Using random walk in models specified by stochastic differential equations to determine the best expression for the bacterial growth rate

DEFF Research Database (Denmark)

method allows us to develop a new expression for the growth rate. The method is based on the stochastic continuous-discrete time state-space model, with a continuous-time state equation (a stochastic differential equation, SDE) combined with a discrete-time measurement equation. In our study the SDE...... described by Kristensen et. al [2]. The resulting time series allows us graphically to inspect the functional dependence of the growth rate on the substrate content. From the method described above we find three new plausible expressions for μ(S). Therefore we apply the likelihood-ratio test to compare...... for the Monod expression. Thus, the method was applied to successfully determine a significant better expression for the substrate dependent growth expression, and we find the method generally applicable for model development. References [1] Kristensen NR, Madsen H, Jørgensen, SB (2004) A method for systematic...

Representing Rate Equations for Enzyme-Catalyzed Reactions

Science.gov (United States)

Ault, Addison

2011-01-01

Rate equations for enzyme-catalyzed reactions are derived and presented in a way that makes it easier for the nonspecialist to see how the rate of an enzyme-catalyzed reaction depends upon kinetic constants and concentrations. This is done with distribution equations that show how the rate of the reaction depends upon the relative quantities of…

Tracer kinetics: Modelling by partial differential equations of inhomogeneous compartments with age-dependent elimination rates. Pt. 1

International Nuclear Information System (INIS)

Winkler, E.

1991-01-01

Mathematical models in tracer kinetics are usually based on ordinary differential equations which correspond to a system of kinetically homogeneous compartments (standard compartments). A generalization is possible by the admission of inhomogeneities in the behaviour of the elements belonging to a compartment. The important special case of the age-dependence of elimination rates is treated in its deterministic version. It leads to partial different equations (i.e., systems with distributed coefficients) with the 'age' or the 'residence time' of an element of the compartment as a variable additional to 'time'. The basic equations for one generalized compartment and for systems of such compartments are given together with their general solutions. (orig.) [de

Differential Equations Models to Study Quorum Sensing.

Science.gov (United States)

Pérez-Velázquez, Judith; Hense, Burkhard A

2018-01-01

Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

Thermodynamic consistency of viscoplastic material models involving external variable rates in the evolution equations for the internal variables

International Nuclear Information System (INIS)

Malmberg, T.

1993-09-01

The objective of this study is to derive and investigate thermodynamic restrictions for a particular class of internal variable models. Their evolution equations consist of two contributions: the usual irreversible part, depending only on the present state, and a reversible but path dependent part, linear in the rates of the external variables (evolution equations of ''mixed type''). In the first instance the thermodynamic analysis is based on the classical Clausius-Duhem entropy inequality and the Coleman-Noll argument. The analysis is restricted to infinitesimal strains and rotations. The results are specialized and transferred to a general class of elastic-viscoplastic material models. Subsequently, they are applied to several viscoplastic models of ''mixed type'', proposed or discussed in the literature (Robinson et al., Krempl et al., Freed et al.), and it is shown that some of these models are thermodynamically inconsistent. The study is closed with the evaluation of the extended Clausius-Duhem entropy inequality (concept of Mueller) where the entropy flux is governed by an assumed constitutive equation in its own right; also the constraining balance equations are explicitly accounted for by the method of Lagrange multipliers (Liu's approach). This analysis is done for a viscoplastic material model with evolution equations of the ''mixed type''. It is shown that this approach is much more involved than the evaluation of the classical Clausius-Duhem entropy inequality with the Coleman-Noll argument. (orig.) [de

Rate equation simulation of temporal characteristics of a pulsed dye ...

Indian Academy of Sciences (India)

-dependent, two-dimensional (in space) rate equation model of a .... fluorescence band of the dye is divided into ten wavelength segments of variable sizes. ... qualitative and reasonably good quantitative agreement with experimental results.

Laser Rate Equation Based Filtering for Carrier Recovery in Characterization and Communication

DEFF Research Database (Denmark)

Piels, Molly; Iglesias Olmedo, Miguel; Xue, Weiqi

2015-01-01

We formulate a semiconductor laser rate equationbased approach to carrier recovery in a Bayesian filtering framework. Filter stability and the effect of model inaccuracies (unknown or un-useable rate equation coefficients) are discussed. Two potential application areas are explored: laser...... characterization and carrier recovery in coherent communication. Two rate equation based Bayesian filters, the particle filter and extended Kalman filter, are used in conjunction with a coherent receiver to measure frequency noise spectrum of a photonic crystal cavity laser with less than 20 nW of fiber...

Universal Rate Model Selector: A Method to Quickly Find the Best-Fit Kinetic Rate Model for an Experimental Rate Profile

Science.gov (United States)

2017-08-01

k2 – k1) 3.3 Universal Kinetic Rate Platform Development Kinetic rate models range from pure chemical reactions to mass transfer...14 8. The rate model that best fits the experimental data is a first-order or homogeneous catalytic reaction ...Avrami (7), and intraparticle diffusion (6) rate equations to name a few. A single fitting algorithm (kinetic rate model ) for a reaction does not

Factors Associated with Asthma ED Visit Rates among Medicaid-enrolled Children: A Structural Equation Modeling Approach

Directory of Open Access Journals (Sweden)

Luceta McRoy

2017-02-01

Full Text Available Background: Asthma is one of the leading causes of emergency department visits and school absenteeism among school-aged children in the United States, but there is significant local-area variation in emergency department visit rates, as well as significant differences across racial-ethnic groups. Analysis: We first calculated emergency department (ED visit rates among Medicaid-enrolled children age 5–12 with asthma using a multi-state dataset. We then performed exploratory factor analysis using over 226 variables to assess whether they clustered around three county-level conceptual factors (socioeconomic status, healthcare capacity, and air quality thought to be associated with variation in asthma ED visit rates. Measured variables (including ED visit rate as the outcome of interest were then standardized and tested in a simple conceptual model through confirmatory factor analysis. Results: County-level (contextual variables did cluster around factors declared a priori in the conceptual model. Structural equation models connecting the ED visit rates to socioeconomic status, air quality, and healthcare system professional capacity factors (consistent with our conceptual framework converged on a solution and achieved a reasonable goodness of fit on confirmatory factor analysis. Conclusion: Confirmatory factor analysis offers an approach for quantitatively testing conceptual models of local-area variation and racial disparities in asthma-related emergency department use.

Quick and Easy Rate Equations for Multistep Reactions

Science.gov (United States)

Savage, Phillip E.

2008-01-01

Students rarely see closed-form analytical rate equations derived from underlying chemical mechanisms that contain more than a few steps unless restrictive simplifying assumptions (e.g., existence of a rate-determining step) are made. Yet, work published decades ago allows closed-form analytical rate equations to be written quickly and easily for…

Rate-equation modelling and ensemble approach to extraction of parameters for viral infection-induced cell apoptosis and necrosis

Energy Technology Data Exchange (ETDEWEB)

Domanskyi, Sergii; Schilling, Joshua E.; Privman, Vladimir, E-mail: privman@clarkson.edu [Department of Physics, Clarkson University, Potsdam, New York 13676 (United States); Gorshkov, Vyacheslav [National Technical University of Ukraine — KPI, Kiev 03056 (Ukraine); Libert, Sergiy, E-mail: libert@cornell.edu [Department of Biomedical Sciences, Cornell University, Ithaca, New York 14853 (United States)

2016-09-07

We develop a theoretical approach that uses physiochemical kinetics modelling to describe cell population dynamics upon progression of viral infection in cell culture, which results in cell apoptosis (programmed cell death) and necrosis (direct cell death). Several model parameters necessary for computer simulation were determined by reviewing and analyzing available published experimental data. By comparing experimental data to computer modelling results, we identify the parameters that are the most sensitive to the measured system properties and allow for the best data fitting. Our model allows extraction of parameters from experimental data and also has predictive power. Using the model we describe interesting time-dependent quantities that were not directly measured in the experiment and identify correlations among the fitted parameter values. Numerical simulation of viral infection progression is done by a rate-equation approach resulting in a system of “stiff” equations, which are solved by using a novel variant of the stochastic ensemble modelling approach. The latter was originally developed for coupled chemical reactions.

The specification of cross exchange rate equations used to test Purchasing Power Parity

OpenAIRE

Hunter, J; Simpson, M

2004-01-01

The Article considers the speciÞcation of models used to test Pur- chasing Power Parity when applied to cross exchange rates. SpeciÞcally, conventional dynamic models used to test stationarity of the real exchange rate are likely to be misspeciÞed, except when the parameters of each ex- change rate equation are the same

Generalized rate-equation analysis of excitation exchange between silicon nanoclusters and erbium ions

International Nuclear Information System (INIS)

Kenyon, A. J.; Wojdak, M.; Ahmad, I.; Loh, W. H.; Oton, C. J.

2008-01-01

We discuss the use of rate equations to analyze the sensitization of erbium luminescence by silicon nanoclusters. In applying the general form of second-order coupled rate-equations to the Si nanocluster-erbium system, we find that the photoluminescence dynamics cannot be described using a simple rate equation model. Both rise and fall times exhibit a stretched exponential behavior, which we propose arises from a combination of a strongly distance-dependent nanocluster-erbium interaction, along with the finite size distribution and indirect band gap of the silicon nanoclusters. Furthermore, the low fraction of erbium ions that can be excited nonresonantly is a result of the small number of ions coupled to nanoclusters

A simple algebraic cancer equation: calculating how cancers may arise with normal mutation rates

Directory of Open Access Journals (Sweden)

Shibata Darryl

2010-01-01

Full Text Available Abstract Background The purpose of this article is to present a relatively easy to understand cancer model where transformation occurs when the first cell, among many at risk within a colon, accumulates a set of driver mutations. The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology. Methods The equation [p = 1 - (1 - (1 - (1 - udkNm ] calculates the probability of cancer (p and contains five parameters: the number of divisions (d, the number of stem cells (N × m, the number of critical rate-limiting pathway driver mutations (k, and the mutation rate (u. In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell. Results When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk. Conclusions The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.

Stochastic differential equation model to Prendiville processes

International Nuclear Information System (INIS)

Granita; Bahar, Arifah

2015-01-01

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution

Stochastic differential equation model to Prendiville processes

Energy Technology Data Exchange (ETDEWEB)

Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)

2015-10-22

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

Stochastic modeling of stock price process induced from the conjugate heat equation

Science.gov (United States)

Paeng, Seong-Hun

2015-02-01

Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.

Equations for the kinetic modeling of supersonically flowing electrically excited lasers

International Nuclear Information System (INIS)

Lind, R.C.

1973-01-01

The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration--vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is discussed

Illness-death model: statistical perspective and differential equations.

Science.gov (United States)

Brinks, Ralph; Hoyer, Annika

2018-01-27

The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.

A Modified Eyring Equation for Modeling Yield and Flow Stresses of Metals at Strain Rates Ranging from 10−5 to 5 × 104 s−1

Directory of Open Access Journals (Sweden)

Ramzi Othman

2015-01-01

Full Text Available In several industrial applications, metallic structures are facing impact loads. Therefore, there is an important need for developing constitutive equations which take into account the strain rate sensitivity of their mechanical properties. The Johnson-Cook equation was widely used to model the strain rate sensitivity of metals. However, it implies that the yield and flow stresses are linearly increasing in terms of the logarithm of strain rate. This is only true up to a threshold strain rate. In this work, a three-constant constitutive equation, assuming an apparent activation volume which decreases as the strain rate increases, is applied here for some metals. It is shown that this equation fits well the experimental yield and flow stresses for a very wide range of strain rates, including quasi-static, high, and very high strain rates (from 10−5 to 5 × 104 s−1. This is the first time that a constitutive equation is showed to be able to fit the yield stress over a so large strain rate range while using only three material constants.

Rate equations modeling for hydrogen inventory studies during a real tokamak material thermal cycle

Energy Technology Data Exchange (ETDEWEB)

Bonnin, X., E-mail: xavier.bonnin@iter.org [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, 99 avenue Jean-Baptiste Clément, F-93430 Villetaneuse (France); Hodille, E. [IRFM, CEA-Cadarache, F-13108 St-Paul-Lez-Durance (France); Ning, N. [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, 99 avenue Jean-Baptiste Clément, F-93430 Villetaneuse (France); Sang, C. [School of Physics and Optoelectronics Technology, Dalian University of Technology, Dalian 116024 (China); Grisolia, Ch. [IRFM, CEA-Cadarache, F-13108 St-Paul-Lez-Durance (France)

2015-08-15

Prediction and control of tritium inventory in plasma-facing components (PFCs) is a critical nuclear safety issue for ITER and future fusion devices. This goal can be achieved through rate equations models as presented here. We calibrate our models with thermal desorption spectrometry results to obtain a validated set of material parameters relevant to hydrogen inventory processes in bulk tungsten. The best fits are obtained with two intrinsic trap types, deep and shallow, and an extrinsic trap created by plasma irradiation and plastic deformation of the tungsten matrix associated with blister formation. We then consider a realistic cycle of plasma discharges consisting of 400 s of plasma exposure followed by a resting period of 1000 s, repeating for several hours. This cycle is then closed by a long “overnight” period, thus providing an estimate of the amount of tritium retained in the PFCs after a full day of standard operation.

Exact and approximate solutions for the decades-old Michaelis-Menten equation: Progress-curve analysis through integrated rate equations.

Science.gov (United States)

Goličnik, Marko

2011-01-01

The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate V, and the Michaelis constant K(M) ) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to understand fully, or can even be misunderstood, by students when based only on the differential form of the Michaelis-Menten equation, and the variety of methods available to calculate the kinetic constants from rate versus substrate concentration "textbook data." Consequently, enzyme kinetics can be confusing if an analytical solution of the Michaelis-Menten equation is not available. Therefore, the still rarely known exact solution to the Michaelis-Menten equation is presented here through the explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, as the W(x) is not available in standard curve-fitting computer programs, the practical use of this direct solution is limited for most life-science students. Thus, the purpose of this article is to provide analytical approximations to the equation for modeling Michaelis-Menten kinetics. The elementary and explicit nature of these approximations can provide students with direct and simple estimations of kinetic parameters from raw experimental time-course data. The Michaelis-Menten kinetics studied in the latter context can provide an ideal alternative to the 100-year-old problems of data transformation, graphical visualization, and data analysis of enzyme-catalyzed reactions. Hence, the content of the course presented here could gradually become an important component of the modern biochemistry curriculum in the 21st century. Copyright © 2011 Wiley Periodicals, Inc.

Kinematic equations for resolved-rate control of an industrial robot arm

Science.gov (United States)

Barker, L. K.

1983-01-01

An operator can use kinematic, resolved-rate equations to dynamically control a robot arm by watching its response to commanded inputs. Known resolved-rate equations for the control of a particular six-degree-of-freedom industrial robot arm and proceeds to simplify the equations for faster computations are derived. Methods for controlling the robot arm in regions which normally cause mathematical singularities in the resolved-rate equations are discussed.

Numerical Analysis Of Hooke Jeeves-Runge Kutta To Determine Reaction Rate Equation In Pyrrole Polymerization

International Nuclear Information System (INIS)

Gunawan, Indra; Sulistyo, Harry; Rochmad

2001-01-01

The numerical analysis of Hooke Jeeves Methods combined with Runge Kutta Methods is used to determine the exact model of reaction rate equation of pyrrole polymerization. Chemical polymerization of pyrrole was conducted with FeCI 3 / pyrrole solution at concentration ratio of 1.62 mole / mole and 2.18 mole / mole with varrying temperature of 28, 40, 50, and 60 o C. FeCl 3 acts as an oxidation agent to form pyrrole cation that will polymerize. The numerical analysis was done to examine the exact model of reaction rate equation which is derived from reaction equation of initiation, propagation, and termination. From its numerical analysis, it is found that the pyrrole polymerization follows third order of pyrrole cation concentration

Modeling inflation rates and exchange rates in Ghana: application of multivariate GARCH models.

Science.gov (United States)

Nortey, Ezekiel Nn; Ngoh, Delali D; Doku-Amponsah, Kwabena; Ofori-Boateng, Kenneth

2015-01-01

This paper was aimed at investigating the volatility and conditional relationship among inflation rates, exchange rates and interest rates as well as to construct a model using multivariate GARCH DCC and BEKK models using Ghana data from January 1990 to December 2013. The study revealed that the cumulative depreciation of the cedi to the US dollar from 1990 to 2013 is 7,010.2% and the yearly weighted depreciation of the cedi to the US dollar for the period is 20.4%. There was evidence that, the fact that inflation rate was stable, does not mean that exchange rates and interest rates are expected to be stable. Rather, when the cedi performs well on the forex, inflation rates and interest rates react positively and become stable in the long run. The BEKK model is robust to modelling and forecasting volatility of inflation rates, exchange rates and interest rates. The DCC model is robust to model the conditional and unconditional correlation among inflation rates, exchange rates and interest rates. The BEKK model, which forecasted high exchange rate volatility for the year 2014, is very robust for modelling the exchange rates in Ghana. The mean equation of the DCC model is also robust to forecast inflation rates in Ghana.

Non-equilibrium reaction rates in chemical kinetic equations

Science.gov (United States)

Gorbachev, Yuriy

2018-05-01

Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the chemical kinetic equations has been derived. Corresponding one-temperature non-equilibrium reaction rates are expressed in terms of specific heat capacities of the species participate in the chemical reactions, bracket integrals connected with the internal energy transfer in inelastic non-reactive collisions and energy transfer coefficients. Reactions of dissociation/recombination of homonuclear and heteronuclear diatomic molecules are considered. It is shown that all reaction rates are the complex functions of the species densities, similarly to the unimolecular reaction rates. For determining the rate coefficients it is recommended to tabulate corresponding bracket integrals, additionally to the equilibrium rate constants. Correlation of the obtained results with the irreversible thermodynamics is established.

Connecting Related Rates and Differential Equations

Science.gov (United States)

Brandt, Keith

2012-01-01

This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.

A rate-equation model for polarized laser-induced fluorescence to measure electric field in glow discharge He plasmas

International Nuclear Information System (INIS)

Takiyama, K.; Watanabe, M.; Oda, T.

1998-01-01

Possibility of applying polarized laser-induced fluorescence (LIF) spectroscopy for measuring the electric field in a plasma with a large collisional depolarization has been investigated. A rate equation model including the depolarization process was employed to analyze the time evolution of LIF polarization components. The polarized LIF pulse shapes observed in the sheath of a He glow discharge plasma were successfully reproduced, and the electric field distribution was obtained with high accuracy. (author)

Non-Equilibrium Turbulence and Two-Equation Modeling

Science.gov (United States)

Rubinstein, Robert

2011-01-01

Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.

Theory of nanolaser devices: Rate equation analysis versus microscopic theory

DEFF Research Database (Denmark)

Lorke, Michael; Skovgård, Troels Suhr; Gregersen, Niels

2013-01-01

A rate equation theory for quantum-dot-based nanolaser devices is developed. We show that these rate equations are capable of reproducing results of a microscopic semiconductor theory, making them an appropriate starting point for complex device simulations of nanolasers. The input...

Validation of resting metabolic rate prediction equations for teenagers

Directory of Open Access Journals (Sweden)

Paulo Henrique Santos da Fonseca

2007-09-01

Full Text Available The resting metabolic rate (RMR can be defi ned as the minimum rate of energy spent and represents the main component of the energetic outlay. The purpose of this study is to validate equations to predict the resting metabolic rate in teenagers (103 individuals, being 51 girls and 52 boys, with age between 10 and 17 years from Florianópolis – SC – Brazil. It was measured: the body weight, body height, skinfolds and obtained the lean and body fat mass through bioimpedance. The nonproteic RMR was measured by Weir’s equation (1949, utilizing AeroSport TEEM-100 gas analyzer. The studied equations were: Harry and Benedict (1919, Schofi eld (1985, WHO/FAO/UNU (1985, Henry and Rees (1991, Molnár et al. (1998, Tverskaya et al. (1998 and Müller et al. (2004. In order to study the cross-validation of the RMR prediction equations and its standard measure (Weir 1949, the following statistics procedure were calculated: Pearson’s correlation (r ≥ 0.70, the “t” test with the signifi cance level of p0.05 in relation to the standard measure, with exception of the equations suggested for Tverskaya et al. (1998, and the two models of Müller et al (2004. Even though there was not a signifi cant difference, only the models considered for Henry and Rees (1991, and Molnár et al. (1995 had gotten constant error variation under 5%. All the equations analyzed in the study in girls had not reached criterion of correlation values of 0.70 with the indirect calorimetry. Analyzing the prediction equations of RMR in boys, all of them had moderate correlation coeffi cients with the indirect calorimetry, however below 0.70. Only the equation developed for Tverskaya et al. (1998 presented differences (p ABSTRACT0,05 em relação à medida padrão (Weir 1949, com exceção das equações sugeridas por Tverskaya et al. (1998 e os dois modelos de Müller et al (2004. Mesmo não havendo diferença signifi cativa, somente os modelos propostos por Henry e Rees (1991

Model Compaction Equation

African Journals Online (AJOL)

The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...

In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis

Science.gov (United States)

Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

2015-01-01

Background There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). Methodology We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δkm=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value of the prediction errors for methadone’s extraction and throughput were less than 2%. Conclusion ODE/PDE modeling of methadone’s hemodialysis is a new approach to study methadone’s removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone’s mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model

In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis.

Science.gov (United States)

Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

2015-01-01

There is a need to have a model to study methadone's losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone's overall intradialytic mass transfer rate coefficient, km ; and, methadone's removal rate, j ME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. The ODE/PDE model revealed a significant increase in the change of methadone's mass transfer with increased dialysate flow rate, %Δkm =18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone's mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone's removal during dialysis. The absolute value of the prediction errors for methadone's extraction and throughput were less than 2%. ODE/PDE modeling of methadone's hemodialysis is a new approach to study methadone's removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone's mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model predictive control during dialysis in humans.

On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or

Thermoviscous Model Equations in Nonlinear Acoustics

DEFF Research Database (Denmark)

Rasmussen, Anders Rønne

Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

Exploring the relationships among performance-based functional ability, self-rated disability, perceived instrumental support, and depression: a structural equation model analysis.

Science.gov (United States)

Weil, Joyce; Hutchinson, Susan R; Traxler, Karen

2014-11-01

Data from the Women's Health and Aging Study were used to test a model of factors explaining depressive symptomology. The primary purpose of the study was to explore the association between performance-based measures of functional ability and depression and to examine the role of self-rated physical difficulties and perceived instrumental support in mediating the relationship between performance-based functioning and depression. The inclusion of performance-based measures allows for the testing of functional ability as a clinical precursor to disability and depression: a critical, but rarely examined, association in the disablement process. Structural equation modeling supported the overall fit of the model and found an indirect relationship between performance-based functioning and depression, with perceived physical difficulties serving as a significant mediator. Our results highlight the complementary nature of performance-based and self-rated measures and the importance of including perception of self-rated physical difficulties when examining depression in older persons. © The Author(s) 2014.

Hybrid dynamic modeling of Escherichia coli central metabolic network combining Michaelis–Menten and approximate kinetic equations

DEFF Research Database (Denmark)

Costa, Rafael S.; Machado, Daniel; Rocha, Isabel

2010-01-01

, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis–Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action......The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters...

Consistent three-equation model for thin films

Science.gov (United States)

Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

2017-11-01

Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

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

Science.gov (United States)

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.

Mathematical modeling and the two-phase constitutive equations

International Nuclear Information System (INIS)

Boure, J.A.

1975-01-01

The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr

Rate equation modelling of erbium luminescence dynamics in erbium-doped silicon-rich-silicon-oxide

Energy Technology Data Exchange (ETDEWEB)

Shah, Miraj, E-mail: m.shah@ee.ucl.ac.uk [Department of Electronic and Electrical Engineering, UCL, Torrington Place, London WC1E 7JE (United Kingdom); Wojdak, Maciej; Kenyon, Anthony J. [Department of Electronic and Electrical Engineering, UCL, Torrington Place, London WC1E 7JE (United Kingdom); Halsall, Matthew P.; Li, Hang; Crowe, Iain F. [Photon Science Institute and School of Electrical and Electronic Engineering, University of Manchester, Sackville St Building, Manchester M13 9PL (United Kingdom)

2012-12-15

Erbium doped silicon-rich silica offers broad band and very efficient excitation of erbium photoluminescence (PL) due to a sensitization effect attributed to silicon nanocrystals (Si-nc), which grow during thermal treatment. PL decay lifetime measurements of sensitised Er{sup 3+} ions are usually reported to be stretched or multi exponential, very different to those that are directly excited, which usually show a single exponential decay component. In this paper, we report on SiO{sub 2} thin films doped with Si-nc's and erbium. Time resolved PL measurements reveal two distinct 1.54 {mu}m Er decay components; a fast microsecond component, and a relatively long lifetime component (10 ms). We also study the structural properties of these samples through TEM measurements, and reveal the formation of Er clusters. We propose that these Er clusters are responsible for the fast {mu}s decay component, and we develop rate equation models that reproduce the experimental transient observations, and can explain some of the reported transient behaviour in previously published literature.

A Model for High-Strain-Rate Deformation of Uranium-Niobium Alloys

Energy Technology Data Exchange (ETDEWEB)

F.L.Addessio; Q.H.Zuo; T.A.Mason; L.C.Brinson

2003-05-01

A thermodynamic approach is used to develop a framework for modeling uranium-niobium alloys under the conditions of high strain rate. Using this framework, a three-dimensional phenomenological model, which includes nonlinear elasticity (equation of state), phase transformation, crystal reorientation, rate-dependent plasticity, and porosity growth is presented. An implicit numerical technique is used to solve the evolution equations for the material state. Comparisons are made between the model and data for low-strain-rate loading and unloading as well as for heating and cooling experiments. Comparisons of the model and data also are made for low- and high-strain-rate uniaxial stress and uniaxial strain experiments. A uranium-6 weight percent niobium alloy is used in the comparisons of model and experiment.

Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

Science.gov (United States)

Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

2014-07-01

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

Slave equations for spin models

International Nuclear Information System (INIS)

Catterall, S.M.; Drummond, I.T.; Horgan, R.R.

1992-01-01

We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)

Rate equation analysis and non-Hermiticity in coupled semiconductor laser arrays

Science.gov (United States)

Gao, Zihe; Johnson, Matthew T.; Choquette, Kent D.

2018-05-01

Optically coupled semiconductor laser arrays are described by coupled rate equations. The coupled mode equations and carrier densities are included in the analysis, which inherently incorporate the carrier-induced nonlinearities including gain saturation and amplitude-phase coupling. We solve the steady-state coupled rate equations and consider the cavity frequency detuning and the individual laser pump rates as the experimentally controlled variables. We show that the carrier-induced nonlinearities play a critical role in the mode control, and we identify gain contrast induced by cavity frequency detuning as a unique mechanism for mode control. Photon-mediated energy transfer between cavities is also discussed. Parity-time symmetry and exceptional points in this system are studied. Unbroken parity-time symmetry can be achieved by judiciously combining cavity detuning and unequal pump rates, while broken symmetry lies on the boundary of the optical locking region. Exceptional points are identified at the intersection between broken symmetry and unbroken parity-time symmetry.

Creatinine Clearance Is Not Equal to Glomerular Filtration Rate and Cockcroft-Gault Equation Is Not Equal to CKD-EPI Collaboration Equation.

Science.gov (United States)

Fernandez-Prado, Raul; Castillo-Rodriguez, Esmeralda; Velez-Arribas, Fernando Javier; Gracia-Iguacel, Carolina; Ortiz, Alberto

2016-12-01

Direct oral anticoagulants (DOACs) may require dose reduction or avoidance when glomerular filtration rate is low. However, glomerular filtration rate is not usually measured in routine clinical practice. Rather, equations that incorporate different variables use serum creatinine to estimate either creatinine clearance in mL/min or glomerular filtration rate in mL/min/1.73 m 2 . The Cockcroft-Gault equation estimates creatinine clearance and incorporates weight into the equation. By contrast, the Modification of Diet in Renal Disease and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations estimate glomerular filtration rate and incorporate ethnicity but not weight. As a result, an individual patient may have very different renal function estimates, depending on the equation used. We now highlight these differences and discuss the impact on routine clinical care for anticoagulation to prevent embolization in atrial fibrillation. Pivotal DOAC clinical trials used creatinine clearance as a criterion for patient enrollment, and dose adjustment and Federal Drug Administration recommendations are based on creatinine clearance. However, clinical biochemistry laboratories provide CKD-EPI glomerular filtration rate estimations, resulting in discrepancies between clinical trial and routine use of the drugs. Copyright © 2016 Elsevier Inc. All rights reserved.

