Elliptic Painlevé equations from next-nearest-neighbor translations on the E_8^{(1)} lattice

NASA Astrophysics Data System (ADS)

Joshi, Nalini; Nakazono, Nobutaka

2017-07-01

The well known elliptic discrete Painlevé equation of Sakai is constructed by a standard translation on the E_8(1) lattice, given by nearest neighbor vectors. In this paper, we give a new elliptic discrete Painlevé equation obtained by translations along next-nearest-neighbor vectors. This equation is a generic (8-parameter) version of a 2-parameter elliptic difference equation found by reduction from Adler’s partial difference equation, the so-called Q4 equation. We also provide a projective reduction of the well known equation of Sakai.

A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations

NASA Astrophysics Data System (ADS)

Zhao, B. B.; Ertekin, R. C.; Duan, W. Y.

2015-02-01

This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green-Naghdi (GN) equations and the Irrotational Green-Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green-Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at different levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.

Navier-Stokes Solutions for Spin-Up from Rest in a Cylindrical Container

DTIC Science & Technology

1979-09-01

CONDITIONS The calculations employ a finite - difference analog of the unsteady axisyimetric Navier-Stokes equations formulated in cylindrical coordinates...derivatives are approximated by second- order accurate one-sided difference formulae involving three time levels. * The following finite - difference ...equation are identical in form to Equations (13). The finite - difference representations for the ?-equation are: "(i)[aJ~lk " /i’,J-l2k] T (14a) •g I

Weather adjustment using seemingly unrelated regression

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

Noll, T.A.

1995-05-01

Seemingly unrelated regression (SUR) is a system estimation technique that accounts for time-contemporaneous correlation between individual equations within a system of equations. SUR is suited to weather adjustment estimations when the estimation is: (1) composed of a system of equations and (2) the system of equations represents either different weather stations, different sales sectors or a combination of different weather stations and different sales sectors. SUR utilizes the cross-equation error values to develop more accurate estimates of the system coefficients than are obtained using ordinary least-squares (OLS) estimation. SUR estimates can be generated using a variety of statistical software packagesmore » including MicroTSP and SAS.« less

A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations

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

Zhao, B.B.; Ertekin, R.C.; College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin

2015-02-15

This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green–Naghdi (GN) equations and the Irrotational Green–Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green–Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at differentmore » levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.« less

Evaluating Equating Accuracy and Assumptions for Groups that Differ in Performance

ERIC Educational Resources Information Center

Powers, Sonya; Kolen, Michael J.

2014-01-01

Accurate equating results are essential when comparing examinee scores across exam forms. Previous research indicates that equating results may not be accurate when group differences are large. This study compared the equating results of frequency estimation, chained equipercentile, item response theory (IRT) true-score, and IRT observed-score…

Finite difference methods for transient signal propagation in stratified dispersive media

NASA Technical Reports Server (NTRS)

Lam, D. H.

1975-01-01

Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.

Laplace and Z Transform Solutions of Differential and Difference Equations With the HP-41C.

ERIC Educational Resources Information Center

Harden, Richard C.; Simons, Fred O., Jr.

1983-01-01

A previously developed program for the HP-41C programmable calculator is extended to handle models of differential and difference equations with multiple eigenvalues. How to obtain difference equation solutions via the Z transform is described. (MNS)

The condition of regular degeneration for singularly perturbed systems of linear differential-difference equations.

NASA Technical Reports Server (NTRS)

Cooke, K. L.; Meyer, K. R.

1966-01-01

Extension of problem of singular perturbation for linear scalar constant coefficient differential- difference equation with single retardation to several retardations, noting degenerate equation solution

Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique

NASA Technical Reports Server (NTRS)

Nordmann, R.; Weiser, P.

1989-01-01

The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Research on Standard Errors of Equating Differences. Research Report. ETS RR-10-25

ERIC Educational Resources Information Center

Moses, Tim; Zhang, Wenmin

2010-01-01

In this paper, the "standard error of equating difference" (SEED) is described in terms of originally proposed kernel equating functions (von Davier, Holland, & Thayer, 2004) and extended to incorporate traditional linear and equipercentile functions. These derivations expand on prior developments of SEEDs and standard errors of equating and…

Exact finite difference schemes for the non-linear unidirectional wave equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

Moisture Transport in Composites during Repair Work,

DTIC Science & Technology

1983-09-01

4 * FINITE DIFFERENCE EQUATIONS. .. . . .. . .. .. .. .. .. 6 INI I A ANBOUNAAYYCONDITIONS................ 7 REASONABLE FIRST...DURING DRYING AND CURING . . . ........ 9 5 CONVERGENCE OF FINITE DIFFERENCE METHOD USING DIFFERENT At . . .. 12 6 CONVERGENCE OF FDA METHOD FOR SAME At...transport we will use a finite difference approach, changing the Fickian equation to a finite number of linear algebraic equations that can be solved by

Dynamic reduction with applications to mathematical biology and other areas.

PubMed

Sacker, Robert J; Von Bremen, Hubertus F

2007-10-01

In a difference or differential equation one is usually interested in finding solutions having certain properties, either intrinsic properties (e.g. bounded, periodic, almost periodic) or extrinsic properties (e.g. stable, asymptotically stable, globally asymptotically stable). In certain instances it may happen that the dependence of these equations on the state variable is such that one may (1) alter that dependency by replacing part of the state variable by a function from a class having some of the above properties and (2) solve the 'reduced' equation for a solution having the remaining properties and lying in the same class. This then sets up a mapping Τ of the class into itself, thus reducing the original problem to one of finding a fixed point of the mapping. The procedure is applied to obtain a globally asymptotically stable periodic solution for a system of difference equations modeling the interaction of wild and genetically altered mosquitoes in an environment yielding periodic parameters. It is also shown that certain coupled periodic systems of difference equations may be completely decoupled so that the mapping Τ is established by solving a set of scalar equations. Periodic difference equations of extended Ricker type and also rational difference equations with a finite number of delays are also considered by reducing them to equations without delays but with a larger period. Conditions are given guaranteeing the existence and global asymptotic stability of periodic solutions.

Asymptotic analysis of numerical wave propagation in finite difference equations

NASA Technical Reports Server (NTRS)

Giles, M.; Thompkins, W. T., Jr.

1983-01-01

An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.

Fractional-order difference equations for physical lattices and some applications

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2015-10-15

Fractional-order operators for physical lattice models based on the Grünwald-Letnikov fractional differences are suggested. We use an approach based on the models of lattices with long-range particle interactions. The fractional-order operators of differentiation and integration on physical lattices are represented by kernels of lattice long-range interactions. In continuum limit, these discrete operators of non-integer orders give the fractional-order derivatives and integrals with respect to coordinates of the Grünwald-Letnikov types. As examples of the fractional-order difference equations for physical lattices, we give difference analogs of the fractional nonlocal Navier-Stokes equations and the fractional nonlocal Maxwell equations for lattices with long-range interactions.more » Continuum limits of these fractional-order difference equations are also suggested.« less

Stable boundary conditions and difference schemes for Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Dutt, P.

1985-01-01

The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.

Measurement of testicular volume in smaller testes: how accurate is the conventional orchidometer?

PubMed

Lin, Chih-Chieh; Huang, William J S; Chen, Kuang-Kuo

2009-01-01

The aim of this study was to evaluate the accuracy of different methods, including the Seager orchidometer (SO) and ultrasonography (US), for assessing testicular volume of smaller testes (testes volume less than 18 mL). Moreover, the equations used for the calculations--the Hansen formula (length [L] x width [W](2) x 0.52, equation A), the prolate ellipsoid formula (L x W x height [H] x 0.52, equation B), and the Lambert equation (L x W x H x 0.71, equation C)--were also examined and compared with the gold standard testicular volume obtained by water displacement (Archimedes principle). In this study, 30 testes from 15 men, mean age 75.3 (+/-8.3) years, were included. They all had advanced prostate cancer and were admitted for orchiectomy. Before the procedure, all the testes were assessed using SO and US. The dimensions were then input into each equation to obtain the volume estimates. The testicular volume by water displacement was 8.1 +/- 3.5 mL. Correlation coefficients (R(2)) of the 2 different methods (SO, US) to the gold standard were 0.70 and 0.85, respectively. The calculated testicular volumes were 9.2 +/- 3.9 mL (measured by SO, equation A), 11.9 +/- 5.2 mL (measured by SO, equation C), 7.3 +/- 4.2 mL (measured by US, equation A), 6.5 +/- 3.3 mL (measured by US, equation B) and 8.9 +/- 4.5 mL (measured by US, equation C). Only the mean size measured by US and volume calculated with the Hansen equation (equation A) and the mean size measured by US and volume calculated with the Lambert equation (equation C) showed no significant differences when compared with the volumes estimated by water displacement (mean difference 0.81 mL, P = .053, and 0.81 mL, P = .056, respectively). Based on our measurements, we categorized testicular volume by different cutoff values (7.0 mL, 7.5 mL, 8.0 mL, and 8.5 mL) to calculate a new constant for use in the Hansen equation. The new constant was 0.59. We then reexamined the equations using the new 0.59 constant, and found that the equation Volume (V) = L x W(2) x 0.59 was the best for describing testicular volume among our subjects (difference between the new equation and the gold standard of water displacement = 0.19 mL, P = .726). We also found that US was more precise in measuring testicular dimensions. We propose a new formula, V = L x W(2) x 0.59, to assess the volumes of smaller testes.

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

Efficacy of generic allometric equations for estimating biomass: a test in Japanese natural forests.

PubMed

Ishihara, Masae I; Utsugi, Hajime; Tanouchi, Hiroyuki; Aiba, Masahiro; Kurokawa, Hiroko; Onoda, Yusuke; Nagano, Masahiro; Umehara, Toru; Ando, Makoto; Miyata, Rie; Hiura, Tsutom

2015-07-01

Accurate estimation of tree and forest biomass is key to evaluating forest ecosystem functions and the global carbon cycle. Allometric equations that estimate tree biomass from a set of predictors, such as stem diameter and tree height, are commonly used. Most allometric equations are site specific, usually developed from a small number of trees harvested in a small area, and are either species specific or ignore interspecific differences in allometry. Due to lack of site-specific allometries, local equations are often applied to sites for which they were not originally developed (foreign sites), sometimes leading to large errors in biomass estimates. In this study, we developed generic allometric equations for aboveground biomass and component (stem, branch, leaf, and root) biomass using large, compiled data sets of 1203 harvested trees belonging to 102 species (60 deciduous angiosperm, 32 evergreen angiosperm, and 10 evergreen gymnosperm species) from 70 boreal, temperate, and subtropical natural forests in Japan. The best generic equations provided better biomass estimates than did local equations that were applied to foreign sites. The best generic equations included explanatory variables that represent interspecific differences in allometry in addition to stem diameter, reducing error by 4-12% compared to the generic equations that did not include the interspecific difference. Different explanatory variables were selected for different components. For aboveground and stem biomass, the best generic equations had species-specific wood specific gravity as an explanatory variable. For branch, leaf, and root biomass, the best equations had functional types (deciduous angiosperm, evergreen angiosperm, and evergreen gymnosperm) instead of functional traits (wood specific gravity or leaf mass per area), suggesting importance of other traits in addition to these traits, such as canopy and root architecture. Inclusion of tree height in addition to stem diameter improved the performance of the generic equation only for stem biomass and had no apparent effect on aboveground, branch, leaf, and root biomass at the site level. The development of a generic allometric equation taking account of interspecific differences is an effective approach for accurately estimating aboveground and component biomass in boreal, temperate, and subtropical natural forests.

Nonlinear truncation error analysis of finite difference schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1983-01-01

It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

Validity of one-repetition maximum predictive equations in men with spinal cord injury.

PubMed

Ribeiro Neto, F; Guanais, P; Dornelas, E; Coutinho, A C B; Costa, R R G

2017-10-01

Cross-sectional study. The study aimed (a) to test the cross-validation of current one-repetition maximum (1RM) predictive equations in men with spinal cord injury (SCI); (b) to compare the current 1RM predictive equations to a newly developed equation based on the 4- to 12-repetition maximum test (4-12RM). SARAH Rehabilitation Hospital Network, Brasilia, Brazil. Forty-five men aged 28.0 years with SCI between C6 and L2 causing complete motor impairment were enrolled in the study. Volunteers were tested, in a random order, in 1RM test or 4-12RM with 2-3 interval days. Multiple regression analysis was used to generate an equation for predicting 1RM. There were no significant differences between 1RM test and the current predictive equations. ICC values were significant and were classified as excellent for all current predictive equations. The predictive equation of Lombardi presented the best Bland-Altman results (0.5 kg and 12.8 kg for mean difference and interval range around the differences, respectively). The two created equation models for 1RM demonstrated the same and a high adjusted R 2 (0.971, P<0.01), but different SEE of measured 1RM (2.88 kg or 5.4% and 2.90 kg or 5.5%). All 1RM predictive equations are accurate to assess individuals with SCI at the bench press exercise. However, the predictive equation of Lombardi presented the best associated cross-validity results. A specific 1RM prediction equation was also elaborated for individuals with SCI. The created equation should be tested in order to verify whether it presents better accuracy than the current ones.

Evaluation of equations that estimate glomerular filtration rate in renal transplant recipients.

PubMed

De Alencastro, M G; Veronese, F V; Vicari, A R; Gonçalves, L F; Manfro, R C

2014-03-01

The accuracy of equations that estimate the glomerular filtration rate (GFR) in renal transplant patients has not been established; thus their performance was assessed in stable renal transplant patients. Renal transplant patients (N.=213) with stable graft function were enrolled. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation was used as the reference method and compared with the Cockcroft-Gault (CG), Modification of Diet in Renal Disease (MDRD), Mayo Clinic (MC) and Nankivell equations. Bias, accuracy and concordance rates were determined for all equation relative to CKD-EPI. Mean estimated GFR values of the equations differed significantly from the CKD-EPI values, though the correlations with the reference method were significant. Values of MDRD differed from the CG, MC and Nankivell estimations. The best agreement to classify the chronic kidney disease (CKD) stages was for the MDRD (Kappa=0.649, P<0.001), and for the other equations the agreement was moderate. The MDRD had less bias and narrower agreement limits but underestimated the GFR at levels above 60 mL/min/1.73 m2. Conversely, the CG, MC and Nankivell equations overestimated the GFR, and the Nankivell equation had the worst performance. The MDRD equation P15 and P30 values were higher than those of the other equations (P<0.001). Despite their correlations, equations estimated the GFR and CKD stage differently. The MDRD equation was the most accurate, but the sub-optimal performance of all the equations precludes their accurate use in clinical practice.

Introduction to the Difference Calculus through the Fibonacci Numbers

ERIC Educational Resources Information Center

Shannon, A. G.; Atanassov, K. T.

2002-01-01

This note explores ways in which the Fibonacci numbers can be used to introduce difference equations as a prelude to differential equations. The rationale is that the formal aspects of discrete mathematics can provide a concrete introduction to the mechanisms of solving difference and differential equations without the distractions of the analytic…

Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations

NASA Astrophysics Data System (ADS)

Berkeley, George; Igonin, Sergei

2016-07-01

Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita-Itoh-Bogoyavlensky, Toda, and Adler-Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new.

Study on Heat Transfer Agent Models of Transmission Line and Transformer

NASA Astrophysics Data System (ADS)

Wang, B.; Zhang, P. P.

2018-04-01

When using heat transfer simulation to study the dynamic overload of transmission line and transformer, it needs to establish the mathematical expression of heat transfer. However, the formula is a nonlinear differential equation or equation set and it is not easy to get general solutions. Aiming at this problem, some different temperature change processes caused by different initial conditions are calculated by differential equation and equation set. New agent models are developed according to the characteristics of different temperature change processes. The results show that the agent models have high precision and can solve the problem that the original equation cannot be directly applied in some practical engineers.

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

ERIC Educational Resources Information Center

Chen, Haiwen

2012-01-01

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

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

PubMed

Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

2018-01-01

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

Alternative bi-Hamiltonian structures for WDVV equations of associativity

NASA Astrophysics Data System (ADS)

Kalayci, J.; Nutku, Y.

1998-01-01

The WDVV equations of associativity in two-dimensional topological field theory are completely integrable third-order Monge-Ampère equations which admit bi-Hamiltonian structure. The time variable plays a distinguished role in the discussion of Hamiltonian structure, whereas in the theory of WDVV equations none of the independent variables merits such a distinction. WDVV equations admit very different alternative Hamiltonian structures under different possible choices of the time variable, but all these various Hamiltonian formulations can be brought together in the framework of the covariant theory of symplectic structure. They can be identified as different components of the covariant Witten-Zuckerman symplectic 2-form current density where a variational formulation of the WDVV equation that leads to the Hamiltonian operator through the Dirac bracket is available.

Turbulence kinetic energy equation for dilute suspensions

NASA Technical Reports Server (NTRS)

Abou-Arab, T. W.; Roco, M. C.

1989-01-01

A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

Evaluating Equity at the Local Level Using Bootstrap Tests. Research Report 2016-4

ERIC Educational Resources Information Center

Kim, YoungKoung; DeCarlo, Lawrence T.

2016-01-01

Because of concerns about test security, different test forms are typically used across different testing occasions. As a result, equating is necessary in order to get scores from the different test forms that can be used interchangeably. In order to assure the quality of equating, multiple equating methods are often examined. Various equity…

Impact of Accumulated Error on Item Response Theory Pre-Equating with Mixed Format Tests

ERIC Educational Resources Information Center

Keller, Lisa A.; Keller, Robert; Cook, Robert J.; Colvin, Kimberly F.

2016-01-01

The equating of tests is an essential process in high-stakes, large-scale testing conducted over multiple forms or administrations. By adjusting for differences in difficulty and placing scores from different administrations of a test on a common scale, equating allows scores from these different forms and administrations to be directly compared…

Reduction of lattice equations to the Painlevé equations: PIV and PV

NASA Astrophysics Data System (ADS)

Nakazono, Nobutaka

2018-02-01

In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

A finite difference scheme for the equilibrium equations of elastic bodies

NASA Technical Reports Server (NTRS)

Phillips, T. N.; Rose, M. E.

1984-01-01

A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques.

A GENERAL MASS-CONSERVATIVE NUMERICAL SOLUTION FOR THE UNSATURATED FLOW EQUATION

EPA Science Inventory

Numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems. Numerical solution based on the standard h-based form of Richards equation generally yields poor results, ch...

A DRBEM for steady infiltration from periodic semi-circular channels with two different types of roots distribution

NASA Astrophysics Data System (ADS)

Solekhudin, Imam; Sumardi

2017-05-01

In this study, problems involving steady Infiltration from periodic semicircular channels with root-water uptake function are considered. These problems are governed by Richards equation. This equation can be studied more conveniently by transforming the equation into a modified Helmholtz equation. In these problems, two different types of root-water uptake are considered. A dual reciprocity boundary element method (DRBEM) with a predictor-corrector scheme is used to solve the modified Helmholtz equation numerically. Using the solution obtained, numerical values of suction potential and root-water uptake function can be computed. In addition, amount of water absorbed by the different plant roots distribution can also be computed and compared.

A third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

Non-invertible transformations of differential-difference equations

NASA Astrophysics Data System (ADS)

Garifullin, R. N.; Yamilov, R. I.; Levi, D.

2016-09-01

We discuss aspects of the theory of non-invertible transformations of differential-difference equations and, in particular, the notion of Miura type transformation. We introduce the concept of non-Miura type linearizable transformation and we present techniques that allow one to construct simple linearizable transformations and might help one to solve classification problems. This theory is illustrated by the example of a new integrable differential-difference equation depending on five lattice points, interesting from the viewpoint of the non-invertible transformation, which relate it to an Itoh-Narita-Bogoyavlensky equation.

On Reductions of the Hirota-Miwa Equation

NASA Astrophysics Data System (ADS)

Hone, Andrew N. W.; Kouloukas, Theodoros E.; Ward, Chloe

2017-07-01

The Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota-Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge transformation), defined by a triple of integers or half-integers, which produce bilinear ordinary difference equations of Somos/Gale-Robinson type. Here it is explained how to obtain Lax pairs and presymplectic structures for these reductions, in order to demonstrate Liouville integrability of some associated maps, certain of which are related to reductions of discrete Toda and discrete KdV equations.

Teaching Modeling with Partial Differential Equations: Several Successful Approaches

ERIC Educational Resources Information Center

Myers, Joseph; Trubatch, David; Winkel, Brian

2008-01-01

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

Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient

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

Ashyralyev, Allaberen; Okur, Ulker

In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

NASA Astrophysics Data System (ADS)

Wu, Zedong; Alkhalifah, Tariq

2018-07-01

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

Simple taper: Taper equations for the field forester

Treesearch

David R. Larsen

2017-01-01

"Simple taper" is set of linear equations that are based on stem taper rates; the intent is to provide taper equation functionality to field foresters. The equation parameters are two taper rates based on differences in diameter outside bark at two points on a tree. The simple taper equations are statistically equivalent to more complex equations. The linear...

Performance of Chronic Kidney Disease Epidemiology Collaboration Creatinine-Cystatin C Equation for Estimating Kidney Function in Cirrhosis

PubMed Central

Mindikoglu, Ayse L.; Dowling, Thomas C.; Weir, Matthew R.; Seliger, Stephen L.; Christenson, Robert H.; Magder, Laurence S.

2013-01-01

Conventional creatinine-based glomerular filtration rate (GFR) equations are insufficiently accurate for estimating GFR in cirrhosis. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) recently proposed an equation to estimate GFR in subjects without cirrhosis using both serum creatinine and cystatin C levels. Performance of the new CKD-EPI creatinine-cystatin C equation (2012) was superior to previous creatinine- or cystatin C-based GFR equations. To evaluate the performance of the CKD-EPI creatinine-cystatin C equation in subjects with cirrhosis, we compared it to GFR measured by non-radiolabeled iothalamate plasma clearance (mGFR) in 72 subjects with cirrhosis. We compared the “bias”, “precision” and “accuracy” of the new CKD-EPI creatinine-cystatin C equation to that of 24-hour urinary creatinine clearance (CrCl), Cockcroft-Gault (CG) and previously reported creatinine- and/or cystatin C-based GFR-estimating equations. Accuracy of CKD-EPI creatinine-cystatin C equation as quantified by root mean squared error of difference scores [differences between mGFR and estimated GFR (eGFR) or between mGFR and CrCl, or between mGFR and CG equation for each subject] (RMSE=23.56) was significantly better than that of CrCl (37.69, P=0.001), CG (RMSE=36.12, P=0.002) and GFR-estimating equations based on cystatin C only. Its accuracy as quantified by percentage of eGFRs that differed by greater than 30% with respect to mGFR was significantly better compared to CrCl (P=0.024), CG (P=0.0001), 4-variable MDRD (P=0.027) and CKD-EPI creatinine 2009 (P=0.012) equations. However, for 23.61% of the subjects, GFR estimated by CKD-EPI creatinine-cystatin C equation differed from the mGFR by more than 30%. CONCLUSIONS The diagnostic performance of CKD-EPI creatinine-cystatin C equation (2012) in patients with cirrhosis was superior to conventional equations in clinical practice for estimating GFR. However, its diagnostic performance was substantially worse than reported in subjects without cirrhosis. PMID:23744636

Comparison of the MDRD study and CKD-EPI equations for the estimation of the glomerular filtration rate in the Korean general population: the fifth Korea National Health and Nutrition Examination Survey (KNHANES V-1), 2010.

PubMed

Jeong, Tae-Dong; Lee, Woochang; Chun, Sail; Lee, Sang Koo; Ryu, Jin-Sook; Min, Won-Ki; Park, Jung Sik

2013-01-01

We compared the accuracy of the Modification of Diet in Renal Disease (MDRD) study and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations in Korean patients and evaluated the difference in CKD prevalence determined using the two equations in the Korean general population. The accuracy of the two equations was evaluated in 607 patients who underwent a chromium-51-ethylenediaminetetraacetic acid GFR measurement. Additionally, we compared the difference in CKD prevalence determined by the two equations among 5,822 participants in the fifth Korea National Health and Nutrition Examination Survey, 2010. Among the 607 subjects, the median bias of the CKD-EPI equation was significantly lower than that of the MDRD study equation (0.9 vs. 2.2, p=0.020). The accuracy of the two equations was not significantly different in patients with mGFR <60 mL/min/1.73m(2); however, the accuracy of the CKD-EPI equation was significantly higher than that of the MDRD study equation in patients with GFR ≥60 mL/min/1.73m(2). The prevalences of the CKD stages 1, 2 and 3 in the Korean general population were 47.56, 49.23, and 3.07%, respectively, for the MDRD study equation; and were 68.48, 28.89, and 2.49%, respectively, for the CKD-EPI equation. These data suggest that the CKD-EPI equation might be more useful in clinical practice than the MDRD study equation in Koreans. © 2013 S. Karger AG, Basel.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

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

PubMed

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

2012-12-01

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

Least Squares Method for Equating Logistic Ability Scales: A General Approach and Evaluation. Iowa Testing Programs Occasional Papers, Number 30.

ERIC Educational Resources Information Center

Haebara, Tomokazu

When several ability scales in item response models are separately derived from different test forms administered to different samples of examinees, these scales must be equated to a common scale because their units and origins are arbitrarily determined and generally different from scale to scale. A general method for equating logistic ability…

The Effects of Different Types of Anchor Tests on Observed Score Equating. Research Report. ETS RR-09-41

ERIC Educational Resources Information Center

Liu, Jinghua; Sinharay, Sandip; Holland, Paul W.; Feigenbaum, Miriam; Curley, Edward

2009-01-01

This study explores the use of a different type of anchor, a "midi anchor", that has a smaller spread of item difficulties than the tests to be equated, and then contrasts its use with the use of a "mini anchor". The impact of different anchors on observed score equating were evaluated and compared with respect to systematic…

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

An algorithm for solving the perturbed gas dynamic equations

NASA Technical Reports Server (NTRS)

Davis, Sanford

1993-01-01

The present application of a compact, higher-order central-difference approximation to the linearized Euler equations illustrates the multimodal character of these equations by means of computations for acoustic, vortical, and entropy waves. Such dissipationless central-difference methods are shown to propagate waves exhibiting excellent phase and amplitude resolution on the basis of relatively large time-steps; they can be applied to wave problems governed by systems of first-order partial differential equations.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. III - Perturbation theory

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1986-01-01

A technique to construct a uniformly valid perturbation series solution to a particular class of nonlinear difference equations is shown. The method allows the determination of approximations to the periodic solutions to these equations. An example illustrating the technique is presented.

Breakdown of the conservative potential equation

NASA Technical Reports Server (NTRS)

Salas, M. D.; Gumbert, C. R.

1986-01-01

The conservative full-potential equation is used to study transonic flow over five airfoil sections. The results of the study indicate that once shock are present in the flow, the qualitative approximation is different from that observed with the Euler equations. The difference in behavior of the potential eventually leads to multiple solutions.

Effect of Differential Item Functioning on Test Equating

ERIC Educational Resources Information Center

Kabasakal, Kübra Atalay; Kelecioglu, Hülya

2015-01-01

This study examines the effect of differential item functioning (DIF) items on test equating through multilevel item response models (MIRMs) and traditional IRMs. The performances of three different equating models were investigated under 24 different simulation conditions, and the variables whose effects were examined included sample size, test…

New explicit global asymptotic stability criteria for higher order difference equations

NASA Astrophysics Data System (ADS)

El-Morshedy, Hassan A.

2007-12-01

New explicit sufficient conditions for the asymptotic stability of the zero solution of higher order difference equations are obtained. These criteria can be applied to autonomous and nonautonomous equations. The celebrated Clark asymptotic stability criterion is improved. Also, applications to models from mathematical biology and macroeconomics are given.

Minimizing Secular J2 Perturbation Effects on Satellite Formations

DTIC Science & Technology

2008-03-01

linear set of differential equations describing the relative motion was established by Hill as well as Clohessy and Wiltshire , with a slightly... Wiltshire (CW) equations, and Hill- Clohessy - Wiltshire (HCW) equations. In the simplest form these differential equations can be expressed as: 2 2 2 3 2...different orientation. Because these equations are much alike, the differential equations established are referred to as Hill’s equations, Clohessy

The applicability of eGFR equations to different populations.

PubMed

Delanaye, Pierre; Mariat, Christophe

2013-09-01

The Cockcroft-Gault equation for estimating glomerular filtration rate has been learnt by every generation of medical students over the decades. Since the publication of the Modification of Diet in Renal Disease (MDRD) study equation in 1999, however, the supremacy of the Cockcroft-Gault equation has been relentlessly disputed. More recently, the Chronic Kidney Disease Epidemiology (CKD-EPI) consortium has proposed a group of novel equations for estimating glomerular filtration rate (GFR). The MDRD and CKD-EPI equations were developed following a rigorous process, are expressed in a way in which they can be used with standardized biomarkers of GFR (serum creatinine and/or serum cystatin C) and have been evaluated in different populations of patients. Today, the MDRD Study equation and the CKD-EPI equation based on serum creatinine level have supplanted the Cockcroft-Gault equation. In many regards, these equations are superior to the Cockcroft-Gault equation and are now specifically recommended by international guidelines. With their generalized use, however, it has become apparent that those equations are not infallible and that they fail to provide an accurate estimate of GFR in certain situations frequently encountered in clinical practice. After describing the processes that led to the development of the new GFR-estimating equations, this Review discusses the clinical situations in which the applicability of these equations is questioned.

Evaluating the Effects of Differences in Group Abilities on the Tucker and the Levine Observed-Score Methods for Common-Item Nonequivalent Groups Equating. ACT Research Report Series 2010-1

ERIC Educational Resources Information Center

Chen, Hanwei; Cui, Zhongmin; Zhu, Rongchun; Gao, Xiaohong

2010-01-01

The most critical feature of a common-item nonequivalent groups equating design is that the average score difference between the new and old groups can be accurately decomposed into a group ability difference and a form difficulty difference. Two widely used observed-score linear equating methods, the Tucker and the Levine observed-score methods,…

A Comparison of the Kernel Equating Method with Traditional Equating Methods Using SAT[R] Data

ERIC Educational Resources Information Center

Liu, Jinghua; Low, Albert C.

2008-01-01

This study applied kernel equating (KE) in two scenarios: equating to a very similar population and equating to a very different population, referred to as a distant population, using SAT[R] data. The KE results were compared to the results obtained from analogous traditional equating methods in both scenarios. The results indicate that KE results…

Kinetic theory of oxygen isotopic exchange between minerals and water

USGS Publications Warehouse

Criss, R.E.; Gregory, R.T.; Taylor, H.P.

1987-01-01

Kinetic and mass conservation equations are used to describe oxygen isotopic exchange between minerals and water in "closed" and open hydrothermal systems. In cases where n coexisting mineral phases having different reaction rates are present, the exchange process is described by a system of n + 1 simultaneous differential equations consisting of n pseudo first-order rate equations and a conservation of mass equation. The simultaneous solutions to these equations generate curved exchange trajectories on ??-?? plots. Families of such trajectories generated under conditions allowing for different fluid mole fractions, different fluid isotopic compositions, or different fluid flow rates are connected by positive-sloped isochronous lines. These isochrons reproduce the effects observed in hydrothermally exchanged mineral pairs including 1) steep positive slopes, 2) common reversals in the measured fractionation factors (??), and 3) measured fractionations that are highly variable over short distances where no thermal gradient can be geologically demonstrated. ?? 1987.

Unveiling the relationships among the viscosity equations of glass liquids and colloidal suspensions for obtaining universal equations with the generic free volume concept.

PubMed

Hao, Tian

2015-09-14

The underlying relationships among viscosity equations of glass liquids and colloidal suspensions are explored with the aid of free volume concept. Viscosity equations of glass liquids available in literature are focused and found to have a same physical basis but different mathematical expressions for the free volume. The glass transitions induced by temperatures in glass liquids and the percolation transition induced by particle volume fractions in colloidal suspensions essentially are a second order phase transition: both those two transitions could induce the free volume changes, which in turn determines how the viscosities are going to change with temperatures and/or particle volume fractions. Unified correlations of the free volume to both temperatures and particle volume fractions are thus proposed. The resulted viscosity equations are reducible to many popular viscosity equations currently widely used in literature; those equations should be able to cover many different types of materials over a wide temperature range. For demonstration purpose, one of the simplified versions of those newly developed equations is compared with popular viscosity equations and the experimental data: it can well fit the experimental data over a wide temperature range. The current work reveals common physical grounds among various viscosity equations, deepening our understanding on viscosity and unifying the free volume theory across many different systems.

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

exponential finite difference technique for solving partial differential equations

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

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less

Double-Plate Penetration Equations

NASA Technical Reports Server (NTRS)

Hayashida, K. B.; Robinson, J. H.

2000-01-01

This report compares seven double-plate penetration predictor equations for accuracy and effectiveness of a shield design. Three of the seven are the Johnson Space Center original, modified, and new Cour-Palais equations. The other four are the Nysmith, Lundeberg-Stern-Bristow, Burch, and Wilkinson equations. These equations, except the Wilkinson equation, were derived from test results, with the velocities ranging up to 8 km/sec. Spreadsheet software calculated the projectile diameters for various velocities for the different equations. The results were plotted on projectile diameter versus velocity graphs for the expected orbital debris impact velocities ranging from 2 to 15 km/sec. The new Cour-Palais double-plate penetration equation was compared to the modified Cour-Palais single-plate penetration equation. Then the predictions from each of the seven double-plate penetration equations were compared to each other for a chosen shield design. Finally, these results from the equations were compared with test results performed at the NASA Marshall Space Flight Center. Because the different equations predict a wide range of projectile diameters at any given velocity, it is very difficult to choose the "right" prediction equation for shield configurations other than those exactly used in the equations' development. Although developed for various materials, the penetration equations alone cannot be relied upon to accurately predict the effectiveness of a shield without using hypervelocity impact tests to verify the design.

Documentation of the Fourth Order Band Model

NASA Technical Reports Server (NTRS)

Kalnay-Rivas, E.; Hoitsma, D.

1979-01-01

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given.

The Boltzmann equation in the difference formulation

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

Szoke, Abraham; Brooks III, Eugene D.

2015-05-06

First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.

Transforming parts of a differential equations system to difference equations as a method for run-time savings in NONMEM.

PubMed

Petersson, K J F; Friberg, L E; Karlsson, M O

2010-10-01

Computer models of biological systems grow more complex as computing power increase. Often these models are defined as differential equations and no analytical solutions exist. Numerical integration is used to approximate the solution; this can be computationally intensive, time consuming and be a large proportion of the total computer runtime. The performance of different integration methods depend on the mathematical properties of the differential equations system at hand. In this paper we investigate the possibility of runtime gains by calculating parts of or the whole differential equations system at given time intervals, outside of the differential equations solver. This approach was tested on nine models defined as differential equations with the goal to reduce runtime while maintaining model fit, based on the objective function value. The software used was NONMEM. In four models the computational runtime was successfully reduced (by 59-96%). The differences in parameter estimates, compared to using only the differential equations solver were less than 12% for all fixed effects parameters. For the variance parameters, estimates were within 10% for the majority of the parameters. Population and individual predictions were similar and the differences in OFV were between 1 and -14 units. When computational runtime seriously affects the usefulness of a model we suggest evaluating this approach for repetitive elements of model building and evaluation such as covariate inclusions or bootstraps.

Smoothing and Equating Methods Applied to Different Types of Test Score Distributions and Evaluated with Respect to Multiple Equating Criteria. Research Report. ETS RR-11-20

ERIC Educational Resources Information Center

Moses, Tim; Liu, Jinghua

2011-01-01

In equating research and practice, equating functions that are smooth are typically assumed to be more accurate than equating functions with irregularities. This assumption presumes that population test score distributions are relatively smooth. In this study, two examples were used to reconsider common beliefs about smoothing and equating. The…

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

Conservation-form equations of unsteady open-channel flow

USGS Publications Warehouse

Lai, C.; Baltzer, R.A.; Schaffranek, R.W.

2002-01-01

The unsteady open-channel flow equations are typically expressed in a variety of forms due to the imposition of differing assumptions, use of varied dependent variables, and inclusion of different source/sink terms. Questions often arise as to whether a particular equation set is expressed in a form consistent with the conservation-law definition. The concept of conservation form is developed to clarify the meaning mathematically. Six sets of unsteady-flow equations typically used in engineering practice are presented and their conservation properties are identified and discussed. Results of the theoretical development and analysis of the equations are substantiated in a set of numerical experiments conducted using alternate equation forms. Findings of these analytical and numerical efforts demonstrate that the choice of dependent variable is the fundamental factor determining the nature of the conservation properties of any particular equation form.

Fokker-Planck Equations of Stochastic Acceleration: A Study of Numerical Methods

NASA Astrophysics Data System (ADS)

Park, Brian T.; Petrosian, Vahe

1996-03-01

Stochastic wave-particle acceleration may be responsible for producing suprathermal particles in many astrophysical situations. The process can be described as a diffusion process through the Fokker-Planck equation. If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables. in an earlier paper (Park & Petrosian 1995, hereafter Paper 1), we studied the analytic properties of the Fokker-Planck equation and found analytic solutions for some simple cases. In this paper, we study the numerical methods which must be used to solve more general forms of the equation. Two classes of numerical methods are finite difference methods and Monte Carlo simulations. We examine six finite difference methods, three fully implicit and three semi-implicit, and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the it5 stochastic differential equation. As discussed in Paper I, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow. We evaluate each method using three sample equations to test its stability, accuracy, efficiency, and robustness for both time-dependent and steady state solutions. We conclude that the most robust finite difference method is the fully implicit Chang-Cooper method, with minor extensions to account for the escape and injection terms. Other methods suffer from stability and accuracy problems when dealing with some Fokker-Planck equations. The stochastic simulation method, although simple to implement, is susceptible to Poisson noise when insufficient test particles are used and is computationally very expensive compared to the finite difference method.

Almost periodic solutions to difference equations

NASA Technical Reports Server (NTRS)

Bayliss, A.

1975-01-01

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

Preconditioned conjugate residual methods for the solution of spectral equations

NASA Technical Reports Server (NTRS)

Wong, Y. S.; Zang, T. A.; Hussaini, M. Y.

1986-01-01

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Bright and singular soliton solutions of the conformable time-fractional Klein-Gordon equations with different nonlinearities

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Ansari, Reza

2018-07-01

Finding the exact solutions of nonlinear fractional differential equations has gained considerable attention, during the past two decades. In this paper, the conformable time-fractional Klein-Gordon equations with quadratic and cubic nonlinearities are studied. Several exact soliton solutions, including the bright (non-topological) and singular soliton solutions are formally extracted by making use of the ansatz method. Results demonstrate that the method can efficiently handle the time-fractional Klein-Gordon equations with different nonlinearities.

A vortex wake capturing method for potential flow calculations

NASA Technical Reports Server (NTRS)

Murman, E. M.; Stremel, P. M.

1982-01-01

A method is presented for modifying finite difference solutions of the potential equation to include the calculation of non-planar vortex wake features. The approach is an adaptation of Baker's 'cloud in cell' algorithm developed for the stream function-vorticity equations. The vortex wake is tracked in a Lagrangian frame of reference as a group of discrete vortex filaments. These are distributed to the Eulerian mesh system on which the velocity is calculated by a finite difference solution of the potential equation. An artificial viscosity introduced by the finite difference equations removes the singular nature of the vortex filaments. Computed examples are given for the two-dimensional time dependent roll-up of vortex wakes generated by wings with different spanwise loading distributions.

