time-local formulation. Importantly, it is shown that the zero-force theorem, violated by the time-dependent Krieger-Li-Iafrate approximation, is fulfilled in the current TDOEP framework. This work was partially supported by DOE.

Stability of the Einstein static universe in open cosmological models

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

Canonico, Rosangela; Parisi, Luca; INFN, Sezione di Napoli, GC di Salerno, Via Ponte Don Melillo, I-84081 Baronissi

2010-09-15

The stability properties of the Einstein static solution of general relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein static solutions in the semiclassical regime of loop quantum cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Horava-Lifshitz gravitymore » under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according to the admitted values of the parameters.« less

The influence of competition between plant functional types in the Canadian Terrestrial Ecosystem Model (CTEM) v. 2.0

NASA Astrophysics Data System (ADS)

Melton, Joe; Arora, Vivek

2015-04-01

The Canadian Terrestrial Ecosystem Model (CTEM) is the interactive vegetation component in the earth system modelling framework of the Canadian Centre for Climate Modelling and Analysis (CCCma). In its current framework, CTEM uses prescribed fractional coverage of plant functional types (PFTs) in each grid cell. In reality, vegetation cover is continually adjusting to changes in climate, atmospheric composition, and anthropogenic forcing, for example, through human-caused fires and CO2 fertilization. These changes in vegetation spatial patterns occur over timescales of years to centuries as tree migration is a slow process and vegetation distributions inherently have inertia. Here, we present version 2.0 of CTEM that includes a representation of competition between PFTs through a modified version of the Lotka-Volterra (L-V) predator-prey equations. The simulated areal extents of CTEM's seven non-crop PFTs are compared with available observation-based estimates, and simulations using unmodified L-V equations (similar to other models like TRIFFID), to demonstrate that the model is able to represent the broad spatial distributions of its seven PFTs at the global scale. Differences remain, however, since representing the multitude of plant species with just seven non-crop PFTs only allows the large scale climatic controls on the distributions of PFTs to be captured. As expected, PFTs that exist in climate niches are difficult to represent either due to the coarse spatial resolution of the model and the corresponding driving climate or the limited number of PFTs used to model the terrestrial ecosystem processes. The geographic and zonal distributions of primary terrestrial carbon pools and fluxes from the versions of CTEM that use prescribed and dynamically simulated fractional coverage of PFTs compare reasonably with each other and observation-based estimates. These results illustrate that the parametrization of competition between PFTs in CTEM behaves in a reasonably realistic manner while the use of unmodified L-V equations results in unrealistic plant distributions.

Model identification using stochastic differential equation grey-box models in diabetes.

PubMed

Duun-Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard; Møller, Jonas Bech; Nørgaard, Kirsten; Jørgensen, John Bagterp; Madsen, Henrik

2013-03-01

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. 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 are estimated on clinical data from four T1DM patients. The optimal SDE-GB is determined from likelihood-ratio tests. Finally, parameter tracking is used to track the variation in the "time to peak of meal response" parameter. We found that the transformation of the ODE model into an SDE-GB resulted in a significant improvement in the prediction and uncorrelated errors. Tracking of the "peak time of meal absorption" parameter showed that the absorption rate varied according to meal type. This study shows the potential of using SDE-GBs in diabetes modeling. Improved model predictions were obtained due to the separation of the prediction error. SDE-GBs offer a solid framework for using statistical tools for model validation and model development. © 2013 Diabetes Technology Society.

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Development of an Integrated Modeling Framework for Simulations of Coastal Processes in Deltaic Environments Using High-Performance Computing

DTIC Science & Technology

2009-01-01

attenuation and mass transport of a water -mud system due to a solitary wave on the free surface has been modeled by using the Chebyshev-Chebyshev...in Lagrangian coordinates and perturbation equations for shallow water waves were 3 derived. An iteration-by-subdomain technique was introduced to...found. Although the model is focused on solitary waves and Newtonian fluid-mud, the methodology can be extended to oscillatory, nonlinear water waves

Pore-scale modeling of phase change in porous media

NASA Astrophysics Data System (ADS)

Juanes, Ruben; Cueto-Felgueroso, Luis; Fu, Xiaojing

2017-11-01

One of the main open challenges in pore-scale modeling is the direct simulation of flows involving multicomponent mixtures with complex phase behavior. Reservoir fluid mixtures are often described through cubic equations of state, which makes diffuse interface, or phase field theories, particularly appealing as a modeling framework. What is still unclear is whether equation-of-state-driven diffuse-interface models can adequately describe processes where surface tension and wetting phenomena play an important role. Here we present a diffuse interface model of single-component, two-phase flow (a van der Waals fluid) in a porous medium under different wetting conditions. We propose a simplified Darcy-Korteweg model that is appropriate to describe flow in a Hele-Shaw cell or a micromodel, with a gap-averaged velocity. We study the ability of the diffuse-interface model to capture capillary pressure and the dynamics of vaporization/condensation fronts, and show that the model reproduces pressure fluctuations that emerge from abrupt interface displacements (Haines jumps) and from the break-up of wetting films.

Dynamic motion planning of 3D human locomotion using gradient-based optimization.

PubMed

Kim, Hyung Joo; Wang, Qian; Rahmatalla, Salam; Swan, Colby C; Arora, Jasbir S; Abdel-Malek, Karim; Assouline, Jose G

2008-06-01

Since humans can walk with an infinite variety of postures and limb movements, there is no unique solution to the modeling problem to predict human gait motions. Accordingly, we test herein the hypothesis that the redundancy of human walking mechanisms makes solving for human joint profiles and force time histories an indeterminate problem best solved by inverse dynamics and optimization methods. A new optimization-based human-modeling framework is thus described for predicting three-dimensional human gait motions on level and inclined planes. The basic unknowns in the framework are the joint motion time histories of a 25-degree-of-freedom human model and its six global degrees of freedom. The joint motion histories are calculated by minimizing an objective function such as deviation of the trunk from upright posture that relates to the human model's performance. A variety of important constraints are imposed on the optimization problem, including (1) satisfaction of dynamic equilibrium equations by requiring the model's zero moment point (ZMP) to lie within the instantaneous geometrical base of support, (2) foot collision avoidance, (3) limits on ground-foot friction, and (4) vanishing yawing moment. Analytical forms of objective and constraint functions are presented and discussed for the proposed human-modeling framework in which the resulting optimization problems are solved using gradient-based mathematical programming techniques. When the framework is applied to the modeling of bipedal locomotion on level and inclined planes, acyclic human walking motions that are smooth and realistic as opposed to less natural robotic motions are obtained. The aspects of the modeling framework requiring further investigation and refinement, as well as potential applications of the framework in biomechanics, are discussed.

Framework for non-coherent interface models at finite displacement jumps and finite strains

NASA Astrophysics Data System (ADS)

Ottosen, Niels Saabye; Ristinmaa, Matti; Mosler, Jörn

2016-05-01

This paper deals with a novel constitutive framework suitable for non-coherent interfaces, such as cracks, undergoing large deformations in a geometrically exact setting. For this type of interface, the displacement field shows a jump across the interface. Within the engineering community, so-called cohesive zone models are frequently applied in order to describe non-coherent interfaces. However, for existing models to comply with the restrictions imposed by (a) thermodynamical consistency (e.g., the second law of thermodynamics), (b) balance equations (in particular, balance of angular momentum) and (c) material frame indifference, these models are essentially fiber models, i.e. models where the traction vector is collinear with the displacement jump. This constraints the ability to model shear and, in addition, anisotropic effects are excluded. A novel, extended constitutive framework which is consistent with the above mentioned fundamental physical principles is elaborated in this paper. In addition to the classical tractions associated with a cohesive zone model, the main idea is to consider additional tractions related to membrane-like forces and out-of-plane shear forces acting within the interface. For zero displacement jump, i.e. coherent interfaces, this framework degenerates to existing formulations presented in the literature. For hyperelasticity, the Helmholtz energy of the proposed novel framework depends on the displacement jump as well as on the tangent vectors of the interface with respect to the current configuration - or equivalently - the Helmholtz energy depends on the displacement jump and the surface deformation gradient. It turns out that by defining the Helmholtz energy in terms of the invariants of these variables, all above-mentioned fundamental physical principles are automatically fulfilled. Extensions of the novel framework necessary for material degradation (damage) and plasticity are also covered.

Growth Points in Students' Developing Understanding of Function in Equation Form

ERIC Educational Resources Information Center

Ronda, Erlina R.

2009-01-01

This paper presents a research-based framework for analyzing and monitoring students' understanding of functions in equation form. The framework consists of "growth points" which describe "big ideas" of students' understanding of the concept. The data were collected from Grades 8, 9, and 10 students using a set of tasks…

Topographies and dynamics on multidimensional potential energy surfaces

NASA Astrophysics Data System (ADS)

Ball, Keith Douglas

The stochastic master equation is a valuable tool for elucidating potential energy surface (PES) details that govern structural relaxation in clusters, bulk systems, and protein folding. This work develops a comprehensive framework for studying non-equilibrium relaxation dynamics using the master equation. Since our master equations depend upon accurate partition function models for use in Rice-Ramsperger-Kassel-Marcus (RRK(M) transition state theory, this work introduces several such models employing various harmonic and anharmonic approximations and compares their predicted equilibrium population distributions with those determined from molecular dynamics. This comparison is performed for the fully-delineated surfaces (KCl)5 and Ar9 to evaluate model performance for potential surfaces with long- and short-range interactions, respectively. For each system, several models perform better than a simple harmonic approximation. While no model gives acceptable results for all minima, and optimal modeling strategies differ for (KCl)5 and Ar9, a particular one-parameter model gives the best agreement with simulation for both systems. We then construct master equations from these models and compare their isothermal relaxation predictions for (KCl)5 and Ar9 with molecular dynamics simulations. This is the first comprehensive test of the kinetic performance of partition function models of its kind. Our results show that accurate modeling of transition-state partition functions is more important for (KCl)5 than for Ar9 in reproducing simulation results, due to a marked stiffening anharmonicity in the transition-state normal modes of (KCl)5. For both systems, several models yield qualitative agreement with simulation over a large temperature range. To examine the robustness of the master equation when applied to larger systems, for which full topographical descriptions would be either impossible or infeasible, we compute relaxation predictions for Ar11 using a master equation constructed from data representing the full PES, and compare these predictions to those of reduced master equations based on statistical samples of the full PES. We introduce a sampling method which generates random, Boltzmann-weighted, energetically 'downhill' sequences. The study reveals that, at moderate temperatures, the slowest relaxation timescale converges as the number of sequences in a sample grows to ~1000. Furthermore, the asymptotic timescale is comparable to the full-PES value.

Optimal intervention strategies for cholera outbreak by education and chlorination

NASA Astrophysics Data System (ADS)

Bakhtiar, Toni

2016-01-01

This paper discusses the control of infectious diseases in the framework of optimal control approach. A case study on cholera control was studied by considering two control strategies, namely education and chlorination. We distinct the former control into one regarding person-to-person behaviour and another one concerning person-to-environment conduct. Model are divided into two interacted populations: human population which follows an SIR model and pathogen population. Pontryagin maximum principle was applied in deriving a set of differential equations which consists of dynamical and adjoin systems as optimality conditions. Then, the fourth order Runge-Kutta method was exploited to numerically solve the equation system. An illustrative example was provided to assess the effectiveness of the control strategies toward a set of control scenarios.

A Multiscale Model for Virus Capsid Dynamics

PubMed Central

Chen, Changjun; Saxena, Rishu; Wei, Guo-Wei

2010-01-01

Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. PMID:20224756

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

PubMed Central

Chevalier, Michael W.; El-Samad, Hana

2014-01-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled. PMID:25481130

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

NASA Astrophysics Data System (ADS)

Chevalier, Michael W.; El-Samad, Hana

2014-12-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.

The Renormalization-Group Method in the Problem on Calculation of the Spectral Energy Density of Fluid Turbulence

NASA Astrophysics Data System (ADS)

Teodorovich, E. V.

2018-03-01

In order to find the shape of energy spectrum within the framework of the model of stationary homogeneous isotropic turbulence, the renormalization-group equations, which reflect the Markovian nature of the mechanism of energy transfer along the wavenumber spectrum, are used in addition to the dimensional considerations and the energy balance equation. For the spectrum, the formula depends on three parameters, namely, the wavenumber, which determines the upper boundary of the range of the turbulent energy production, the spectral flux through this boundary, and the fluid kinematic viscosity.

Toward Improved Fidelity of Thermal Explosion Simulations

NASA Astrophysics Data System (ADS)

Nichols, A. L.; Becker, R.; Howard, W. M.; Wemhoff, A.

2009-12-01

We will present results of an effort to improve the thermal/chemical/mechanical modeling of HMX based explosives like LX04 and LX10 for thermal cook-off The original HMX model and analysis scheme were developed by Yoh et al. for use in the ALE3D modeling framework. The current results were built to remedy the deficiencies of that original model. We concentrated our efforts in four areas. The first area was addition of porosity to the chemical material model framework in ALE3D that is used to model the HMX explosive formulation. This is needed to handle the roughly 2% porosity in solid explosives. The second area was the improvement of the HMX reaction network, which included a reactive phase change model base on work by Henson et al. The third area required adding early decomposition gas species to the CHEETAH material database to develop more accurate equations of state for gaseous intermediates and products. Finally, it was necessary to improve the implicit mechanics module in ALE3D to more naturally handle the long time scales associated with thermal cook-off The application of the resulting framework to the analysis of the Scaled Thermal Explosion (STEX) experiments will be discussed.

Modelling Spread of Oncolytic Viruses in Heterogeneous Cell Populations

NASA Astrophysics Data System (ADS)

Ellis, Michael; Dobrovolny, Hana

2014-03-01

One of the most promising areas in current cancer research and treatment is the use of viruses to attack cancer cells. A number of oncolytic viruses have been identified to date that possess the ability to destroy or neutralize cancer cells while inflicting minimal damage upon healthy cells. Formulation of predictive models that correctly describe the evolution of infected tumor systems is critical to the successful application of oncolytic virus therapy. A number of different models have been proposed for analysis of the oncolytic virus-infected tumor system, with approaches ranging from traditional coupled differential equations such as the Lotka-Volterra predator-prey models, to contemporary modeling frameworks based on neural networks and cellular automata. Existing models are focused on tumor cells and the effects of virus infection, and offer the potential for improvement by including effects upon normal cells. We have recently extended the traditional framework to a 2-cell model addressing the full cellular system including tumor cells, normal cells, and the impacts of viral infection upon both populations. Analysis of the new framework reveals complex interaction between the populations and potential inability to simultaneously eliminate the virus and tumor populations.