A Study of Residual Amplitude Modulation Suppression in Injection Locked Quantum Cascade Lasers Based on a Simplified Rate Equation Model

International Nuclear Information System (INIS)

Webb, J F; Yong, K S C; Haldar, M K

2015-01-01

Using results that come out of a simplified rate equation model, the suppression of residual amplitude modulation in injection locked quantum cascade lasers with the master laser modulated by its drive current is investigated. Quasi-static and dynamic expressions for intensity modulation are used. The suppression peaks at a specific value of the injection ratio for a given detuning and linewidth enhancement factor. The intensity modulation suppression remains constant over a range of frequencies. The effects of injection ratio, detuning, coupling efficiency and linewidth enhancement factor are considered. (paper)

Coupled force-balance and particle-occupation rate equations for high-field electron transport

International Nuclear Information System (INIS)

Lei, X. L.

2008-01-01

It is pointed out that in the framework of balance-equation approach, the coupled force-balance and particle-occupation rate equations can be used as a complete set of equations to determine the high-field transport of semiconductors in both strong and weak electron-electron interaction limits. We call to attention that the occupation rate equation conserves the total particle number and maintains the energy balance of the relative electron system, and there is no need to introduce any other term in it. The addition of an energy-drift term in the particle-occupation rate equation [Phys. Rev. B 71, 195205 (2005)] is physically inadequate for the violation of the total particle-number conservation and the energy balance. It may lead to a substantial unphysical increase of the total particle number by the application of a dc electric field

Modeling Electric Discharges with Entropy Production Rate Principles

Directory of Open Access Journals (Sweden)

Thomas Christen

2009-12-01

Full Text Available Under which circumstances are variational principles based on entropy production rate useful tools for modeling steady states of electric (gas discharge systems far from equilibrium? It is first shown how various different approaches, as Steenbeck’s minimum voltage and Prigogine’s minimum entropy production rate principles are related to the maximum entropy production rate principle (MEPP. Secondly, three typical examples are discussed, which provide a certain insight in the structure of the models that are candidates for MEPP application. It is then thirdly argued that MEPP, although not being an exact physical law, may provide reasonable model parameter estimates, provided the constraints contain the relevant (nonlinear physical effects and the parameters to be determined are related to disregarded weak constraints that affect mainly global entropy production. Finally, it is additionally conjectured that a further reason for the success of MEPP in certain far from equilibrium systems might be based on a hidden linearity of the underlying kinetic equation(s.

Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions.

Science.gov (United States)

Langlands, T A M; Henry, B I; Wearne, S L

2009-12-01

We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.

Structural-equation models of migration: an example from the Upper Midwest USA.

Science.gov (United States)

Cadwallader, M

1985-01-01

"To date, most migration models have been specified in terms of a single equation, whereby a set of regional characteristics are used to predict migration rates for various kinds of spatial units. These models are inadequate in at least two respects. First, they omit any causal links between the explanatory variables, thus ignoring indirect effects between these variables and migration. Second, they ignore the possibility of reciprocal causation, or feedback effects, between migration and the explanatory variables...." The author uses data for State Economic Areas to construct a path model and simultaneous-equation model to identify both indirect and feedback effects on migration in the Upper Midwestern United States. "On the basis of the path model, it is suggested that the direct effects of many variables on migration are at least partially offset by the indirect effects, whereas the simultaneous-equation model emphasizes the reciprocal relationship between income and migration." excerpt

In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis

Directory of Open Access Journals (Sweden)

Linares OA

2015-07-01

Full Text Available Oscar A Linares,1 William E Schiesser,2 Jeffrey Fudin,3–6 Thien C Pham,6 Jeffrey J Bettinger,6 Roy O Mathew,6 Annemarie L Daly7 1Translational Genomic Medicine Lab, Plymouth Pharmacokinetic Modeling Study Group, Plymouth, MI, 2Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA, 3University of Connecticut School of Pharmacy, Storrs, CT, 4Western New England College of Pharmacy, Springfield, MA, 5Albany College of Pharmacy and Health Sciences, Albany, NY, 6Stratton VA Medical Center, Albany, NY, 7Grace Hospice of Ann Arbor, Ann Arbor, MI, USA Background: There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim: To build a one-dimensional (1-D, hollow-fiber geometry, ordinary differential equation (ODE and partial differential equation (PDE countercurrent hemodialyzer model (ODE/PDE model. Methodology: We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results: The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δ km=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11. This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11. The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value

Dissolution process analysis using model-free Noyes-Whitney integral equation.

Science.gov (United States)

Hattori, Yusuke; Haruna, Yoshimasa; Otsuka, Makoto

2013-02-01

Drug dissolution process of solid dosages is theoretically described by Noyes-Whitney-Nernst equation. However, the analysis of the process is demonstrated assuming some models. Normally, the model-dependent methods are idealized and require some limitations. In this study, Noyes-Whitney integral equation was proposed and applied to represent the drug dissolution profiles of a solid formulation via the non-linear least squares (NLLS) method. The integral equation is a model-free formula involving the dissolution rate constant as a parameter. In the present study, several solid formulations were prepared via changing the blending time of magnesium stearate (MgSt) with theophylline monohydrate, α-lactose monohydrate, and crystalline cellulose. The formula could excellently represent the dissolution profile, and thereby the rate constant and specific surface area could be obtained by NLLS method. Since the long time blending coated the particle surface with MgSt, it was found that the water permeation was disturbed by its layer dissociating into disintegrant particles. In the end, the solid formulations were not disintegrated; however, the specific surface area gradually increased during the process of dissolution. The X-ray CT observation supported this result and demonstrated that the rough surface was dominant as compared to dissolution, and thus, specific surface area of the solid formulation gradually increased. Copyright © 2012 Elsevier B.V. All rights reserved.

Impact of noise on self-rated job satisfaction and health in open-plan offices: a structural equation modelling approach.

Science.gov (United States)

Lee, Pyoung Jik; Lee, Byung Kwon; Jeon, Jin Yong; Zhang, Mei; Kang, Jian

2016-01-01

This study uses a structural equation model to examine the effects of noise on self-rated job satisfaction and health in open-plan offices. A total of 334 employees from six open-plan offices in China and Korea completed a questionnaire survey. The questionnaire included questions assessing noise disturbances and speech privacy, as well as job satisfaction and health. The results indicated that noise disturbance affected self-rated health. Contrary to popular expectation, the relationship between noise disturbance and job satisfaction was not significant. Rather, job satisfaction and satisfaction with the environment were negatively correlated with lack of speech privacy. Speech privacy was found to be affected by noise sensitivity, and longer noise exposure led to decreased job satisfaction. There was also evidence that speech privacy was a stronger predictor of satisfaction with environment and job satisfaction for participants with high noise sensitivity. In addition, fit models for employees from China and Korea showed slight differences. This study is motivated by strong evidence that noise is the key source of complaints in open-plan offices. Survey results indicate that self-rated job satisfaction of workers in open-plan offices was negatively affected by lack of speech privacy and duration of disturbing noise.

Modification of the Kolmogorov-Johnson-Mehl-Avrami rate equation for non-isothermal experiments and its analytical solution

OpenAIRE

Farjas, Jordi; Roura, Pere

2008-01-01

Avrami's model describes the kinetics of phase transformation under the assumption of spatially random nucleation. In this paper we provide a quasi-exact analytical solution of Avrami's model when the transformation takes place under continuous heating. This solution has been obtained with different activation energies for both nucleation and growth rates. The relation obtained is also a solution of the so-called Kolmogorov-Johnson-Mehl-Avrami transformation rate equation. The corresponding n...

A matlab framework for estimation of NLME models using stochastic differential equations: applications for estimation of insulin secretion rates.

Science.gov (United States)

Mortensen, Stig B; Klim, Søren; Dammann, Bernd; Kristensen, Niels R; Madsen, Henrik; Overgaard, Rune V

2007-10-01

The non-linear mixed-effects model based on stochastic differential equations (SDEs) provides an attractive residual error model, that is able to handle serially correlated residuals typically arising from structural mis-specification of the true underlying model. The use of SDEs also opens up for new tools for model development and easily allows for tracking of unknown inputs and parameters over time. An algorithm for maximum likelihood estimation of the model has earlier been proposed, and the present paper presents the first general implementation of this algorithm. The implementation is done in Matlab and also demonstrates the use of parallel computing for improved estimation times. The use of the implementation is illustrated by two examples of application which focus on the ability of the model to estimate unknown inputs facilitated by the extension to SDEs. The first application is a deconvolution-type estimation of the insulin secretion rate based on a linear two-compartment model for C-peptide measurements. In the second application the model is extended to also give an estimate of the time varying liver extraction based on both C-peptide and insulin measurements.

Status of rates and rate equations for thermal leptogenesis

Science.gov (United States)

Biondini, S.; Bödeker, D.; Brambilla, N.; Garny, M.; Ghiglieri, J.; Hohenegger, A.; Laine, M.; Mendizabal, S.; Millington, P.; Salvio, A.; Vairo, A.

2018-02-01

In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter-antimatter asymmetry generated when the temperature of the hot plasma T exceeds the right-handed neutrino mass scale M is efficiently erased, and one can focus on the temperature window T ≪ M. We review recent progress in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number densities, their rigorous formulation and applicability are also discussed.

Emergent user behavior on Twitter modelled by a stochastic differential equation.

Science.gov (United States)

Mollgaard, Anders; Mathiesen, Joachim

2015-01-01

Data from the social-media site, Twitter, is used to study the fluctuations in tweet rates of brand names. The tweet rates are the result of a strongly correlated user behavior, which leads to bursty collective dynamics with a characteristic 1/f noise. Here we use the aggregated "user interest" in a brand name to model collective human dynamics by a stochastic differential equation with multiplicative noise. The model is supported by a detailed analysis of the tweet rate fluctuations and it reproduces both the exact bursty dynamics found in the data and the 1/f noise.

Modeling Long-term Behavior of Stock Market Prices Using Differential Equations

Science.gov (United States)

Yang, Xiaoxiang; Zhao, Conan; Mazilu, Irina

2015-03-01

Due to incomplete information available in the market and uncertainties associated with the price determination process, the stock prices fluctuate randomly during a short period of time. In the long run, however, certain economic factors, such as the interest rate, the inflation rate, and the company's revenue growth rate, will cause a gradual shift in the stock price. Thus, in this paper, a differential equation model has been constructed in order to study the effects of these factors on the stock prices. The model obtained accurately describes the general trends in the AAPL and XOM stock price changes over the last ten years.

Structural equation modeling methods and applications

CERN Document Server

Wang, Jichuan

2012-01-01

A reference guide for applications of SEM using Mplus Structural Equation Modeling: Applications Using Mplus is intended as both a teaching resource and a reference guide. Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling (SEM). Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, Mplus, is also featured and provides researchers with a

Modeling the exchange rate of the euro against the dollar using the ARCH/GARCH models

Directory of Open Access Journals (Sweden)

Kovačević Radovan

2016-01-01

Full Text Available The analysis of time series with conditional heteroskedasticity (changeable time variability, conditional variance instability, the phenomenon called volatility is the main task of ARCH and GARCH models. The aim of these models is to calculate some of the volatility indicators needed for financial decisions. This paper examines the performance of generalized autoregressive conditional heteroscedasticity (GARCH model in modeling the daily changes of the log exchange rate of the euro against the dollar. Several GARCH models have been applied for modeling the daily log exchange rate returns of the euro, with a different number of parameters. The characteristic of estimated GARCH models is that the obtained coefficients of lagged squared residuals and the conditional variance parameters in the equation of conditional variance have a strong statistical significance. The sum of these two coefficients' estimates is close to a unit, which is typical for GARCH models that are applied on the data of financial assets returns. This means that the shocks in the conditional variance equation will be long lasting. The great value of the sum of these two coefficients shows that the high rates of positive or negative returns leads to a large forecasted value of the variance in the prolonged period. The asymmetrical EGARCH (1,1 model has showed the best results in modeling the euro exchange rate returns. The asymmetry term in the conditional variance equation of this model is negative and statistically significant. A negative value of this term suggests that the positive shock has less impact on the conditional variance than the negative shocks. The asymmetric EGARCH (1,1 model provides evidence of a leverage effect.

Predicting fractional bed load transport rates: Application of the Wilcock‐Crowe equations to a regulated gravel bed river

Science.gov (United States)

Gaeuman, David; Andrews, E.D.; Krause, Andreas; Smith, Wes

2009-01-01

Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock‐Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (τ*rm) is largest near the dam, but varies relatively little between the more downstream locations. The relation between τ*rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock‐Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock‐Crowe equations nonetheless consistently under‐predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of τ*rm estimated from bed load samples are up to 50% larger than those predicted with the Wilcock‐Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to the Wilcock‐Crowe equation for determining τ*rm and the hiding function used to scale τ*rm to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River.

General particle transport equation. Final report

International Nuclear Information System (INIS)

Lafi, A.Y.; Reyes, J.N. Jr.

1994-12-01

The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

Population decay time and distribution of exciton states analyzed by rate equations based on theoretical phononic and electron-collisional rate coefficients

Science.gov (United States)

Oki, Kensuke; Ma, Bei; Ishitani, Yoshihiro

2017-11-01

Population distributions and transition fluxes of the A exciton in bulk GaN are theoretically analyzed using rate equations of states of the principal quantum number n up to 5 and the continuum. These rate equations consist of the terms of radiative, electron-collisional, and phononic processes. The dependence of the rate coefficients on temperature is revealed on the basis of the collisional-radiative model of hydrogen plasma for the electron-collisional processes and theoretical formulation using Fermi's "golden rule" for the phononic processes. The respective effects of the variations in electron, exciton, and lattice temperatures are exhibited. This analysis is a base of the discussion on nonthermal equilibrium states of carrier-exciton-phonon dynamics. It is found that the exciton dissociation is enhanced even below 150 K mainly by the increase in the lattice temperature. When the thermal-equilibrium temperature increases, the population fluxes between the states of n >1 and the continuum become more dominant. Below 20 K, the severe deviation from the Saha-Boltzmann distribution occurs owing to the interband excitation flux being higher than the excitation flux from the 1 S state. The population decay time of the 1 S state at 300 K is more than ten times longer than the recombination lifetime of excitons with kinetic energy but without the upper levels (n >1 and the continuum). This phenomenon is caused by a shift of population distribution to the upper levels. This phonon-exciton-radiation model gives insights into the limitations of conventional analyses such as the ABC model, the Arrhenius plot, the two-level model (n =1 and the continuum), and the neglect of the upper levels.

Meta-analysis a structural equation modeling approach

CERN Document Server

Cheung, Mike W-L

2015-01-01

Presents a novel approach to conducting meta-analysis using structural equation modeling. Structural equation modeling (SEM) and meta-analysis are two powerful statistical methods in the educational, social, behavioral, and medical sciences. They are often treated as two unrelated topics in the literature. This book presents a unified framework on analyzing meta-analytic data within the SEM framework, and illustrates how to conduct meta-analysis using the metaSEM package in the R statistical environment. Meta-Analysis: A Structural Equation Modeling Approach begins by introducing the impo

Formal derivation of a 6 equation macro scale model for two-phase flows - link with the 4 equation macro scale model implemented in Flica 4; Etablissement formel d'un modele diphasique macroscopique a 6 equations - lien avec le modele macroscopique a 4 equations flica 4

Energy Technology Data Exchange (ETDEWEB)

Gregoire, O

2008-07-01

In order to simulate nuclear reactor cores, we presently use the 4 equation model implemented within FLICA4 code. This model is complemented with 2 algebraic closures for thermal disequilibrium and relative velocity between phases. Using such closures, means an 'a priori' knowledge of flows calculated in order to ensure that modelling assumptions apply. In order to improve the degree of universality to our macroscopic modelling, we propose in the report to derive a more general 6 equation model (balance equations for mass, momentum and enthalpy for each phase) for 2-phase flows. We apply the up-scaling procedure (Whitaker, 1999) classically used in porous media analysis to the statistically averaged equations (Aniel-Buchheit et al., 2003). By doing this, we apply the double-averaging procedure (Pedras and De Lemos, 2001 and Pinson et al. 2006): statistical and spatial averages. Then, using weighted averages (analogous to Favre's average) we extend the spatial averaging concept to variable density and 2-phase flows. This approach allows the global recovering of the structure of the systems of equations implemented in industrial codes. Supplementary contributions, such as dispersion, are also highlighted. Mechanical and thermal exchanges between solids and fluid are formally derived. Then, thanks to realistic simplifying assumptions, we show how it is possible to derive the original 4 equation model from the full 6 equation model. (author)

Comparisons of Multilevel Modeling and Structural Equation Modeling Approaches to Actor-Partner Interdependence Model.

Science.gov (United States)

Hong, Sehee; Kim, Soyoung

2018-01-01

There are basically two modeling approaches applicable to analyzing an actor-partner interdependence model: the multilevel modeling (hierarchical linear model) and the structural equation modeling. This article explains how to use these two models in analyzing an actor-partner interdependence model and how these two approaches work differently. As an empirical example, marital conflict data were used to analyze an actor-partner interdependence model. The multilevel modeling and the structural equation modeling produced virtually identical estimates for a basic model. However, the structural equation modeling approach allowed more realistic assumptions on measurement errors and factor loadings, rendering better model fit indices.

A first course in structural equation modeling

CERN Document Server

Raykov, Tenko

2012-01-01

In this book, authors Tenko Raykov and George A. Marcoulides introduce students to the basics of structural equation modeling (SEM) through a conceptual, nonmathematical approach. For ease of understanding, the few mathematical formulas presented are used in a conceptual or illustrative nature, rather than a computational one.Featuring examples from EQS, LISREL, and Mplus, A First Course in Structural Equation Modeling is an excellent beginner's guide to learning how to set up input files to fit the most commonly used types of structural equation models with these programs. The basic ideas and methods for conducting SEM are independent of any particular software.Highlights of the Second Edition include: Review of latent change (growth) analysis models at an introductory level Coverage of the popular Mplus program Updated examples of LISREL and EQS A CD that contains all of the text's LISREL, EQS, and Mplus examples.A First Course in Structural Equation Modeling is intended as an introductory book for students...

Association between Body Image Dissatisfaction and Self-Rated Health, as Mediated by Physical Activity and Eating Habits: Structural Equation Modelling in ELSA-Brasil.

Science.gov (United States)

de Oliveira da Silva, Patricia; Miguez Nery Guimarães, Joanna; Härter Griep, Rosane; Caetano Prates Melo, Enirtes; Maria Alvim Matos, Sheila; Del Carmem Molina, Maria; Maria Barreto, Sandhi; de Jesus Mendes da Fonseca, Maria

2018-04-18

This study investigated whether the association between body image dissatisfaction and poor self-rated health is mediated by insufficient physical activity and unhealthy eating habits. The participants were 6727 men and 8037 women from the baseline (2008–2010) of the Longitudinal Study of Adult Health (Estudo Longitudinal de Saúde do Adulto, ELSA-Brasil). Structural equation modelling was used. Associations were found between body image dissatisfaction and poor self-rated health in both sexes. Insufficient physical activity was a mediator. However, unhealthy eating habits were found to exert a mediator effect only via insufficient physical activity. Body image dissatisfaction was found to associate, both directly and possibly indirectly, with poor self-rated health, mediated by insufficient physical activity and unhealthy eating habits. Accordingly, encouraging physical activity and healthy eating can contribute to reducing body image dissatisfaction and favour better self-rated health.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model

Science.gov (United States)

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.

Structural Equation Model Trees

Science.gov (United States)

Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

2013-01-01

In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…

Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation

KAUST Repository

Said-Houari, Belkacem

2014-01-01

In this paper, we study the decay rates of solutions for the generalized Benjamin-Bona-Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314-340 and Nonlinear Anal. 75(7) (2012), 3385-3392. © 2014-IOS Press.

Using Difference Equation to Model Discrete-time Behavior in System Dynamics Modeling

NARCIS (Netherlands)

Hesan, R.; Ghorbani, A.; Dignum, M.V.

2014-01-01

In system dynamics modeling, differential equations have been used as the basic mathematical operator. Using difference equation to build system dynamics models instead of differential equation, can be insightful for studying small organizations or systems with micro behavior. In this paper we

Bayesian simultaneous equation models for the analysis of energy intake and partitioning in growing pigs

DEFF Research Database (Denmark)

Strathe, Anders Bjerring; Jørgensen, Henry; Kebreab, E

2012-01-01

ABSTRACT SUMMARY The objective of the current study was to develop Bayesian simultaneous equation models for modelling energy intake and partitioning in growing pigs. A key feature of the Bayesian approach is that parameters are assigned prior distributions, which may reflect the current state...... of nature. In the models, rates of metabolizable energy (ME) intake, protein deposition (PD) and lipid deposition (LD) were treated as dependent variables accounting for residuals being correlated. Two complementary equation systems were used to model ME intake (MEI), PD and LD. Informative priors were...... developed, reflecting current knowledge about metabolic scaling and partial efficiencies of PD and LD rates, whereas flat non-informative priors were used for the reminder of the parameters. The experimental data analysed originate from a balance and respiration trial with 17 cross-bred pigs of three...

Model Identification Using Stochastic Differential Equation Grey-Box Models in Diabetes

DEFF Research Database (Denmark)

Duun-Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard

2013-01-01

are uncorrelated and provides the possibility to pinpoint model deficiencies. METHODS: An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters...... 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. CONCLUSION: This study shows the potential of using SDE-GBs in diabetes modeling. Improved model predictions were obtained...... 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. RESULTS: We found that the transformation of the ODE model into an SDE-GB resulted...

Random-Effects Models for Meta-Analytic Structural Equation Modeling: Review, Issues, and Illustrations

Science.gov (United States)

Cheung, Mike W.-L.; Cheung, Shu Fai

2016-01-01

Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM.…

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

Science.gov (United States)

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Macroscopic balance equations for two-phase flow models

International Nuclear Information System (INIS)

Hughes, E.D.

1979-01-01

The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analysed. The equations obtained supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. (Auth.)

Study of the Bellman equation in a production model with unstable demand

Science.gov (United States)

Obrosova, N. K.; Shananin, A. A.

2014-09-01

A production model with allowance for a working capital deficit and a restricted maximum possible sales volume is proposed and analyzed. The study is motivated by the urgency of analyzing well-known problems of functioning low competitive macroeconomic structures. The original formulation of the task represents an infinite-horizon optimal control problem. As a result, the model is formalized in the form of a Bellman equation. It is proved that the corresponding Bellman operator is a contraction and has a unique fixed point in the chosen class of functions. A closed-form solution of the Bellman equation is found using the method of steps. The influence of the credit interest rate on the firm market value assessment is analyzed by applying the developed model.

Equations to Estimate Creatinine Excretion Rate : The CKD Epidemiology Collaboration

NARCIS (Netherlands)

Ix, Joachim H.; Wassel, Christina L.; Stevens, Lesley A.; Beck, Gerald J.; Froissart, Marc; Navis, Gerjan; Rodby, Roger; Torres, Vicente E.; Zhang, Yaping (Lucy); Greene, Tom; Levey, Andrew S.

Background and objectives Creatinine excretion rate (CER) indicates timed urine collection accuracy. Although equations to estimate CER exist, their bias and precision are untested and none simultaneously include age, sex, race, and weight. Design, setting, participants, & measurements Participants

Introduction to computation and modeling for differential equations

CERN Document Server

Edsberg, Lennart

2008-01-01

An introduction to scientific computing for differential equationsIntroduction to Computation and Modeling for Differential Equations provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique ""Five-M"" approach: Modeling, Mathematics, Methods, MATLAB, and Multiphysics. This approach facilitates a thorough understanding of h

Modeling Inflation Using a Non-Equilibrium Equation of Exchange

Science.gov (United States)

Chamberlain, Robert G.

2013-01-01

Inflation is a change in the prices of goods that takes place without changes in the actual values of those goods. The Equation of Exchange, formulated clearly in a seminal paper by Irving Fisher in 1911, establishes an equilibrium relationship between the price index P (also known as "inflation"), the economy's aggregate output Q (also known as "the real gross domestic product"), the amount of money available for spending M (also known as "the money supply"), and the rate at which money is reused V (also known as "the velocity of circulation of money"). This paper offers first a qualitative discussion of what can cause these factors to change and how those causes might be controlled, then develops a quantitative model of inflation based on a non-equilibrium version of the Equation of Exchange. Causal relationships are different from equations in that the effects of changes in the causal variables take time to play out-often significant amounts of time. In the model described here, wages track prices, but only after a distributed lag. Prices change whenever the money supply, aggregate output, or the velocity of circulation of money change, but only after a distributed lag. Similarly, the money supply depends on the supplies of domestic and foreign money, which depend on the monetary base and a variety of foreign transactions, respectively. The spreading of delays mitigates the shocks of sudden changes to important inputs, but the most important aspect of this model is that delays, which often have dramatic consequences in dynamic systems, are explicitly incorporated.macroeconomics, inflation, equation of exchange, non-equilibrium, Athena Project

Determining the spill flow discharge of combined sewer overflows using rating curves based on computational fluid dynamics instead of the standard weir equation.

Science.gov (United States)

Fach, S; Sitzenfrei, R; Rauch, W

2009-01-01

It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.

Picard Approximation of Stochastic Differential Equations and Application to LIBOR Models

DEFF Research Database (Denmark)

Papapantoleon, Antonis; Skovmand, David

The aim of this work is to provide fast and accurate approximation schemes for the Monte Carlo pricing of derivatives in LIBOR market models. Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods are generally slow. Our...... exponential to quadratic using truncated expansions of the product terms. We include numerical illustrations of the accuracy and speed of our method pricing caplets, swaptions and forward rate agreements....

Differential equation models for sharp threshold dynamics.

Science.gov (United States)

Schramm, Harrison C; Dimitrov, Nedialko B

2014-01-01

We develop an extension to differential equation models of dynamical systems to allow us to analyze probabilistic threshold dynamics that fundamentally and globally change system behavior. We apply our novel modeling approach to two cases of interest: a model of infectious disease modified for malware where a detection event drastically changes dynamics by introducing a new class in competition with the original infection; and the Lanchester model of armed conflict, where the loss of a key capability drastically changes the effectiveness of one of the sides. We derive and demonstrate a step-by-step, repeatable method for applying our novel modeling approach to an arbitrary system, and we compare the resulting differential equations to simulations of the system's random progression. Our work leads to a simple and easily implemented method for analyzing probabilistic threshold dynamics using differential equations. Published by Elsevier Inc.

Fitting ARMA Time Series by Structural Equation Models.

Science.gov (United States)

van Buuren, Stef

1997-01-01

This paper outlines how the stationary ARMA (p,q) model (G. Box and G. Jenkins, 1976) can be specified as a structural equation model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. The method is applied to three problem types. (SLD)

The reservoir model: a differential equation model of psychological regulation.

Science.gov (United States)

Deboeck, Pascal R; Bergeman, C S

2013-06-01

Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might "add up" over time (e.g., life stressors, inputs), but individuals simultaneously take action to "blow off steam" (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the "height" (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

Comprehensive solutions to the Bloch equations and dynamical models for open two-level systems

Science.gov (United States)

Skinner, Thomas E.

2018-01-01

The Bloch equation and its variants constitute the fundamental dynamical model for arbitrary two-level systems. Many important processes, including those in more complicated systems, can be modeled and understood through the two-level approximation. It is therefore of widespread relevance, especially as it relates to understanding dissipative processes in current cutting-edge applications of quantum mechanics. Although the Bloch equation has been the subject of considerable analysis in the 70 years since its inception, there is still, perhaps surprisingly, significant work that can be done. This paper extends the scope of previous analyses. It provides a framework for more fully understanding the dynamics of dissipative two-level systems. A solution is derived that is compact, tractable, and completely general, in contrast to previous results. Any solution of the Bloch equation depends on three roots of a cubic polynomial that are crucial to the time dependence of the system. The roots are typically only sketched out qualitatively, with no indication of their dependence on the physical parameters of the problem. Degenerate roots, which modify the solutions, have been ignored altogether. Here the roots are obtained explicitly in terms of a single real-valued root that is expressed as a simple function of the system parameters. For the conventional Bloch equation, a simple graphical representation of this root is presented that makes evident the explicit time dependence of the system for each point in the parameter space. Several intuitive, visual models of system dynamics are developed. A Euclidean coordinate system is identified in which any generalized Bloch equation is separable, i.e., the sum of commuting rotation and relaxation operators. The time evolution in this frame is simply a rotation followed by relaxation at modified rates that play a role similar to the standard longitudinal and transverse rates. These rates are functions of the applied field, which

Asymptotics of steady states of a selection–mutation equation for small mutation rate

KAUST Repository

Calsina, Àngel

2013-12-01

We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.

Asymptotics of steady states of a selection–mutation equation for small mutation rate

KAUST Repository

Calsina, À ngel; Cuadrado, Sí lvia; Desvillettes, Laurent; Raoul, Gaë l

2013-01-01

We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.