Derivation of kinetic equations from non-Wiener stochastic differential equations

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2013-12-01

Kinetic differential-difference equations containing terms with fractional derivatives and describing α -stable Levy processes with 0 < α < 1 have been derived in a unified manner in terms of one-dimensional stochastic differential equations controlled merely by the Poisson processes.

The Examination of the Classification of Students into Performance Categories by Two Different Equating Methods

ERIC Educational Resources Information Center

Keller, Lisa A.; Keller, Robert R.; Parker, Pauline A.

2011-01-01

This study investigates the comparability of two item response theory based equating methods: true score equating (TSE), and estimated true equating (ETE). Additionally, six scaling methods were implemented within each equating method: mean-sigma, mean-mean, two versions of fixed common item parameter, Stocking and Lord, and Haebara. Empirical…

Using the Kernel Method of Test Equating for Estimating the Standard Errors of Population Invariance Measures

ERIC Educational Resources Information Center

Moses, Tim

2008-01-01

Equating functions are supposed to be population invariant, meaning that the choice of subpopulation used to compute the equating function should not matter. The extent to which equating functions are population invariant is typically assessed in terms of practical difference criteria that do not account for equating functions' sampling…

An Exploration of Kernel Equating Using SAT® Data: Equating to a Similar Population and to a Distant Population. Research Report. ETS RR-07-17

ERIC Educational Resources Information Center

Liu, Jinghua; Low, Albert C.

2007-01-01

This study applied kernel equating (KE) in two scenarios: equating to a very similar population and equating to a very different population, referred to as a distant population, using SAT® data. The KE results were compared to the results obtained from analogous classical equating methods in both scenarios. The results indicate that KE results are…

Entire solutions of nonlinear differential-difference equations.

PubMed

Li, Cuiping; Lü, Feng; Xu, Junfeng

2016-01-01

In this paper, we describe the properties of entire solutions of a nonlinear differential-difference equation and a Fermat type equation, and improve several previous theorems greatly. In addition, we also deduce a uniqueness result for an entire function f(z) that shares a set with its shift [Formula: see text], which is a generalization of a result of Liu.

Family differences in equations for predicting biomass and leaf area in Douglas-fir (Pseudotsuga menziesii var. menziesii).

Treesearch

J.B. St. Clair

1993-01-01

Logarithmic regression equations were developed to predict component biomass and leaf area for an 18-yr-old genetic test of Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco var. menziesii) based on stem diameter or cross-sectional sapwood area. Equations did not differ among open-pollinated families in slope, but intercepts...

A Comparative Structural Equation Modeling Investigation of the Relationships among Teaching, Cognitive and Social Presence

ERIC Educational Resources Information Center

Kozan, Kadir

2016-01-01

The present study investigated the relationships among teaching, cognitive, and social presence through several structural equation models to see which model would better fit the data. To this end, the present study employed and compared several different structural equation models because different models could fit the data equally well. Among…

On the equivalence of the dual-wavelength and polarimetric equations for estimation of the raindrop size distribution

NASA Technical Reports Server (NTRS)

Meneghini, Robert; Liao, Liang

2006-01-01

In writing the integral equations for the median mass diameter and particle concentration, or comparable parameters of the raindrop size distribution, it is apparent that when attenuation effects are included, the forms of the equations for polarimetric and dual wavelength radars are identical. In both sets of equations, differences in the backscattering and extinction cross sections appear: in the polarimetric equations, the differences are taken with respect polarization at a fixed frequency while for the dual wavelength equations, the differences are taken with respect to wavelength at a fixed polarization. Because the forms of the equations are the same, the ways in which they can be solved are similar as well. To avoid instabilities in the forward recursion procedure, the equations can be expressed in the form of a final-value. Solving the equations in this way traditionally has required estimates of the path attenuations to the final gate: either the attenuations at horizontal and vertical polarizations at the same frequency or attenuations at two frequencies with the same polarization. This has been done for dual-frequency (air/spaceborne case) and polarimetric radars by the respective use of the surface reference technique and the differential phase shift. An alternative to solving the constrained version of the equations is an iterative procedure recently proposed in which independent estimates of path attenuation are not required. Although the procedure has limitations, it appears to be quite useful. Simulations of the retrievals help clarify the relationship between the constrained and unconstrained approaches and their application to the polarimetric and dual-wavelength equations.

Predictive Variables of Half-Marathon Performance for Male Runners

PubMed Central

Gómez-Molina, Josué; Ogueta-Alday, Ana; Camara, Jesus; Stickley, Christoper; Rodríguez-Marroyo, José A.; García-López, Juan

2017-01-01

The aims of this study were to establish and validate various predictive equations of half-marathon performance. Seventy-eight half-marathon male runners participated in two different phases. Phase 1 (n = 48) was used to establish the equations for estimating half-marathon performance, and Phase 2 (n = 30) to validate these equations. Apart from half-marathon performance, training-related and anthropometric variables were recorded, and an incremental test on a treadmill was performed, in which physiological (VO2max, speed at the anaerobic threshold, peak speed) and biomechanical variables (contact and flight times, step length and step rate) were registered. In Phase 1, half-marathon performance could be predicted to 90.3% by variables related to training and anthropometry (Equation 1), 94.9% by physiological variables (Equation 2), 93.7% by biomechanical parameters (Equation 3) and 96.2% by a general equation (Equation 4). Using these equations, in Phase 2 the predicted time was significantly correlated with performance (r = 0.78, 0.92, 0.90 and 0.95, respectively). The proposed equations and their validation showed a high prediction of half-marathon performance in long distance male runners, considered from different approaches. Furthermore, they improved the prediction performance of previous studies, which makes them a highly practical application in the field of training and performance. Key points The present study obtained four equations involving anthropometric, training, physiological and biomechanical variables to estimate half-marathon performance. These equations were validated in a different population, demonstrating narrows ranges of prediction than previous studies and also their consistency. As a novelty, some biomechanical variables (i.e. step length and step rate at RCT, and maximal step length) have been related to half-marathon performance. PMID:28630571

A Longitudinal Study on Human Outdoor Decomposition in Central Texas.

PubMed

Suckling, Joanna K; Spradley, M Katherine; Godde, Kanya

2016-01-01

The development of a methodology that estimates the postmortem interval (PMI) from stages of decomposition is a goal for which forensic practitioners strive. A proposed equation (Megyesi et al. 2005) that utilizes total body score (TBS) and accumulated degree days (ADD) was tested using longitudinal data collected from human remains donated to the Forensic Anthropology Research Facility (FARF) at Texas State University-San Marcos. Exact binomial tests examined the rate of the equation to successfully predict ADD. Statistically significant differences were found between ADD estimated by the equation and the observed value for decomposition stage. Differences remained significant after carnivore scavenged donations were removed from analysis. Low success rates for the equation to predict ADD from TBS and the wide standard errors demonstrate the need to re-evaluate the use of this equation and methodology for PMI estimation in different environments; rather, multivariate methods and equations should be derived that are environmentally specific. © 2015 American Academy of Forensic Sciences.

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students' mathematical performance

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-12-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students' mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students' simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students' formulation and combination of equations. Several reasons may explain this difference, including the students' different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

Evaluation of Piecewise Polynomial Equations for Two Types of Thermocouples

PubMed Central

Chen, Andrew; Chen, Chiachung

2013-01-01

Thermocouples are the most frequently used sensors for temperature measurement because of their wide applicability, long-term stability and high reliability. However, one of the major utilization problems is the linearization of the transfer relation between temperature and output voltage of thermocouples. The linear calibration equation and its modules could be improved by using regression analysis to help solve this problem. In this study, two types of thermocouple and five temperature ranges were selected to evaluate the fitting agreement of different-order polynomial equations. Two quantitative criteria, the average of the absolute error values |e|ave and the standard deviation of calibration equation estd, were used to evaluate the accuracy and precision of these calibrations equations. The optimal order of polynomial equations differed with the temperature range. The accuracy and precision of the calibration equation could be improved significantly with an adequate higher degree polynomial equation. The technique could be applied with hardware modules to serve as an intelligent sensor for temperature measurement. PMID:24351627

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

A fundamental equation of state for 1,1-difluoroethane (HFC-152a)

NASA Astrophysics Data System (ADS)

Tillner-Roth, R.

1995-01-01

A fundamental equation ofstale for HFC-152a ( 1,1-dilluorocthane) is presented covering temperatures between the triple-point temperature ( 154.56 K) and 435 K for pressures up to 311 M Pa. The equation is based on reliable ( p, g, T) data in the range mentioned above. These are generally represented within ±0.1 % of density. Furthermore. experimental values of the vapor pressure, the saturated liquid density, and some isobaric heat capacities in the liquid were included during the correlation process. The new equation of state is compared with experimental data and also with the equation of state developed by Tamatsu et al. Differences between the two equations of state generally result from using different experimental input data. It is shown that the new equation of state allows an accurate calculation of various thermodynamic properties for most technical applications.

Equating accelerometer estimates among youth: the Rosetta Stone 2

PubMed Central

Brazendale, Keith; Beets, Michael W.; Bornstein, Daniel B.; Moore, Justin B.; Pate, Russell R.; Weaver, Robert G.; Falck, Ryan S.; Chandler, Jessica L.; Andersen, Lars B.; Anderssen, Sigmund A.; Cardon, Greet; Cooper, Ashley; Davey, Rachel; Froberg, Karsten; Hallal, Pedro C.; Janz, Kathleen F.; Kordas, Katarzyna; Kriemler, Susi; Puder, Jardena J.; Reilly, John J.; Salmon, Jo; Sardinha, Luis B.; Timperio, Anna; van Sluijs, Esther MF

2017-01-01

Objectives Different accelerometer cutpoints used by different researchers often yields vastly different estimates of moderate-to-vigorous intensity physical activity (MVPA). This is recognized as cutpoint non-equivalence (CNE), which reduces the ability to accurately compare youth MVPA across studies. The objective of this research is to develop a cutpoint conversion system that standardizes minutes of MVPA for six different sets of published cutpoints. Design Secondary data analysis Methods Data from the International Children’s Accelerometer Database (ICAD; Spring 2014) consisting of 43,112 Actigraph accelerometer data files from 21 worldwide studies (children 3-18 years, 61.5% female) were used to develop prediction equations for six sets of published cutpoints. Linear and non-linear modeling, using a leave one out cross-validation technique, was employed to develop equations to convert MVPA from one set of cutpoints into another. Bland Altman plots illustrate the agreement between actual MVPA and predicted MVPA values. Results Across the total sample, mean MVPA ranged from 29.7 MVPA min.d-1 (Puyau) to 126.1 MVPA min.d-1 (Freedson 3 METs). Across conversion equations, median absolute percent error was 12.6% (range: 1.3 to 30.1) and the proportion of variance explained ranged from 66.7% to 99.8%. Mean difference for the best performing prediction equation (VC from EV) was -0.110 min.d-1 (limits of agreement (LOA), -2.623 to 2.402). The mean difference for the worst performing prediction equation (FR3 from PY) was 34.76 min.d-1 (LOA, -60.392 to 129.910). Conclusions For six different sets of published cutpoints, the use of this equating system can assist individuals attempting to synthesize the growing body of literature on Actigraph, accelerometry-derived MVPA. PMID:25747468

Preconditioning Strategies for Solving Elliptic Difference Equations on a Multiprocessor.

DTIC Science & Technology

1982-01-01

162, 1977. (MiGr8O] Mitchell, A., Griffiths, D., The Finite Difference Method in Partial Differential Equations , John Wiley & Sons, 1980. [Munk80...ADAL1b T35 AIR FO"CE INST OF TECH WRITG-PATTERSON AFS OH F/6 12/17PR CO ITIONIN STRATEGIES FOR SOLVING ELLIPTIC DIFFERENCE EWA-ETClU) 9UN S C K...TI TLE (ard S.tbr,,I) 5 TYPE OF REP’ORT & F IFIOD C_JVEFO Preconditioning Strategies for Solving Elliptic THESIS/VYYRY#YY0N Difference Equations on

Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views

NASA Astrophysics Data System (ADS)

Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.

2018-01-01

Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.

Numerical solution of the stochastic parabolic equation with the dependent operator coefficient

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

Ashyralyev, Allaberen; Department of Mathematics, ITTU, Ashgabat; Okur, Ulker

2015-09-18

In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

Experimental Investigation of Hydrodynamic Self-Acting Gas Bearings at High Knudsen Numbers.

DTIC Science & Technology

1980-07-01

Reynolds equation. Two finite - difference algorithms were used to solve the equation. Numerical results - the predicted load and pitch angle - from the two...that should be used. The majority of the numerical solution are still based on the finite difference approximation of the governing equation. But in... finite difference method. Reddi and Chu [26) also noted that it is very difficult to compare the two techniques on the same level since the solution

The analysis of solutions behaviour of Van der Pol Duffing equation describing local brain hemodynamics

NASA Astrophysics Data System (ADS)

Cherevko, A. A.; Bord, E. E.; Khe, A. K.; Panarin, V. A.; Orlov, K. J.

2017-10-01

This article proposes the generalized model of Van der Pol — Duffing equation for describing the relaxation oscillations in local brain hemodynamics. This equation connects the velocity and pressure of blood flow in cerebral vessels. The equation is individual for each patient, since the coefficients are unique. Each set of coefficients is built based on clinical data obtained during neurosurgical operation in Siberian Federal Biomedical Research Center named after Academician E. N. Meshalkin. The equation has solutions of different structure defined by the coefficients and right side. We investigate the equations for different patients considering peculiarities of their vessel systems. The properties of approximate analytical solutions are studied. Amplitude-frequency and phase-frequency characteristics are built for the small-dimensional solution approximations.

The use of spectral methods in bidomain studies.

PubMed

Trayanova, N; Pilkington, T

1992-01-01

A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

ERIC Educational Resources Information Center

Ozdemir, Burhanettin

2017-01-01

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

Fault Tolerant Optimal Control.

DTIC Science & Technology

1982-08-01

subsystem is modelled by deterministic or stochastic finite-dimensional vector differential or difference equations. The parameters of these equations...is no partial differential equation that must be solved. Thus we can sidestep the inability to solve the Bellman equation for control problems with x...transition models and cost functionals can be reduced to the search for solutions of nonlinear partial differential equations using ’verification

Validity of Bioelectrical Impedance Analysis to Estimation Fat-Free Mass in the Army Cadets.

PubMed

Langer, Raquel D; Borges, Juliano H; Pascoa, Mauro A; Cirolini, Vagner X; Guerra-Júnior, Gil; Gonçalves, Ezequiel M

2016-03-11

Bioelectrical Impedance Analysis (BIA) is a fast, practical, non-invasive, and frequently used method for fat-free mass (FFM) estimation. The aims of this study were to validate predictive equations of BIA to FFM estimation in Army cadets and to develop and validate a specific BIA equation for this population. A total of 396 males, Brazilian Army cadets, aged 17-24 years were included. The study used eight published predictive BIA equations, a specific equation in FFM estimation, and dual-energy X-ray absorptiometry (DXA) as a reference method. Student's t-test (for paired sample), linear regression analysis, and Bland-Altman method were used to test the validity of the BIA equations. Predictive BIA equations showed significant differences in FFM compared to DXA (p < 0.05) and large limits of agreement by Bland-Altman. Predictive BIA equations explained 68% to 88% of FFM variance. Specific BIA equations showed no significant differences in FFM, compared to DXA values. Published BIA predictive equations showed poor accuracy in this sample. The specific BIA equations, developed in this study, demonstrated validity for this sample, although should be used with caution in samples with a large range of FFM.

Time dependent wave envelope finite difference analysis of sound propagation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1984-01-01

A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.

Development of low-frequency kernel-function aerodynamics for comparison with time-dependent finite-difference methods

NASA Technical Reports Server (NTRS)

Bland, S. R.

1982-01-01

Finite difference methods for unsteady transonic flow frequency use simplified equations in which certain of the time dependent terms are omitted from the governing equations. Kernel functions are derived for two dimensional subsonic flow, and provide accurate solutions of the linearized potential equation with the same time dependent terms omitted. These solutions make possible a direct evaluation of the finite difference codes for the linear problem. Calculations with two of these low frequency kernel functions verify the accuracy of the LTRAN2 and HYTRAN2 finite difference codes. Comparisons of the low frequency kernel function results with the Possio kernel function solution of the complete linear equations indicate the adequacy of the HYTRAN approximation for frequencies in the range of interest for flutter calculations.

A Case of Inconsistent Equatings: How the Man with Four Watches Decides What Time It Is

ERIC Educational Resources Information Center

Livingston, Samuel A.; Antal, Judit

2010-01-01

A simultaneous equating of four new test forms to each other and to one previous form was accomplished through a complex design incorporating seven separate equating links. Each new form was linked to the reference form by four different paths, and each path produced a different score conversion. The procedure used to resolve these inconsistencies…

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials

NASA Astrophysics Data System (ADS)

Britt, S.; Tsynkov, S.; Turkel, E.

2018-02-01

We solve the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time. This is accomplished using an implicit finite difference (FD) scheme for the wave equation and solving an elliptic (modified Helmholtz) equation at each time step with fourth order spatial accuracy by the method of difference potentials (MDP). High-order MDP utilizes compact FD schemes on regular structured grids to efficiently solve problems on nonconforming domains while maintaining the design convergence rate of the underlying FD scheme. Asymptotically, the computational complexity of high-order MDP scales the same as that for FD.

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Differentiation of subspecies and sexes of Beringian Dunlins using morphometric measures

USGS Publications Warehouse

Gates, H. River; Yezerinac, Stephen; Powell, Abby N.; Tomkovich, Pavel S.; Valchuk, Olga P.; Lanctot, Richard B.

2013-01-01

Five subspecies of Dunlins (Calidris alpina) that breed in Beringia are potentially sympatric during the non-breeding season. Studying their ecology during this period requires techniques to distinguish individuals by subspecies. Our objectives were to determine (1) if five morphometric measures (body mass, culmen, head, tarsus, and wing chord) differed between sexes and among subspecies (C. a. actites, arcticola, kistchinski, pacifica, and sakhalina), and (2) if these differences were sufficient to allow for correct classification of individuals using equations derived from discriminant function analyses. We conducted analyses using morphometric data from 10 Dunlin populations breeding in northern Russia and Alaska, USA. Univariate tests revealed significant differences between sexes in most morphometric traits of all subspecies, and discriminant function equations predicted the sex of individuals with an accuracy of 83–100% for each subspecies. We provide equations to determine sex and subspecies of individuals in mixed subspecies groups, including the (1) Western Alaska group of arcticola and pacifica (known to stage together in western Alaska) and (2) East Asia group of arcticola, actites, kistchinski, and sakhalina (known to winter together in East Asia). Equations that predict the sex of individuals in mixed groups had classification accuracies between 75% and 87%, yielding reliable classification equations. We also provide equations that predict the subspecies of individuals with an accuracy of 22–96% for different mixed subspecies groups. When the sex of individuals can be predetermined, the accuracy of these equations is increased substantially. Investigators are cautioned to consider limitations due to age and feather wear when using these equations during the non-breeding season. These equations will allow determination of sexual and subspecies segregation in non-breeding areas, allowing implementation of taxonomic-specific conservation actions.

Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.

PubMed

Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

2016-11-01

In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

Validating Reference Equations for Impulse Oscillometry in Healthy Mexican Children.

PubMed

Gochicoa-Rangel, Laura; Del Río-Hidalgo, Rodrigo; Hernández-Ruiz, Juana; Rodríguez-Moreno, Luis; Martínez-Briseño, David; Mora-Romero, Uri; Cid-Juárez, Silvia; García-Sancho, Cecilia; Torre-Bouscoulet, Luis

2017-09-01

The impulse oscillometry system (IOS) measures the impedance (Z) of the respiratory system, but proper interpretation of its results requires adequate reference values. The objectives of this work were: (1) to validate the reference equations for the IOS published previously by our group and (2) to compare the adjustment of new available reference equations for the IOS from different countries in a sample of healthy children. Subjects were healthy 4-15-y-old children from the metropolitan area of Mexico City, who performed an IOS test. The functional IOS parameters obtained were compared with the predicted values from 12 reference equations determined in studies of different ethnic groups. The validation methods applied were: analysis of the differences between measured and predicted values for each reference equation; correlation and concordance coefficients; adjustment by Z-score values; percentage of predicted value; and the percentage of patients below the lower limit of normality or above the upper limit of normality. Of the 224 participants, 117 (52.3%) were girls, and the mean age was 8.6 ± 2.3 y. The equations that showed the best adjustment for the different parameters were those from the studies by Nowowiejska et al (2008) and Gochicoa et al (2015). The equations proposed by Frei et al (2005), Hellinckx et al (1998), Kalhoff et al (2011), Klug and Bisgaard (1998), de Assumpção et al (2016), and Dencker et al (2006) overestimated the airway resistance of the children in our sample, whereas the equation of Amra et al (2008) underestimated it. In the analysis of the lower and upper limits of normality, Gochicoa et al equation was the closest, since 5% of subjects were below or above percentiles 5 and 95, respectively. The study found that, in general, all of the equations showed greater error at the extremes of the age distribution. Because of the robust adjustment of the present study reference equations for the IOS, it can be recommended for both clinical and research purposes in our population. The differential adjustment of other equations underlines the need to obtain local reference values. Copyright © 2017 by Daedalus Enterprises.

Finite Difference Modeling of Wave Progpagation in Acoustic TiltedTI Media

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

Zhang, Linbin; Rector III, James W.; Hoversten, G. Michael

2005-03-21

Based on an acoustic assumption (shear wave velocity is zero) and a dispersion relation, we derive an acoustic wave equation for P-waves in tilted transversely isotropic (TTI) media (transversely isotropic media with a tilted symmetry axis). This equation has fewer parameters than an elastic wave equation in TTI media and yields an accurate description of P-wave traveltimes and spreading-related attenuation. Our TTI acoustic wave equation is a fourth-order equation in time and space. We demonstrate that the acoustic approximation allows the presence of shear waves in the solution. The substantial differences in traveltime and amplitude between data created using VTImore » and TTI assumptions is illustrated in examples.« less

New explicit equations for the accurate calculation of the growth and evaporation of hydrometeors by the diffusion of water vapor

NASA Technical Reports Server (NTRS)

Srivastava, R. C.; Coen, J. L.

1992-01-01

The traditional explicit growth equation has been widely used to calculate the growth and evaporation of hydrometeors by the diffusion of water vapor. This paper reexamines the assumptions underlying the traditional equation and shows that large errors (10-30 percent in some cases) result if it is used carelessly. More accurate explicit equations are derived by approximating the saturation vapor-density difference as a quadratic rather than a linear function of the temperature difference between the particle and ambient air. These new equations, which reduce the error to less than a few percent, merit inclusion in a broad range of atmospheric models.

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

NASA Technical Reports Server (NTRS)

Steger, J. L.; Caradonna, F. X.

1980-01-01

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

Formulation and application of optimal homotopty asymptotic method to coupled differential-difference equations.

PubMed

Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

2015-01-01

In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit.

Formulation and Application of Optimal Homotopty Asymptotic Method to Coupled Differential - Difference Equations

PubMed Central

Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

2015-01-01

In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential- difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit. PMID:25874457

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

PubMed

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.

Assessing Equating Results on Different Equating Criteria

ERIC Educational Resources Information Center

Tong, Ye; Kolen, Michael

2005-01-01

The performance of three equating methods--the presmoothed equipercentile method, the item response theory (IRT) true score method, and the IRT observed score method--were examined based on three equating criteria: the same distributions property, the first-order equity property, and the second-order equity property. The magnitude of the…

Solitary traveling wave solutions of pressure equation of bubbly liquids with examination for viscosity and heat transfer

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-03-01

In this research, we investigate one of the most popular model in nature and also industrial which is the pressure equation of bubbly liquids with examination for viscosity and heat transfer which has many application in nature and engineering. Understanding the physical meaning of exact and solitary traveling wave solutions for this equation gives the researchers in this field a great clear vision of the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer and also dynamics of contrast agents in the blood flow at ultrasonic researches. To achieve our goal, we apply three different methods which are extended tanh-function method, extended simple equation method and a new auxiliary equation method on this equation. We obtained exact and solitary traveling wave solutions and we also discuss the similarity and difference between these three method and make a comparison between results that we obtained with another results that obtained with the different researchers using different methods. All of these results and discussion explained the fact that our new auxiliary equation method is considered to be the most general, powerful and the most result-oriented. These kinds of solutions and discussion allow for the understanding of the phenomenon and its intrinsic properties as well as the ease of way of application and its applicability to other phenomena.

Rapid and Cost-Effective Quantification of Glucosinolates and Total Phenolic Content in Rocket Leaves by Visible/Near-Infrared Spectroscopy.

PubMed

Toledo-Martín, Eva María; Font, Rafael; Obregón-Cano, Sara; De Haro-Bailón, Antonio; Villatoro-Pulido, Myriam; Del Río-Celestino, Mercedes

2017-05-20

The potential of visible-near infrared spectroscopy to predict glucosinolates and total phenolic content in rocket ( Eruca vesicaria ) leaves has been evaluated. Accessions of the E. vesicaria species were scanned by NIRS as ground leaf, and their reference values regressed against different spectral transformations by modified partial least squares (MPLS) regression. The coefficients of determination in the external validation (R²VAL) for the different quality components analyzed in rocket ranged from 0.59 to 0.84, which characterize those equations as having from good to excellent quantitative information. These results show that the total glucosinolates, glucosativin and glucoerucin equations obtained, can be used to identify those samples with low and high contents. The glucoraphanin equation obtained can be used for rough predictions of samples and in case of total phenolic content, the equation showed good correlation. The standard deviation (SD) to standard error of prediction ratio (RPD) and SD to range (RER) were variable for the different quality compounds and showed values that were characteristic of equations suitable for screening purposes or to perform accurate analyses. From the study of the MPLS loadings of the first three terms of the different equations, it can be concluded that some major cell components such as protein and cellulose, highly participated in modelling the equations for glucosinolates.

Analysis of three different equations for predicting quadriceps femoris muscle strength in patients with COPD *

PubMed Central

Nellessen, Aline Gonçalves; Donária, Leila; Hernandes, Nidia Aparecida; Pitta, Fabio

2015-01-01

Abstract Objective: To compare equations for predicting peak quadriceps femoris (QF) muscle force; to determine the agreement among the equations in identifying QF muscle weakness in COPD patients; and to assess the differences in characteristics among the groups of patients classified as having or not having QF muscle weakness by each equation. Methods: Fifty-six COPD patients underwent assessment of peak QF muscle force by dynamometry (maximal voluntary isometric contraction of knee extension). Predicted values were calculated with three equations: an age-height-weight-gender equation (Eq-AHWG); an age-weight-gender equation (Eq-AWG); and an age-fat-free mass-gender equation (Eq-AFFMG). Results: Comparison of the percentage of predicted values obtained with the three equations showed that the Eq-AHWG gave higher values than did the Eq-AWG and Eq-AFFMG, with no difference between the last two. The Eq-AHWG showed moderate agreement with the Eq-AWG and Eq-AFFMG, whereas the last two also showed moderate, albeit lower, agreement with each other. In the sample as a whole, QF muscle weakness (< 80% of predicted) was identified by the Eq-AHWG, Eq-AWG, and Eq-AFFMG in 59%, 68%, and 70% of the patients, respectively (p > 0.05). Age, fat-free mass, and body mass index are characteristics that differentiate between patients with and without QF muscle weakness. Conclusions: The three equations were statistically equivalent in classifying COPD patients as having or not having QF muscle weakness. However, the Eq-AHWG gave higher peak force values than did the Eq-AWG and the Eq-AFFMG, as well as showing greater agreement with the other equations. PMID:26398750

Composite solitons and two-pulse generation in passively mode-locked lasers modeled by the complex quintic Swift-Hohenberg equation

NASA Astrophysics Data System (ADS)

Soto-Crespo, J. M.; Akhmediev, Nail

2002-12-01

The complex quintic Swift-Hohenberg equation (CSHE) is a model for describing pulse generation in mode-locked lasers with fast saturable absorbers and a complicated spectral response. Using numerical simulations, we study the single- and two-soliton solutions of the (1+1)-dimensional complex quintic Swift-Hohenberg equations. We have found that several types of stationary and moving composite solitons of this equation are generally stable and have a wider range of existence than for those of the complex quintic Ginzburg-Landau equation. We have also found that the CSHE has a wider variety of localized solutions. In particular, there are three types of stable soliton pairs with π and π/2 phase difference and three different fixed separations between the pulses. Different types of soliton pairs can be generated by changing the parameter corresponding to the nonlinear gain (ɛ).

Loop equations and bootstrap methods in the lattice

DOE PAGES

Anderson, Peter D.; Kruczenski, Martin

2017-06-17

Pure gauge theories can be formulated in terms of Wilson Loops by means of the loop equation. In the large-N limit this equation closes in the expectation value of single loops. In particular, using the lattice as a regulator, it becomes a well defined equation for a discrete set of loops. In this paper we study different numerical approaches to solving this equation.

Gender disparity in BMD conversion: a comparison between Lunar and Hologic densitometers.

PubMed

Ganda, Kirtan; Nguyen, Tuan V; Pocock, Nicholas

2014-01-01

Female-derived inter-conversion and standardised BMD equations at the lumbar spine and hip have not been validated in men. This study of 110 male subjects scanned on Hologic and Lunar densitometers demonstrates that published equations may not applicable to men at the lumbar spine. Male inter-conversion equations have also been derived. Currently, available equations for inter-manufacturer conversion of bone mineral density (BMD) and calculation of standardised BMD (sBMD) are used in both males and females, despite being derived and validated only in women. Our aim was to test the validity of the published equations in men. One hundred ten men underwent lumbar spine (L2-4), femoral neck (FN) and total hip (TH) dual X-ray absorptiometry (DXA) using Hologic and Lunar scanners. Hologic BMD was converted to Lunar using published equations derived from women for L2-4 and FN. Actual Lunar BMD (A-Lunar) was compared to converted (Lunar equivalent) Hologic BMD values (H-Lunar). sBMD was calculated separately using Hologic (sBMD-H) and Lunar BMD (sBMD-L) at L2-4, FN and TH. Conversion equations in men for Hologic to Lunar BMD were derived using Deming regression analysis. There was a strong linear correlation between Lunar and Hologic BMD at all skeletal sites. A-Lunar BMD was however significantly higher than derived H-Lunar BMD (p < 0.001) at L2-L4 (mean difference, 0.07 g/cm(2)). There was no significant difference at the FN (mean difference, 0.01 g/cm(2)). sBMD-L at the spine was significantly higher than sBMD-H (mean difference, 0.06 g/cm(2), p < 0.001), whilst there was little difference at the FN and TH (mean difference, 0.01 g/cm(2)). Published conversion equations for Lunar BMD to Hologic BMD, and formulae for lumbar spine sBMD, derived in women may not be applicable to men.

On the nature of liquid junction and membrane potentials.

PubMed

Perram, John W; Stiles, Peter J

2006-09-28

Whenever a spatially inhomogeneous electrolyte, composed of ions with different mobilities, is allowed to diffuse, charge separation and an electric potential difference is created. Such potential differences across very thin membranes (e.g. biomembranes) are often interpreted using the steady state Goldman equation, which is usually derived by assuming a spatially constant electric field. Through the fundamental Poisson equation of electrostatics, this implies the absence of free charge density that must provide the source of any such field. A similarly paradoxical situation is encountered for thick membranes (e.g. in ion-selective electrodes) for which the diffusion potential is normally interpreted using the Henderson equation. Standard derivations of the Henderson equation appeal to local electroneutrality, which is also incompatible with sources of electric fields, as these require separated charges. We analyse self-consistent solutions of the Nernst-Planck-Poisson equations for a 1 : 1-univalent electrolyte to show that the Goldman and Henderson steady-state membrane potentials are artefacts of extraneous charges created in the reservoirs of electrolyte solution on either side of the membrane, due to the unphysical nature of the usual (Dirichlet) boundary conditions assumed to apply at the membrane-electrolyte interfaces. We also show, with the aid of numerical simulations, that a transient electric potential difference develops in any confined, but initially non-uniform, electrolyte solution. This potential difference ultimately decays to zero in the real steady state of the electrolyte, which corresponds to thermodynamic equilibrium. We explain the surprising fact that such transient potential differences are well described by the Henderson equation by using a computer algebra system to extend previous steady-state singular perturbation theories to the time-dependent case. Our work therefore accounts for the success of the Henderson equation in analysing experimental liquid-junction potentials.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. II - Equivalent linearization

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

The classical method of equivalent linearization is extended to a particular class of nonlinear difference equations. It is shown that the method can be used to obtain an approximation of the periodic solutions of these equations. In particular, the parameters of the limit cycle and the limit points can be determined. Three examples illustrating the method are presented.

Single- versus Double-Scoring of Trend Responses in Trend Score Equating with Constructed-Response Tests. Research Report. ETS RR-10-12

ERIC Educational Resources Information Center

Tan, Xuan; Ricker, Kathryn L.; Puhan, Gautam

2010-01-01

This study examines the differences in equating outcomes between two trend score equating designs resulting from two different scoring strategies for trend scoring when operational constructed-response (CR) items are double-scored--the single group (SG) design, where each trend CR item is double-scored, and the nonequivalent groups with anchor…

Are Predictive Equations for Estimating Resting Energy Expenditure Accurate in Asian Indian Male Weightlifters?

PubMed

Joseph, Mini; Gupta, Riddhi Das; Prema, L; Inbakumari, Mercy; Thomas, Nihal

2017-01-01

The accuracy of existing predictive equations to determine the resting energy expenditure (REE) of professional weightlifters remains scarcely studied. Our study aimed at assessing the REE of male Asian Indian weightlifters with indirect calorimetry and to compare the measured REE (mREE) with published equations. A new equation using potential anthropometric variables to predict REE was also evaluated. REE was measured on 30 male professional weightlifters aged between 17 and 28 years using indirect calorimetry and compared with the eight formulas predicted by Harris-Benedicts, Mifflin-St. Jeor, FAO/WHO/UNU, ICMR, Cunninghams, Owen, Katch-McArdle, and Nelson. Pearson correlation coefficient, intraclass correlation coefficient, and multiple linear regression analysis were carried out to study the agreement between the different methods, association with anthropometric variables, and to formulate a new prediction equation for this population. Pearson correlation coefficients between mREE and the anthropometric variables showed positive significance with suprailiac skinfold thickness, lean body mass (LBM), waist circumference, hip circumference, bone mineral mass, and body mass. All eight predictive equations underestimated the REE of the weightlifters when compared with the mREE. The highest mean difference was 636 kcal/day (Owen, 1986) and the lowest difference was 375 kcal/day (Cunninghams, 1980). Multiple linear regression done stepwise showed that LBM was the only significant determinant of REE in this group of sportspersons. A new equation using LBM as the independent variable for calculating REE was computed. REE for weightlifters = -164.065 + 0.039 (LBM) (confidence interval -1122.984, 794.854]. This new equation reduced the mean difference with mREE by 2.36 + 369.15 kcal/day (standard error = 67.40). The significant finding of this study was that all the prediction equations underestimated the REE. The LBM was the sole determinant of REE in this population. In the absence of indirect calorimetry, the REE equation developed by us using LBM is a better predictor for calculating REE of professional male weightlifters of this region.

Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Webb, Jay C.

1994-01-01

In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The effectiveness of the correction factor in providing improvements to the computed solution is demonstrated in this paper.

Efficiency trade-offs of steady-state methods using FEM and FDM. [iterative solutions for nonlinear flow equations

NASA Technical Reports Server (NTRS)

Gartling, D. K.; Roache, P. J.

1978-01-01

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

Methods of Attenuation Correction for Dual-Wavelength and Dual-Polarization Weather Radar Data

NASA Technical Reports Server (NTRS)

Meneghini, R.; Liao, L.

2007-01-01

In writing the integral equations for the median mass diameter and number concentration, or comparable parameters of the raindrop size distribution, it is apparent that the forms of the equations for dual-polarization and dual-wavelength radar data are identical when attenuation effects are included. The differential backscattering and extinction coefficients appear in both sets of equations: for the dual-polarization equations, the differences are taken with respect to polarization at a fixed frequency while for the dual-wavelength equations, the differences are taken with respect to frequency at a fixed polarization. An alternative to the integral equation formulation is that based on the k-Z (attenuation coefficient-radar reflectivity factor) parameterization. This-technique was originally developed for attenuating single-wavelength radars, a variation of which has been applied to the TRMM Precipitation Radar data (PR). Extensions of this method have also been applied to dual-polarization data. In fact, it is not difficult to show that nearly identical equations are applicable as well to dualwavelength radar data. In this case, the equations for median mass diameter and number concentration take the form of coupled, but non-integral equations. Differences between this and the integral equation formulation are a consequence of the different ways in which attenuation correction is performed under the two formulations. For both techniques, the equations can be solved either forward from the radar outward or backward from the final range gate toward the radar. Although the forward-going solutions tend to be unstable as the attenuation out to the range of interest becomes large in some sense, an independent estimate of path attenuation is not required. This is analogous to the case of an attenuating single-wavelength radar where the forward solution to the Hitschfeld-Bordan equation becomes unstable as the attenuation increases. To circumvent this problem, the equations can be expressed in the form of a final-value problem so that the recursion begins at the far range gate and proceeds inward towards the radar. Solving the problem in this way traditionally requires estimates of path attenuation to the final gate: in the case of orthogonal linear polarizations, the attenuations at horizontal and vertical polarizations (same frequency) are required while in the dual-wavelength case, attenuations at the two frequencies (same polarization) are required.

Study of stability of the difference scheme for the model problem of the gaslift process

NASA Astrophysics Data System (ADS)

Temirbekov, Nurlan; Turarov, Amankeldy

2017-09-01

The paper studies a model of the gaslift process where the motion in a gas-lift well is described by partial differential equations. The system describing the studied process consists of equations of motion, continuity, equations of thermodynamic state, and hydraulic resistance. A two-layer finite-difference Lax-Vendroff scheme is constructed for the numerical solution of the problem. The stability of the difference scheme for the model problem is investigated using the method of a priori estimates, the order of approximation is investigated, the algorithm for numerical implementation of the gaslift process model is given, and the graphs are presented. The development and investigation of difference schemes for the numerical solution of systems of equations of gas dynamics makes it possible to obtain simultaneously exact and monotonic solutions.

A critical review and database of biomass and volume allometric equation for trees and shrubs of Bangladesh

NASA Astrophysics Data System (ADS)

Mahmood, H.; Siddique, M. R. H.; Akhter, M.