Determining the predictors of innovation implementation in healthcare: a quantitative analysis of implementation effectiveness.

PubMed

Jacobs, Sara R; Weiner, Bryan J; Reeve, Bryce B; Hofmann, David A; Christian, Michael; Weinberger, Morris

2015-01-22

The failure rates for implementing complex innovations in healthcare organizations are high. Estimates range from 30% to 90% depending on the scope of the organizational change involved, the definition of failure, and the criteria to judge it. The innovation implementation framework offers a promising approach to examine the organizational factors that determine effective implementation. To date, the utility of this framework in a healthcare setting has been limited to qualitative studies and/or group level analyses. Therefore, the goal of this study was to quantitatively examine this framework among individual participants in the National Cancer Institute's Community Clinical Oncology Program using structural equation modeling. We examined the innovation implementation framework using structural equation modeling (SEM) among 481 physician participants in the National Cancer Institute's Community Clinical Oncology Program (CCOP). The data sources included the CCOP Annual Progress Reports, surveys of CCOP physician participants and administrators, and the American Medical Association Physician Masterfile. Overall the final model fit well. Our results demonstrated that not only did perceptions of implementation climate have a statistically significant direct effect on implementation effectiveness, but physicians' perceptions of implementation climate also mediated the relationship between organizational implementation policies and practices (IPP) and enrollment (p <0.05). In addition, physician factors such as CCOP PI status, age, radiological oncologists, and non-oncologist specialists significantly influenced enrollment as well as CCOP organizational size and structure, which had indirect effects on implementation effectiveness through IPP and implementation climate. Overall, our results quantitatively confirmed the main relationship postulated in the innovation implementation framework between IPP, implementation climate, and implementation effectiveness among individual physicians. This finding is important, as although the model has been discussed within healthcare organizations before, the studies have been predominately qualitative in nature and/or at the organizational level. In addition, our findings have practical applications. Managers looking to increase implementation effectiveness of an innovation should focus on creating an environment that physicians perceive as encouraging implementation. In addition, managers should consider instituting specific organizational IPP aimed at increasing positive perceptions of implementation climate. For example, IPP should include specific expectations, support, and rewards for innovation use.

Dominican and Puerto Rican Mother-Adolescent Communication: Maternal Self-Disclosure and Youth Risk Intentions

ERIC Educational Resources Information Center

Guilamo-Ramos, Vincent

2010-01-01

A communication framework was developed to examine the influence of maternal use of self-disclosure on adolescent intentions to smoke cigarettes and to engage in sexual intercourse. Data were collected from 516 Dominican and Puerto Rican mother-adolescent dyads. Statistical analyses were conducted in AMOS using structural equation modeling.…

Effects of Social Capital in Multiple Contexts on the Psychosocial Adjustment of Chinese Migrant Children

ERIC Educational Resources Information Center

Wu, Qiaobing

2017-01-01

Drawing upon a sample of 772 migrant children and their parents in Shanghai, China, this study used an ecological framework to investigate how social capital embedded in a range of social contexts (i.e., family, school, peer, and community) influenced the psychosocial adjustment of Chinese migrant children. Using structural equation modeling with…

A Study of the Interrelationships among Service Recovery, Relationship Quality, and Brand Image in Higher Education Industries

ERIC Educational Resources Information Center

Chen, Yu-Chuan

2015-01-01

This study aims to investigate the direction and strength of the relationships among service recovery, relationship quality, and brand image in higher education industries. This research provides a framework for school managers to understand service recovery from an operations perspective. Structural equation models were used to test the proposed…

A Structural Equation Modeling Investigation of the Theory of Planned Behavior Applied to Accounting Professors' Enforcement of Cheating Rules

ERIC Educational Resources Information Center

Brigham, Stephen Scott

2010-01-01

This dissertation concerns factors that influence accounting professors' formal enforcement of academic misconduct rules using the theory of planned behavior ("TPB") as a theoretical framework. The theory posits that intentional behavior, such as enforcement, can be predicted by peoples' perceived behavioral control and…

How School Context and Educator Characteristics Predict Distributed Leadership: A Hierarchical Structural Equation Model with 2013 TALIS Data

ERIC Educational Resources Information Center

Liu, Yan; Bellibas, Mehmet Sukru; Printy, Susan

2018-01-01

Distributed leadership is a dynamic process and reciprocal interaction of the leader, the subordinates and the situation. This research was inspired by the theoretical framework of Spillane in order to contextualize distributed leadership and compare the variations using the Teaching and Learning International Survey 2013 data. The two-level…

Validation of Virtual Learning Team Competencies for Individual Students in a Distance Education Setting

ERIC Educational Resources Information Center

Topchyan, Ruzanna; Zhang, Jie

2014-01-01

The purpose of this study was twofold. First, the study aimed to validate the scale of the Virtual Team Competency Inventory in distance education, which had initially been designed for a corporate setting. Second, the methodological advantages of Exploratory Structural Equation Modeling (ESEM) framework over Confirmatory Factor Analysis (CFA)…

BurnMan: Towards a multidisciplinary toolkit for reproducible deep Earth science

NASA Astrophysics Data System (ADS)

Myhill, R.; Cottaar, S.; Heister, T.; Rose, I.; Unterborn, C. T.; Dannberg, J.; Martin-Short, R.

2016-12-01

BurnMan (www.burnman.org) is an open-source toolbox to compute thermodynamic and thermoelastic properties as a function of pressure and temperature using published mineral physical parameters and equations-of-state. The framework is user-friendly, written in Python, and modular, allowing the user to implement their own equations of state, endmember and solution model libraries, geotherms, and averaging schemes. Here we introduce various new modules, which can be used to: Fit thermodynamic variables to data from high pressure static and shock wave experiments, Calculate equilibrium assemblages given a bulk composition, pressure and temperature, Calculate chemical potentials and oxygen fugacities for given assemblages Compute 3D synthetic seismic models using output from geodynamic models and compare these results with global seismic tomographic models, Create input files for synthetic seismogram codes. Users can contribute scripts that reproduce the results from peer-reviewed articles and practical demonstrations (e.g. Cottaar et al., 2014).

Constraint reasoning in deep biomedical models.

PubMed

Cruz, Jorge; Barahona, Pedro

2005-05-01

Deep biomedical models are often expressed by means of differential equations. Despite their expressive power, they are difficult to reason about and make decisions, given their non-linearity and the important effects that the uncertainty on data may cause. The objective of this work is to propose a constraint reasoning framework to support safe decisions based on deep biomedical models. The methods used in our approach include the generic constraint propagation techniques for reducing the bounds of uncertainty of the numerical variables complemented with new constraint reasoning techniques that we developed to handle differential equations. The results of our approach are illustrated in biomedical models for the diagnosis of diabetes, tuning of drug design and epidemiology where it was a valuable decision-supporting tool notwithstanding the uncertainty on data. The main conclusion that follows from the results is that, in biomedical decision support, constraint reasoning may be a worthwhile alternative to traditional simulation methods, especially when safe decisions are required.

Effects of Low Anisotropy on Generalized Ghost Dark Energy in Galileon Gravity

NASA Astrophysics Data System (ADS)

Hossienkhani, H.; Fayaz, V.; Jafari, A.; Yousefi, H.

2018-04-01

The definition of the Galileon gravity form is extended to the Brans-Dicke theory. Given, the framework of the Galileon theory, the generalized ghost dark energy model in an anisotropic universe is investigated. We study the cosmological implications of this model. In particular, we obtain the equation of state and the deceleration parameters and a differential equation governing the evolution of this dark energy in Bianchi type I model. We also probe observational constraints by using the latest observational data on the generalized ghost dark energy models as the unification of dark matter and dark energy. In order to do so, we focus on observational determinations of the Hubble expansion rate (namely, the expansion history) H(z). As a result, we show the influence of the anisotropy (although low) on the evolution of the universe in the statefinder diagrams for Galileon gravity.

A hydroeconomic modeling framework for optimal integrated management of forest and water

NASA Astrophysics Data System (ADS)

Garcia-Prats, Alberto; del Campo, Antonio D.; Pulido-Velazquez, Manuel

2016-10-01

Forests play a determinant role in the hydrologic cycle, with water being the most important ecosystem service they provide in semiarid regions. However, this contribution is usually neither quantified nor explicitly valued. The aim of this study is to develop a novel hydroeconomic modeling framework for assessing and designing the optimal integrated forest and water management for forested catchments. The optimization model explicitly integrates changes in water yield in the stands (increase in groundwater recharge) induced by forest management and the value of the additional water provided to the system. The model determines the optimal schedule of silvicultural interventions in the stands of the catchment in order to maximize the total net benefit in the system. Canopy cover and biomass evolution over time were simulated using growth and yield allometric equations specific for the species in Mediterranean conditions. Silvicultural operation costs according to stand density and canopy cover were modeled using local cost databases. Groundwater recharge was simulated using HYDRUS, calibrated and validated with data from the experimental plots. In order to illustrate the presented modeling framework, a case study was carried out in a planted pine forest (Pinus halepensis Mill.) located in south-western Valencia province (Spain). The optimized scenario increased groundwater recharge. This novel modeling framework can be used in the design of a "payment for environmental services" scheme in which water beneficiaries could contribute to fund and promote efficient forest management operations.

Dynamical analysis of an n‑H‑T cosmological quintessence real gas model with a general equation of state

NASA Astrophysics Data System (ADS)

Ivanov, Rossen I.; Prodanov, Emil M.

2018-01-01

The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter and the temperature. Two global first integrals are found and examples for gas with virial expansion and van der Waals gas are presented. The van der Waals system is completely integrable. In addition to the unbounded trajectories, stemming from the presence of the conserved quantities, stable periodic solutions (closed orbits) also exist under certain conditions and these represent models of a cyclic Universe. The cyclic solutions exhibit regions characterized by inflation and deflation, while the open trajectories are characterized by inflation in a “fly-by” near an unstable critical point.

Net migration estimation in an extended, multiregional gravity model.

PubMed

Foot, D K; Milne, W J

1984-02-01

A multi-regional framework is developed in order to analyze net migration over time to all 10 Canadian provinces within an integrated system of equations. "An extended gravity model is the basis for the equation specification and the use of constrained econometric estimation techniques allows for the provincial interdependence of the migration decision while at the same time ensuring that an important system-wide requirement is respected." The model is estimated using official Canadian data for the 1960s and 1970s. "The results suggest the predominance of the push factor for interprovincial migration for most provinces, although net migration to the Atlantic provinces is also shown to be subject to pull forces from the rest of the country." The effects of wage rate variables, unemployment, and political disturbances in Quebec on inter-provincial migration are noted. excerpt

Lattice Boltzmann model for three-phase viscoelastic fluid flow

NASA Astrophysics Data System (ADS)

Xie, Chiyu; Lei, Wenhai; Wang, Moran

2018-02-01

A lattice Boltzmann (LB) framework is developed for simulation of three-phase viscoelastic fluid flows in complex geometries. This model is based on a Rothman-Keller type model for immiscible multiphase flows which ensures mass conservation of each component in porous media even for a high density ratio. To account for the viscoelastic effects, the Maxwell constitutive relation is correctly introduced into the momentum equation, which leads to a modified lattice Boltzmann evolution equation for Maxwell fluids by removing the normal but excess viscous term. Our simulation tests indicate that this excess viscous term may induce significant errors. After three benchmark cases, the displacement processes of oil by dispersed polymer are studied as a typical example of three-phase viscoelastic fluid flow. The results show that increasing either the polymer intrinsic viscosity or the elastic modulus will enhance the oil recovery.

Joseph Boussinesq et son approximation : un aperçu actuel

NASA Astrophysics Data System (ADS)

Zeytounian, Radyadour Kh.

2003-08-01

A hundred years ago, in his 1903 volume II of the monograph devoted to 'Théorie Analytique de la Chaleur', Joseph Valentin Boussinesq observes that: "The v ariations of density can be ignored except were they are multiplied by the acceleration of gravity in equation of motion for the vertical component of the velocity vector." A spectacular consequence of this Boussinesq observation (called, in 1916, by Rayleigh, the 'Boussinesq approximation') is the possibility to work with a quasi-incompressible system of coupled dynamic, (Navier) and thermal (Fourier) equations where buoyancy is the main driving force. After a few words on the life of Boussinesq and on his observation, the applicability of this approximation is briefly discussed for various thermal, geophysical, astrophysical and magnetohydrodynamic problems in the framework of 'Boussinesquian fluid dynamics'. An important part of our contemporary view is devoted to a logical (100 years later) justification of this Boussinesq approximation for a perfect gas and an ideal liquid in the framework of an asymptotic modelling of the full fluid dynamics (Euler and Navier-Stokes-Fourier) equations with especially careful attention given to the validity of this approximation. To cite this article: R.Kh. Zeytounian, C. R. Mecanique 331 (2003).

Using EIGER for Antenna Design and Analysis

NASA Technical Reports Server (NTRS)

Champagne, Nathan J.; Khayat, Michael; Kennedy, Timothy F.; Fink, Patrick W.

2007-01-01

EIGER (Electromagnetic Interactions GenERalized) is a frequency-domain electromagnetics software package that is built upon a flexible framework, designed using object-oriented techniques. The analysis methods used include moment method solutions of integral equations, finite element solutions of partial differential equations, and combinations thereof. The framework design permits new analysis techniques (boundary conditions, Green#s functions, etc.) to be added to the software suite with a sensible effort. The code has been designed to execute (in serial or parallel) on a wide variety of platforms from Intel-based PCs and Unix-based workstations. Recently, new potential integration scheme s that avoid singularity extraction techniques have been added for integral equation analysis. These new integration schemes are required for facilitating the use of higher-order elements and basis functions. Higher-order elements are better able to model geometrical curvature using fewer elements than when using linear elements. Higher-order basis functions are beneficial for simulating structures with rapidly varying fields or currents. Results presented here will demonstrate curren t and future capabilities of EIGER with respect to analysis of installed antenna system performance in support of NASA#s mission of exploration. Examples include antenna coupling within an enclosed environment and antenna analysis on electrically large manned space vehicles.

A new theoretical framework for modeling respiratory protection based on the beta distribution.