Linear causal modeling with structural equations

CERN Document Server

Mulaik, Stanley A

2009-01-01

Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal

Modeling and Prediction Using Stochastic Differential Equations

DEFF Research Database (Denmark)

Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp

2016-01-01

Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup...... deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs...

Enhancement of leak rate estimation model for corroded cracked thin tubes

International Nuclear Information System (INIS)

Chang, Y.S.; Jeong, J.U.; Kim, Y.J.; Hwang, S.S.; Kim, H.P.

2010-01-01

During the last couple of decades, lots of researches on structural integrity assessment and leak rate estimation have been carried out to prevent unanticipated catastrophic failures of pressure retaining nuclear components. However, from the standpoint of leakage integrity, there are still some arguments for predicting the leak rate of cracked components due primarily to uncertainties attached to various parameters in flow models. The purpose of present work is to suggest a leak rate estimation method for thin tubes with artificial cracks. In this context, 23 leak rate tests are carried out for laboratory generated stress corrosion cracked tube specimens subjected to internal pressure. Engineering equations to calculate crack opening displacements are developed from detailed three-dimensional elastic-plastic finite element analyses and then a simplified practical model is proposed based on the equations as well as test data. Verification of the proposed method is done through comparing leak rates and it will enable more reliable design and/or operation of thin tubes.

Validity of predictive equations for basal metabolic rate in Japanese adults.

Science.gov (United States)

Miyake, Rieko; Tanaka, Shigeho; Ohkawara, Kazunori; Ishikawa-Takata, Kazuko; Hikihara, Yuki; Taguri, Emiko; Kayashita, Jun; Tabata, Izumi

2011-01-01

Many predictive equations for basal metabolic rate (BMR) based on anthropometric measurements, age, and sex have been developed, mainly for healthy Caucasians. However, it has been reported that many of these equations, used widely, overestimate BMR not only for Asians, but also for Caucasians. The present study examined the accuracy of several predictive equations for BMR in Japanese subjects. In 365 healthy Japanese male and female subjects, aged 18 to 79 y, BMR was measured in the post-absorptive state using a mask and Douglas bag. Six predictive equations were examined. Total error was used as an index of the accuracy of each equation's prediction. Predicted BMR values by Dietary Reference Intakes for Japanese (Japan-DRI), Adjusted Dietary Reference Intakes for Japanese (Adjusted-DRI), and Ganpule equations were not significantly different from the measured BMR in either sex. On the other hand, Harris-Benedict, Schofield, and Food and Agriculture Organization of the United Nations/World Health Organization/United Nations University equations were significantly higher than the measured BMR in both sexes. The prediction error by Japan-DRI, Adjusted-DRI, and Harris-Benedict equations was significantly correlated with body weight in both sexes. Total error using the Ganpule equation was low in both males and females (125 and 99 kcal/d, respectively). In addition, total error using the Adjusted-DRI equation was low in females (95 kcal/d). Thus, the Ganpule equation was the most accurate in predicting BMR in our healthy Japanese subjects, because the difference between the predicted and measured BMR was relatively small, and body weight had no effect on the prediction error.

How "Hot Precursors" Modify Island Nucleation: A Rate-Equation Model

Science.gov (United States)

Morales-Cifuentes, Josue R.; Einstein, T. L.; Pimpinelli, A.

2014-12-01

We propose a novel island nucleation and growth model explicitly including transient (ballistic) mobility of the monomers deposited at rate F , assumed to be in a hot precursor state before thermalizing. In limiting regimes, corresponding to fast (diffusive) and slow (ballistic) thermalization, the island density N obeys scaling N ∝Fα . In between is found a rich, complex behavior, with various distinctive scaling regimes, characterized by effective exponents αeff and activation energies that we compute exactly. Application to N (F ,T ) of recent organic-molecule deposition experiments yields an excellent fit.

CONTINUOUS MODELING OF FOREIGN EXCHANGE RATE OF USD VERSUS TRY

Directory of Open Access Journals (Sweden)

Yakup Arı

2011-01-01

Full Text Available This study aims to construct continuous-time autoregressive (CAR model and continuous-time GARCH (COGARCH model from discrete time data of foreign exchange rate of United States Dollar (USD versus Turkish Lira (TRY. These processes are solutions to stochastic differential equation Lévy-driven processes. We have shown that CAR(1 and COGARCH(1,1 processes are proper models to represent foreign exchange rate of USD and TRY for different periods of time February 2002- June 2010.

Partial Differential Equations Modeling and Numerical Simulation

CERN Document Server

Glowinski, Roland

2008-01-01

This book is dedicated to Olivier Pironneau. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schrödinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this book several experts in this field present their latest results and discuss trends in the numerical analy...

Study of a Model Equation in Detonation Theory

KAUST Repository

Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.

2014-01-01

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation

Generalized latent variable modeling multilevel, longitudinal, and structural equation models

CERN Document Server

Skrondal, Anders; Rabe-Hesketh, Sophia

2004-01-01

This book unifies and extends latent variable models, including multilevel or generalized linear mixed models, longitudinal or panel models, item response or factor models, latent class or finite mixture models, and structural equation models.

Rate dependent inelastic behavior of polycrystalline solids using a dislocation model

International Nuclear Information System (INIS)

Werne, R.W.; Kelly, J.M.

1980-01-01

A rate dependent theory of polycrystalline plasticity is presented in which the solid is modeled as an isotropic continuum with internal variables. The rate of plastic deformation is shown to be a function of the deviatoric portion of the Cauchy stress tensor as well as two scalar internal variables. The scalar internal variables, which are the dislocation density and mobile fraction, are governed by rate equations which reflect the evolution of microstructural processes. The model has been incorporated into a two dimensional finite element code and several example multidimensional problems are presented which exhibit the rate dependence of the material model

Model Servqual Dengan Pendekatan Structural Equation Modeling (Studi Pada Mahasiswa Sistem Informasi)

OpenAIRE

Nurfaizal, Yusmedi

2015-01-01

Penelitian ini berjudul “MODEL SERVQUAL DENGAN PENDEKATAN STRUCTURAL EQUATION MODELING (Studi Pada Mahasiswa Sistem Informasi)”. Tujuan penelitian ini adalah untuk mengetahui model Servqual dengan pendekatan Structural Equation Modeling pada mahasiswa sistem informasi. Peneliti memutuskan untuk mengambil sampel sebanyak 100 responden. Untuk menguji model digunakan analisis SEM. Hasil penelitian menunjukkan bahwa tangibility, reliability responsiveness, assurance dan emphaty mempunyai pengaruh...

arXiv Status of rates and rate equations for thermal leptogenesis

CERN Document Server

Biondini, Simone; Brambilla, Nora; Garny, Mathias; Ghiglieri, Jacopo; Hohenegger, Andreas; Laine, Mikko; Mendizabal, Sebastian; Millington, Peter; Salvio, Alberto; Vairo, Antonio

2018-02-28

In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter-antimatter asymmetry generated when the temperature of the hot plasma $T$ exceeds the right-handed neutrino mass scale $M$ is efficiently erased, and one can focus on the temperature window $T \\ll M$. We review recent progresses in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number...

A discrete model of a modified Burgers' partial differential equation

Science.gov (United States)

Mickens, R. E.; Shoosmith, J. N.

1990-01-01

A new finite-difference scheme is constructed for a modified Burger's equation. Three special cases of the equation are considered, and the 'exact' difference schemes for the space- and time-independent forms of the equation are presented, along with the diffusion-free case of Burger's equation modeled by a difference equation. The desired difference scheme is then obtained by imposing on any difference model of the initial equation the requirement that, in the appropriate limits, its difference scheme must reduce the results of the obtained equations.

Methods of mathematical modelling continuous systems and differential equations

CERN Document Server

Witelski, Thomas

2015-01-01

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

Analytical solutions of time-fractional models for homogeneous Gardner equation and non-homogeneous differential equations

Directory of Open Access Journals (Sweden)

Olaniyi Samuel Iyiola

2014-09-01

Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.

Prior Sensitivity Analysis in Default Bayesian Structural Equation Modeling.

Science.gov (United States)

van Erp, Sara; Mulder, Joris; Oberski, Daniel L

2017-11-27

Bayesian structural equation modeling (BSEM) has recently gained popularity because it enables researchers to fit complex models and solve some of the issues often encountered in classical maximum likelihood estimation, such as nonconvergence and inadmissible solutions. An important component of any Bayesian analysis is the prior distribution of the unknown model parameters. Often, researchers rely on default priors, which are constructed in an automatic fashion without requiring substantive prior information. However, the prior can have a serious influence on the estimation of the model parameters, which affects the mean squared error, bias, coverage rates, and quantiles of the estimates. In this article, we investigate the performance of three different default priors: noninformative improper priors, vague proper priors, and empirical Bayes priors-with the latter being novel in the BSEM literature. Based on a simulation study, we find that these three default BSEM methods may perform very differently, especially with small samples. A careful prior sensitivity analysis is therefore needed when performing a default BSEM analysis. For this purpose, we provide a practical step-by-step guide for practitioners to conducting a prior sensitivity analysis in default BSEM. Our recommendations are illustrated using a well-known case study from the structural equation modeling literature, and all code for conducting the prior sensitivity analysis is available in the online supplemental materials. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Lattice Boltzmann model for high-order nonlinear partial differential equations.

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Lattice Boltzmann model for high-order nonlinear partial differential equations

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Dynamic data analysis modeling data with differential equations

CERN Document Server

Ramsay, James

2017-01-01

This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in...

Application of a mechanism-based rate equation to black liquor gasification rate data

Energy Technology Data Exchange (ETDEWEB)

Overacker, N.L.; Waag, K.J.; Frederick, W.J. [Oregon State University, OR (United States). Dept. of Chemical Engineering; Whitty, K.J.

1995-09-01

There is growing interest worldwide to develop alternate chemical recovery processes for paper mills which are cheaper, safer, more efficient and more environmentally sound than traditional technology. Pressurized gasification of black liquor is the basis for many proposed schemes and offers the possibility to double the amount of electricity generated per unit of dry black liquor solids. Such technology also has capital, safety and environmental advantages. One of the most important considerations regarding this emerging technology is the kinetics of the gasification reaction. This has been studied empirically at Aabo Akademi University for the pressurized gasification with carbon dioxide and steam. For the purposes of reactor modeling and scale-up, however, a thorough understanding of the mechanism behind the reaction is desirable. This report discusses the applicability of a mechanism-based rate equation to gasification of black liquor. The mechanism considered was developed for alkali-catalyzed gasification of carbon and is tested using black liquor gasification data obtained during simultaneous reaction with H{sub 2}O and CO. Equilibrium considerations and the influence of the water-gas shift reaction are also discussed. The work presented here is a cooperative effort between Aabo Akademi University and Oregon State University. The experimental work and some of the data analysis was performed at Aabo Akademi University. Development of the models and consideration of their applicability was performed primarily at Oregon State University

On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory

Directory of Open Access Journals (Sweden)

Appleby JohnAD

2010-01-01

Full Text Available We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. The result is considered both for a linear Volterra integrodifferential equation as well as for the delay logistic equation from population biology.

First-order partial differential equations

CERN Document Server

Rhee, Hyun-Ku; Amundson, Neal R

2001-01-01

This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo

Reduction of structured population models to threshold-type delay equations and functional differential equations: A case study

Energy Technology Data Exchange (ETDEWEB)

Smith, H.L. (Arizona State Univ., Tempe (United States))

1993-01-01

It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability. 28 refs., 2 figs.

Multigrid solution of incompressible turbulent flows by using two-equation turbulence models

Energy Technology Data Exchange (ETDEWEB)

Zheng, X.; Liu, C. [Front Range Scientific Computations, Inc., Denver, CO (United States); Sung, C.H. [David Taylor Model Basin, Bethesda, MD (United States)

1996-12-31

Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.

The dispersionless Lax equations and topological minimal models

International Nuclear Information System (INIS)

Krichever, I.

1992-01-01

It is shown that perturbed rings of the primary chiral fields of the topological minimal models coincide with some particular solutions of the dispersionless Lax equations. The exact formulae for the tree level partition functions, of A n topological minimal models are found. The Virasoro constraints for the analogue of the τ-function of the dispersionless Lax equation corresponding to these models are proved. (orig.)

Generalized rate-code model for neuron ensembles with finite populations

International Nuclear Information System (INIS)

Hasegawa, Hideo

2007-01-01

We have proposed a generalized Langevin-type rate-code model subjected to multiplicative noise, in order to study stationary and dynamical properties of an ensemble containing a finite number N of neurons. Calculations using the Fokker-Planck equation have shown that, owing to the multiplicative noise, our rate model yields various kinds of stationary non-Gaussian distributions such as Γ, inverse-Gaussian-like, and log-normal-like distributions, which have been experimentally observed. The dynamical properties of the rate model have been studied with the use of the augmented moment method (AMM), which was previously proposed by the author from a macroscopic point of view for finite-unit stochastic systems. In the AMM, the original N-dimensional stochastic differential equations (DEs) are transformed into three-dimensional deterministic DEs for the means and fluctuations of local and global variables. The dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the AMM are in good agreement with those obtained by direct simulation. The synchronization in the neuronal ensemble is discussed. The variabilities of the firing rate and of the interspike interval are shown to increase with increasing magnitude of multiplicative noise, which may be a conceivable origin of the observed large variability in cortical neurons

Derivation of simplified basic equations of gas-liquid two-phase dispersed flow based on two-fluid model

International Nuclear Information System (INIS)

Kataoka, Isao; Tomiyama, Akio

2004-01-01

The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill

Teaching Modeling with Partial Differential Equations: Several Successful Approaches

Science.gov (United States)

Myers, Joseph; Trubatch, David; Winkel, Brian

2008-01-01

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Fixation of waste materials in grouts: Part 3, Equation for critical flow rate

International Nuclear Information System (INIS)

Tallent, O.K.; McDaniel, E.W.; Spence, R.D.; Godsey, T.T.; Dodson, K.E.

1986-12-01

Critical flow rate data for grouts prepared from three distinctly different nuclear waste materials have been correlated. The wastes include Oak Ridge National Laboratory (ORNL) low-level waste (LLW) solution, Hanford Facility waste (HFW) solution, and cladding removal waste (CRW) slurry. Data for the three wastes have been correlated with a 0.96 coefficient of correlation by the following equation: log V/sub E/ = 0.289 + 0.707 log μ/sub E/, where V/sub E/ and μ/sub E/ denote critical flow rate in m 3 /min and apparent viscosity in Pa.s, respectively. The equation may be used to estimate critical flow rate for grouts prepared within the compositional range of the investigation. 5 refs., 4 figs., 7 tabs

Bogomolny equations in certain generalized baby BPS Skyrme models

Science.gov (United States)

Stępień, Ł. T.

2018-01-01

By using the concept of strong necessary conditions (CSNCs), we derive Bogomolny equations and Bogomol’nyi-Prasad-Sommerfield (BPS) bounds for two certain modifications of the baby BPS Skyrme model: the nonminimal coupling to the gauge field and the k-deformed ungauged model. In particular, we study how the Bogomolny equations and the equation for the potential reflect these two modifications. In both examples, the CSNC method appears to be a very useful tool. We also find certain localized solutions of these Bogomolny equations.

A practical course in differential equations and mathematical modeling

CERN Document Server

Ibragimov , Nail H

2009-01-01

A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame

Cell membrane temperature rate sensitivity predicted from the Nernst equation.

Science.gov (United States)

Barnes, F S

1984-01-01

A hyperpolarized current is predicted from the Nernst equation for conditions of positive temperature derivatives with respect to time. This ion current, coupled with changes in membrane channel conductivities, is expected to contribute to a transient potential shift across the cell membrane for silent cells and to a change in firing rate for pacemaker cells.

Revised predictive equations for salt intrusion modelling in estuaries

NARCIS (Netherlands)

Gisen, J.I.A.; Savenije, H.H.G.; Nijzink, R.C.

2015-01-01

For one-dimensional salt intrusion models to be predictive, we need predictive equations to link model parameters to observable hydraulic and geometric variables. The one-dimensional model of Savenije (1993b) made use of predictive equations for the Van der Burgh coefficient $K$ and the dispersion

Modeling animal movements using stochastic differential equations

Science.gov (United States)

Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie

2004-01-01

We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...

Applicability of the Schwartz Equation and the Chronic Kidney Disease in Children Bedside Equation for Estimating Glomerular Filtration Rate in Overweight Children.

Science.gov (United States)

Lewis, Teresa V; Harrison, Donald L; Gildon, Brooke L; Carter, Sandra M; Turman, Martin A

2016-06-01

To determine if significant correlations exist between glomerular filtration rate (GFR) prediction equation values, derived by using the original Schwartz equation and the Chronic Kidney Disease in Children (CKiD) bedside equation with a 24-hour urine creatinine clearance (Clcr ) value normalized to a body surface area of 1.73 m(2) in overweight and obese children. Prospective analysis (20 patients) and retrospective analysis (43 patients). Pediatric inpatient ward and pediatric nephrology clinic at a comprehensive academic medical center. Sixty-three pediatric patients (aged 5-17 years), of whom 27 were overweight (body mass index [BMI] at the 85th percentile or higher) and 36 were not overweight (BMI lower than the 85th percentile [controls]) between 2007 and 2012. Data from the overweight patients were compared with nonoverweight controls. GFR values were calculated by using the original Schwartz equation and the CKiD bedside equation. Each patient's 24-hour urine Clcr value normalized to a body surface area of 1.73 m(2) served as the index value. A Pearson correlation coefficient model was used to determine association between the 24-hour urine Clcr value (index value) with the Schwartz and CKiD GFR estimations. Significant correlation was found to exist between the Schwartz and CKiD bedside GFR estimations relative to the 24-hour urine Clcr in the control subjects (r = 0.85, poverweight subjects (r = 0.86, poverweight children with a kidney disorder. The CKiD bedside GFR estimations were not significantly different compared with 24-hour urine Clcr values for the overweight group with kidney disorder (p=0.85). The Schwartz and CKiD bedside estimations of GFR correlated with 24-hour urine Clcr values in both overweight and nonoverweight children. Compared with the Schwartz equation, which tended to overestimate renal function, the CKiD bedside equation appeared to approximate 24-hour urine Clcr more closely in overweight children with kidney disorder. © 2016

Parameter Estimates in Differential Equation Models for Chemical Kinetics

Science.gov (United States)

Winkel, Brian

2011-01-01

We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…

Effective dark energy equation of state in interacting dark energy models

International Nuclear Information System (INIS)

Avelino, P.P.; Silva, H.M.R. da

2012-01-01

In models where dark matter and dark energy interact non-minimally, the total amount of matter in a fixed comoving volume may vary from the time of recombination to the present time due to energy transfer between the two components. This implies that, in interacting dark energy models, the fractional matter density estimated using the cosmic microwave background assuming no interaction between dark matter and dark energy will in general be shifted with respect to its true value. This may result in an incorrect determination of the equation of state of dark energy if the interaction between dark matter and dark energy is not properly accounted for, even if the evolution of the Hubble parameter as a function of redshift is known with arbitrary precision. In this Letter we find an exact expression, as well as a simple analytical approximation, for the evolution of the effective equation of state of dark energy, assuming that the energy transfer rate between dark matter and dark energy is described by a simple two-parameter model. We also provide analytical examples where non-phantom interacting dark energy models mimic the background evolution and primary cosmic microwave background anisotropies of phantom dark energy models.

Effective dark energy equation of state in interacting dark energy models

Energy Technology Data Exchange (ETDEWEB)

Avelino, P.P., E-mail: ppavelin@fc.up.pt [Centro de Astrofisica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto (Portugal); Departamento de Fisica e Astronomia da Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Silva, H.M.R. da, E-mail: hilberto.silva@gmail.com [Departamento de Fisica e Astronomia da Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal)

2012-07-24

In models where dark matter and dark energy interact non-minimally, the total amount of matter in a fixed comoving volume may vary from the time of recombination to the present time due to energy transfer between the two components. This implies that, in interacting dark energy models, the fractional matter density estimated using the cosmic microwave background assuming no interaction between dark matter and dark energy will in general be shifted with respect to its true value. This may result in an incorrect determination of the equation of state of dark energy if the interaction between dark matter and dark energy is not properly accounted for, even if the evolution of the Hubble parameter as a function of redshift is known with arbitrary precision. In this Letter we find an exact expression, as well as a simple analytical approximation, for the evolution of the effective equation of state of dark energy, assuming that the energy transfer rate between dark matter and dark energy is described by a simple two-parameter model. We also provide analytical examples where non-phantom interacting dark energy models mimic the background evolution and primary cosmic microwave background anisotropies of phantom dark energy models.

Structural Equation Modeling of Multivariate Time Series

Science.gov (United States)

du Toit, Stephen H. C.; Browne, Michael W.

2007-01-01

The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be…

Analytical Modeling of the High Strain Rate Deformation of Polymer Matrix Composites

Science.gov (United States)

Goldberg, Robert K.; Roberts, Gary D.; Gilat, Amos

2003-01-01

The results presented here are part of an ongoing research program to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric matrix materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical 5 plasticity theory definitions of effective stress and effective plastic strain are modified by applying variations of the Drucker-Prager yield criterion. To verify the revised formulation, the shear and tensile deformation of a representative toughened epoxy is analyzed across a wide range of strain rates (from quasi-static to high strain rates) and the results are compared to experimentally obtained values. For the analyzed polymers, both the tensile and shear stress-strain curves computed using the analytical model correlate well with values obtained through experimental tests. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. In the micromechanics, the unit cell is divided up into a number of independently analyzed slices, and laminate theory is then applied to obtain the effective deformation of the unit cell. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite (composed using the representative polymer analyzed for the correlation of the polymer constitutive equations) for several fiber orientation angles across a variety of strain rates. The computed values compare favorably to experimentally obtained results.

Eight equation model for arbitrary shaped pipe conveying fluid

International Nuclear Information System (INIS)

Gale, J.; Tiselj, I.

2006-01-01

Linear eight-equation system for two-way coupling of single-phase fluid transient and arbitrary shaped one-dimensional pipeline movement is described and discussed. The governing phenomenon described with this system is also known as Fluid-Structure Interaction. Standard Skalak's four-equation model for axial coupling was improved with additional four Timoshenko's beam equations for description of flexural displacements and rotations. In addition to the conventional eight-equation system that enables coupling of straight sections, the applied mathematical model was improved for description of the arbitrary shaped pipeline located in two-dimensional plane. The applied model was solved with second-order accurate numerical method that is based on Godounov's characteristic upwind schemes. The model was successfully used for simulation of the rod impact induced transient and conventional instantaneous valve closure induced transient in the tank-pipe-valve system. (author)

Simulating sympathetic detonation using the hydrodynamic models and constitutive equations

Energy Technology Data Exchange (ETDEWEB)

Kim, Bo Hoon; Kim, Min Sung; Yoh, Jack J. [Dept. of Mechanical and Aerospace Engineering, Seoul National University, Seoul (Korea, Republic of); Sun, Tae Boo [Hanwha Corporation Defense Rand D Center, Daejeon (Korea, Republic of)

2016-12-15

A Sympathetic detonation (SD) is a detonation of an explosive charge by a nearby explosion. Most of times it is unintended while the impact of blast fragments or strong shock waves from the initiating donor explosive is the cause of SD. We investigate the SD of a cylindrical explosive charge (64 % RDX, 20 % Al, 16 % HTPB) contained in a steel casing. The constitutive relations for high explosive are obtained from a thermo-chemical code that provides the size effect data without the rate stick data typically used for building the rate law and equation of state. A full size SD test of eight pallet-packaged artillery shells is performed that provides the pressure data while the hydrodynamic model with proper constitutive relations for reactive materials and the fragmentation model for steel casing is conducted to replicate the experimental findings. The work presents a novel effort to accurately model and reproduce the sympathetic detonation event with a reduced experimental effort.

Rate equation description of quantum noise in nanolasers with few emitters

DEFF Research Database (Denmark)

Mørk, Jesper; Lippi, G. L.

2018-01-01

Rate equations for micro- and nanocavity lasers are formulated which take account of the finite number of emitters, Purcell effects as well as stochastic effects of spontaneous emission quantum noise. Analytical results are derived for the intensity noise and intensity correlation properties, g(2...

Statistical mechanics of normal grain growth in one dimension: A partial integro-differential equation model

International Nuclear Information System (INIS)

Ng, Felix S.L.

2016-01-01

We develop a statistical-mechanical model of one-dimensional normal grain growth that does not require any drift-velocity parameterization for grain size, such as used in the continuity equation of traditional mean-field theories. The model tracks the population by considering grain sizes in neighbour pairs; the probability of a pair having neighbours of certain sizes is determined by the size-frequency distribution of all pairs. Accordingly, the evolution obeys a partial integro-differential equation (PIDE) over ‘grain size versus neighbour grain size’ space, so that the grain-size distribution is a projection of the PIDE's solution. This model, which is applicable before as well as after statistically self-similar grain growth has been reached, shows that the traditional continuity equation is invalid outside this state. During statistically self-similar growth, the PIDE correctly predicts the coarsening rate, invariant grain-size distribution and spatial grain size correlations observed in direct simulations. The PIDE is then reducible to the standard continuity equation, and we derive an explicit expression for the drift velocity. It should be possible to formulate similar parameterization-free models of normal grain growth in two and three dimensions.

Handbook of structural equation modeling

CERN Document Server

Hoyle, Rick H

2012-01-01

The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu

Forecasting the mortality rates using Lee-Carter model and Heligman-Pollard model

Science.gov (United States)

Ibrahim, R. I.; Ngataman, N.; Abrisam, W. N. A. Wan Mohd

2017-09-01

Improvement in life expectancies has driven further declines in mortality. The sustained reduction in mortality rates and its systematic underestimation has been attracting the significant interest of researchers in recent years because of its potential impact on population size and structure, social security systems, and (from an actuarial perspective) the life insurance and pensions industry worldwide. Among all forecasting methods, the Lee-Carter model has been widely accepted by the actuarial community and Heligman-Pollard model has been widely used by researchers in modelling and forecasting future mortality. Therefore, this paper only focuses on Lee-Carter model and Heligman-Pollard model. The main objective of this paper is to investigate how accurately these two models will perform using Malaysian data. Since these models involves nonlinear equations that are explicitly difficult to solve, the Matrix Laboratory Version 8.0 (MATLAB 8.0) software will be used to estimate the parameters of the models. Autoregressive Integrated Moving Average (ARIMA) procedure is applied to acquire the forecasted parameters for both models as the forecasted mortality rates are obtained by using all the values of forecasted parameters. To investigate the accuracy of the estimation, the forecasted results will be compared against actual data of mortality rates. The results indicate that both models provide better results for male population. However, for the elderly female population, Heligman-Pollard model seems to underestimate to the mortality rates while Lee-Carter model seems to overestimate to the mortality rates.

Empirical Model for Predicting Rate of Biogas Production | Adamu ...

African Journals Online (AJOL)

Rate of biogas production using cow manure as substrate was monitored in two laboratory scale batch reactors (13 liter and 108 liter capacities). Two empirical models based on the Gompertz and the modified logistic equations were used to fit the experimental data based on non-linear regression analysis using Solver tool ...

A Constitutive Model for Superelastic Shape Memory Alloys Considering the Influence of Strain Rate

Directory of Open Access Journals (Sweden)

Hui Qian

2013-01-01

Full Text Available Shape memory alloys (SMAs are a relatively new class of functional materials, exhibiting special thermomechanical behaviors, such as shape memory effect and superelasticity, which enable their applications in seismic engineering as energy dissipation devices. This paper investigates the properties of superelastic NiTi shape memory alloys, emphasizing the influence of strain rate on superelastic behavior under various strain amplitudes by cyclic tensile tests. A novel constitutive equation based on Graesser and Cozzarelli’s model is proposed to describe the strain-rate-dependent hysteretic behavior of superelastic SMAs at different strain levels. A stress variable including the influence of strain rate is introduced into Graesser and Cozzarelli’s model. To verify the effectiveness of the proposed constitutive equation, experiments on superelastic NiTi wires with different strain rates and strain levels are conducted. Numerical simulation results based on the proposed constitutive equation and experimental results are in good agreement. The findings in this paper will assist the future design of superelastic SMA-based energy dissipation devices for seismic protection of structures.

A simple recipe for modeling reaction-rate in flows with turbulent-combustion

Science.gov (United States)

Girimaji, Sharath S.

1991-01-01

A computationally viable scheme to account for chemical reaction in turbulent flows is presented. The multivariate beta-pdf model for multiple scalar mixing forms the basis of this scheme. Using the model scalar joint pdf and a general form of the instantaneous reaction-rate, the unclosed chemical reaction terms are expressed as simple functions of scalar means and the turbulent scalar energy. The calculation procedure requires that the mean scalar equations and only one other transport equation - for the turbulent scalar energy - be solved.