2016-08-01

Estimations of biomass, volume and carbon stock are important in the decision making process for the sustainable management of a forest. These estimations can be conducted by using available allometric equations of biomass and volume. Present study aims to: i. develop a compilation with verified allometric equations of biomass, volume, and carbon for trees and shrubs of Bangladesh, ii. find out the gaps and scope for further development of allometric equations for different trees and shrubs of Bangladesh. Key stakeholders (government departments, research organizations, academic institutions, and potential individual researchers) were identified considering their involvement in use and development of allometric equations. A list of documents containing allometric equations was prepared from secondary sources. The documents were collected, examined, and sorted to avoid repetition, yielding 50 documents. These equations were tested through a quality control scheme involving operational verification, conceptual verification, applicability, and statistical credibility. A total of 517 allometric equations for 80 species of trees, shrubs, palm, and bamboo were recorded. In addition, 222 allometric equations for 39 species were validated through the quality control scheme. Among the verified equations, 20%, 12% and 62% of equations were for green-biomass, oven-dried biomass, and volume respectively and 4 tree species contributed 37% of the total verified equations. Five gaps have been pinpointed for the existing allometric equations of Bangladesh: a. little work on allometric equation of common tree and shrub species, b. most of the works were concentrated on certain species, c. very little proportion of allometric equations for biomass estimation, d. no allometric equation for belowground biomass and carbon estimation, and d. lower proportion of valid allometric equations. It is recommended that site and species specific allometric equations should be developed and consistency in field sampling, sample processing, data recording and selection of allometric equations should be maintained to ensure accuracy in estimation of biomass, volume, and carbon stock in different forest types of Bangladesh.

A moving mesh finite difference method for equilibrium radiation diffusion equations

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

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Local and global Hopf bifurcation analysis in a neutral-type neuron system with two delays

NASA Astrophysics Data System (ADS)

Lv, Qiuyu; Liao, Xiaofeng

2018-03-01

In recent years, neutral-type differential-difference equations have been applied extensively in the field of engineering, and their dynamical behaviors are more complex than that of the delay differential-difference equations. In this paper, the equations used to describe a neutral-type neural network system of differential difference equation with two delays are studied (i.e. neutral-type differential equations). Firstly, by selecting τ1, τ2 respectively as a parameter, we provide an analysis about the local stability of the zero equilibrium point of the equations, and sufficient conditions of asymptotic stability for the system are derived. Secondly, by using the theory of normal form and applying the theorem of center manifold introduced by Hassard et al., the Hopf bifurcation is found and some formulas for deciding the stability of periodic solutions and the direction of Hopf bifurcation are given. Moreover, by applying the theorem of global Hopf bifurcation, the existence of global periodic solution of the system is studied. Finally, an example is given, and some computer numerical simulations are taken to demonstrate and certify the correctness of the presented results.

Difference equation model for isothermal gas chromatography expresses retention behavior of homologues of n-alkanes excluding the influence of holdup time

PubMed Central

Wu, Liejun; Chen, Yongli; Caccamise, Sarah A.L.; Li, Qing X.

2012-01-01

A difference equation (DE) model is developed using the methylene retention increment (Δtz) of n-alkanes to avoid the influence of gas holdup time (tM). The effects of the equation orders (1st–5th) on the accuracy of a curve fitting show that a linear equation (LE) is less satisfactory and it is not necessary to use a complicated cubic or higher order equation. The relationship between the logarithm of Δtz and the carbon number (z) of the n-alkanes under isothermal conditions closely follows the quadratic equation for C3–C30 n-alkanes at column temperatures of 24–260 °C. The first and second order forward differences of the expression (Δlog Δtz and Δ2log Δtz, respectively) are linear and constant, respectively, which validates the DE model. This DE model lays a necessary foundation for further developing a retention model to accurately describe the relationship between the adjusted retention time and z of n-alkanes. PMID:22939376

Calibrations between chlorophyll meter values and chlorophyll contents vary as the result of differences in leaf structure

USDA-ARS?s Scientific Manuscript database

In order to relate leaf chlorophyll meter values with total leaf chlorophyll contents (µg cm-2), calibration equations are established with measured data on leaves. Many studies have documented differences in calibration equations using different species and using different growing conditions for th...

The equations of motion for moist atmospheric air

NASA Astrophysics Data System (ADS)

Makarieva, Anastassia M.; Gorshkov, Victor G.; Nefiodov, Andrei V.; Sheil, Douglas; Nobre, Antonio Donato; Bunyard, Peter; Nobre, Paulo; Li, Bai-Lian

2017-07-01

How phase transitions affect the motion of moist atmospheric air remains controversial. In the early 2000s two distinct differential equations of motion were proposed. Besides their contrasting formulations for the acceleration of condensate, the equations differ concerning the presence/absence of a term equal to the rate of phase transitions multiplied by the difference in velocity between condensate and air. This term was interpreted in the literature as the "reactive motion" associated with condensation. The reasoning behind this reactive motion was that when water vapor condenses and droplets begin to fall the remaining gas must move upward to conserve momentum. Here we show that the two contrasting formulations imply distinct assumptions about how gaseous air and condensate particles interact. We show that these assumptions cannot be simultaneously applicable to condensation and evaporation. Reactive motion leading to an upward acceleration of air during condensation does not exist. The reactive motion term can be justified for evaporation only; it describes the downward acceleration of air. We emphasize the difference between the equations of motion (i.e., equations constraining velocity) and those constraining momentum (i.e., equations of motion and continuity combined). We show that owing to the imprecise nature of the continuity equations, consideration of total momentum can be misleading and that this led to the reactive motion controversy. Finally, we provide a revised and generally applicable equation for the motion of moist air.

Accuracy of Anthropometric Equations for Estimating Body Fat in Professional Male Soccer Players Compared with DXA

PubMed Central

López-Taylor, Juan R.; Jiménez-Alvarado, Juan Antonio; Villegas-Balcázar, Marisol; Jáuregui-Ulloa, Edtna E.; Torres-Naranjo, Francisco

2018-01-01

Background There are several published anthropometric equations to estimate body fat percentage (BF%), and this may prompt uncertainty about their application. Purpose To analyze the accuracy of several anthropometric equations (developed in athletic [AT] and nonathletic [NAT] populations) that estimate BF% comparing them with DXA. Methods We evaluated 131 professional male soccer players (body mass: 73.2 ± 8.0 kg; height: 177.5 ± 5.8 cm; DXA BF% [median, 25th–75th percentile]: 14.0, 11.9–16.4%) aged 18 to 37 years. All subjects were evaluated with anthropometric measurements and a whole body DXA scan. BF% was estimated through 14 AT and 17 NAT anthropometric equations and compared with the measured DXA BF%. Mean differences and 95% limits of agreement were calculated for those anthropometric equations without significant differences with DXA. Results Five AT and seven NAT anthropometric equations did not differ significantly with DXA. From these, Oliver's and Civar's (AT) and Ball's and Wilmore's (NAT) equations showed the highest agreement with DXA. Their 95% limits of agreement ranged from −3.9 to 2.3%, −4.8 to 1.8%, −3.4 to 3.1%, and −3.9 to 3.0%, respectively. Conclusion Oliver's, Ball's, Civar's, and Wilmore's equations were the best to estimate BF% accurately compared with DXA in professional male soccer players. PMID:29736402

An explicit predictor-corrector solver with applications to Burgers' equation

NASA Technical Reports Server (NTRS)

Dey, S. K.; Dey, C.

1983-01-01

Forward Euler's explicit, finite-difference formula of extrapolation, is used as a predictor and a convex formula as a corrector to integrate differential equations numerically. An application has been made to Burger's equation.

Assessment and correction of skinfold thickness equations in estimating body fat in children with cerebral palsy.

PubMed

Gurka, Matthew J; Kuperminc, Michelle N; Busby, Marjorie G; Bennis, Jacey A; Grossberg, Richard I; Houlihan, Christine M; Stevenson, Richard D; Henderson, Richard C

2010-02-01

To assess the accuracy of skinfold equations in estimating percentage body fat in children with cerebral palsy (CP), compared with assessment of body fat from dual energy X-ray absorptiometry (DXA). Data were collected from 71 participants (30 females, 41 males) with CP (Gross Motor Function Classification System [GMFCS] levels I-V) between the ages of 8 and 18 years. Estimated percentage body fat was computed using established (Slaughter) equations based on the triceps and subscapular skinfolds. A linear model was fitted to assess the use of a simple correction to these equations for children with CP. Slaughter's equations consistently underestimated percentage body fat (mean difference compared with DXA percentage body fat -9.6/100 [SD 6.2]; 95% confidence interval [CI] -11.0 to -8.1). New equations were developed in which a correction factor was added to the existing equations based on sex, race, GMFCS level, size, and pubertal status. These corrected equations for children with CP agree better with DXA (mean difference 0.2/100 [SD=4.8]; 95% CI -1.0 to 1.3) than existing equations. A simple correction factor to commonly used equations substantially improves the ability to estimate percentage body fat from two skinfold measures in children with CP.

Predictive Variables of Half-Marathon Performance for Male Runners.

PubMed

Gómez-Molina, Josué; Ogueta-Alday, Ana; Camara, Jesus; Stickley, Christoper; Rodríguez-Marroyo, José A; García-López, Juan

2017-06-01

The aims of this study were to establish and validate various predictive equations of half-marathon performance. Seventy-eight half-marathon male runners participated in two different phases. Phase 1 (n = 48) was used to establish the equations for estimating half-marathon performance, and Phase 2 (n = 30) to validate these equations. Apart from half-marathon performance, training-related and anthropometric variables were recorded, and an incremental test on a treadmill was performed, in which physiological (VO 2max , speed at the anaerobic threshold, peak speed) and biomechanical variables (contact and flight times, step length and step rate) were registered. In Phase 1, half-marathon performance could be predicted to 90.3% by variables related to training and anthropometry (Equation 1), 94.9% by physiological variables (Equation 2), 93.7% by biomechanical parameters (Equation 3) and 96.2% by a general equation (Equation 4). Using these equations, in Phase 2 the predicted time was significantly correlated with performance (r = 0.78, 0.92, 0.90 and 0.95, respectively). The proposed equations and their validation showed a high prediction of half-marathon performance in long distance male runners, considered from different approaches. Furthermore, they improved the prediction performance of previous studies, which makes them a highly practical application in the field of training and performance.

Predicting of biomass in Brazilian tropical dry forest: a statistical evaluation of generic equations.

PubMed

Lima, Robson B DE; Alves, Francisco T; Oliveira, Cinthia P DE; Silva, José A A DA; Ferreira, Rinaldo L C

2017-01-01

Dry tropical forests are a key component in the global carbon cycle and their biomass estimates depend almost exclusively of fitted equations for multi-species or individual species data. Therefore, a systematic evaluation of statistical models through validation of estimates of aboveground biomass stocks is justifiable. In this study was analyzed the capacity of generic and specific equations obtained from different locations in Mexico and Brazil, to estimate aboveground biomass at multi-species levels and for four different species. Generic equations developed in Mexico and Brazil performed better in estimating tree biomass for multi-species data. For Poincianella bracteosa and Mimosa ophthalmocentra, only the Sampaio and Silva (2005) generic equation was the most recommended. These equations indicate lower tendency and lower bias, and biomass estimates for these equations are similar. For the species Mimosa tenuiflora, Aspidosperma pyrifolium and for the genus Croton the specific regional equations are more recommended, although the generic equation of Sampaio and Silva (2005) is not discarded for biomass estimates. Models considering gender, families, successional groups, climatic variables and wood specific gravity should be adjusted, tested and the resulting equations should be validated at both local and regional levels as well as on the scales of tropics with dry forest dominance.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Hierarchical coarse-graining transform.

PubMed

Pancaldi, Vera; King, Peter R; Christensen, Kim

2009-03-01

We present a hierarchical transform that can be applied to Laplace-like differential equations such as Darcy's equation for single-phase flow in a porous medium. A finite-difference discretization scheme is used to set the equation in the form of an eigenvalue problem. Within the formalism suggested, the pressure field is decomposed into an average value and fluctuations of different kinds and at different scales. The application of the transform to the equation allows us to calculate the unknown pressure with a varying level of detail. A procedure is suggested to localize important features in the pressure field based only on the fine-scale permeability, and hence we develop a form of adaptive coarse graining. The formalism and method are described and demonstrated using two synthetic toy problems.

On the validity of the modified equation approach to the stability analysis of finite-difference methods

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1987-01-01

The validity of the modified equation stability analysis introduced by Warming and Hyett was investigated. It is shown that the procedure used in the derivation of the modified equation is flawed and generally leads to invalid results. Moreover, the interpretation of the modified equation as the exact partial differential equation solved by a finite-difference method generally cannot be justified even if spatial periodicity is assumed. For a two-level scheme, due to a series of mathematical quirks, the connection between the modified equation approach and the von Neuman method established by Warming and Hyett turns out to be correct despite its questionable original derivation. However, this connection is only partially valid for a scheme involving more than two time levels. In the von Neumann analysis, the complex error multiplication factor associated with a wave number generally has (L-1) roots for an L-level scheme. It is shown that the modified equation provides information about only one of these roots.

A differential equation for the Generalized Born radii.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2013-06-28

The Generalized Born (GB) model offers a convenient way of representing electrostatics in complex macromolecules like proteins or nucleic acids. The computation of atomic GB radii is currently performed by different non-local approaches involving volume or surface integrals. Here we obtain a non-linear second-order partial differential equation for the Generalized Born radius, which may be solved using local iterative algorithms. The equation is derived under the assumption that the usual GB approximation to the reaction field obeys Laplace's equation. The equation admits as particular solutions the correct GB radii for the sphere and the plane. The tests performed on a set of 55 different proteins show an overall agreement with other reference GB models and "perfect" Poisson-Boltzmann based values.

A new modified CKD-EPI equation for Chinese patients with type 2 diabetes.

PubMed

Liu, Xun; Gan, Xiaoliang; Chen, Jinxia; Lv, Linsheng; Li, Ming; Lou, Tanqi

2014-01-01

To improve the performance of glomerular filtration rate (GFR) estimating equation in Chinese type 2 diabetic patients by modification of the CKD-EPI equation. A total of 1196 subjects were enrolled. Measured GFR was calibrated to the dual plasma sample 99mTc-DTPA-GFR. GFRs estimated by the re-expressed 4-variable MDRD equation, the CKD-EPI equation and the Asian modified CKD-EPI equation were compared in 351 diabetic/non-diabetic pairs. And a new modified CKD-EPI equation was reconstructed in a total of 589 type 2 diabetic patients. In terms of both precision and accuracy, GFR estimating equations all achieved better results in the non-diabetic cohort comparing with those in the type 2 diabetic cohort (30% accuracy, P≤0.01 for all comparisons). In the validation data set, the new modified equation showed less bias (median difference, 2.3 ml/min/1.73 m2 for the new modified equation vs. ranged from -3.8 to -7.9 ml/min/1.73 m2 for the other 3 equations [P<0.001 for all comparisons]), as was precision (IQR of the difference, 24.5 ml/min/1.73 m2 vs. ranged from 27.3 to 30.7 ml/min/1.73 m2), leading to a greater accuracy (30% accuracy, 71.4% vs. 55.2% for the re-expressed 4 variable MDRD equation and 61.0% for the Asian modified CKD-EPI equation [P = 0.001 and P = 0.02]). A new modified CKD-EPI equation for type 2 diabetic patients was developed and validated. The new modified equation improves the performance of GFR estimation.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Numerical Analysis of a Class of THM Coupled Model for Porous Materials

NASA Astrophysics Data System (ADS)

Liu, Tangwei; Zhou, Jingying; Lu, Hongzhi

2018-01-01

We consider the coupled models of the Thermo-hydro-mechanical (THM) problem for porous materials which arises in many engineering applications. Firstly, mathematical models of the THM coupled problem for porous materials were discussed. Secondly, for different cases, some numerical difference schemes of coupled model were constructed, respectively. Finally, aassuming that the original water vapour effect is neglectable and that the volume fraction of liquid phase and the solid phase are constants, the nonlinear equations can be reduced to linear equations. The discrete equations corresponding to the linear equations were solved by the Arnodli method.

Nonlinear ordinary difference equations

NASA Technical Reports Server (NTRS)

Caughey, T. K.

1979-01-01

Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

Interpreting Linked Psychomotor Performance Scores

ERIC Educational Resources Information Center

Looney, Marilyn A.

2013-01-01

Given that equating/linking applications are now appearing in kinesiology literature, this article provides an overview of the different types of linked test scores: equated, concordant, and predicted. It also addresses the different types of evidence required to determine whether the scores from two different field tests (measuring the same…

The Difference Equation xn=axn-1+b.

ERIC Educational Resources Information Center

Spence, Lawrence E.

1990-01-01

Applications of generalizations of both arithmetic and geometric progressions are presented. The first-order difference equation is used in solving seven examples from finance, business, and medicine. Detailed directions are included for each example. (KR)

Finite-difference models of ordinary differential equations - Influence of denominator functions

NASA Technical Reports Server (NTRS)

Mickens, Ronald E.; Smith, Arthur

1990-01-01

This paper discusses the influence on the solutions of finite-difference schemes of using a variety of denominator functions in the discrete modeling of the derivative for any ordinary differential equation. The results obtained are a consequence of using a generalized definition of the first derivative. A particular example of the linear decay equation is used to illustrate in detail the various solution possibilities that can occur.

A nodal domain theorem for integrable billiards in two dimensions

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

Samajdar, Rhine; Jain, Sudhir R., E-mail: srjain@barc.gov.in

Eigenfunctions of integrable planar billiards are studied — in particular, the number of nodal domains, ν of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrödinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, ν satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of mmodkn, given a particular k, for a set of quantum numbers, m,n. Further, we observe that the patterns in a familymore » are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. - Highlights: • We find that the number of nodal domains of eigenfunctions of integrable, planar billiards satisfy a class of difference equations. • The eigenfunctions labelled by quantum numbers (m,n) can be classified in terms of mmodkn. • A theorem is presented, realising algebraic representations of geometrical patterns exhibited by the domains. • This work presents a connection between integrable systems and difference equations.« less

Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation

NASA Astrophysics Data System (ADS)

Poleshkin, Sergey O.; Malkov, Ewgenij A.; Kudryavtsev, Alexey N.; Shershnev, Anton A.; Bondar, Yevgeniy A.; Kohanchik, A. A.

2017-10-01

There are various methods for calculating rarefied gas flows, in particular, statistical methods and deterministic methods based on the finite-difference solutions of the Boltzmann nonlinear kinetic equation and on the solutions of model kinetic equations. There is no universal method; each has its disadvantages in terms of efficiency or accuracy. The choice of the method depends on the problem to be solved and on parameters of calculated flows. Qualitative theoretical arguments help to determine the range of parameters of effectively solved problems for each method; however, it is advisable to perform comparative tests of calculations of the classical problems performed by different methods and with different parameters to have quantitative confirmation of this reasoning. The paper provides the results of the calculations performed by the authors with the help of the Direct Simulation Monte Carlo method and finite-difference methods of solving the Boltzmann equation and model kinetic equations. Based on this comparison, conclusions are made on selecting a particular method for flow simulations in various ranges of flow parameters.

Application of a New Spirometric Reference Equation and Its Impact on the Staging of Korean Chronic Obstructive Pulmonary Disease Patients

PubMed Central

Hwang, Yong Il; Kim, Eun Ji; Lee, Chang Youl; Park, Sunghoon; Choi, Jeong Hee; Park, Yong Bum; Jang, Seung Hun; Kim, Cheol Hong; Shin, Tae Rim; Park, Sang Myeon; Kim, Dong-Gyu; Lee, Myung-Goo; Hyun, In-Gyu

2012-01-01

Purpose A new spirometric reference equation was recently developed from the first national chronic obstructive pulmonary disease (COPD) survey in Korea. However, Morris' equation has been preferred for evaluating spirometric values instead. The objective of this study was to evaluate changes in severity staging in Korean COPD patients by adopting the newly developed Korean equation. Materials and Methods We evaluated the spirometric data of 441 COPD patients. The presence of airflow limitation was defined as an observed post-bronchodilator forced expiratory volume in one second/forced vital capacity (FEV1/FVC) less than 0.7, and the severity of airflow limitation was assessed according to GOLD stages. Spirometric values were reassessed using the new Korean equation, Morris' equation and other reference equations. Results The severity of airflow limitation was differently graded in 143 (32.4%) patients after application of the new Korean equation when compared with Morris' equation. All 143 patients were reallocated into more severe stages (49 at mild stage, 65 at moderate stage, and 29 at severe stage were changed to moderate, severe and very severe stages, respectively). Stages according to other reference equations were changed in 18.6-49.4% of the patients. Conclusion These results indicate that equations from different ethnic groups do not sufficiently reflect the airflow limitation of Korean COPD patients. The Korean reference equation should be used for Korean COPD patients in order to administer proper treatment. PMID:22318825

Bilinear, trilinear forms, and exact solution of certain fourth order integrable difference equations

NASA Astrophysics Data System (ADS)

Sahadevan, R.; Rajakumar, S.

2008-03-01

A systematic investigation of finding bilinear or trilinear representations of fourth order autonomous ordinary difference equation, x(n +4)=F(x(n),x(n+1),x(n+2),x(n+3)) or xn +4=F(xn,xn +1,xn +2,xn +3), is made. As an illustration, we consider fourth order symplectic integrable difference equations reported by [Capel and Sahadevan, Physica A 289, 86 (2001)] and derived their bilinear or trilinear forms. Also, it is shown that the obtained bilinear representations admit exact solution of rational form.

Incompressible spectral-element method: Derivation of equations

NASA Technical Reports Server (NTRS)

Deanna, Russell G.

1993-01-01

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

NASA Astrophysics Data System (ADS)

Tay, Wei Choon; Tan, Eng Leong

2014-07-01

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.

Calculation of force and power during bench throws using a Smith machine: the importance of considering the effect of counterweights.

PubMed

Kobayashi, Y; Narazaki, K; Akagi, R; Nakagaki, K; Kawamori, N; Ohta, K

2013-09-01

For achieving accurate and safe measurements of the force and power exerted on a load during resistance exercise, the Smith machine has been used instead of free weights. However, because some Smith machines possess counterweights, the equation for the calculation of force and power in this system should be different from the one used for free weights. The purpose of this investigation was to calculate force and power using an equation derived from a dynamic equation for a Smith machine with counterweights and to determine the differences in force and power calculated using 2 different equations. One equation was established ignoring the effect of the counterweights (Method 1). The other equation was derived from a dynamic equation for a barbell and counterweight system (Method 2). 9 female collegiate judo athletes performed bench throws using a Smith machine with a counterweight at 6 different loading conditions. Barbell displacement was recorded using a linear position transducer. The force and power were subsequently calculated by Methods 1 and 2. The results showed that the mean and peak power and force in Method 1 were significantly lower relative to those of Method 2 under all loading conditions. These results indicate that the mean and peak power and force during bench throwing using a Smith machine with counterweights would be underestimated when the calculations used to determine these parameters do not account for the effect of counterweights. © Georg Thieme Verlag KG Stuttgart · New York.

Behavior of respiratory muscle strength in morbidly obese women by using different predictive equations.

PubMed

Pazzianotto-Forti, Eli M; Peixoto-Souza, Fabiana S; Piconi-Mendes, Camila; Rasera-Junior, Irineu; Barbalho-Moulim, Marcela

2012-01-01

Studies on the behavior of respiratory muscle strength (RMS) in morbidly obese patients have found conflicting results. To evaluate RMS in morbidly obese women and to compare the results by using different predictive equations. This is a cross-sectional study that recruited 30 morbidly obese women and a control group of 30 normal-weight women. The subjects underwent anthropometric and maximal respiratory pressure measurement. Visual inspection of the Bland-Altman plots was performed to evaluate the correlation between the different equations, with a p value lower than 0.05 considered as statistically significant. The obese women showed a significant increase in maximal inspiratory pressure (MIP) values (-87.83±21.40 cmH(2)O) compared with normal-weight women (-72±15.23 cmH(2)O) and a significant reduction of MIP (-87.83±21.40 cmH(2)O) according to the values predicted by the EHarik equation (-130.71±11.98 cmH(2)O). Regarding the obtained maximal expiratory pressure (MEP), there were no between-group differences (p>0.05), and no agreeement was observed between obtained and predicted values of MEP and the ENeder and ECosta equations. Inspiratory muscle strength was greater in the morbidly obese subjects. The most appropriate equation for calculating the predicted MIP values for the morbidly obese seems to be Harik-Khan equation. There seem to be similarities between the respiratory muscle strength behavior of morbidly obese and normal-weight women, however, these findings are still inconclusive.

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

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

PubMed

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.

Masses from an inhomogeneous partial difference equation with higher-order isospin contributions

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

Masson, P.J.; Jaenecke, J.

In the present work, a mass equation obtained as the solution of an inhomogeneous partial difference equation is used to predict masses of unknown neutron-rich and proton-rich nuclei. The inhomogeneous source terms contain shell-dependent symmetry energy expressions (quadratic in isospin), and include, as well, an independently derived shell-model Coulomb energy equation which describes all known Coulomb displacement energies with a standarad deviation of sigma/sub c/ = 41 keV. Perturbations of higher order in isospin, previously recognized as a cause of systematic effects in long-range mass extrapolations, are also incorporated. The most general solutions of the inhomogeneous difference equation have beenmore » deduced from a chi/sup 2/-minimization procedure based on the recent atomic mass adjustment of Wapstra, Audi, and Hoekstra. Subjecting the solutions further to the condition of charge symmetry preserves the accuracy of Coulomb energies and allows mass predictions for nuclei with both Ngreater than or equal toZ and Z>N. The solutions correspond to a mass equation with 470 parameters. Using this equation, 4385 mass values have been calculated for nuclei with Agreater than or equal to16 (except N = Z = odd for A<40), with a standard deviation of sigma/sub m/ = 194 keV from the experimental masses. copyright 1988 Academic Press, Inc.« less

Development and validation of a predictive equation for lean body mass in children and adolescents.

PubMed

Foster, Bethany J; Platt, Robert W; Zemel, Babette S

2012-05-01

Lean body mass (LBM) is not easy to measure directly in the field or clinical setting. Equations to predict LBM from simple anthropometric measures, which account for the differing contributions of fat and lean to body weight at different ages and levels of adiposity, would be useful to both human biologists and clinicians. To develop and validate equations to predict LBM in children and adolescents across the entire range of the adiposity spectrum. Dual energy X-ray absorptiometry was used to measure LBM in 836 healthy children (437 females) and linear regression was used to develop sex-specific equations to estimate LBM from height, weight, age, body mass index (BMI) for age z-score and population ancestry. Equations were validated using bootstrapping methods and in a local independent sample of 332 children and in national data collected by NHANES. The mean difference between measured and predicted LBM was - 0.12% (95% limits of agreement - 11.3% to 8.5%) for males and - 0.14% ( - 11.9% to 10.9%) for females. Equations performed equally well across the entire adiposity spectrum, as estimated by BMI z-score. Validation indicated no over-fitting. LBM was predicted within 5% of measured LBM in the validation sample. The equations estimate LBM accurately from simple anthropometric measures.

Validation of Field Methods to Assess Body Fat Percentage in Elite Youth Soccer Players.

PubMed

Munguia-Izquierdo, Diego; Suarez-Arrones, Luis; Di Salvo, Valter; Paredes-Hernandez, Victor; Alcazar, Julian; Ara, Ignacio; Kreider, Richard; Mendez-Villanueva, Alberto

2018-05-01

This study determined the most effective field method for quantifying body fat percentage in male elite youth soccer players and developed prediction equations based on anthropometric variables. Forty-four male elite-standard youth soccer players aged 16.3-18.0 years underwent body fat percentage assessments, including bioelectrical impedance analysis and the calculation of various skinfold-based prediction equations. Dual X-ray absorptiometry provided a criterion measure of body fat percentage. Correlation coefficients, bias, limits of agreement, and differences were used as validity measures, and regression analyses were used to develop soccer-specific prediction equations. The equations from Sarria et al. (1998) and Durnin & Rahaman (1967) reached very large correlations and the lowest biases, and they reached neither the practically worthwhile difference nor the substantial difference between methods. The new youth soccer-specific skinfold equation included a combination of triceps and supraspinale skinfolds. None of the practical methods compared in this study are adequate for estimating body fat percentage in male elite youth soccer players, except for the equations from Sarria et al. (1998) and Durnin & Rahaman (1967). The new youth soccer-specific equation calculated in this investigation is the only field method specifically developed and validated in elite male players, and it shows potentially good predictive power. © Georg Thieme Verlag KG Stuttgart · New York.

Involution and Difference Schemes for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.

In the present paper we consider the Navier-Stokes equations for the two-dimensional viscous incompressible fluid flows and apply to these equations our earlier designed general algorithmic approach to generation of finite-difference schemes. In doing so, we complete first the Navier-Stokes equations to involution by computing their Janet basis and discretize this basis by its conversion into the integral conservation law form. Then we again complete the obtained difference system to involution with eliminating the partial derivatives and extracting the minimal Gröbner basis from the Janet basis. The elements in the obtained difference Gröbner basis that do not contain partial derivatives of the dependent variables compose a conservative difference scheme. By exploiting arbitrariness in the numerical integration approximation we derive two finite-difference schemes that are similar to the classical scheme by Harlow and Welch. Each of the two schemes is characterized by a 5×5 stencil on an orthogonal and uniform grid. We also demonstrate how an inconsistent difference scheme with a 3×3 stencil is generated by an inappropriate numerical approximation of the underlying integrals.

Reconstruction of the modified discrete Langevin equation from persistent time series

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

Czechowski, Zbigniew

The discrete Langevin-type equation, which can describe persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data, with short and long-tail distributions, generated by different Langevin equations. Corrections due to the finite sampling rates were derived. For an exemplary meteorological time series, an appropriate Langevin equation, which constitutes a stochastic macroscopic model of the phenomenon, was reconstructed.

Comparison of the One- and Bi-Direction Chained Equipercentile Equating

ERIC Educational Resources Information Center

Oh, Hyeonjoo; Moses, Tim

2012-01-01

This study investigated differences between two approaches to chained equipercentile (CE) equating (one- and bi-direction CE equating) in nearly equal groups and relatively unequal groups. In one-direction CE equating, the new form is linked to the anchor in one sample of examinees and the anchor is linked to the reference form in the other…

Managing Element Interactivity in Equation Solving

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Phan, Huy P.; Yeung, Alexander Seeshing; Chung, Siu Fung

2018-01-01

Between two popular teaching methods (i.e., balance method vs. inverse method) for equation solving, the main difference occurs at the operational line (e.g., +2 on both sides vs. -2 becomes +2), whereby it alters the state of the equation and yet maintains its equality. Element interactivity occurs on both sides of the equation in the balance…

Quantum spectral curve for ( q, t)-matrix model

NASA Astrophysics Data System (ADS)

Zenkevich, Yegor

2018-02-01

We derive quantum spectral curve equation for ( q, t)-matrix model, which turns out to be a certain difference equation. We show that in Nekrasov-Shatashvili limit this equation reproduces the Baxter TQ equation for the quantum XXZ spin chain. This chain is spectral dual to the Seiberg-Witten integrable system associated with the AGT dual gauge theory.

Statistical Assessment of Estimated Transformations in Observed-Score Equating

ERIC Educational Resources Information Center

Wiberg, Marie; González, Jorge

2016-01-01

Equating methods make use of an appropriate transformation function to map the scores of one test form into the scale of another so that scores are comparable and can be used interchangeably. The equating literature shows that the ways of judging the success of an equating (i.e., the score transformation) might differ depending on the adopted…

Measurement and Interpretation of Flow Stress Data for the Simulation of Metal-Forming Processes

DTIC Science & Technology

2010-01-01

fitting constants that differ in each equation): Ludwik Equation: c)εb(aσ += , (29) Voce Equation: )]εcexp([1*a][baσ −−−+= (30) Swift...stress at low strains (ɘ.2) and to overestimate the stress for high strains. For heavily prestrained materials, c ~ 1. The Voce and Swift equations tend

Recent Developments in Computational Techniques for Applied Hydrodynamics.

DTIC Science & Technology

1979-12-07

by block number) Numerical Method Fluids Incompressible Flow Finite Difference Methods Poisson Equation Convective Equations -MABSTRACT (Continue on...weaknesses of the different approaches are analyzed. Finite - difference techniques have particularly attractive properties in this framework. Hence it will...be worthwhile to correct, at least partially, the difficulties from which Eulerian and Lagrangian finite - difference techniques suffer, discussed in

Asymptotic proportionality (weak ergodicity) and conditional asymptotic equality of solutions to time-heterogeneous sublinear difference and differential equations

NASA Astrophysics Data System (ADS)

Thieme, Horst R.

The concept of asymptotic proportionality and conditional asymptotic equality which is presented here aims at making global asymptotic stability statements for time-heterogeneous difference and differential equations. For such non-autonomous problems (apart from special cases) no prominent special solutions (equilibra, periodic solutions) exist which are natural candidates for the asymptotic behaviour of arbitrary solutions. One way out of this dilemma consists in looking for conditions under which any two solutions to the problem (with different initial conditions) behave in a similar or even the same way as time tends to infinity. We study a general sublinear difference equation in an ordered Banach space and, for illustration, time-heterogeneous versions of several well-known differential equations modelling the spread of gonorrhea in a heterogeneous population, the spread of a vector-borne infectious disease, and the dynamics of a logistically growing spatially diffusing population.

The eight tetrahedron equations

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

Hietarinta, J.; Nijhoff, F.

1997-07-01

In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that represents integrable structures in three dimensions generalizing the Yang{endash}Baxter equation. Under additional restrictions this system reduces to the usual tetrahedron equation in the vertex form. Most known solutions fall under this class, but it is by no means necessary. Comparison is made with the work on braided monoidal 2-categories also leading to eight tetrahedron equations. {copyright} {ital 1997 American Institute of Physics.}

Dissipative Relativistic Fluid Dynamics: A New Way to Derive the Equations of Motion from Kinetic Theory

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

Denicol, G. S.; Koide, T.; Rischke, D. H.

2010-10-15

We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.

Observed Score Equating Using a Mini-Version Anchor and an Anchor with Less Spread of Difficulty: A Comparison Study

ERIC Educational Resources Information Center

Liu, Jinghua; Sinharay, Sandip; Holland, Paul; Feigenbaum, Miriam; Curley, Edward

2011-01-01

Two different types of anchors are investigated in this study: a mini-version anchor and an anchor that has a less spread of difficulty than the tests to be equated. The latter is referred to as a midi anchor. The impact of these two different types of anchors on observed score equating are evaluated and compared with respect to systematic error…

The picosecond structure of ultra-fast rogue waves

NASA Astrophysics Data System (ADS)

Klein, Avi; Shahal, Shir; Masri, Gilad; Duadi, Hamootal; Sulimani, Kfir; Lib, Ohad; Steinberg, Hadar; Kolpakov, Stanislav A.; Fridman, Moti

2018-02-01

We investigated ultrafast rogue waves in fiber lasers and found three different patterns of rogue waves: single- peaks, twin-peaks, and triple-peaks. The statistics of the different patterns as a function of the pump power of the laser reveals that the probability for all rogue waves patterns increase close to the laser threshold. We developed a numerical model which prove that the ultrafast rogue waves patterns result from both the polarization mode dispersion in the fiber and the non-instantaneous nature of the saturable absorber. This discovery reveals that there are three different types of rogue waves in fiber lasers: slow, fast, and ultrafast, which relate to three different time-scales and are governed by three different sets of equations: the laser rate equations, the nonlinear Schrodinger equation, and the saturable absorber equations, accordingly. This discovery is highly important for analyzing rogue waves and other extreme events in fiber lasers and can lead to realizing types of rogue waves which were not possible so far such as triangular rogue waves.

Body composition in elderly people: effect of criterion estimates on predictive equations

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

Baumgartner, R.N.; Heymsfield, S.B.; Lichtman, S.

1991-06-01

The purposes of this study were to determine whether there are significant differences between two- and four-compartment model estimates of body composition, whether these differences are associated with aqueous and mineral fractions of the fat-free mass (FFM); and whether the differences are retained in equations for predicting body composition from anthropometry and bioelectric resistance. Body composition was estimated in 98 men and women aged 65-94 y by using a four-compartment model based on hydrodensitometry, {sup 3}H{sub 2}O dilution, and dual-photon absorptiometry. These estimates were significantly different from those obtained by using Siri's two-compartment model. The differences were associated significantly (Pmore » less than 0.0001) with variation in the aqueous fraction of FFM. Equations for predicting body composition from anthropometry and resistance, when calibrated against two-compartment model estimates, retained these systematic errors. Equations predicting body composition in elderly people should be calibrated against estimates from multicompartment models that consider variability in FFM composition.« less

Bell-polynomial approach and Wronskian determinant solutions for three sets of differential-difference nonlinear evolution equations with symbolic computation

NASA Astrophysics Data System (ADS)

Qin, Bo; Tian, Bo; Wang, Yu-Feng; Shen, Yu-Jia; Wang, Ming

2017-10-01

Under investigation in this paper are the Belov-Chaltikian (BC), Leznov and Blaszak-Marciniak (BM) lattice equations, which are associated with the conformal field theory, UToda(m_1,m_2) system and r-matrix, respectively. With symbolic computation, the Bell-polynomial approach is developed to directly bilinearize those three sets of differential-difference nonlinear evolution equations (NLEEs). This Bell-polynomial approach does not rely on any dependent variable transformation, which constitutes the key step and main difficulty of the Hirota bilinear method, and thus has the advantage in the bilinearization of the differential-difference NLEEs. Based on the bilinear forms obtained, the N-soliton solutions are constructed in terms of the N × N Wronskian determinant. Graphic illustrations demonstrate that those solutions, more general than the existing results, permit some new properties, such as the solitonic propagation and interactions for the BC lattice equations, and the nonnegative dark solitons for the BM lattice equations.

Concircular vector fields on Lorentzian manifold of Bianchi type-I spacetimes

NASA Astrophysics Data System (ADS)

Mahmood, Amjad; Ali, Ahmad T.; Khan, Suhail

2018-04-01

Our aim in this paper is to obtain concircular vector fields (CVFs) on the Lorentzian manifold of Bianchi type-I spacetimes. For this purpose, two different sets of coupled partial differential equations comprising ten equations each are obtained. The first ten equations, known as conformal Killing equations are solved completely and components of conformal Killing vector fields (CKVFs) are obtained in different possible cases. These CKVFs are then substituted into second set of ten differential equations to obtain CVFs. It comes out that Bianchi type-I spacetimes admit four-, five-, six-, seven- or 15-dimensional CVFs for particular choices of the metric functions. In many cases, the CKVFs of a particular metric are same as CVFs while there exists few cases where proper CKVFs are not CVFs.