PubMed

Klausner, Ziv; Fattal, Eyal

2014-08-01

The problem of modeling respiratory protection is well known and has been dealt with extensively in the literature. Often the efficiency of respiratory protection is quantified in terms of penetration, defined as the proportion of an ambient contaminant concentration that penetrates the respiratory protection equipment. Typically, the penetration modeling framework in the literature is based on the assumption that penetration measurements follow the lognormal distribution. However, the analysis in this study leads to the conclusion that the lognormal assumption is not always valid, making it less adequate for analyzing respiratory protection measurements. This work presents a formulation of the problem from first principles, leading to a stochastic differential equation whose solution is the probability density function of the beta distribution. The data of respiratory protection experiments were reexamined, and indeed the beta distribution was found to provide the data a better fit than the lognormal. We conclude with a suggestion for a new theoretical framework for modeling respiratory protection. © The Author 2014. Published by Oxford University Press on behalf of the British Occupational Hygiene Society.

A mathematical view for ordinary differential equation models. Comment on ;Epigenetic game theory: How to compute the epigenetic control of maternal-to-zygotic transition; by Qian Wang et al.

NASA Astrophysics Data System (ADS)

Fu, Guifang

2017-03-01

Qian Wang et al. have written an interesting article to propose a modeling framework named epiGame in this issue of Physics of Life Reviews [1]. The epiGame framework models how the methylation state of paternal and maternal genomes regulates the embryogenesis as an ecological system in which two highly distinct and specialized gametes coordinate through either cooperation or competition, or both, to maximize the fitness of embryos. Qian Wang et al. also provide solid simulation studies and real data analysis to validate the correctness of their epiGame framework. The importance of embryo development and fertility mechanism cannot be overemphasized, hence, I think that the present review by Qian Wang et al. will stand as a useful modeling guide for practicing biologists or researchers in fertility health to quantify how sperms and oocytes interact through epigenetic process to determine embryo development. In addition, it will serve as a source of many important references to work in the reproductive biology field.

A discrete mechanics framework for real time virtual surgical simulations with application to virtual laparoscopic nephrectomy.

PubMed

Zhou, Xiangmin; Zhang, Nan; Sha, Desong; Shen, Yunhe; Tamma, Kumar K; Sweet, Robert

2009-01-01

The inability to render realistic soft-tissue behavior in real time has remained a barrier to face and content aspects of validity for many virtual reality surgical training systems. Biophysically based models are not only suitable for training purposes but also for patient-specific clinical applications, physiological modeling and surgical planning. When considering the existing approaches for modeling soft tissue for virtual reality surgical simulation, the computer graphics-based approach lacks predictive capability; the mass-spring model (MSM) based approach lacks biophysically realistic soft-tissue dynamic behavior; and the finite element method (FEM) approaches fail to meet the real-time requirement. The present development stems from physics fundamental thermodynamic first law; for a space discrete dynamic system directly formulates the space discrete but time continuous governing equation with embedded material constitutive relation and results in a discrete mechanics framework which possesses a unique balance between the computational efforts and the physically realistic soft-tissue dynamic behavior. We describe the development of the discrete mechanics framework with focused attention towards a virtual laparoscopic nephrectomy application.

Undular bore theory for the Gardner equation

NASA Astrophysics Data System (ADS)

Kamchatnov, A. M.; Kuo, Y.-H.; Lin, T.-C.; Horng, T.-L.; Gou, S.-C.; Clift, R.; El, G. A.; Grimshaw, R. H. J.

2012-09-01

We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg-de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg-de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV-type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves, and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations.

Low-complexity stochastic modeling of wall-bounded shear flows

NASA Astrophysics Data System (ADS)

Zare, Armin

Turbulent flows are ubiquitous in nature and they appear in many engineering applications. Transition to turbulence, in general, increases skin-friction drag in air/water vehicles compromising their fuel-efficiency and reduces the efficiency and longevity of wind turbines. While traditional flow control techniques combine physical intuition with costly experiments, their effectiveness can be significantly enhanced by control design based on low-complexity models and optimization. In this dissertation, we develop a theoretical and computational framework for the low-complexity stochastic modeling of wall-bounded shear flows. Part I of the dissertation is devoted to the development of a modeling framework which incorporates data-driven techniques to refine physics-based models. We consider the problem of completing partially known sample statistics in a way that is consistent with underlying stochastically driven linear dynamics. Neither the statistics nor the dynamics are precisely known. Thus, our objective is to reconcile the two in a parsimonious manner. To this end, we formulate optimization problems to identify the dynamics and directionality of input excitation in order to explain and complete available covariance data. For problem sizes that general-purpose solvers cannot handle, we develop customized optimization algorithms based on alternating direction methods. The solution to the optimization problem provides information about critical directions that have maximal effect in bringing model and statistics in agreement. In Part II, we employ our modeling framework to account for statistical signatures of turbulent channel flow using low-complexity stochastic dynamical models. We demonstrate that white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics and develop models for colored-in-time forcing of the linearized Navier-Stokes equations. We also examine the efficacy of stochastically forced linearized NS equations and their parabolized equivalents in the receptivity analysis of velocity fluctuations to external sources of excitation as well as capturing the effect of the slowly-varying base flow on streamwise streaks and Tollmien-Schlichting waves. In Part III, we develop a model-based approach to design surface actuation of turbulent channel flow in the form of streamwise traveling waves. This approach is capable of identifying the drag reducing trends of traveling waves in a simulation-free manner. We also use the stochastically forced linearized NS equations to examine the Reynolds number independent effects of spanwise wall oscillations on drag reduction in turbulent channel flows. This allows us to extend the predictive capability of our simulation-free approach to high Reynolds numbers.

Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

ERIC Educational Resources Information Center

Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen

2012-01-01

This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

Computational Analyses of Pressurization in Cryogenic Tanks

NASA Technical Reports Server (NTRS)

Ahuja, Vineet; Hosangadi, Ashvin; Mattick, Stephen; Lee, Chun P.; Field, Robert E.; Ryan, Harry

2008-01-01

A) Advanced Gas/Liquid Framework with Real Fluids Property Routines: I. A multi-fluid formulation in the preconditioned CRUNCH CFD(Registered TradeMark) code developed where a mixture of liquid and gases can be specified: a) Various options for Equation of state specification available (from simplified ideal fluid mixtures, to real fluid EOS such as SRK or BWR models). b) Vaporization of liquids driven by pressure value relative to vapor pressure and combustion of vapors allowed. c) Extensive validation has been undertaken. II. Currently working on developing primary break-up models and surface tension effects for more rigorous phase-change modeling and interfacial dynamics B) Framework Applied to Run-time Tanks at Ground Test Facilities C) Framework Used For J-2 Upper Stage Tank Modeling: 1) NASA MSFC tank pressurization: a) Hydrogen and oxygen tank pre-press, repress and draining being modeled at NASA MSFC. 2) NASA AMES tank safety effort a) liquid hydrogen and oxygen are separated by a baffle in the J-2 tank. We are modeling pressure rise and possible combustion if a hole develops in the baffle and liquid hydrogen leaks into the oxygen tank. Tank pressure rise rates simulated and risk of combustion evaluated.

Five easy equations for patient flow through an emergency department.

PubMed

Madsen, Thomas Lill; Kofoed-Enevoldsen, Allan

2011-10-01

Queue models are effective tools for framing management decisions and Danish hospitals could benefit from awareness of such models. Currently, as emergency departments (ED) are under reorganization, we deem it timely to empirically investigate the applicability of the standard "M/M/1" queue model in order to document its relevance. We compared actual versus theoretical distributions of hourly patient flow from 27,000 patient cases seen at Frederiksberg Hospital's ED. Formulating equations for arrivals and capacity, we wrote and tested a five equation simulation model. The Poisson distribution fitted arrivals with an hour-of-the-day specific parameter. Treatment times exceeding 15 minutes were well-described by an exponential distribution. The ED can be modelled as a black box with an hourly capacity that can be estimated either as admissions per hour when the ED operates full hilt Poisson distribution or from the linear dependency of waiting times on queue number. The results show that our ED capacity is surprisingly constant despite variations in staffing. These findings led to the formulation of a model giving a compact framework for assessing the behaviour of the ED under different assumptions about opening hours, capacity and workload. The M/M/1 almost perfectly fits our. Thus modeling and simulations have contributed to the management process. not relevant. not relevant.

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation. Volume 1: Study results

NASA Technical Reports Server (NTRS)

Lowrie, J. W.; Fermelia, A. J.; Haley, D. C.; Gremban, K. D.; Vanbaalen, J.; Walsh, R. W.

1982-01-01

A variety of artificial intelligence techniques which could be used with regard to NASA space applications and robotics were evaluated. The techniques studied were decision tree manipulators, problem solvers, rule based systems, logic programming languages, representation language languages, and expert systems. The overall structure of a robotic simulation tool was defined and a framework for that tool developed. Nonlinear and linearized dynamics equations were formulated for n link manipulator configurations. A framework for the robotic simulation was established which uses validated manipulator component models connected according to a user defined configuration.

Moose: An Open-Source Framework to Enable Rapid Development of Collaborative, Multi-Scale, Multi-Physics Simulation Tools

NASA Astrophysics Data System (ADS)

Slaughter, A. E.; Permann, C.; Peterson, J. W.; Gaston, D.; Andrs, D.; Miller, J.

2014-12-01

The Idaho National Laboratory (INL)-developed Multiphysics Object Oriented Simulation Environment (MOOSE; www.mooseframework.org), is an open-source, parallel computational framework for enabling the solution of complex, fully implicit multiphysics systems. MOOSE provides a set of computational tools that scientists and engineers can use to create sophisticated multiphysics simulations. Applications built using MOOSE have computed solutions for chemical reaction and transport equations, computational fluid dynamics, solid mechanics, heat conduction, mesoscale materials modeling, geomechanics, and others. To facilitate the coupling of diverse and highly-coupled physical systems, MOOSE employs the Jacobian-free Newton-Krylov (JFNK) method when solving the coupled nonlinear systems of equations arising in multiphysics applications. The MOOSE framework is written in C++, and leverages other high-quality, open-source scientific software packages such as LibMesh, Hypre, and PETSc. MOOSE uses a "hybrid parallel" model which combines both shared memory (thread-based) and distributed memory (MPI-based) parallelism to ensure efficient resource utilization on a wide range of computational hardware. MOOSE-based applications are inherently modular, which allows for simulation expansion (via coupling of additional physics modules) and the creation of multi-scale simulations. Any application developed with MOOSE supports running (in parallel) any other MOOSE-based application. Each application can be developed independently, yet easily communicate with other applications (e.g., conductivity in a slope-scale model could be a constant input, or a complete phase-field micro-structure simulation) without additional code being written. This method of development has proven effective at INL and expedites the development of sophisticated, sustainable, and collaborative simulation tools.

Multiobjective optimization of temporal processes.

PubMed

Song, Zhe; Kusiak, Andrew

2010-06-01

This paper presents a dynamic predictive-optimization framework of a nonlinear temporal process. Data-mining (DM) and evolutionary strategy algorithms are integrated in the framework for solving the optimization model. DM algorithms learn dynamic equations from the process data. An evolutionary strategy algorithm is then applied to solve the optimization problem guided by the knowledge extracted by the DM algorithm. The concept presented in this paper is illustrated with the data from a power plant, where the goal is to maximize the boiler efficiency and minimize the limestone consumption. This multiobjective optimization problem can be either transformed into a single-objective optimization problem through preference aggregation approaches or into a Pareto-optimal optimization problem. The computational results have shown the effectiveness of the proposed optimization framework.

Physical consistency of subgrid-scale models for large-eddy simulation of incompressible turbulent flows

NASA Astrophysics Data System (ADS)

Silvis, Maurits H.; Remmerswaal, Ronald A.; Verstappen, Roel

2017-01-01

We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is desirable that subgrid-scale models are consistent with the mathematical and physical properties of the Navier-Stokes equations and the turbulent stresses. To that end, we first discuss in detail the symmetries of the Navier-Stokes equations, and the near-wall scaling behavior, realizability and dissipation properties of the turbulent stresses. We furthermore summarize the requirements that subgrid-scale models have to satisfy in order to preserve these important mathematical and physical properties. In this fashion, a framework of model constraints arises that we apply to analyze the behavior of a number of existing subgrid-scale models that are based on the local velocity gradient. We show that these subgrid-scale models do not satisfy all the desired properties, after which we explain that this is partly due to incompatibilities between model constraints and limitations of velocity-gradient-based subgrid-scale models. However, we also reason that the current framework shows that there is room for improvement in the properties and, hence, the behavior of existing subgrid-scale models. We furthermore show how compatible model constraints can be combined to construct new subgrid-scale models that have desirable properties built into them. We provide a few examples of such new models, of which a new model of eddy viscosity type, that is based on the vortex stretching magnitude, is successfully tested in large-eddy simulations of decaying homogeneous isotropic turbulence and turbulent plane-channel flow.

Cusping, transport and variance of solutions to generalized Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Carnaffan, Sean; Kawai, Reiichiro

2017-06-01

We study properties of solutions to generalized Fokker-Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker-Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.

Unifying Time to Contact Estimation and Collision Avoidance across Species

PubMed Central

Keil, Matthias S.; López-Moliner, Joan

2012-01-01

The -function and the -function are phenomenological models that are widely used in the context of timing interceptive actions and collision avoidance, respectively. Both models were previously considered to be unrelated to each other: is a decreasing function that provides an estimation of time-to-contact (ttc) in the early phase of an object approach; in contrast, has a maximum before ttc. Furthermore, it is not clear how both functions could be implemented at the neuronal level in a biophysically plausible fashion. Here we propose a new framework – the corrected modified Tau function – capable of predicting both -type (“”) and -type (“”) responses. The outstanding property of our new framework is its resilience to noise. We show that can be derived from a firing rate equation, and, as , serves to describe the response curves of collision sensitive neurons. Furthermore, we show that predicts the psychophysical performance of subjects determining ttc. Our new framework is thus validated successfully against published and novel experimental data. Within the framework, links between -type and -type neurons are established. Therefore, it could possibly serve as a model for explaining the co-occurrence of such neurons in the brain. PMID:22915999

Noise in Neuronal and Electronic Circuits: A General Modeling Framework and Non-Monte Carlo Simulation Techniques.