Generalized heat-transport equations: parabolic and hyperbolic models

Science.gov (United States)

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

2018-03-01

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

Validation of estimated glomerular filtration rate equations for Japanese children.

Science.gov (United States)

Gotoh, Yoshimitsu; Uemura, Osamu; Ishikura, Kenji; Sakai, Tomoyuki; Hamasaki, Yuko; Araki, Yoshinori; Hamda, Riku; Honda, Masataka

2018-01-25

The gold standard for evaluation of kidney function is renal inulin clearance (Cin). However, the methodology for Cin is complicated and difficult, especially for younger children and/or patients with bladder dysfunction. Therefore, we developed a simple and easier method for obtaining the estimated glomerular filtration rate (eGFR) using equations and values for several biomarkers, i.e., serum creatinine (Cr), serum cystatin C (cystC), serum beta-2 microglobulin (β 2 MG), and creatinine clearance (Ccr). The purpose of the present study was to validate these equations with a new data set. To validate each equation, we used data of 140 patients with CKD with clinical need for Cin, using the measured GFR (mGFR). We compared the results for each eGFR equation with the mGFR using mean error (ME), root mean square error (RMSE), P 30 , and Bland-Altman analysis. The ME of Cr, cystC, β 2 MG, and Ccr based on eGFR was 15.8 ± 13.0, 17.2 ± 16.5, 15.4 ± 14.3, and 10.6 ± 13.0 ml/min/1.73 m 2 , respectively. The RMSE was 29.5, 23.8, 20.9, and 16.7, respectively. The P 30 was 79.4, 71.1, 69.5, and 92.9%, respectively. The Bland-Altman bias analysis showed values of 4.0 ± 18.6, 5.3 ± 16.8, 12.7 ± 17.0, and 2.5 ± 17.2 ml/min/1.73 m 2 , respectively, for these parameters. The bias of each eGFR equation was not large. Therefore, each eGFR equation could be used.

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

Science.gov (United States)

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

Stochastic differential equations used to model conjugation

DEFF Research Database (Denmark)

Philipsen, Kirsten Riber; Christiansen, Lasse Engbo

Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can...

Finite element modeling of penetration of rigid cylindrical bar impacting on a clamped circular plate, employing a strain rate dependent flow rate and a Gruneisen equation of state

International Nuclear Information System (INIS)

Tariq, M.; Khan, I.A.

2003-01-01

A time dependent Finite Element simulation of penetration of a rigid cylindrical bar impacting on a copper plate is conducted, to demonstrate how material behavior appears to change when Johnson-Cook plasticity rule is employed along with a Gruneisen, equation of state with cubic shock velocity-particle relationship, and defining pressure both for compressed and expanded materials, as compared to the behavior when only isotropic strain-hardening model is employed. The bar impacts the plate with a velocity of 1000 m/s, and penetrates the plate, a portion of it coming out of the other side. Results are obtained and compared taking both an isotropic strain-hardening model, and a model incorporating Johnson-Cook flow rule along with Gruneisen equation of state. (author)

Relations between the kinetic equation and the Langevin models in two-phase flow modelling

International Nuclear Information System (INIS)

Minier, J.P.; Pozorski, J.

1997-05-01

The purpose of this paper is to discuss PDF and stochastic models which are used in two-phase flow modelling. The aim of the present analysis is essentially to try to determine relations and consistency between different models. It is first recalled that different approaches actually correspond to PDF models written either in terms of the process trajectories or in terms of the PDF itself. The main difference lies in the choice of the independent variables which are retained. Two particular models are studied, the Kinetic Equation and the Langevin Equation model. The latter uses a Langevin equation to model the fluid velocities seen along particle trajectories. The Langevin model is more general since it contains an additional variable. It is shown that, in certain cases, this variable can be summed up exactly to retrieve the Kinetic Equation model as a marginal PDF. A joint fluid and solid particle PDF which includes the characteristics of both phases is proposed at the end of the paper. (author)

Existing creatinine-based equations overestimate glomerular filtration rate in Indians.

Science.gov (United States)

Kumar, Vivek; Yadav, Ashok Kumar; Yasuda, Yoshinari; Horio, Masaru; Kumar, Vinod; Sahni, Nancy; Gupta, Krishan L; Matsuo, Seiichi; Kohli, Harbir Singh; Jha, Vivekanand

2018-02-01

Accurate estimation of glomerular filtration rate (GFR) is important for diagnosis and risk stratification in chronic kidney disease and for selection of living donors. Ethnic differences have required correction factors in the originally developed creatinine-based GFR estimation equations for populations around the world. Existing equations have not been validated in the vegetarian Indian population. We examined the performance of creatinine and cystatin-based GFR estimating equations in Indians. GFR was measured by urinary clearance of inulin. Serum creatinine was measured using IDMS-traceable Jaffe's and enzymatic assays, and cystatin C by colloidal gold immunoassay. Dietary protein intake was calculated by measuring urinary nitrogen appearance. Bias, precision and accuracy were calculated for the eGFR equations. A total of 130 participants (63 healthy kidney donors and 67 with CKD) were studied. About 50% were vegetarians, and the remainder ate meat 3.8 times every month. The average creatinine excretion were 14.7 mg/kg/day (95% CI: 13.5 to 15.9 mg/kg/day) and 12.4 mg/kg/day (95% CI: 11.2 to 13.6 mg/kg/day) in males and females, respectively. The average daily protein intake was 46.1 g/day (95% CI: 43.2 to 48.8 g/day). The mean mGFR in the study population was 51.66 ± 31.68 ml/min/1.73m 2 . All creatinine-based eGFR equations overestimated GFR (p < 0.01 for each creatinine based eGFR equation). However, eGFR by CKD-EPI Cys was not significantly different from mGFR (p = 0.38). The CKD-EPI Cys exhibited lowest bias [mean bias: -3.53 ± 14.70 ml/min/1.73m 2 (95% CI: -0.608 to -0.98)] and highest accuracy (P 30 : 74.6%). The GFR in the healthy population was 79.44 ± 20.19 (range: 41.90-134.50) ml/min/1.73m 2 . Existing creatinine-based GFR estimating equations overestimate GFR in Indians. An appropriately powered study is needed to develop either a correction factor or a new equation for accurate assessment of kidney function in the

Time-dependent integral transport equation kernels, leakage rates and collision rates for plane and spherical geometry

International Nuclear Information System (INIS)

Henderson, D.L.

1987-01-01

Time-dependent integral transport equation flux and current kernels for plane and spherical geometry are derived for homogeneous media. Using the multiple collision formalism, isotropic sources that are delta distributions in time are considered for four different problems. The plane geometry flux kernel is applied to a uniformly distributed source within an infinite medium and to a surface source in a semi-infinite medium. The spherical flux kernel is applied to a point source in an infinite medium and to a point source at the origin of a finite sphere. The time-dependent first-flight leakage rates corresponding to the existing steady state first-flight escape probabilities are computed by the Laplace transform technique assuming a delta distribution source in time. The case of a constant source emitting neutrons over a time interval, Δt, for a spatially uniform source is obtained for a slab and a sphere. Time-dependent first-flight leakage rates are also determined for the general two region spherical medium problem for isotropic sources with a delta distribution in time uniformly distributed throughout both the inner and outer regions. The time-dependent collision rates due to the uncollided neutrons are computed for a slab and a sphere using the time-dependent first-flight leakage rates and the time-dependent continuity equation. The case of a constant source emitting neutrons over a time interval, Δt, is also considered

on the properties of solutions and some applications on the TOV differential equation with a model of nuclear equation of state

International Nuclear Information System (INIS)

Esmail, S.F.H.

2006-01-01

the mathematical formulation of numerous physical problems results in differential equations actually non-linear differential equations . in our study we are interested in solutions of differential equations which describe the structure of neutron star in non-relativistic and relativistic cases. the aim of this work is to determine the mass and the radius of a neutron star, by solving the tolmann-oppenheimer-volkoff (TOV) differential equation using different models of the nuclear equation of state (EOS). analytically solutions are obtained for a simple form of the nuclear equation of state of Clayton model and poly trope model. for a more realistic equation of state the TOV differential equation is solved numerically using rung -Kutta method

Factors influencing creep model equation selection

International Nuclear Information System (INIS)

Holdsworth, S.R.; Askins, M.; Baker, A.; Gariboldi, E.; Holmstroem, S.; Klenk, A.; Ringel, M.; Merckling, G.; Sandstrom, R.; Schwienheer, M.; Spigarelli, S.

2008-01-01

During the course of the EU-funded Advanced-Creep Thematic Network, ECCC-WG1 reviewed the applicability and effectiveness of a range of model equations to represent the accumulation of creep strain in various engineering alloys. In addition to considering the experience of network members, the ability of several models to describe the deformation characteristics of large single and multi-cast collations of ε(t,T,σ) creep curves have been evaluated in an intensive assessment inter-comparison activity involving three steels, 21/4 CrMo (P22), 9CrMoVNb (Steel-91) and 18Cr13NiMo (Type-316). The choice of the most appropriate creep model equation for a given application depends not only on the high-temperature deformation characteristics of the material under consideration, but also on the characteristics of the dataset, the number of casts for which creep curves are available and on the strain regime for which an analytical representation is required. The paper focuses on the factors which can influence creep model selection and model-fitting approach for multi-source, multi-cast datasets

Implementation of two-equation soot flamelet models for laminar diffusion flames

Energy Technology Data Exchange (ETDEWEB)

Carbonell, D.; Oliva, A.; Perez-Segarra, C.D. [Centre Tecnologic de Transferencia de Calor (CTTC), Universitat Politecnica de Catalunya (UPC), ETSEIAT, Colom 11, E-08222, Terrassa (Barcelona) (Spain)

2009-03-15

The two-equation soot model proposed by Leung et al. [K.M. Leung, R.P. Lindstedt, W.P. Jones, Combust. Flame 87 (1991) 289-305] has been derived in the mixture fraction space. The model has been implemented using both Interactive and Non-Interactive flamelet strategies. An Extended Enthalpy Defect Flamelet Model (E-EDFM) which uses a flamelet library obtained neglecting the soot formation is proposed as a Non-Interactive method. The Lagrangian Flamelet Model (LFM) is used to represent the Interactive models. This model uses direct values of soot mass fraction from flamelet calculations. An Extended version (E-LFM) of this model is also suggested in which soot mass fraction reaction rates are used from flamelet calculations. Results presented in this work show that the E-EDFM predict acceptable results. However, it overpredicts the soot volume fraction due to the inability of this model to couple the soot and gas-phase mechanisms. It has been demonstrated that the LFM is not able to predict accurately the soot volume fraction. On the other hand, the extended version proposed here has been shown to be very accurate. The different flamelet mathematical formulations have been tested and compared using well verified reference calculations obtained solving the set of the Full Transport Equations (FTE) in the physical space. (author)

Exact Solutions of Fragmentation Equations with General Fragmentation Rates and Separable Particles Distribution Kernels

Directory of Open Access Journals (Sweden)

S. C. Oukouomi Noutchie

2014-01-01

Full Text Available We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.

Mathematical model for predicting molecular-beam epitaxy growth rates for wafer production

International Nuclear Information System (INIS)

Shi, B.Q.

2003-01-01

An analytical mathematical model for predicting molecular-beam epitaxy (MBE) growth rates is reported. The mathematical model solves the mass-conservation equation for liquid sources in conical crucibles and predicts the growth rate by taking into account the effect of growth source depletion on the growth rate. Assumptions made for deducing the analytical model are discussed. The model derived contains only one unknown parameter, the value of which can be determined by using data readily available to MBE growers. Procedures are outlined for implementing the model in MBE production of III-V compound semiconductor device wafers. Results from use of the model to obtain targeted layer compositions and thickness of InP-based heterojunction bipolar transistor wafers are presented

Converting differential-equation models of biological systems to membrane computing.

Science.gov (United States)

Muniyandi, Ravie Chandren; Zin, Abdullah Mohd; Sanders, J W

2013-12-01

This paper presents a method to convert the deterministic, continuous representation of a biological system by ordinary differential equations into a non-deterministic, discrete membrane computation. The dynamics of the membrane computation is governed by rewrite rules operating at certain rates. That has the advantage of applying accurately to small systems, and to expressing rates of change that are determined locally, by region, but not necessary globally. Such spatial information augments the standard differentiable approach to provide a more realistic model. A biological case study of the ligand-receptor network of protein TGF-β is used to validate the effectiveness of the conversion method. It demonstrates the sense in which the behaviours and properties of the system are better preserved in the membrane computing model, suggesting that the proposed conversion method may prove useful for biological systems in particular. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Nonlinear integral equations for the sausage model

Science.gov (United States)

Ahn, Changrim; Balog, Janos; Ravanini, Francesco

2017-08-01

The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to ‘sausage’ shape by a deformation parameter ν. This model is defined by a factorizable S-matrix which is obtained by deforming that of the O(3) sigma model by a parameter λ. Clues for the deformed sigma model are provided by various UV and IR information through the thermodynamic Bethe ansatz (TBA) analysis based on the S-matrix. Application of TBA to the sausage model is, however, limited to the case of 1/λ integer where the coupled integral equations can be truncated to a finite number. In this paper, we propose a finite set of nonlinear integral equations (NLIEs), which are applicable to generic value of λ. Our derivation is based on T-Q relations extracted from the truncated TBA equations. For a consistency check, we compute next-leading order corrections of the vacuum energy and extract the S-matrix information in the IR limit. We also solved the NLIE both analytically and numerically in the UV limit to get the effective central charge and compared with that of the zero-mode dynamics to obtain exact relation between ν and λ. Dedicated to the memory of Petr Petrovich Kulish.

On the Use of Structural Equation Models in Marketing Modeling

NARCIS (Netherlands)

Steenkamp, J.E.B.M.; Baumgartner, H.

2000-01-01

We reflect on the role of structural equation modeling (SEM) in marketing modeling and managerial decision making. We discuss some benefits provided by SEM and alert marketing modelers to several recent developments in SEM in three areas: measurement analysis, analysis of cross-sectional data, and

Is the Langevin phase equation an efficient model for oscillating neurons?

Science.gov (United States)

Ota, Keisuke; Tsunoda, Takamasa; Omori, Toshiaki; Watanabe, Shigeo; Miyakawa, Hiroyoshi; Okada, Masato; Aonishi, Toru

2009-12-01

The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.

Is the Langevin phase equation an efficient model for oscillating neurons?

International Nuclear Information System (INIS)

Ota, Keisuke; Tsunoda, Takamasa; Aonishi, Toru; Omori, Toshiaki; Okada, Masato; Watanabe, Shigeo; Miyakawa, Hiroyoshi

2009-01-01

The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.

Qualitative analysis of nonlinear incidence rate upon the behaviour of an epidemiological model

International Nuclear Information System (INIS)

Li Xiaogui.

1988-12-01

Two theorems concerning the solutions of the system of differential equations describing an epidemiological model with nonlinear incidence rate per infective individual are demonstrated. 2 refs, 1 fig

ESTIMATION OF CONSTANT AND TIME-VARYING DYNAMIC PARAMETERS OF HIV INFECTION IN A NONLINEAR DIFFERENTIAL EQUATION MODEL.

Science.gov (United States)

Liang, Hua; Miao, Hongyu; Wu, Hulin

2010-03-01

Modeling viral dynamics in HIV/AIDS studies has resulted in deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper, we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies. We applied the proposed techniques to estimate the key HIV viral dynamic parameters for two individual AIDS patients treated with antiretroviral therapies. We demonstrate that HIV viral dynamics can be well characterized and

Optimal harvesting for a predator-prey agent-based model using difference equations.

Science.gov (United States)

Oremland, Matthew; Laubenbacher, Reinhard

2015-03-01

In this paper, a method known as Pareto optimization is applied in the solution of a multi-objective optimization problem. The system in question is an agent-based model (ABM) wherein global dynamics emerge from local interactions. A system of discrete mathematical equations is formulated in order to capture the dynamics of the ABM; while the original model is built up analytically from the rules of the model, the paper shows how minor changes to the ABM rule set can have a substantial effect on model dynamics. To address this issue, we introduce parameters into the equation model that track such changes. The equation model is amenable to mathematical theory—we show how stability analysis can be performed and validated using ABM data. We then reduce the equation model to a simpler version and implement changes to allow controls from the ABM to be tested using the equations. Cohen's weighted κ is proposed as a measure of similarity between the equation model and the ABM, particularly with respect to the optimization problem. The reduced equation model is used to solve a multi-objective optimization problem via a technique known as Pareto optimization, a heuristic evolutionary algorithm. Results show that the equation model is a good fit for ABM data; Pareto optimization provides a suite of solutions to the multi-objective optimization problem that can be implemented directly in the ABM.

An effective rate equation approach to reaction kinetics in small volumes: theory and application to biochemical reactions in nonequilibrium steady-state conditions.

Science.gov (United States)

Grima, R

2010-07-21

Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the

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

Science.gov (United States)

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.

[Estimating glomerular filtration rate in 2012: which adding value for the CKD-EPI equation?].

Science.gov (United States)

Delanaye, Pierre; Mariat, Christophe; Moranne, Olivier; Cavalier, Etienne; Flamant, Martin

2012-07-01

Measuring or estimating glomerular filtration rate (GFR) is still considered as the best way to apprehend global renal function. In 2009, the new Chronic Kidney Disease Epidemiology (CKD-EPI) equation has been proposed as a better estimator of GFR than the Modification of Diet in Renal Disease (MDRD) study equation. This new equation is supposed to underestimate GFR to a lesser degree in higher GFR levels. In this review, we will present and deeply discuss the performances of this equation. Based on articles published between 2009 and 2012, this review will underline advantages, notably the better knowledge of chronic kidney disease prevalence, but also limitations of this new equation, especially in some specific populations. We eventually insist on the fact that all these equations are estimations and nephrologists should remain cautious in their interpretation. Copyright © 2012 Association Société de néphrologie. Published by Elsevier SAS. All rights reserved.

Half-trek criterion for generic identifiability of linear structural equation models

NARCIS (Netherlands)

Foygel, R.; Draisma, J.; Drton, M.

2012-01-01

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations

Half-trek criterion for generic identifiability of linear structural equation models

NARCIS (Netherlands)

Foygel, R.; Draisma, J.; Drton, M.

2011-01-01

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations

Macroscopic rate equation modeling of trapping/detrapping of hydrogen isotopes in tungsten materials

Energy Technology Data Exchange (ETDEWEB)

Hodille, E.A., E-mail: etienne.hodille@cea.fr [CEA, IRFM, F-13108 Saint Paul lez Durance (France); Bonnin, X. [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, F-93430 Villetaneuse (France); Bisson, R.; Angot, T. [Aix-Marseille Université, PIIM, CNRS, UMR 7345, 13397 Marseille (France); Becquart, C.S. [Université Lille I, UMET, UMR 8207, 59655 Villeneuve d’Ascq cédex France (France); Layet, J.M. [Aix-Marseille Université, PIIM, CNRS, UMR 7345, 13397 Marseille (France); Grisolia, C. [CEA, IRFM, F-13108 Saint Paul lez Durance (France)

2015-12-15

Relevant parameters for trapping of Hydrogen Isotopes (HIs) in polycrystalline tungsten are determined with the MHIMS code (Migration of Hydrogen Isotopes in MaterialS) which is used to reproduce Thermal Desorption Spectrometry experiments. Three types of traps are found: two intrinsic traps (detrapping energy of 0.87 eV and 1.00 eV) and one extrinsic trap created by ion irradiation (detrapping energy of 1.50 eV). Then MHIMS is used to simulate HIs retention at different fluences and different implantation temperatures. Simulation results agree well with experimental data. It is shown that at 300 K the retention is limited by diffusion in the bulk. For implantation temperatures above 500 K, the retention is limited by trap creation processes. Above 600 K, the retention drops by two orders of magnitude as compared to the retention at 300 K. With the determined detrapping energies, HIs outgassing at room temperature is predicted. After ions implantation at 300 K, 45% of the initial retention is lost to vacuum in 300 000 s while during this time the remaining trapped HIs diffuse twice as deep into the bulk. - Highlights: • Code development to solve numerically the model equations of diffusion and trapping of hydrogen in metals. • Parametrization of the model trapping parameters (detrapping energies and density): fitting of experimental TDS spectrum. • Confrontation model/experiment: evolution of retention with fluence and implantation temperature. • Investigation of period of rest between implantation and TDS on retention and depth profile.

Structural equation modeling and natural systems

Science.gov (United States)

Grace, James B.

2006-01-01

This book, first published in 2006, presents an introduction to the methodology of structural equation modeling, illustrates its use, and goes on to argue that it has revolutionary implications for the study of natural systems. A major theme of this book is that we have, up to this point, attempted to study systems primarily using methods (such as the univariate model) that were designed only for considering individual processes. Understanding systems requires the capacity to examine simultaneous influences and responses. Structural equation modeling (SEM) has such capabilities. It also possesses many other traits that add strength to its utility as a means of making scientific progress. In light of the capabilities of SEM, it can be argued that much of ecological theory is currently locked in an immature state that impairs its relevance. It is further argued that the principles of SEM are capable of leading to the development and evaluation of multivariate theories of the sort vitally needed for the conservation of natural systems.

Equation-free modeling unravels the behavior of complex ecological systems

Science.gov (United States)

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.

Comment on 'A Forecasting Equation for the Canada-US Dollar Real Exchange Rate'

OpenAIRE

Kollmann, Robert

1993-01-01

This paper is a comment on the paper 'A Forecasting Equation for the Canada-US Dollar Exchange Rate' (Robert Amano and Simon van Norden, Bank of Canada). The comment was published in: The Exchange Rate and the Economy, Proceedings of 1992 Bank of Canada Conference; Bank of Canada, 1993, Ottawa (ISBN 0-660-15195-2), pp. 266-271.

A Finite-Rate-Catalytic Model For Hypersonic Flows Informed By Molecular Dynamics

Science.gov (United States)

Schwartzentruber, T. E.; Valentini, P.; Norman, P.; Sorensen, C.

2011-05-01

The implementation of a finite-rate catalytic (FRC) wall boundary condition within a general 3D unstructured CFD solver is described. A set of one-step gas-surface chemical equations and atomistic parameters that deter- mine the reaction rates must be prescribed as input to the model. The chemical rate equations are solved at each wall face in the CFD simulation and result in a net production of species at the wall. In order for a finite- rate gas-surface reaction model to be consistent at equilibrium, it is determined that not all forward and back- ward rates can be specified arbitrarily. Provided that the forward rates for each surface recombination are as- signed, the backward rates must be determined using equilibrium constants that are consistent with the gas- phase chemistry model and thermodynamics. Reactive molecular dynamics (MD) simulations are performed us- ing the ReaxFFSiO potential to investigate oxygen-silica interactions. β-quartz and amorphous SiO2 surfaces are accommodated to a high temperature gas via MD simulation and reach a steady-state surface coverage. In addition to stable surface reconstructions a number of active sites are observed on which recombination occurs. Single collision MD simulations are performed where gas-phase oxygen atoms interact with the most dominant active site. Probabilities of recombination are found to have an exponential trend with gas-surface system temperature. The MD simulations are used to determine the activation energy for Eley-Rideal recombination of oxygen on a specific silica active site which is an important input parameter for the FRC model.

Generalized Ordinary Differential Equation Models.

Science.gov (United States)

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-10-01

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method.

Applications of Multilevel Structural Equation Modeling to Cross-Cultural Research

Science.gov (United States)

Cheung, Mike W.-L.; Au, Kevin

2005-01-01

Multilevel structural equation modeling (MSEM) has been proposed as an extension to structural equation modeling for analyzing data with nested structure. We have begun to see a few applications in cross-cultural research in which MSEM fits well as the statistical model. However, given that cross-cultural studies can only afford collecting data…

Equations of motion for a (non-linear) scalar field model as derived from the field equations

International Nuclear Information System (INIS)

Kaniel, S.; Itin, Y.

2006-01-01

The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

A complex-valued firing-rate model that approximates the dynamics of spiking networks.

Directory of Open Access Journals (Sweden)

Evan S Schaffer

2013-10-01

Full Text Available Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons.

A complex-valued firing-rate model that approximates the dynamics of spiking networks.

Science.gov (United States)

Schaffer, Evan S; Ostojic, Srdjan; Abbott, L F

2013-10-01

Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons.

Decay Rates of Interactive Hyperbolic-Parabolic PDE Models with Thermal Effects on the Interface

International Nuclear Information System (INIS)

Lasiecka, I.; Lebiedzik, C.

2000-01-01

We consider coupled PDE systems comprising of a hyperbolic and a parabolic-like equation with an interface on a portion of the boundary. These models are motivated by structural acoustic problems. A specific prototype consists of a wave equation defined on a three-dimensional bounded domain Ω coupled with a thermoelastic plate equation defined on Γ 0 -a flat surface of the boundary Ω. Thus, the coupling between the wave and the plate takes place on the interface Γ 0 . The main issue studied here is that of uniform stability of the overall interactive model. Since the original (uncontrolled) model is only strongly stable, but not uniformly stable, the question becomes: what is the 'minimal amount' of dissipation necessary to obtain uniform decay rates for the energy of the overall system? Our main result states that boundary nonlinear dissipation placed only on a suitable portion of the part of the boundary which is complementary to Γ 0 , suffices for the stabilization of the entire structure. This result is new with respect to the literature on several accounts: (i) thermoelasticity is accounted for in the plate model; (ii) the plate model does not account for any type of mechanical damping, including the structural damping most often considered in the literature; (iii) there is no mechanical damping placed on the interface Γ 0 ; (iv) the boundary damping is nonlinear without a prescribed growth rate at the origin; (v) the undamped portions of the boundary partial Ω are subject to Neumann (rather than Dirichlet) boundary conditions, which is a recognized difficulty in the context of stabilization of wave equations, due to the fact that the strong Lopatinski condition does not hold. The main mathematical challenge is to show how the thermal energy is propagated onto the hyperbolic component of the structure. This is achieved by using a recently developed sharp theory of boundary traces corresponding to wave and plate equations, along with the analytic

A model for reaction rates in turbulent reacting flows

Science.gov (United States)

Chinitz, W.; Evans, J. S.

1984-01-01

To account for the turbulent temperature and species-concentration fluctuations, a model is presented on the effects of chemical reaction rates in computer analyses of turbulent reacting flows. The model results in two parameters which multiply the terms in the reaction-rate equations. For these two parameters, graphs are presented as functions of the mean values and intensity of the turbulent fluctuations of the temperature and species concentrations. These graphs will facilitate incorporation of the model into existing computer programs which describe turbulent reacting flows. When the model was used in a two-dimensional parabolic-flow computer code to predict the behavior of an experimental, supersonic hydrogen jet burning in air, some improvement in agreement with the experimental data was obtained in the far field in the region near the jet centerline. Recommendations are included for further improvement of the model and for additional comparisons with experimental data.

The issue of statistical power for overall model fit in evaluating structural equation models

Directory of Open Access Journals (Sweden)

Richard HERMIDA

2015-06-01

Full Text Available Statistical power is an important concept for psychological research. However, examining the power of a structural equation model (SEM is rare in practice. This article provides an accessible review of the concept of statistical power for the Root Mean Square Error of Approximation (RMSEA index of overall model fit in structural equation modeling. By way of example, we examine the current state of power in the literature by reviewing studies in top Industrial-Organizational (I/O Psychology journals using SEMs. Results indicate that in many studies, power is very low, which implies acceptance of invalid models. Additionally, we examined methodological situations which may have an influence on statistical power of SEMs. Results showed that power varies significantly as a function of model type and whether or not the model is the main model for the study. Finally, results indicated that power is significantly related to model fit statistics used in evaluating SEMs. The results from this quantitative review imply that researchers should be more vigilant with respect to power in structural equation modeling. We therefore conclude by offering methodological best practices to increase confidence in the interpretation of structural equation modeling results with respect to statistical power issues.

Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate

Directory of Open Access Journals (Sweden)

Li Yingke

2011-01-01

Full Text Available Based on some well-known SIR models, a revised nonautonomous SIR epidemic model with distributed delay and density-dependent birth rate was considered. Applying some classical analysis techniques for ordinary differential equations and the method proposed by Wang (2002, the threshold value for the permanence and extinction of the model was obtained.

Transport and relaxation properties of superfluid 3He. I. Kinetic equation and Bogoliubov quasiparticle relaxation rate

International Nuclear Information System (INIS)

Einzel, D.; Woelfle, P.