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1986-01-01

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

PREFACE: Symmetries and integrability of difference equations Symmetries and integrability of difference equations

NASA Astrophysics Data System (ADS)

Levi, Decio; Olver, Peter; Thomova, Zora; Winternitz, Pavel

2009-11-01

The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first meeting with the name `Symmetries and Integrability of Discrete Equations (SIDE)' was held in Estérel, Québec, Canada. This was organized by D Levi, P Winternitz and L Vinet. After the success of the first meeting the scientific community decided to hold bi-annual SIDE meetings. They were held in 1996 at the University of Kent (UK), 1998 in Sabaudia (Italy), 2000 at the University of Tokyo (Japan), 2002 in Giens (France), 2004 in Helsinki (Finland) and in 2006 at the University of Melbourne (Australia). In 2008 the SIDE 8 meeting was again organized near Montreal, in Ste-Adèle, Québec, Canada. The SIDE 8 International Advisory Committee (also the SIDE steering committee) consisted of Frank Nijhoff, Alexander Bobenko, Basil Grammaticos, Jarmo Hietarinta, Nalini Joshi, Decio Levi, Vassilis Papageorgiou, Junkichi Satsuma, Yuri Suris, Claude Vialet and Pavel Winternitz. The local organizing committee consisted of Pavel Winternitz, John Harnad, Véronique Hussin, Decio Levi, Peter Olver and Luc Vinet. Financial support came from the Centre de Recherches Mathématiques in Montreal and the National Science Foundation (through the University of Minnesota). Proceedings of the first three SIDE meetings were published in the LMS Lecture Note series. Since 2000 the emphasis has been on publishing selected refereed articles in response to a general call for papers issued after the conference. This allows for a wider author base, since the call for papers is not restricted to conference participants. The SIDE topics thus are represented in special issues of Journal of Physics A: Mathematical and General 34 (48) and Journal of Physics A: Mathematical and Theoretical, 40 (42) (SIDE 4 and SIDE 7, respectively), Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2) (SIDE 5 and SIDE 6 respectively). The SIDE 8 meeting was organized around several topics and the contributions to this special issue reflect the diversity presented during the meeting. The papers presented at the SIDE 8 meeting were organized into the following special sessions: geometry of discrete and continuous Painlevé equations; continuous symmetries of discrete equations—theory and computational applications; algebraic aspects of discrete equations; singularity confinement, algebraic entropy and Nevanlinna theory; discrete differential geometry; discrete integrable systems and isomonodromy transformations; special functions as solutions of difference and q-difference equations. This special issue of the journal is organized along similar lines. The first three articles are topical review articles appearing in alphabetical order (by first author). The article by Doliwa and Nieszporski describes the Darboux transformations in a discrete setting, namely for the discrete second order linear problem. The article by Grammaticos, Halburd, Ramani and Viallet concentrates on the integrability of the discrete systems, in particular they describe integrability tests for difference equations such as singularity confinement, algebraic entropy (growth and complexity), and analytic and arithmetic approaches. The topical review by Konopelchenko explores the relationship between the discrete integrable systems and deformations of associative algebras. All other articles are presented in alphabetical order (by first author). The contributions were solicited from all participants as well as from the general scientific community. The contributions published in this special issue can be loosely grouped into several overlapping topics, namely: •Geometry of discrete and continuous Painlevé equations (articles by Spicer and Nijhoff and by Lobb and Nijhoff). •Continuous symmetries of discrete equations—theory and applications (articles by Dorodnitsyn and Kozlov; Levi, Petrera and Scimiterna; Scimiterna; Ste-Marie and Tremblay; Levi and Yamilov; Rebelo and Winternitz). •Yang--Baxter maps (article by Xenitidis and Papageorgiou). •Algebraic aspects of discrete equations (articles by Doliwa and Nieszporski; Konopelchenko; Tsarev and Wolf). •Singularity confinement, algebraic entropy and Nevanlinna theory (articles by Grammaticos, Halburd, Ramani and Viallet; Grammaticos, Ramani and Tamizhmani). •Discrete integrable systems and isomonodromy transformations (article by Dzhamay). •Special functions as solutions of difference and q-difference equations (articles by Atakishiyeva, Atakishiyev and Koornwinder; Bertola, Gekhtman and Szmigielski; Vinet and Zhedanov). •Other topics (articles by Atkinson; Grünbaum Nagai, Kametaka and Watanabe; Nagiyev, Guliyeva and Jafarov; Sahadevan and Uma Maheswari; Svinin; Tian and Hu; Yao, Liu and Zeng). This issue is the result of the collaboration of many individuals. We would like to thank the authors who contributed and everyone else involved in the preparation of this special issue.

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

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

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

2015-03-15

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

Fundamental equations of a mixture of gas and small spherical solid particles from simple kinetic theory.

NASA Technical Reports Server (NTRS)

Pai, S. I.

1973-01-01

The fundamental equations of a mixture of a gas and pseudofluid of small spherical solid particles are derived from the Boltzmann equation of two-fluid theory. The distribution function of the gas molecules is defined in the same manner as in the ordinary kinetic theory of gases, but the distribution function for the solid particles is different from that of the gas molecules, because it is necessary to take into account the different size and physical properties of solid particles. In the proposed simple kinetic theory, two additional parameters are introduced: one is the radius of the spheres and the other is the instantaneous temperature of the solid particles in the distribution of the solid particles. The Boltzmann equation for each species of the mixture is formally written, and the transfer equations of these Boltzmann equations are derived and compared to the well-known fundamental equations of the mixture of a gas and small solid particles from continuum theory. The equations obtained reveal some insight into various terms in the fundamental equations. For instance, the partial pressure of the pseudofluid of solid particles is not negligible if the volume fraction of solid particles is not negligible as in the case of lunar ash flow.

Kernel Equating Under the Non-Equivalent Groups With Covariates Design

PubMed Central

Bränberg, Kenny

2015-01-01

When equating two tests, the traditional approach is to use common test takers and/or common items. Here, the idea is to use variables correlated with the test scores (e.g., school grades and other test scores) as a substitute for common items in a non-equivalent groups with covariates (NEC) design. This is performed in the framework of kernel equating and with an extension of the method developed for post-stratification equating in the non-equivalent groups with anchor test design. Real data from a college admissions test were used to illustrate the use of the design. The equated scores from the NEC design were compared with equated scores from the equivalent group (EG) design, that is, equating with no covariates as well as with equated scores when a constructed anchor test was used. The results indicate that the NEC design can produce lower standard errors compared with an EG design. When covariates were used together with an anchor test, the smallest standard errors were obtained over a large range of test scores. The results obtained, that an EG design equating can be improved by adjusting for differences in test score distributions caused by differences in the distribution of covariates, are useful in practice because not all standardized tests have anchor tests. PMID:29881012

Kernel Equating Under the Non-Equivalent Groups With Covariates Design.

PubMed

Wiberg, Marie; Bränberg, Kenny

2015-07-01

When equating two tests, the traditional approach is to use common test takers and/or common items. Here, the idea is to use variables correlated with the test scores (e.g., school grades and other test scores) as a substitute for common items in a non-equivalent groups with covariates (NEC) design. This is performed in the framework of kernel equating and with an extension of the method developed for post-stratification equating in the non-equivalent groups with anchor test design. Real data from a college admissions test were used to illustrate the use of the design. The equated scores from the NEC design were compared with equated scores from the equivalent group (EG) design, that is, equating with no covariates as well as with equated scores when a constructed anchor test was used. The results indicate that the NEC design can produce lower standard errors compared with an EG design. When covariates were used together with an anchor test, the smallest standard errors were obtained over a large range of test scores. The results obtained, that an EG design equating can be improved by adjusting for differences in test score distributions caused by differences in the distribution of covariates, are useful in practice because not all standardized tests have anchor tests.

Effect of picric acid and enzymatic creatinine on the efficiency of the glomerular filtration rate predicator formula.

PubMed

Qiu, Ling; Guo, Xiuzhi; Zhu, Yan; Shou, Weilin; Gong, Mengchun; Zhang, Lin; Han, Huijuan; Quan, Guoqiang; Xu, Tao; Li, Hang; Li, Xuewang

2013-01-01

To investigate the impact of serum creatinine measurement on the applicability of glomerular filtration rate (GFR) evaluation equations. 99mTc-DTPA plasma clearance rate was used as GFR reference (rGFR) in patients with chronic kidney disease (CKD). Serum creatinine was measureded using enzymatic or picric acid creatinine reagent. The GFR of the patients were estimated using the Cockcroft-Gault equation corrected for body surface area, simplified Modification of Diet in Renal Disease (MDRD) equation, simplified MDRD equation corrected to isotopes dilution mass spectrometry, the CKD epidemiology collaborative research equation, and two Chinese simplified MDRD equations. Significant differences in the eGFR results estimated through enzymatic and picric acid methods were observed for the same evaluation equation. The intraclass correlation coefficient (ICC) of eGFR when the creatinine was measured by the picric acid method was significantly lower than that of the enzymatic method. The assessment accuracy of every equation using the enzymatic method to measure creatinine was significantly higher than that measured by the picric acid method when rGFR was > or = 60 mL/min/1.73m2. A significant difference was demonstrated in the same GFR evaluation equation using the picric acid and enzymatic methods. The enzymatic creatinine method was better than the picric acid method.

Assessment and correction of skinfold thickness equations in estimating body fat in children with cerebral palsy

PubMed Central

GURKA, MATTHEW J; KUPERMINC, MICHELLE N; BUSBY, MARJORIE G; BENNIS, JACEY A; GROSSBERG, RICHARD I; HOULIHAN, CHRISTINE M; STEVENSON, RICHARD D; HENDERSON, RICHARD C

2010-01-01

AIM To assess the accuracy of skinfold equations in estimating percentage body fat in children with cerebral palsy (CP), compared with assessment of body fat from dual energy X-ray absorptiometry (DXA). METHOD Data were collected from 71 participants (30 females, 41 males) with CP (Gross Motor Function Classification System [GMFCS] levels I–V) between the ages of 8 and 18 years. Estimated percentage body fat was computed using established (Slaughter) equations based on the triceps and subscapular skinfolds. A linear model was fitted to assess the use of a simple correction to these equations for children with CP. RESULTS Slaughter’s equations consistently underestimated percentage body fat (mean difference compared with DXA percentage body fat −9.6/100 [SD 6.2]; 95% confidence interval [CI] −11.0 to −8.1). New equations were developed in which a correction factor was added to the existing equations based on sex, race, GMFCS level, size, and pubertal status. These corrected equations for children with CP agree better with DXA (mean difference 0.2/100 [SD=4.8]; 95% CI −1.0 to 1.3) than existing equations. INTERPRETATION A simple correction factor to commonly used equations substantially improves the ability to estimate percentage body fat from two skinfold measures in children with CP. PMID:19811518

Ordinary differential equations with applications in molecular biology.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2012-01-01

Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances. Ordinary differential equations are used to model biological processes on various levels ranging from DNA molecules or biosynthesis phospholipids on the cellular level.

Comparison of stochastic lung deposition fractions with experimental data.

PubMed

Majid, Hussain; Hofmann, Werner; Winkler-Heil, Renate

2012-04-01

Deposition fractions of inhaled particles predicted by different computational models vary with respect to physical and biological factors and mathematical modeling techniques. These models must be validated by comparison with available experimental data. Experimental data supplied by different deposition studies with surrogate airway models or lung casts were used in this study to evaluate the stochastic deposition model Inhalation, Deposition and Exhalation of Aerosols in the Lung at the airway generation level. Furthermore, different analytical equations derived for the three major deposition mechanisms, diffusion, impaction, and sedimentation, were applied to different cast or airway models to quantify their effect on calculated particle deposition fractions. The experimental results for ultrafine particles (0.00175 and 0.01) were found to be in close agreement with the stochastic model predictions; however, for coarse particles (3 and 8 μm), experimental deposition fractions became higher with increasing flow rate. An overall fair agreement among the calculated deposition fractions for the different cast geometries was found. However, alternative deposition equations resulted in up to 300% variation in predicted deposition fractions, although all equations predicted the same trends as functions of particle diameter and breathing conditions. From this comparative study, it can be concluded that structural differences in lung morphologies among different individuals are responsible for the apparent variability in particle deposition in each generation. The use of different deposition equations yields varying deposition results caused primarily by (i) different lung morphometries employed in their derivation and the choice of the central bifurcation zone geometry, (ii) the assumption of specific flow profiles, and (iii) different methods used in the derivation of these equations.

Analyzing the uncertainties in use of forest-derived biomass equations for open-grown trees in agricultural land

Treesearch

Xinhua Zhou; Michele M. Schoeneberger; James R. Brandle; Tala N. Awada; Jianmin Chu; Derrel L. Martin; Jihong Li; Yuqiang Li; Carl W. Mize

2014-01-01

Quantifying carbon in agroforestry trees requires biomass equations that capture the growth differences (e.g., tree specific gravity and architecture) created in the more open canopies of agroforestry plantings compared with those generally encountered in forests. Whereas forest-derived equations are available, equations for open-grown trees are not. Data from...

Propagation and stability of wavelike solutions of finite difference equations with variable coefficients

NASA Technical Reports Server (NTRS)

Giles, M. B.; Thompkins, W. T., Jr.

1985-01-01

The propagation and dissipation of wavelike solutions to finite difference equations is analyzed on the basis of an asymptotic approach in which a wave solution is expressed as a product of a complex amplitude and an oscillatory phase function whose frequency and wavenumber may also be complex. An asymptotic expansion leads to a local dispersion relation for wavenumber and frequency; the first-order terms produce an equation for the amplitude in which the local group velocity appears as the convection velocity of the amplitude. Equations for the motion of wavepackets and their interaction at boundaries are derived, and a global stability analysis is carried out.

Properties of the two-dimensional heterogeneous Lennard-Jones dimers: An integral equation study

PubMed Central

Urbic, Tomaz

2016-01-01

Structural and thermodynamic properties of a planar heterogeneous soft dumbbell fluid are examined using Monte Carlo simulations and integral equation theory. Lennard-Jones particles of different sizes are the building blocks of the dimers. The site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions and the thermodynamic properties. Obtained results are compared to Monte Carlo simulation data. The critical parameters for selected types of dimers were also estimated and the influence of the Lennard-Jones parameters was studied. We have also tested the correctness of the site-site integral equation theory using different closures. PMID:27875894

Comparison of Fully-Compressible Equation Sets for Atmospheric Dynamics

NASA Technical Reports Server (NTRS)

Ahmad, Nashat N.

2016-01-01

Traditionally, the equation for the conservation of energy used in atmospheric models is based on potential temperature and is used in place of the total energy conservation. This paper compares the application of the two equations sets for both the Euler and the Navier-Stokes solutions using several benchmark test cases. A high-resolution wave-propagation method which accurately takes into account the source term due to gravity is used for computing the non-hydrostatic atmospheric flows. It is demonstrated that there is little to no difference between the results obtained using the two different equation sets for Euler as well as Navier-Stokes solutions.

Application of viscous-inviscid interaction methods to transonic turbulent flows

NASA Technical Reports Server (NTRS)

Lee, D.; Pletcher, R. H.

1986-01-01

Two different viscous-inviscid interaction schemes were developed for the analysis of steady, turbulent, transonic, separated flows over axisymmetric bodies. The viscous and inviscid solutions are coupled through the displacement concept using a transpiration velocity approach. In the semi-inverse interaction scheme, the viscous and inviscid equations are solved in an explicitly separate manner and the displacement thickness distribution is iteratively updated by a simple coupling algorithm. In the simultaneous interaction method, local solutions of viscous and inviscid equations are treated simultaneously, and the displacement thickness is treated as an unknown and is obtained as a part of the solution through a global iteration procedure. The inviscid flow region is described by a direct finite-difference solution of a velocity potential equation in conservative form. The potential equation is solved on a numerically generated mesh by an approximate factorization (AF2) scheme in the semi-inverse interaction method and by a successive line overrelaxation (SLOR) scheme in the simultaneous interaction method. The boundary-layer equations are used for the viscous flow region. The continuity and momentum equations are solved inversely in a coupled manner using a fully implicit finite-difference scheme.

Dust acoustic solitary waves in a dusty plasma with two kinds of nonthermal ions at different temperatures

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

Dorranian, Davoud; Sabetkar, Akbar

The nonlinear dust acoustic solitary waves in a dusty plasma with two nonthermal ion species at different temperatures is studied analytically. Using reductive perturbation method, the Kadomtsev-Petviashivili (KP) equation is derived, and the effects of nonthermal coefficient, ions temperature, and ions number density on the amplitude and width of soliton in dusty plasma are investigated. It is shown that the amplitude of solitary wave of KP equation diverges at critical points of plasma parameters. The modified KP equation is also derived, and from there, the soliton like solutions of modified KP equation with finite amplitude is extracted. Results show thatmore » generation of rarefactive or compressive solitary waves strongly depends on the number and temperature of nonthermal ions. Results of KP equation confirm that for different magnitudes of ions temperature (mass) and number density, mostly compressive solitary waves are generated in a dusty plasma. In this case, the amplitude of solitary wave is decreased, while the width of solitary waves is increased. According to the results of modified KP equation for some certain magnitudes of parameters, there is a condition for generation of an evanescent solitary wave in a dusty plasma.« less

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

Discrete Painlevé equations for a class of PVI τ-functions given as U(N) averages

NASA Astrophysics Data System (ADS)

Forrester, P. J.; Witte, N. S.

2005-09-01

In a recent work, difference equations (Laguerre-Freud equations) for the bi-orthogonal polynomials and related quantities corresponding to the weight on the unit circle w(z)=\\prod^m_{j=1}(z-z_j(t))^{\\rho_j} were derived. It is shown here that in the case m = 3, these difference equations, when applied to the calculation of the underlying U(N) average, reduce to a coupled system identifiable with that obtained by Adler and van Moerbeke, using the methods of the Toeplitz lattice and Virasoro constraints. Moreover, it is shown that this coupled system can be reduced to yield the discrete fifth Painlevé equation dPV as it occurs in the theory of the sixth Painlevé system. Methods based on affine Weyl group symmetries of Bäcklund transformations have previously yielded the dPV equation, but with different parameters for the same problem. We find an explicit mapping between the two forms. Applications of our results are made to give recurrences for the gap probabilities and moments in the circular unitary ensemble of random matrices, and to the diagonal spin-spin correlation function of the square lattice Ising model.

Empirical improvements for estimating earthquake response spectra with random‐vibration theory

USGS Publications Warehouse

Boore, David; Thompson, Eric M.

2012-01-01

The stochastic method of ground‐motion simulation is often used in combination with the random‐vibration theory to directly compute ground‐motion intensity measures, thereby bypassing the more computationally intensive time‐domain simulations. Key to the application of random‐vibration theory to simulate response spectra is determining the duration (Drms) used in computing the root‐mean‐square oscillator response. Boore and Joyner (1984) originally proposed an equation for Drms , which was improved upon by Liu and Pezeshk (1999). Though these equations are both substantial improvements over using the duration of the ground‐motion excitation for Drms , we document systematic differences between the ground‐motion intensity measures derived from the random‐vibration and time‐domain methods for both of these Drms equations. These differences are generally less than 10% for most magnitudes, distances, and periods of engineering interest. Given the systematic nature of the differences, however, we feel that improved equations are warranted. We empirically derive new equations from time‐domain simulations for eastern and western North America seismological models. The new equations improve the random‐vibration simulations over a wide range of magnitudes, distances, and oscillator periods.

Numerical simulation of vortical ideal fluid flow through curved channel

NASA Astrophysics Data System (ADS)

Moshkin, N. P.; Mounnamprang, P.

2003-04-01

A numerical algorithm to study the boundary-value problem in which the governing equations are the steady Euler equations and the vorticity is given on the inflow parts of the domain boundary is developed. The Euler equations are implemented in terms of the stream function and vorticity. An irregular physical domain is transformed into a rectangle in the computational domain and the Euler equations are rewritten with respect to a curvilinear co-ordinate system. The convergence of the finite-difference equations to the exact solution is shown experimentally for the test problems by comparing the computational results with the exact solutions on the sequence of grids. To find the pressure from the known vorticity and stream function, the Euler equations are utilized in the Gromeka-Lamb form. The numerical algorithm is illustrated with several examples of steady flow through a two-dimensional channel with curved walls. The analysis of calculations shows strong dependence of the pressure field on the vorticity given at the inflow parts of the boundary. Plots of the flow structure and isobars, for different geometries of channel and for different values of vorticity on entrance, are also presented.

Test Bias: An Objective Definition for Test Items.

ERIC Educational Resources Information Center

Durovic, Jerry J.

A test bias definition, applicable at the item-level of a test is presented. The definition conceptually equates test bias with measuring different things in different groups, and operationally equates test bias with a difference in item fit to the Rasch Model, greater than one, between groups. It is suggested that the proposed definition avoids…

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

EPA Science Inventory

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic_¯¯parabolic (convection_¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

Evaluating morphometric body mass prediction equations with a juvenile human test sample: accuracy and applicability to small-bodied hominins.

PubMed

Walker, Christopher S; Yapuncich, Gabriel S; Sridhar, Shilpa; Cameron, Noël; Churchill, Steven E

2018-02-01

Body mass is an ecologically and biomechanically important variable in the study of hominin biology. Regression equations derived from recent human samples allow for the reasonable prediction of body mass of later, more human-like, and generally larger hominins from hip joint dimensions, but potential differences in hip biomechanics across hominin taxa render their use questionable with some earlier taxa (i.e., Australopithecus spp.). Morphometric prediction equations using stature and bi-iliac breadth avoid this problem, but their applicability to early hominins, some of which differ in both size and proportions from modern adult humans, has not been demonstrated. Here we use mean stature, bi-iliac breadth, and body mass from a global sample of human juveniles ranging in age from 6 to 12 years (n = 530 age- and sex-specific group annual means from 33 countries/regions) to evaluate the accuracy of several published morphometric prediction equations when applied to small humans. Though the body proportions of modern human juveniles likely differ from those of small-bodied early hominins, human juveniles (like fossil hominins) often differ in size and proportions from adult human reference samples and, accordingly, serve as a useful model for assessing the robustness of morphometric prediction equations. Morphometric equations based on adults systematically underpredict body mass in the youngest age groups and moderately overpredict body mass in the older groups, which fall in the body size range of adult Australopithecus (∼26-46 kg). Differences in body proportions, notably the ratio of lower limb length to stature, influence predictive accuracy. Ontogenetic changes in these body proportions likely influence the shift in prediction error (from under- to overprediction). However, because morphometric equations are reasonably accurate when applied to this juvenile test sample, we argue these equations may be used to predict body mass in small-bodied hominins, despite the potential for some error induced by differing body proportions and/or extrapolation beyond the original reference sample range. Copyright © 2017 Elsevier Ltd. All rights reserved.

Selection of site specific vibration equation by using analytic hierarchy process in a quarry

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

Kalayci, Ulku, E-mail: ukalayci@istanbul.edu.tr; Ozer, Umit, E-mail: uozer@istanbul.edu.tr

This paper presents a new approach for the selection of the most accurate SSVA (Site Specific Vibration Attenuation) equation for blasting processes in a quarry located near settlements in Istanbul, Turkey. In this context, the SSVA equations obtained from the same study area in the literature were considered in terms of distance between the shot points and buildings and the amount of explosive charge. In this purpose, 11 different SSVA equations obtained from the study area in the past 12 years, forecasting capabilities according to designated new conditions, using 102 vibration records as test data obtained from the study areamore » was investigated. In this study, AHP (Analytic Hierarchy Process) was selected as an analysis method in order to determine the most accurate equation among 11 SSAV equations, and the parameters such as year, distance, charge, and r{sup 2} of the equations were used as criteria for AHP. Finally, the most appropriate equation was selected among the existing ones, and the process of selecting according to different target criteria was presented. Furthermore, it was noted that the forecasting results of the selected equation is more accurate than that formed using the test results. - Highlights: • The optimum Site Specific Vibration Attenuation equation for blasting in a quarry located near settlements was determined. • It is indicated that SSVA equations changing over the years don’t give always accurate estimates at changing conditions. • Selection of the blast induced SSVA equation was made using AHP. • Equation selection method was highlighted based on parameters such as charge, distance, and quarry geometry changes (year).« less

Optimal Assignment Problem Applications of Finite Mathematics to Business and Economics. [and] Difference Equations with Applications. Applications of Difference Equations to Economics and Social Sciences. [and] Selected Applications of Mathematics to Finance and Investment. Applications of Elementary Algebra to Finance. [and] Force of Interest. Applications of Calculus to Finance. UMAP Units 317, 322, 381, 382.

ERIC Educational Resources Information Center

Gale, David; And Others

Four units make up the contents of this document. The first examines applications of finite mathematics to business and economies. The user is expected to learn the method of optimization in optimal assignment problems. The second module presents applications of difference equations to economics and social sciences, and shows how to: 1) interpret…

Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

NASA Technical Reports Server (NTRS)

Baumeiste, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Existence of entire solutions of some non-linear differential-difference equations.

PubMed

Chen, Minfeng; Gao, Zongsheng; Du, Yunfei

2017-01-01

In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are two non-zero polynomials, [Formula: see text] is a polynomial and [Formula: see text]. In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation [Formula: see text], where [Formula: see text], [Formula: see text] are two non-constant polynomials, [Formula: see text], m , n are positive integers and satisfy [Formula: see text] except for [Formula: see text], [Formula: see text].

Using data from colloid transport experiments to parameterize filtration model parameters for favorable conditions

NASA Astrophysics Data System (ADS)

Kamai, Tamir; Nassar, Mohamed K.; Nelson, Kirk E.; Ginn, Timothy R.

2017-04-01

Colloid filtration in porous media spans across many disciplines and includes scenarios such as in-situ bioremediation, colloid-facilitated transport, water treatment of suspended particles and pathogenic bacteria, and transport of natural and engineered nanoparticles in the environment. Transport and deposition of colloid particles in porous media are determined by a combination of complex processes and forces. Given the convoluted physical, chemical, and biological processes involved, and the complexity of porous media in natural settings, it should not come as surprise that colloid filtration theory does not always sufficiently predict colloidal transport, and that there is still a pressing need for improved predictive capabilities. Here, instead of developing the macroscopic equation from pore-scale models, we parametrize the different terms in the macroscopic collection equation through fitting it to experimental data, by optimizing the parameters in the different terms of the equation. This way we combine a mechanistically-based filtration-equation with empirical evidence. The impact of different properties of colloids and porous media are studied by comparing experimental properties with different terms of the correlation equation. This comparison enables insight about different processes that occur during colloid transport and retention under in porous media under favorable conditions, and provides directions for future theoretical developments.

Development of computational methods for unsteady aerodynamics at the NASA Langley Research Center

NASA Technical Reports Server (NTRS)

Yates, E. Carson, Jr.; Whitlow, Woodrow, Jr.

1987-01-01

The current scope, recent progress, and plans for research and development of computational methods for unsteady aerodynamics at the NASA Langley Research Center are reviewed. Both integral equations and finite difference methods for inviscid and viscous flows are discussed. Although the great bulk of the effort has focused on finite difference solution of the transonic small perturbation equation, the integral equation program is given primary emphasis here because it is less well known.

Development of computational methods for unsteady aerodynamics at the NASA Langley Research Center

NASA Technical Reports Server (NTRS)

Yates, E. Carson, Jr.; Whitlow, Woodrow, Jr.

1987-01-01

The current scope, recent progress, and plans for research and development of computational methods for unsteady aerodynamics at the NASA Langley Research Center are reviewed. Both integral-equations and finite-difference method for inviscid and viscous flows are discussed. Although the great bulk of the effort has focused on finite-difference solution of the transonic small-perturbation equation, the integral-equation program is given primary emphasis here because it is less well known.

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

NASA Technical Reports Server (NTRS)

Zhao, C. Y.; So, R. M. C.; Gatski, T. B.

2001-01-01

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

Kalman filters for assimilating near-surface observations into the Richards equation - Part 1: Retrieving state profiles with linear and nonlinear numerical schemes

NASA Astrophysics Data System (ADS)

Chirico, G. B.; Medina, H.; Romano, N.

2014-07-01

This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations into a one-dimensional Richards equation governing soil water flow in soil. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms in retrieving matric pressure head profiles when they are implemented with different numerical schemes of the Richards equation; (ii) to evaluate the performance of these algorithms when nonlinearities arise from the nonlinearity of the observation equation, i.e. when surface soil water content observations are assimilated to retrieve matric pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. Our first objective is achieved by implementing a Standard Kalman Filter (SKF) algorithm with both an explicit finite difference scheme (EX) and a Crank-Nicolson (CN) linear finite difference scheme of the Richards equation. The Unscented (UKF) and Ensemble Kalman Filters (EnKF) are applied to handle the nonlinearity of a backward Euler finite difference scheme. To accomplish the second objective, an analogous framework is applied, with the exception of replacing SKF with the Extended Kalman Filter (EKF) in combination with a CN numerical scheme, so as to handle the nonlinearity of the observation equation. While the EX scheme is computationally too inefficient to be implemented in an operational assimilation scheme, the retrieval algorithm implemented with a CN scheme is found to be computationally more feasible and accurate than those implemented with the backward Euler scheme, at least for the examined one-dimensional problem. The UKF appears to be as feasible as the EnKF when one has to handle nonlinear numerical schemes or additional nonlinearities arising from the observation equation, at least for systems of small dimensionality as the one examined in this study.

Comparison of finite-difference schemes for analysis of shells of revolution. [stress and free vibration analysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

On one solution of Volterra integral equations of second kind

NASA Astrophysics Data System (ADS)

Myrhorod, V.; Hvozdeva, I.

2016-10-01

A solution of Volterra integral equations of the second kind with separable and difference kernels based on solutions of corresponding equations linking the kernel and resolvent is suggested. On the basis of a discrete functions class, the equations linking the kernel and resolvent are obtained and the methods of their analytical solutions are proposed. A mathematical model of the gas-turbine engine state modification processes in the form of Volterra integral equation of the second kind with separable kernel is offered.

Solitons of the Kadomtsev-Petviashvili equation based on lattice Boltzmann model

NASA Astrophysics Data System (ADS)

Wang, Huimin

2017-01-01

In this paper, a lattice Boltzmann model for the Kadomtsev-Petviashvili equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales are obtained. Due to the asymmetry in x direction and y direction of the equation, the moments of the equilibrium distribution function are selected are asymmetric. The numerical results demonstrate the lattice Boltzmann method is an effective method to simulate the solitons of the Kadomtsev-Petviashvili equation.

Automatic computation and solution of generalized harmonic balance equations

NASA Astrophysics Data System (ADS)

Peyton Jones, J. C.; Yaser, K. S. A.; Stevenson, J.

2018-02-01

Generalized methods are presented for generating and solving the harmonic balance equations for a broad class of nonlinear differential or difference equations and for a general set of harmonics chosen by the user. In particular, a new algorithm for automatically generating the Jacobian of the balance equations enables efficient solution of these equations using continuation methods. Efficient numeric validation techniques are also presented, and the combined algorithm is applied to the analysis of dc, fundamental, second and third harmonic response of a nonlinear automotive damper.

The State-of-the-Art Parabolic Equation Approximation as Applied to Underwater Acoustic Propagation with Discussions on Intensive Computations: An Invited Paper Presented at the Meeting of the Acoustical Society of America (108th) Held in Minneapolis, Minnesota on 8-12 October 1984

DTIC Science & Technology

1984-10-12

MCYwWWm M& de4 l 8.id iW d by N1wk "wt Finite Difference Reference Wavenumber Interface Split-Step Ordinary Difference Equation Wide Angle Parabolic...Problems D. Lee and S. Praiser J. Comp. & Math. with Appls., 7(2), pp. 195-202 (1981) Finite - Difference Solution to the Parabolic Wave Equation D. Lee, G...was incorporated into the ODE and finite difference models. At that time, we did not have a better implementation of the ODE solution, but we

Prediction equation of resting energy expenditure in an adult Spanish population of obese adult population.

PubMed

de Luis, D A; Aller, R; Izaola, O; Romero, E

2006-01-01

The aim of our study was to evaluate the accuracy of the equations to estimate REE in obese patents and develop a new equation in our obese population. A population of 200 obesity outpatients was analyzed in a prospective way. The following variables were specifically recorded: age, weight, body mass index (BMI), waist circumference, and waist-to-hip ratio. Basal glucose, insulin, and TSH (thyroid-stimulating hormone) were measured. An indirect calorimetry and a tetrapolar electrical bioimpedance were performed. REE measured by indirect calorimetry was compared with REE obtained by prediction equations to obese or nonobese patients. The mean age was 44.8 +/- 16.81 years and the mean BMI 34.4 +/- 5.3. Indirect calorimetry showed that, as compared to women, men had higher resting energy expenditure (REE) (1,998.1 +/- 432 vs. 1,663.9 +/- 349 kcal/day; p < 0.05) and oxygen consumption (284.6 +/- 67.7 vs. 238.6 +/- 54.3 ml/min; p < 0.05). Correlation analysis among REE obtained by indirect calorimetry and REE predicted by prediction equations showed the next data; Berstein's equation (r = 0.65; p < 0.05), Harris Benedict's equation (r = 0.58; p < 0.05), Owen's equation (r = 0.56; p < 0.05), Ireton's equation (r = 0.58; p < 0.05) and WHO's equation (r = 0.57; p < 0.05). Both the Berstein's and the Ireton's equations overpredicted REE and showed nonsignificant mean differences form measured REE. The Owen's, WHO's, and Harris Benedict's equations underpredicted REE. Our male prediction equation was REE = 58.6 + (6.1 x weight (kg)) + (1,023.7 x height (m)) - (9.5 x age). The female model was REE = 1,272.5 + (9.8 x weight (kg)) - (61.6 x height (m)) - (8.2 x age). Our prediction equations showed a nonsignificant difference with REE measured (-3.7 kcal/day) with a significant correlation coefficient (r = 0.67; p < 0.05). Previously developed prediction equations overestimated and underestimated REE measured. WHO equation developed in normal weight individuals provided the closest values. The two new equations (male and female equations) developed in our study had a good accuracy. Copyright 2006 S. Karger AG, Basel.

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations.

PubMed

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, R e . Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

Numerical simulation of KdV equation by finite difference method

NASA Astrophysics Data System (ADS)

Yokus, A.; Bulut, H.

2018-05-01

In this study, the numerical solutions to the KdV equation with dual power nonlinearity by using the finite difference method are obtained. Discretize equation is presented in the form of finite difference operators. The numerical solutions are secured via the analytical solution to the KdV equation with dual power nonlinearity which is present in the literature. Through the Fourier-Von Neumann technique and linear stable, we have seen that the FDM is stable. Accuracy of the method is analyzed via the L2 and L_{∞} norm errors. The numerical, exact approximations and absolute error are presented in tables. We compare the numerical solutions with the exact solutions and this comparison is supported with the graphic plots. Under the choice of suitable values of parameters, the 2D and 3D surfaces for the used analytical solution are plotted.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, Re. Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

Gravitational Agglomeration of Post-HCDA LMFBR Nonspherical Aerosols.

DTIC Science & Technology

1980-12-01

equations for two particle motions are developed . A computer program NGCEFF is constructed., the Navier-Stokes equation is solved by the finite difference...dynamic equations for two particle motions are developed . A computer program NGCEFF I is constructed, the Navier-Stokes equation is solved by the...spatial inhomogeneities for the aerosol. Thus, following an HCDA, an aerosol mixture of sodium compounds, fuel and core structural materials will

Development of a well-behaved site index equation: jack pine in north central Ontario

Treesearch

J. C. G. Goelz; T. E. Burke

1992-01-01

A base-age invariant site index equation for jack pine based on the Chapman-Richards function was produced that satisfied nine criteria of preferred behavior for site index equations. A difference form of the Chapman-Richards equation produced the best behavior; height equaled site index at base age, and the shape of the curves reflected the data. The data structure...

The Use of Two Anchors in Nonequivalent Groups with Anchor Test (NEAT) Equating. Research Report. ETS RR-10-23

ERIC Educational Resources Information Center

Moses, Tim; Deng, Weiling; Zhang, Yu-Li

2010-01-01

In the equating literature, a recurring concern is that equating functions that utilize a single anchor to account for examinee groups' nonequivalence are biased when the groups are extremely different and/or when the anchor only weakly measures what the tests measure. Several proposals have been made to address this equating bias by incorporating…

The Impact of Test Dimensionality, Common-Item Set Format, and Scale Linking Methods on Mixed-Format Test Equating

ERIC Educational Resources Information Center

Öztürk-Gübes, Nese; Kelecioglu, Hülya

2016-01-01

The purpose of this study was to examine the impact of dimensionality, common-item set format, and different scale linking methods on preserving equity property with mixed-format test equating. Item response theory (IRT) true-score equating (TSE) and IRT observed-score equating (OSE) methods were used under common-item nonequivalent groups design.…

Improving North American forest biomass estimates from literature synthesis and meta-analysis of existing biomass equations

Treesearch

David C. Chojnacky; Jennifer C. Jenkins; Amanda K. Holland

2009-01-01

Thousands of published equations purport to estimate biomass of individual trees. These equations are often based on very small samples, however, and can provide widely different estimates for trees of the same species. We addressed this issue in a previous study by devising 10 new equations that estimated total aboveground biomass for all species in North America (...

Finite Difference Schemes as Algebraic Correspondences between Layers

NASA Astrophysics Data System (ADS)

Malykh, Mikhail; Sevastianov, Leonid

2018-02-01

For some differential equations, especially for Riccati equation, new finite difference schemes are suggested. These schemes define protective correspondences between the layers. Calculation using these schemes can be extended to the area beyond movable singularities of exact solution without any error accumulation.

Evaluation of infiltration models in contaminated landscape.

PubMed

Sadegh Zadeh, Kouroush; Shirmohammadi, Adel; Montas, Hubert J; Felton, Gary

2007-06-01

The infiltration models of Kostiakov, Green-Ampt, and Philip (two and three terms equations) were used, calibrated, and evaluated to simulate in-situ infiltration in nine different soil types. The Osborne-Moré modified version of the Levenberg-Marquardt optimization algorithm was coupled with the experimental data obtained by the double ring infiltrometers and the infiltration equations, to estimate the model parameters. Comparison of the model outputs with the experimental data indicates that the models can successfully describe cumulative infiltration in different soil types. However, since Kostiakov's equation fails to accurately simulate the infiltration rate as time approaches infinity, Philip's two-term equation, in some cases, produces negative values for the saturated hydraulic conductivity of soils, and the Green-Ampt model uses piston flow assumptions, we suggest using Philip's three-term equation to simulate infiltration and to estimate the saturated hydraulic conductivity of soils.

On the interpretations of Langevin stochastic equation in different coordinate systems

NASA Astrophysics Data System (ADS)

Martínez, E.; López-Díaz, L.; Torres, L.; Alejos, O.

2004-01-01

The stochastic Langevin Landau-Lifshitz equation is usually utilized in micromagnetics formalism to account for thermal effects. Commonly, two different interpretations of the stochastic integrals can be made: Ito and Stratonovich. In this work, the Langevin-Landau-Lifshitz (LLL) equation is written in both Cartesian and Spherical coordinates. If Spherical coordinates are employed, the noise is additive, and therefore, Ito and Stratonovich solutions are equal. This is not the case when (LLL) equation is written in Cartesian coordinates. In this case, the Langevin equation must be interpreted in the Stratonovich sense in order to reproduce correct statistical results. Nevertheless, the statistics of the numerical results obtained from Euler-Ito and Euler-Stratonovich schemes are equivalent due to the additional numerical constraint imposed in Cartesian system after each time step, which itself assures that the magnitude of the magnetization is preserved.

The Liouville equation for flavour evolution of neutrinos and neutrino wave packets

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

Hansen, Rasmus Sloth Lundkvist; Smirnov, Alexei Yu., E-mail: rasmus@mpi-hd.mpg.de, E-mail: smirnov@mpi-hd.mpg.de

We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of momentum changing collisions, the LE can be reduced to a single derivative equation over amore » trajectory coordinate. Additional time and spatial dependence may stem from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.« less

Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

A general method to determine the stability of compressible flows

NASA Technical Reports Server (NTRS)

Guenther, R. A.; Chang, I. D.