PubMed

Kilinc, Deniz; Demir, Alper

2017-08-01

The brain is extremely energy efficient and remarkably robust in what it does despite the considerable variability and noise caused by the stochastic mechanisms in neurons and synapses. Computational modeling is a powerful tool that can help us gain insight into this important aspect of brain mechanism. A deep understanding and computational design tools can help develop robust neuromorphic electronic circuits and hybrid neuroelectronic systems. In this paper, we present a general modeling framework for biological neuronal circuits that systematically captures the nonstationary stochastic behavior of ion channels and synaptic processes. In this framework, fine-grained, discrete-state, continuous-time Markov chain models of both ion channels and synaptic processes are treated in a unified manner. Our modeling framework features a mechanism for the automatic generation of the corresponding coarse-grained, continuous-state, continuous-time stochastic differential equation models for neuronal variability and noise. Furthermore, we repurpose non-Monte Carlo noise analysis techniques, which were previously developed for analog electronic circuits, for the stochastic characterization of neuronal circuits both in time and frequency domain. We verify that the fast non-Monte Carlo analysis methods produce results with the same accuracy as computationally expensive Monte Carlo simulations. We have implemented the proposed techniques in a prototype simulator, where both biological neuronal and analog electronic circuits can be simulated together in a coupled manner.

A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: Multi-center molecular Ornstein-Zernike self-consistent field approach

NASA Astrophysics Data System (ADS)

Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi

2015-07-01

In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl- + CH3Cl → ClCH3 + Cl-) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.

A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: multi-center molecular Ornstein-Zernike self-consistent field approach.

PubMed

Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi

2015-07-07

In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl(-) + CH3Cl → ClCH3 + Cl(-)) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.

A unifying kinetic framework for modeling oxidoreductase-catalyzed reactions.

PubMed

Chang, Ivan; Baldi, Pierre

2013-05-15

Oxidoreductases are a fundamental class of enzymes responsible for the catalysis of oxidation-reduction reactions, crucial in most bioenergetic metabolic pathways. From their common root in the ancient prebiotic environment, oxidoreductases have evolved into diverse and elaborate protein structures with specific kinetic properties and mechanisms adapted to their individual functional roles and environmental conditions. While accurate kinetic modeling of oxidoreductases is thus important, current models suffer from limitations to the steady-state domain, lack empirical validation or are too specialized to a single system or set of conditions. To address these limitations, we introduce a novel unifying modeling framework for kinetic descriptions of oxidoreductases. The framework is based on a set of seven elementary reactions that (i) form the basis for 69 pairs of enzyme state transitions for encoding various specific microscopic intra-enzyme reaction networks (micro-models), and (ii) lead to various specific macroscopic steady-state kinetic equations (macro-models) via thermodynamic assumptions. Thus, a synergistic bridge between the micro and macro kinetics can be achieved, enabling us to extract unitary rate constants, simulate reaction variance and validate the micro-models using steady-state empirical data. To help facilitate the application of this framework, we make available RedoxMech: a Mathematica™ software package that automates the generation and customization of micro-models. The Mathematica™ source code for RedoxMech, the documentation and the experimental datasets are all available from: http://www.igb.uci.edu/tools/sb/metabolic-modeling. pfbaldi@ics.uci.edu Supplementary data are available at Bioinformatics online.

General linear methods and friends: Toward efficient solutions of multiphysics problems

NASA Astrophysics Data System (ADS)

Sandu, Adrian

2017-07-01

Time dependent multiphysics partial differential equations are of great practical importance as they model diverse phenomena that appear in mechanical and chemical engineering, aeronautics, astrophysics, meteorology and oceanography, financial modeling, environmental sciences, etc. There is no single best time discretization for the complex multiphysics systems of practical interest. We discuss "multimethod" approaches that combine different time steps and discretizations using the rigourous frameworks provided by Partitioned General Linear Methods and Generalize-structure Additive Runge Kutta Methods..

Rasch Model Analysis with the BICAL Computer Program

DTIC Science & Technology

1976-09-01

and persons which lead to measures that persist from trial to trial . The measurement model is essential in this process because it provides a framework...and his students. Section 15 two derives the estimating equations for the Bernoulli (i.e. one trial per task) form : " and then generalizes to the...Binomial form (several trials per task). Finall) goodness of fit tests are presented for assessing the adequacy of the calibration. t { ) I I I 41 CHAPTER

A dynamic subgrid scale model for Large Eddy Simulations based on the Mori-Zwanzig formalism

NASA Astrophysics Data System (ADS)

Parish, Eric J.; Duraisamy, Karthik

2017-11-01

The development of reduced models for complex multiscale problems remains one of the principal challenges in computational physics. The optimal prediction framework of Chorin et al. [1], which is a reformulation of the Mori-Zwanzig (M-Z) formalism of non-equilibrium statistical mechanics, provides a framework for the development of mathematically-derived reduced models of dynamical systems. Several promising models have emerged from the optimal prediction community and have found application in molecular dynamics and turbulent flows. In this work, a new M-Z-based closure model that addresses some of the deficiencies of existing methods is developed. The model is constructed by exploiting similarities between two levels of coarse-graining via the Germano identity of fluid mechanics and by assuming that memory effects have a finite temporal support. The appeal of the proposed model, which will be referred to as the 'dynamic-MZ-τ' model, is that it is parameter-free and has a structural form imposed by the mathematics of the coarse-graining process (rather than the phenomenological assumptions made by the modeler, such as in classical subgrid scale models). To promote the applicability of M-Z models in general, two procedures are presented to compute the resulting model form, helping to bypass the tedious error-prone algebra that has proven to be a hindrance to the construction of M-Z-based models for complex dynamical systems. While the new formulation is applicable to the solution of general partial differential equations, demonstrations are presented in the context of Large Eddy Simulation closures for the Burgers equation, decaying homogeneous turbulence, and turbulent channel flow. The performance of the model and validity of the underlying assumptions are investigated in detail.

Multiloop functional renormalization group for general models

NASA Astrophysics Data System (ADS)

Kugler, Fabian B.; von Delft, Jan

2018-02-01

We present multiloop flow equations in the functional renormalization group (fRG) framework for the four-point vertex and self-energy, formulated for a general fermionic many-body problem. This generalizes the previously introduced vertex flow [F. B. Kugler and J. von Delft, Phys. Rev. Lett. 120, 057403 (2018), 10.1103/PhysRevLett.120.057403] and provides the necessary corrections to the self-energy flow in order to complete the derivative of all diagrams involved in the truncated fRG flow. Due to its iterative one-loop structure, the multiloop flow is well suited for numerical algorithms, enabling improvement of many fRG computations. We demonstrate its equivalence to a solution of the (first-order) parquet equations in conjunction with the Schwinger-Dyson equation for the self-energy.

A statistical mechanical theory of proton transport kinetics in hydrogen-bonded networks based on population correlation functions with applications to acids and bases.

PubMed

Tuckerman, Mark E; Chandra, Amalendu; Marx, Dominik

2010-09-28

Extraction of relaxation times, lifetimes, and rates associated with the transport of topological charge defects in hydrogen-bonded networks from molecular dynamics simulations is a challenge because proton transfer reactions continually change the identity of the defect core. In this paper, we present a statistical mechanical theory that allows these quantities to be computed in an unbiased manner. The theory employs a set of suitably defined indicator or population functions for locating a defect structure and their associated correlation functions. These functions are then used to develop a chemical master equation framework from which the rates and lifetimes can be determined. Furthermore, we develop an integral equation formalism for connecting various types of population correlation functions and derive an iterative solution to the equation, which is given a graphical interpretation. The chemical master equation framework is applied to the problems of both hydronium and hydroxide transport in bulk water. For each case it is shown that the theory establishes direct links between the defect's dominant solvation structures, the kinetics of charge transfer, and the mechanism of structural diffusion. A detailed analysis is presented for aqueous hydroxide, examining both reorientational time scales and relaxation of the rotational anisotropy, which is correlated with recent experimental results for these quantities. Finally, for OH(-)(aq) it is demonstrated that the "dynamical hypercoordination mechanism" is consistent with available experimental data while other mechanistic proposals are shown to fail. As a means of going beyond the linear rate theory valid from short up to intermediate time scales, a fractional kinetic model is introduced in the Appendix in order to describe the nonexponential long-time behavior of time-correlation functions. Within the mathematical framework of fractional calculus the power law decay ∼t(-σ), where σ is a parameter of the model and depends on the dimensionality of the system, is obtained from Mittag-Leffler functions due to their long-time asymptotics, whereas (stretched) exponential behavior is found for short times.

Unified Computational Methods for Regression Analysis of Zero-Inflated and Bound-Inflated Data

PubMed Central

Yang, Yan; Simpson, Douglas

2010-01-01

Bounded data with excess observations at the boundary are common in many areas of application. Various individual cases of inflated mixture models have been studied in the literature for bound-inflated data, yet the computational methods have been developed separately for each type of model. In this article we use a common framework for computing these models, and expand the range of models for both discrete and semi-continuous data with point inflation at the lower boundary. The quasi-Newton and EM algorithms are adapted and compared for estimation of model parameters. The numerical Hessian and generalized Louis method are investigated as means for computing standard errors after optimization. Correlated data are included in this framework via generalized estimating equations. The estimation of parameters and effectiveness of standard errors are demonstrated through simulation and in the analysis of data from an ultrasound bioeffect study. The unified approach enables reliable computation for a wide class of inflated mixture models and comparison of competing models. PMID:20228950

The nature and outcomes of work: a replication and extension of interdisciplinary work-design research.

PubMed

Edwards, J R; Scully, J A; Brtek, M D

2000-12-01

Research into the changing nature of work requires comprehensive models of work design. One such model is the interdisciplinary framework (M. A. Campion, 1988), which integrates 4 work-design approaches (motivational, mechanistic, biological, perceptual-motor) and links each approach to specific outcomes. Unfortunately, studies of this framework have used methods that disregard measurement error, overlook dimensions within each work-design approach, and treat each approach and outcome separately. This study reanalyzes data from M. A. Campion (1988), using structural equation models that incorporate measurement error, specify multiple dimensions for each work-design approach, and examine the work-design approaches and outcomes jointly. Results show that previous studies underestimate relationships between work-design approaches and outcomes and that dimensions within each approach exhibit relationships with outcomes that differ in magnitude and direction.

Electroweak baryogenesis and the standard model effective field theory

NASA Astrophysics Data System (ADS)

de Vries, Jordy; Postma, Marieke; van de Vis, Jorinde; White, Graham

2018-01-01

We investigate electroweak baryogenesis within the framework of the Standard Model Effective Field Theory. The Standard Model Lagrangian is supplemented by dimension-six operators that facilitate a strong first-order electroweak phase transition and provide sufficient CP violation. Two explicit scenarios are studied that are related via the classical equations of motion and are therefore identical at leading order in the effective field theory expansion. We demonstrate that formally higher-order dimension-eight corrections lead to large modifications of the matter-antimatter asymmetry. The effective field theory expansion breaks down in the modified Higgs sector due to the requirement of a first-order phase transition. We investigate the source of the breakdown in detail and show how it is transferred to the CP-violating sector. We briefly discuss possible modifications of the effective field theory framework.

Proto-Plasm: parallel language for adaptive and scalable modelling of biosystems

PubMed Central

Bajaj, Chandrajit; DiCarlo, Antonio; Paoluzzi, Alberto

2008-01-01

This paper discusses the design goals and the first developments of Proto-Plasm, a novel computational environment to produce libraries of executable, combinable and customizable computer models of natural and synthetic biosystems, aiming to provide a supporting framework for predictive understanding of structure and behaviour through multiscale geometric modelling and multiphysics simulations. Admittedly, the Proto-Plasm platform is still in its infancy. Its computational framework—language, model library, integrated development environment and parallel engine—intends to provide patient-specific computational modelling and simulation of organs and biosystem, exploiting novel functionalities resulting from the symbolic combination of parametrized models of parts at various scales. Proto-Plasm may define the model equations, but it is currently focused on the symbolic description of model geometry and on the parallel support of simulations. Conversely, CellML and SBML could be viewed as defining the behavioural functions (the model equations) to be used within a Proto-Plasm program. Here we exemplify the basic functionalities of Proto-Plasm, by constructing a schematic heart model. We also discuss multiscale issues with reference to the geometric and physical modelling of neuromuscular junctions. PMID:18559320

The Janus Cosmological Model (JCM) : An answer to the missing cosmological antimatter

NASA Astrophysics Data System (ADS)

D'Agostini, Gilles; Petit, Jean-Pierre

2017-01-01

Cosmological antimatter absence remains unexplained. Twin universes 1967 Sakarov's model suggests an answer: excess of matter and anti-quarks production in our universe is balanced by equivalent excess of antimatter and quark in twin universe. JCM provides geometrical framework, with a single manifold , two metrics solutions of two coupled field equations, to describe two populations of particles, one with positive energy-mass and the other with negative energy-mass : the `twin matter'. In a quantum point of view, it's a copy of the standard matter but with negative mass and energy. The matter-antimatter duality holds in both sectors. The standard and twin matters do not interact except through the gravitational coupling expressed in field equations. The twin matter is unobservable from matter-made apparatus. Field equations shows that matter and twin matter repel each other. Twin matter surrounding galaxies explains their confinement (dark matter role) and, in the dust universe era, mainly drives the process of expansion of the positive sector, responsible of the observed acceleration (dark energy role).

The Motion of a Leaking Oscillator: A Study for the Physics Class

ERIC Educational Resources Information Center

Rodrigues, Hilário; Panza, Nelson; Portes, Dirceu; Soares, Alexandre

2014-01-01

This paper is essentially about the general form of Newton's second law for variable mass problems. We develop a model for describing the motion of the one-dimensional oscillator with a variable mass within the framework of classroom physics. We present a simple numerical procedure for the solution of the equation of motion of the system to…

Examination of Bidirectional Relationships between Parent Stress and Two Types of Problem Behavior in Children with Autism Spectrum Disorder

ERIC Educational Resources Information Center

Zaidman-Zait, Anat; Mirenda, Pat; Duku, Eric; Szatmari, Peter; Georgiades, Stelios; Volden, Joanne; Zwaigenbaum, Lonnie; Vaillancourt, Tracy; Bryson, Susan; Smith, Isabel; Fombonne, Eric; Roberts, Wendy; Waddell, Charlotte; Thompson, Ann

2014-01-01

Path analysis within a structural equation modeling framework was employed to examine the relationships between two types of parent stress and children's externalizing and internalizing behaviors over a 4-year period, in a sample of 184 mothers of young children with autism spectrum disorder. Parent stress was measured with the Parenting Stress…

Model-independent cosmological constraints from growth and expansion

NASA Astrophysics Data System (ADS)

L'Huillier, Benjamin; Shafieloo, Arman; Kim, Hyungjin

2018-05-01

Reconstructing the expansion history of the Universe from Type Ia supernovae data, we fit the growth rate measurements and put model-independent constraints on some key cosmological parameters, namely, Ωm, γ, and σ8. The constraints are consistent with those from the concordance model within the framework of general relativity, but the current quality of the data is not sufficient to rule out modified gravity models. Adding the condition that dark energy density should be positive at all redshifts, independently of its equation of state, further constrains the parameters and interestingly supports the concordance model.