1978-01-01

The kinetic equation for Bogoliubov quasiparticles for both the A and B phases of superfluid 3 He is derived from the general matrix kinetic equation. A condensed expression for the exact spin-symmetric collision integral is given. The quasiparticle relaxation rate is calculated for the BW state using the s--p approximation for the quasiparticle scattering amplitude. By using the results for the quasiparticle relaxation rate, the mean free path of Bogoliubov quasiparticles is calculated for all temperatures

Money market rates and implied CCAPM rates: some international evidence

OpenAIRE

Yamin Ahmad

2004-01-01

New Neoclassical Synthesis models equate the instrument of monetary policy to the implied CCAPM rate arising from an Euler equation. This paper identifies monetary policy shocks within six of the G7 countries and examines the movement of money market and implied CCAPM rates. The key result is that an increase in the nominal interest rate leads to a fall in the implied CCAPM rate. Incorporating habit still yields the same result. The findings suggest that the movement of these two rates implie...

Strain Rate Dependant Material Model for Orthotropic Metals

International Nuclear Information System (INIS)

Vignjevic, Rade

2016-01-01

In manufacturing processes anisotropic metals are often exposed to the loading with high strain rates in the range from 10"2 s"-"1 to 10"6 s"-"1 (e.g. stamping, cold spraying and explosive forming). These types of loading often involve generation and propagation of shock waves within the material. The material behaviour under such a complex loading needs to be accurately modelled, in order to optimise the manufacturing process and achieve appropriate properties of the manufactured component. The presented research is related to development and validation of a thermodynamically consistent physically based constitutive model for metals under high rate loading. The model is capable of modelling damage, failure and formation and propagation of shock waves in anisotropic metals. The model has two main parts: the strength part which defines the material response to shear deformation and an equation of state (EOS) which defines the material response to isotropic volumetric deformation [1]. The constitutive model was implemented into the transient nonlinear finite element code DYNA3D [2] and our in house SPH code. Limited model validation was performed by simulating a number of high velocity material characterisation and validation impact tests. The new damage model was developed in the framework of configurational continuum mechanics and irreversible thermodynamics with internal state variables. The use of the multiplicative decomposition of deformation gradient makes the model applicable to arbitrary plastic and damage deformations. To account for the physical mechanisms of failure, the concept of thermally activated damage initially proposed by Tuller and Bucher [3], Klepaczko [4] was adopted as the basis for the new damage evolution model. This makes the proposed damage/failure model compatible with the Mechanical Threshold Strength (MTS) model Follansbee and Kocks [5], 1988; Chen and Gray [6] which was used to control evolution of flow stress during plastic

Current use of equations for estimating glomerular filtration rate in Spanish laboratories.

Science.gov (United States)

Gràcia-Garcia, Sílvia; Montañés-Bermúdez, Rosario; Morales-García, Luis J; Díez-de Los Ríos, M José; Jiménez-García, Juan Á; Macías-Blanco, Carlos; Martínez-López, Rosalina; Ruiz-Altarejos, Joaquín; Ruiz-Martín, Guadalupe; Sanz-Hernández, Sonia; Ventura-Pedret, Salvador

2012-07-17

In 2006 the Spanish Society of Clinical Biochemistry and Molecular Pathology (SEQC) and the Spanish Society of Nephrology (S.E.N.) developed a consensus document in order to facilitate the diagnosis and monitoring of chronic kidney disease with the incorporation of equations for estimating glomerular filtration rate (eGFR) into laboratory reports. The current national prevalence of eGFR reporting and the degree of adherence to these recommendations among clinical laboratories is unknown. We administered a national survey in 2010-11 to Spanish clinical laboratories. The survey was through e-mail or telephone to laboratories that participated in the SEQC’s Programme for External Quality Assurance, included in the National Hospitals Catalogue 2010, including both primary care and private laboratories. A total of 281 laboratories answered to the survey. Of these, 88.2% reported on the eGFR, with 61.9% reporting on the MDRD equation and 31.6% using the MDRD-IDMS equation. A total of 42.5% of laboratories always reported serum creatinine values, and other variables only when specifically requested. Regarding the way results were presented, 46.2% of laboratories reported the exact numerical value only when the filtration rate was below 60mL/min/1.73m2, while 50.6% reported all values regardless. In 56.3% of the cases reporting eGFR, an interpretive commentary of it was enclosed. Although a high percentage of Spanish laboratories have added eGFR in their reports, this metric is not universally used. Moreover, some aspects, such as the equation used and the correct expression of eGFR results, should be improved.

Michaelis - Menten equation for degradation of insoluble substrate

DEFF Research Database (Denmark)

Andersen, Morten; Kari, Jeppe; Borch, Kim

2017-01-01

substrate it is difficult to assess whether the requirement of the MM equation is met. In this paper we study a simple kinetic model, where removal of attack sites expose new ones which preserve the total accessible substrate, and denote this approach the substrate conserving model. The kinetic equations...... are solved in closed form, both steady states and progress curves, for any admissible values of initial conditions and rate constants. The model is shown to merge with the MM equation and the reverse MM equation when these are valid. The relation between available molar concentration of attack sites and mass...

Development of two-group interfacial area transport equation for confined flow-1. Modeling of bubble interactions

International Nuclear Information System (INIS)

Sun, Xiaodong; Kim, Seungjin; Ishii, Mamoru; Beus, Stephen G.

2003-01-01

This paper presents the modeling of bubble interaction mechanisms in the two-group interfacial area transport equation (IATE) for confined gas-liquid two-phase flow. The transport equation is applicable to bubbly, cap-turbulent, and churn-turbulent flow regimes. In the two-group IATE, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Five major bubble interaction mechanisms are identified for the gas-liquid two-phase flow of interest, and are analytically modeled as the source/sink terms for the transport equations based on certain assumptions for the confined flow. These models include both intra-group (within a certain group) and inter-group (between two groups) bubble interactions. The comparisons of the prediction by the one-dimensional two-group IATE with experimental data are presented in the second paper of this series. (author)

Stochastic fractional differential equations: Modeling, method and analysis

International Nuclear Information System (INIS)

Pedjeu, Jean-C.; Ladde, Gangaram S.

2012-01-01

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.

The lattice Boltzmann model for the second-order Benjamin–Ono equations

International Nuclear Information System (INIS)

Lai, Huilin; Ma, Changfeng

2010-01-01

In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin–Ono equation. With the Taylor expansion and the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations

Variability of glomerular filtration rate estimation equations in elderly Chinese patients with chronic kidney disease

Directory of Open Access Journals (Sweden)

Liu X

2012-10-01

Full Text Available Xun Liu,1,2,* Mu-hua Cheng,3,* Cheng-gang Shi,1 Cheng Wang,1 Cai-lian Cheng,1 Jin-xia Chen,1 Hua Tang,1 Zhu-jiang Chen,1 Zeng-chun Ye,1 Tan-qi Lou11Division of Nephrology, Department of Internal Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China; 2College of Biology Engineering, South China University of Technology, Guangzhou, China; 3Department of Nuclear Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China *These authors contributed equally to this paperBackground: Chronic kidney disease (CKD is recognized worldwide as a public health problem, and its prevalence increases as the population ages. However, the applicability of formulas for estimating the glomerular filtration rate (GFR based on serum creatinine (SC levels in elderly Chinese patients with CKD is limited.Materials and methods: Based on values obtained with the technetium-99m diethylenetriaminepentaacetic acid (99mTc-DTPA renal dynamic imaging method, 319 elderly Chinese patients with CKD were enrolled in this study. Serum creatinine was determined by the enzymatic method. The GFR was estimated using the Cockroft–Gault (CG equation, the Modification of Diet in Renal Disease (MDRD equations, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equation, the Jelliffe-1973 equation, and the Hull equation.Results: The median of difference ranged from −0.3–4.3 mL/min/1.73 m2. The interquartile range (IQR of differences ranged from 13.9–17.6 mL/min/1.73 m2. Accuracy with a deviation less than 15% ranged from 27.6%–32.9%. Accuracy with a deviation less than 30% ranged from 53.6%–57.7%. Accuracy with a deviation less than 50% ranged from 74.9%–81.5%. None of the equations had accuracy up to the 70% level with a deviation less than 30% from the standard glomerular filtration rate (sGFR. Bland–Altman analysis demonstrated that the mean difference ranged from −3.0–2.4 mL/min/1.73 m2. However, the

Best-fitting prediction equations for basal metabolic rate: informing obesity interventions in diverse populations.

Science.gov (United States)

Sabounchi, N S; Rahmandad, H; Ammerman, A

2013-10-01

Basal metabolic rate (BMR) represents the largest component of total energy expenditure and is a major contributor to energy balance. Therefore, accurately estimating BMR is critical for developing rigorous obesity prevention and control strategies. Over the past several decades, numerous BMR formulas have been developed targeted to different population groups. A comprehensive literature search revealed 248 BMR estimation equations developed using diverse ranges of age, gender, race, fat-free mass, fat mass, height, waist-to-hip ratio, body mass index and weight. A subset of 47 studies included enough detail to allow for development of meta-regression equations. Utilizing these studies, meta-equations were developed targeted to 20 specific population groups. This review provides a comprehensive summary of available BMR equations and an estimate of their accuracy. An accompanying online BMR prediction tool (available at http://www.sdl.ise.vt.edu/tutorials.html) was developed to automatically estimate BMR based on the most appropriate equation after user-entry of individual age, race, gender and weight.

Translational control of a graphically simulated robot arm by kinematic rate equations that overcome elbow joint singularity

Science.gov (United States)

Barker, L. K.; Houck, J. A.; Carzoo, S. W.

1984-01-01

An operator commands a robot hand to move in a certain direction relative to its own axis system by specifying a velocity in that direction. This velocity command is then resolved into individual joint rotational velocities in the robot arm to effect the motion. However, the usual resolved-rate equations become singular when the robot arm is straightened. To overcome this elbow joint singularity, equations were developed which allow continued translational control of the robot hand even though the robot arm is (or is nearly) fully extended. A feature of the equations near full arm extension is that an operator simply extends and retracts the robot arm to reverse the direction of the elbow bend (difficult maneuver for the usual resolved-rate equations). Results show successful movement of a graphically simulated robot arm.

One-equation near-wall turbulence modeling with the aid of direct simulation data

Science.gov (United States)

Rodi, W.; Mansour, N. N.; Michelassi, V.

1993-01-01

The length scales appearing in the relations for the eddy viscosity and dissipation rate in one-equation models were evaluated from direct numerical (DNS) simulation data for developed channel and boundary-layer flow at two Reynolds numbers each. To prepare the ground for the evaluation, the distribution of the most relevant mean-flow and turbulence quantities is presented and discussed, also with respect to Reynolds-number influence and to differences between channel and boundary-layer flow. An alternative model is tested as near wall component of a two-layer model by application to developed-channel, boundary-layer and backward-facing-step flows.

Evolution of a Network of Vortex Loops in He-II: Exact Solution of the Rate Equation

International Nuclear Information System (INIS)

Nemirovskii, Sergey K.

2006-01-01

The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the ''rate equation'' for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact powerlike solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l)∝l -5/2 obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection

Evolution of a network of vortex loops in He-II: exact solution of the rate equation.

Science.gov (United States)

Nemirovskii, Sergey K

2006-01-13

The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the "rate equation" for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact power-like solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l) proportional l(-5/2) obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection.

Modeling High Frequency Semiconductor Devices Using Maxwell's Equations

National Research Council Canada - National Science Library

El-Ghazaly, Samier

1999-01-01

.... In this research, we first replaced the conventional semiconductor device models, which are based on Poisson's Equation as a semiconductor model, with a new one that uses the full-wave electro...

Development of the Galaxy Chronic Obstructive Pulmonary Disease (COPD) Model Using Data from ECLIPSE: Internal Validation of a Linked-Equations Cohort Model.

Science.gov (United States)

Briggs, Andrew H; Baker, Timothy; Risebrough, Nancy A; Chambers, Mike; Gonzalez-McQuire, Sebastian; Ismaila, Afisi S; Exuzides, Alex; Colby, Chris; Tabberer, Maggie; Muellerova, Hana; Locantore, Nicholas; Rutten van Mölken, Maureen P M H; Lomas, David A

2017-05-01

The recent joint International Society for Pharmacoeconomics and Outcomes Research / Society for Medical Decision Making Modeling Good Research Practices Task Force emphasized the importance of conceptualizing and validating models. We report a new model of chronic obstructive pulmonary disease (COPD) (part of the Galaxy project) founded on a conceptual model, implemented using a novel linked-equation approach, and internally validated. An expert panel developed a conceptual model including causal relationships between disease attributes, progression, and final outcomes. Risk equations describing these relationships were estimated using data from the Evaluation of COPD Longitudinally to Identify Predictive Surrogate Endpoints (ECLIPSE) study, with costs estimated from the TOwards a Revolution in COPD Health (TORCH) study. Implementation as a linked-equation model enabled direct estimation of health service costs and quality-adjusted life years (QALYs) for COPD patients over their lifetimes. Internal validation compared 3 years of predicted cohort experience with ECLIPSE results. At 3 years, the Galaxy COPD model predictions of annual exacerbation rate and annual decline in forced expiratory volume in 1 second fell within the ECLIPSE data confidence limits, although 3-year overall survival was outside the observed confidence limits. Projections of the risk equations over time permitted extrapolation to patient lifetimes. Averaging the predicted cost/QALY outcomes for the different patients within the ECLIPSE cohort gives an estimated lifetime cost of £25,214 (undiscounted)/£20,318 (discounted) and lifetime QALYs of 6.45 (undiscounted/5.24 [discounted]) per ECLIPSE patient. A new form of model for COPD was conceptualized, implemented, and internally validated, based on a series of linked equations using epidemiological data (ECLIPSE) and cost data (TORCH). This Galaxy model predicts COPD outcomes from treatment effects on disease attributes such as lung function

Testing strong factorial invariance using three-level structural equation modeling

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Suzanne eJak

2014-07-01

Full Text Available Within structural equation modeling, the most prevalent model to investigate measurement bias is the multigroup model. Equal factor loadings and intercepts across groups in a multigroup model represent strong factorial invariance (absence of measurement bias across groups. Although this approach is possible in principle, it is hardly practical when the number of groups is large or when the group size is relatively small. Jak, Oort and Dolan (2013 showed how strong factorial invariance across large numbers of groups can be tested in a multilevel structural equation modeling framework, by treating group as a random instead of a fixed variable. In the present study, this model is extended for use with three-level data. The proposed method is illustrated with an investigation of strong factorial invariance across 156 school classes and 50 schools in a Dutch dyscalculia test, using three-level structural equation modeling.

Mathematical analysis of partial differential equations modeling electrostatic MEMS

CERN Document Server

Esposito, Pierpaolo; Guo, Yujin

2010-01-01

Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing "electrostatically actuated" MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems-where the stationary MEMS models fit-are a well-developed

A Structural Equation Modeling Analysis of Influences on Juvenile Delinquency

Science.gov (United States)

Barrett, David E.; Katsiyannis, Antonis; Zhang, Dalun; Zhang, Dake

2014-01-01

This study examined influences on delinquency and recidivism using structural equation modeling. The sample comprised 199,204 individuals: 99,602 youth whose cases had been processed by the South Carolina Department of Juvenile Justice and a matched control group of 99,602 youth without juvenile records. Structural equation modeling for the…

Malaria model with periodic mosquito birth and death rates.

Science.gov (United States)

Dembele, Bassidy; Friedman, Avner; Yakubu, Abdul-Aziz

2009-07-01

In this paper, we introduce a model of malaria, a disease that involves a complex life cycle of parasites, requiring both human and mosquito hosts. The novelty of the model is the introduction of periodic coefficients into the system of one-dimensional equations, which account for the seasonal variations (wet and dry seasons) in the mosquito birth and death rates. We define a basic reproduction number R(0) that depends on the periodic coefficients and prove that if R(0)1 then the disease is endemic and may even be periodic.

The discretized Schroedinger equation and simple models for semiconductor quantum wells

International Nuclear Information System (INIS)

Boykin, Timothy B; Klimeck, Gerhard

2004-01-01

The discretized Schroedinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schroedinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schroedinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one

Dynamic modeling of interfacial structures via interfacial area transport equation

International Nuclear Information System (INIS)

Seungjin, Kim; Mamoru, Ishii

2005-01-01

The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. In the present paper, the interfacial area transport equations currently available are reviewed to address the feasibility and reliability of the model along with extensive experimental results. These include the data from adiabatic upward air-water two-phase flow in round tubes of various sizes, from a rectangular duct, and from adiabatic co-current downward air-water two-phase flow in round pipes of two sizes. (authors)

Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models

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Narcisa Apreutesei

2014-05-01

Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.

Dynamic modeling of interfacial structures via interfacial area transport equation

International Nuclear Information System (INIS)

Seungjin, Kim; Mamoru, Ishii

2004-01-01

Full text of publication follows:In the current thermal-hydraulic system analysis codes using the two-fluid model, the empirical correlations that are based on the two-phase flow regimes and regime transition criteria are being employed as closure relations for the interfacial transfer terms. Due to its inherent shortcomings, however, such static correlations are inaccurate and present serious problems in the numerical analysis. In view of this, a new dynamic approach employing the interfacial area transport equation has been studied. The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Therefore, the interfacial area transport equation can make a leapfrog improvement in the current capability of the two-fluid model from both scientific and practical point of view. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. The coalescence mechanisms include the random collision driven by turbulence, and the entrainment of trailing bubbles in the wake region of the preceding bubble. The disintegration mechanisms include the break-up by turbulence impact, shearing-off at the rim of large cap bubbles and the break-up of large cap

Continuous Time Structural Equation Modeling with R Package ctsem

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Charles C. Driver

2017-04-01

Full Text Available We introduce ctsem, an R package for continuous time structural equation modeling of panel (N > 1 and time series (N = 1 data, using full information maximum likelihood. Most dynamic models (e.g., cross-lagged panel models in the social and behavioural sciences are discrete time models. An assumption of discrete time models is that time intervals between measurements are equal, and that all subjects were assessed at the same intervals. Violations of this assumption are often ignored due to the difficulty of accounting for varying time intervals, therefore parameter estimates can be biased and the time course of effects becomes ambiguous. By using stochastic differential equations to estimate an underlying continuous process, continuous time models allow for any pattern of measurement occasions. By interfacing to OpenMx, ctsem combines the flexible specification of structural equation models with the enhanced data gathering opportunities and improved estimation of continuous time models. ctsem can estimate relationships over time for multiple latent processes, measured by multiple noisy indicators with varying time intervals between observations. Within and between effects are estimated simultaneously by modeling both observed covariates and unobserved heterogeneity. Exogenous shocks with different shapes, group differences, higher order diffusion effects and oscillating processes can all be simply modeled. We first introduce and define continuous time models, then show how to specify and estimate a range of continuous time models using ctsem.

Mechanical modeling for magnetorheological elastomer isolators based on constitutive equations and electromagnetic analysis

Science.gov (United States)

Wang, Qi; Dong, Xufeng; Li, Luyu; Ou, Jinping

2018-06-01

As constitutive models are too complicated and existing mechanical models lack universality, these models are beyond satisfaction for magnetorheological elastomer (MRE) devices. In this article, a novel universal method is proposed to build concise mechanical models. Constitutive model and electromagnetic analysis were applied in this method to ensure universality, while a series of derivations and simplifications were carried out to obtain a concise formulation. To illustrate the proposed modeling method, a conical MRE isolator was introduced. Its basic mechanical equations were built based on equilibrium, deformation compatibility, constitutive equations and electromagnetic analysis. An iteration model and a highly efficient differential equation editor based model were then derived to solve the basic mechanical equations. The final simplified mechanical equations were obtained by re-fitting the simulations with a novel optimal algorithm. In the end, verification test of the isolator has proved the accuracy of the derived mechanical model and the modeling method.

TBA equations for excited states in the sine-Gordon model

International Nuclear Information System (INIS)

Balog, Janos; Hegedus, Arpad

2004-01-01

We propose thermodynamic Bethe ansatz (TBA) integral equations for multi-particle soliton (fermion) states in the sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-de Vega equation) description of the model is given. At the special value β 2 = 6π of the sine-Gordon coupling, exact expressions for energy and momentum eigenvalues of one-particle states are found

Integrable hydrodynamics of Calogero-Sutherland model: bidirectional Benjamin-Ono equation

International Nuclear Information System (INIS)

Abanov, Alexander G; Bettelheim, Eldad; Wiegmann, Paul

2009-01-01

We develop a hydrodynamic description of the classical Calogero-Sutherland liquid: a Calogero-Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analog of the Benjamin-Ono equation. The latter is known to describe internal waves of deep stratified fluids. We show that the bidirectional Benjamin-Ono equation appears as a real reduction of the modified KP hierarchy. We derive the chiral nonlinear equation which appears as a chiral reduction of the bidirectional equation. The conventional Benjamin-Ono equation is a degeneration of the chiral nonlinear equation at large density. We construct multi-phase solutions of the bidirectional Benjamin-Ono equations and of the chiral nonlinear equations

Excited TBA equations I: Massive tricritical Ising model

International Nuclear Information System (INIS)

Pearce, Paul A.; Chim, Leung; Ahn, Changrim

2001-01-01

We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator phi (cursive,open) Greek 1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A 4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m,n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r,s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters χ r,s (q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II

On the Schroedinger equation for the minisuperspace models

International Nuclear Information System (INIS)

Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.

2000-01-01

We obtain a time-dependent Schroedinger equation for the Friedmann-Robertson-Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necessary to include an additional action invariant under the reparametrization of time. The last one does not change the equations of motion of the system, but changes only the constraint which at the quantum level becomes time-dependent Schroedinger equation. The same procedure is applied to the supersymmetric case and the supersymmetric quantum constraints are obtained, one of them is a square root of the Schroedinger operator

Modeling ultrashort electromagnetic pulses with a generalized Kadomtsev-Petviashvili equation

Science.gov (United States)

Hofstrand, A.; Moloney, J. V.

2018-03-01

In this paper we derive a properly scaled model for the nonlinear propagation of intense, ultrashort, mid-infrared electromagnetic pulses (10-100 femtoseconds) through an arbitrary dispersive medium. The derivation results in a generalized Kadomtsev-Petviashvili (gKP) equation. In contrast to envelope-based models such as the Nonlinear Schrödinger (NLS) equation, the gKP equation describes the dynamics of the field's actual carrier wave. It is important to resolve these dynamics when modeling ultrashort pulses. We proceed by giving an original proof of sufficient conditions on the initial pulse for a singularity to form in the field after a finite propagation distance. The model is then numerically simulated in 2D using a spectral-solver with initial data and physical parameters highlighting our theoretical results.

A four-equation friction model for water hammer calculation in quasi-rigid pipelines

International Nuclear Information System (INIS)

Ghodhbani, Abdelaziz; Haj Taïeb, Ezzeddine

2017-01-01

Friction coupling affects water hammer evolution in pipelines according to the initial flow regime. Unsteady friction models are only validated with uncoupled formulation. On the other hand, coupled models such as four-equation model, provide more accurate prediction of water hammer since fluid-structure interaction (FSI) is taken into account, but they are limited to steady-state friction formulation. This paper deals with the creation of the “four-equation friction model” which is based on the incorporation of the unsteady head loss given by an unsteady friction model into the four-equation model. For transient laminar flow cases, the Zielke model is considered. The proposed model is applied to a quasi-rigid pipe with axial moving valve, and then calculated by the method of characteristics (MOC). Damping and shape of the numerical solution are in good agreement with experimental data. Thus, the proposed model can be incorporated into a new computer code. - Highlights: • Both Zielke model and four-equation model are insufficient to predict water hammer. • The four-equation friction model proposed is obtained by incorporating the unsteady head loss in the four-equation model. • The solution obtained by the proposed model is in good agreement with experimental data. • The wave-speed adjustment scheme is more efficient than interpolations schemes.

equateIRT: An R Package for IRT Test Equating

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Michela Battauz

2015-12-01

Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

Correction factor determination on failure rate equation of MacLaurin series for low and high mode application

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Totok R. Biyanto

2016-06-01

Full Text Available Safety Instrumented Function (SIF is implemented on the system to prevent hazard in process industry. In general, most of SIF implementation in process industry works in low demand condition. Safety valuation of SIF that works in low demand can be solved by using quantitative method. The quantitative method is a simplified exponential equation form of MacLaurin series, which can be called simplified equation. Simplified equation used in high demand condition will generate a higher Safety Integrity Level (SIL and it will affect the higher safety cost. Therefore, the value of low or high demand rate limit should be determined to prevent it. The result of this research is a first order equation that can fix the error of SIL, which arises from the usage of simplified equation, without looking the demand rate limit for low and high demand. This equation is applied for SIL determination on SIF with 1oo1 vote. The new equation from this research is λ = 0.9428 λMC + 1.062E−04 H/P, with 5% average of error, where λMC is a value of λ from the simplified equation, Hazardous event frequency (H is a probabilistic frequency of hazard event and P is Probability of Failure on Demand (PFD in Independent Protection Layers (IPLs. The equation generated from this research could correct SIL of SIF in various H and P. Therefore, SIL design problem could be solved and it provides an appropriate SIL.

Modified two-fluid model for the two-group interfacial area transport equation

International Nuclear Information System (INIS)

Sun Xiaodong; Ishii, Mamoru; Kelly, Joseph M.

2003-01-01

This paper presents a modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not practical to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model

The Limit Behavior of a Stochastic Logistic Model with Individual Time-Dependent Rates

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Yilun Shang

2013-01-01

Full Text Available We investigate a variant of the stochastic logistic model that allows individual variation and time-dependent infection and recovery rates. The model is described as a heterogeneous density dependent Markov chain. We show that the process can be approximated by a deterministic process defined by an integral equation as the population size grows.

Two-equation and multi-fluid turbulence models for Rayleigh–Taylor mixing

International Nuclear Information System (INIS)

Kokkinakis, I.W.; Drikakis, D.; Youngs, D.L.; Williams, R.J.R.

2015-01-01

Highlights: • We present a new improved version of the K–L model. • The improved K–L is found in good agreement with the multi-fluid model and ILES. • The study concerns Rayleigh–Taylor flows at initial density ratios 3:1 and 20:1. - Abstract: This paper presents a new, improved version of the K–L model, as well as a detailed investigation of K–L and multi-fluid models with reference to high-resolution implicit large eddy simulations of compressible Rayleigh–Taylor mixing. The accuracy of the models is examined for different interface pressures and specific heat ratios for Rayleigh–Taylor flows at initial density ratios 3:1 and 20:1. It is shown that the original version of the K–L model requires modifications in order to provide comparable results to the multi-fluid model. The modifications concern the addition of an enthalpy diffusion term to the energy equation; the formulation of the turbulent kinetic energy (source) term in the K equation; and the calculation of the local Atwood number. The proposed modifications significantly improve the results of the K–L model, which are found in good agreement with the multi-fluid model and implicit large eddy simulations with respect to the self-similar mixing width; peak turbulent kinetic energy growth rate, as well as volume fraction and turbulent kinetic energy profiles. However, a key advantage of the two-fluid model is that it can represent the degree of molecular mixing in a direct way, by transferring mass between the two phases. The limitations of the single-fluid K–L model as well as the merits of more advanced Reynolds-averaged Navier–Stokes models are also discussed throughout the paper.

Calculus for cognitive scientists partial differential equation models

CERN Document Server

Peterson, James K

2016-01-01

This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics.  A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.

A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate

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Min Sun

2014-01-01

Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.

Neural networks dynamic hysteresis model for piezoceramic actuator based on hysteresis operator of first-order differential equation

International Nuclear Information System (INIS)

Dang Xuanju; Tan Yonghong

2005-01-01

A new neural networks dynamic hysteresis model for piezoceramic actuator is proposed by combining the Preisach model with diagonal recurrent neural networks. The Preisach model is based on elementary rate-independent operators and is not suitable for modeling piezoceramic actuator across a wide frequency band because of the rate-dependent hysteresis characteristic of the piezoceramic actuator. The structure of the developed model is based on the structure of the Preisach model, in which the rate-independent relay hysteresis operators (cells) are replaced by the rate-dependent hysteresis operators of first-order differential equation. The diagonal recurrent neural networks being modified by an adjustable factor can be used to model the hysteresis behavior of the pizeoceramic actuator because its structure is similar to the structure of the modified Preisach model. Therefore, the proposed model not only possesses that of the Preisach model, but also can be used for describing its dynamic hysteresis behavior. Through the experimental results of both the approximation and the prediction, the effectiveness of the neural networks dynamic hysteresis model for the piezoceramic actuator is demonstrated

String beta function equations from c=1 matrix model

CERN Document Server

Dhar, A; Wadia, S R; Dhar, Avinash; Mandal, Gautam; Wadia, Spenta R

1995-01-01

We derive the \\sigma-model tachyon \\beta-function equation of 2-dimensional string theory, in the background of flat space and linear dilaton, working entirely within the c=1 matrix model. The tachyon \\beta-function equation is satisfied by a \\underbar{nonlocal} and \\underbar{nonlinear} combination of the (massless) scalar field of the matrix model. We discuss the possibility of describing the `discrete states' as well as other possible gravitational and higher tensor backgrounds of 2-dimensional string theory within the c=1 matrix model. We also comment on the realization of the W-infinity symmetry of the matrix model in the string theory. The present work reinforces the viewpoint that a nonlocal (and nonlinear) transform is required to extract the space-time physics of 2-dimensional string theory from the c=1 matrix model.