1982-01-01

Several problems were studied using two completely different approaches. The initial method was to use the standard linearized perturbation theory by finding the value of the individual small disturbance quantities based on the equations of motion. These were serially eliminated from the equations of motion to derive a single equation that governs the stability of fluid dynamic system. These equations could not be reduced unless the steady state variable depends only on one coordinate. The stability equation based on one dependent variable was found and was examined to determine the stability of a compressible swirling jet. The second method applied a Lagrangian approach to the problem. Since the equations developed were based on different assumptions, the condition of stability was compared only for the Rayleigh problem of a swirling flow, both examples reduce to the Rayleigh criterion. This technique allows including the viscous shear terms which is not possible in the first method. The same problem was then examined to see what effect shear has on stability.

Lax representations for matrix short pulse equations

NASA Astrophysics Data System (ADS)

Popowicz, Z.

2017-10-01

The Lax representation for different matrix generalizations of Short Pulse Equations (SPEs) is considered. The four-dimensional Lax representations of four-component Matsuno, Feng, and Dimakis-Müller-Hoissen-Matsuno equations are obtained. The four-component Feng system is defined by generalization of the two-dimensional Lax representation to the four-component case. This system reduces to the original Feng equation, to the two-component Matsuno equation, or to the Yao-Zang equation. The three-component version of the Feng equation is presented. The four-component version of the Matsuno equation with its Lax representation is given. This equation reduces the new two-component Feng system. The two-component Dimakis-Müller-Hoissen-Matsuno equations are generalized to the four-parameter family of the four-component SPE. The bi-Hamiltonian structure of this generalization, for special values of parameters, is defined. This four-component SPE in special cases reduces to the new two-component SPE.

Structural Equation Modeling of Group Differences in CES-D Ratings of Native Hawaiian and Non-Hawaiian High School Students.

ERIC Educational Resources Information Center

McArdle, John J.; Johnson, Ronald C.; Hishinuma, Earl S.; Miyamoto, Robin H.; Andrade, Naleen N.

2001-01-01

Analyzes differences in self-reported Center for Epidemiologic Studies Depression inventory results among ethnic Hawaiian and non-Hawaiian high school students, using different forms of latent variable structural equation models. Finds a high degree of invariance between students on depression. Discusses issues about common features and…

Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation

ERIC Educational Resources Information Center

Prentice, J. S. C.

2012-01-01

An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Approach to the origin of turbulence on the basis of two-point kinetic theory

NASA Technical Reports Server (NTRS)

Tsuge, S.

1974-01-01

Equations for the fluctuation correlation in an incompressible shear flow are derived on the basis of kinetic theory, utilizing the two-point distribution function which obeys the BBGKY hierarchy equation truncated with the hypothesis of 'ternary' molecular chaos. The step from the molecular to the hydrodynamic description is accomplished by a moment expansion which is a two-point version of the thirteen-moment method, and which leads to a series of correlation equations, viz., the two-point counterparts of the continuity equation, the Navier-Stokes equation, etc. For almost parallel shearing flows the two-point equation is separable and reduces to two Orr-Sommerfeld equations with different physical implications.

CALL FOR PAPERS: Special issue on Symmetries and Integrability of Difference Equations

NASA Astrophysics Data System (ADS)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stephane

2006-10-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Special issue on Symmetries and Integrability of Difference Equations' as featured at the SIDE VII meeting held during July 2006 in Melbourne (http://web.maths.unsw.edu.au/%7Eschief/side/side.html). Participants at that meeting, as well as other researchers working in the field of difference equations and discrete systems, are invited to submit a research paper to this issue. This meeting was the seventh of a series of biennial meetings devoted to the study of integrable difference equations and related topics. The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations, just as differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as: mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, quantum field theory, etc. It is thus crucial to develop tools to study and solve difference equations. While the theory of symmetry and integrability for differential equations is now well-established, this is not yet the case for discrete equations. The situation has undergone impressive development in recent years and has affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups, symmetries of difference equations, discrete (difference) geometry, etc. Consequently, the aim of the special issue is to benefit from the occasion offered by the SIDE VII meeting to provide a collection of papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. Scope of the special issue The special issue will feature papers which deal with themes that were covered by the SIDE VII Conference. These are •Integrability testing •Discrete geometry and visualization •Laurent phenomena and cluster algebras •Ultra-discrete systems •Random matrix theory •Algebraic-geometric approaches to integrability •Yang-Baxter equations •Quantum and classical integrable systems •Difference Galois theory Editorial policy •The subject of the paper should relate to the subject of the meeting. The Guest Editors will reserve the right to judge whether a contribution fits the scope of the topic of the special issue. •Contributions will be refereed and processed according to the usual procedure of the journal. •Conference papers may be based on already published work but should either •contain significant additional new results and/or insights or •give a survey of the present state of the art, a critical assessment of the present understanding of a topic, and a discussion of open problems. •Papers submitted by non-participants should be original and contain substantial new results. Guidelines for preparation of contributions • The deadline for contributed papers will be 15 January 2007. •There is a page limit of 16 printed pages (approximately 9600 words) per contribution. For submitted papers exceeding this length the Guest Editors reserve the right to request a reduction in length. Further advice on document preparation can be found at www.iop.org/Journals/jphysa •Contributions to the special issue should if possible be submitted electronically by web upload at www.iop.org/Journals/jphysa, or by email to jphysa@iop.org, quoting 'J. Phys. A Special Issue: SIDE VII'. Submissions should ideally be in standard LaTeX form; we are, however, able to accept most formats including Microsoft Word. Please see the website for further information on electronic submissions. •Authors unable to submit electronically may send hard-copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing electronic code on floppy disk if available and quoting 'J. Phys. A Special Issue: SIDE VII'. • All contributions should be accompanied by a read-me file or covering letter giving the postal and email address for correspondence. The Publishing Office should be notified of any subsequent change of address. •The special issue will be published in the paper and online version of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue.

Properties of finite difference models of non-linear conservative oscillators

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1988-01-01

Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.

The Davey-Stewartson Equation on the Half-Plane

NASA Astrophysics Data System (ADS)

Fokas, A. S.

2009-08-01

The Davey-Stewartson (DS) equation is a nonlinear integrable evolution equation in two spatial dimensions. It provides a multidimensional generalisation of the celebrated nonlinear Schrödinger (NLS) equation and it appears in several physical situations. The implementation of the Inverse Scattering Transform (IST) to the solution of the initial-value problem of the NLS was presented in 1972, whereas the analogous problem for the DS equation was solved in 1983. These results are based on the formulation and solution of certain classical problems in complex analysis, namely of a Riemann Hilbert problem (RH) and of either a d-bar or a non-local RH problem respectively. A method for solving the mathematically more complicated but physically more relevant case of boundary-value problems for evolution equations in one spatial dimension, like the NLS, was finally presented in 1997, after interjecting several novel ideas to the panoply of the IST methodology. Here, this method is further extended so that it can be applied to evolution equations in two spatial dimensions, like the DS equation. This novel extension involves several new steps, including the formulation of a d-bar problem for a sectionally non-analytic function, i.e. for a function which has different non-analytic representations in different domains of the complex plane. This, in addition to the computation of a d-bar derivative, also requires the computation of the relevant jumps across the different domains. This latter step has certain similarities (but is more complicated) with the corresponding step for those initial-value problems in two dimensions which can be solved via a non-local RH problem, like KPI.

Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes

NASA Astrophysics Data System (ADS)

Kyriakopoulos, Charalampos; Grossmann, Gerrit; Wolf, Verena; Bortolussi, Luca

2018-01-01

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree kmax of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large kmax. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.

Macroscopic descriptions of rarefied gases from the elimination of fast variables

NASA Astrophysics Data System (ADS)

Dellar, Paul J.

2007-10-01

The Boltzmann equation describing a dilute monatomic gas is equivalent to an infinite hierarchy of evolution equations for successive moments of the distribution function. The five moments giving the macroscopic mass, momentum, and energy densities are unaffected by collisions between atoms, while all other moments naturally evolve on a fast collisional time scale. We show that the macroscopic equations of Chen, Rao, and Spiegel [Phys. Lett. A 271, 87 (2000)], like the familiar Navier-Stokes-Fourier equations, emerge from using a systematic procedure to eliminate the higher moments, leaving closed evolution equations for the five moments unaffected by collisions. The two equation sets differ through their treatment of contributions from the temperature to the momentum and energy fluxes. Using moment equations offers a definitive treatment of the Prandtl number problem using model collision operators, greatly reduces the labor of deriving equations for different collision operators, and clarifies the role of solvability conditions applied to the distribution function. The original Chen-Rao-Spiegel approach offers greatly improved agreement with experiments for the phase speed of ultrasound, but when corrected to match the Navier-Stokes-Fourier equations at low frequencies, it then underestimates the phase speed at high frequencies. Our introduction of a translational temperature, as in the kinetic theory of polyatomic gases, motivates a distinction in the energy flux between advection of internal energy and the work done by the pressure. Exploiting this distinction yields macroscopic equations that offer further improvement in agreement with experimental data, and arise more naturally as an approximation to the infinite hierarchy of evolution equations for moments.

Turbulent fluid motion 2: Scalars, vectors, and tensors

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1991-01-01

The author shows that the sum or difference of two vectors is a vector. Similarly the sum of any two tensors of the same order is a tensor of that order. No meaning is attached to the sum of tensors of different orders, say u(sub i) + u(sub ij); that is not a tensor. In general, an equation containing tensors has meaning only if all the terms in the equation are tensors of the same order, and if the same unrepeated subscripts appear in all the terms. These facts will be used in obtaining appropriate equations for fluid turbulence. With the foregoing background, the derivation of appropriate continuum equations for turbulence should be straightforward.

FDM study of ion exchange diffusion equation in glass

NASA Astrophysics Data System (ADS)

Zhou, Zigang; Yang, Yongjia; Wang, Qiang; Sun, Guangchun

2009-05-01

Ion-exchange technique in glass was developed to fabricate gradient refractive index optical devices. In this paper, the Finite Difference Method(FDM), which is used for the solution of ion-diffusion equation, is reported. This method transforms continual diffusion equation to separate difference equation. It unitizes the matrix of MATLAB program to solve the iteration process. The collation results under square boundary condition show that it gets a more accurate numerical solution. Compared to experiment data, the relative error is less than 0.2%. Furthermore, it has simply operation and kinds of output solutions. This method can provide better results for border-proliferation of the hexagonal and the channel devices too.

Modulational Instability of Cylindrical and Spherical NLS Equations. Statistical Approach

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

Grecu, A. T.; Grecu, D.; Visinescu, Anca

2010-01-21

The modulational (Benjamin-Feir) instability for cylindrical and spherical NLS equations (c/s NLS equations) is studied using a statistical approach (SAMI). A kinetic equation for a two-point correlation function is written and analyzed using the Wigner-Moyal transform. The linear stability of the Fourier transform of the two-point correlation function is studied and an implicit integral form for the dispersion relation is found. This is solved for different expressions of the initial spectrum (delta-spectrum, Lorentzian, Gaussian), and in the case of a Lorentzian spectrum the total growth of the instability is calculated. The similarities and differences with the usual one-dimensional NLS equationmore » are emphasized.« less

Ability of commonly used prediction equations to predict resting energy expenditure in children with inflammatory bowel disease.

PubMed

Hill, Rebecca J; Lewindon, Peter J; Withers, Geoffrey D; Connor, Frances L; Ee, Looi C; Cleghorn, Geoffrey J; Davies, Peter S W

2011-07-01

Paediatric onset inflammatory bowel disease (IBD) may cause alterations in energy requirements and invalidate the use of standard prediction equations. Our aim was to evaluate four commonly used prediction equations for resting energy expenditure (REE) in children with IBD. Sixty-three children had repeated measurements of REE as part of a longitudinal research study yielding a total of 243 measurements. These were compared with predicted REE from Schofield, Oxford, FAO/WHO/UNU, and Harris-Benedict equations using the Bland-Altman method. Mean (±SD) age of the patients was 14.2 (2.4) years. Mean measured REE was 1566 (336) kcal per day compared with 1491 (236), 1441 (255), 1481 (232), and 1435 (212) kcal per day calculated from Schofield, Oxford, FAO/WHO/UNU, and Harris-Benedict, respectively. While the Schofield equation demonstrated the least difference between measured and predicted REE, it, along with the other equations tested, did not perform uniformly across all subjects, indicating greater errors at either end of the spectrum of energy expenditure. Smaller differences were found for all prediction equations for Crohn's disease compared with ulcerative colitis. Of the commonly used equations, the equation of Schofield should be used in pediatric patients with IBD when measured values are not able to be obtained. Copyright © 2010 Crohn's & Colitis Foundation of America, Inc.

Numberical Solution to Transient Heat Flow Problems

ERIC Educational Resources Information Center

Kobiske, Ronald A.; Hock, Jeffrey L.

1973-01-01

Discusses the reduction of the one- and three-dimensional diffusion equation to the difference equation and its stability, convergence, and heat-flow applications under different boundary conditions. Indicates the usefulness of this presentation for beginning students of physics and engineering as well as college teachers. (CC)

Modeling animal movements using stochastic differential equations

Treesearch

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...

Structural Equation Modeling of Multivariate Time Series

ERIC Educational Resources Information Center

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…

The Complex-Step-Finite-Difference method

NASA Astrophysics Data System (ADS)

Abreu, Rafael; Stich, Daniel; Morales, Jose

2015-07-01

We introduce the Complex-Step-Finite-Difference method (CSFDM) as a generalization of the well-known Finite-Difference method (FDM) for solving the acoustic and elastic wave equations. We have found a direct relationship between modelling the second-order wave equation by the FDM and the first-order wave equation by the CSFDM in 1-D, 2-D and 3-D acoustic media. We present the numerical methodology in order to apply the introduced CSFDM and show an example for wave propagation in simple homogeneous and heterogeneous models. The CSFDM may be implemented as an extension into pre-existing numerical techniques in order to obtain fourth- or sixth-order accurate results with compact three time-level stencils. We compare advantages of imposing various types of initial motion conditions of the CSFDM and demonstrate its higher-order accuracy under the same computational cost and dispersion-dissipation properties. The introduced method can be naturally extended to solve different partial differential equations arising in other fields of science and engineering.

A comparison of turbulence models in computing multi-element airfoil flows

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.; Menter, Florian; Durbin, Paul A.; Mansour, Nagi N.

1994-01-01

Four different turbulence models are used to compute the flow over a three-element airfoil configuration. These models are the one-equation Baldwin-Barth model, the one-equation Spalart-Allmaras model, a two-equation k-omega model, and a new one-equation Durbin-Mansour model. The flow is computed using the INS2D two-dimensional incompressible Navier-Stokes solver. An overset Chimera grid approach is utilized. Grid resolution tests are presented, and manual solution-adaptation of the grid was performed. The performance of each of the models is evaluated for test cases involving different angles-of-attack, Reynolds numbers, and flap riggings. The resulting surface pressure coefficients, skin friction, velocity profiles, and lift, drag, and moment coefficients are compared with experimental data. The models produce very similar results in most cases. Excellent agreement between computational and experimental surface pressures was observed, but only moderately good agreement was seen in the velocity profile data. In general, the difference between the predictions of the different models was less than the difference between the computational and experimental data.

Use of digital land-cover data from the Landsat satellite in estimating streamflow characteristics in the Cumberland Plateau of Tennessee

USGS Publications Warehouse

Hollyday, E.F.; Hansen, G.R.

1983-01-01

Streamflow may be estimated with regression equations that relate streamflow characteristics to characteristics of the drainage basin. A statistical experiment was performed to compare the accuracy of equations using basin characteristics derived from maps and climatological records (control group equations) with the accuracy of equations using basin characteristics derived from Landsat data as well as maps and climatological records (experimental group equations). Results show that when the equations in both groups are arranged into six flow categories, there is no substantial difference in accuracy between control group equations and experimental group equations for this particular site where drainage area accounts for more than 90 percent of the variance in all streamflow characteristics (except low flows and most annual peak logarithms). (USGS)

Equating Two Forms of a Criterion-Referenced Test by Using Norm Referenced Data: An Illustration of Two Methods.

ERIC Educational Resources Information Center

Garcia-Quintana, Roan A.; Johnson, Lynne M.

Three different computational procedures for equating two forms of a test were applied to a pair of mathematics tests to compare the results of the three procedures. The tests that were being equated were two forms of the SRA Mastery Mathematics Tests. The common, linking test used for equating was the Comprehensive Tests of Basic Skills, Form S,…

On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations.

PubMed

Edelman, Mark

2015-07-01

In this paper, we consider a simple general form of a deterministic system with power-law memory whose state can be described by one variable and evolution by a generating function. A new value of the system's variable is a total (a convolution) of the generating functions of all previous values of the variable with weights, which are powers of the time passed. In discrete cases, these systems can be described by difference equations in which a fractional difference on the left hand side is equal to a total (also a convolution) of the generating functions of all previous values of the system's variable with the fractional Eulerian number weights on the right hand side. In the continuous limit, the considered systems can be described by the Grünvald-Letnikov fractional differential equations, which are equivalent to the Volterra integral equations of the second kind. New properties of the fractional Eulerian numbers and possible applications of the results are discussed.

Computation of steady and unsteady quasi-one-dimensional viscous/inviscid interacting internal flows at subsonic, transonic, and supersonic Mach numbers

NASA Technical Reports Server (NTRS)

Swafford, Timothy W.; Huddleston, David H.; Busby, Judy A.; Chesser, B. Lawrence

1992-01-01

Computations of viscous-inviscid interacting internal flowfields are presented for steady and unsteady quasi-one-dimensional (Q1D) test cases. The unsteady Q1D Euler equations are coupled with integral boundary-layer equations for unsteady, two-dimensional (planar or axisymmetric), turbulent flow over impermeable, adiabatic walls. The coupling methodology differs from that used in most techniques reported previously in that the above mentioned equation sets are written as a complete system and solved simultaneously; that is, the coupling is carried out directly through the equations as opposed to coupling the solutions of the different equation sets. Solutions to the coupled system of equations are obtained using both explicit and implicit numerical schemes for steady subsonic, steady transonic, and both steady and unsteady supersonic internal flowfields. Computed solutions are compared with measurements as well as Navier-Stokes and inverse boundary-layer methods. An analysis of the eigenvalues of the coefficient matrix associated with the quasi-linear form of the coupled system of equations indicates the presence of complex eigenvalues for certain flow conditions. It is concluded that although reasonable solutions can be obtained numerically, these complex eigenvalues contribute to the overall difficulty in obtaining numerical solutions to the coupled system of equations.

Code Development of Three-Dimensional General Relativistic Hydrodynamics with AMR (Adaptive-Mesh Refinement) and Results from Special and General Relativistic Hydrodynamics

NASA Astrophysics Data System (ADS)

Dönmez, Orhan

2004-09-01

In this paper, the general procedure to solve the general relativistic hydrodynamical (GRH) equations with adaptive-mesh refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of GRH equations are obtained by high resolution shock Capturing schemes (HRSC), specifically designed to solve nonlinear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second-order convergence of the code in one, two and three dimensions. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the GRH equations are tested using two different test problems which are Geodesic flow and Circular motion of particle In order to do this, the flux part of GRH equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time.

Evaluation of various equations for estimating renal function in elderly Chinese patients with type 2 diabetes mellitus

PubMed Central

Guo, Mei; Niu, Jian-Ying; Ye, Xian-Wu; Han, Xiao-Jie; Zha, Ying; Hong, Yang; Fang, Hong; Gu, Yong

2017-01-01

Background The clinical assessment of kidney function based on the estimated glomerular filtration rate (GFR) in older patients remains controversial. This study evaluated the concordance and feasibility of using various creatinine-based equations for estimating GFR in elderly Chinese patients with type 2 diabetes mellitus (T2DM). Methods A cross-sectional analytical study was conducted in 21,723 older diabetic patients (≥60 years) based on electronic health records (EHR) for Minhang District, Shanghai, China. The concordance of chronic kidney disease (CKD) classification among different creatinine-based equations was assessed based on Kappa values, intraclass correlation coefficient (ICC) statistics, and the eGFR agreement between the equations was tested using Bland–Altman plots. The GFR was estimated using the Cockcroft–Gault (CG), Berlin Initiative Study 1 (BIS1), simplified Modification of Diet in Renal Disease (MDRD), MDRD modified for Chinese populations (mMDRD), chronic kidney disease epidemiology collaboration (CKD-EPI), CKD-EPI in Asians (CKD-EPI-Asia), and Ruijin equations. Results Overall, the proportion of CKD stages 3–5 (eGFR <60 mL/min/1.73 m2) was calculated as 28.9%, 39.1%, 11.8%, 8.4%, 14.3%, 11.5%, and 12.7% by the eGFRCG, eGFRBIS1, eGFRMDRD, eGFRmMDRD, eGFRCKD-EPI, eGFRCKD-EPI-Asia, and eGFRRuijin equations, respectively. The concordance of albuminuria and decreased eGFR based on the different equations was poor by both the Kappa (<0.2) and ICC (<0.4) statistics. The CKD-EPI-Asia equation resulted in excellent concordance with the CKD-EPI (ICC =0.931), MDRD (ICC =0.963), mMDRD (ICC =0.892), and Ruijin (ICC =0.956) equations for the classification of CKD stages, whereas the BIS1 equation exhibited good concordance with the CG equation (ICC =0.809). In addition, significant differences were observed for CKD stage 1 among all these equations. Conclusion Accurate GFR values are difficult to estimate using creatinine-based equations in older diabetic patients. Kidney function is complex, and the staff need to be aware of the individualized consideration of other risk factors or markers of reduced renal function in clinical practice. PMID:29070944

Iontophoretic transdermal drug delivery: a multi-layered approach.

PubMed

Pontrelli, Giuseppe; Lauricella, Marco; Ferreira, José A; Pena, Gonçalo

2017-12-11

We present a multi-layer mathematical model to describe the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describes the basic convection-diffusion process, with the electric potential obtained by solving the Laplace's equation. These equations are complemented with suitable interface and boundary conditions in a multi-domain. The stability of the mathematical problem is discussed in different scenarios and a finite-difference method is used to solve the coupled system. Numerical experiments are included to illustrate the drug dynamics under different conditions. © The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Veneva, Milena; Ayriyan, Alexander

2018-04-01

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed - diagonal dominantization and symbolic algorithms.

Flux vector splitting of the inviscid equations with application to finite difference methods

NASA Technical Reports Server (NTRS)

Steger, J. L.; Warming, R. F.

1979-01-01

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

PubMed

Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

2013-09-01

Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

Applying different equations to evaluate the level of mismatch between students and school furniture.

PubMed

Castellucci, H I; Arezes, P M; Molenbroek, J F M

2014-07-01

The mismatch between students and school furniture is likely to result in a number of negative effects, such as uncomfortable body posture, pain, and ultimately, it may also affect the learning process. This study's main aim is to review the literature describing the criteria equations for defining the mismatch between students and school furniture, to apply these equations to a specific sample and, based on the results, to propose a methodology to evaluate school furniture suitability. The literature review comprises one publications database, which was used to identify the studies carried out in the field of the abovementioned mismatch. The sample used for testing the different equations was composed of 2261 volunteer subjects from 14 schools. Fifteen studies were found to meet the criteria of this review and 21 equations to test 6 furniture dimensions were identified. Regarding seat height, there are considerable differences between the two most frequently used equations. Although seat to desk clearance was evaluated by knee height, this condition seems to be based on the false assumption that students are sitting on a chair with a proper seat height. Finally, the proposed methodology for suitability evaluation of school furniture should allow for a more reliable analysis of school furniture. Copyright © 2014 Elsevier Ltd and The Ergonomics Society. All rights reserved.

Examining Potential Boundary Bias Effects in Kernel Smoothing on Equating: An Introduction for the Adaptive and Epanechnikov Kernels.

PubMed

Cid, Jaime A; von Davier, Alina A

2015-05-01

Test equating is a method of making the test scores from different test forms of the same assessment comparable. In the equating process, an important step involves continuizing the discrete score distributions. In traditional observed-score equating, this step is achieved using linear interpolation (or an unscaled uniform kernel). In the kernel equating (KE) process, this continuization process involves Gaussian kernel smoothing. It has been suggested that the choice of bandwidth in kernel smoothing controls the trade-off between variance and bias. In the literature on estimating density functions using kernels, it has also been suggested that the weight of the kernel depends on the sample size, and therefore, the resulting continuous distribution exhibits bias at the endpoints, where the samples are usually smaller. The purpose of this article is (a) to explore the potential effects of atypical scores (spikes) at the extreme ends (high and low) on the KE method in distributions with different degrees of asymmetry using the randomly equivalent groups equating design (Study I), and (b) to introduce the Epanechnikov and adaptive kernels as potential alternative approaches to reducing boundary bias in smoothing (Study II). The beta-binomial model is used to simulate observed scores reflecting a range of different skewed shapes.

Comparative analysis of the 1-mile run test evaluation formulae: assessment of aerobic capacity in male law enforcement officers aged 20-23 years.

PubMed

Kayihan, Gürhan; Özkan, Ali; Köklü, Yusuf; Eyuboğlu, Ender; Akça, Firat; Koz, Mitat; Ersöz, Gülfem

2014-04-01

The purpose of this study was to compare values of aerobic performance in the 1-mile run test (1-MRT) using different formulae. Aerobic capacities of 351 male volunteers working for the Turkish National Police within the age range of 20-23 years were evaluated by the 1-MRT and the 20-metre shuttle run (20-MST). VO2max values were estimated by the prediction equations developed by George et al. (1993), Cureton et al. (1995) and Kline et al. (1987) for the 1-MRT and by Leger and Lambert (1982) for the 20-MST. The difference between the results of the different formulae was significant (p = 0.000). The correlation coefficient between the estimated VO2max using Cureton's equation, George's equation, Kline's equation and the 20-MST were 0.691 (p < 0.001), 0.486 (p < 0.001) and 0.608 (p < 0.001), respectively. The highest correlation coefficient was between the VO2max estimated by the 20-MST and Cureton's equation. Similarly, the highest correlation coefficient (r = -0.779) was between the 1-mile run time and the VO2max estimated by Cureton's equation. When analysing more vigorous exercise than sub-maximal exercise, we suggest that Cureton's equation be used to predict the VO2max from 1-mile run/walk performance in large numbers of healthy individuals with high VO2max. This research compares the use of 3 different formulae to estimate VO2max from 1-mile run/walk performance in male law enforcement officers aged 20-23 years for the first time and reports the most accurate formula to use when evaluating aerobic capacities of large numbers of healthy individuals.

Observed-Score Equating with a Heterogeneous Target Population

ERIC Educational Resources Information Center

Duong, Minh Q.; von Davier, Alina A.

2012-01-01

Test equating is a statistical procedure for adjusting for test form differences in difficulty in a standardized assessment. Equating results are supposed to hold for a specified target population (Kolen & Brennan, 2004; von Davier, Holland, & Thayer, 2004) and to be (relatively) independent of the subpopulations from the target population (see…

The many facets of the (non-relativistic) Nuclear Equation of State

NASA Astrophysics Data System (ADS)

Giuliani, G.; Zheng, H.; Bonasera, A.

2014-05-01

A nucleus is a quantum many body system made of strongly interacting Fermions, protons and neutrons (nucleons). This produces a rich Nuclear Equation of State whose knowledge is crucial to our understanding of the composition and evolution of celestial objects. The nuclear equation of state displays many different features; first neutrons and protons might be treated as identical particles or nucleons, but when the differences between protons and neutrons are spelled out, we can have completely different scenarios, just by changing slightly their interactions. At zero temperature and for neutron rich matter, a quantum liquid-gas phase transition at low densities or a quark-gluon plasma at high densities might occur. Furthermore, the large binding energy of the α particle, a Boson, might also open the possibility of studying a system made of a mixture of Bosons and Fermions, which adds to the open problems of the nuclear equation of state.

Investigation of Damping Physics and CFD Tool Validation for Simulation of Baffled Tanks at Variable Slosh Amplitude

NASA Technical Reports Server (NTRS)

Yang, H. Q.; West, Jeffrey

2016-01-01

To meet the flight control damping requirement, baffles of various configurations have been devised to increase the natural viscous damping and decrease the magnitude of the slosh forces and torques. In the design of slosh baffles, the most widely used damping equation is the one derived by Miles, which is based on the experiments of Keulegan and Carpenter. This equation has been used in predicting damping of the baffled tanks in different diameters ranging from 12 to 112 inches. The analytical expression of Miles equation is easy to use, especially in the design of complex baffle system. Previous investigations revealed that some experiments had shown good agreements with the prediction method of Miles, whereas other experiments have shown significant deviations. For example, damping from Miles equation differs from experimental measurements by as much as 100 percent over a range of tank diameters from 12 to 112 inches, oscillation amplitudes from 0.1 to 1.5 baffle widths, and baffle depths of 0.3 to 0.5 tank radius. Previously, much of this difference has been attributed to experimental scatter. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between Miles equation and experimental measurement, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use CFD technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. A well validated CFD solver, developed at NASA MSFC, Loci-STREAM-VOF, is applied to study vorticity field around the baffle and around the fluid interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data are then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (h/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

Exact solutions to the time-fractional differential equations via local fractional derivatives

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

Decoupling of the nernst-planck and poisson equations. Application to a membrane system at overlimiting currents.

PubMed

Urtenov, Mahamet A-Kh; Kirillova, Evgeniya V; Seidova, Natalia M; Nikonenko, Victor V

2007-12-27

This paper deals with one-dimensional stationary Nernst-Planck and Poisson (NPP) equations describing ion electrodiffusion in multicomponent solution/electrode or ion-conductive membrane systems. A general method for resolving ordinary and singularly perturbed problems with these equations is developed. This method is based on the decoupling of NPP equations that results in deduction of an equation containing only the terms with different powers of the electrical field and its derivatives. Then, the solution of this equation, analytical in several cases or numerical, is substituted into the Nernst-Planck equations for calculating the concentration profile for each ion present in the system. Different ionic species are grouped in valency classes that allows one to reduce the dimension of the original set of equations and leads to a relatively easy treatment of multi-ion systems. When applying the method developed, the main attention is paid to ion transfer at limiting and overlimiting currents, where a significant deviation from local electroneutrality occurs. The boundary conditions and different approximations are examined: the local electroneutrality (LEN) assumption and the original assumption of quasi-uniform distribution of the space charge density (QCD). The relations between the ion fluxes at limiting and overlimiting currents are discussed. In particular, attention is paid to the "exaltation" of counterion transfer toward an ion-exchange membrane by co-ion flux leaking through the membrane or generated at the membrane/solution interface. The structure of the multi-ion concentration field in a depleted diffusion boundary layer (DBL) near an ion-exchange membrane at overlimiting currents is analyzed. The presence of salt ions and hydrogen and hydroxyl ions generated in the course of the water "splitting" reaction is considered. The thickness of the DBL and its different zones, as functions of applied current density, are found by fitting experimental current-voltage curves.

New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

Application of the implicit MacCormack scheme to the PNS equations

NASA Technical Reports Server (NTRS)

Lawrence, S. L.; Tannehill, J. C.; Chaussee, D. S.

1983-01-01

The two-dimensional parabolized Navier-Stokes equations are solved using MacCormack's (1981) implicit finite-difference scheme. It is shown that this method for solving the parabolized Navier-Stokes equations does not require the inversion of block tridiagonal systems of algebraic equations and allows the original explicit scheme to be employed in those regions where implicit treatment is not needed. The finite-difference algorithm is discussed and the computational results for two laminar test cases are presented. Results obtained using this method for the case of a flat plate boundary layer are compared with those obtained using the conventional Beam-Warming scheme, as well as those obtained from a boundary layer code. The computed results for a more severe test of the method, the hypersonic flow past a 15 deg compression corner, are found to compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

Synesthesia affects verification of simple arithmetic equations.

PubMed

Ghirardelli, Thomas G; Mills, Carol Bergfeld; Zilioli, Monica K C; Bailey, Leah P; Kretschmar, Paige K

2010-01-01

To investigate the effects of color-digit synesthesia on numerical representation, we presented a synesthete, called SE, in the present study, and controls with mathematical equations for verification. In Experiment 1, SE verified addition equations made up of digits that either matched or mismatched her color-digit photisms or were in black. In Experiment 2A, the addends were presented in the different color conditions and the solution was presented in black, whereas in Experiment 2B the addends were presented in black and the solutions were presented in the different color conditions. In Experiment 3, multiplication and division equations were presented in the same color conditions as in Experiment 1. SE responded significantly faster to equations that matched her photisms than to those that did not; controls did not show this effect. These results suggest that photisms influence the processing of digits in arithmetic verification, replicating and extending previous findings.

Relation of Different Type Love-Shida Numbers Determined with the Use of Time-Varying Incremental Gravitational Potential

NASA Astrophysics Data System (ADS)

Varga, Peter; Grafarend, Erik; Engels, Johannes

2017-03-01

There are different equations to describe relations between different classes of Love-Shida numbers. In this study with the use of the time-varying gravitational potential an integral relation was obtained which connects tidal Love-Shida numbers (h, l, k), load numbers (h', l', k'), potential free Love-Shida numbers generated by normal (h″, l″, k″) and horizontal (h‴, l‴, k‴) stresses. The equations obtained in frame of present study is the only one which - holds for every type of Love-Shida numbers, - describes a relationship not between different, but the same type of Love-Shida numbers, - does not follow from the sixth-order differential equation system of motion usually applied to calculate the Love-Shida numbers.

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

Differences between Expected Answers and the Answers Given by Computer Algebra Systems to School Equations

ERIC Educational Resources Information Center

Tonisson, Eno

2015-01-01

Sometimes Computer Algebra Systems (CAS) offer an answer that is somewhat different from the answer that is probably expected by the student or teacher. These (somewhat unexpected) answers could serve as a catalyst for rich mathematical discussion. In this study, over 120 equations from school mathematics were solved using 8 different CAS. Many…

Three Dimensional Time Dependent Stochastic Method for Cosmic-ray Modulation

NASA Astrophysics Data System (ADS)

Pei, C.; Bieber, J. W.; Burger, R. A.; Clem, J. M.

2009-12-01

A proper understanding of the different behavior of intensities of galactic cosmic rays in different solar cycle phases requires solving the modulation equation with time dependence. We present a detailed description of our newly developed stochastic approach for cosmic ray modulation which we believe is the first attempt to solve the time dependent Parker equation in 3D evolving from our 3D steady state stochastic approach, which has been benchmarked extensively by using the finite difference method. Our 3D stochastic method is different from other stochastic approaches in literature (Ball et al 2005, Miyake et al 2005, and Florinski 2008) in several ways. For example, we employ spherical coordinates which makes the code much more efficient by reducing coordinate transformations. What's more, our stochastic differential equations are different from others because our map from Parker's original equation to the Fokker-Planck equation extends the method used by Jokipii and Levy 1977 while others don't although all 3D stochastic methods are essentially based on Ito formula. The advantage of the stochastic approach is that it also gives the probability information of travel times and path lengths of cosmic rays besides the intensities. We show that excellent agreement exists between solutions obtained by our steady state stochastic method and by the traditional finite difference method. We also show time dependent solutions for an idealized heliosphere which has a Parker magnetic field, a planar current sheet, and a simple initial condition.

Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons

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

Sardar, Sankirtan; Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com; Das, K. P.

A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KPmore » and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.« less

Validity of bioelectrical impedance analysis in estimation of fat-free mass in colorectal cancer patients.

PubMed

Ræder, Hanna; Kværner, Ane Sørlie; Henriksen, Christine; Florholmen, Geir; Henriksen, Hege Berg; Bøhn, Siv Kjølsrud; Paur, Ingvild; Smeland, Sigbjørn; Blomhoff, Rune

2018-02-01

Bioelectrical impedance analysis (BIA) is an accessible and cheap method to measure fat-free mass (FFM). However, BIA estimates are subject to uncertainty in patient populations with altered body composition and hydration. The aim of the current study was to validate a whole-body and a segmental BIA device against dual-energy X-ray absorptiometry (DXA) in colorectal cancer (CRC) patients, and to investigate the ability of different empiric equations for BIA to predict DXA FFM (FFM DXA ). Forty-three non-metastatic CRC patients (aged 50-80 years) were enrolled in this study. Whole-body and segmental BIA FFM estimates (FFM whole-bodyBIA , FFM segmentalBIA ) were calculated using 14 empiric equations, including the equations from the manufacturers, before comparison to FFM DXA estimates. Strong linear relationships were observed between FFM BIA and FFM DXA estimates for all equations (R 2  = 0.94-0.98 for both devices). However, there were large discrepancies in FFM estimates depending on the equations used with mean differences in the ranges -6.5-6.8 kg and -11.0-3.4 kg for whole-body and segmental BIA, respectively. For whole-body BIA, 77% of BIA derived FFM estimates were significantly different from FFM DXA , whereas for segmental BIA, 85% were significantly different. For whole-body BIA, the Schols* equation gave the highest agreement with FFM DXA with mean difference ±SD of -0.16 ± 1.94 kg (p = 0.582). The manufacturer's equation gave a small overestimation of FFM with 1.46 ± 2.16 kg (p < 0.001) with a tendency towards proportional bias (r = 0.28, p = 0.066). For segmental BIA, the Heitmann* equation gave the highest agreement with FFM DXA (0.17 ± 1.83 kg (p = 0.546)). Using the manufacturer's equation, no difference in FFM estimates was observed (-0.34 ± 2.06 kg (p = 0.292)), however, a clear proportional bias was detected (r = 0.69, p < 0.001). Both devices demonstrated acceptable ability to detect low FFM compared to DXA using the optimal equation. In a population of non-metastatic CRC patients, mostly consisting of Caucasian adults and with a wide range of body composition measures, both the whole-body BIA and segmental BIA device provide FFM estimates that are comparable to FFM DXA on a group level when the appropriate equations are applied. At the individual level (i.e. in clinical practice) BIA may be a valuable tool to identify patients with low FFM as part of a malnutrition diagnosis. Copyright © 2017 The Author(s). Published by Elsevier Ltd.. All rights reserved.

A fully vectorized numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Patel, N.

1983-01-01

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Manafian, Jalil

2018-03-01

This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

A more fundamental approach to the derivation of nonlinear acoustic wave equations with fractional loss operators (L).

PubMed

Prieur, Fabrice; Vilenskiy, Gregory; Holm, Sverre

2012-10-01

A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["Nonlinear acoustic wave equations with fractional loss operators," J. Acoust. Soc. Am. 130(3), 1125-1132 (2011)]. The loss operator of the obtained nonlinear wave equations differs from the previous derivations as well as the dispersion equation, but when approximating for low frequencies the expressions for the frequency dependent attenuation and velocity dispersion remain unchanged.

Infinite Conservation Laws, Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Zhang, Xiang-Zhi; Dong, Huan-He

2017-12-01

Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and (1+1)-dimensional and (2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally, we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the (1+1) and (2+1)-dimensional Toda-type equations. Supported by the Fundamental Research Funds for the Central University under Grant No. 2017XKZD11

High Agreement was Obtained Across Scores from Multiple Equated Scales for Social Anxiety Disorder using Item Response Theory.