Climatic and physiographic controls of spatial variability in surface water balance over the contiguous United States using the Budyko relationship

NASA Astrophysics Data System (ADS)

Abatzoglou, John T.; Ficklin, Darren L.

2017-09-01

The geographic variability in the partitioning of precipitation into surface runoff (Q) and evapotranspiration (ET) is fundamental to understanding regional water availability. The Budyko equation suggests this partitioning is strictly a function of aridity, yet observed deviations from this relationship for individual watersheds impede using the framework to model surface water balance in ungauged catchments and under future climate and land use scenarios. A set of climatic, physiographic, and vegetation metrics were used to model the spatial variability in the partitioning of precipitation for 211 watersheds across the contiguous United States (CONUS) within Budyko's framework through the free parameter ω. A generalized additive model found that four widely available variables, precipitation seasonality, the ratio of soil water holding capacity to precipitation, topographic slope, and the fraction of precipitation falling as snow, explained 81.2% of the variability in ω. The ω model applied to the Budyko equation explained 97% of the spatial variability in long-term Q for an independent set of watersheds. The ω model was also applied to estimate the long-term water balance across the CONUS for both contemporary and mid-21st century conditions. The modeled partitioning of observed precipitation to Q and ET compared favorably across the CONUS with estimates from more sophisticated land-surface modeling efforts. For mid-21st century conditions, the model simulated an increase in the fraction of precipitation used by ET across the CONUS with declines in Q for much of the eastern CONUS and mountainous watersheds across the western United States.

The social determinants of oral health: new approaches to conceptualizing and researching complex causal networks.

PubMed

Newton, J Timothy; Bower, Elizabeth J

2005-02-01

Oral epidemiological research into the social determinants of oral health has been limited by the absence of a theoretical framework which reflects the complexity of real life social processes and the network of causal pathways between social structure and oral health and disease. In the absence of such a framework, social determinants are treated as isolated risk factors, attributable to the individual, having a direct impact on oral health. There is little sense of how such factors interrelate over time and place and the pathways between the factors and oral health. Features of social life which impact on individuals' oral health but are not reducible to the individual remain under-researched. A conceptual framework informing mainstream epidemiological research into the social determinants of health is applied to oral epidemiology. The framework suggests complex causal pathways between social structure and health via interlinking material, psychosocial and behavioural pathways. Methodological implications for oral epidemiological research informed by the framework, such as the use of multilevel modelling, path analysis and structural equation modelling, combining qualitative and quantitative research methods, and collaborative research, are discussed. Copyright Blackwell Munksgaard, 2005.

A Layer Framework to Investigate Student Understanding and Application of the Existence and Uniqueness Theorems of Differential Equations

ERIC Educational Resources Information Center

Raychaudhuri, D.

2007-01-01

The focus of this paper is on student interpretation and usage of the existence and uniqueness theorems for first-order ordinary differential equations. The inherent structure of the theorems is made explicit by the introduction of a framework of layers concepts-conditions-connectives-conclusions, and we discuss the manners in which students'…

Emergent properties of interacting populations of spiking neurons.

PubMed

Cardanobile, Stefano; Rotter, Stefan

2011-01-01

Dynamic neuronal networks are a key paradigm of increasing importance in brain research, concerned with the functional analysis of biological neuronal networks and, at the same time, with the synthesis of artificial brain-like systems. In this context, neuronal network models serve as mathematical tools to understand the function of brains, but they might as well develop into future tools for enhancing certain functions of our nervous system. Here, we present and discuss our recent achievements in developing multiplicative point processes into a viable mathematical framework for spiking network modeling. The perspective is that the dynamic behavior of these neuronal networks is faithfully reflected by a set of non-linear rate equations, describing all interactions on the population level. These equations are similar in structure to Lotka-Volterra equations, well known by their use in modeling predator-prey relations in population biology, but abundant applications to economic theory have also been described. We present a number of biologically relevant examples for spiking network function, which can be studied with the help of the aforementioned correspondence between spike trains and specific systems of non-linear coupled ordinary differential equations. We claim that, enabled by the use of multiplicative point processes, we can make essential contributions to a more thorough understanding of the dynamical properties of interacting neuronal populations.

Emergent Properties of Interacting Populations of Spiking Neurons

PubMed Central

Cardanobile, Stefano; Rotter, Stefan

2011-01-01

Dynamic neuronal networks are a key paradigm of increasing importance in brain research, concerned with the functional analysis of biological neuronal networks and, at the same time, with the synthesis of artificial brain-like systems. In this context, neuronal network models serve as mathematical tools to understand the function of brains, but they might as well develop into future tools for enhancing certain functions of our nervous system. Here, we present and discuss our recent achievements in developing multiplicative point processes into a viable mathematical framework for spiking network modeling. The perspective is that the dynamic behavior of these neuronal networks is faithfully reflected by a set of non-linear rate equations, describing all interactions on the population level. These equations are similar in structure to Lotka-Volterra equations, well known by their use in modeling predator-prey relations in population biology, but abundant applications to economic theory have also been described. We present a number of biologically relevant examples for spiking network function, which can be studied with the help of the aforementioned correspondence between spike trains and specific systems of non-linear coupled ordinary differential equations. We claim that, enabled by the use of multiplicative point processes, we can make essential contributions to a more thorough understanding of the dynamical properties of interacting neuronal populations. PMID:22207844

Investigating the two-moment characterisation of subcellular biochemical networks.

PubMed

Ullah, Mukhtar; Wolkenhauer, Olaf

2009-10-07

While ordinary differential equations (ODEs) form the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise. The most common formulation of stochastic models for biochemical networks is the chemical master equation (CME). While stochastic simulations are a practical way to realise the CME, analytical approximations offer more insight into the influence of noise. Towards that end, the two-moment approximation (2MA) is a promising addition to the established analytical approaches including the chemical Langevin equation (CLE) and the related linear noise approximation (LNA). The 2MA approach directly tracks the mean and (co)variance which are coupled in general. This coupling is not obvious in CME and CLE and ignored by LNA and conventional ODE models. We extend previous derivations of 2MA by allowing (a) non-elementary reactions and (b) relative concentrations. Often, several elementary reactions are approximated by a single step. Furthermore, practical situations often require the use of relative concentrations. We investigate the applicability of the 2MA approach to the well-established fission yeast cell cycle model. Our analytical model reproduces the clustering of cycle times observed in experiments. This is explained through multiple resettings of M-phase promoting factor (MPF), caused by the coupling between mean and (co)variance, near the G2/M transition.

Performance Estimation for Two-Dimensional Brownian Rotary Ratchet Systems

NASA Astrophysics Data System (ADS)

Tutu, Hiroki; Horita, Takehiko; Ouchi, Katsuya

2015-04-01

Within the context of the Brownian ratchet model, a molecular rotary system that can perform unidirectional rotations induced by linearly polarized ac fields and produce positive work under loads was studied. The model is based on the Langevin equation for a particle in a two-dimensional (2D) three-tooth ratchet potential of threefold symmetry. The performance of the system is characterized by the coercive torque, i.e., the strength of the load competing with the torque induced by the ac driving field, and the energy efficiency in force conversion from the driving field to the torque. We propose a master equation for coarse-grained states, which takes into account the boundary motion between states, and develop a kinetic description to estimate the mean angular momentum (MAM) and powers relevant to the energy balance equation. The framework of analysis incorporates several 2D characteristics and is applicable to a wide class of models of smooth 2D ratchet potential. We confirm that the obtained expressions for MAM, power, and efficiency of the model can enable us to predict qualitative behaviors. We also discuss the usefulness of the torque/power relationship for experimental analyses, and propose a characteristic for 2D ratchet systems.

Growth of structure in the Szekeres class-II inhomogeneous cosmological models and the matter-dominated era

NASA Astrophysics Data System (ADS)

Ishak, Mustapha; Peel, Austin

2012-04-01

This study belongs to a series devoted to using the Szekeres inhomogeneous models in order to develop a theoretical framework where cosmological observations can be investigated with a wider range of possible interpretations. While our previous work addressed the question of cosmological distances versus redshift in these models, the current study is a start at looking into the growth rate of large-scale structure. The Szekeres models are exact solutions to Einstein’s equations that were originally derived with no symmetries. We use here a formulation of the Szekeres models that is due to Goode and Wainwright, who considered the models as exact perturbations of a Friedmann-Lemaître-Robertson-Walker (FLRW) background. Using the Raychaudhuri equation we write, for the two classes of the models, exact growth equations in terms of the under/overdensity and measurable cosmological parameters. The new equations in the overdensity split into two informative parts. The first part, while exact, is identical to the growth equation in the usual linearly perturbed FLRW models, while the second part constitutes exact nonlinear perturbations. We integrate numerically the full exact growth rate equations for the flat and curved cases. We find that for the matter-dominated cosmic era, the Szekeres growth rate is up to a factor of three to five stronger than the usual linearly perturbed FLRW cases, reflecting the effect of exact Szekeres nonlinear perturbations. We also find that the Szekeres growth rate with an Einstein-de Sitter background is stronger than that of the well-known nonlinear spherical collapse model, and the difference between the two increases with time. This highlights the distinction when we use general inhomogeneous models where shear and a tidal gravitational field are present and contribute to the gravitational clustering. Additionally, it is worth observing that the enhancement of the growth found in the Szekeres models during the matter-dominated era could suggest a substitute to the argument that dark matter is needed when using FLRW models to explain the enhanced growth and resulting large-scale structures that we observe today.

Local Observed-Score Kernel Equating

ERIC Educational Resources Information Center

Wiberg, Marie; van der Linden, Wim J.; von Davier, Alina A.

2014-01-01

Three local observed-score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias--as defined by Lord's criterion of equity--and percent relative error. The local kernel item response…

Adaptive unified continuum FEM modeling of a 3D FSI benchmark problem.

PubMed

Jansson, Johan; Degirmenci, Niyazi Cem; Hoffman, Johan

2017-09-01

In this paper, we address a 3D fluid-structure interaction benchmark problem that represents important characteristics of biomedical modeling. We present a goal-oriented adaptive finite element methodology for incompressible fluid-structure interaction based on a streamline diffusion-type stabilization of the balance equations for mass and momentum for the entire continuum in the domain, which is implemented in the Unicorn/FEniCS software framework. A phase marker function and its corresponding transport equation are introduced to select the constitutive law, where the mesh tracks the discontinuous fluid-structure interface. This results in a unified simulation method for fluids and structures. We present detailed results for the benchmark problem compared with experiments, together with a mesh convergence study. Copyright © 2016 John Wiley & Sons, Ltd.

Various continuum approaches for studying shock wave structure in carbon dioxide

NASA Astrophysics Data System (ADS)

Alekseev, I. V.; Kosareva, A. A.; Kustova, E. V.; Nagnibeda, E. A.

2018-05-01

Shock wave structure in carbon dioxide is studied using different continuum models within the framework of one-temperature thermal equilibrium flow description. Navier-Stokes and Euler equations as well as commonly used Rankine-Hugoniot equations with different specific heat ratios are used to find the gas-dynamic parameters behind the shock wave. The accuracy of the Rankine-Hugoniot relations in polyatomic gases is assessed, and it is shown that they give a considerable error in the predicted values of fluid-dynamic variables. The effect of bulk viscosity on the shock wave structure in CO2 is evaluated. Taking into account bulk viscosity yields a significant increase in the shock wave width; for the complete model, the shock wave thickness varies non-monotonically with the Mach number.

The thermodynamics of dense granular flow and jamming

NASA Astrophysics Data System (ADS)

Lu, Shih Yu

The scope of the thesis is to propose, based on experimental evidence and theoretical validation, a quantifiable connection between systems that exhibit the jamming phenomenon. When jammed, some materials that flow are able to resist deformation so that they appear solid-like on the laboratory scale. But unlike ordinary fusion, which has a critically defined criterion in pressure and temperature, jamming occurs under a wide range of conditions. These condition have been rigorously investigated but at the moment, no self-consistent framework can apply to grains, foam and colloids that may have suddenly ceased to flow. To quantify the jamming behavior, a constitutive model of dense granular flows is deduced from shear-flow experiments. The empirical equations are then generalized, via a thermodynamic approach, into an equation-of-state for jamming. Notably, the unifying theory also predicts the experimental data on the behavior of molecular glassy liquids. This analogy paves a crucial road map for a unifying theoretical framework in condensed matter, for example, ranging from sand to fire retardants to toothpaste.

Pattern production through a chiral chasing mechanism

NASA Astrophysics Data System (ADS)

Woolley, Thomas E.

2017-09-01

Recent experiments on zebrafish pigmentation suggests that their typical black and white striped skin pattern is made up of a number of interacting chromatophore families. Specifically, two of these cell families have been shown to interact through a nonlocal chasing mechanism, which has previously been modeled using integro-differential equations. We extend this framework to include the experimentally observed fact that the cells often exhibit chiral movement, in that the cells chase, and run away, at angles different to the line connecting their centers. This framework is simplified through the use of multiple small limits leading to a coupled set of partial differential equations which are amenable to Fourier analysis. This analysis results in the production of dispersion relations and necessary conditions for a patterning instability to occur. Beyond the theoretical development and the production of new pattern planiforms we are able to corroborate the experimental hypothesis that the global pigmentation patterns can be dependent on the chirality of the chromatophores.

Models and finite element approximations for interacting nanosized piezoelectric bodies and acoustic medium

NASA Astrophysics Data System (ADS)

Nasedkin, A. V.