Gross-Pitaevskii equation for Bose particles in a double-well potential: Two-mode models and beyond

International Nuclear Information System (INIS)

Ananikian, D.; Bergeman, T.

2006-01-01

In this work, our primary goal has been to explore the range of validity of two-mode models for Bose-Einstein condensates in double-well potentials. Our derivation, like others, uses symmetric and antisymmetric condensate basis functions for the Gross-Pitaevskii equation. In what we call an 'improved two-mode model' (I2M), the tunneling coupling energy explicitly includes a nonlinear interaction term, which has been given previously in the literature but not widely appreciated. We show that when the atom number (and hence the extent of the wave function) in each well vary appreciably with time, the nonlinear interaction term produces a temporal change in the tunneling energy or rate, which has not previously been considered to our knowledge. In addition, we obtain a parameter, labeled ''interaction tunneling,'' that produces a decrease of the tunneling energy when the wave functions in the two wells overlap to some extent. Especially for larger values of the nonlinear interaction term, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in one and three dimensions, as compared with models that have no interaction term in the tunneling energy. The usefulness of this model is demonstrated by good agreement with recent experimental results for the tunneling oscillation frequency [Albiez et al., Phys. Rev. Lett. 95, 010402 (2005)]. We also present equations and results for a multimode approach, and use the I2M model to obtain modified equations for the second-quantized version of the Bose-Einstein double-well problem

An Adjusted Discount Rate Model for Fuel Cycle Cost Estimation

Energy Technology Data Exchange (ETDEWEB)

Kim, S. K.; Kang, G. B.; Ko, W. I. [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2013-10-15

Owing to the diverse nuclear fuel cycle options available, including direct disposal, it is necessary to select the optimum nuclear fuel cycles in consideration of the political and social environments as well as the technical stability and economic efficiency of each country. Economic efficiency is therefore one of the significant evaluation standards. In particular, because nuclear fuel cycle cost may vary in each country, and the estimated cost usually prevails over the real cost, when evaluating the economic efficiency, any existing uncertainty needs to be removed when possible to produce reliable cost information. Many countries still do not have reprocessing facilities, and no globally commercialized HLW (High-level waste) repository is available. A nuclear fuel cycle cost estimation model is therefore inevitably subject to uncertainty. This paper analyzes the uncertainty arising out of a nuclear fuel cycle cost evaluation from the viewpoint of a cost estimation model. Compared to the same discount rate model, the nuclear fuel cycle cost of a different discount rate model is reduced because the generation quantity as denominator in Equation has been discounted. Namely, if the discount rate reduces in the back-end process of the nuclear fuel cycle, the nuclear fuel cycle cost is also reduced. Further, it was found that the cost of the same discount rate model is overestimated compared with the different discount rate model as a whole.

An Adjusted Discount Rate Model for Fuel Cycle Cost Estimation

International Nuclear Information System (INIS)

Kim, S. K.; Kang, G. B.; Ko, W. I.

2013-01-01

Owing to the diverse nuclear fuel cycle options available, including direct disposal, it is necessary to select the optimum nuclear fuel cycles in consideration of the political and social environments as well as the technical stability and economic efficiency of each country. Economic efficiency is therefore one of the significant evaluation standards. In particular, because nuclear fuel cycle cost may vary in each country, and the estimated cost usually prevails over the real cost, when evaluating the economic efficiency, any existing uncertainty needs to be removed when possible to produce reliable cost information. Many countries still do not have reprocessing facilities, and no globally commercialized HLW (High-level waste) repository is available. A nuclear fuel cycle cost estimation model is therefore inevitably subject to uncertainty. This paper analyzes the uncertainty arising out of a nuclear fuel cycle cost evaluation from the viewpoint of a cost estimation model. Compared to the same discount rate model, the nuclear fuel cycle cost of a different discount rate model is reduced because the generation quantity as denominator in Equation has been discounted. Namely, if the discount rate reduces in the back-end process of the nuclear fuel cycle, the nuclear fuel cycle cost is also reduced. Further, it was found that the cost of the same discount rate model is overestimated compared with the different discount rate model as a whole

Differential equations and integrable models: the SU(3) case

International Nuclear Information System (INIS)

Dorey, Patrick; Tateo, Roberto

2000-01-01

We exhibit a relationship between the massless a 2 (2) integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schroedinger equation. This forms part of a more general correspondence involving A 2 -related Bethe ansatz systems and third-order differential equations. A non-linear integral equation for the generalised spectral problem is derived, and some numerical checks are performed. Duality properties are discussed, and a simple variant of the non-linear equation is suggested as a candidate to describe the finite volume ground state energies of minimal conformal field theories perturbed by the operators phi 12 , phi 21 and phi 15 . This is checked against previous results obtained using the thermodynamic Bethe ansatz

Heat transport in two-dimensional materials by directly solving the phonon Boltzmann equation under Callaway's dual relaxation model

Science.gov (United States)

Guo, Yangyu; Wang, Moran

2017-10-01

The single mode relaxation time approximation has been demonstrated to greatly underestimate the lattice thermal conductivity of two-dimensional materials due to the collective effect of phonon normal scattering. Callaway's dual relaxation model represents a good approximation to the otherwise ab initio solution of the phonon Boltzmann equation. In this work we develop a discrete-ordinate-method (DOM) scheme for the numerical solution of the phonon Boltzmann equation under Callaway's model. Heat transport in a graphene ribbon with different geometries is modeled by our scheme, which produces results quite consistent with the available molecular dynamics, Monte Carlo simulations, and experimental measurements. Callaway's lattice thermal conductivity model with empirical boundary scattering rates is examined and shown to overestimate or underestimate the direct DOM solution. The length convergence of the lattice thermal conductivity of a rectangular graphene ribbon is explored and found to depend appreciably on the ribbon width, with a semiquantitative correlation provided between the convergence length and the width. Finally, we predict the existence of a phonon Knudsen minimum in a graphene ribbon only at a low system temperature and isotope concentration so that the average normal scattering rate is two orders of magnitude stronger than the intrinsic resistive one. The present work will promote not only the methodology for the solution of the phonon Boltzmann equation but also the theoretical modeling and experimental detection of hydrodynamic phonon transport in two-dimensional materials.

Modeling biological gradient formation: combining partial differential equations and Petri nets.

Science.gov (United States)

Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J

2016-01-01

Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.

Modelling equation of knee force during instep kicking using ...

African Journals Online (AJOL)

This paper presents the biomechanics analysis of the football players, to obtain the equation that relates with the variables and to get the force model equation when the kicking was made. The subjects delivered instep kicking by using the dominant's leg where one subjects using right and left leg. 2 Dimensional analysis ...

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

Science.gov (United States)

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

2009-06-01

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

Toward a General Theory for Multiphase Turbulence Part I: Development and Gauging of the Model Equations

Energy Technology Data Exchange (ETDEWEB)

B. A. Kashiwa; W. B. VanderHeyden

2000-12-01

A formalism for developing multiphase turbulence models is introduced by analogy to the phenomenological method used for single-phase turbulence. A sample model developed using the formalism is given in detail. The procedure begins with ensemble averaging of the exact conservation equations, with closure accomplished by using a combination of analytical and experimental results from the literature. The resulting model is applicable to a wide range of common multiphase flows including gas-solid, liquid-solid and gas-liquid (bubbly) flows. The model is positioned for ready extension to three-phase turbulence, or for use in two-phase turbulence in which one phase is accounted for in multiple size classes, representing polydispersivity. The formalism is expected to suggest directions toward a more fundamentally based theory, similar to the way that early work in single-phase turbulence has led to the spectral theory. The approach is unique in that a portion of the total energy decay rate is ascribed to each phase, as is dictated by the exact averaged equations, and results in a transport equation for energy decay rate associated with each phase. What follows is a straightforward definition of a turbulent viscosity for each phase, and accounts for the effect of exchange of fluctuational energy among phases on the turbulent shear viscosity. The model also accounts for the effect of slip momentum transfer among the phases on the production of turbulence kinetic energy and on the tensor character of the Reynolds stress. Collisional effects, when appropriate, are included by superposition. The model reduces to a standard form in limit of a single, pure material, and is expected to do a credible job of describing multiphase turbulent flows in a wide variety of regimes using a single set of coefficients.

A lattice Boltzmann model for the Burgers-Fisher equation.

Science.gov (United States)

Zhang, Jianying; Yan, Guangwu

2010-06-01

A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.

Empiric model for mean generation time adjustment factor for classic point kinetics equations

Energy Technology Data Exchange (ETDEWEB)

Goes, David A.B.V. de; Martinez, Aquilino S.; Goncalves, Alessandro da C., E-mail: david.goes@poli.ufrj.br, E-mail: aquilino@lmp.ufrj.br, E-mail: alessandro@con.ufrj.br [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Departamento de Engenharia Nuclear

2017-11-01

Point reactor kinetics equations are the easiest way to observe the neutron production time behavior in a nuclear reactor. These equations are derived from the neutron transport equation using an approximation called Fick's law leading to a set of first order differential equations. The main objective of this study is to review classic point kinetics equation in order to approximate its results to the case when it is considered the time variation of the neutron currents. The computational modeling used for the calculations is based on the finite difference method. The results obtained with this model are compared with the reference model and then it is determined an empirical adjustment factor that modifies the point reactor kinetics equation to the real scenario. (author)

Empiric model for mean generation time adjustment factor for classic point kinetics equations

International Nuclear Information System (INIS)

Goes, David A.B.V. de; Martinez, Aquilino S.; Goncalves, Alessandro da C.

2017-01-01

Point reactor kinetics equations are the easiest way to observe the neutron production time behavior in a nuclear reactor. These equations are derived from the neutron transport equation using an approximation called Fick's law leading to a set of first order differential equations. The main objective of this study is to review classic point kinetics equation in order to approximate its results to the case when it is considered the time variation of the neutron currents. The computational modeling used for the calculations is based on the finite difference method. The results obtained with this model are compared with the reference model and then it is determined an empirical adjustment factor that modifies the point reactor kinetics equation to the real scenario. (author)

Structural Equation Modeling with the Smartpls

Directory of Open Access Journals (Sweden)

Christian M. Ringle

2014-05-01

Full Text Available The objective of this article is to present a didactic example of Structural Equation Modeling using the software SmartPLS 2.0 M3. The program mentioned uses the method of Partial Least Squares and seeks to address the following situations frequently observed in marketing research: Absence of symmetric distributions of variables measured by a theory still in its beginning phase or with little “consolidation”, formative models, and/or a limited amount of data. The growing use of SmartPLS has demonstrated its robustness and the applicability of the model in the areas that are being studied. 

THE CONTENT MODEL AND THE EQUATIONS OF MOTION OF ELECTRIC VEHICLE

Directory of Open Access Journals (Sweden)

K. O. Soroka

2015-06-01

Full Text Available Purpose. The calculation methods improvement of the electric vehicle curve movement and the cost of electricity with the aim of performance and accuracy of calculations improving are considered in the paper. Methodology. The method is based upon the general principles of mathematical simulation, when a conceptual model of problem domain is created and then a mathematic model is formulated according to the conceptual model. Development of an improved conceptual model of electric vehicles motion is proposed and a corresponding mathematical model is studied. Findings. The authors proposed model in which the vehicle considers as a system of interacting point-like particles with defined interactions under the influence of external forces. As a mathematical model the Euler-Lagrange equation of the second kind is used. Conservative and dissipative forces affecting the system dynamics are considered. Equations for calculating motion of electric vehicles with taking into account the energy consumption are proposed. Originality. In the paper the conceptual model of motion for electric vehicles with distributed masses has been developed as a system of interacting point-like particles. In the easiest case the system has only one degree of freedom. The mathematical model is based on Lagrange equations. The shown approach allows a detailed and physically based description of the electric vehicles dynamics. The derived motion equations for public electric transport are substantially more precise than the equations recommended in textbooks and the reference documentation. The motion equations and energy consumption calculations for transportation of one passenger with a trolleybus are developed. It is shown that the energy consumption depends on the data of vehicle and can increase when the manload is above the certain level. Practical value. The authors received the equations of motion and labour costs in the calculations focused on the use of computer methods

A constitutive model for particulate-reinforced titanium matrix composites subjected to high strain rates and high temperatures

Directory of Open Access Journals (Sweden)

Song Wei-Dong

2013-01-01

Full Text Available Quasi-static and dynamic tension tests were conducted to study the mechanical properties of particulate-reinforced titanium matrix composites at strain rates ranging from 0.0001/s to 1000/s and at temperatures ranging from 20 °C to 650 °C Based on the experimental results, a constitutive model, which considers the effects of strain rate and temperature on hot deformation behavior, was proposed for particulate-reinforced titanium matrix composites subjected to high strain rates and high temperatures by using Zener-Hollomon equations including Arrhenius terms. All the material constants used in the model were identified by fitting Zener-Hollomon equations against the experimental results. By comparison of theoretical predictions presented by the model with experimental results, a good agreement was achieved, which indicates that this constitutive model can give an accurate and precise estimate for high temperature flow stress for the studied titanium matrix composites and can be used for numerical simulations of hot deformation behavior of the composites.

Ginzburg-Landau equation as a heuristic model for generating rogue waves

Science.gov (United States)

Lechuga, Antonio

2016-04-01

Envelope equations have many applications in the study of physical systems. Particularly interesting is the case 0f surface water waves. In steady conditions, laboratory experiments are carried out for multiple purposes either for researches or for practical problems. In both cases envelope equations are useful for understanding qualitative and quantitative results. The Ginzburg-Landau equation provides an excellent model for systems of that kind with remarkable patterns. Taking into account the above paragraph the main aim of our work is to generate waves in a water tank with almost a symmetric spectrum according to Akhmediev (2011) and thus, to produce a succession of rogue waves. The envelope of these waves gives us some patterns whose model is a type of Ginzburg-Landau equation, Danilov et al (1988). From a heuristic point of view the link between the experiment and the model is achieved. Further, the next step consists of changing generating parameters on the water tank and also the coefficients of the Ginzburg-Landau equation, Lechuga (2013) in order to reach a sufficient good approach.

Chaotic attractors in tumor growth and decay: a differential equation model.

Science.gov (United States)

Harney, Michael; Yim, Wen-sau

2015-01-01

Tumorigenesis can be modeled as a system of chaotic nonlinear differential equations. A simulation of the system is realized by converting the differential equations to difference equations. The results of the simulation show that an increase in glucose in the presence of low oxygen levels decreases tumor growth.

Roll paper pilot. [mathematical model for predicting pilot rating of aircraft in roll task

Science.gov (United States)

Naylor, F. R.; Dillow, J. D.; Hannen, R. A.

1973-01-01

A mathematical model for predicting the pilot rating of an aircraft in a roll task is described. The model includes: (1) the lateral-directional aircraft equations of motion; (2) a stochastic gust model; (3) a pilot model with two free parameters; and (4) a pilot rating expression that is a function of rms roll angle and the pilot lead time constant. The pilot gain and lead time constant are selected to minimize the pilot rating expression. The pilot parameters are then adjusted to provide a 20% stability margin and the adjusted pilot parameters are used to compute a roll paper pilot rating of the aircraft/gust configuration. The roll paper pilot rating was computed for 25 aircraft/gust configurations. A range of actual ratings from 2 to 9 were encountered and the roll paper pilot ratings agree quite well with the actual ratings. In addition there is good correlation between predicted and measured rms roll angle.

Theoretical Analysis of Fas Ligand-Induced Apoptosis with an Ordinary Differential Equation Model.

Science.gov (United States)

Shi, Zhimin; Li, Yan; Liu, Zhihai; Mi, Jun; Wang, Renxiao

2012-12-01

Upon the treatment of Fas ligand, different types of cells exhibit different apoptotic mechanisms, which are determined by a complex network of biological pathways. In order to derive a quantitative interpretation of the cell sensitivity and apoptosis pathways, we have developed an ordinary differential equation model. Our model is intended to include all of the known major components in apoptosis pathways mediated by Fas receptor. It is composed of 29 equations using a total of 49 rate constants and 13 protein concentrations. All parameters used in our model were derived through nonlinear fitting to experimentally measured concentrations of four selected proteins in Jurkat T-cells, including caspase-3, caspase-8, caspase-9, and Bid. Our model is able to correctly interpret the role of kinetic parameters and protein concentrations in cell sensitivity to FasL. It reveals the possible reasons for the transition between type-I and type-II pathways and also provides some interesting predictions, such as the more decisive role of Fas over Bax in apoptosis pathway and a possible feedback mechanism between type-I and type-II pathways. But our model failed in predicting FasL-induced apoptotic mechanism of NCI-60 cells from their gene-expression levels. Limitations in our model are also discussed. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Modeling strategy of the source and sink terms in the two-group interfacial area transport equation

International Nuclear Information System (INIS)

Ishii, Mamoru; Sun Xiaodong; Kim, Seungjin

2003-01-01

This paper presents the general strategy for modeling the source and sink terms in the two-group interfacial area transport equation. The two-group transport equation is applicable in bubbly, cap bubbly, slug, and churn-turbulent flow regimes to predict the change of the interfacial area concentration. This dynamic approach has an advantage of flow regime-independence over the conventional empirical correlation approach for the interfacial area concentration in the applications with the two-fluid model. In the two-group interfacial area transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Based upon a detailed literature review of the research on the bubble interactions, five major bubble interaction mechanisms are identified for the gas-liquid two-phase flow of interest. A systematic integral approach, in which the significant variations of bubble volume and shape are accounted for, is suggested for the modeling of two-group bubble interactions. To obtain analytical forms for the various bubble interactions, a simplification is made for the bubble number density distribution function

The Schroedinger-Newton equation as model of self-gravitating quantum systems

International Nuclear Information System (INIS)

Grossardt, Andre

2013-01-01

The Schroedinger-Newton equation (SN equation) describes a quantummechanical one-particle-system with gravitational self-interaction and might play a role answering the question if gravity must be quantised. As non-relativistic limit of semi-classical gravity, it provides testable predictions of the effects that classical gravity has on genuinely quantum mechanical systems in the mass regime between a few thousand proton masses and the Planck mass, which is experimentally unexplored. In this thesis I subsume the mathematical properties of the SN equation and justify it as a physical model. I will give a short outline of the controversial debate around semi-classical gravity as a fundamental theory, along with the idea of the SN equation as a model of quantum state reduction. Subsequently, I will respond to frequent objections against nonlinear Schrodinger equations. I will show how the SN equation can be obtained from Einstein's General Relativity coupled to either a KleinGordon or a Dirac equation, in the same sense as the linear Schroedinger equation can be derived in flat Minkowski space-time. The equation is, to this effect, a non-relativistic approximation of the semi-classical Einstein equations. Additionally, I will discuss, first by means of analytic estimations and later numerically, in which parameter range effects of gravitational selfinteraction - e.g. in molecular-interferometry experiments - should be expected. Besides the one-particle SN equation I will provide justification for a modified equation describing the centre-of-mass wave-function of a many-particle system. Furthermore, for this modified equation, I will examine, numerically, the consequences for experiments. Although one arrives at the conclusion that no effects of the SN equation can be expected for masses up to six or seven orders of magnitude above those considered in contemporary molecular interferometry experiments, tests of the equation, for example in satellite experiments, seem

Modelling biochemical reaction systems by stochastic differential equations with reflection.

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Informed Conjecturing of Solutions for Differential Equations in a Modeling Context

Science.gov (United States)

Winkel, Brian

2015-01-01

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

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

Science.gov (United States)

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.

A Study of Analytical Solution for the Special Dissolution Rate Model of Rock Salt

Directory of Open Access Journals (Sweden)

Xin Yang

2017-01-01

Full Text Available By calculating the concentration distributions of rock salt solutions at the boundary layer, an ordinary differential equation for describing a special dissolution rate model of rock salt under the assumption of an instantaneous diffusion process was established to investigate the dissolution mechanism of rock salt under transient but stable conditions. The ordinary differential equation was then solved mathematically to give an analytical solution and related expressions for the dissolved radius and solution concentration. Thereafter, the analytical solution was fitted with transient dissolution test data of rock salt to provide the dissolution parameters at different flow rates, and the physical meaning of the analytical formula was also discussed. Finally, the influential factors of the analytical formula were investigated. There was approximately a linear relationship between the dissolution parameters and the flow rate. The effects of the dissolution area and initial volume of the solution on the dissolution rate equation of rock salt were computationally investigated. The results showed that the present analytical solution gives a good description of the dissolution mechanism of rock salt under some special conditions, which may provide a primary theoretical basis and an analytical way to investigate the dissolution characteristics of rock salt.

A Structural Equation Approach to Models with Spatial Dependence

NARCIS (Netherlands)

Oud, Johan H. L.; Folmer, Henk

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it

A structural equation approach to models with spatial dependence

NARCIS (Netherlands)

Oud, J.H.L.; Folmer, H.

2008-01-01

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it

A Structural Equation Approach to Models with Spatial Dependence

NARCIS (Netherlands)

Oud, J.H.L.; Folmer, H.

2008-01-01

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it

Integral equation models for image restoration: high accuracy methods and fast algorithms

International Nuclear Information System (INIS)

Lu, Yao; Shen, Lixin; Xu, Yuesheng

2010-01-01

Discrete models are consistently used as practical models for image restoration. They are piecewise constant approximations of true physical (continuous) models, and hence, inevitably impose bottleneck model errors. We propose to work directly with continuous models for image restoration aiming at suppressing the model errors caused by the discrete models. A systematic study is conducted in this paper for the continuous out-of-focus image models which can be formulated as an integral equation of the first kind. The resulting integral equation is regularized by the Lavrentiev method and the Tikhonov method. We develop fast multiscale algorithms having high accuracy to solve the regularized integral equations of the second kind. Numerical experiments show that the methods based on the continuous model perform much better than those based on discrete models, in terms of PSNR values and visual quality of the reconstructed images

A numerical model for the solution of the Shallow Water equations in composite channels with movable bed

Science.gov (United States)

minatti, L.

2013-12-01

A finite volume model solving the shallow water equations coupled with the sediments continuity equation in composite channels with irregular geometry is presented. The model is essentially 1D but can handle composite cross-sections in which bedload transport is considered to occur inside the main channel only. This assumption is coherent with the observed behavior of rivers on short time scales where main channel areas exhibit more relevant morphological variations than overbanks. Furthermore, such a model allows a more precise prediction of thalweg elevation and cross section shape variations than fully 1D models where bedload transport is considered to occur uniformly over the entire cross section. The coupling of the equations describing water and sediments dynamics results in a hyperbolic non-conservative system that cannot be solved numerically with the use of a conservative scheme. Therefore, a path-conservative scheme, based on the approach proposed by Pares and Castro (2004) has been devised in order to account for the coupling with the sediments continuity equation and for the concurrent presence of bottom elevation and breadth variations of the cross section. In order to correctly compute numerical fluxes related to bedload transport in main channel areas, a special treatment of the equations is employed in the model. The resulting scheme is well balanced and fully coupled and can accurately model abrupt time variations of flow and bedload transport conditions in wide rivers, characterized by the presence of overbank areas that are less active than the main channel. The accuracy of the model has been first tested in fixed bed conditions by solving problems with a known analytical solution: in these tests the model proved to be able to handle shocks and supercritical flow conditions properly(see Fig. 01). A practical application of the model to the Ombrone river, southern Tuscany (Italy) is shown. The river has shown relevant morphological changes during

Ising models and soliton equations

International Nuclear Information System (INIS)

Perk, J.H.H.; Au-Yang, H.

1985-01-01

Several new results for the critical point of correlation functions of the Hirota equation are derived within the two-dimensional Ising model. The recent success of the conformal-invariance approach in the determination of a critical two-spin correration function is analyzed. The two-spin correlation function is predicted to be rotationally invariant and to decay with a power law in this approach. In the approach suggested here systematic corrections due to the underlying lattice breaking the rotational invariance are obtained

About the Properties of a Modified Generalized Beverton-Holt Equation in Ecology Models

OpenAIRE

De La Sen, M.

2008-01-01

Es reproducción del documento publicado en http://dx.doi.org/10.1155/2008/592950 This paper is devoted to the study of a generalized modified version of the well-known Beverton-Holt equation in ecology. The proposed model describes the population evolution of some species in a certain habitat driven by six parametrical sequences, namely, the intrinsic growth rate (associated with the reproduction capability), the degree of sympathy of the species with the habitat (described by a so-called ...

Modeling imperfectly repaired system data via grey differential equations with unequal-gapped times

International Nuclear Information System (INIS)

Guo Renkuan

2007-01-01

In this paper, we argue that grey differential equation models are useful in repairable system modeling. The arguments starts with the review on GM(1,1) model with equal- and unequal-spaced stopping time sequence. In terms of two-stage GM(1,1) filtering, system stopping time can be partitioned into system intrinsic function and repair effect. Furthermore, we propose an approach to use grey differential equation to specify a semi-statistical membership function for system intrinsic function times. Also, we engage an effort to use GM(1,N) model to model system stopping times and the associated operating covariates and propose an unequal-gapped GM(1,N) model for such analysis. Finally, we investigate the GM(1,1)-embed systematic grey equation system modeling of imperfectly repaired system operating data. Practical examples are given in step-by-step manner to illustrate the grey differential equation modeling of repairable system data

Loop equations for multi-cut matrix models

International Nuclear Information System (INIS)

Akemann, G.

1995-03-01

The loop equation for the complex one-matrix model with a multi-cut structure is derived and solved in the planar limit. An iterative scheme for higher genus contributions to the free energy and the multi-loop correlators is presented for the two-cut model, where explicit results are given up to and including genus two. The double-scaling limit is analyzed and the relation to the one-cut solution of the hermitian and complex one-matrix model is discussed. (orig.)

Stochastic Differential Equation-Based Flexible Software Reliability Growth Model

Directory of Open Access Journals (Sweden)

P. K. Kapur

2009-01-01

Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.

Fitting Data to Model: Structural Equation Modeling Diagnosis Using Two Scatter Plots

Science.gov (United States)

Yuan, Ke-Hai; Hayashi, Kentaro

2010-01-01

This article introduces two simple scatter plots for model diagnosis in structural equation modeling. One plot contrasts a residual-based M-distance of the structural model with the M-distance for the factor score. It contains information on outliers, good leverage observations, bad leverage observations, and normal cases. The other plot contrasts…

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian

2015-01-01

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean

2015-02-03

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

Fractal diffusion equations: Microscopic models with anomalous diffusion and its generalizations

International Nuclear Information System (INIS)

Arkhincheev, V.E.

2001-04-01

To describe the ''anomalous'' diffusion the generalized diffusion equations of fractal order are deduced from microscopic models with anomalous diffusion as Comb model and Levy flights. It is shown that two types of equations are possible: with fractional temporal and fractional spatial derivatives. The solutions of these equations are obtained and the physical sense of these fractional equations is discussed. The relation between diffusion and conductivity is studied and the well-known Einstein relation is generalized for the anomalous diffusion case. It is shown that for Levy flight diffusion the Ohm's law is not applied and the current depends on electric field in a nonlinear way due to the anomalous character of Levy flights. The results of numerical simulations, which confirmed this conclusion, are also presented. (author)

Modeling decay rates of dead wood in a neotropical forest.

Science.gov (United States)

Hérault, Bruno; Beauchêne, Jacques; Muller, Félix; Wagner, Fabien; Baraloto, Christopher; Blanc, Lilian; Martin, Jean-Michel

2010-09-01

Variation of dead wood decay rates among tropical trees remains one source of uncertainty in global models of the carbon cycle. Taking advantage of a broad forest plot network surveyed for tree mortality over a 23-year period, we measured the remaining fraction of boles from 367 dead trees from 26 neotropical species widely varying in wood density (0.23-1.24 g cm(-3)) and tree circumference at death time (31.5-272.0 cm). We modeled decay rates within a Bayesian framework assuming a first order differential equation to model the decomposition process and tested for the effects of forest management (selective logging vs. unexploited), of mode of death (standing vs. downed) and of topographical levels (bottomlands vs. hillsides vs. hilltops) on wood decay rates. The general decay model predicts the observed remaining fraction of dead wood (R2 = 60%) with only two biological predictors: tree circumference at death time and wood specific density. Neither selective logging nor local topography had a differential effect on wood decay rates. Including the mode of death into the model revealed that standing dead trees decomposed faster than downed dead trees, but the gain of model accuracy remains rather marginal. Overall, these results suggest that the release of carbon from tropical dead trees to the atmosphere can be simply estimated using tree circumference at death time and wood density.