PubMed

Sunderland, Matthew; Batterham, Philip; Calear, Alison; Carragher, Natacha; Baillie, Andrew; Slade, Tim

2018-04-10

There is no standardized approach to the measurement of social anxiety. Researchers and clinicians are faced with numerous self-report scales with varying strengths, weaknesses, and psychometric properties. The lack of standardization makes it difficult to compare scores across populations that utilise different scales. Item response theory offers one solution to this problem via equating different scales using an anchor scale to set a standardized metric. This study is the first to equate several scales for social anxiety disorder. Data from two samples (n=3,175 and n=1,052), recruited from the Australian community using online advertisements, were utilised to equate a network of 11 self-report social anxiety scales via a fixed parameter item calibration method. Comparisons between actual and equated scores for most of the scales indicted a high level of agreement with mean differences <0.10 (equivalent to a mean difference of less than one point on the standardized metric). This study demonstrates that scores from multiple scales that measure social anxiety can be converted to a common scale. Re-scoring observed scores to a common scale provides opportunities to combine research from multiple studies and ultimately better assess social anxiety in treatment and research settings. Copyright © 2018. Published by Elsevier Inc.

Simulation of hot spots formation and evolution in HMX

NASA Astrophysics Data System (ADS)

Wang, Cheng; Yang, Tonghui

2017-06-01

In order to study the formation and evolution of hot spots under shock loading, HMX explosives were selected as the object of study for the two-dimensional finite difference numerical simulation. A fifth order finite difference weighted essentially non-oscillatory (WENO) scheme and a third order TVD Runge-Kutta method are utilized for the spatial discretization and the time advance, respectively. The governing equations are based on the fluid elasto-plastic control equations. The Mie-Gruneisen equation of state and the ideal gas equation of state are selected to use in the state equation of the solid explosives and gas material. In order to simplify the calculation of the model, the reaction can be considered to complete in one step. The calculated area is [ 3.0 ×10-5 m ] × [ 3.0 ×10-5 m ] . The radius is 0.6 ×10-5 m, and the internal gas is not involved in the reaction. The calculation area is divided into 300×300 grids and 10 grids are selected from the bottom of each column to give the particle velocity u as the initial condition. In the selected grid, different initial velocity 100m/s and 200m/s are loaded respectively to study the influence of hot spot formation and evolution in different impact intensity.

Symplectic partitioned Runge-Kutta scheme for Maxwell's equations

NASA Astrophysics Data System (ADS)

Huang, Zhi-Xiang; Wu, Xian-Liang

Using the symplectic partitioned Runge-Kutta (PRK) method, we construct a new scheme for approximating the solution to infinite dimensional nonseparable Hamiltonian systems of Maxwell's equations for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Several numerical examples are presented to verify the efficiency of the scheme.

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

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

Granita, E-mail: granitafc@gmail.com; Bahar, A.

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

Baecklund transformation for the Ernst equation of general relativity

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

Harrison, B.K.

A Baecklund transformation for the Ernst equation arising in general relativity in connection with several physical problems is derived, using the pseudopotential method of Wahlquist and Estabrook. A prolongation structure is also constructed, using a method of writing the equations in terms of differential forms, and an equation in the spirit of Lax is constructed, somewhat different from that given by Maison. Possible uses of the Baecklund transformation to generate new solutions are mentioned.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. IV - Multi-discrete time method

NASA Technical Reports Server (NTRS)

Mickens, Ronald E.

1987-01-01

It is shown that a discrete multi-time method can be constructed to obtain approximations to the periodic solutions of a special class of second-order nonlinear difference equations containing a small parameter. Three examples illustrating the method are presented.

Nested Structural Equation Models: Noncentrality and Power of Restriction Test.

ERIC Educational Resources Information Center

Raykov, Tenko; Penev, Spiridon

1998-01-01

Discusses the difference in noncentrality parameters of nested structural equation models and their utility in evaluating statistical power associated with the pertinent restriction test. Asymptotic confidence intervals for that difference are presented. These intervals represent a useful adjunct to goodness-of-fit indexes in assessing constraints…

Separated spin-up and spin-down quantum hydrodynamics of degenerated electrons: Spin-electron acoustic wave appearance.

PubMed

Andreev, Pavel A

2015-03-01

The quantum hydrodynamic (QHD) model of charged spin-1/2 particles contains physical quantities defined for all particles of a species including particles with spin-up and with spin-down. Different populations of states with different spin directions are included in the spin density (the magnetization). In this paper I derive a QHD model, which separately describes spin-up electrons and spin-down electrons. Hence electrons with different projections of spins on the preferable direction are considered as two different species of particles. It is shown that the numbers of particles with different spin directions do not conserve. Hence the continuity equations contain sources of particles. These sources are caused by the interactions of the spins with the magnetic field. Terms of similar nature arise in the Euler equation. The z projection of the spin density is no longer an independent variable. It is proportional to the difference between the concentrations of the electrons with spin-up and the electrons with spin-down. The propagation of waves in the magnetized plasmas of degenerate electrons is considered. Two regimes for the ion dynamics, the motionless ions and the motion of the degenerate ions as the single species with no account of the spin dynamics, are considered. It is shown that this form of the QHD equations gives all solutions obtained from the traditional form of QHD equations with no distinction of spin-up and spin-down states. But it also reveals a soundlike solution called the spin-electron acoustic wave. Coincidence of most solutions is expected since this derivation was started with the same basic equation: the Pauli equation. Solutions arise due to the different Fermi pressures for the spin-up electrons and the spin-down electrons in the magnetic field. The results are applied to degenerate electron gas of paramagnetic and ferromagnetic metals in the external magnetic field. The dispersion of the spin-electron acoustic waves in the partially spin-polarized degenerate neutron matter are also considered.

Optimal equation for estimation of glomerular filtration rate in autosomal dominant polycystic kidney disease: influence of tolvaptan.

PubMed

Yamaguchi, Tsuyoshi; Higashihara, Eiji; Okegawa, Takatsugu; Miyazaki, Isao; Nutahara, Kikuo

2018-05-22

The reliability of various equations for estimating the GFR in ADPKD patients and the influence of tolvaptan on the resulting estimates have not been examined when GFR is calculated on the basis of inulin clearance. We obtained baseline and on-tolvaptan measured GFRs (mGFRs), calculated on the basis of inulin clearance, in 114 ADPKD, and these mGFRs were compared with eGFRs calculated according to four basic equations: the MDRD, CKD-EPI, and JSN-CKDI equations and the Cockcroft-Gault formula, as well as the influence of tolvaptan and of inclusion of cystatin C on accuracy of the results. Accuracy of each of the seven total equations was evaluated on the basis of the percentage of eGFR values within mGFR ± 30% (P 30 ). mGFRs were distributed throughout CKD stages 1-5. Regardless of the CKD stage, P 30 s of the MDRD, CKD-EPI, and JSN-CKDI equations did not differ significantly between baseline values and on-tolvaptan values. In CKD 1-2 patients, P 30 of the CKD-EPI equation was 100.0%, whether or not the patient was on-tolvaptan. In CKD 3-5 patients, P 30 s of the MDRD, CKD-EPI, and JSN-CKDI equations were similar. For all four equations, regression coefficients and intercepts did not differ significantly between baseline and on-tolvaptan values, but accuracy of the Cockcroft-Gault formula was inferior to that of the other three equations. Incorporation of serum cystatin C reduced accuracy. The CKD-EPI equation is most reliable, regardless of the severity of CKD. Tolvaptain intake has minimal influence and cystatin C incorporation does not improve accuracy.

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

PubMed

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 regions of parameter space in which there are maximum differences between the solutions of the master equation and the corresponding rate equations. We show that these differences depend sensitively on the Fano factors and on the inherent structure and topology of the chemical network. The theory of effective mesoscopic rate equations generalizes the conventional rate equations of physical chemistry to describe kinetics in systems of mesoscopic size such as biological cells.

A diffuse-interface method for two-phase flows with soluble surfactants

PubMed Central

Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel

2010-01-01

A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier–Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed. PMID:21218125

Homoclinic snaking in the discrete Swift-Hohenberg equation

NASA Astrophysics Data System (ADS)

Kusdiantara, R.; Susanto, H.

2017-12-01

We consider the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial derivatives of the Swift-Hohenberg equation using central finite differences. We investigate the discretization effect on the bifurcation behavior, where we identify three regions of the coupling parameter, i.e., strong, weak, and intermediate coupling. Within the regions, the discrete Swift-Hohenberg equation behaves either similarly or differently from the continuum limit. In the intermediate coupling region, multiple Maxwell points can occur for the periodic solutions and may cause irregular snaking and isolas. Numerical continuation is used to obtain and analyze localized and periodic solutions for each case. Theoretical analysis for the snaking and stability of the corresponding solutions is provided in the weak coupling region.

Neuronal models in infinite-dimensional spaces and their finite-dimensional projections: Part II.

PubMed

Brzychczy, S; Leszczyński, H; Poznanski, R R

2012-09-01

Application of comparison theorem is used to examine the validitiy of the "lumped parameter assumption" in describing the behavior of solutions of the continuous cable equation U(t) = DU(xx)+f(U) with the discrete cable equation dV(n)/dt = d*(V(n+1) - 2V(n) + V(n-1)) + f(V(n)), where f is a nonlinear functional describing the internal diffusion of electrical potential in single neurons. While the discrete cable equation looks like a finite difference approximation of the continuous cable equation, solutions of the two reveal significantly different behavior which imply that the compartmental models (spiking neurons) are poor quantifiers of neurons, contrary to what is commonly accepted in computational neuroscience.

Nonautonomous discrete bright soliton solutions and interaction management for the Ablowitz-Ladik equation.

PubMed

Yu, Fajun

2015-03-01

We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.

Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes.

PubMed

Kyriakopoulos, Charalampos; Grossmann, Gerrit; Wolf, Verena; Bortolussi, Luca

2018-01-01

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree k_{max} of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large k_{max}. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.

Creatinine-based equations for the adjustment of drug dosage in an obese population.

PubMed

Bouquegneau, Antoine; Vidal-Petiot, Emmanuelle; Moranne, Olivier; Mariat, Christophe; Boffa, Jean-Jacques; Vrtovsnik, François; Scheen, André-Jean; Krzesinski, Jean-Marie; Flamant, Martin; Delanaye, Pierre

2016-02-01

For drug dosing adaptation, the Kidney Disease: Improving Global Outcomes (KDIGO) guidelines recommend using estimated glomerular filtration rate (eGFR) by the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation, after 'de-indexation' by body surface area (BSA). In pharmacology, the Cockcroft-Gault (CG) equation is still recommended to adapt drug dosage. In the context of obesity, adjusted ideal body weight (AIBW) is sometimes preferred to actual body weight (ABW) for the CG equation. The aim of the present study was to compare the performance of the different GFR-estimating equations, non-indexed or de-indexed by BSA for the purpose of drug-dosage adaptation in obese patients. We analysed data from patients with a body mass index (BMI) higher than 30 kg m(-2) who underwent a GFR measurement. eGFR was calculated using the CKD-EPI and Modification of Diet in Renal Disease (MDRD) equations, de-indexed by BSA, and the CG equation, using either ABW, AIBW or lean body weight (LBW) for the weight variable and compared with measured GFR, expressed in ml min(-1). In our population of obese patients, use of the AIBW instead of the ABW in the CG equation, markedly improved the overall accuracy of this equation [57% for CGABW and 79% for CGAIBW (P < 0.05)]. For high BMI (over 40 kg m(-2)), the accuracy of the CG equations is no different when using LBW than when using AIBW. The MDRD and CKD-EPI equations de-indexed by the BSA also performed well, with an overall higher accuracy for the MDRD de-indexed equation [(80% and 76%, respectively (P < 0.05)]. The de-indexed MDRD equation appeared to be the most suitable for estimating the non-indexed GFR for the purpose of drug dosage adaptation in obese patients. © 2015 The British Pharmacological Society.

A local equation for differential diagnosis of β-thalassemia trait and iron deficiency anemia by logistic regression analysis in Southeast Iran.

PubMed

Sargolzaie, Narjes; Miri-Moghaddam, Ebrahim

2014-01-01

The most common differential diagnosis of β-thalassemia (β-thal) trait is iron deficiency anemia. Several red blood cell equations were introduced during different studies for differential diagnosis between β-thal trait and iron deficiency anemia. Due to genetic variations in different regions, these equations cannot be useful in all population. The aim of this study was to determine a native equation with high accuracy for differential diagnosis of β-thal trait and iron deficiency anemia for the Sistan and Baluchestan population by logistic regression analysis. We selected 77 iron deficiency anemia and 100 β-thal trait cases. We used binary logistic regression analysis and determined best equations for probability prediction of β-thal trait against iron deficiency anemia in our population. We compared diagnostic values and receiver operative characteristic (ROC) curve related to this equation and another 10 published equations in discriminating β-thal trait and iron deficiency anemia. The binary logistic regression analysis determined the best equation for best probability prediction of β-thal trait against iron deficiency anemia with area under curve (AUC) 0.998. Based on ROC curves and AUC, Green & King, England & Frazer, and then Sirdah indices, respectively, had the most accuracy after our equation. We suggest that to get the best equation and cut-off in each region, one needs to evaluate specific information of each region, specifically in areas where populations are homogeneous, to provide a specific formula for differentiating between β-thal trait and iron deficiency anemia.

Finite difference and Runge-Kutta methods for solving vibration problems

NASA Astrophysics Data System (ADS)

Lintang Renganis Radityani, Scolastika; Mungkasi, Sudi

2017-11-01

The vibration of a storey building can be modelled into a system of second order ordinary differential equations. If the number of floors of a building is large, then the result is a large scale system of second order ordinary differential equations. The large scale system is difficult to solve, and if it can be solved, the solution may not be accurate. Therefore, in this paper, we seek for accurate methods for solving vibration problems. We compare the performance of numerical finite difference and Runge-Kutta methods for solving large scale systems of second order ordinary differential equations. The finite difference methods include the forward and central differences. The Runge-Kutta methods include the Euler and Heun methods. Our research results show that the central finite difference and the Heun methods produce more accurate solutions than the forward finite difference and the Euler methods do.

Test problems for inviscid transonic flow

NASA Technical Reports Server (NTRS)

Carlson, L. A.

1979-01-01

Solving of test problems with the TRANDES program is discussed. This method utilizes the full, inviscid, perturbation potential flow equation in a Cartesian grid system that is stretched to infinity. This equation is represented by a nonconservative system of finite difference equations that includes at supersonic points a rotated difference scheme and is solved by column relaxation. The solution usually starts from a zero perturbation potential on a very coarse grid (typically 13 by 7) followed by several grid halvings until a final solution is obtained on a fine grid (97 by 49).

Varieties of operator manipulation. [for solving differential equations and calculating finite differences

NASA Technical Reports Server (NTRS)

Doohovskoy, A.

1977-01-01

A change in MACSYMA syntax is proposed to accommodate the operator manipulators necessary to implement direct and indirect methods for the solution of differential equations, calculus of finite differences, and the fractional calculus, as well as their modern counterparts. To illustrate the benefits and convenience of this syntax extension, an example is given to show how MACSYMA's pattern-matching capability can be used to implement a particular set of operator identities which can then be used to obtain exact solutions to nonlinear differential equations.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Validity of Miles Equation in Predicting Propellant Slosh Damping in Baffled Tanks at Variable Slosh Amplitude

NASA Technical Reports Server (NTRS)

Yang, H. Q.; West, Jeff

2018-01-01

Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involves the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations were mainly carried out by extensive experiments. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between the empirical Miles equation and experimental measurements, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use Computational Fluid Dynamics (CFD) technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. Loci-STREAM-VOF, a well validated CFD solver developed at NASA MSFC, is applied to study the vorticity field around a baffle and around the fluid-gas interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data is then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (d/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

Differences between true mean daily, monthly and annual air temperatures and air temperatures calculated with three equations: a case study from three Croatian stations

NASA Astrophysics Data System (ADS)

Bonacci, Ognjen; Željković, Ivana; Trogrlić, Robert Šakić; Milković, Janja

2013-10-01

Differences between true mean daily, monthly and annual air temperatures T0 [Eq. (1)] and temperatures calculated with three different equations [(2), (3) and (4)] (commonly used in climatological practice) were investigated at three main meteorological Croatian stations from 1 January 1999 to 31 December 2011. The stations are situated in the following three climatically distinct areas: (1) Zagreb-Grič (mild continental climate), (2) Zavižan (cold mountain climate), and (3) Dubrovnik (hot Mediterranean climate). T1 [Eq. (2)] and T3 [Eq. (4)] mean temperatures are defined by the algorithms based on the weighted means of temperatures measured at irregularly spaced, yet fixed hours. T2 [Eq. (3)] is the mean temperature defined as the average of daily maximum and minimum temperature. The equation as well as the time of observations used introduces a bias into mean temperatures. The largest differences occur for mean daily temperatures. The calculated daily difference value from all three equations and all analysed stations varies from -3.73 °C to +3.56 °C, from -1.39 °C to +0.79 °C for monthly differences and from -0.76 °C to +0.30 °C for annual differences.

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

Walton, Mark A.

Quantum mechanics in phase space (or deformation quantization) appears to fail as an autonomous quantum method when infinite potential walls are present. The stationary physical Wigner functions do not satisfy the normal eigen equations, the *-eigen equations, unless an ad hoc boundary potential is added [N.C. Dias, J.N. Prata, J. Math. Phys. 43 (2002) 4602 (quant-ph/0012140)]. Alternatively, they satisfy a different, higher-order, '*-eigen-* equation', locally, i.e. away from the walls [S. Kryukov, M.A. Walton, Ann. Phys. 317 (2005) 474 (quant-ph/0412007)]. Here we show that this substitute equation can be written in a very simple form, even in the presence ofmore » an additional, arbitrary, but regular potential. The more general applicability of the *-eigen-* equation is then demonstrated. First, using an idea from [D.B. Fairlie, C.A. Manogue, J. Phys. A 24 (1991) 3807], we extend it to a dynamical equation describing time evolution. We then show that also for general contact interactions, the *-eigen-* equation is satisfied locally. Specifically, we treat the most general possible (Robin) boundary conditions at an infinite wall, general one-dimensional point interactions, and a finite potential jump. Finally, we examine a smooth potential, that has simple but different expressions for x positive and negative. We find that the *-eigen-* equation is again satisfied locally. It seems, therefore, that the *-eigen-* equation is generally relevant to the matching of Wigner functions; it can be solved piece-wise and its solutions then matched.« less

Poor agreement between continuous measurements of energy expenditure and routinely used prediction equations in intensive care unit patients.

PubMed

Reid, Clare L

2007-10-01

A wide variation in 24h energy expenditure has been demonstrated previously in intensive care unit (ICU) patients. The accuracy of equations used to predict energy expenditure in critically ill patients is frequently compared with single or short-duration indirect calorimetry measurements, which may not represent the total energy expenditure (TEE) of these patients. To take into account this variability in energy expenditure, estimates have been compared with continuous indirect calorimetry measurements. Continuous (24h/day for 5 days) indirect calorimetry measurements were made in patients requiring mechanical ventilation for 5 days. The Harris-Benedict, Schofield and Ireton-Jones equations and the American College of Chest Physicians recommendation of 25 kcal/kg/day were used to estimate energy requirements. A total of 192 days of measurements, in 27 patients, were available for comparison with the different equations. Agreement between the equations and measured values was poor. The Harris-Benedict, Schofield and ACCP equations provided more estimates (66%, 66% and 65%, respectively) within 80% and 110% of TEE values. However, each of these equations would have resulted in clinically significant underfeeding (<80% of TEE) in 16%, 15% and 22% of patients, respectively, and overfeeding (>110% of TEE) in 18%, 19% and 13% of patients, respectively. Limits of agreement between the different equations and TEE values were unacceptably wide. Prediction equations may result in significant under or overfeeding in the clinical setting.

Note: equation of state and the freezing point in the hard-sphere model.

PubMed

Robles, Miguel; López de Haro, Mariano; Santos, Andrés

2014-04-07

The merits of different analytical equations of state for the hard-sphere system with respect to the recently computed high-accuracy value of the freezing-point packing fraction are assessed. It is found that the Carnahan-Starling-Kolafa and the branch-point approximant equations of state yield the best performance.

Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains

NASA Astrophysics Data System (ADS)

Adler, V. E.

2018-04-01

We consider differential-difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a secondorder scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.

Updated generalized biomass equations for North American tree species

Treesearch

David C. Chojnacky; Linda S. Heath; Jennifer C. Jenkins

2014-01-01

Historically, tree biomass at large scales has been estimated by applying dimensional analysis techniques and field measurements such as diameter at breast height (dbh) in allometric regression equations. Equations often have been developed using differing methods and applied only to certain species or isolated areas. We previously had compiled and combined (in meta-...

Performance and Difficulties of Students in Formulating and Solving Quadratic Equations with One Unknown

ERIC Educational Resources Information Center

Didis, Makbule Gozde; Erbas, Ayhan Kursat

2015-01-01

This study attempts to investigate the performance of tenth-grade students in solving quadratic equations with one unknown, using symbolic equation and word-problem representations. The participants were 217 tenth-grade students, from three different public high schools. Data was collected through an open-ended questionnaire comprising eight…

Non-Markovian stochastic Schrödinger equations: Generalization to real-valued noise using quantum-measurement theory

NASA Astrophysics Data System (ADS)

Gambetta, Jay; Wiseman, H. M.

2002-07-01

Do stochastic Schrödinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system on average obeys a master equation, the answer is yes. Markovian stochastic Schrödinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic Schrödinger equation introduced by Strunz, Diósi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum-measurement theory approach, we rederive their unraveling that involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection, respectively. Although we use quantum-measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction.

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

PubMed

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

Spirometric Reference Equations for Elderly Chinese in Jinan Aged 60–84 Years

PubMed Central

Tian, Xin-Yu; Liu, Chun-Hong; Wang, De-Xiang; Ji, Xiu-Li; Shi, Hui; Zheng, Chun-Yan; Xie, Meng-Shuang; Xiao, Wei

2018-01-01

Background: The interpretation of spirometry varies on different reference values. Older people are usually underrepresented in published predictive values. This study aimed at developing spirometric reference equations for elderly Chinese in Jinan aged 60–84 years and to compare them to previous equations. Methods: The project covered all of Jinan city, and the recruitment period lasted 9 months from January 1, 2017 to September 30, 2017, 434 healthy people aged 60–84 years who had never smoked (226 females and 208 males) were recruited to undergo spirometry. Vital capacity (VC), forced VC (FVC), forced expiratory volume in 1 s (FEV1), FEV1/FVC, FEV1/VC, FEV6, peak expiratory flow, and forced expiratory flow at 25%, 50%, 75%, and 25–75% of FVC exhaled (FEF25%, FEF50%, FEF75%, and FEF25–75%) were analyzed. Reference equations for mean and the lower limit of normal (LLN) were derived using the lambda-mu-sigma method. Comparisons between new and previous equations were performed by paired t-test. Results: New reference equations were developed from the sample. The LLN of FEV1/FVC, FEF25–75% computed using the 2012-Global Lung Function Initiative (GLI) and 2006-Hong Kong equations were both lower than the new equations. The biggest degree of difference for FEV1/FVC was 19% (70.46% vs. 59.29%, t = 33.954, P < 0.01) and for maximal midexpiratory flow (MMEF, equals to FEF25–75%) was 22% (0.82 vs. 0.67, t = 21.303, P < 0.01). The 1990-North China and 2009-North China equations predicted higher mean values of FEV1/FVC and FEF25–75% than the present model. The biggest degrees of difference were −4% (78.31% vs. 81.27%, t = −85.359, P < 0.01) and −60% (2.11 vs. 4.68, t = −170.287, P < 0.01), respectively. Conclusions: The newly developed spirometric reference equations are applicable to elderly Chinese in Jinan. The 2012-GLI and 2006-Hong Kong equations may lead to missed diagnoses of obstructive ventilatory defects and the small airway dysfunction, while traditional linear equations for all ages may lead to overdiagnosis. PMID:29553052

Modeling Latent Growth Curves With Incomplete Data Using Different Types of Structural Equation Modeling and Multilevel Software

ERIC Educational Resources Information Center

Ferrer, Emilio; Hamagami, Fumiaki; McArdle, John J.

2004-01-01

This article offers different examples of how to fit latent growth curve (LGC) models to longitudinal data using a variety of different software programs (i.e., LISREL, Mx, Mplus, AMOS, SAS). The article shows how the same model can be fitted using both structural equation modeling and multilevel software, with nearly identical results, even in…

Quantified Choice of Root-Mean-Square Errors of Approximation for Evaluation and Power Analysis of Small Differences between Structural Equation Models

ERIC Educational Resources Information Center

Li, Libo; Bentler, Peter M.

2011-01-01

MacCallum, Browne, and Cai (2006) proposed a new framework for evaluation and power analysis of small differences between nested structural equation models (SEMs). In their framework, the null and alternative hypotheses for testing a small difference in fit and its related power analyses were defined by some chosen root-mean-square error of…

Canonical forms of multidimensional steady inviscid flows

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1993-01-01

Canonical forms and canonical variables for inviscid flow problems are derived. In these forms the components of the system governed by different types of operators (elliptic and hyperbolic) are separated. Both the incompressible and compressible cases are analyzed, and their similarities and differences are discussed. The canonical forms obtained are block upper triangular operator form in which the elliptic and non-elliptic parts reside in different blocks. The full nonlinear equations are treated without using any linearization process. This form enables a better analysis of the equations as well as better numerical treatment. These forms are the analog of the decomposition of the one dimensional Euler equations into characteristic directions and Riemann invariants.

Scale-dependent behavior of scale equations.

PubMed

Kim, Pilwon

2009-09-01

We propose a new mathematical framework to formulate scale structures of general systems. Stack equations characterize a system in terms of accumulative scales. Their behavior at each scale level is determined independently without referring to other levels. Most standard geometries in mathematics can be reformulated in such stack equations. By involving interaction between scales, we generalize stack equations into scale equations. Scale equations are capable to accommodate various behaviors at different scale levels into one integrated solution. On contrary to standard geometries, such solutions often reveal eccentric scale-dependent figures, providing a clue to understand multiscale nature of the real world. Especially, it is suggested that the Gaussian noise stems from nonlinear scale interactions.

Calculation of transonic flows using an extended integral equation method

NASA Technical Reports Server (NTRS)

Nixon, D.

1976-01-01

An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

A note on a corrector formula for the numerical solution of ordinary differential equations

NASA Technical Reports Server (NTRS)

Chien, Y.-C.; Agrawal, K. M.

1979-01-01

A new corrector formula for predictor-corrector methods for numerical solutions of ordinary differential equations is presented. Two considerations for choosing corrector formulas are given: (1) the coefficient in the error term and (2) its stability properties. The graph of the roots of an equation plotted against its stability region, of different values, is presented along with the tables that correspond to various corrector equations, including Hamming's and Milne and Reynolds'.

Structure-Antimicrobial Activity Relationship for a New Class of Antimicrobials, Silanols, in Comparison to Alcohols and Phenols

DTIC Science & Technology

2006-08-01

equations for the antimicrobial activities and the structural properties of the silanols, the alcohols, and the phenols against four bacteria.........59 4... equations in Table 4-3. ...................................69 ix 4-6 Comparison data of PRESS and RMSPE of different classes of external compounds against...manner as shown in Equation 1-1. Hansch and Fujita derived a correlation model Equation 1-2 based on the linear free energy approach using

Multigrid Techniques for Highly Indefinite Equations

NASA Technical Reports Server (NTRS)

Shapira, Yair

1996-01-01

A multigrid method for the solution of finite difference approximations of elliptic PDE's is introduced. A parallelizable version of it, suitable for two and multi level analysis, is also defined, and serves as a theoretical tool for deriving a suitable implementation for the main version. For indefinite Helmholtz equations, this analysis provides a suitable mesh size for the coarsest grid used. Numerical experiments show that the method is applicable to diffusion equations with discontinuous coefficients and highly indefinite Helmholtz equations.

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

The accuracy of the compressible Reynolds equation for predicting the local pressure in gas-lubricated textured parallel slider bearings

PubMed Central

Qiu, Mingfeng; Bailey, Brian N.; Stoll, Rob

2014-01-01

The validity of the compressible Reynolds equation to predict the local pressure in a gas-lubricated, textured parallel slider bearing is investigated. The local bearing pressure is numerically simulated using the Reynolds equation and the Navier-Stokes equations for different texture geometries and operating conditions. The respective results are compared and the simplifying assumptions inherent in the application of the Reynolds equation are quantitatively evaluated. The deviation between the local bearing pressure obtained with the Reynolds equation and the Navier-Stokes equations increases with increasing texture aspect ratio, because a significant cross-film pressure gradient and a large velocity gradient in the sliding direction develop in the lubricant film. Inertia is found to be negligible throughout this study. PMID:25049440

Soliton solutions for ABS lattice equations: I. Cauchy matrix approach

NASA Astrophysics Data System (ADS)

Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo

2009-10-01

In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.

Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Ma, Li-Yuan; Shen, Shou-Feng; Zhu, Zuo-Nong

2017-10-01

In this paper, we prove that an integrable nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity 29, 915-946 (2016)] is gauge equivalent to a spin-like model. From the gauge equivalence, one can see that there exists significant difference between the nonlocal complex mKdV equation and the classical complex mKdV equation. Through constructing the Darboux transformation for nonlocal complex mKdV equation, a variety of exact solutions including dark soliton, W-type soliton, M-type soliton, and periodic solutions are derived.

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Soh, Woo Y.

1992-01-01

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

An efficient numerical scheme for the study of equal width equation

NASA Astrophysics Data System (ADS)

Ghafoor, Abdul; Haq, Sirajul

2018-06-01

In this work a new numerical scheme is proposed in which Haar wavelet method is coupled with finite difference scheme for the solution of a nonlinear partial differential equation. The scheme transforms the partial differential equation to a system of algebraic equations which can be solved easily. The technique is applied to equal width equation in order to study the behaviour of one, two, three solitary waves, undular bore and soliton collision. For efficiency and accuracy of the scheme, L2 and L∞ norms and invariants are computed. The results obtained are compared with already existing results in literature.

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Normative equations for central augmentation index: assessment of inter-population applicability and how it could be improved

PubMed Central

Jeroncic, Ana; Gunjaca, Grgo; Mrsic, Danijela Budimir; Mudnic, Ivana; Brizic, Ivica; Polasek, Ozren; Boban, Mladen

2016-01-01

Common reference values of arterial stiffness indices could be effective screening tool in detecting vascular phenotypes at risk. However, populations of the same ethnicity may differ in vascular phenotype due to different environmental pressure. We examined applicability of normative equations for central augmentation index (cAIx) derived from Danish population with low cardiovascular risk on the corresponding Croatian population from the Mediterranean area. Disagreement between measured and predicted cAIx was assessed by Bland-Altman analysis. Both, cAIx-age distribution and normative equation fitted on Croatian data were highly comparable to Danish low-risk sample. Contrarily, Bland-Altman analysis of cAIx disagreement revealed a curvilinear deviation from the line of full agreement indicating that the equations were not equally applicable across age ranges. Stratification of individual data into age decades eliminated curvilinearity in all but the 30–39 (men) and 40–49 (women) decades. In other decades, linear disagreement independent of age persisted indicating that cAIx determinants other than age were not envisaged/compensated for by proposed equations. Therefore, established normative equations are equally applicable to both Nordic and Mediterranean populations but are of limited use. If designed for narrower age ranges, the equations’ sensitivity in detecting vascular phenotypes at risk and applicability to different populations could be improved. PMID:27230110

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

The Measurement and Cost of Removing Unexplained Gender Differences in Faculty Salaries.

ERIC Educational Resources Information Center

Becker, William E.; Toutkoushian, Robert K.

1995-01-01

In assessing sex-discrimination suit damages, debate rages over the type and number of variables included in a single-equation model of the salary-determination process. This article considers single- and multiple-equation models, providing 36 different damage calculations. For University of Minnesota data, equalization cost hinges on the…

A Comparison of Regional and SiteSpecific Volume Estimation Equations

Treesearch

Joe P. McClure; Jana Anderson; Hans T. Schreuder

1987-01-01

Regression equations for volume by region and site class were examined for lobiolly pine. The regressions for the Coastal Plain and Piedmont regions had significantly different slopes. The results shared important practical differences in percentage of confidence intervals containing the true total volume and in percentage of estimates within a specific proportion of...

Reliability of tanoak volume equations when applied to different areas

Treesearch

Norman H. Pillsbury; Philip M. McDonald; Victor Simon

1995-01-01

Tree volume equations for tanoak (Lithocarpus densiflorus) were developed for seven stands throughout its natural range and compared by a volume prediction and a parameter difference method. The objective was to test if volume estimates from a species growing in a local, relatively uniform habitat could be applied more widely. Results indicated...

Fibonacci Numbers Revisited: Technology-Motivated Inquiry into a Two-Parametric Difference Equation

ERIC Educational Resources Information Center

Abramovich, Sergei; Leonov, Gennady A.

2008-01-01

This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article…

Equivalence and Differences between Structural Equation Modeling and State-Space Modeling Techniques

ERIC Educational Resources Information Center

Chow, Sy-Miin; Ho, Moon-ho R.; Hamaker, Ellen L.; Dolan, Conor V.

2010-01-01

State-space modeling techniques have been compared to structural equation modeling (SEM) techniques in various contexts but their unique strengths have often been overshadowed by their similarities to SEM. In this article, we provide a comprehensive discussion of these 2 approaches' similarities and differences through analytic comparisons and…

Wind velocity-change (gust rise) criteria for wind turbine design

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

Cliff, W.C.; Fichtl, G.H.

1978-07-01

A closed-form equation is derived for root mean square (rms) value of velocity change (gust rise) that occurs over the swept area of wind turbine rotor systems and an equation for rms value of velocity change that occurs at a single point in space. These formulas confirm the intuitive assumption that a large system will encounter a less severe environment than a small system when both are placed at the same location. Assuming a normal probability density function for the velocity differences, an equation is given for calculating the expected number of velocity differences that will occur in 1 hrmore » and will be larger than an arbitrary value. A formula is presented that gives the expected number of velocity differences larger than an arbitrary value that will be encountered during the design life of a wind turbine. In addition, a method for calculating the largest velocity difference expected during the life of a turbine and a formula for estimating the risk of exceeding a given velocity difference during the life of the structure are given. The equations presented are based upon general atmospheric boundary-layer conditions and do not include information regarding events such as tornados, hurricanes, etc.« less

Predictive Demi-Span Equations for Estimation of Stature in Aged Mexican Americans.

PubMed

Siordia, C; Panas, L J; Markides, K

2012-01-01

To develop demi-span height predictive equations for older Mexican Americans. Cross-sectional study. Data files housed by the Sociomedical Division in the department of Community Health and Preventive Medicine at the University of Texas Medical Branch in Galveston, Texas. 1,078 (700 females, 378 males) Southwest U.S.A. community-dwelling older Mexican Americans, aged 80-102 years. Demi-span, height, weight, BMI, demi-span equivalent height (DSEH), DSEH derived BMI (DS-BMI). Bland and Altman agreement analysis on: height and DSEH; BMI and DS-BMI. Paired t-test comparing derived and actual measures by single-age units and sex. DSEH with Bassey equations (DSEHBassey) are significantly different than actual measures. DSEHBassey derived BMIs (DSBasseyBMIs) are significantly different than BMIs computed from actual measures. DSEH with Mexican equations (DSEHMexican) are not significantly different than real measures. DSEHMexican derived BMIs (DSMexicanBMIs) are not significantly different than real measures. These findings provide evidence that both DSEHBassey and DSBasseyBMIs estimates are significantly different from measured height and BMI. Both DSEHMexican and DSMexicanBMIs estimates are shown to produce similar height and BMI estimates to those obtained from real measures. .

Joint modelling rationale for chained equations

PubMed Central

2014-01-01

Background Chained equations imputation is widely used in medical research. It uses a set of conditional models, so is more flexible than joint modelling imputation for the imputation of different types of variables (e.g. binary, ordinal or unordered categorical). However, chained equations imputation does not correspond to drawing from a joint distribution when the conditional models are incompatible. Concurrently with our work, other authors have shown the equivalence of the two imputation methods in finite samples. Methods Taking a different approach, we prove, in finite samples, sufficient conditions for chained equations and joint modelling to yield imputations from the same predictive distribution. Further, we apply this proof in four specific cases and conduct a simulation study which explores the consequences when the conditional models are compatible but the conditions otherwise are not satisfied. Results We provide an additional “non-informative margins” condition which, together with compatibility, is sufficient. We show that the non-informative margins condition is not satisfied, despite compatible conditional models, in a situation as simple as two continuous variables and one binary variable. Our simulation study demonstrates that as a consequence of this violation order effects can occur; that is, systematic differences depending upon the ordering of the variables in the chained equations algorithm. However, the order effects appear to be small, especially when associations between variables are weak. Conclusions Since chained equations is typically used in medical research for datasets with different types of variables, researchers must be aware that order effects are likely to be ubiquitous, but our results suggest they may be small enough to be negligible. PMID:24559129

Investigation of a Coupled Arrhenius-Type/Rossard Equation of AH36 Material.

PubMed

Qin, Qin; Tian, Ming-Liang; Zhang, Peng

2017-04-13

High-temperature tensile testing of AH36 material in a wide range of temperatures (1173-1573 K) and strain rates (10 -4 -10 -2 s -1 ) has been obtained by using a Gleeble system. These experimental stress-strain data have been adopted to develop the constitutive equation. The constitutive equation of AH36 material was suggested based on the modified Arrhenius-type equation and the modified Rossard equation respectively. The results indicate that the constitutive equation is strongly influenced by temperature and strain, especially strain. Moreover, there is a good agreement between the predicted data of the modified Arrhenius-type equation and the experimental results when the strain is greater than 0.02. There is also good agreement between the predicted data of the Rossard equation and the experimental results when the strain is less than 0.02. Therefore, a coupled equation where the modified Arrhenius-type equation and Rossard equation are combined has been proposed to describe the constitutive equation of AH36 material according to the different strain values in order to improve the accuracy. The correlation coefficient between the computed and experimental flow stress data was 0.998. The minimum value of the average absolute relative error shows the high accuracy of the coupled equation compared with the two modified equations.

Impact of switching from Caucasian to Indian reference equations for spirometry interpretation.

PubMed

Chhabra, S K; Madan, M

2018-03-01

In the absence of ethnically appropriate prediction equations, spirometry data in Indian subjects are often interpreted using equations for other ethnic populations. To evaluate the impact of switching from Caucasian (National Health and Nutrition Examination Survey III [NHANES III] and Global Lung Function Initiative [GLI]) equations to the recently published North Indian equations on spirometric interpretation, and to examine the suitability of GLI-Mixed equations for this population. Spirometry data on 12 323 North Indian patients were analysed using the North Indian equations as well as NHANES III, GLI-Caucasian and GLI-Mixed equations. Abnormalities and ventilatory patterns were categorised and agreement in interpretation was evaluated. The NHANES III and GLI-Caucasian equations and, to a lesser extent, the GLI-Mixed equations, predicted higher values and labelled more measurements as abnormal. In up to one third of the patients, these differed from Indian equations in the categorisation of ventilatory patterns, with more patients classified as having restrictive and mixed disease. The NHANES III and GLI-Caucasian equations substantially overdiagnose abnormalities and misclassify ventilatory patterns on spirometry in Indian patients. Such errors of interpretation, although less common with the GLI-Mixed equations, remain substantial and are clinically unacceptable. A switch to Indian equations will have a major impact on interpretation.

Steady state conductance in a double quantum dot array: the nonequilibrium equation-of-motion Green function approach.