2017-01-01

This research presents the new size-dependent models of piezoelectric materials oriented to finite element applications. The proposed models include the facilities of taking into account different mechanisms of damping for mechanical and electric fields. The coupled models also incorporate the equations of the theory of acoustics for viscous fluids. In particular cases, these models permit to use the mode superposition method with full separation of the finite element systems into independent equations for the independent modes for transient and harmonic problems. The main boundary conditions were supplemented with the facilities of taking into account the coupled surface effects, allowing to explore the nanoscale piezoelectric materials in the framework of theories of continuous media with surface stresses and their generalizations. For the considered problems we have implemented the finite element technologies and various numerical algorithms to maintain a symmetrical structure of the finite element quasi-definite matrices (matrix structure for the problems with a saddle point).

Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders.

PubMed

Kanazawa, Kiyoshi; Sueshige, Takumi; Takayasu, Hideki; Takayasu, Misako

2018-03-30

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders

NASA Astrophysics Data System (ADS)

Kanazawa, Kiyoshi; Sueshige, Takumi; Takayasu, Hideki; Takayasu, Misako

2018-03-01

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

A theoretical framework for analyzing the effect of external change on tidal dynamics in estuaries

NASA Astrophysics Data System (ADS)

CAI, H.; Savenije, H.; Toffolon, M.

2013-12-01

The most densely populated areas of the world are usually located in coastal areas near estuaries. As a result, estuaries are often subject to intense human interventions, such as dredging for navigation, dam construction and fresh water withdrawal etc., which in some areas has led to serious deterioration of invaluable ecosystems. Hence it is important to understand the influence of such interventions on tidal dynamics in these areas. In this study, we present one consistent theoretical framework for tidal hydrodynamics, which can be used as a rapid assessment technique that assist policy maker and managers to make considered decisions for the protection and management of estuarine environment when assessing the effect of human interventions in estuaries. Analytical solutions to the one-dimensional St. Venant equations for the tidal hydrodynamics in convergent unbounded estuaries with negligible river discharge can be cast in the form of a set of four implicit dimensionless equations for phase lag, velocity amplitude, damping, and wave celerity, as a function of two localized parameters describing friction and convergence. This method allows for the comparison of the different analytical approaches by rewriting the different solutions in the same format. In this study, classical and more recent formulations are compared, showing the differences and similarities associated to their specific simplifications. The envelope method, which is based on the consideration of the dynamics at high water and low water, can be used to derive damping equations that use different friction approximations. This results in as many analytical solutions, and thereby allows one to build a consistent theoretical framework. Analysis of the asymptotic behaviour of the equations shows that an equilibrium tidal amplitude exits reflecting the balance between friction and channel convergence. The framework is subsequently extended to take into account the effect of river discharge. Hence, the analytical solutions are applicable even in the upstream part of an estuary, where the influence of river discharge is remarkable. The proposed analytical solutions are transparent and practical, allowing a quantitative and qualitative assessment of human interventions (e.g., dredging, flow reduction) on tidal dynamics. Moreover, they are rapid assessment techniques that enable the users to set up a simple model and to understand the functioning of the system with a minimum of information required. The analytical model is illustrated in three large-scale estuaries with significant influence by human activities, i.e., the Scheldt estuary in the Netherlands, the Modaomen and the Yangtze estuaries in China. In these estuaries, the correspondence with observations is good, which suggests that the proposed model is a useful, yet realistic and reliable instrument for quick detection of the effect of human interventions on tidal dynamics and subsequent environmental issues, such as salt intrusion.

MHD-model for low-frequency waves in a tokamak with toroidal plasma rotation and problem of existence of global geodesic acoustic modes

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

Lakhin, V. P.; Sorokina, E. A., E-mail: sorokina.ekaterina@gmail.com, E-mail: vilkiae@gmail.com; Ilgisonis, V. I.

2015-12-15

A set of reduced linear equations for the description of low-frequency perturbations in toroidally rotating plasma in axisymmetric tokamak is derived in the framework of ideal magnetohydrodynamics. The model suitable for the study of global geodesic acoustic modes (GGAMs) is designed. An example of the use of the developed model for derivation of the integral conditions for GGAM existence and of the corresponding dispersion relation is presented. The paper is dedicated to the memory of academician V.D. Shafranov.

On spatial mutation-selection models

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

Kondratiev, Yuri, E-mail: kondrat@math.uni-bielefeld.de; Kutoviy, Oleksandr, E-mail: kutoviy@math.uni-bielefeld.de, E-mail: kutovyi@mit.edu; Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

2013-11-15

We discuss the selection procedure in the framework of mutation models. We study the regulation for stochastically developing systems based on a transformation of the initial Markov process which includes a cost functional. The transformation of initial Markov process by cost functional has an analytic realization in terms of a Kimura-Maruyama type equation for the time evolution of states or in terms of the corresponding Feynman-Kac formula on the path space. The state evolution of the system including the limiting behavior is studied for two types of mutation-selection models.

Markov State Models of gene regulatory networks.

PubMed

Chu, Brian K; Tse, Margaret J; Sato, Royce R; Read, Elizabeth L

2017-02-06

Gene regulatory networks with dynamics characterized by multiple stable states underlie cell fate-decisions. Quantitative models that can link molecular-level knowledge of gene regulation to a global understanding of network dynamics have the potential to guide cell-reprogramming strategies. Networks are often modeled by the stochastic Chemical Master Equation, but methods for systematic identification of key properties of the global dynamics are currently lacking. The method identifies the number, phenotypes, and lifetimes of long-lived states for a set of common gene regulatory network models. Application of transition path theory to the constructed Markov State Model decomposes global dynamics into a set of dominant transition paths and associated relative probabilities for stochastic state-switching. In this proof-of-concept study, we found that the Markov State Model provides a general framework for analyzing and visualizing stochastic multistability and state-transitions in gene networks. Our results suggest that this framework-adopted from the field of atomistic Molecular Dynamics-can be a useful tool for quantitative Systems Biology at the network scale.

Hyper-elastoplastic/damage modeling of rock with application to porous limestone

DOE PAGES

Bennett, Kane C.; Borja, Ronaldo I.

2018-03-13

Relations between porosity, damage, and bulk plasticity are examined in the context of continuum damage and hyper-elastoplasticity of porous rocks. Attention is given to a thermodynamically consistent derivation of the damage evolution equations and their role in the constitutive equations, for which the Eshelby stress is found to be important. The provided phenomenological framework allows for volumetric damage associated with pore growth to be distinguished from the isochoric damage associated with distributed microcracks, and a novel Drucker-Prager/cap type material model that includes damage evolution is presented. The model is shown to capture well the hardening/softening behavior and pressure dependence ofmore » the so-called brittle-ductile transition by comparison with confined triaxial compression measurements from the literature. Non-linear finite element simulations are also provided of the prediction of damage within porous limestone around a horizontal borehole wall.« less

Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Karpel, Mordechay

1989-01-01

Various control analysis, design, and simulation techniques for aeroelastic applications require the equations of motion to be cast in a linear time-invariant state-space form. Unsteady aerodynamics forces have to be approximated as rational functions of the Laplace variable in order to put them in this framework. For the minimum-state method, the number of denominator roots in the rational approximation. Results are shown of applying various approximation enhancements (including optimization, frequency dependent weighting of the tabular data, and constraint selection) with the minimum-state formulation to the active flexible wing wind-tunnel model. The results demonstrate that good models can be developed which have an order of magnitude fewer augmenting aerodynamic equations more than traditional approaches. This reduction facilitates the design of lower order control systems, analysis of control system performance, and near real-time simulation of aeroservoelastic phenomena.

Hyper-elastoplastic/damage modeling of rock with application to porous limestone

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

Bennett, Kane C.; Borja, Ronaldo I.

Relations between porosity, damage, and bulk plasticity are examined in the context of continuum damage and hyper-elastoplasticity of porous rocks. Attention is given to a thermodynamically consistent derivation of the damage evolution equations and their role in the constitutive equations, for which the Eshelby stress is found to be important. The provided phenomenological framework allows for volumetric damage associated with pore growth to be distinguished from the isochoric damage associated with distributed microcracks, and a novel Drucker-Prager/cap type material model that includes damage evolution is presented. The model is shown to capture well the hardening/softening behavior and pressure dependence ofmore » the so-called brittle-ductile transition by comparison with confined triaxial compression measurements from the literature. Non-linear finite element simulations are also provided of the prediction of damage within porous limestone around a horizontal borehole wall.« less

Growth Angle: A Microscopic View

NASA Technical Reports Server (NTRS)

Mazuruk, Konstantin; Croll, Arne; Volz, Martin P.

2017-01-01

A microscopic continuum mechanical model of the growth angle is proposed. It is based on the van der Waals type framework that is used for surface force phenomena. The obtained augmented Laplace type integro-differential equations are, in general, difficult to analyze. Here we focused primarily on the particular case of equal melt and crystal surface energies. We derived an approximate equation for the meniscus shape, and obtained an analytical relationship between the contact and the growth angle. Interestingly, the same result can be obtained using the macroscopic model of Herring. The case of a macroscopically sharp corner is also considered. For this case, the macroscopic angle is not defined and it can be any angle between the contact angles of both flat surfaces. The microscopic model yields the smooth shape for the meniscus that also is not unique, but depends on the initial position of the meniscus.

Identification of dominant interactions between climatic seasonality, catchment characteristics and agricultural activities on Budyko-type equation parameter estimation

NASA Astrophysics Data System (ADS)

Xing, Wanqiu; Wang, Weiguang; Shao, Quanxi; Yong, Bin

2018-01-01

Quantifying precipitation (P) partition into evapotranspiration (E) and runoff (Q) is of great importance for global and regional water availability assessment. Budyko framework serves as a powerful tool to make simple and transparent estimation for the partition, using a single parameter, to characterize the shape of the Budyko curve for a "specific basin", where the single parameter reflects the overall effect by not only climatic seasonality, catchment characteristics (e.g., soil, topography and vegetation) but also agricultural activities (e.g., cultivation and irrigation). At the regional scale, these influencing factors are interconnected, and the interactions between them can also affect the single parameter of Budyko-type equations' estimating. Here we employ the multivariate adaptive regression splines (MARS) model to estimate the Budyko curve shape parameter (n in the Choudhury's equation, one form of the Budyko framework) of the selected 96 catchments across China using a data set of long-term averages for climatic seasonality, catchment characteristics and agricultural activities. Results show average storm depth (ASD), vegetation coverage (M), and seasonality index of precipitation (SI) are three statistically significant factors affecting the Budyko parameter. More importantly, four pairs of interactions are recognized by the MARS model as: The interaction between CA (percentage of cultivated land area to total catchment area) and ASD shows that the cultivation can weaken the reducing effect of high ASD (>46.78 mm) on the Budyko parameter estimating. Drought (represented by the value of Palmer drought severity index < -0.74) and uneven distribution of annual rainfall (represented by the value of coefficient of variation of precipitation > 0.23) tend to enhance the Budyko parameter reduction by large SI (>0.797). Low vegetation coverage (34.56%) is likely to intensify the rising effect on evapotranspiration ratio by IA (percentage of irrigation area to total catchment area). The Budyko n values estimated by the MARS model reproduce the calculated ones by the observation well for the selected 96 catchments (with R = 0.817, MAE = 4.09). Compared to the multiple stepwise regression model estimating the parameter n taken the influencing factors as independent inputs, the MARS model enhances the capability of the Budyko framework for assessing water availability at regional scale using readily available data.

Validation of an Information-Motivation-Behavioral Skills model of diabetes self-care (IMB-DSC).

PubMed

Osborn, Chandra Y; Egede, Leonard E

2010-04-01

Comprehensive behavior change frameworks are needed to provide guidance for the design, implementation, and evaluation of diabetes self-care programs in diverse populations. We applied the Information-Motivation-Behavioral Skills (IMB) model, a well-validated, comprehensive health behavior change framework, to diabetes self-care. Patients with diabetes were recruited from an outpatient clinic. Information gathered pertained to demographics, diabetes knowledge (information); diabetes fatalism (personal motivation); social support (social motivation); and diabetes self-care (behavior). Hemoglobin A1C values were extracted from the patient medical record. Structural equation models tested the IMB framework. More diabetes knowledge (r=0.22 p<0.05), less fatalistic attitudes (r=-0.20, p<0.05), and more social support (r=0.27, p<0.01) were independent, direct predictors of diabetes self-care behavior; and through behavior, were related to glycemic control (r=-0.20, p<0.05). Consistent with the IMB model, having more information (more diabetes knowledge), personal motivation (less fatalistic attitudes), and social motivation (more social support) was associated with behavior; and behavior was the sole predictor of glycemic control. The IMB model is an appropriate, comprehensive health behavior change framework for diabetes self-care. The findings indicate that in addition to knowledge, diabetes education programs should target personal and social motivation to effect behavior change. 2009 Elsevier Ireland Ltd. All rights reserved.

A thermodynamic framework for the study of crystallization in polymers

NASA Astrophysics Data System (ADS)

Rao, I. J.; Rajagopal, K. R.

In this paper, we present a new thermodynamic framework within the context of continuum mechanics, to predict the behavior of crystallizing polymers. The constitutive models that are developed within this thermodynamic setting are able to describe the main features of the crystallization process. The model is capable of capturing the transition from a fluid like behavior to a solid like behavior in a rational manner without appealing to any adhoc transition criterion. The anisotropy of the crystalline phase is built into the model and the specific anisotropy of the crystalline phase depends on the deformation in the melt. These features are incorporated into a recent framework that associates different natural configurations and material symmetries with distinct microstructural features within the body that arise during the process under consideration. Specific models are generated by choosing particular forms for the internal energy, entropy and the rate of dissipation. Equations governing the evolution of the natural configurations and the rate of crystallization are obtained by maximizing the rate of dissipation, subject to appropriate constraints. The initiation criterion, marking the onset of crystallization, arises naturally in this setting in terms of the thermodynamic functions. The model generated within such a framework is used to simulate bi-axial extension of a polymer film that is undergoing crystallization. The predictions of the theory that has been proposed are consistent with the experimental results (see [28] and [7]).

Dynamic optimization and its relation to classical and quantum constrained systems

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

2017-08-01

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

Determining rural risk for aneurysmal subarachnoid hemorrhages: A structural equation modeling approach.