Study of a Model Equation in Detonation Theory

KAUST Repository

Faria, Luiz

2014-04-24

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1/2 (u2-uu (0-, t))x=f (x, u (0-, t)), x > 0, t < 0. It describes a detonation shock at x = 0 with the reaction zone in x > 0. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos. © 2014 Society for Industrial and Applied Mathematics.

Annotated bibliography of structural equation modelling: technical work.

Science.gov (United States)

Austin, J T; Wolfle, L M

1991-05-01

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

Population stochastic modelling (PSM)-An R package for mixed-effects models based on stochastic differential equations

DEFF Research Database (Denmark)

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode

2009-01-01

are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE1 approximation......The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model...... development, J. Pharmacokinet. Pharmacodyn. 32 (February(l)) (2005) 109-141; C.W. Tornoe, R.V Overgaard, H. Agerso, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8...

Continuum model of the two-component Becker-Döring equations

Directory of Open Access Journals (Sweden)

Ali Reza Soheili

2004-01-01

Full Text Available The process of collision between particles is a subject of interest in many fields of physics, astronomy, polymer physics, atmospheric physics, and colloid chemistry. If two types of particles are allowed to participate in the cluster coalescence, then the time evolution of the cluster distribution has been described by an infinite system of ordinary differential equations. In this paper, we describe the model with a second-order two-dimensional partial differential equation, as a continuum model.

How the 2SLS/IV estimator can handle equality constraints in structural equation models: a system-of-equations approach.

Science.gov (United States)

Nestler, Steffen

2014-05-01

Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non-iterative, equation-by-equation estimator that uses instrumental variables. Although this two-stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models. © 2013 The British Psychological Society.

Reduction of static field equation of Faddeev model to first order PDE

International Nuclear Information System (INIS)

Hirayama, Minoru; Shi Changguang

2007-01-01

A method to solve the static field equation of the Faddeev model is presented. For a special combination of the concerned field, we adopt a form which is compatible with the field equation and involves two arbitrary complex functions. As a result, the static field equation is reduced to a set of first order partial differential equations

Validation of predictive equations for glomerular filtration rate in the Saudi population

Directory of Open Access Journals (Sweden)

Al Wakeel Jamal

2009-01-01

Full Text Available Predictive equations provide a rapid method of assessing glomerular filtration rate (GFR. To compare the various predictive equations for the measurement of this parameter in the Saudi population, we measured GFR by the Modification of Diet in Renal Disease (MDRD and Cockcroft-Gault formulas, cystatin C, reciprocal of cystatin C, creatinine clearance, reciprocal of creatinine, and inulin clearance in 32 Saudi subjects with different stages of renal disease. We com-pared GFR measured by inulin clearance and the estimated GFR by the equations. The study included 19 males (59.4% and 13 (40.6% females with a mean age of 42.3 ± 15.2 years and weight of 68.6 ± 17.7 kg. The mean serum creatinine was 199 ± 161 μmol/L. The GFR measured by inulin clearance was 50.9 ± 33.5 mL/min, and the estimated by Cockcroft-Gault and by MDRD equations was 56.3 ± 33.3 and 52.8 ± 32.0 mL/min, respectively. The GFR estimated by MDRD revealed the strongest correlation with the measured inulin clearance (r= 0.976, P= 0.0000 followed by the GFR estimated by Cockcroft-Gault, serum cystatin C, and serum creatinine (r= 0.953, P= 0.0000 (r= 0.787, P= 0.0001 (r= -0.678, P= 0.001, respectively. The reciprocal of cystatin C and serum creatinine revealed a correlation coefficient of 0.826 and 0.93, respectively. Cockroft-Gault for-mula overestimated the GFR by 5.40 ± 10.3 mL/min in comparison to the MDRD formula, which exhibited the best correlation with inulin clearance in different genders, age groups, body mass index, renal transplant recipients, chronic kidney disease stages when compared to other GFR predictive equations.

River water quality model no. 1 (RWQM1): II. Biochemical process equations

DEFF Research Database (Denmark)

Reichert, P.; Borchardt, D.; Henze, Mogens

2001-01-01

In this paper, biochemical process equations are presented as a basis for water quality modelling in rivers under aerobic and anoxic conditions. These equations are not new, but they summarise parts of the development over the past 75 years. The primary goals of the presentation are to stimulate...... transformation processes. This paper is part of a series of three papers. In the first paper, the general modelling approach is described; in the present paper, the biochemical process equations of a complex model are presented; and in the third paper, recommendations are given for the selection of a reasonable...

On singularity formation of a 3D model for incompressible Navier–Stokes equations

OpenAIRE

Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu

2012-01-01

We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei (2009) in [15] for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier–Stokes equations is that the convection term is neglected in the 3D model. This model shares many properties of the 3D incompressible Navier–Stokes equations. One of the main results of this paper is that we prove rigorously th...

Modeling a Predictive Energy Equation Specific for Maintenance Hemodialysis.

Science.gov (United States)

Byham-Gray, Laura D; Parrott, J Scott; Peters, Emily N; Fogerite, Susan Gould; Hand, Rosa K; Ahrens, Sean; Marcus, Andrea Fleisch; Fiutem, Justin J

2017-03-01

Hypermetabolism is theorized in patients diagnosed with chronic kidney disease who are receiving maintenance hemodialysis (MHD). We aimed to distinguish key disease-specific determinants of resting energy expenditure to create a predictive energy equation that more precisely establishes energy needs with the intent of preventing protein-energy wasting. For this 3-year multisite cross-sectional study (N = 116), eligible participants were diagnosed with chronic kidney disease and were receiving MHD for at least 3 months. Predictors for the model included weight, sex, age, C-reactive protein (CRP), glycosylated hemoglobin, and serum creatinine. The outcome variable was measured resting energy expenditure (mREE). Regression modeling was used to generate predictive formulas and Bland-Altman analyses to evaluate accuracy. The majority were male (60.3%), black (81.0%), and non-Hispanic (76.7%), and 23% were ≥65 years old. After screening for multicollinearity, the best predictive model of mREE ( R 2 = 0.67) included weight, age, sex, and CRP. Two alternative models with acceptable predictability ( R 2 = 0.66) were derived with glycosylated hemoglobin or serum creatinine. Based on Bland-Altman analyses, the maintenance hemodialysis equation that included CRP had the best precision, with the highest proportion of participants' predicted energy expenditure classified as accurate (61.2%) and with the lowest number of individuals with underestimation or overestimation. This study confirms disease-specific factors as key determinants of mREE in patients on MHD and provides a preliminary predictive energy equation. Further prospective research is necessary to test the reliability and validity of this equation across diverse populations of patients who are receiving MHD.

Testing strong factorial invariance using three-level structural equation modeling

NARCIS (Netherlands)

Jak, Suzanne

Within structural equation modeling, the most prevalent model to investigate measurement bias is the multigroup model. Equal factor loadings and intercepts across groups in a multigroup model represent strong factorial invariance (absence of measurement bias) across groups. Although this approach is

Parameter Estimates in Differential Equation Models for Population Growth

Science.gov (United States)

Winkel, Brian J.

2011-01-01

We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist,…

Reflected‑Point‑Reactor Kinetics Model for Neutron Coincidence Counting: Comments on the Equation for the Leakage Self‑Multiplication

International Nuclear Information System (INIS)

Croft, S.; McElroy, RD.; Favalli, A.; Hauck, D.; Henzlova, D.; Henzl, V.; Santi, PA.

2015-01-01

Passive neutron correlation counting is widely used, for example by international inspection agencies, for the non‑destructive assay of spontaneously fissile nuclear materials for nuclear safeguards. The mass of special nuclear material present in an item is usually estimated from the observed neutron counting rates by using equations based on mathematically describing the object as an isolated multiplying point‑like source. Calibration using representative physical standards can often adequately compensate for this theoretical oversimplification through the introduction and use of effective‑interpretational‑model‑parameters meaning that useful assay results are obtained. In this work we extend the point‑model treatment by including a simple reflector around the fissioning material. Specifically we show how the leakage self‑multiplication equation mathematically connects the traditional bare source and the reflected source cases. In doing so we explicitly demonstrate that although the presence of a simple reflector changes the leakage self‑multiplication the traditional bare‑item point model multiplicity equations retain the same mathematical form. Making and explaining this connection is important because it helps to explain and justify the practical success and use of the traditional point‑model equations even when the assumptions used to generate the key functional dependences are violated. We are not aware that this point has been recognized previously.

Linear Equating for the NEAT Design: Parameter Substitution Models and Chained Linear Relationship Models

Science.gov (United States)

Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

2009-01-01

This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…

Utility rate equations of group population dynamics in biological and social systems.

Directory of Open Access Journals (Sweden)

Vyacheslav I Yukalov

Full Text Available We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors and of three groups (cooperators, defectors, and regulators and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about [Formula: see text] each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita.

Utility Rate Equations of Group Population Dynamics in Biological and Social Systems

Science.gov (United States)

Yukalov, Vyacheslav I.; Yukalova, Elizaveta P.; Sornette, Didier

2013-01-01

We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita. PMID:24386163

About the Properties of a Modified Generalized Beverton-Holt Equation in Ecology Models

Directory of Open Access Journals (Sweden)

M. De La Sen

2008-01-01

Full Text Available This paper is devoted to the study of a generalized modified version of the well-known Beverton-Holt equation in ecology. The proposed model describes the population evolution of some species in a certain habitat driven by six parametrical sequences, namely, the intrinsic growth rate (associated with the reproduction capability, the degree of sympathy of the species with the habitat (described by a so-called environment carrying capacity, a penalty term to deal with overpopulation levels, the harvesting (fishing or hunting regulatory quota, or related to use of pesticides when fighting damaging plagues, and the independent consumption which basically quantifies predation. The independent consumption is considered as a part of a more general additive disturbance which also potentially includes another extra additive disturbance term which might be attributed to net migration from or to the habitat or modeling measuring errors. Both potential contributions are included for generalization purposes in the proposed modified generalized Beverton-Holt equation. The properties of stability and boundedness of the solution sequences, equilibrium points of the stationary model, and the existence of oscillatory solution sequences are investigated. A numerical example for a population of aphids is investigated with the theoretical tools developed in the paper.

A Study of Enhanced, Higher Order Boussinesq-Type Equations and Their Numerical Modelling

DEFF Research Database (Denmark)

Banijamali, Babak

model is designated for the solution of higher-order Boussinesq-type equations, formulated in terms of the horizontal velocity at an arbitrary depth vector. Various discretisation techniques and grid definitions have been considered in this endeavour, undertaking a detailed analysis of the selected......This project has encompassed efforts in two separate veins: on the one hand, the acquiring of highly accurate model equations of the Boussinesq-type, and on the other hand, the theoretical and practical work in implementing such equations in the form of conventional numerical models, with obvious...... potential for applications to the realm of numerical modelling in coastal engineering. The derivation and analysis of several forms of higher-order in dispersion and non-linearity Boussinesq-type equations have been undertaken, obtaining and investigating the properties of a new and generalised class...

Fast and accurate calculation of dilute quantum gas using Uehling–Uhlenbeck model equation

Energy Technology Data Exchange (ETDEWEB)

Yano, Ryosuke, E-mail: ryosuke.yano@tokiorisk.co.jp

2017-02-01

The Uehling–Uhlenbeck (U–U) model equation is studied for the fast and accurate calculation of a dilute quantum gas. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U–U model equation. DSMC analysis based on the U–U model equation is expected to enable the thermalization to be accurately obtained using a small number of sample particles and the dilute quantum gas dynamics to be calculated in a practical time. Finally, the applicability of DSMC analysis based on the U–U model equation to the fast and accurate calculation of a dilute quantum gas is confirmed by calculating the viscosity coefficient of a Bose gas on the basis of the Green–Kubo expression and the shock layer of a dilute Bose gas around a cylinder.

Self-dual form of Ruijsenaars–Schneider models and ILW equation with discrete Laplacian

Directory of Open Access Journals (Sweden)

A. Zabrodin

2018-02-01

Full Text Available We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable glN Ruijsenaars–Schneider model. It is based on the first order equations in N+M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the glM Ruijsenaars–Schneider model. In the elliptic case it holds M=N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero–Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars–Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian by means of the simple pole ansatz likewise the Calogero–Moser models arise from ordinary intermediate long wave and Benjamin–Ono equations.

A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers

Science.gov (United States)

Schüler, L.; Suciu, N.; Knabner, P.; Attinger, S.

2016-10-01

Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

Science.gov (United States)

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

Exponential decay rate of the power spectrum for solutions of the Navier--Stokes equations

International Nuclear Information System (INIS)

Doering, C.R.; Titi, E.S.

1995-01-01

Using a method developed by Foias and Temam [J. Funct. Anal. 87, 359 (1989)], exponential decay of the spatial Fourier power spectrum for solutions of the incompressible Navier--Stokes equations is established and explicit rigorous lower bounds on a small length scale defined by the exponential decay rate are obtained

Critical Domain Problem for the Reaction–Telegraph Equation Model of Population Dynamics

Directory of Open Access Journals (Sweden)

Weam Alharbi

2018-04-01

Full Text Available A telegraph equation is believed to be an appropriate model of population dynamics as it accounts for the directional persistence of individual animal movement. Being motivated by the problem of habitat fragmentation, which is known to be a major threat to biodiversity that causes species extinction worldwide, we consider the reaction–telegraph equation (i.e., telegraph equation combined with the population growth on a bounded domain with the goal to establish the conditions of species survival. We first show analytically that, in the case of linear growth, the expression for the domain’s critical size coincides with the critical size of the corresponding reaction–diffusion model. We then consider two biologically relevant cases of nonlinear growth, i.e., the logistic growth and the growth with a strong Allee effect. Using extensive numerical simulations, we show that in both cases the critical domain size of the reaction–telegraph equation is larger than the critical domain size of the reaction–diffusion equation. Finally, we discuss possible modifications of the model in order to enhance the positivity of its solutions.

Application of Fokker-Planck equation in positron diffusion trapping model

International Nuclear Information System (INIS)

Bartosova, I.; Ballo, P.

2015-01-01

This paper is a theoretical prelude to future work involving positron diffusion in solids for the purpose of positron annihilation lifetime spectroscopy (PALS). PALS is a powerful tool used to study defects present in materials. However, the behavior of positrons in solids is a process hard to describe. Various models have been established to undertake this task. Our preliminary model is based on the Diffusion Trapping Model (DTM) described by partial differential Fokker-Planck equation and is solved via time discretization. Fokker-Planck equation describes the time evolution of the probability density function of velocity of a particle under the influence of various forces. (authors)

Modelling with Difference Equations Supported by GeoGebra: Exploring the Kepler Problem

Science.gov (United States)

Kovacs, Zoltan

2010-01-01

The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…

Determination and evaluation of gas holdup time with the quadratic equation model and comparison with nonlinear equation models for isothermal gas chromatography

Science.gov (United States)

Wu, Liejun; Chen, Maoxue; Chen, Yongli; Li, Qing X.

2013-01-01

Gas holdup time (tM) is a basic parameter in isothermal gas chromatography (GC). Determination and evaluation of tM and retention behaviors of n-alkanes under isothermal GC conditions have been extensively studied since the 1950s, but still remains unresolved. The difference equation (DE) model [J. Chromatogr. A 1260:215–223] reveals retention behaviors of n-alkanes excluding tM, while the quadratic equation (QE) model [J. Chromatogr. A 1260:224–231] including tM is suitable for applications. In the present study, tM values were calculated with the QE model, which is referred to as tMT, evaluated and compared with other three typical nonlinear models. The QE model gives an accurate estimation of tM in isothermal GC. The tMT values are highly accurate, stable, and easy to calculate and use. There is only one tMT value at each GC condition. The proper classification of tM values can clarify their disagreement and facilitate GC retention data standardization for which tMT values are promising reference tM values. PMID:23726077

A Matérn model of the spatial covariance structure of point rain rates

KAUST Repository

Sun, Ying; Bowman, Kenneth P.; Genton, Marc G.; Tokay, Ali

2014-01-01

It is challenging to model a precipitation field due to its intermittent and highly scale-dependent nature. Many models of point rain rates or areal rainfall observations have been proposed and studied for different time scales. Among them, the spectral model based on a stochastic dynamical equation for the instantaneous point rain rate field is attractive, since it naturally leads to a consistent space–time model. In this paper, we note that the spatial covariance structure of the spectral model is equivalent to the well-known Matérn covariance model. Using high-quality rain gauge data, we estimate the parameters of the Matérn model for different time scales and demonstrate that the Matérn model is superior to an exponential model, particularly at short time scales.

A Matérn model of the spatial covariance structure of point rain rates

KAUST Repository

Sun, Ying

2014-07-15

It is challenging to model a precipitation field due to its intermittent and highly scale-dependent nature. Many models of point rain rates or areal rainfall observations have been proposed and studied for different time scales. Among them, the spectral model based on a stochastic dynamical equation for the instantaneous point rain rate field is attractive, since it naturally leads to a consistent space–time model. In this paper, we note that the spatial covariance structure of the spectral model is equivalent to the well-known Matérn covariance model. Using high-quality rain gauge data, we estimate the parameters of the Matérn model for different time scales and demonstrate that the Matérn model is superior to an exponential model, particularly at short time scales.

Dose-rate dependent stochastic effects in radiation cell-survival models

International Nuclear Information System (INIS)

Sachs, R.K.; Hlatky, L.R.

1990-01-01

When cells are subjected to ionizing radiation the specific energy rate (microscopic analog of dose-rate) varies from cell to cell. Within one cell, this rate fluctuates during the course of time; a crossing of a sensitive cellular site by a high energy charged particle produces many ionizations almost simultaneously, but during the interval between events no ionizations occur. In any cell-survival model one can incorporate the effect of such fluctuations without changing the basic biological assumptions. Using stochastic differential equations and Monte Carlo methods to take into account stochastic effects we calculated the dose-survival rfelationships in a number of current cell survival models. Some of the models assume quadratic misrepair; others assume saturable repair enzyme systems. It was found that a significant effect of random fluctuations is to decrease the theoretically predicted amount of dose-rate sparing. In the limit of low dose-rates neglecting the stochastic nature of specific energy rates often leads to qualitatively misleading results by overestimating the surviving fraction drastically. In the opposite limit of acute irradiation, analyzing the fluctuations in rates merely amounts to analyzing fluctuations in total specific energy via the usual microdosimetric specific energy distribution function, and neglecting fluctuations usually underestimates the surviving fraction. The Monte Carlo methods interpolate systematically between the low dose-rate and high dose-rate limits. As in other approaches, the slope of the survival curve at low dose-rates is virtually independent of dose and equals the initial slope of the survival curve for acute radiation. (orig.)

Advanced diffusion model in compacted bentonite based on modified Poisson-Boltzmann equations

International Nuclear Information System (INIS)

Yotsuji, K.; Tachi, Y.; Nishimaki, Y.

2012-01-01

Document available in extended abstract form only. Diffusion and sorption of radionuclides in compacted bentonite are the key processes in the safe geological disposal of radioactive waste. JAEA has developed the integrated sorption and diffusion (ISD) model for compacted bentonite by coupling the pore water chemistry, sorption and diffusion processes in consistent way. The diffusion model accounts consistently for cation excess and anion exclusion in narrow pores in compacted bentonite by the electric double layer (EDL) theory. The firstly developed ISD model could predict the diffusivity of the monovalent cation/anion in compacted bentonite as a function of dry density. This ISD model was modified by considering the visco-electric effect, and applied for diffusion data for various radionuclides measured under wide range of conditions (salinity, density, etc.). This modified ISD model can give better quantitative agreement with diffusion data for monovalent cation/anion, however, the model predictions still disagree with experimental data for multivalent cation and complex species. In this study we extract the additional key factors influencing diffusion model in narrow charged pores, and the effects of these factors were investigated to reach a better understanding of diffusion processes in compacted bentonite. We investigated here the dielectric saturation effect and the excluded volume effect into the present ISD model and numerically solved these modified Poisson-Boltzmann equations. In the vicinity of the negatively charged clay surfaces, it is necessary to evaluate concentration distribution of electrolytes considering the dielectric saturation effects. The Poisson-Boltzmann (P-B) equation coupled with the dielectric saturation effects was solved numerically by using Runge-Kutta and Shooting methods. Figure 1(a) shows the concentration distributions of Na + as numerical solutions of the modified and original P-B equations for 0.01 M pore water, 800 kg m -3

Calculations radiobiological using the quadratic lineal model in the use of the medium dose rate absorbed in brachytherapy. Pt. 3

International Nuclear Information System (INIS)

2002-01-01

Calculations with the quadratic lineal model for medium rate using the equation dose-effect. Several calculations for system of low dose rate brachytherapy plus teletherapy, calculations for brachytherapy with medium dose rate together with teletherapy, dose for fraction and the one numbers of fractions in medium rate

Fractional Bhatnagar-Gross-Krook kinetic equation

Science.gov (United States)

Goychuk, Igor

2017-11-01

The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.

Exact solutions for some discrete models of the Boltzmann equation

International Nuclear Information System (INIS)

Cabannes, H.; Hong Tiem, D.

1987-01-01

For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr

Parametric reduced models for the nonlinear Schrödinger equation.

Science.gov (United States)

Harlim, John; Li, Xiantao

2015-05-01

Reduced models for the (defocusing) nonlinear Schrödinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced parametric models are obtained by employing a rational approximation and a colored-noise approximation, respectively, on the memory terms and the random noise of a generalized Langevin equation that is derived from the standard Mori-Zwanzig formalism. The parameters in the resulting reduced models are inferred from noisy observations with a recently developed ensemble Kalman filter-based parametrization method. The forecasting skill across different temperature regimes are verified by comparing the moments up to order four, a two-time correlation function statistics, and marginal densities of the coarse-grained variables.

Meta-analytic structural equation modelling

CERN Document Server

Jak, Suzanne

2015-01-01

This book explains how to employ MASEM, the combination of meta-analysis (MA) and structural equation modelling (SEM). It shows how by using MASEM, a single model can be tested to explain the relationships between a set of variables in several studies. This book gives an introduction to MASEM, with a focus on the state of the art approach: the two stage approach of Cheung and Cheung & Chan. Both, the fixed and the random approach to MASEM are illustrated with two applications to real data. All steps that have to be taken to perform the analyses are discussed extensively. All data and syntax files are available online, so that readers can imitate all analyses. By using SEM for meta-analysis, this book shows how to benefit from all available information from all available studies, even if few or none of the studies report about all relationships that feature in the full model of interest.

Modeling blowing snow accumulation downwind of an obstruction: The Ohara Eulerian particle distribution equation

Science.gov (United States)

Kinar, N. J.

2017-05-01

An equation was proposed to model the height of blowing snow accumulation downwind of an obstacle such as vegetation, a snow fence, a building, or a topographic feature. The equation does not require aerodynamic flow condition parameters such as wind speed, allowing for the spatial distribution of snow to be determined at locations where meteorological data is not available. However, snow particle diffusion, drift, and erosion coefficients must be estimated for application of the equation. These coefficients can be used to provide insight into the relative magnitude of blowing snow processes at a field location. Further research is required to determine efficient methods for coefficient estimation. The equation could be used with other models of wind-transported snow to predict snow accumulation downwind of an obstacle without the need for wind speed adjustments or correction equations. Applications for this equation include the design of snow fences, and the use of this equation with other hydrological models to predict snow distribution, climate change, drought, flooding, and avalanches.

Homogeneous axisymmetric model with a limitting stiff equation of state

International Nuclear Information System (INIS)

Korkina, M.P.; Martynenko, V.G.

1976-01-01

A solution is obtained for Einstein's equations in which all metric coefficients are time functions for a limiting stiff equation of the substance state. Thr solution describes a homogeneous cosmological model with cylindrical symmetry. It is shown that the same metrics can be induced by a massless scalar only time-dependent field. Analysis of this solution is presented

An estimator for the relative entropy rate of path measures for stochastic differential equations

Energy Technology Data Exchange (ETDEWEB)

Opper, Manfred, E-mail: manfred.opper@tu-berlin.de

2017-02-01

We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.

Modeling the effect of temperature on survival rate of Salmonella Enteritidis in yogurt.

Science.gov (United States)

Szczawiński, J; Szczawińska, M E; Łobacz, A; Jackowska-Tracz, A

2014-01-01

The aim of the study was to determine the inactivation rates of Salmonella Enteritidis in commercially produced yogurt and to generate primary and secondary mathematical models to predict the behaviour of these bacteria during storage at different temperatures. The samples were inoculated with the mixture of three S. Enteritidis strains and stored at 5 degrees C, 10 degrees C, 15 degrees C, 20 degrees C and 25 degrees C for 24 h. The number of salmonellae was determined every two hours. It was found that the number of bacteria decreased linearly with storage time in all samples. Storage temperature and pH of yogurt significantly influenced survival rate of S. Enteritidis (p bacteria was the most dynamic. The natural logarithm of mean inactivation rates of Salmonella calculated from primary model was fitted to two secondary models: linear and polynomial. Equations obtained from both secondary models can be applied as a tool for prediction of inactivation rate of Salmonella in yogurt stored under temperature range from 5 to 25 degrees C; however, polynomial model gave the better fit to the experimental data.

A mathematical model of a crocodilian population using delay-differential equations.

Science.gov (United States)

Gallegos, Angela; Plummer, Tenecia; Uminsky, David; Vega, Cinthia; Wickman, Clare; Zawoiski, Michael

2008-11-01

The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong age-dependence. We develop delay-differential equation (DDE) models describing the evolution of a crocodilian population. In using the delay formulation, we are able to account for both the TSD and the age-dependence of the life parameters while maintaining some analytical tractability. In our single-delay model we also find an equilibrium point and prove its local asymptotic stability. We numerically solve the different models and investigate the effects of multiple delays on the age structure of the population as well as the sex ratio of the population. For all models we obtain very strong agreement with the age structure of crocodilian population data as reported in Smith and Webb (Aust. Wild. Res. 12, 541-554, 1985). We also obtain reasonable values for the sex ratio of the simulated population.

The analysis of the derivation principles of kinetic equations based on exactly solvable models of the bulk reaction A + B → Product

International Nuclear Information System (INIS)

Kipriyanov, A.A.; Doktorov, A.B.

2005-01-01

We have considered two many-particle models of the irreversible reaction A + B → Product for which closed kinetic equations for the mean concentration N A (t) of A species can be exactly obtained. These equations are identically recast into a unified form of integro-differential equation of general kinetic theory. It is shown that the memory functions for both models under consideration can be represented as a sum of the Markovian and non-Markovian parts. It is essential that the Markovian part of the Laplace transform of any kernel can be obtained using the Laplace transform of the kernel itself, and is the root of the non-Markovian part of the Laplace transform of the kernel. The properties established allowed us to perform correct approximation of the memory functions at small concentrations [B] of B species and derive the binary non-Markovian integro-differential equation. Within the binary theory accuracy this equation has been rewritten in a regular frame of a familiar rate equation satisfying general principles of binary kinetic equations. Thus using particular exactly solvable many-particle models, we have reproduced the most essential steps of the known general way for the derivation of the binary kinetic equation avoiding the sophisticated many-particle technique and the corresponding approximations. Besides, the results obtained can serve as an additional evidence of the approximations made in a general many-particle approach to the derivation of the binary kinetic equation

A validated disease specific prediction equation for resting metabolic rate in underweight patients with COPD

Directory of Open Access Journals (Sweden)

Anita Nordenson

2010-09-01

Full Text Available Anita Nordenson2, Anne Marie Grönberg1,2, Lena Hulthén1, Sven Larsson2, Frode Slinde11Department of Clinical Nutrition, Sahlgrenska Academy at University of Gothenburg, Göteborg, Sweden; 2Department of Internal Medicine/Respiratory Medicine and Allergology, Sahlgrenska Academy at University of Gothenburg, SwedenAbstract: Malnutrition is a serious condition in chronic obstructive pulmonary disease (COPD. Successful dietary intervention calls for calculations of resting metabolic rate (RMR. One disease-specific prediction equation for RMR exists based on mainly male patients. To construct a disease-specific equation for RMR based on measurements in underweight or weight-losing women and men with COPD, RMR was measured by indirect calorimetry in 30 women and 11 men with a diagnosis of COPD and body mass index <21 kg/m2. The following variables, possibly influencing RMR were measured: length, weight, middle upper arm circumference, triceps skinfold, body composition by dual energy x-ray absorptiometry and bioelectrical impedance, lung function, and markers of inflammation. Relations between RMR and measured variables were studied using univariate analysis according to Pearson. Gender and variables that were associated with RMR with a P value <0.15 were included in a forward multiple regression analysis. The best-fit multiple regression equation included only fat-free mass (FFM: RMR (kJ/day = 1856 + 76.0 FFM (kg. To conclude, FFM is the dominating factor influencing RMR. The developed equation can be used for prediction of RMR in underweight COPD patients.Keywords: pulmonary disease, chronic obstructive, basal metabolic rate, malnutrition, body composition

A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy.