PubMed

Levy, Tal J; Rabani, Eran

2013-04-28

We study steady state transport through a double quantum dot array using the equation-of-motion approach to the nonequilibrium Green functions formalism. This popular technique relies on uncontrolled approximations to obtain a closure for a hierarchy of equations; however, its accuracy is questioned. We focus on 4 different closures, 2 of which were previously proposed in the context of the single quantum dot system (Anderson impurity model) and were extended to the double quantum dot array, and develop 2 new closures. Results for the differential conductance are compared to those attained by a master equation approach known to be accurate for weak system-leads couplings and high temperatures. While all 4 closures provide an accurate description of the Coulomb blockade and other transport properties in the single quantum dot case, they differ in the case of the double quantum dot array, where only one of the developed closures provides satisfactory results. This is rationalized by comparing the poles of the Green functions to the exact many-particle energy differences for the isolate system. Our analysis provides means to extend the equation-of-motion technique to more elaborate models of large bridge systems with strong electronic interactions.

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches.

PubMed

Xu, Zhenli; Ma, Manman; Liu, Pei

2014-07-01

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

On Bi-Grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Ibraheem, S. O.; Demuren, A. O.

1994-01-01

A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely Spatial, Eigenvalue and Combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergence rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central scheme.

High-order rogue waves of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Liu, Wei

2017-10-01

High-order rogue wave solutions of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin-Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

Applications of the ETEM for obtaining optical soliton solutions for the Lakshmanan-Porsezian-Daniel model

NASA Astrophysics Data System (ADS)

Manafian, Jalil; Foroutan, Mohammadreza; Guzali, Aref

2017-11-01

This paper examines the effectiveness of an integration scheme which is called the extended trial equation method (ETEM) for solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the Lakshmanan-Porsezian-Daniel (LPD) equation with Kerr and power laws of nonlinearity which describes higher-order dispersion, full nonlinearity and spatiotemporal dispersion is considered, and as an achievement, a series of exact travelling-wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of LPD equation. The movement of obtained solutions is shown graphically, which helps to understand the physical phenomena of this optical soliton equation. Many other such types of nonlinear equations arising in basic fabric of communications network technology and nonlinear optics can also be solved by this method.

MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model - User Guide to Modularization Concepts and the Ground-Water Flow Process

USGS Publications Warehouse

Harbaugh, Arlen W.; Banta, Edward R.; Hill, Mary C.; McDonald, Michael G.

2000-01-01

MODFLOW is a computer program that numerically solves the three-dimensional ground-water flow equation for a porous medium by using a finite-difference method. Although MODFLOW was designed to be easily enhanced, the design was oriented toward additions to the ground-water flow equation. Frequently there is a need to solve additional equations; for example, transport equations and equations for estimating parameter values that produce the closest match between model-calculated heads and flows and measured values. This report documents a new version of MODFLOW, called MODFLOW-2000, which is designed to accommodate the solution of equations in addition to the ground-water flow equation. This report is a user's manual. It contains an overview of the old and added design concepts, documents one new package, and contains input instructions for using the model to solve the ground-water flow equation.

An Evaluation of Statistical Strategies for Making Equating Function Selections. Research Report. ETS RR-08-60

ERIC Educational Resources Information Center

Moses, Tim

2008-01-01

Nine statistical strategies for selecting equating functions in an equivalent groups design were evaluated. The strategies of interest were likelihood ratio chi-square tests, regression tests, Kolmogorov-Smirnov tests, and significance tests for equated score differences. The most accurate strategies in the study were the likelihood ratio tests…

Teaching E=mc2: An Exploration of Some Issues.

ERIC Educational Resources Information Center

Baierlein, Ralph

1991-01-01

A discussion of what E=mc2 means and other issues associated with the equation are presented. The differences between matter, mass, and energy, a derivation of the equation, the history of the word mass and examples of how it is used, misconceptions surrounding the equation, and a discussion of uranium fission are included. (KR)

An Analysis of Test Equating Models for the Alabama High School Graduation Examination.

ERIC Educational Resources Information Center

Glowacki, Margaret L.

The purpose of this study was to determine which equating models are appropriate for the Alabama High School Graduation Examination (AHSGE) by equating two previously administered fall forms for each subject area of the AHSGE and determining whether differences exist in the test score distributions or passing scores resulting from the equating…

Estimating Slash Quantity from Standing Loblolly Pine

Treesearch

Dale D. Wade

1969-01-01

No significant difference were found between variances of two prediction equations for estimating loblolly pine crown weight from diameter breast height (d.b.h). One equation was developed from trees on the Georgia Piedmont and the other from tress on the South Carolina Coastal Plain. An equation and table are presented for estimating loblolly pine slash weights from...

Generalized Path Analysis and Generalized Simultaneous Equations Model for Recursive Systems with Responses of Mixed Types

ERIC Educational Resources Information Center

Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang

2006-01-01

This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…

Factors Affecting Differential Equation Problem Solving Ability of Students at Pre-University Level: A Conceptual Model

ERIC Educational Resources Information Center

Aisha, Bibi; Zamri, Sharifa NorulAkmar Syed; Abdallah, Nabeel; Abedalaziz, Mohammad; Ahmad, Mushtaq; Satti, Umbreen

2017-01-01

In this study, different factors affecting students' differential equations (DEs) solving abilities were explored at pre university level. To explore main factors affecting students' differential equations problem solving ability, articles for a 19-year period, from 1996 to 2015, were critically reviewed and analyzed. It was revealed that…

New Results on the Linear Equating Methods for the Non-Equivalent-Groups Design

ERIC Educational Resources Information Center

von Davier, Alina A.

2008-01-01

The two most common observed-score equating functions are the linear and equipercentile functions. These are often seen as different methods, but von Davier, Holland, and Thayer showed that any equipercentile equating function can be decomposed into linear and nonlinear parts. They emphasized the dominant role of the linear part of the nonlinear…

Multigrid method for the equilibrium equations of elasticity using a compact scheme

NASA Technical Reports Server (NTRS)

Taasan, S.

1986-01-01

A compact difference scheme is derived for treating the equilibrium equations of elasticity. The scheme is inconsistent and unstable. A multigrid method which takes into account these properties is described. The solution of the discrete equations, up to the level of discretization errors, is obtained by this method in just two multigrid cycles.

Collateral Information for Equating in Small Samples: A Preliminary Investigation

ERIC Educational Resources Information Center

Kim, Sooyeon; Livingston, Samuel A.; Lewis, Charles

2011-01-01

This article describes a preliminary investigation of an empirical Bayes (EB) procedure for using collateral information to improve equating of scores on test forms taken by small numbers of examinees. Resampling studies were done on two different forms of the same test. In each study, EB and non-EB versions of two equating methods--chained linear…

Numerical study of hydrogen-air supersonic combustion by using elliptic and parabolized equations

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.

1986-01-01

The two-dimensional Navier-Stokes and species continuity equations are used to investigate supersonic chemically reacting flow problems which are related to scramjet-engine configurations. A global two-step finite-rate chemistry model is employed to represent the hydrogen-air combustion in the flow. An algebraic turbulent model is adopted for turbulent flow calculations. The explicit unsplit MacCormack finite-difference algorithm is used to develop a computer program suitable for a vector processing computer. The computer program developed is then used to integrate the system of the governing equations in time until convergence is attained. The chemistry source terms in the species continuity equations are evaluated implicitly to alleviate stiffness associated with fast chemical reactions. The problems solved by the elliptic code are re-investigated by using a set of two-dimensional parabolized Navier-Stokes and species equations. A linearized fully-coupled fully-implicit finite difference algorithm is used to develop a second computer code which solves the governing equations by marching in spce rather than time, resulting in a considerable saving in computer resources. Results obtained by using the parabolized formulation are compared with the results obtained by using the fully-elliptic equations. The comparisons indicate fairly good agreement of the results of the two formulations.

Complex Riccati equations as a link between different approaches for the description of dissipative and irreversible systems

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2012-08-01

Quantum mechanics is essentially described in terms of complex quantities like wave functions. The interesting point is that phase and amplitude of the complex wave function are not independent of each other, but coupled by some kind of conservation law. This coupling exists in time-independent quantum mechanics and has a counterpart in its time-dependent form. It can be traced back to a reformulation of quantum mechanics in terms of nonlinear real Ermakov equations or equivalent complex nonlinear Riccati equations, where the quadratic term in the latter equation explains the origin of the phase-amplitude coupling. Since realistic physical systems are always in contact with some kind of environment this aspect is also taken into account. In this context, different approaches for describing open quantum systems, particularly effective ones, are discussed and compared. Certain kinds of nonlinear modifications of the Schrödinger equation are discussed as well as their interrelations and their relations to linear approaches via non-unitary transformations. The modifications of the aforementioned Ermakov and Riccati equations when environmental effects are included can be determined in the time-dependent case. From formal similarities conclusions can be drawn how the equations of time-independent quantum mechanics can be modified to also incluce the enviromental aspects.

Solving Equations Today.

ERIC Educational Resources Information Center

Shumway, Richard J.

1989-01-01

Illustrated is the problem of solving equations and some different strategies students might employ when using available technology. Gives illustrations for: exact solutions, approximate solutions, and approximate solutions which are graphically generated. (RT)

Recursive utility in a Markov environment with stochastic growth

PubMed Central

Hansen, Lars Peter; Scheinkman, José A.

2012-01-01

Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron–Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility. PMID:22778428

Rogue-wave solutions of the Zakharov equation

NASA Astrophysics Data System (ADS)

Rao, Jiguang; Wang, Lihong; Liu, Wei; He, Jingsong

2017-12-01

Using the bilinear transformation method, we derive general rogue-wave solutions of the Zakharov equation. We present these Nth-order rogue-wave solutions explicitly in terms of Nth-order determinants whose matrix elements have simple expressions. We show that the fundamental rogue wave is a line rogue wave with a line profile on the plane ( x, y) arising from a constant background at t ≪ 0 and then gradually tending to the constant background for t ≫ 0. Higher-order rogue waves arising from a constant background and later disappearing into it describe the interaction of several fundamental line rogue waves. We also consider different structures of higher-order rogue waves. We present differences between rogue waves of the Zakharov equation and of the first type of the Davey-Stewartson equation analytically and graphically.

The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation

NASA Astrophysics Data System (ADS)

Oliveira, F. De; Franco, S. R.; Pinto, M. A. Villela

2018-02-01

The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.

Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules

NASA Astrophysics Data System (ADS)

Sazonov, S. V.; Ustinov, N. V.

2017-02-01

The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky-Vakhnenko equation. Different types of solutions of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.

Kinetic treatment of nonlinear ion-acoustic waves in multi-ion plasma

NASA Astrophysics Data System (ADS)

Ahmad, Zulfiqar; Ahmad, Mushtaq; Qamar, A.

2017-09-01

By applying the kinetic theory of the Valsove-Poisson model and the reductive perturbation technique, a Korteweg-de Vries (KdV) equation is derived for small but finite amplitude ion acoustic waves in multi-ion plasma composed of positive and negative ions along with the fraction of electrons. A correspondent equation is also derived from the basic set of fluid equations of adiabatic ions and isothermal electrons. Both kinetic and fluid KdV equations are stationary solved with different nature of coefficients. Their differences are discussed both analytically and numerically. The criteria of the fluid approach as a limiting case of kinetic theory are also discussed. The presence of negative ion makes some modification in the solitary structure that has also been discussed with its implication at the laboratory level.

Recursive utility in a Markov environment with stochastic growth.

PubMed

Hansen, Lars Peter; Scheinkman, José A

2012-07-24

Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron-Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility.

A novel unsplit perfectly matched layer for the second-order acoustic wave equation.

PubMed

Ma, Youneng; Yu, Jinhua; Wang, Yuanyuan

2014-08-01

When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach. Copyright © 2014 Elsevier B.V. All rights reserved.

Explicit solution of integrated 1 - exp equation for predicting accumulation and decline of concentrations for drugs obeying nonlinear saturation kinetics.

PubMed

Keller, Frieder; Hartmann, Bertram; Czock, David

2009-12-01

To describe nonlinear, saturable pharmacokinetics, the Michaelis-Menten equation is frequently used. However, the Michaelis-Menten equation has no integrated solution for concentrations but only for the time factor. Application of the Lambert W function was proposed recently to obtain an integrated solution of the Michaelis-Menten equation. As an alternative to the Michaelis-Menten equation, a 1 - exp equation has been used to describe saturable kinetics, with the advantage that the integrated 1 - exp equation has an explicit solution for concentrations. We used the integrated 1 - exp equation to predict the accumulation kinetics and the nonlinear concentration decline for a proposed fictive drug. In agreement with the recently proposed method, we found that for the integrated 1 - exp equation no steady state is obtained if the maximum rate of change in concentrations (Vmax) within interval (Tau) is less than the difference between peak and trough concentrations (Vmax x Tau < C peak - C trough).

A Variational Formalism for the Radiative Transfer Equation and a Geostrophic, Hydrostatic Atmosphere: Prelude to Model 3

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.

1991-01-01

The second step in development of MODEL III is summarized. It combines the four radiative transfer equations of the first step with the equations for a geostrophic and hydrostatic atmosphere. This step is intended to bring radiance into a three dimensional balance with wind, height, and temperature. The use of the geostrophic approximation in place of the full set of primitive equations allows for an easier evaluation of how the inclusion of the radiative transfer equation increases the complexity of the variational equations. Seven different variational formulations were developed for geostrophic, hydrostatic, and radiative transfer equations. The first derivation was too complex to yield solutions that were physically meaningful. For the remaining six derivations, the variational method gave the same physical interpretation (the observed brightness temperatures could provide no meaningful input to a geostrophic, hydrostatic balance) at least through the problem solving methodology used in these studies. The variational method is presented and the Euler-Lagrange equations rederived for the geostrophic, hydrostatic, and radiative transfer equations.

Evaluation of mean-monthly streamflow-regression equations for Colorado, 2014

USGS Publications Warehouse

Kohn, Michael S.; Stevens, Michael R.; Bock, Andrew R.; Char, Stephen J.

2015-01-01

The median absolute differences between the observed and computed mean-monthly streamflow for Mountain, Northwest, and Southwest hydrologic regions are fairly uniform throughout the year, with the exception of late summer and early fall (July, August, and September), when each hydrologic region exhibits a substantial increase in median absolute percent difference. The greatest difference occurs in the Northwest hydrologic region, and the smallest difference occurs in the Mountain hydrologic region. The Rio Grande hydrologic region shows seasonal variation in median absolute percent difference with March, April, August, and September having a median absolute difference near or below 40 percent, and the remaining months of the year having a median absolute difference near or above 50 percent. In the Mountain, Northwest, and Southwest hydrologic regions, the mean-monthly streamflow equations perform the best during spring (March, April, and May). However, in the Rio Grande hydrologic region, the mean-monthly streamflow equations perform the best during late summer and early fall (August and September).

On differential operators generating iterative systems of linear ODEs of maximal symmetry algebra

NASA Astrophysics Data System (ADS)

Ndogmo, J. C.

2017-06-01

Although every iterative scalar linear ordinary differential equation is of maximal symmetry algebra, the situation is different and far more complex for systems of linear ordinary differential equations, and an iterative system of linear equations need not be of maximal symmetry algebra. We illustrate these facts by examples and derive families of vector differential operators whose iterations are all linear systems of equations of maximal symmetry algebra. Some consequences of these results are also discussed.

Exact RG flow equations and quantum gravity

NASA Astrophysics Data System (ADS)

de Alwis, S. P.

2018-03-01

We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg's asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.

Time-delayed reaction-diffusion fronts

NASA Astrophysics Data System (ADS)

Isern, Neus; Fort, Joaquim

2009-11-01

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic transition. For this application the new equation yields speeds about 10% slower than the previous one.

USACE National Coastal Mapping Program and the Next Generation of Data Products

DTIC Science & Technology

2010-06-01

Difference Vegetation Index ( NDVI ) equation. This equation uses a near infrared band (NIR) at 738 nm and a red band (RED) at 624 nm [6]. This equation is...shown in (1), NIR - RED / NIR + RED = NDVI value. (1) The pixels that have a NDVI value less than -0.05 are then classified into the...classify these pixels as the “No Lidar” class. Step 5 utilizes the NDVI equation, (1), to separate out the vegetation pixels from the non

A new unified theory of electromagnetic and gravitational interactions

NASA Astrophysics Data System (ADS)

Li, Li-Xin

2016-12-01

In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the fivedimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is obtained: ∇a F ab - ξ R b a A a = -4π J b with ξ = -2, where F ab is the antisymmetric electromagnetic field tensor defined by the potential vector A a , R ab is the Ricci curvature tensor of the hypersurface, and J a is the electric current density vector. The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term ξ R b a A a , whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge, as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. 48, 28 (2016)]. Hence, the new unified theory is physically different from Kaluza-Klein theory and its variants in which the Einstein-Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under certain conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2016-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

Generalized spheroidal wave equation and limiting cases

NASA Astrophysics Data System (ADS)

Figueiredo, B. D. Bonorino

2007-01-01

We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the complex plane but present series coefficients proportional to each other. These solutions for the GSWE afford solutions to a double-confluent Heun equation by a taking-limit process due to Leaver. [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)]. Another procedure, called Whittaker-Ince limit [B. D. Figueiredo, J. Math. Phys. 46, 113503 (2005)], provides solutions in series of powers and Bessel functions for two other equations with a different type of singularity at infinity. In addition, new solutions are obtained for the Whittaker-Hill and Mathieu equations [F. M. Arscott, Proc. R. Soc. Edinburg A67, 265 (1967)] by considering these as special cases of both the confluent and double-confluent Heun equations. In particular, we find that each of the Lindemann-Stieltjes solutions for the Mathieu equation [E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press (1945)] is associated with two expansions in series of Bessel functions. We also discuss a set of solutions in series of hypergeometric and confluent hypergeometric functions for the GSWE and use their Leaver limits to obtain infinite-series solutions for the Schrödinger equation with an asymmetric double-Morse potential. Finally, the possibility of extending the solutions of the GSWE to the general Heun equation is briefly discussed.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2017-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

Predictive validity of four bioelectrical impedance equations in determining percent fat mass in overweight and obese children.

PubMed

Cleary, Jane; Daniells, Suzie; Okely, Anthony D; Batterham, Marijka; Nicholls, Jessie

2008-01-01

Bioelectrical impedance equations are frequently used by food and nutrition professionals to estimate percent fat mass in overweight and obese children. However, it is not known whether they are accurate for such children, as they have been primarily developed for children of varying body weights. The aim of this cross-sectional study was to evaluate the predictive validity of four previously published prediction equations developed for the pediatric population, among a sample of overweight and obese children. Thirty overweight or obese children (mean age=7.57+/-1.28 years) underwent measurement of fat mass, percent fat mass, and fat-free mass using dual-energy x-ray absorptiometry (DEXA) and bioelectrical impedance analysis (BIA). Impedance values from the BIA were entered into the four prediction equations and Pearson correlations used to determine the significance of associations between each of the BIA prediction equations and DEXA for percent fat mass, fat mass, and fat-free mass. For percent fat mass, paired t tests were used to assess differences between the methods and the technique of Bland and Altman was used to determine bias and error. Results showed that the mean percent fat mass as determined by DEXA for this age group was 40.79%. In comparison with other BIA prediction equations, the Schaefer equation had the closest mean value of 41.98%, and was the only equation not to significantly differ from the DEXA (P=0.121). This study suggests that the Schaefer equation is the only accurate BIA prediction equation for assessing percent fat mass in this sample of overweight and obese children from primarily white backgrounds.

Glottal flow through a two-mass model: comparison of Navier-Stokes solutions with simplified models.

PubMed

de Vries, M P; Schutte, H K; Veldman, A E P; Verkerke, G J

2002-04-01

A new numerical model of the vocal folds is presented based on the well-known two-mass models of the vocal folds. The two-mass model is coupled to a model of glottal airflow based on the incompressible Navier-Stokes equations. Glottal waves are produced using different initial glottal gaps and different subglottal pressures. Fundamental frequency, glottal peak flow, and closed phase of the glottal waves have been compared with values known from the literature. The phonation threshold pressure was determined for different initial glottal gaps. The phonation threshold pressure obtained using the flow model with Navier-Stokes equations corresponds better to values determined in normal phonation than the phonation threshold pressure obtained using the flow model based on the Bernoulli equation. Using the Navier-Stokes equations, an increase of the subglottal pressure causes the fundamental frequency and the glottal peak flow to increase, whereas the fundamental frequency in the Bernoulli-based model does not change with increasing pressure.

Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

NASA Astrophysics Data System (ADS)

Su, Bo; Tuo, Xianguo; Xu, Ling

2017-08-01

Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

NASA Technical Reports Server (NTRS)

Bates, J. R.; Semazzi, F. H. M.; Higgins, R. W.; Barros, Saulo R. M.

1990-01-01

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. I - Adiabatic formulation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Moorthi, S.; Higgins, R. W.

1993-01-01

An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.

A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations

NASA Technical Reports Server (NTRS)

Gerritsen, Margot; Olsson, Pelle

1996-01-01

We derive a high-order finite difference scheme for the Euler equations that satisfies a semi-discrete energy estimate, and present an efficient strategy for the treatment of discontinuities that leads to sharp shock resolution. The formulation of the semi-discrete energy estimate is based on a symmetrization of the Euler equations that preserves the homogeneity of the flux vector, a canonical splitting of the flux derivative vector, and the use of difference operators that satisfy a discrete analogue to the integration by parts procedure used in the continuous energy estimate. Around discontinuities or sharp gradients, refined grids are created on which the discrete equations are solved after adding a newly constructed artificial viscosity. The positioning of the sub-grids and computation of the viscosity are aided by a detection algorithm which is based on a multi-scale wavelet analysis of the pressure grid function. The wavelet theory provides easy to implement mathematical criteria to detect discontinuities, sharp gradients and spurious oscillations quickly and efficiently.

Equation of state of an ideal gas with nonergodic behavior in two connected vessels.

PubMed

Naplekov, D M; Semynozhenko, V P; Yanovsky, V V

2014-01-01

We consider a two-dimensional collisionless ideal gas in the two vessels connected through a small hole. One of them is a well-behaved chaotic billiard, another one is known to be nonergodic. A significant part of the second vessel's phase space is occupied by an island of stability. In the works of Zaslavsky and coauthors, distribution of Poincaré recurrence times in similar systems was considered. We study the gas pressure in the vessels; it is uniform in the first vessel and not uniform in second one. An equation of the gas state in the first vessel is obtained. Despite the very different phase-space structure, behavior of the second vessel is found to be very close to the behavior of a good ergodic billiard but of different volume. The equation of state differs from the ordinary equation of ideal gas state by an amendment to the vessel's volume. Correlation of this amendment with a share of the phase space under remaining intact islands of stability is shown.

PREFACE: Symmetries and Integrability of Difference Equations

NASA Astrophysics Data System (ADS)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane

2007-10-01

The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of Kent in Canterbury, UK (1996), in Sabaudia near Rome, Italy (1998), at the University of Tokyo, Japan (2000), in Giens, France (2002), and in Helsinki, Finland (2004). The SIDE VII meeting was held at the University of Melbourne from 10-14 July 2006. The scientific committee consisted of Nalini Joshi (The University of Sydney), Frank W Nijhoff (University of Leeds), Reinout Quispel (La Trobe University) and Colin Rogers (University of New South Wales). The local organization was in the hands of John A G Roberts and Wolfgang K Schief. Proceedings of all the previous SIDE meetings have been published; the 1994 and 1988 meetings (edited respectively by D Levi, L Vinet and P Winternitz, and by D Levi and O Ragnisco) as volumes of the CRM Proceedings and Lecture Notes (AMS Publications), the 1996 meeting (edited by P Clarkson and F W Nijhoff) as Volume 255 in the LMS Lecture Note Series. Starting from the 1996 meeting the formula of publication has been changed to include rather selected refereed contributions submitted in response to a call for papers issued after the meetings and not restricted to their participants. Thus publications reflecting the scope of the 1996 meeting (edited by J Hietarinta, F W Nijhoff and J Satsuma) appeared in Journal of Physics A: Mathematical and General 34 48 (special issue), and of the 1998 and 2000 meetings (edited respectively by F W Nijhoff, Yu B Suris and C-M Viallet, and by J F van Diejen and R Halburd) in Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2). The aim of this special issue is to benefit from the occasion offered by the SIDE VII meeting, producing an issue containing papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. This special issue features high quality research papers and invited reviews which deal with themes that were covered by the SIDE VII conference. These are in alphabetical order: Algebraic-geometric approaches to integrability. The first section contains a paper by T Hamamoto and K Kajiwara on hypergeometric solutions to the q-Painlevé equation of type A4(1). Discrete geometry. In this category there are three papers. J Cielinski offers a geometric definition and a spectral approach on pseudospherical surfaces on time scales, while A Doliwa considers generalized isothermic lattices. The paper by U Pinkall, B Springborn and S Weiss mann is concerned with a new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow. Integrable systems in statistical physics. Under this heading there is a paper by R J Baxter on corner transfer matrices in statistical mechanics, and a paper by S Boukraa, S Hassani, J-M Maillard, B M McCoy, J-A Weil and N Zenine where the authors consider Fuchs-Painlevé elliptic representation of the Painlevé VI equation. KP lattices and differential-difference hierarchies. In this section we have seven articles. C R Gilson, J J C Nimmo and Y Ohta consider quasideterminant solutions of a non-Abelian Hirota-Miwa equation, while B Grammaticos, A Ramani, V Papageorgiou, J Satsuma and R Willox discuss the construction of lump-like solutions of the Hirota-Miwa equation. J Hietarinta and C Viallet analyze the factorization process for lattice maps searching for integrable cases, the paper by X-B Hu and G-F Yu is concerned with integrable discretizations of the (2+1)-dimensional sinh-Gordon equation, and K Kajiwara, M Mazzocco and Y Ohta consider the Hankel determinant formula of the tau-functions of the Toda equation. Finally, V G Papageorgiou and A G Tongas study Yang-Baxter maps and multi-field integrable lattice equations, and H-Y Wang, X-B Hu and H-W Tam consider the two-dimensional Leznov lattice equation with self-consistent sources. Quantum integrable systems. This category contains a paper on q-extended eigenvectors of the integral and finite Fourier transforms by N M Atakishiyev, J P Rueda and K B Wolf, and an article by S M Sergeev on quantization of three-wave equations. Random matrix theory. This section contains a paper by A V Kitaev on the boundary conditions for scaled random matrix ensembles in the bulk of the spectrum. Symmetries and conservation laws. In this section we have five articles. H Gegen, X-B Hu, D Levi and S Tsujimoto consider a difference-analogue of Davey-Stewartson system giving its discrete Gram-type determinant solution and Lax pair. The paper by D Levi, M Petrera, and C Scimiterna is about the lattice Schwarzian KDV equation and its symmetries, while O G Rasin and P E Hydon study the conservation laws for integrable difference equations. S Saito and N Saitoh discuss recurrence equations associated with invariant varieties of periodic points, and P H van der Kamp presents closed-form expressions for integrals of MKDV and sine-Gordon maps. Ultra-discrete systems. This final category contains an article by C Ormerod on connection matrices for ultradiscrete linear problems. We would like to express our sincerest thanks to all contributors, and to everyone involved in compiling this special issue.

Fourth order difference methods for hyperbolic IBVP's

NASA Technical Reports Server (NTRS)

Gustafsson, Bertil; Olsson, Pelle

1994-01-01

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Selection by consequences, behavioral evolution, and the price equation.

PubMed

Baum, William M

2017-05-01

Price's equation describes evolution across time in simple mathematical terms. Although it is not a theory, but a derived identity, it is useful as an analytical tool. It affords lucid descriptions of genetic evolution, cultural evolution, and behavioral evolution (often called "selection by consequences") at different levels (e.g., individual vs. group) and at different time scales (local and extended). The importance of the Price equation for behavior analysis lies in its ability to precisely restate selection by consequences, thereby restating, or even replacing, the law of effect. Beyond this, the equation may be useful whenever one regards ontogenetic behavioral change as evolutionary change, because it describes evolutionary change in abstract, general terms. As an analytical tool, the behavioral Price equation is an excellent aid in understanding how behavior changes within organisms' lifetimes. For example, it illuminates evolution of response rate, analyses of choice in concurrent schedules, negative contingencies, and dilemmas of self-control. © 2017 Society for the Experimental Analysis of Behavior.

Certain bright soliton interactions of the Sasa-Satsuma equation in a monomode optical fiber

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Chai, Han-Peng; Yuan, Yu-Qiang

2017-03-01

Under investigation in this paper is the Sasa-Satsuma equation, which describes the propagation of ultrashort pulses in a monomode fiber with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Based on the known bilinear forms, through the modified expanded formulas and symbolic computation, we construct the bright two-soliton solutions. Through classifying the interactions under different parameter conditions, we reveal six cases of interactions between the two solitons via an asymptotic analysis. With the help of the analytic and graphic analysis, we find that such interactions are different from those of the nonlinear Schrödinger equation and Hirota equation. When those solitons interact with each other, the singular-I soliton is shape-preserving, while the singular-II and nonsingular solitons may be shape preserving or shape changing. Such elastic and inelastic interaction phenomena in a scalar equation might enrich the knowledge of soliton behavior, which could be expected to be experimentally observed.

Certain bright soliton interactions of the Sasa-Satsuma equation in a monomode optical fiber.

PubMed

Liu, Lei; Tian, Bo; Chai, Han-Peng; Yuan, Yu-Qiang

2017-03-01

Under investigation in this paper is the Sasa-Satsuma equation, which describes the propagation of ultrashort pulses in a monomode fiber with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Based on the known bilinear forms, through the modified expanded formulas and symbolic computation, we construct the bright two-soliton solutions. Through classifying the interactions under different parameter conditions, we reveal six cases of interactions between the two solitons via an asymptotic analysis. With the help of the analytic and graphic analysis, we find that such interactions are different from those of the nonlinear Schrödinger equation and Hirota equation. When those solitons interact with each other, the singular-I soliton is shape-preserving, while the singular-II and nonsingular solitons may be shape preserving or shape changing. Such elastic and inelastic interaction phenomena in a scalar equation might enrich the knowledge of soliton behavior, which could be expected to be experimentally observed.

Fiber-dependent deautonomization of integrable 2D mappings and discrete Painlevé equations

NASA Astrophysics Data System (ADS)

Carstea, Adrian Stefan; Dzhamay, Anton; Takenawa, Tomoyuki

2017-10-01

It is well known that two-dimensional mappings preserving a rational elliptic fibration, like the Quispel-Roberts-Thompson mappings, can be deautonomized to discrete Painlevé equations. However, the dependence of this procedure on the choice of a particular elliptic fiber has not been sufficiently investigated. In this paper we establish a way of performing the deautonomization for a pair of an autonomous mapping and a fiber. Starting from a single autonomous mapping but varying the type of a chosen fiber, we obtain different types of discrete Painlevé equations using this deautonomization procedure. We also introduce a technique for reconstructing a mapping from the knowledge of its induced action on the Picard group and some additional geometric data. This technique allows us to obtain factorized expressions of discrete Painlevé equations, including the elliptic case. Further, by imposing certain restrictions on such non-autonomous mappings we obtain new and simple elliptic difference Painlevé equations, including examples whose symmetry groups do not appear explicitly in Sakai’s classification.

Simulation of subwavelength metallic gratings using a new implementation of the recursive convolution finite-difference time-domain algorithm.

PubMed

Banerjee, Saswatee; Hoshino, Tetsuya; Cole, James B

2008-08-01

We introduce a new implementation of the finite-difference time-domain (FDTD) algorithm with recursive convolution (RC) for first-order Drude metals. We implemented RC for both Maxwell's equations for light polarized in the plane of incidence (TM mode) and the wave equation for light polarized normal to the plane of incidence (TE mode). We computed the Drude parameters at each wavelength using the measured value of the dielectric constant as a function of the spatial and temporal discretization to ensure both the accuracy of the material model and algorithm stability. For the TE mode, where Maxwell's equations reduce to the wave equation (even in a region of nonuniform permittivity) we introduced a wave equation formulation of RC-FDTD. This greatly reduces the computational cost. We used our methods to compute the diffraction characteristics of metallic gratings in the visible wavelength band and compared our results with frequency-domain calculations.

Ill-posedness of Dynamic Equations of Compressible Granular Flow

NASA Astrophysics Data System (ADS)

Shearer, Michael; Gray, Nico

2017-11-01

We introduce models for 2-dimensional time-dependent compressible flow of granular materials and suspensions, based on the rheology of Pouliquen and Forterre. The models include density dependence through a constitutive equation in which the density or volume fraction of solid particles with material density ρ* is taken as a function of an inertial number I: ρ = ρ * Φ(I), in which Φ(I) is a decreasing function of I. This modelling has different implications from models relying on critical state soil mechanics, in which ρ is treated as a variable in the equations, contributing to a flow rule. The analysis of the system of equations builds on recent work of Barker et al in the incompressible case. The main result is the identification of a criterion for well-posedness of the equations. We additionally analyze a modification that applies to suspensions, for which the rheology takes a different form and the inertial number reflects the role of the fluid viscosity.

A solution to neural field equations by a recurrent neural network method

NASA Astrophysics Data System (ADS)

Alharbi, Abir

2012-09-01

Neural field equations (NFE) are used to model the activity of neurons in the brain, it is introduced from a single neuron 'integrate-and-fire model' starting point. The neural continuum is spatially discretized for numerical studies, and the governing equations are modeled as a system of ordinary differential equations. In this article the recurrent neural network approach is used to solve this system of ODEs. This consists of a technique developed by combining the standard numerical method of finite-differences with the Hopfield neural network. The architecture of the net, energy function, updating equations, and algorithms are developed for the NFE model. A Hopfield Neural Network is then designed to minimize the energy function modeling the NFE. Results obtained from the Hopfield-finite-differences net show excellent performance in terms of accuracy and speed. The parallelism nature of the Hopfield approaches may make them easier to implement on fast parallel computers and give them the speed advantage over the traditional methods.

Solutions of the cylindrical nonlinear Maxwell equations.

PubMed

Xiong, Hao; Si, Liu-Gang; Ding, Chunling; Lü, Xin-You; Yang, Xiaoxue; Wu, Ying

2012-01-01

Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical nonlinear Maxwell equations and presents an interesting connection between the exact solutions for different cylindrical nonlinear Maxwell equations. We also provide some examples and discussion to show the application of the results we obtained. Our results provide the basis for solving complex systems of nonlinearity and inhomogeneity with simple systems.

Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation

PubMed Central

Garić-Demirović, M.; Kulenović, M. R. S.; Nurkanović, M.

2013-01-01

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x n+1 = x n−1 2/(ax n 2 + bx n x n−1 + cx n−1 2), n = 0,1, 2,…, where the parameters a,  b, and  c are positive numbers and the initial conditions x −1 and x 0 are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable. PMID:24369451

Regularization of the Perturbed Spatial Restricted Three-Body Problem by L-Transformations

NASA Astrophysics Data System (ADS)

Poleshchikov, S. M.

2018-03-01

Equations of motion for the perturbed circular restricted three-body problem have been regularized in canonical variables in a moving coordinate system. Two different L-matrices of the fourth order are used in the regularization. Conditions for generalized symplecticity of the constructed transform have been checked. In the unperturbed case, the regular equations have a polynomial structure. The regular equations have been numerically integrated using the Runge-Kutta-Fehlberg method. The results of numerical experiments are given for the Earth-Moon system parameters taking into account the perturbation of the Sun for different L-matrices.

Preconditioning and the limit to the incompressible flow equations

NASA Technical Reports Server (NTRS)

Turkel, E.; Fiterman, A.; Vanleer, B.

1993-01-01

The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations are considered. The relation between them for both the continuous problem and the finite difference approximation is also considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Hence, the steady state of the preconditioned system is the same as the steady state of the original system. For finite difference methods the preconditioning can change and improve the steady state solutions. An application to flow around an airfoil is presented.

Novel Equations for Estimating Lean Body Mass in Patients With Chronic Kidney Disease.

PubMed

Tian, Xue; Chen, Yuan; Yang, Zhi-Kai; Qu, Zhen; Dong, Jie

2018-05-01

Simplified methods to estimate lean body mass (LBM), an important nutritional measure representing muscle mass and somatic protein, are lacking in nondialyzed patients with chronic kidney disease (CKD). We developed and tested 2 reliable equations for estimation of LBM in daily clinical practice. The development and validation groups both included 150 nondialyzed patients with CKD Stages 3 to 5. Two equations for estimating LBM based on mid-arm muscle circumference (MAMC) or handgrip strength (HGS) were developed and validated in CKD patients with dual-energy x-ray absorptiometry as referenced gold method. We developed and validated 2 equations for estimating LBM based on HGS and MAMC. These equations, which also incorporated sex, height, and weight, were developed and validated in CKD patients. The new equations were found to exhibit only small biases when compared with dual-energy x-ray absorptiometry, with median differences of 0.94 and 0.46 kg observed in the HGS and MAMC equations, respectively. Good precision and accuracy were achieved for both equations, as reflected by small interquartile ranges in the differences and in the percentages of estimates that were 20% of measured LBM. The bias, precision, and accuracy of each equation were found to be similar when it was applied to groups of patients divided by the median measured LBM, the median ratio of extracellular to total body water, and the stages of CKD. LBM estimated from MAMC or HGS were found to provide accurate estimates of LBM in nondialyzed patients with CKD. Copyright © 2017 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.

A modified exponential behavioral economic demand model to better describe consumption data.

PubMed

Koffarnus, Mikhail N; Franck, Christopher T; Stein, Jeffrey S; Bickel, Warren K

2015-12-01

Behavioral economic demand analyses that quantify the relationship between the consumption of a commodity and its price have proven useful in studying the reinforcing efficacy of many commodities, including drugs of abuse. An exponential equation proposed by Hursh and Silberberg (2008) has proven useful in quantifying the dissociable components of demand intensity and demand elasticity, but is limited as an analysis technique by the inability to correctly analyze consumption values of zero. We examined an exponentiated version of this equation that retains all the beneficial features of the original Hursh and Silberberg equation, but can accommodate consumption values of zero and improves its fit to the data. In Experiment 1, we compared the modified equation with the unmodified equation under different treatments of zero values in cigarette consumption data collected online from 272 participants. We found that the unmodified equation produces different results depending on how zeros are treated, while the exponentiated version incorporates zeros into the analysis, accounts for more variance, and is better able to estimate actual unconstrained consumption as reported by participants. In Experiment 2, we simulated 1,000 datasets with demand parameters known a priori and compared the equation fits. Results indicated that the exponentiated equation was better able to replicate the true values from which the test data were simulated. We conclude that an exponentiated version of the Hursh and Silberberg equation provides better fits to the data, is able to fit all consumption values including zero, and more accurately produces true parameter values. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

Superposition of elliptic functions as solutions for a large number of nonlinear equations

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

Khare, Avinash; Saxena, Avadh

2014-03-15

For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ{sup 4}, the discrete MKdV as well asmore » for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn{sup 2}(x, m), it also admits solutions in terms of dn {sup 2}(x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations.« less

An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher-KPP equation

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.; Trifonov, A. Yu.

A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP) equation under the supposition of weak diffusion. In terms of the semiclassical formalism developed, the original nonlinear equation is reduced to an associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation with a given accuracy of the asymptotic parameter. The solutions of the nonlinear equation are constructed from the solutions of both the linear equation and the algebraic equations. The solutions of the linear problem are found with the use of symmetry operators. A countable family of the leading terms of the semiclassical asymptotics is constructed in explicit form. The semiclassical asymptotics are valid by construction in a finite time interval. We construct asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher-KPP equation at large times. In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Methods of separation of variables in turbulence theory

NASA Technical Reports Server (NTRS)

Tsuge, S.

1978-01-01

Two schemes of closing turbulent moment equations are proposed both of which make double correlation equations separated into single-point equations. The first is based on neglected triple correlation, leading to an equation differing from small perturbed gasdynamic equations where the separation constant appears as the frequency. Grid-produced turbulence is described in this light as time-independent, cylindrically-isotropic turbulence. Application to wall turbulence guided by a new asymptotic method for the Orr-Sommerfeld equation reveals a neutrally stable mode of essentially three dimensional nature. The second closure scheme is based on an assumption of identity of the separated variables through which triple and quadruple correlations are formed. The resulting equation adds, to its equivalent of the first scheme, an integral of nonlinear convolution in the frequency describing a role due to triple correlation of direct energy-cascading.

The nonlinear modified equation approach to analyzing finite difference schemes

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1981-01-01

The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound

NASA Astrophysics Data System (ADS)

Perelomova, Anna

2006-08-01

The equation of energy balance is subdivided into two dynamics equations, one describing evolution of the dominative sound, and the second one responsible for acoustic heating. The first one is the famous KZK equation, and the second one is a novel equation governing acoustic heating. The novel dynamic equation considers both periodic and non-periodic sound. Quasi-plane geometry of flow is supposed. Subdividing is provided on the base of specific links of every mode. Media with arbitrary thermic T(p,ρ) and caloric e(p,ρ) equations of state are considered. Individual roles of thermal conductivity and viscosity in the heating induced by aperiodic sound in the ideal gases and media different from ideal gases are discussed.

Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

NASA Astrophysics Data System (ADS)

Adem, Abdullahi Rashid; Moawad, Salah M.

2018-05-01

In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

The study of nonlinear almost periodic differential equations without recourse to the H-classes of these equations

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

Slyusarchuk, V. E., E-mail: V.E.Slyusarchuk@gmail.com, E-mail: V.Ye.Slyusarchuk@NUWM.rv.ua

2014-06-01

The well-known theorems of Favard and Amerio on the existence of almost periodic solutions to linear and nonlinear almost periodic differential equations depend to a large extent on the H-classes and the requirement that the bounded solutions of these equations be separated. The present paper provides different conditions for the existence of almost periodic solutions. These conditions, which do not depend on the H-classes of the equations, are formulated in terms of a special functional on the set of bounded solutions of the equations under consideration. This functional is used, in particular, to test whether solutions are separated. Bibliography: 24more » titles. (paper)« less

Power-spectral-density relationship for retarded differential equations

NASA Technical Reports Server (NTRS)

Barker, L. K.

1974-01-01

The power spectral density (PSD) relationship between input and output of a set of linear differential-difference equations of the retarded type with real constant coefficients and delays is discussed. The form of the PSD relationship is identical with that applicable to unretarded equations. Since the PSD relationship is useful if and only if the system described by the equations is stable, the stability must be determined before applying the PSD relationship. Since it is sometimes difficult to determine the stability of retarded equations, such equations are often approximated by simpler forms. It is pointed out that some common approximations can lead to erroneous conclusions regarding the stability of a system and, therefore, to the possibility of obtaining PSD results which are not valid.

Solution of transonic flows by an integro-differential equation method

NASA Technical Reports Server (NTRS)

Ogana, W.

1978-01-01

Solutions of steady transonic flow past a two-dimensional airfoil are obtained from a singular integro-differential equation which involves a tangential derivative of the perturbation velocity potential. Subcritical flows are solved by taking central differences everywhere. For supercritical flows with shocks, central differences are taken in subsonic flow regions and backward differences in supersonic flow regions. The method is applied to a nonlifting parabolic-arc airfoil and to a lifting NACA 0012 airfoil. Results compare favorably with those of finite-difference schemes.

Meta-Analytic Methods of Pooling Correlation Matrices for Structural Equation Modeling under Different Patterns of Missing Data

ERIC Educational Resources Information Center

Furlow, Carolyn F.; Beretvas, S. Natasha

2005-01-01

Three methods of synthesizing correlations for meta-analytic structural equation modeling (SEM) under different degrees and mechanisms of missingness were compared for the estimation of correlation and SEM parameters and goodness-of-fit indices by using Monte Carlo simulation techniques. A revised generalized least squares (GLS) method for…

Closed solutions to a differential-difference equation and an associated plate solidification problem.

PubMed

Layeni, Olawanle P; Akinola, Adegbola P; Johnson, Jesse V

2016-01-01

Two distinct and novel formalisms for deriving exact closed solutions of a class of variable-coefficient differential-difference equations arising from a plate solidification problem are introduced. Thereupon, exact closed traveling wave and similarity solutions to the plate solidification problem are obtained for some special cases of time-varying plate surface temperature.

On Solving Systems of Equations by Successive Reduction Using 2×2 Matrices

ERIC Educational Resources Information Center

Carley, Holly

2014-01-01

Usually a student learns to solve a system of linear equations in two ways: "substitution" and "elimination." While the two methods will of course lead to the same answer they are considered different because the thinking process is different. In this paper the author solves a system in these two ways to demonstrate the…

Creating a Project on Difference Equations with Primary Sources: Challenges and Opportunities

ERIC Educational Resources Information Center

Ruch, David

2014-01-01

This article discusses the creation of a student project about linear difference equations using primary sources. Early 18th-century developments in the area are outlined, focusing on efforts by Abraham De Moivre (1667-1754) and Daniel Bernoulli (1700-1782). It is explained how primary sources from these authors can be used to cover material…

Equations with Technology: Different Tools, Different Views

ERIC Educational Resources Information Center

Drijvers, Paul; Barzel, Barbel

2012-01-01

Has technology revolutionised the mathematics classroom, or is it still a device waiting to be exploited for the benefit of the learner? There are applets that will enable the user to solve complex equations at the push of a button. So, does this jeopardise other methods, make other methods redundant, or even diminish other methods in the mind of…

Solving Navier-Stokes' equation using Castillo-Grone's mimetic difference operators on GPUs

NASA Astrophysics Data System (ADS)

Abouali, Mohammad; Castillo, Jose

2012-11-01

This paper discusses the performance and the accuracy of Castillo-Grone's (CG) mimetic difference operator in solving the Navier-Stokes' equation in order to simulate oceanic and atmospheric flows. The implementation is further adapted to harness the power of the many computing cores available on the Graphics Processing Units (GPUs) and the speedup is discussed.

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bailey, Harry E.; Beam, Richard M.

1991-01-01

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

Density scaling for multiplets

NASA Astrophysics Data System (ADS)

Nagy, Á.

2011-02-01

Generalized Kohn-Sham equations are presented for lowest-lying multiplets. The way of treating non-integer particle numbers is coupled with an earlier method of the author. The fundamental quantity of the theory is the subspace density. The Kohn-Sham equations are similar to the conventional Kohn-Sham equations. The difference is that the subspace density is used instead of the density and the Kohn-Sham potential is different for different subspaces. The exchange-correlation functional is studied using density scaling. It is shown that there exists a value of the scaling factor ζ for which the correlation energy disappears. Generalized OPM and Krieger-Li-Iafrate (KLI) methods incorporating correlation are presented. The ζKLI method, being as simple as the original KLI method, is proposed for multiplets.

Integrating different tracking systems in football: multiple camera semi-automatic system, local position measurement and GPS technologies.

PubMed

Buchheit, Martin; Allen, Adam; Poon, Tsz Kit; Modonutti, Mattia; Gregson, Warren; Di Salvo, Valter

2014-12-01

Abstract During the past decade substantial development of computer-aided tracking technology has occurred. Therefore, we aimed to provide calibration equations to allow the interchangeability of different tracking technologies used in soccer. Eighty-two highly trained soccer players (U14-U17) were monitored during training and one match. Player activity was collected simultaneously with a semi-automatic multiple-camera (Prozone), local position measurement (LPM) technology (Inmotio) and two global positioning systems (GPSports and VX). Data were analysed with respect to three different field dimensions (small, <30 m 2 to full-pitch, match). Variables provided by the systems were compared, and calibration equations (linear regression models) between each system were calculated for each field dimension. Most metrics differed between the 4 systems with the magnitude of the differences dependant on both pitch size and the variable of interest. Trivial-to-small between-system differences in total distance were noted. However, high-intensity running distance (>14.4 km · h -1 ) was slightly-to-moderately greater when tracked with Prozone, and accelerations, small-to-very largely greater with LPM. For most of the equations, the typical error of the estimate was of a moderate magnitude. Interchangeability of the different tracking systems is possible with the provided equations, but care is required given their moderate typical error of the estimate.

Method of controlling chaos in laser equations

NASA Astrophysics Data System (ADS)

Duong-van, Minh

1993-01-01

A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)].

A functional equation for the specular reflection of rays.

PubMed

Le Bot, A

2002-10-01

This paper aims to generalize the "radiosity method" when applied to specular reflection. Within the field of thermics, the radiosity method is also called the "standard procedure." The integral equation for incident energy, which is usually derived for diffuse reflection, is replaced by a more appropriate functional equation. The latter is used to solve some specific problems and it is shown that all the classical features of specular reflection, for example, the existence of image sources, are embodied within this equation. This equation can be solved with the ray-tracing technique, despite the implemented mathematics being quite different. Several interesting features of the energy field are presented.

Stable Algorithm For Estimating Airdata From Flush Surface Pressure Measurements

NASA Technical Reports Server (NTRS)

Whitmore, Stephen, A. (Inventor); Cobleigh, Brent R. (Inventor); Haering, Edward A., Jr. (Inventor)

2001-01-01

An airdata estimation and evaluation system and method, including a stable algorithm for estimating airdata from nonintrusive surface pressure measurements. The airdata estimation and evaluation system is preferably implemented in a flush airdata sensing (FADS) system. The system and method of the present invention take a flow model equation and transform it into a triples formulation equation. The triples formulation equation eliminates the pressure related states from the flow model equation by strategically taking the differences of three surface pressures, known as triples. This triples formulation equation is then used to accurately estimate and compute vital airdata from nonintrusive surface pressure measurements.

Dark Soliton Solutions of Space-Time Fractional Sharma-Tasso-Olver and Potential Kadomtsev-Petviashvili Equations

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Korkmaz, Alper; Bekir, Ahmet

2017-02-01

Dark soliton solutions for space-time fractional Sharma-Tasso-Olver and space-time fractional potential Kadomtsev-Petviashvili equations are determined by using the properties of modified Riemann-Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the \\tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma-Tasso-Olver equation as only one solution for the potential Kadomtsev-Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Anderson, W. Kyle

1998-01-01

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

MagIC: Fluid dynamics in a spherical shell simulator

NASA Astrophysics Data System (ADS)

Wicht, J.; Gastine, T.; Barik, A.; Putigny, B.; Yadav, R.; Duarte, L.; Dintrans, B.

2017-09-01

MagIC simulates fluid dynamics in a spherical shell. It solves for the Navier-Stokes equation including Coriolis force, optionally coupled with an induction equation for Magneto-Hydro Dynamics (MHD), a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations. MagIC uses either Chebyshev polynomials or finite differences in the radial direction and spherical harmonic decomposition in the azimuthal and latitudinal directions. The time-stepping scheme relies on a semi-implicit Crank-Nicolson for the linear terms of the MHD equations and a Adams-Bashforth scheme for the non-linear terms and the Coriolis force.

Nonlinear Equations of Equilibrium for Elastic Helicopter or Wind Turbine Blades Undergoing Moderate Deformation

NASA Technical Reports Server (NTRS)

Rosen, A.; Friedmann, P. P.

1978-01-01

A set of nonlinear equations of equilibrium for an elastic wind turbine or helicopter blades are presented. These equations are derived for the case of small strains and moderate rotations (slopes). The derivation includes several assumptions which are carefully stated. For the convenience of potential users the equations are developed with respect to two different systems of coordinates, the undeformed and the deformed coordinates of the blade. Furthermore, the loads acting on the blade are given in a general form so as to make them suitable for a variety of applications. The equations obtained in the study are compared with those obtained in previous studies.

Alternative supply specifications and estimates of regional supply and demand for stumpage.

Treesearch

Kent P. Connaughton; David H. Jackson; Gerard A. Majerus

1988-01-01

Four plausible sets of stumpage supply and demand equations were developed and estimated; the demand equation was the same for each set, although the supply equation differed. The supply specifications varied from the model of regional excess demand in which National Forest harvest levels were assumed fixed to a more realistic model in which the harvest on the National...

Hamiltonian formulation of the KdV equation

NASA Astrophysics Data System (ADS)

Nutku, Y.

1984-06-01

We consider the canonical formulation of Whitham's variational principle for the KdV equation. This Lagrangian is degenerate and we have found it necessary to use Dirac's theory of constrained systems in constructing the Hamiltonian. Earlier discussions of the Hamiltonian structure of the KdV equation were based on various different decompositions of the field which is avoided by this new approach.

Weighting Test Samples in IRT Linking and Equating: Toward an Improved Sampling Design for Complex Equating. Research Report. ETS RR-13-39

ERIC Educational Resources Information Center

Qian, Jiahe; Jiang, Yanming; von Davier, Alina A.

2013-01-01

Several factors could cause variability in item response theory (IRT) linking and equating procedures, such as the variability across examinee samples and/or test items, seasonality, regional differences, native language diversity, gender, and other demographic variables. Hence, the following question arises: Is it possible to select optimal…

Deriving Biomass Estimation Equations for Seven Plantation Hardwood Species

Treesearch

Bryce E. Schlaegel; Harvey E. Kennedy

1986-01-01

Trees of seven species sampled from a plantation over 7 years were used to derive weight equations to predict primary tree components. The seven species required the use of five different model forms to insure the greatest precision. Regardless of model form, all equations include variables for tree diameter, tree height, age, and number of trees planted. The most...

Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

ERIC Educational Resources Information Center

Pathak, H. K.; Grewal, A. S.

2002-01-01

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

Calibration of volume and component biomass equations for Douglas-fir and lodgepole pine in Western Oregon forests

Treesearch

Krishna P. Poudel; Temesgen Hailemariam

2016-01-01

Using data from destructively sampled Douglas-fir and lodgepole pine trees, we evaluated the performance of regional volume and component biomass equations in terms of bias and RMSE. The volume and component biomass equations were calibrated using three different adjustment methods that used: (a) a correction factor based on ordinary least square regression through...

Aquarius reveals salinity structure of tropical instability waves

NASA Astrophysics Data System (ADS)

Lee, Tong; Lagerloef, Gary; Gierach, Michelle M.; Kao, Hsun-Ying; Yueh, Simon; Dohan, Kathleen

2012-06-01

Sea surface salinity (SSS) measurements from the Aquarius/SAC-D satellite during September-December 2011 provide the first satellite observations of the salinity structure of tropical instability waves (TIWs) in the Pacific. The related SSS anomaly has a magnitude of approximately ±0.5 PSU. Different from sea surface temperature (SST) and sea surface height anomaly (SSHA) where TIW-related propagating signals are stronger a few degrees away from the equator, the SSS signature of TIWs is largest near the equator in the eastern equatorial Pacific where salty South Pacific water meets the fresher Inter-tropical Convergence Zone water. The dominant westward propagation speed of SSS near the equator is approximately 1 m/s. This is twice as fast as the 0.5 m/s TIW speed widely reported in the literature, typically from SST and SSHA away from the equator. This difference is attributed to the more dominant 17-day TIWs near the equator that have a 1 m/s dominant phase speed and the stronger 33-day TIWs away from the equator that have a 0.5 m/s dominant phase speed. The results demonstrate the important value of Aquarius in studying TIWs.

The staircase method: integrals for periodic reductions of integrable lattice equations

NASA Astrophysics Data System (ADS)

van der Kamp, Peter H.; Quispel, G. R. W.

2010-11-01

We show, in full generality, that the staircase method (Papageorgiou et al 1990 Phys. Lett. A 147 106-14, Quispel et al 1991 Physica A 173 243-66) provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the quotient-difference (QD)-algorithm and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r, then one can introduce q <= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular {\\ Z}^2 lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.

Fluid flow in porous media using image-based modelling to parametrize Richards' equation.

PubMed

Cooper, L J; Daly, K R; Hallett, P D; Naveed, M; Koebernick, N; Bengough, A G; George, T S; Roose, T

2017-11-01

The parameters in Richards' equation are usually calculated from experimentally measured values of the soil-water characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards' equation from these indirect measurements, image-based modelling is used to investigate the relationship between the pore structure and the parameters. A three-dimensional, X-ray computed tomography image stack of a soil sample with voxel resolution of 6 μm has been used to create a computational mesh. The Cahn-Hilliard-Stokes equations for two-fluid flow, in this case water and air, were applied to this mesh and solved using the finite-element method in COMSOL Multiphysics. The upscaled parameters in Richards' equation are then obtained via homogenization. The effect on the soil-water retention curve due to three different contact angles, 0°, 20° and 60°, was also investigated. The results show that the pore structure affects the properties of the flow on the large scale, and different contact angles can change the parameters for Richards' equation.

Time-domain comparisons of power law attenuation in causal and noncausal time-fractional wave equations

PubMed Central

Zhao, Xiaofeng; McGough, Robert J.

2016-01-01

The attenuation of ultrasound propagating in human tissue follows a power law with respect to frequency that is modeled by several different causal and noncausal fractional partial differential equations. To demonstrate some of the similarities and differences that are observed in three related time-fractional partial differential equations, time-domain Green's functions are calculated numerically for the power law wave equation, the Szabo wave equation, and for the Caputo wave equation. These Green's functions are evaluated for water with a power law exponent of y = 2, breast with a power law exponent of y = 1.5, and liver with a power law exponent of y = 1.139. Simulation results show that the noncausal features of the numerically calculated time-domain response are only evident very close to the source and that these causal and noncausal time-domain Green's functions converge to the same result away from the source. When noncausal time-domain Green's functions are convolved with a short pulse, no evidence of noncausal behavior remains in the time-domain, which suggests that these causal and noncausal time-fractional models are equally effective for these numerical calculations. PMID:27250193

Numerical investigations of low-density nozzle flow by solving the Boltzmann equation

NASA Technical Reports Server (NTRS)

Deng, Zheng-Tao; Liaw, Goang-Shin; Chou, Lynn Chen

1995-01-01

A two-dimensional finite-difference code to solve the BGK-Boltzmann equation has been developed. The solution procedure consists of three steps: (1) transforming the BGK-Boltzmann equation into two simultaneous partial differential equations by taking moments of the distribution function with respect to the molecular velocity u(sub z), with weighting factors 1 and u(sub z)(sup 2); (2) solving the transformed equations in the physical space based on the time-marching technique and the four-stage Runge-Kutta time integration, for a given discrete-ordinate. The Roe's second-order upwind difference scheme is used to discretize the convective terms and the collision terms are treated as source terms; and (3) using the newly calculated distribution functions at each point in the physical space to calculate the macroscopic flow parameters by the modified Gaussian quadrature formula. Repeating steps 2 and 3, the time-marching procedure stops when the convergent criteria is reached. A low-density nozzle flow field has been calculated by this newly developed code. The BGK Boltzmann solution and experimental data show excellent agreement. It demonstrated that numerical solutions of the BGK-Boltzmann equation are ready to be experimentally validated.

Plasma Theory and Simulation

DTIC Science & Technology

1988-06-30

equation using finite difference methods. The distribution function is represented by a large number of particles. The particle’s velocities change as a...Small angle Coulomb collisions The FP equation for describing small angle Coulomb collisions can be solved numerically using finite difference techniques...A finite Fourrier transform (FT) is made in z, then we can solve for each k using the following finite difference scheme [5]: 2{r 1 +l1 2 (,,+ 1 - fj

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

Choudhury, Sourav; Das, Tushar Kanti; Chatterjee, Prasanta

The influence of exchange-correlation potential, quantum Bohm term, and degenerate pressure on the nature of solitary waves in a quantum semiconductor plasma is investigated. It is found that an amplitude and a width of the solitary waves change with variation of different parameters for different semiconductors. A deformed Korteweg-de Vries equation is obtained for propagation of nonlinear waves in a quantum semiconductor plasma, and the effects of different plasma parameters on the solution of the equation are also presented.

Single wall penetration equations

NASA Technical Reports Server (NTRS)

Hayashida, K. B.; Robinson, J. H.

1991-01-01

Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

Investigation of a Coupled Arrhenius-Type/Rossard Equation of AH36 Material

PubMed Central

Qin, Qin; Tian, Ming-Liang; Zhang, Peng

2017-01-01

High-temperature tensile testing of AH36 material in a wide range of temperatures (1173–1573 K) and strain rates (10−4–10−2 s−1) has been obtained by using a Gleeble system. These experimental stress-strain data have been adopted to develop the constitutive equation. The constitutive equation of AH36 material was suggested based on the modified Arrhenius-type equation and the modified Rossard equation respectively. The results indicate that the constitutive equation is strongly influenced by temperature and strain, especially strain. Moreover, there is a good agreement between the predicted data of the modified Arrhenius-type equation and the experimental results when the strain is greater than 0.02. There is also good agreement between the predicted data of the Rossard equation and the experimental results when the strain is less than 0.02. Therefore, a coupled equation where the modified Arrhenius-type equation and Rossard equation are combined has been proposed to describe the constitutive equation of AH36 material according to the different strain values in order to improve the accuracy. The correlation coefficient between the computed and experimental flow stress data was 0.998. The minimum value of the average absolute relative error shows the high accuracy of the coupled equation compared with the two modified equations. PMID:28772767

Comparison of estimated glomerular filtration rate equations for dosing new oral anticoagulants in patients with atrial fibrillation.

PubMed

Manzano-Fernández, Sergio; Andreu-Cayuelas, José M; Marín, Francisco; Orenes-Piñero, Esteban; Gallego, Pilar; Valdés, Mariano; Vicente, Vicente; Lip, Gregory Y H; Roldán, Vanessa

2015-06-01

New oral anticoagulants require dosing adjustment according to renal function. We aimed to determine discordance in hypothetical recommended dosing of these drugs using different estimated glomerular filtration rate equations in patients with atrial fibrillation. Cross-sectional analysis of 910 patients with atrial fibrillation and an indication for oral anticoagulation. The glomerular filtration rate was estimated using the Cockcroft-Gault, Modification of Diet in Renal Disease and Chronic Kidney Disease Epidemiology Collaboration equations. For dabigatran, rivaroxaban, and apixaban we identified dose discordance when there was disagreement in the recommended dose based on different equations. Among the overall population, relative to Cockcroft-Gault, discordance in dabigatran dosage was 11.4% for Modification of Diet in Renal Disease and 10% for Chronic Kidney Disease Epidemiology Collaboration, discordance in rivaroxaban dosage was 10% for Modification of Diet in Renal Disease and 8.5% for the Chronic Kidney Disease Epidemiology Collaboration. The lowest discordance was observed for apixaban: 1.4% for Modification of Diet in Renal Disease and 1.5% for the Chronic Kidney Disease Epidemiology Collaboration. In patients with Cockcroft-Gault<60mL/min or elderly patients, discordances in dabigatran and rivaroxaban dosages were higher, ranging from 13.2% to 30.4%. Discordance in apixaban dosage remained<5% in these patients. Discordance in new oral anticoagulation dosages using different equations is frequent, especially among elderly patients with renal impairment. This discordance was higher in dabigatran and rivaroxaban dosages than in apixaban dosages. Further studies are needed to clarify the clinical importance of these discordances and the optimal anticoagulant dosages depending on the use of different equations to estimate renal function. Copyright © 2014 Sociedad Española de Cardiología. Published by Elsevier España, S.L.U. All rights reserved.

Nonlinear propagation of vector extremely short pulses in a medium of symmetric and asymmetric molecules

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

Sazonov, S. V., E-mail: sazonov.sergey@gmail.com; Ustinov, N. V., E-mail: n-ustinov@mail.ru

The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky–Vakhnenko equation. Different types of solutionsmore » of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.« less

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1976-01-01

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

The Laguerre finite difference one-way equation solver

NASA Astrophysics Data System (ADS)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

Multiscale functions, scale dynamics, and applications to partial differential equations

NASA Astrophysics Data System (ADS)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

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

Cheviakov, Alexei F., E-mail: chevaikov@math.usask.ca

Partial differential equations of the form divN=0, N{sub t}+curl M=0 involving two vector functions in R{sup 3} depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R{sup 4}(t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations,more » it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented.« less

Estimation of body density based on hydrostatic weighing without head submersion in young Japanese adults.

PubMed

Demura, S; Sato, S; Kitabayashi, T

2006-06-01

This study examined a method of predicting body density based on hydrostatic weighing without head submersion (HWwithoutHS). Donnelly and Sintek (1984) developed a method to predict body density based on hydrostatic weight without head submersion. This method predicts the difference (D) between HWwithoutHS and hydrostatic weight with head submersion (HWwithHS) from anthropometric variables (head length and head width), and then calculates body density using D as a correction factor. We developed several prediction equations to estimate D based on head anthropometry and differences between the sexes, and compared their prediction accuracy with Donnelly and Sintek's equation. Thirty-two males and 32 females aged 17-26 years participated in the study. Multiple linear regression analysis was performed to obtain the prediction equations, and the systematic errors of their predictions were assessed by Bland-Altman plots. The best prediction equations obtained were: Males: D(g) = -164.12X1 - 125.81X2 - 111.03X3 + 100.66X4 + 6488.63, where X1 = head length (cm), X2 = head circumference (cm), X3 = head breadth (cm), X4 = head thickness (cm) (R = 0.858, R2 = 0.737, adjusted R2 = 0.687, standard error of the estimate = 224.1); Females: D(g) = -156.03X1 - 14.03X2 - 38.45X3 - 8.87X4 + 7852.45, where X1 = head circumference (cm), X2 = body mass (g), X3 = head length (cm), X4 = height (cm) (R = 0.913, R2 = 0.833, adjusted R2 = 0.808, standard error of the estimate = 137.7). The effective predictors in these prediction equations differed from those of Donnelly and Sintek's equation, and head circumference and head length were included in both equations. The prediction accuracy was improved by statistically selecting effective predictors. Since we did not assess cross-validity, the equations cannot be used to generalize to other populations, and further investigation is required.

Experimental realization of the Yang-Baxter Equation via NMR interferometry.

PubMed

Vind, F Anvari; Foerster, A; Oliveira, I S; Sarthour, R S; Soares-Pinto, D O; Souza, A M; Roditi, I

2016-02-10

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.

Pure quasi-P wave equation and numerical solution in 3D TTI media

NASA Astrophysics Data System (ADS)

Zhang, Jian-Min; He, Bing-Shou; Tang, Huai-Gu

2017-03-01

Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis (VTI media), a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis (TTI media). This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ɛ. The finite difference method is used to solve the equation. In addition, a perfectly matched layer (PML) absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium.

Non-Archimedean reaction-ultradiffusion equations and complex hierarchic systems

NASA Astrophysics Data System (ADS)

Zúñiga-Galindo, W. A.

2018-06-01

We initiate the study of non-Archimedean reaction-ultradiffusion equations and their connections with models of complex hierarchic systems. From a mathematical perspective, the equations studied here are the p-adic counterpart of the integro-differential models for phase separation introduced by Bates and Chmaj. Our equations are also generalizations of the ultradiffusion equations on trees studied in the 1980s by Ogielski, Stein, Bachas, Huberman, among others, and also generalizations of the master equations of the Avetisov et al models, which describe certain complex hierarchic systems. From a physical perspective, our equations are gradient flows of non-Archimedean free energy functionals and their solutions describe the macroscopic density profile of a bistable material whose space of states has an ultrametric structure. Some of our results are p-adic analogs of some well-known results in the Archimedean setting, however, the mechanism of diffusion is completely different due to the fact that it occurs in an ultrametric space.

The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.

PubMed

Lehtonen, Jussi

2018-01-01

A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.

Quantization of Differences Between Atomic and Nuclear Rest Masses and Self-organization of Atoms and Nuclei

NASA Astrophysics Data System (ADS)

Gareev, F. A.; Zhidkova, I. E.

2007-03-01

We come to the conclusion that all atomic models based on either the Newton equation and the Kepler laws, or the Maxwell equations, or the Schrodinger and Dirac equations are in reasonable agreement with experimental data. We can only suspect that these equations are grounded on the same fundamental principle(s) which is (are) not known or these equations can be transformed into each other. We proposed a new mechanism of LENR: cooperative processes in the whole system nuclei + atoms + condensed matter - nuclear reactions in plasma - can occur at smaller threshold energies than the corresponding ones on free constituents. We were able to quantize phenomenologically the first time the differences between atomic and nuclear rest masses by the formula: δδM =n1/n2 X 0.0076294 (in MeV/ c^2), ni=1,2,3,.... Note that this quantization rule is justified for atoms and nuclei with different A, N and Z and the nuclei and atoms represent a coherent synchronized systems - a complex of coupled oscillators (resonators). The cooperative resonance synchronization mechanisms can explain how electron volt (atomic-) scale processes can induce and control nuclear MeV (nuclear-) scale processes and reactions., F.A. Gareev, I.E. Zhidkova, E-print arXiv Nucl-th/ 0610002 2006.

A novel approach for calculating shelf life of minimally processed vegetables.

PubMed

Corbo, Maria Rosaria; Del Nobile, Matteo Alessandro; Sinigaglia, Milena

2006-01-15

Shelf life of minimally processed vegetables is often calculated by using the kinetic parameters of Gompertz equation as modified by Zwietering et al. [Zwietering, M.H., Jongenburger, F.M., Roumbouts, M., van't Riet, K., 1990. Modelling of the bacterial growth curve. Applied and Environmental Microbiology 56, 1875-1881.] taking 5x10(7) CFU/g as the maximum acceptable contamination value consistent with acceptable quality of these products. As this method does not allow estimation of the standard errors of the shelf life, in this paper the modified Gompertz equation was re-parameterized to directly include the shelf life as a fitting parameter among the Gompertz parameters. Being the shelf life a fitting parameter is possible to determine its confidence interval by fitting the proposed equation to the experimental data. The goodness-of-fit of this new equation was tested by using mesophilic bacteria cell loads from different minimally processed vegetables (packaged fresh-cut lettuce, fennel and shredded carrots) that differed for some process operations or for package atmosphere. The new equation was able to describe the data well and to estimate the shelf life. The results obtained emphasize the importance of using the standard errors for the shelf life value to show significant differences among the samples.

Novel Numerical Approaches to Loop Quantum Cosmology

NASA Astrophysics Data System (ADS)

Diener, Peter

2015-04-01

Loop Quantum Gravity (LQG) is an (as yet incomplete) approach to the quantization of gravity. When applied to symmetry reduced cosmological spacetimes (Loop Quantum Cosmology or LQC) one of the predictions of the theory is that the Big Bang is replaced by a Big Bounce, i.e. a previously existing contracting universe underwent a bounce at finite volume before becoming our expanding universe. The evolution equations of LQC take the form of difference equations (with the discretization given by the theory) that in the large volume limit can be approximated by partial differential equations (PDEs). In this talk I will first discuss some of the unique challenges encountered when trying to numerically solve these difference equations. I will then present some of the novel approaches that have been employed to overcome the challenges. I will here focus primarily on the Chimera scheme that takes advantage of the fact that the LQC difference equations can be approximated by PDEs in the large volume limit. I will finally also briefly discuss some of the results that have been obtained using these numerical techniques by performing simulations in regions of parameter space that were previously unreachable. This work is supported by a grant from the John Templeton Foundation and by NSF grant PHYS1068743.

Measuring the contour of a wavefront using the Irradiance Transport Equation (ITE)

NASA Astrophysics Data System (ADS)

Castillo-Rodríguez, Luis; Granados-Agustín, Fermín; Fernández-Guasti, Manuel; Cornejo-Rodríguez, Alejandro

2006-01-01

The Irradiance Transport Equation (ITE), found by Teague, had been used in optics with different applications. One of the field where had been used is in optical testing, for example, with the method developed by Takeda. In this paper following the idea of using different optical and mathematical analysis method, theorical and experimental results are presented.

A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Danabasoglu, G.; Biringen, S.

1989-01-01

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

Examining the Differences of Linear Systems between Finnish and Taiwanese Textbooks

ERIC Educational Resources Information Center

Yang, Der-Ching; Lin, Yung-Chi

2015-01-01

The purpose of this study was to examine the differences between Finnish and Taiwanese textbooks for grades 7 to 9 on the topic of solving systems of linear equations (simultaneous equations). The specific textbooks examined were TK in Taiwan and FL in Finland. The content analysis method was used to examine (a) the teaching sequence, (b)…

A site model for Pyrenean oak (Quercus pyrenaica) stands using a dynamic algebraic difference equation

Treesearch

Joao P. Carvalho; Bernard R. Parresol

2005-01-01

This paper presents a growth model for dominant-height and site-quality estimations for Pyrenean oak (Quercus pyrenaica Willd.) stands. The Bertalanffy–Richards function is used with the generalized algebraic difference approach to derive a dynamic site equation. This allows dominant-height and site-index estimations in a compatible way, using any...

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

NASA Technical Reports Server (NTRS)

Scott, R. K.

1972-01-01

A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

Determination of body composition using air displacement plethysmography, anthropometry and bio-electrical impedance in rural elderly Mexican men and women.

PubMed

Aleman-Mateo, H; Esparza Romero, J; Macias Morales, N; Salazar, G; Wyatt, J; Valencia, M E

2004-01-01

Air displacement plethysmography with the BOD-POD is a new densitometry technique, and has been found to be an accurate method to measure body composition. The aim of this study was to assess body composition in a group of free living healthy subjects 60 years of age or older from a rural area of Northwest Mexico, and to evaluate body composition by anthropometry and bioelectrical impedance (BIA) using equations reported for other elderly populations. Body composition was evaluated in 21 women and 26 men with the BOD-POD, by anthropometry, and BIA and compared to different equations using the Bland- Altman procedure. Body fat in elderly women and men was 42.7 and 30.2 % respectively. In women, Segal's equation using BIA 1, based on standing height, showed no significant differences with the BOD-POD. There was satisfactory agreement between Segal's equation and BOD-POD. In men similar results was found with Deurenberg's equation using B1A 2 based on recumbent length. Segal's and Deurenberg's equations were accurate and precise for the estimation of body fat in the elderly of this study. The use of these equations could improve the estimation of body composition for similar elderly subjects. Further studies are recommended with a larger size samples to include elderly subjects from other Latin American countries.

A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

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

Gamba, Irene M.; ICES, The University of Texas at Austin, 201 E. 24th St., Stop C0200, Austin, TX 78712; Haack, Jeffrey R.

2014-08-01

We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit tomore » the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation.« less

An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation

NASA Astrophysics Data System (ADS)

Zhan, Ge; Pestana, Reynam C.; Stoffa, Paul L.

2013-04-01

The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward-backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations.

Production of a sterile species: Quantum kinetics

NASA Astrophysics Data System (ADS)

Boyanovsky, D.; Ho, C. M.

2007-10-01

Production of a sterile species is studied within an effective model of active-sterile neutrino mixing in a medium in thermal equilibrium. The quantum kinetic equations for the distribution functions and coherences are obtained from two independent methods: the effective action and the quantum master equation. The decoherence time scale for active-sterile oscillations is τdec=2/Γaa, but the evolution of the distribution functions is determined by the two different time scales associated with the damping rates of the quasiparticle modes in the medium: Γ1=Γaacos⁡2θm; Γ2=Γaasin⁡2θm where Γaa is the interaction rate of the active species in the absence of mixing and θm the mixing angle in the medium. These two time scales are widely different away from Mikheyev-Smirnov-Wolfenstein resonances and preclude the kinetic description of active-sterile production in terms of a simple rate equation. We give the complete set of quantum kinetic equations for the active and sterile populations and coherences and discuss in detail the various approximations. A generalization of the active-sterile transition probability in a medium is provided via the quantum master equation. We derive explicitly the usual quantum kinetic equations in terms of the “polarization vector” and show their equivalence to those obtained from the quantum master equation and effective action.

Comparison of Various Equations for Estimating GFR in Malawi: How to Determine Renal Function in Resource Limited Settings?

PubMed Central

Phiri, Sam; Rothenbacher, Dietrich; Neuhann, Florian

2015-01-01

Background Chronic kidney disease (CKD) is a probably underrated public health problem in Sub-Saharan-Africa, in particular in combination with HIV-infection. Knowledge about the CKD prevalence is scarce and in the available literature different methods to classify CKD are used impeding comparison and general prevalence estimates. Methods This study assessed different serum-creatinine based equations for glomerular filtration rates (eGFR) and compared them to a cystatin C based equation. The study was conducted in Lilongwe, Malawi enrolling a population of 363 adults of which 32% were HIV-positive. Results Comparison of formulae based on Bland-Altman-plots and accuracy revealed best performance for the CKD-EPI equation without the correction factor for black Americans. Analyzing the differences between HIV-positive and –negative individuals CKD-EPI systematically overestimated eGFR in comparison to cystatin C and therefore lead to underestimation of CKD in HIV-positives. Conclusions Our findings underline the importance for standardization of eGFR calculation in a Sub-Saharan African setting, to further investigate the differences with regard to HIV status and to develop potential correction factors as established for age and sex. PMID:26083345

Given a one-step numerical scheme, on which ordinary differential equations is it exact?

NASA Astrophysics Data System (ADS)

Villatoro, Francisco R.

2009-01-01

A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.

Semigroup theory and numerical approximation for equations in linear viscoelasticity

NASA Technical Reports Server (NTRS)

Fabiano, R. H.; Ito, K.

1990-01-01

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Nonlinear fluctuations-induced rate equations for linear birth-death processes

NASA Astrophysics Data System (ADS)

Honkonen, J.

2008-05-01

The Fock-space approach to the solution of master equations for one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability of occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov’s ecological model and Lanchester’s model of modern warfare.

Mass conservation: 1-D open channel flow equations

USGS Publications Warehouse

DeLong, Lewis L.

1989-01-01

Unsteady flow simulation in natural rivers is often complicated by meandering channels of compound section. Hydraulic properties and the length of the wetted channel may vary significantly as a meandering river inundates its adjacent floodplain. The one-dimensional, unsteady, open-channel flow equations can be extended to simulate floods in channels of compound section. It will be shown that equations derived from the addition of differential equations individually describing flow in main and overbank channels do not in general conserve mass when overbank and main channels are of different lengths.

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

NASA Astrophysics Data System (ADS)

Rivera, R.; Villarroel, D.

2002-10-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1983-01-01

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1998-01-01

Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.

Vortex Formation and Particle Transport in a Cross-Field Plasma Sheath.

DTIC Science & Technology

1988-03-20

equations is similar to the cross-field equations of Horton et al.[27], differing by the addition of the first term in Eq.(17), which allows for a finite ...free energy winch maintains -, these structures resides in the temperature difference between tbe reservoir * of hot ions and electrons, which are...temperature gradient. However, the detailed * dynamics of each system, and the physics of the media considered, are, of course, very different . The work