PubMed

Nichols, Linda Jayne; Gall, Seana; Stirling, Christine

2016-01-01

An aneurysmal subarachnoid hemorrhage (aSAH) carries a high disability burden. The true impact of rurality as a predictor of outcome severity is unknown. Our aim is to clarify the relationship between the proposed explanations of regional and rural health disparities linked to severity of outcome following an aSAH. An initial literature search identified limited data directly linking geographical location, rurality, rural vulnerability, and aSAH. A further search noting parallels with ischemic stroke and acute myocardial infarct literature presented a number of diverse and interrelated predictors. This a priori knowledge informed the development of a conceptual framework that proposes the relationship between rurality and severity of outcome following an aSAH utilizing structural equation modeling. The presented conceptual framework explores a number of system, environmental, and modifiable risk factors. Socioeconomic characteristics, modifiable risk factors, and timely treatment that were identified as predictors of severity of outcome following an aSAH and within each of these defined predictors a number of contributing specific individual predictors are proposed. There are considerable gaps in the current knowledge pertaining to the impact of rurality on the severity of outcome following an aSAH. Absent from the literature is any investigation of the cumulative impact and multiplicity of risk factors associated with rurality. The proposed conceptual framework hypothesizes a number of relationships between both individual level and system level predictors, acknowledging that intervening predictors may mediate the effect of one variable on another.

Asymptotic-Preserving methods and multiscale models for plasma physics

NASA Astrophysics Data System (ADS)

Degond, Pierre; Deluzet, Fabrice

2017-05-01

The purpose of the present paper is to provide an overview of Asymptotic-Preserving methods for multiscale plasma simulations by addressing three singular perturbation problems. First, the quasi-neutral limit of fluid and kinetic models is investigated in the framework of non-magnetized as well as magnetized plasmas. Second, the drift limit for fluid descriptions of thermal plasmas under large magnetic fields is addressed. Finally efficient numerical resolutions of anisotropic elliptic or diffusion equations arising in magnetized plasma simulation are reviewed.

Toward Improved Fidelity of Thermal Explosion Simulations

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

Nichols, A L; Becker, R; Howard, W M

2009-07-17

We will present results of an effort to improve the thermal/chemical/mechanical modeling of HMX based explosive like LX04 and LX10 for thermal cook-off. The original HMX model and analysis scheme were developed by Yoh et.al. for use in the ALE3D modeling framework. The current results were built to remedy the deficiencies of that original model. We concentrated our efforts in four areas. The first area was addition of porosity to the chemical material model framework in ALE3D that is used to model the HMX explosive formulation. This is needed to handle the roughly 2% porosity in solid explosives. The secondmore » area was the improvement of the HMX reaction network, which included the inclusion of a reactive phase change model base on work by Henson et.al. The third area required adding early decomposition gas species to the CHEETAH material database to develop more accurate equations of state for gaseous intermediates and products. Finally, it was necessary to improve the implicit mechanics module in ALE3D to more naturally handle the long time scales associated with thermal cook-off. The application of the resulting framework to the analysis of the Scaled Thermal Explosion (STEX) experiments will be discussed.« less

Proposed Framework for Determining Added Mass of Orion Drogue Parachutes

NASA Technical Reports Server (NTRS)

Fraire, Usbaldo, Jr.; Dearman, James; Morris, Aaron

2011-01-01

The Crew Exploration Vehicle (CEV) Parachute Assembly System (CPAS) project is executing a program to qualify a parachute system for a next generation human spacecraft. Part of the qualification process involves predicting parachute riser tension during system descent with flight simulations. Human rating the CPAS hardware requires a high degree of confidence in the simulation models used to predict parachute loads. However, uncertainty exists in the heritage added mass models used for loads predictions due to a lack of supporting documentation and data. Even though CPAS anchors flight simulation loads predictions to flight tests, extrapolation of these models outside the test regime carries the risk of producing non-bounding loads. A set of equations based on empirically derived functions of skirt radius is recommended as the simplest and most viable method to test and derive an enhanced added mass model for an inflating parachute. This will increase confidence in the capability to predict parachute loads. The selected equations are based on those published in A Simplified Dynamic Model of Parachute Inflation by Dean Wolf. An Ames 80x120 wind tunnel test campaign is recommended to acquire the reefing line tension and canopy photogrammetric data needed to quantify the terms in the Wolf equations and reduce uncertainties in parachute loads predictions. Once the campaign is completed, the Wolf equations can be used to predict loads in a typical CPAS Drogue Flight test. Comprehensive descriptions of added mass test techniques from the Apollo Era to the current CPAS project are included for reference.

Parallelization of fine-scale computation in Agile Multiscale Modelling Methodology

NASA Astrophysics Data System (ADS)

Macioł, Piotr; Michalik, Kazimierz

2016-10-01

Nowadays, multiscale modelling of material behavior is an extensively developed area. An important obstacle against its wide application is high computational demands. Among others, the parallelization of multiscale computations is a promising solution. Heterogeneous multiscale models are good candidates for parallelization, since communication between sub-models is limited. In this paper, the possibility of parallelization of multiscale models based on Agile Multiscale Methodology framework is discussed. A sequential, FEM based macroscopic model has been combined with concurrently computed fine-scale models, employing a MatCalc thermodynamic simulator. The main issues, being investigated in this work are: (i) the speed-up of multiscale models with special focus on fine-scale computations and (ii) on decreasing the quality of computations enforced by parallel execution. Speed-up has been evaluated on the basis of Amdahl's law equations. The problem of `delay error', rising from the parallel execution of fine scale sub-models, controlled by the sequential macroscopic sub-model is discussed. Some technical aspects of combining third-party commercial modelling software with an in-house multiscale framework and a MPI library are also discussed.

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

NASA Astrophysics Data System (ADS)

Roohi, Ehsan; Stefanov, Stefan

2016-10-01

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

Mechanisms of complex network growth: Synthesis of the preferential attachment and fitness models

NASA Astrophysics Data System (ADS)

Golosovsky, Michael

2018-06-01

We analyze growth mechanisms of complex networks and focus on their validation by measurements. To this end we consider the equation Δ K =A (t ) (K +K0) Δ t , where K is the node's degree, Δ K is its increment, A (t ) is the aging constant, and K0 is the initial attractivity. This equation has been commonly used to validate the preferential attachment mechanism. We show that this equation is undiscriminating and holds for the fitness model [Caldarelli et al., Phys. Rev. Lett. 89, 258702 (2002), 10.1103/PhysRevLett.89.258702] as well. In other words, accepted method of the validation of the microscopic mechanism of network growth does not discriminate between "rich-gets-richer" and "good-gets-richer" scenarios. This means that the growth mechanism of many natural complex networks can be based on the fitness model rather than on the preferential attachment, as it was believed so far. The fitness model yields the long-sought explanation for the initial attractivity K0, an elusive parameter which was left unexplained within the framework of the preferential attachment model. We show that the initial attractivity is determined by the width of the fitness distribution. We also present the network growth model based on recursive search with memory and show that this model contains both the preferential attachment and the fitness models as extreme cases.

Coupled nonlinear aeroelasticity and flight dynamics of fully flexible aircraft

NASA Astrophysics Data System (ADS)

Su, Weihua

This dissertation introduces an approach to effectively model and analyze the coupled nonlinear aeroelasticity and flight dynamics of highly flexible aircraft. A reduced-order, nonlinear, strain-based finite element framework is used, which is capable of assessing the fundamental impact of structural nonlinear effects in preliminary vehicle design and control synthesis. The cross-sectional stiffness and inertia properties of the wings are calculated along the wing span, and then incorporated into the one-dimensional nonlinear beam formulation. Finite-state unsteady subsonic aerodynamics is used to compute airloads along lifting surfaces. Flight dynamic equations are then introduced to complete the aeroelastic/flight dynamic system equations of motion. Instead of merely considering the flexibility of the wings, the current work allows all members of the vehicle to be flexible. Due to their characteristics of being slender structures, the wings, tail, and fuselage of highly flexible aircraft can be modeled as beams undergoing three dimensional displacements and rotations. New kinematic relationships are developed to handle the split beam systems, such that fully flexible vehicles can be effectively modeled within the existing framework. Different aircraft configurations are modeled and studied, including Single-Wing, Joined-Wing, Blended-Wing-Body, and Flying-Wing configurations. The Lagrange Multiplier Method is applied to model the nodal displacement constraints at the joint locations. Based on the proposed models, roll response and stability studies are conducted on fully flexible and rigidized models. The impacts of the flexibility of different vehicle members on flutter with rigid body motion constraints, flutter in free flight condition, and roll maneuver performance are presented. Also, the static stability of the compressive member of the Joined-Wing configuration is studied. A spatially-distributed discrete gust model is incorporated into the time simulation of the framework. Gust responses of the Flying-Wing configuration subject to stall effects are investigated. A bilinear torsional stiffness model is introduced to study the skin wrinkling due to large bending curvature of the Flying-Wing. The numerical studies illustrate the improvements of the existing reduced-order formulation with new capabilities of both structural modeling and coupled aeroelastic and flight dynamic analysis of fully flexible aircraft.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model.

PubMed

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-28

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model

NASA Astrophysics Data System (ADS)

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-01

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

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

Chevalier, Michael W., E-mail: Michael.Chevalier@ucsf.edu; El-Samad, Hana, E-mail: Hana.El-Samad@ucsf.edu

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation timesmore » of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.« less

A Systematic Approach to Determining the Identifiability of Multistage Carcinogenesis Models.

PubMed

Brouwer, Andrew F; Meza, Rafael; Eisenberg, Marisa C

2017-07-01

Multistage clonal expansion (MSCE) models of carcinogenesis are continuous-time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous-time Markov processes. © 2016 Society for Risk Analysis.

Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations

NASA Astrophysics Data System (ADS)

Satoh, M.; Matsuno, T.; Tomita, H.; Miura, H.; Nasuno, T.; Iga, S.

2008-03-01

A new type of ultra-high resolution atmospheric global circulation model is developed. The new model is designed to perform "cloud resolving simulations" by directly calculating deep convection and meso-scale circulations, which play key roles not only in the tropical circulations but in the global circulations of the atmosphere. Since cores of deep convection have a few km in horizontal size, they have not directly been resolved by existing atmospheric general circulation models (AGCMs). In order to drastically enhance horizontal resolution, a new framework of a global atmospheric model is required; we adopted nonhydrostatic governing equations and icosahedral grids to the new model, and call it Nonhydrostatic ICosahedral Atmospheric Model (NICAM). In this article, we review governing equations and numerical techniques employed, and present the results from the unique 3.5-km mesh global experiments—with O(10 9) computational nodes—using realistic topography and land/ocean surface thermal forcing. The results show realistic behaviors of multi-scale convective systems in the tropics, which have not been captured by AGCMs. We also argue future perspective of the roles of the new model in the next generation atmospheric sciences.

A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks.

PubMed

Laomettachit, Teeraphan; Chen, Katherine C; Baumann, William T; Tyson, John J

2016-01-01

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a "standard component" modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with "standard components" can capture in quantitative detail many essential properties of cell cycle control in budding yeast.

A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks

PubMed Central

Laomettachit, Teeraphan; Chen, Katherine C.; Baumann, William T.

2016-01-01

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a “standard component” modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with “standard components” can capture in quantitative detail many essential properties of cell cycle control in budding yeast. PMID:27187804

A robust nonparametric framework for reconstruction of stochastic differential equation models

NASA Astrophysics Data System (ADS)

Rajabzadeh, Yalda; Rezaie, Amir Hossein; Amindavar, Hamidreza

2016-05-01

In this paper, we employ a nonparametric framework to robustly estimate the functional forms of drift and diffusion terms from discrete stationary time series. The proposed method significantly improves the accuracy of the parameter estimation. In this framework, drift and diffusion coefficients are modeled through orthogonal Legendre polynomials. We employ the least squares regression approach along with the Euler-Maruyama approximation method to learn coefficients of stochastic model. Next, a numerical discrete construction of mean squared prediction error (MSPE) is established to calculate the order of Legendre polynomials in drift and diffusion terms. We show numerically that the new method is robust against the variation in sample size and sampling rate. The performance of our method in comparison with the kernel-based regression (KBR) method is demonstrated through simulation and real data. In case of real dataset, we test our method for discriminating healthy electroencephalogram (EEG) signals from epilepsy ones. We also demonstrate the efficiency of the method through prediction in the financial data. In both simulation and real data, our algorithm outperforms the KBR method.

LQR Control of Shell Vibrations Via Piezoceramic Actuators

NASA Technical Reports Server (NTRS)

delRosario, R. C. H.; Smith, R. C.

1997-01-01

A model-based Linear Quadratic Regulator (LQR) method for controlling vibrations in cylindrical shells is presented. Surface-mounted piezo-ceramic patches are employed as actuators which leads to unbounded control input operators. Modified Donnell-Mushtari shell equations incorporating strong or Kelvin-Voigt damping are used to model the system. The model is then abstractly formulated in terms of sesquilinear forms. This provides a framework amenable for proving model well-posedness and convergence of LQR gains using analytic semigroup results combined with LQR theory for unbounded input operators. Finally, numerical examples demonstrating the effectiveness of the method are presented.

Differential Geometry Based Multiscale Models

PubMed Central

Wei, Guo-Wei

2010-01-01

Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that are coupled to generalized Navier–Stokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micro-macro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluid-electro-elastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation. PMID:20169418

Do the freak waves exist in soliton gas?

NASA Astrophysics Data System (ADS)

Shurgalina, Ekaterina; Pelinovsky, Efim

2016-04-01

The possibility of short-lived anomalous large waves (rogue waves) in soliton gas in the frameworks of integrable models like the Korteweg - de Vries - type equations is studied. It is shown that the dynamics of heteropolar soliton gas differs sufficiently from the dynamics of unipolar soliton fields. In particular, in the wave fields consisting of solitons with different polarities the freak wave appearance is possible. It is shown numerically in [Shurgalina and Pelinovsky, 2015]. Freak waves in the framework of the modified Korteweg-de Vries equation have been studied previously in the case of narrowband initial conditions [Grimshaw et al, 2005, 2010; Talipova, 2011]. In this case, the mechanism of freak wave generation was modulation instability of modulated quasi-sinusoidal wave packets. At the same time the modulation instability of modulated cnoidal waves was studied in the mathematical work [Driscoll & O'Neil, 1976]. Since a sequence of solitary waves can be a special case of cnoidal wave, the modulation instability can be a possible mechanism of freak wave appearance in a soliton gas. Thus, we expect that rogue wave phenomenon in soliton gas appears in nonlinear integrable models admitting an existence of modulation instability of periodic waves (like cnoidal waves). References: 1. Shurgalina E.G., Pelinovsky E.N. Dynamics of irregular wave ensembles in the coastal zone, Nizhny Novgorod State Technical University n.a. R.E. Alekseev. - Nizhny Novgorod, 2015, 179 pp. 2. Grimshaw R., Pelinovsky E., Talipova T., Sergeeva A. Rogue internal waves in the ocean: long wave model. European Physical Journal Special Topics, 2010, 185, 195 - 208. 3. Grimshaw R., Pelinovsky E., Talipova T., Ruderman M. Erdelyi R. Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg-de Vries equation. Studied Applied Mathematics, 2005, 114 (2), 189. 4. Talipova T.G. Mechanisms of internal freak waves, Fundamental and Applied Hydrophysics, 2011, 4(4), 58-70. 5. Driscoll F., O'Neil T.M. Modulational instability of cnoidal wave solutions of the modified Korteweg-de Vries equation. Journal of Mathematical Physics, 1976, 17 (7), 1196-1200.