Science.gov (United States)

Tao, Youshan; Guo, Qian; Aihara, Kazuyuki

2014-10-01

Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.

The Influence of Herbivory on the net rate of Increase of Gypsy Moth Abundance: A Modeling Analysis

Science.gov (United States)

 Harry T.  Valentine

1983-01-01

A differential equation model of gypsy moth abundance, average larval dry weight, and food abundance was used to analyze the effects of changes in foliar chemistry on the net per capita rate of increase in a gypsy moth population. If relative consumption rate per larva is unaffected by herbivory, a reduction in the nutritional value of foliage reduces the net rate of...

Ordinary Differential Equation Models for Adoptive Immunotherapy.

Science.gov (United States)

Talkington, Anne; Dantoin, Claudia; Durrett, Rick

2018-05-01

Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.

Solution of spatially homogeneous model Boltzmann equations by means of Lie groups of transformations

International Nuclear Information System (INIS)

Foroutan, A.

1992-05-01

The essential mathematical challenge in transport theory is based on the nonlinearity of the integro-differential equations governing classical thermodynamic systems on molecular kinetic level. It is the aim of this thesis to gain exact analytical solutions to the model Boltzmann equation suggested by Tjon and Wu. Such solutions afford a deeper insight into the dynamics of rarefied gases. Tjon and Wu have provided a stochastic model of a Boltzmann equation. Its transition probability depends only on the relative speed of the colliding particles. This assumption leads in the case of two translational degrees of freedom to an integro-differential equation of convolution type. According to this convolution structure the integro-differential equation is Laplace transformed. The result is a nonlinear partial differential equation. The investigation of the symmetries of this differential equation by means of Lie groups of transformation enables us to transform the originally nonlinear partial differential equation into ordinary differential equation into ordinary differential equations of Bernoulli type. (author)

Multiloop soliton and multibreather solutions of the short pulse model equation

International Nuclear Information System (INIS)

Matsuno, Yoshimasa

2007-01-01

We develop a systematic procedure for constructing the multisoliton solutions of the short pulse (SP) model equation which describes the propagation of ultra-short pulses in nonlinear medica. We first introduce a novel hodograph transformation to convert the SP equation into the sine-Gordon (sG) equation. With the soliton solutions of the sG equation, the system of linear partial differential equations governing the inverse mapping can be integrated analytically to obtain the soliton solutions of the SP equation in the form of the parametric representation. By specifying the soliton parameters, we obtain the multiloop and multibreather solutions. We investigate the asymptotic behavior of both solutions and confirm their solitonic feature. The nonsingular breather solutions may play an important role in studying the propagation of ultra-short pulses in an optical fibre. (author)

Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies

Directory of Open Access Journals (Sweden)

Oldiges Marco

2009-01-01

Full Text Available Abstract Background To understand the dynamic behavior of cellular systems, mathematical modeling is often necessary and comprises three steps: (1 experimental measurement of participating molecules, (2 assignment of rate laws to each reaction, and (3 parameter calibration with respect to the measurements. In each of these steps the modeler is confronted with a plethora of alternative approaches, e. g., the selection of approximative rate laws in step two as specific equations are often unknown, or the choice of an estimation procedure with its specific settings in step three. This overall process with its numerous choices and the mutual influence between them makes it hard to single out the best modeling approach for a given problem. Results We investigate the modeling process using multiple kinetic equations together with various parameter optimization methods for a well-characterized example network, the biosynthesis of valine and leucine in C. glutamicum. For this purpose, we derive seven dynamic models based on generalized mass action, Michaelis-Menten and convenience kinetics as well as the stochastic Langevin equation. In addition, we introduce two modeling approaches for feedback inhibition to the mass action kinetics. The parameters of each model are estimated using eight optimization strategies. To determine the most promising modeling approaches together with the best optimization algorithms, we carry out a two-step benchmark: (1 coarse-grained comparison of the algorithms on all models and (2 fine-grained tuning of the best optimization algorithms and models. To analyze the space of the best parameters found for each model, we apply clustering, variance, and correlation analysis. Conclusion A mixed model based on the convenience rate law and the Michaelis-Menten equation, in which all reactions are assumed to be reversible, is the most suitable deterministic modeling approach followed by a reversible generalized mass action kinetics

Parabolic Equation Modeling of Propagation over Terrain Using Digital Elevation Model

Directory of Open Access Journals (Sweden)

Xiao-Wei Guan

2018-01-01

Full Text Available The parabolic equation method based on digital elevation model (DEM is applied on propagation predictions over irregular terrains. Starting from a parabolic approximation to the Helmholtz equation, a wide-angle parabolic equation is deduced under the assumption of forward propagation and the split-step Fourier transform algorithm is used to solve it. The application of DEM is extended to the Cartesian coordinate system and expected to provide a precise representation of a three-dimensional surface with high efficiency. In order to validate the accuracy, a perfectly conducting Gaussian terrain profile is simulated and the results are compared with the shift map. As a consequence, a good agreement is observed. Besides, another example is given to provide a theoretical basis and reference for DEM selection. The simulation results demonstrate that the prediction errors will be obvious only when the resolution of the DEM used is much larger than the range step in the PE method.

Advanced structural equation modeling issues and techniques

CERN Document Server

Marcoulides, George A

2013-01-01

By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.

Airline Sustainability Modeling: A New Framework with Application of Bayesian Structural Equation Modeling

DEFF Research Database (Denmark)

Salarzadeh Jenatabadi, Hashem; Babashamsi, Peyman; Khajeheian, Datis

2016-01-01

There are many factors which could influence the sustainability of airlines. The main purpose of this study is to introduce a framework for a financial sustainability index and model it based on structural equation modeling (SEM) with maximum likelihood and Bayesian predictors. The introduced...

Calibration of short rate term structure models from bid-ask coupon bond prices

Science.gov (United States)

Gomes-Gonçalves, Erika; Gzyl, Henryk; Mayoral, Silvia

2018-02-01

In this work we use the method of maximum entropy in the mean to provide a model free, non-parametric methodology that uses only market data to provide the prices of the zero coupon bonds, and then, a term structure of the short rates. The data used consists of the prices of the bid-ask ranges of a few coupon bonds quoted in the market. The prices of the zero coupon bonds obtained in the first stage, are then used as input to solve a recursive set of equations to determine a binomial recombinant model of the short term structure of the interest rates.

Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

Science.gov (United States)

Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

2012-10-01

A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.

A Structural Equation Model of Expertise in College Physics

Science.gov (United States)

Taasoobshirazi, Gita; Carr, Martha

2009-01-01

A model of expertise in physics was tested on a sample of 374 college students in 2 different level physics courses. Structural equation modeling was used to test hypothesized relationships among variables linked to expert performance in physics including strategy use, pictorial representation, categorization skills, and motivation, and these…

A Structural Equation Model of Conceptual Change in Physics

Science.gov (United States)

Taasoobshirazi, Gita; Sinatra, Gale M.

2011-01-01

A model of conceptual change in physics was tested on introductory-level, college physics students. Structural equation modeling was used to test hypothesized relationships among variables linked to conceptual change in physics including an approach goal orientation, need for cognition, motivation, and course grade. Conceptual change in physics…

Principles and practice of structural equation modeling

CERN Document Server

Kline, Rex B

2015-01-01

Emphasizing concepts and rationale over mathematical minutiae, this is the most widely used, complete, and accessible structural equation modeling (SEM) text. Continuing the tradition of using real data examples from a variety of disciplines, the significantly revised fourth edition incorporates recent developments such as Pearl's graphing theory and the structural causal model (SCM), measurement invariance, and more. Readers gain a comprehensive understanding of all phases of SEM, from data collection and screening to the interpretation and reporting of the results. Learning is enhanced by ex

Comparison of Control Approaches in Genetic Regulatory Networks by Using Stochastic Master Equation Models, Probabilistic Boolean Network Models and Differential Equation Models and Estimated Error Analyzes

Science.gov (United States)

Caglar, Mehmet Umut; Pal, Ranadip

2011-03-01

Central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid''. However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of cell level data and probabilistic - nonlinear nature of interactions. Several models widely used to analyze and simulate these types of nonlinear interactions. Stochastic Master Equation (SME) models give probabilistic nature of the interactions in a detailed manner, with a high calculation cost. On the other hand Probabilistic Boolean Network (PBN) models give a coarse scale picture of the stochastic processes, with a less calculation cost. Differential Equation (DE) models give the time evolution of mean values of processes in a highly cost effective way. The understanding of the relations between the predictions of these models is important to understand the reliability of the simulations of genetic regulatory networks. In this work the success of the mapping between SME, PBN and DE models is analyzed and the accuracy and affectivity of the control policies generated by using PBN and DE models is compared.

Asymptotics for Estimating Equations in Hidden Markov Models

DEFF Research Database (Denmark)

Hansen, Jørgen Vinsløv; Jensen, Jens Ledet

Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...

Ratiometric analysis in hyperpolarized NMR (I): test of the two-site exchange model and the quantification of reaction rate constants.

Science.gov (United States)

Li, Lin Z; Kadlececk, Stephen; Xu, He N; Daye, Dania; Pullinger, Benjamin; Profka, Harrilla; Chodosh, Lewis; Rizi, Rahim

2013-10-01

Conventional methods for the analysis of in vivo hyperpolarized (13) C NMR data from the lactate dehydrogenase (LDH) reaction usually make assumptions on the stability of rate constants and/or the validity of the two-site exchange model. In this study, we developed a framework to test the validity of the assumption of stable reaction rate constants and the two-site exchange model in vivo via ratiometric fitting of the time courses of the signal ratio L(t)/P(t). Our analysis provided evidence that the LDH enzymatic kinetics observed by hyperpolarized NMR are in near-equilibrium and satisfy the two-site exchange model for only a specific time window. In addition, we quantified both the forward and reverse exchange rate constants of the LDH reaction for the transgenic and mouse xenograft models of breast cancer using the ratio fitting method developed, which includes only two modeling parameters and is less sensitive to the influence of instrument settings/protocols, such as flip angles, degree of polarization and tracer dosage. We further compared the ratio fitting method with a conventional two-site exchange modeling method, i.e. the differential equation fitting method, using both the experimental and simulated hyperpolarized NMR data. The ratio fitting method appeared to fit better than the differential equation fitting method for the reverse rate constant on the mouse tumor data, with less relative errors on average, whereas the differential equation fitting method also resulted in a negative reverse rate constant for one tumor. The simulation results indicated that the accuracy of both methods depends on the width of the transport function, noise level and rate constant ratio; one method may be more accurate than the other based on the experimental/biological conditions aforementioned. We were able to categorize our tumor models into specific conditions of the computer simulation and to estimate the errors of rate quantification. We also discussed possible

Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices

Science.gov (United States)

Deboeck, Pascal R.; Boker, Steven M.

2010-01-01

Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for…

On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory

OpenAIRE

John A. D. Appleby

2010-01-01

We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. ...

Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces

Science.gov (United States)

Wang, Chi R.

2005-01-01

This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one-equation

A model for rate-dependent but time-independent material behavior in cyclic plasticity

International Nuclear Information System (INIS)

Dafalias, Y.F.; Ramey, M.R.; Sheikh, I.

1977-01-01

This paper presents a model for rate-dependent but time independent material behavior under cyclic loading in the plastic range. What is referred to as time independent behavior here, is the absence of creep and relaxation phenomena from the behavior of the model. The notion of plastic internal variables (piv) is introduced, as properly invariant scalars or second order tensors, whose constitutive relations are rate-type equations not necessarily homogeneous of order one in the rates, as it would be required for independent plasticity. The concept of a yield surface in the strain space and a loading function in terms of the total strain rate is introduced, where the sign of the loading function defines zero or non-zero value of the rate of piv. Thus rate dependence is achieved without time dependent behaviour (no creep or relaxation). In addition, discrete memory parameters associated with the most recent event of unloading-reloading in different directions enter the constitutive relations for the piv. (Auth.)

Computer models for kinetic equations of magnetically confined plasmas

International Nuclear Information System (INIS)

Killeen, J.; Kerbel, G.D.; McCoy, M.G.; Mirin, A.A.; Horowitz, E.J.; Shumaker, D.E.

1987-01-01

This paper presents four working computer models developed by the computational physics group of the National Magnetic Fusion Energy Computer Center. All of the models employ a kinetic description of plasma species. Three of the models are collisional, i.e., they include the solution of the Fokker-Planck equation in velocity space. The fourth model is collisionless and treats the plasma ions by a fully three-dimensional particle-in-cell method

Validation of an employee satisfaction model: A structural equation model approach

OpenAIRE

Ophillia Ledimo; Nico Martins

2015-01-01

The purpose of this study was to validate an employee satisfaction model and to determine the relationships between the different dimensions of the concept, using the structural equation modelling approach (SEM). A cross-sectional quantitative survey design was used to collect data from a random sample of (n=759) permanent employees of a parastatal organisation. Data was collected using the Employee Satisfaction Survey (ESS) to measure employee satisfaction dimensions. Following the steps of ...

An Equation-of-State Compositional In-Situ Combustion Model: A Study of Phase Behavior Sensitivity

DEFF Research Database (Denmark)

Kristensen, Morten Rode; Gerritsen, M. G.; Thomsen, Per Grove

2009-01-01

phase behavior sensitivity for in situ combustion, a thermal oil recovery process. For the one-dimensional model we first study the sensitivity to numerical discretization errors and provide grid density guidelines for proper resolution of in situ combustion behavior. A critical condition for success...... to ignition. For a particular oil we show that the simplified approach overestimates the required air injection rate for sustained front propagation by 17% compared to the equation of state-based approach....

Connection between Einstein equations, nonlinear sigma models, and self-dual Yang-Mills theory

International Nuclear Information System (INIS)

Sanchez, N.; Whiting, B.

1986-01-01

The authors analyze the connection between nonlinear sigma models self-dual Yang-Mills theory, and general relativity (self-dual and non-self-dual, with and without killing vectors), both at the level of the equations and at the level of the different type of solutions (solitons and calorons) of these theories. They give a manifestly gauge invariant formulation of the self-dual gravitational field analogous to that given by Yang for the self-dual Yang-Mills field. This formulation connects in a direct and explicit way the self-dual Yang-Mills and the general relativity equations. They give the ''R gauge'' parametrization of the self-dual gravitational field (which corresponds to modified Yang's-type and Ernst equations) and analyze the correspondence between their different types of solutions. No assumption about the existence of symmetries in the space-time is needed. For the general case (non-self-dual), they show that the Einstein equations contain an O nonlinear sigma model. This connection with the sigma model holds irrespective of the presence of symmetries in the space-time. They found a new class of solutions of Einstein equations depending on holomorphic and antiholomorphic functions and we relate some subclasses of these solutions to solutions of simpler nonlinear field equations that are well known in other branches of physics, like sigma models, SineGordon, and Liouville equations. They include gravitational plane wave solutions. They analyze the response of different accelerated quantum detector models, compare them to the case when the detectors are linterial in an ordinary Planckian gas at a given temperature, and discuss the anisotropy of the detected response for Rindler observers

Macroscopic Modeling of a One-Dimensional Electrochemical Cell using the Poisson-Nernst-Planck Equations

Science.gov (United States)

Yan, David

This thesis presents the one-dimensional equations, numerical method and simulations of a model to characterize the dynamical operation of an electrochemical cell. This model extends the current state-of-the art in that it accounts, in a primitive way, for the physics of the electrolyte/electrode interface and incorporates diffuse-charge dynamics, temperature coupling, surface coverage, and polarization phenomena. The one-dimensional equations account for a system with one or two mobile ions of opposite charge, and the electrode reaction we consider (when one is needed) is a one-electron electrodeposition reaction. Though the modeled system is far from representing a realistic electrochemical device, our results show a range of dynamics and behaviors which have not been observed previously, and explore the numerical challenges required when adding more complexity to a model. Furthermore, the basic transport equations (which are developed in three spatial dimensions) can in future accomodate the inclusion of additional physics, and coupling to more complex boundary conditions that incorporate two-dimensional surface phenomena and multi-rate reactions. In the model, the Poisson-Nernst-Planck equations are used to model diffusion and electromigration in an electrolyte, and the generalized Frumkin-Butler-Volmer equation is used to model reaction kinetics at electrodes. An energy balance equation is derived and coupled to the diffusion-migration equation. The model also includes dielectric polarization effects by introducing different values of the dielectric permittivity in different regions of the bulk, as well as accounting for surface coverage effects due to adsorption, and finite size "crowding", or steric effects. Advection effects are not modeled but could in future be incorporated. In order to solve the coupled PDE's, we use a variable step size second order scheme in time and finite differencing in space. Numerical tests are performed on a simplified system and

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

Science.gov (United States)

Umut Caglar, Mehmet; Pal, Ranadip

2010-10-01

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

Application of flexible model in neutron dynamics equations

International Nuclear Information System (INIS)

Liu Cheng; Zhao Fuyu; Fu Xiangang

2009-01-01

Big errors will occur in the modeling by multimode methodology when the available core physical parameter sets are insufficient. In this paper, the fuzzy logic membership function is introduced to figure out the values of these parameters on any point of lifetime through limited several sets of values, and thus to obtain the neutron dynamics equations on any point of lifetime. In order to overcome the effect of subjectivity in the membership function selection on the parameter calculation, quadratic optimization is carried out to the membership function by genetic algorithm, to result in a more accurate neutron kinetics equation on any point of lifetime. (authors)

Generalised and Fractional Langevin Equations-Implications for Energy Balance Models

Science.gov (United States)

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).

Partial differential equation models in the socio-economic sciences

KAUST Repository

Burger, Martin; Caffarelli, Luis; Markowich, Peter A.

2014-01-01

Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences

Climate Modeling in the Calculus and Differential Equations Classroom

Science.gov (United States)

Kose, Emek; Kunze, Jennifer

2013-01-01

Students in college-level mathematics classes can build the differential equations of an energy balance model of the Earth's climate themselves, from a basic understanding of the background science. Here we use variable albedo and qualitative analysis to find stable and unstable equilibria of such a model, providing a problem or perhaps a…

The modified CKD-EPI equation may be not more accurate than CKD-EPI equation in determining glomerular filtration rate in Chinese patients with chronic kidney disease.

Science.gov (United States)

Xie, Peng; Huang, Jian-Min; Li, Ying; Liu, Huai-Jun; Qu, Yan

2017-06-01

To investigate the application of the new modified Chronic Kidney Disease Epidemiology Collaboration (mCKD-EPI) equation developed by Liu for the measurement of glomerular filtration rate (GFR) in Chinese patients with chronic kidney disease (CKD) and to evaluate whether this modified form is more accurate than the original one in clinical practice. GFR was determined simultaneously by 3 methods: (a) 99m Tc-diethylene triamine pentaacetic acid ( 99m Tc-DTPA) dual plasma sample clearance method (mGFR), which was used as the reference standard; (b) CKD-EPI equation (eGFRckdepi); (c) modified CKD-EPI equation (eGFRmodified). Concordance correlation and Passing-Bablok regression were used to compare the validity of eGFRckdepi and eGFRmodified. Bias, precision and accuracy were compared to identify which equation showed the better performance in determining GFR. A total of 170 patients were enrolled. Both eGFRckdepi and eGFRmodified correlated well with mGFR (concordance correlation coefficient 0.90 and 0.74, respectively) and the Passing-Bablok regression equation of eGFRckdepi and eGFRmodified against mGFR was mGFR = 0.37 + 1.04 eGFRckdepi and -49.25 + 1.74 eGFRmodified, respectively. In terms of bias, precision and 30 % accuracy, eGFRmodified showed a worse performance compared to eGFRckdepi, in the whole cohort. The new modified CKD-EPI equation cannot replace the original CKD-EPI equation in determining GFR in Chinese patients with CKD.

Modeling of superconductors based on the timedependent Ginsburg-Landau equations

Science.gov (United States)

Grishakov, K. S.; Degtyarenko, P. N.; Degtyarenko, N. N.; Elesin, V. F.; Kruglov, V. S.

2009-11-01

Results of modeling of superconductor magnetization process based on a numerical solution of the timedependent Ginsburg-Landau equations are presented. Methods of grid approximation of the equations and method of finite elements are used. Two-dimensional patterns of changes in the order parameter and supercurrent distribution in superconductors are calculated and visualized. The main results are in agreement with the well-known representations for type I and II superconductors.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

Science.gov (United States)

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

Science.gov (United States)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

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

Science.gov (United States)

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.

Algebraic models for the hierarchy structure of evolution equations at small x

International Nuclear Information System (INIS)

Rembiesa, P.; Stasto, A.M.

2005-01-01

We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the equations that include the processes of pomeron splittings. We examine the algebraic structures of the governing equation hierarchies, as well as the asymptotic behavior of their solutions in the large-rapidity limit

MINI-TRAC code: a driver program for assessment of constitutive equations of two-fluid model

International Nuclear Information System (INIS)

Akimoto, Hajime; Abe, Yutaka; Ohnuki, Akira; Murao, Yoshio

1991-05-01

MINI-TRAC code, a driver program for assessment of constitutive equations of two-fluid model, has been developed to perform assessment and improvement of constitutive equations of two-fluid model widely and efficiently. The MINI-TRAC code uses one-dimensional conservation equations for mass, momentum and energy based on the two-fluid model. The code can work on a personal computer because it can be operated with a core memory size less than 640 KB. The MINI-TRAC code includes constitutive equations of TRAC-PF1/MOD1 code, TRAC-BF1 code and RELAP5/MOD2 code. The code is modulated so that one can easily change constitutive equations to perform a test calculation. This report is a manual of the MINI-TRAC code. The basic equations, numerics, constitutive, equations included in the MINI-TRAC code will be described. The user's manual such as input description will be presented. The program structure and contents of main variables will also be mentioned in this report. (author)

Comparing the measured basal metabolic rates in patients with chronic disorders of consciousness to the estimated basal metabolic rate calculated from common predictive equations.

Science.gov (United States)

Xiao, Guizhen; Xie, Qiuyou; He, Yanbin; Wang, Ziwen; Chen, Yan; Jiang, Mengliu; Ni, Xiaoxiao; Wang, Qinxian; Murong, Min; Guo, Yequn; Qiu, Xiaowen; Yu, Ronghao

2017-10-01

Accurately predicting the basal metabolic rate (BMR) of patients in a vegetative state (VS) or minimally conscious state (MCS) is critical to proper nutritional therapy, but commonly used equations have not been shown to be accurate. Therefore, we compared the BMR measured by indirect calorimetry (IC) to BMR values estimated using common predictive equations in VS and MCS patients. Body composition variables were measured using the bioelectric impedance analysis (BIA) technique. BMR was measured by IC in 82 patients (64 men and 18 women) with VS or MCS. Patients were classified by body mass index as underweight (BMR was estimated for each group using the Harris-Benedict (H-B), Schofield, or Cunningham equations and compared to the measured BMR using Bland-Altman analyses. For the underweight group, there was a significant difference between the measured BMR values and the estimated BMR values calculated using the H-B, Schofield, and Cunningham equations (p BMR values estimated using the H-B and Cunningham equations were different significantly from the measured BMR (p BMR in the normal-weight group. The Schofield equation showed the best concordance (only 41.5%) with the BMR values measured by IC. None of the commonly used equations to estimate BMR were suitable for the VS or MCS populations. Indirect calorimetry is the preferred way to avoid either over or underestimate of BMR values. Copyright © 2016. Published by Elsevier Ltd.

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

Science.gov (United States)

Lu, Benzhuo; Zhou, Y.C.

2011-01-01

The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

Tap density equations of granular powders based on the rate process theory and the free volume concept.

Science.gov (United States)

Hao, Tian

2015-02-28

The tap density of a granular powder is often linked to the flowability via the Carr index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in the literature: the inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept under the assumption that particles will obey similar thermodynamic laws during the tapping process if the "granular temperature" is defined in a different way, we obtain the tap density equations, and they are reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environmental temperature are grouped into this parameter that weighs the pace of the packing process. The current results, in conjunction with our previous findings, may imply that both "dry" (granular) and "wet" (colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process).

Alternans promotion in cardiac electrophysiology models by delay differential equations.

Science.gov (United States)

Gomes, Johnny M; Dos Santos, Rodrigo Weber; Cherry, Elizabeth M

2017-09-01

Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate's recovery between consecutive action potentials.

Alternans promotion in cardiac electrophysiology models by delay differential equations

Science.gov (United States)

Gomes, Johnny M.; dos Santos, Rodrigo Weber; Cherry, Elizabeth M.

2017-09-01

Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate's recovery between consecutive action potentials.

Guidelines for a graph-theoretic implementation of structural equation modeling

Science.gov (United States)

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

A modified two-fluid model for the application of two-group interfacial area transport equation

International Nuclear Information System (INIS)

Sun, X.; Ishii, M.; Kelly, J.

2003-01-01

This paper presents the modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not desirable to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model

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

Science.gov (United States)

Hu, Yueqin; Treinen, Raymond

2018-04-06

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

Hidden physics models: Machine learning of nonlinear partial differential equations

Science.gov (United States)

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.

Neutron star models with realistic high-density equations of state

International Nuclear Information System (INIS)

Malone, R.C.; Johnson, M.B.; Bethe, H.A.

1975-01-01

We calculate neutron star models using four realistic high-density models of the equation of state. We conclude that the maximum mass of a neutron star is unlikely to exceed 2 M/sub sun/. All of the realistic models are consistent with current estimates of the moment of inertia of the Crab pulsar

A new lattice hydrodynamic model based on control method considering the flux change rate and delay feedback signal

Science.gov (United States)

Qin, Shunda; Ge, Hongxia; Cheng, Rongjun

2018-02-01

In this paper, a new lattice hydrodynamic model is proposed by taking delay feedback and flux change rate effect into account in a single lane. The linear stability condition of the new model is derived by control theory. By using the nonlinear analysis method, the mKDV equation near the critical point is deduced to describe the traffic congestion. Numerical simulations are carried out to demonstrate the advantage of the new model in suppressing traffic jam with the consideration of flux change rate effect in delay feedback model.

Anti-symmetrically fused model and non-linear integral equations in the three-state Uimin-Sutherland model

International Nuclear Information System (INIS)

Fujii, Akira; Kluemper, Andreas

1999-01-01

We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation

Modelling the heat dynamics of a building using stochastic differential equations

DEFF Research Database (Denmark)

Andersen, Klaus Kaae; Madsen, Henrik; Hansen, Lars Henrik

2000-01-01

estimation and model validation, while physical knowledge is used in forming the model structure. The suggested lumped parameter model is thus based on thermodynamics and formulated as a system of stochastic differential equations. Due to the continuous time formulation the parameters of the model...

Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

Science.gov (United States)

Saveliev, V L; Gorokhovski, M A

2005-07-01

On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

Newtonian nudging for a Richards equation-based distributed hydrological model

Science.gov (United States)

Paniconi, Claudio; Marrocu, Marino; Putti, Mario; Verbunt, Mark

The objective of data assimilation is to provide physically consistent estimates of spatially distributed environmental variables. In this study a relatively simple data assimilation method has been implemented in a relatively complex hydrological model. The data assimilation technique is Newtonian relaxation or nudging, in which model variables are driven towards observations by a forcing term added to the model equations. The forcing term is proportional to the difference between simulation and observation (relaxation component) and contains four-dimensional weighting functions that can incorporate prior knowledge about the spatial and temporal variability and characteristic scales of the state variable(s) being assimilated. The numerical model couples a three-dimensional finite element Richards equation solver for variably saturated porous media and a finite difference diffusion wave approximation based on digital elevation data for surface water dynamics. We describe the implementation of the data assimilation algorithm for the coupled model and report on the numerical and hydrological performance of the resulting assimilation scheme. Nudging is shown to be successful in improving the hydrological simulation results, and it introduces little computational cost, in terms of CPU and other numerical aspects of the model's behavior, in some cases even improving numerical performance compared to model runs without nudging. We also examine the sensitivity of the model to nudging term parameters including the spatio-temporal influence coefficients in the weighting functions. Overall the nudging algorithm is quite flexible, for instance in dealing with concurrent observation datasets, gridded or scattered data, and different state variables, and the implementation presented here can be readily extended to any of these features not already incorporated. Moreover the nudging code and tests can serve as a basis for implementation of more sophisticated data assimilation

Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

Science.gov (United States)

Yan, Wei; Chang, Yuwen

2016-12-01

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

Role of secondary instability theory and parabolized stability equations in transition modeling