Validating a new methodology for strain estimation from cardiac cine MRI

NASA Astrophysics Data System (ADS)

Elnakib, Ahmed; Beache, Garth M.; Gimel'farb, Georgy; Inanc, Tamer; El-Baz, Ayman

2013-10-01

This paper focuses on validating a novel framework for estimating the functional strain from cine cardiac magnetic resonance imaging (CMRI). The framework consists of three processing steps. First, the left ventricle (LV) wall borders are segmented using a level-set based deformable model. Second, the points on the wall borders are tracked during the cardiac cycle based on solving the Laplace equation between the LV edges. Finally, the circumferential and radial strains are estimated at the inner, mid-wall, and outer borders of the LV wall. The proposed framework is validated using synthetic phantoms of the material strains that account for the physiological features and the LV response during the cardiac cycle. Experimental results on simulated phantom images confirm the accuracy and robustness of our method.

Robust boundary treatment for open-channel flows in divergence-free incompressible SPH

NASA Astrophysics Data System (ADS)

Pahar, Gourabananda; Dhar, Anirban

2017-03-01

A robust Incompressible Smoothed Particle Hydrodynamics (ISPH) framework is developed to simulate specified inflow and outflow boundary conditions for open-channel flow. Being purely divergence-free, the framework offers smoothed and structured pressure distribution. An implicit treatment of Pressure Poison Equation and Dirichlet boundary condition is applied on free-surface to minimize error in velocity-divergence. Beyond inflow and outflow threshold, multiple layers of dummy particles are created according to specified boundary condition. Inflow boundary acts as a soluble wave-maker. Fluid particles beyond outflow threshold are removed and replaced with dummy particles with specified boundary velocity. The framework is validated against different cases of open channel flow with different boundary conditions. The model can efficiently capture flow evolution and vortex generation for random geometry and variable boundary conditions.

Hydrodynamic model for expansion and collisional relaxation of x-ray laser-excited multi-component nanoplasma

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

Saxena, Vikrant, E-mail: vikrant.saxena@desy.de; Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg; Ziaja, Beata, E-mail: ziaja@mail.desy.de

The irradiation of an atomic cluster with a femtosecond x-ray free-electron laser pulse results in a nanoplasma formation. This typically occurs within a few hundred femtoseconds. By this time the x-ray pulse is over, and the direct photoinduced processes no longer contributing. All created electrons within the nanoplasma are thermalized. The nanoplasma thus formed is a mixture of atoms, electrons, and ions of various charges. While expanding, it is undergoing electron impact ionization and three-body recombination. Below we present a hydrodynamic model to describe the dynamics of such multi-component nanoplasmas. The model equations are derived by taking the moments ofmore » the corresponding Boltzmann kinetic equations. We include the equations obtained, together with the source terms due to electron impact ionization and three-body recombination, in our hydrodynamic solver. Model predictions for a test case, expanding spherical Ar nanoplasma, are obtained. With this model, we complete the two-step approach to simulate x-ray created nanoplasmas, enabling computationally efficient simulations of their picosecond dynamics. Moreover, the hydrodynamic framework including collisional processes can be easily extended for other source terms and then applied to follow relaxation of any finite non-isothermal multi-component nanoplasma with its components relaxed into local thermodynamic equilibrium.« less

Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media.

PubMed

Ma, Manman; Xu, Zhenli

2014-12-28

Electrostatic correlations and variable permittivity of electrolytes are essential for exploring many chemical and physical properties of interfaces in aqueous solutions. We propose a continuum electrostatic model for the treatment of these effects in the framework of the self-consistent field theory. The model incorporates a space- or field-dependent dielectric permittivity and an excluded ion-size effect for the correlation energy. This results in a self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation together with state equations for the self energy and the dielectric function. We show that the ionic size is of significant importance in predicting a finite self energy for an ion in an inhomogeneous medium. Asymptotic approximation is proposed for the solution of a generalized Debye-Hückel equation, which has been shown to capture the ionic correlation and dielectric self energy. Through simulating ionic distribution surrounding a macroion, the modified self-consistent field model is shown to agree with particle-based Monte Carlo simulations. Numerical results for symmetric and asymmetric electrolytes demonstrate that the model is able to predict the charge inversion at high correlation regime in the presence of multivalent interfacial ions which is beyond the mean-field theory and also show strong effect to double layer structure due to the space- or field-dependent dielectric permittivity.

Is Small Still Beautiful for the Strengths and Difficulties Questionnaire? Novel Findings Using Exploratory Structural Equation Modeling.

PubMed

Garrido, Luis Eduardo; Barrada, Juan Ramón; Aguasvivas, José Armando; Martínez-Molina, Agustín; Arias, Víctor B; Golino, Hudson F; Legaz, Eva; Ferrís, Gloria; Rojo-Moreno, Luis

2018-06-01

During the present decade a large body of research has employed confirmatory factor analysis (CFA) to evaluate the factor structure of the Strengths and Difficulties Questionnaire (SDQ) across multiple languages and cultures. However, because CFA can produce strongly biased estimations when the population cross-loadings differ meaningfully from zero, it may not be the most appropriate framework to model the SDQ responses. With this in mind, the current study sought to assess the factorial structure of the SDQ using the more flexible exploratory structural equation modeling approach. Using a large-scale Spanish sample composed of 67,253 youths aged between 10 and 18 years ( M = 14.16, SD = 1.07), the results showed that CFA provided a severely biased and overly optimistic assessment of the underlying structure of the SDQ. In contrast, exploratory structural equation modeling revealed a generally weak factorial structure, including questionable indicators with large cross-loadings, multiple error correlations, and significant wording variance. A subsequent Monte Carlo study showed that sample sizes greater than 4,000 would be needed to adequately recover the SDQ loading structure. The findings from this study prevent recommending the SDQ as a screening tool and suggest caution when interpreting previous results in the literature based on CFA modeling.

Quantum model of a hysteresis in a single-domain magnetically soft ferromagnetic

NASA Astrophysics Data System (ADS)

Ignatiev, V. K.; Lebedev, N. G.; Orlov, A. A.

2018-01-01

A quantum model of a single-domain magnetically soft ferromagnetic is proposed. The α-Fe crystal in a state of the saturation magnetization and a variable magnetic field is considered as a sample. The method of an effective Hamiltonian, including the operators of the Zeeman energy, the spin-orbit interaction and the interaction with the crystal field, is used in the model. An expansion of trial single-electron wave function in a series in small parameter of the spin-orbit interaction is suggested to account for the magnetic anisotropy. Within the framework of the Heisenberg representation, the nonlinear equations of motion for the magnetization and the orbital moment of single domain are obtained. Parameters of the modelling Hamiltonian are found from a comparison with experimental data on the magnetic anisotropy of iron. A phenomenological term of the magnetic friction is introduced into equation of the magnetization motion. Nonlinear equations are solved numerically by the Runge-Kutta method. A dependence of the single domain magnetization on magnetic field intensity has a characteristic form of a hysteresis loop which parameters are quantitatively coordinated with experimental data of researches of magnetic properties of nanoparticles of iron and iron oxide. The method is extended for modelling the magnetization dynamics of multi-domain ferromagnetic in the approximation of a strong crystal field.

On the Eikonal equation in the pedestrian flow problem

NASA Astrophysics Data System (ADS)

Felcman, J.; Kubera, P.

2017-07-01

We consider the Pedestrian Flow Equations (PFEs) as the coupled system formed by the Eikonal equation and the first order hyperbolic system with the source term. The hyperbolic system consists of the continuity equation and momentum equation of fluid dynamics. Specifying the social and pressure forces in the momentum equation we come to the assumption that each pedestrian is trying to move in a desired direction (e.g. to the exit in the panic situation) with a desired velocity, where his velocity and the direction of movement depend on the density of pedestrians in his neighborhood. In [1] we used the model, where the desired direction of movement is given by the solution of the Eikonal equation (more precisely by the gradient of the solution). Here we avoid the solution of the Eikonal equation, which is the novelty of the paper. Based on the fact that the solution of the Eikonal equation has the meaning of the shortest time to reach the exit, we define explicitly such a function in the framework of the Dijkstra's algorithm for the shortest path in the graph. This is done at the discrete level of the solution. As the graph we use the underlying triangulation, where the norm of each edge is density depending and has the dimension of the time. The numerical examples of the solution of the PFEs with and without the solution of the Eikonal equation are presented.

Isotropic cosmological models in F(T,TG) theory

NASA Astrophysics Data System (ADS)

Sharif, M.; Nazir, Kanwal

2016-09-01

This paper is devoted to study evolution of the isotropic universe models in the framework of F(T,TG) gravity (T represents torsion scalar and TG is the teleparallel equivalent of the Gauss-Bonnet (GB) term). We construct F(T,TG) models by taking different eras of the universe like non-relativistic and relativistic matter eras, dark energy (DE) dominated era and their combinations. It is found that the reconstructed models indicate decreasing behavior for DE dominated era and its combination with other eras. We also discuss stability of each reconstructed model. Finally, we evaluate equation of state (EoS) parameter by considering two models and study its behavior graphically.

Modified Chapman-Enskog moment approach to diffusive phonon heat transport.

PubMed

Banach, Zbigniew; Larecki, Wieslaw

2008-12-01

A detailed treatment of the Chapman-Enskog method for a phonon gas is given within the framework of an infinite system of moment equations obtained from Callaway's model of the Boltzmann-Peierls equation. Introducing no limitations on the magnitudes of the individual components of the drift velocity or the heat flux, this method is used to derive various systems of hydrodynamic equations for the energy density and the drift velocity. For one-dimensional flow problems, assuming that normal processes dominate over resistive ones, it is found that the first three levels of the expansion (i.e., the zeroth-, first-, and second-order approximations) yield the equations of hydrodynamics which are linearly stable at all wavelengths. This result can be achieved either by examining the dispersion relations for linear plane waves or by constructing the explicit quadratic Lyapunov entropy functionals for the linear perturbation equations. The next order in the Chapman-Enskog expansion leads to equations which are unstable to some perturbations. Precisely speaking, the linearized equations of motion that describe the propagation of small disturbances in the flow have unstable plane-wave solutions in the short-wavelength limit of the dispersion relations. This poses no problem if the equations are used in their proper range of validity.

Modellus: Learning Physics with Mathematical Modelling

NASA Astrophysics Data System (ADS)

Teodoro, Vitor

Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations--differential equations--are the most important mathematical objects used for modelling Natural phenomena. In traditional approaches, they are introduced only at advanced level, because it takes a long time for students to be introduced to the fundamental principles of Calculus. With the new proposed approach, rates of change can be introduced also at early stages on learning if teachers stress semi-quantitative reasoning and use adequate computer tools. In this thesis, there is also presented Modellus, a computer tool for modelling and experimentation. This computer tool has a user interface that allows students to start doing meaningful conceptual and empirical experiments without the need to learn new syntax, as is usual with established tools. The different steps in the process of constructing and exploring models can be done with Modellus, both from physical points of view and from mathematical points of view. Modellus activities show how mathematics and physics have a unity that is very difficult to see with traditional approaches. Mathematical models are treated as concrete-abstract objects: concrete in the sense that they can be manipulated directly with a computer and abstract in the sense that they are representations of relations between variables. Data gathered from two case studies, one with secondary school students and another with first year undergraduate students support the main ideas of the thesis. Also data gathered from teachers (from college and secondary schools), mainly through an email structured questionnaire, shows that teachers agree on the potential of modelling in the learning of physics (and mathematics) and of the most important aspects of the proposed framework to integrate modelling as an essential component of the curriculum. Schools, as all institutions, change at a very slow rate. There are a multitude of reasons for this. And traditional curricula, where the emphasis is on rote learning of facts, can only be changed if schools have access to new and powerful views of learning and to new tools, that support meaningful conceptual learning and are as common and easy to use as pencil and paper.

Transfer of Training: Does It Truly Happen?: An Examination of Support, Instrumentality, Retention and Learner Readiness on the Transfer Motivation and Transfer of Training

ERIC Educational Resources Information Center

Bhatti, Muhammad Awais; Battour, Mohamed Mohamed; Sundram, Veera Pandiyan Kaliani; Othman, Akmal Aini

2013-01-01

Purpose: The purpose of this study is to highlight the importance of selected environmental, situational and individual factors in the training transfer process. Design/methodology/approach: This study proposes and tests a framework via structural equation modelling by including supervisor and peer support, instrumentality and learner readiness on…

Modelling of anisotropic growth in biological tissues. A new approach and computational aspects.

PubMed

Menzel, A

2005-03-01

In this contribution, we develop a theoretical and computational framework for anisotropic growth phenomena. As a key idea of the proposed phenomenological approach, a fibre or rather structural tensor is introduced, which allows the description of transversely isotropic material behaviour. Based on this additional argument, anisotropic growth is modelled via appropriate evolution equations for the fibre while volumetric remodelling is realised by an evolution of the referential density. Both the strength of the fibre as well as the density follow Wolff-type laws. We however elaborate on two different approaches for the evolution of the fibre direction, namely an alignment with respect to strain or with respect to stress. One of the main benefits of the developed framework is therefore the opportunity to address the evolutions of the fibre strength and the fibre direction separately. It is then straightforward to set up appropriate integration algorithms such that the developed framework fits nicely into common, finite element schemes. Finally, several numerical examples underline the applicability of the proposed formulation.

Finite element analysis of low speed viscous and inviscid aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1977-01-01

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC.