On the effects of nonlinear boundary conditions in diffusive logistic equations on bounded domains

NASA Astrophysics Data System (ADS)

Cantrell, Robert Stephen; Cosner, Chris

We study a diffusive logistic equation with nonlinear boundary conditions. The equation arises as a model for a population that grows logistically inside a patch and crosses the patch boundary at a rate that depends on the population density. Specifically, the rate at which the population crosses the boundary is assumed to decrease as the density of the population increases. The model is motivated by empirical work on the Glanville fritillary butterfly. We derive local and global bifurcation results which show that the model can have multiple equilibria and in some parameter ranges can support Allee effects. The analysis leads to eigenvalue problems with nonstandard boundary conditions.

Apparatus and method for determining solids circulation rate

DOEpatents

Ludlow, J Christopher [Morgantown, WV; Spenik, James L [Morgantown, WV

2012-02-14

The invention relates to a method of determining bed velocity and solids circulation rate in a standpipe experiencing a moving packed bed flow, such as the in the standpipe section of a circulating bed fluidized reactor The method utilizes in-situ measurement of differential pressure over known axial lengths of the standpipe in conjunction with in-situ gas velocity measurement for a novel application of Ergun equations allowing determination of standpipe void fraction and moving packed bed velocity. The method takes advantage of the moving packed bed property of constant void fraction in order to integrate measured parameters into simultaneous solution of Ergun-based equations and conservation of mass equations across multiple sections of the standpipe.

Epidemic Spreading in a Multi-compartment System

NASA Astrophysics Data System (ADS)

Gao, Zong-Mao; Gu, Jiao; Li, Wei

2012-02-01

We introduce the variant rate and white noise into the susceptible-infected-removed (SIR) model for epidemics, discuss the epidemic dynamics of a multiple-compartment system, and describe this system by using master equations. For both the local epidemic spreading system and the whole multiple-compartment system, we find that a threshold could be useful in forecasting when the epidemic vanishes. Furthermore, numerical simulations show that a model with the variant infection rate and white noise can improve fitting with real SARS data.

Estimation of basal metabolic rate in Chinese: are the current prediction equations applicable?

PubMed

Camps, Stefan G; Wang, Nan Xin; Tan, Wei Shuan Kimberly; Henry, C Jeyakumar

2016-08-31

Measurement of basal metabolic rate (BMR) is suggested as a tool to estimate energy requirements. Therefore, BMR prediction equations have been developed in multiple populations because indirect calorimetry is not always feasible. However, there is a paucity of data on BMR measured in overweight and obese adults living in Asia and equations developed for this group of interest. The aim of this study was to develop a new BMR prediction equation for Chinese adults applicable for a large BMI range and compare it with commonly used prediction equations. Subjects were 121 men and 111 women (age: 21-67 years, BMI: 16-41 kg/m(2)). Height, weight, and BMR were measured. Continuous open-circuit indirect calorimetry using a ventilated hood system for 30 min was used to measure BMR. A regression equation was derived using stepwise regression and accuracy was compared to 6 existing equations (Harris-Benedict, Henry, Liu, Yang, Owen and Mifflin). Additionally, the newly derived equation was cross-validated in a separate group of 70 Chinese subjects (26 men and 44 women, age: 21-69 years, BMI: 17-39 kg/m(2)). The equation developed from our data was: BMR (kJ/d) = 52.6 x weight (kg) + 828 x gender + 1960 (women = 0, men = 1; R(2) = 0.81). The accuracy rate (within 10 % accurate) was 78 % which compared well to Owen (70 %), Henry (67 %), Mifflin (67 %), Liu (58 %), Harris-Benedict (45 %) and Yang (37 %) for the whole range of BMI. For a BMI greater than 23, the Singapore equation reached an accuracy rate of 76 %. Cross-validation proved an accuracy rate of 80 %. To date, the newly developed Singapore equation is the most accurate BMR prediction equation in Chinese and is applicable for use in a large BMI range including those overweight and obese.

Impact of Clear, Loud, and Slow Speech on Scaled Intelligibility and Speech Severity in Parkinson's Disease and Multiple Sclerosis

ERIC Educational Resources Information Center

Tjaden, Kris; Sussman, Joan E.; Wilding, Gregory E.

2014-01-01

Purpose: The perceptual consequences of rate reduction, increased vocal intensity, and clear speech were studied in speakers with multiple sclerosis (MS), Parkinson's disease (PD), and healthy controls. Method: Seventy-eight speakers read sentences in habitual, clear, loud, and slow conditions. Sentences were equated for peak amplitude and…

Optimal growth trajectories with finite carrying capacity.

PubMed

Caravelli, F; Sindoni, L; Caccioli, F; Ududec, C

2016-08-01

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Optimal growth trajectories with finite carrying capacity

NASA Astrophysics Data System (ADS)

Caravelli, F.; Sindoni, L.; Caccioli, F.; Ududec, C.

2016-08-01

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

GFR Estimation: From Physiology to Public Health

PubMed Central

Levey, Andrew S.; Inker, Lesley A.; Coresh, Josef

2014-01-01

Estimating glomerular filtration rate (GFR) is essential for clinical practice, research, and public health. Appropriate interpretation of estimated GFR (eGFR) requires understanding the principles of physiology, laboratory medicine, epidemiology and biostatistics used in the development and validation of GFR estimating equations. Equations developed in diverse populations are less biased at higher GFR than equations developed in CKD populations and are more appropriate for general use. Equations that include multiple endogenous filtration markers are more precise than equations including a single filtration marker. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations are the most accurate GFR estimating equations that have been evaluated in large, diverse populations and are applicable for general clinical use. The 2009 CKD-EPI creatinine equation is more accurate in estimating GFR and prognosis than the 2006 Modification of Diet in Renal Disease (MDRD) Study equation and provides lower estimates of prevalence of decreased eGFR. It is useful as a “first” test for decreased eGFR and should replace the MDRD Study equation for routine reporting of serum creatinine–based eGFR by clinical laboratories. The 2012 CKD-EPI cystatin C equation is as accurate as the 2009 CKD-EPI creatinine equation in estimating eGFR, does not require specification of race, and may be more accurate in patients with decreased muscle mass. The 2012 CKD-EPI creatinine–cystatin C equation is more accurate than the 2009 CKD-EPI creatinine and 2012 CKD-EPI cystatin C equations and is useful as a confirmatory test for decreased eGFR as determined by an equation based on serum creatinine. Further improvement in GFR estimating equations will require development in more broadly representative populations, including diverse racial and ethnic groups, use of multiple filtration markers, and evaluation using statistical techniques to compare eGFR to “true GFR”. PMID:24485147

Near-wall turbulence model and its application to fully developed turbulent channel and pipe flows

NASA Technical Reports Server (NTRS)

Kim, S.-W.

1990-01-01

A near-wall turbulence model and its incorporation into a multiple-timescale turbulence model are presented. The near-wall turbulence model is obtained from a k-equation turbulence model and a near-wall analysis. In the method, the equations for the conservation of mass, momentum, and turbulent kinetic energy are integrated up to the wall, and the energy transfer and the dissipation rates inside the near-wall layer are obtained from algebraic equations. Fully developed turbulent channel and pipe flows are solved using a finite element method. The computational results compare favorably with experimental data. It is also shown that the turbulence model can resolve the overshoot phenomena of the turbulent kinetic energy and the dissipation rate in the region very close to the wall.

Restoration of acidic mine spoils with sewage sludge: II measurement of solids applied

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

Stucky, D.J.; Zoeller, A.L.

1980-01-01

Sewage sludge was incorporated in acidic strip mine spoils at rates equivalent to 0, 224, 336, and 448 dry metric tons (dmt)/ha and placed in pots in a greenhouse. Spoil parameters were determined 48 hours after sludge incorporation, Time Planting (P), and five months after orchardgrass (Dactylis glomerata L.) was planted, Time Harvest (H), in the pots. Parameters measured were: pH, organic matter content (OM), cation exchange capacity (CEC), electrical conductivity (EC) and yield. Values for each parameter were significantly different at the two sampling times. Correlation coefficient values were calculated for all parameters versus rates of applied sewage sludgemore » and all parameters versus each other. Multiple regressions were performed, stepwise, for all parameters versus rates of applied sewage sludge. Equations to predict amounts of sewage sludge incorporated in spoils were derived for individual and multiple parameters. Generally, measurements made at Time P achieved the highest correlation coefficient and multiple correlation coefficient values; therefore, the authors concluded data from Time P had the greatest predictability value. The most important value measured to predict rate of applied sewage sludge was pH and some additional accuracy was obtained by including CEC in equation. This experiment indicated that soil properties can be used to estimate amounts of sewage sludge solids required to reclaim acidic mine spoils and to estimate quantities incorporated.« less

Modeling techniques for quantum cascade lasers

NASA Astrophysics Data System (ADS)

Jirauschek, Christian; Kubis, Tillmann

2014-03-01

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.

Modeling techniques for quantum cascade lasers

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

Jirauschek, Christian; Kubis, Tillmann

2014-03-15

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation ofmore » quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.« less

Weakly nonparallel and curvature effects on stationary crossflow instability: Comparison of results from multiple-scales analysis and parabolized stability equations

NASA Technical Reports Server (NTRS)

Singer, Bart A.; Choudhari, Meelan; Li, Fei

1995-01-01

A multiple-scales approach is used to approximate the effects of nonparallelism and streamwise surface curvature on the growth of stationary crossflow vortices in incompressible, three-dimesional boundary layers. The results agree with results predicted by solving the parabolized stability equations in regions where the nonparallelism is sufficiently weak. As the nonparallelism increases, the agreement between the two approaches worsens. An attempt has been made to quantify the nonparallelism on flow stability in terms of a nondimensional number that describes the rate of change of the mean flow relative to the disturbance wavelength. We find that the above nondimensional number provides useful information about the adequacy of the multiple-scales approximation for different disturbances for a given flow geometry, but the number does not collapse data for different flow geometries onto a single curve.

Local multiplicative Schwarz algorithms for convection-diffusion equations

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Sarkis, Marcus

1995-01-01

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

The effects of temperature dependent recombination rates on performance of InGaN/GaN blue superluminescent light emitting diodes

NASA Astrophysics Data System (ADS)

Moslehi Milani, N.; Mohadesi, V.; Asgari, A.

2015-07-01

The effects of temperature dependent radiative and nonradiative recombination (Shockley-Read-Hall, spontaneous radiative, and Auger coefficients) on the spectral and power characteristics of a blue multiple quantum well (MQW) superluminescent light emitting diode (SLD or SLED) have been studied. The study is based on the rate equations model, where three rate equations corresponding to MQW active region, separate confinement heterostructure (SCH) layer, and spectral density of optical power are solved self-consistently with no k-selection energy dependent gain and quasi-Fermi level functions at steady state. We have taken into account the temperature effects on Shockley-Read-Hall (SRH), spontaneous radiative, and Auger recombination in the rate equations and have investigated the effects of temperature rising from 300 K to 375 K at a fixed current density. We examine this procedure for a moderate current density and interpret the spectral radiation power and light output power diagrams. The investigation reveals that the main loss due to temperature is related to Auger coefficient.

SAM-CE; A Three Dimensional Monte Carlo Code for the Dolution of the Forward Neutron and Forward and Adjoint Gamma Ray Transport Equations. Revision C

DTIC Science & Technology

1974-07-31

Multiple scoring regions are permitted and these may be either finite volume regions or point detectors or both. Other sccres of interest, e.g., collision... Multiplicities ...... . . . . 43 2,3.5.2 Photon Production Cross Sections. . 44 2.3.5.3 Anisotropy of Photon Production . . 44 2.3.5.4 Continuous...hepting, count rates, etc., are calculated as functions of energy, time and position. Multiple scoring regions are permitted and these may be either

Predicting basal metabolic rates in Malaysian adult elite athletes.

PubMed

Wong, Jyh Eiin; Poh, Bee Koon; Nik Shanita, Safii; Izham, Mohd Mohamad; Chan, Kai Quin; Tai, Meng De; Ng, Wei Wei; Ismail, Mohd Noor

2012-11-01

This study aimed to measure the basal metabolic rate (BMR) of elite athletes and develop a gender specific predictive equation to estimate their energy requirements. 92 men and 33 women (aged 18-31 years) from 15 sports, who had been training six hours daily for at least one year, were included in the study. Body composition was measured using the bioimpedance technique, and BMR by indirect calorimetry. The differences between measured and estimated BMR using various predictive equations were calculated. The novel equation derived from stepwise multiple regression was evaluated using Bland and Altman analysis. The predictive equations of Cunningham and the Food and Agriculture Organization/World Health Organization/United Nations University either over- or underestimated the measured BMR by up to ± 6%, while the equations of Ismail et al, developed from the local non-athletic population, underestimated the measured BMR by 14%. The novel predictive equation for the BMR of athletes was BMR (kcal/day) = 669 + 13 (weight in kg) + 192 (gender: 1 for men and 0 for women) (R2 0.548; standard error of estimates 163 kcal). Predicted BMRs of elite athletes by this equation were within 1.2% ± 9.5% of the measured BMR values. The novel predictive equation presented in this study can be used to calculate BMR for adult Malaysian elite athletes. Further studies may be required to validate its predictive capabilities for other sports, nationalities and age groups.

Stochastic modeling of soil salinity

NASA Astrophysics Data System (ADS)

Suweis, S.; Porporato, A. M.; Daly, E.; van der Zee, S.; Maritan, A.; Rinaldo, A.

2010-12-01

A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The equations for the probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equations to a single stochastic differential equation (generalized Langevin equation) driven by multiplicative Poisson noise. Generalized Langevin equations with multiplicative white Poisson noise pose the usual Ito (I) or Stratonovich (S) prescription dilemma. Different interpretations lead to different results and then choosing between the I and S prescriptions is crucial to describe correctly the dynamics of the model systems. We show how this choice can be determined by physical information about the timescales involved in the process. We also show that when the multiplicative noise is at most linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We then apply these results to the generalized Langevin equation that drives the salt mass dynamics. The stationary analytical solutions for the probability density functions of salt mass and concentration provide insight on the interplay of the main soil, plant and climate parameters responsible for long term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in longterm soil salinization trends, with significant consequences, e.g. for climate change impacts on rain fed agriculture.

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

NASA Astrophysics Data System (ADS)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-07-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

Reaeration equations derived from U.S. geological survey database

USGS Publications Warehouse

Melching, C.S.; Flores, H.E.

1999-01-01

Accurate estimation of the reaeration-rate coefficient (K2) is extremely important for waste-load allocation. Currently, available K2 estimation equations generally yield poor estimates when applied to stream conditions different from those for which the equations were derived because they were derived from small databases composed of potentially highly inaccurate measurements. A large data set of K2 measurements made with tracer-gas methods was compiled from U.S. Geological Survey studies. This compilation included 493 reaches on 166 streams in 23 states. Careful screening to detect and eliminate erroneous measurements reduced the date set to 371 measurements. These measurements were divided into four subgroups on the basis of flow regime (channel control or pool and riffle) and stream scale (discharge greater than or less than 0.556 m3/s). Multiple linear regression in logarithms was applied to relate K2 to 12 stream hydraulic and water-quality characteristics. The resulting best-estimation equations had the form of semiempirical equations that included the rate of energy dissipation and discharge or depth and width as variables. For equation verification, a data set of K2 measurements made with tracer-gas procedures by other agencies was compiled from the literature. This compilation included 127 reaches on at least 24 streams in at least seven states. The standard error of estimate obtained when applying the developed equations to the U.S. Geological Survey data set ranged from 44 to 61%, whereas the standard error of estimate was 78% when applied to the verification data set.Accurate estimation of the reaeration-rate coefficient (K2) is extremely important for waste-load allocation. Currently, available K2 estimation equations generally yield poor estimates when applied to stream conditions different from those for which the equations were derived because they were derived from small databases composed of potentially highly inaccurate measurements. A large data set of K2 measurements made with tracer-gas methods was compiled from U.S. Geological Survey studies. This compilation included 493 reaches on 166 streams in 23 states. Careful screening to detect and eliminate erroneous measurements reduced the data set to 371 measurements. These measurements were divided into four subgroups on the basis of flow regime (channel control or pool and riffle) and stream scale (discharge greater than or less than 0.556 m3/s). Multiple linear regression in logarithms was applied to relate K2 to 12 stream hydraulic and water-quality characteristics. The resulting best-estimation equations had the form of semiempirical equations that included the rate of energy dissipation and discharge or depth and width as variables. For equation verification, a data set of K2 measurements made with tracer-gas procedures by other agencies was compiled from the literature. This compilation included 127 reaches on at least 24 streams in at least seven states. The standard error of estimate obtained when applying the developed equations to the U.S. Geological Survey data set ranged from 44 to 61%, whereas the standard error of estimate was 78% when applied to the verification data set.

User’s Guide for Biodegradation Reactions in TMVOCBio

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

Jung, Yoojin; Battistelli, Alfredo

TMVOCBio is an extended version of the TMVOC numerical reservoir simulator, with the capability of simulating multiple biodegradation reactions mediated by different microbial populations or based on different redox reactions, thus involving different electron acceptors. This modeling feature is implemented within the existing TMVOC module in iTOUGH2. TMVOCBio, originally developed by Battistelli (2003; 2004), uses a general modified form of the Monod kinetic rate equation to simulate biodegradation reactions, which effectively simulates the uptake of a substrate while accounting for various limiting factors (i.e., the limitation by substrate, electron acceptor, or nutrients). Two approaches are included: 1) a multiple Monodmore » kinetic rate equation, which assumes all the limiting factors simultaneously affect the substrate uptake rate, and 2) a minimum Monod model, which assumes that the substrate uptake rate is controlled by the most limiting factor among those acting for the specific substrate. As the limiting factors, biomass growth inhibition, toxicity effects, as well as competitive and non-competitive inhibition effects are included. The temperature and moisture dependence of biodegradation reactions is also considered. This report provides mathematical formulations and assumptions used for modeling the biodegradation reactions, and describes additional modeling capabilities. Detailed description of input format for biodegradation reactions is presented along with sample problems.« less

Computational multiple steady states for enzymatic esterification of ethanol and oleic acid in an isothermal CSTR.

PubMed

Ho, Pang-Yen; Chuang, Guo-Syong; Chao, An-Chong; Li, Hsing-Ya

2005-05-01

The capacity of complex biochemical reaction networks (consisting of 11 coupled non-linear ordinary differential equations) to show multiple steady states, was investigated. The system involved esterification of ethanol and oleic acid by lipase in an isothermal continuous stirred tank reactor (CSTR). The Deficiency One Algorithm and the Subnetwork Analysis were applied to determine the steady state multiplicity. A set of rate constants and two corresponding steady states are computed. The phenomena of bistability, hysteresis and bifurcation are discussed. Moreover, the capacity of steady state multiplicity is extended to the family of the studied reaction networks.

Quantifying the combined effects of attempt rate and swimming capacity on passage through velocity barriers

USGS Publications Warehouse

Castro-Santos, T.

2004-01-01

The ability of fish to migrate past velocity barriers results from both attempt rate and swimming capacity. Here, I formalize this relationship, providing equations for estimating the proportion of a population successfully passing a barrier over a range of distances and times. These equations take into account the cumulative effect of multiple attempts, the time required to stage those attempts, and both the distance traversed on each attempt and its variability. I apply these equations to models of white sucker (Catostomus commersoni) and walleye (Stizostedion vitreum) ascending a 23-m-long flume against flows ranging from 1.5 to 4.5 m??s-1. Attempt rate varied between species, attempts, and over time and was influenced by hydraulic variables (velocity of flow and discharge). Distance of ascent was primarily influenced by flow velocity. Although swimming capacity was similar, white sucker had greater attempt rates, and consequently better passage success, than walleye. Over short distances, models for both species predict greater passage success against higher velocities owing to the associated increased attempt rate. These results highlight the importance of attraction to fish passage and the need for further investigation into the hydraulic and other environmental conditions required to simultaneously optimize both attempt rate and passage success.

Mortality rates in OECD countries converged during the period 1990-2010.

PubMed

Bremberg, Sven G

2017-06-01

Since the scientific revolution of the 18th century, human health has gradually improved, but there is no unifying theory that explains this improvement in health. Studies of macrodeterminants have produced conflicting results. Most studies have analysed health at a given point in time as the outcome; however, the rate of improvement in health might be a more appropriate outcome. Twenty-eight OECD member countries were selected for analysis in the period 1990-2010. The main outcomes studied, in six age groups, were the national rates of decrease in mortality in the period 1990-2010. The effects of seven potential determinants on the rates of decrease in mortality were analysed in linear multiple regression models using least squares, controlling for country-specific history constants, which represent the mortality rate in 1990. The multiple regression analyses started with models that only included mortality rates in 1990 as determinants. These models explained 87% of the intercountry variation in the children aged 1-4 years and 51% in adults aged 55-74 years. When added to the regression equations, the seven determinants did not seem to significantly increase the explanatory power of the equations. The analyses indicated a decrease in mortality in all nations and in all age groups. The development of mortality rates in the different nations demonstrated significant catch-up effects. Therefore an important objective of the national public health sector seems to be to reduce the delay between international research findings and the universal implementation of relevant innovations.

q-Gaussian distributions and multiplicative stochastic processes for analysis of multiple financial time series

NASA Astrophysics Data System (ADS)

Sato, Aki-Hiro

2010-12-01

This study considers q-Gaussian distributions and stochastic differential equations with both multiplicative and additive noises. In the M-dimensional case a q-Gaussian distribution can be theoretically derived as a stationary probability distribution of the multiplicative stochastic differential equation with both mutually independent multiplicative and additive noises. By using the proposed stochastic differential equation a method to evaluate a default probability under a given risk buffer is proposed.

Basic governing equations for the flight regimes of aeroassisted orbital transfer vehicles

NASA Technical Reports Server (NTRS)

Lee, J.-H.

1984-01-01

The basic governing equations for the low-density, high-enthalpy flow regimes expected in the shock layers over the heat shields of the proposed aeroassisted orbital transfer vehicles are derived by combining and extending existing theories. The conservation equations are derived from gas kinetic principles for a four-component ionized gas consisting of neutral molecules, neutral atoms, singly ionized ions, and electrons, assuming a continuum flow. The differences among translational-rotational, vibrational, and electron temperatures are accounted for, as well as chemical nonequilibrium and electric-charge separation. Expressions for convective and viscous fluxes, transport properties, and the terms representing interactions among various energy modes are given explicitly. The expressions for the rate of electron-vibration energy transfer, which violates the Landau-Teller conditions, is derived by solving the system of master equations accounting for the multiple-level transitions.

Basic Governing Equations for the Flight Regimes of Aeroassisted Orbital Transfer Vehicles

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1985-01-01

The basic governing equations for the low-density, high-enthalpy flow regimes expected in the shock layers over the heat shields of the proposed aeroassisted orbital transfer vehicles are derived by combining and extending existing theories. The conservation equations are derived from gas kinetic principles for a four-component ionized gas consisting of neutral molecules, neutral atoms, singly ionized ions, and electrons, assuming a continuum flow. The differences among translational-rotational, vibrational, and electron temperatures are accounted for, as well as chemical nonequilibrium and electric-charge separation. Expressions for convective and viscous fluxes, transport properties, and the terms representing interactions among various energy modes are explicitly given. The expressions for the rate of electron-vibration energy transfer, which violates the Landau-Teller conditions, are derived by solving the system of master equations accounting for the multiple-level transitions.

Poisson-Nernst-Planck equations with steric effects - non-convexity and multiple stationary solutions

NASA Astrophysics Data System (ADS)

Gavish, Nir

2018-04-01

We study the existence and stability of stationary solutions of Poisson-Nernst-Planck equations with steric effects (PNP-steric equations) with two counter-charged species. We show that within a range of parameters, steric effects give rise to multiple solutions of the corresponding stationary equation that are smooth. The PNP-steric equation, however, is found to be ill-posed at the parameter regime where multiple solutions arise. Following these findings, we introduce a novel PNP-Cahn-Hilliard model, show that it is well-posed and that it admits multiple stationary solutions that are smooth and stable. The various branches of stationary solutions and their stability are mapped utilizing bifurcation analysis and numerical continuation methods.

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

NASA Technical Reports Server (NTRS)

Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order

DOE PAGES

Favalli, Andrea; Croft, Stephen; Santi, Peter

2015-06-15

Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclearmore » data constants by a series of coupled algebraic equations – the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This study represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.« less

The allometric relationship between resting metabolic rate and body mass in wild waterfowl (Anatidae) and an application to estimation of winter habitat requirements

USGS Publications Warehouse

Miller, M.R.; Eadie, J. McA

2006-01-01

We examined the allometric relationship between resting metabolic rate (RMR; kJ day-1) and body mass (kg) in wild waterfowl (Anatidae) by regressing RMR on body mass using species means from data obtained from published literature (18 sources, 54 measurements, 24 species; all data from captive birds). There was no significant difference among measurements from the rest (night; n = 37), active (day; n = 14), and unspecified (n = 3) phases of the daily cycle (P > 0.10), and we pooled these measurements for analysis. The resulting power function (aMassb) for all waterfowl (swans, geese, and ducks) had an exponent (b; slope of the regression) of 0.74, indistinguishable from that determined with commonly used general equations for nonpasserine birds (0.72-0.73). In contrast, the mass proportionality coefficient (b; y-intercept at mass = 1 kg) of 422 exceeded that obtained from the nonpasserine equations by 29%-37%. Analyses using independent contrasts correcting for phylogeny did not substantially alter the equation. Our results suggest the waterfowl equation provides a more appropriate estimate of RMR for bioenergetics analyses of waterfowl than do the general nonpasserine equations. When adjusted with a multiple to account for energy costs of free living, the waterfowl equation better estimates daily energy expenditure. Using this equation, we estimated that the extent of wetland habitat required to support wintering waterfowl populations could be 37%-50% higher than previously predicted using general nonpasserine equations. ?? The Cooper Ornithological Society 2006.

Emergent properties of interacting populations of spiking neurons.

PubMed

Cardanobile, Stefano; Rotter, Stefan

2011-01-01

Dynamic neuronal networks are a key paradigm of increasing importance in brain research, concerned with the functional analysis of biological neuronal networks and, at the same time, with the synthesis of artificial brain-like systems. In this context, neuronal network models serve as mathematical tools to understand the function of brains, but they might as well develop into future tools for enhancing certain functions of our nervous system. Here, we present and discuss our recent achievements in developing multiplicative point processes into a viable mathematical framework for spiking network modeling. The perspective is that the dynamic behavior of these neuronal networks is faithfully reflected by a set of non-linear rate equations, describing all interactions on the population level. These equations are similar in structure to Lotka-Volterra equations, well known by their use in modeling predator-prey relations in population biology, but abundant applications to economic theory have also been described. We present a number of biologically relevant examples for spiking network function, which can be studied with the help of the aforementioned correspondence between spike trains and specific systems of non-linear coupled ordinary differential equations. We claim that, enabled by the use of multiplicative point processes, we can make essential contributions to a more thorough understanding of the dynamical properties of interacting neuronal populations.

Emergent Properties of Interacting Populations of Spiking Neurons

PubMed Central

Cardanobile, Stefano; Rotter, Stefan

2011-01-01

Dynamic neuronal networks are a key paradigm of increasing importance in brain research, concerned with the functional analysis of biological neuronal networks and, at the same time, with the synthesis of artificial brain-like systems. In this context, neuronal network models serve as mathematical tools to understand the function of brains, but they might as well develop into future tools for enhancing certain functions of our nervous system. Here, we present and discuss our recent achievements in developing multiplicative point processes into a viable mathematical framework for spiking network modeling. The perspective is that the dynamic behavior of these neuronal networks is faithfully reflected by a set of non-linear rate equations, describing all interactions on the population level. These equations are similar in structure to Lotka-Volterra equations, well known by their use in modeling predator-prey relations in population biology, but abundant applications to economic theory have also been described. We present a number of biologically relevant examples for spiking network function, which can be studied with the help of the aforementioned correspondence between spike trains and specific systems of non-linear coupled ordinary differential equations. We claim that, enabled by the use of multiplicative point processes, we can make essential contributions to a more thorough understanding of the dynamical properties of interacting neuronal populations. PMID:22207844

Describing the dynamics of processes consisting simultaneously of Poissonian and non-Poissonian kinetics

NASA Astrophysics Data System (ADS)

Eule, S.; Friedrich, R.

2013-03-01

Dynamical processes exhibiting non-Poissonian kinetics with nonexponential waiting times are frequently encountered in nature. Examples are biochemical processes like gene transcription which are known to involve multiple intermediate steps. However, often a second process, obeying Poissonian statistics, affects the first one simultaneously, such as the degradation of mRNA in the above example. The aim of the present article is to provide a concise treatment of such random systems which are affected by regular and non-Poissonian kinetics at the same time. We derive the governing master equation and provide a controlled approximation scheme for this equation. The simplest approximation leads to generalized reaction rate equations. For a simple model of gene transcription we solve the resulting equation and show how the time evolution is influenced significantly by the type of waiting time distribution assumed for the non-Poissonian process.

Obligatory versus elective single embryo transfer in in vitro fertilization. A population-based analysis of data from the U.K. Human Fertilisation and Embryology Authority.

PubMed

Straughen, Jennifer K; Salihu, Hamisu M; Keith, Louis; Petrozzino, Jeffrey; Jones, Christopher

2013-01-01

To determine how obligatory single embryo transfer (SET) and elective SET influence pregnancy outcome. We compared women who underwent obligatory and elective SET using data from a comprehensive, population-based register from the United Kingdom Human Fertilisation and Embryology Authority, which contained all in vitro fertilization (IVF) treatments administered between 1991 and 1998. Generalized estimating equations were used to generate adjusted odds ratios (ORs) and 95% confidence intervals (CIs) to compare clinical pregnancy, live birth, and multiple birth rates. Obligatory and elective SET had similar clinical pregnancy and live birth rates and comparable multiple birth rates. Obligatory and elective SET were equally likely to end in a live birth (OR = 1.08; 95% CI = 0.90, 1.30). Similar results were found after restricting the data to women without previous IVF births (OR = 1.18; 95% CI = 0.98, 1.42) and without previous naturally conceived live births (OR = 1.16; 95% CI = 0.95, 1.43). This study suggests that obligatory SET can achieve pregnancy and live birth rates that are at least as good as elective SET. Equally important is the low multiple birth rate which was maintained in both forms of SET. More studies comparing elective versus obligatory SET can assist with achieving optimal pregnancy rates while preventing multiple births.

Multidimensional Predictors of Fatigue among Octogenarians and Centenarians

PubMed Central

Cho, Jinmyoung; Martin, Peter; Margrett, Jennifer; MacDonald, Maurice; Johnson, Mary Ann; Poon, Leonard W.

2012-01-01

Background Fatigue is a common and frequently observed complaint among older adults. However, knowledge about the nature and correlates of fatigue in old age is very limited. Objective: This study examined the relationship of functional indicators, psychological and situational factors and fatigue for 210 octogenarians and centenarians from the Georgia Centenarian Study. Methods Three indicators of functional capacity (self-rated health, instrumental activities of daily living, physical activities of daily living), two indicators of psychological well-being (positive and negative affect), two indicators of situational factors (social network and social support), and a multidimensional fatigue scale were used. Blocked multiple regression analyses were computed to examine significant factors related to fatigue. In addition, multi-group analysis in structural equation modeling was used to investigate residential differences (i.e., long-term care facilities vs. private homes) in the relationship between significant factors and fatigue. Results Blocked multiple regression analyses indicated that two indicators of functional capacity, self-rated health and instrumental activities of daily living, both positive and negative affect, and social support were significant predictors of fatigue among oldest-old adults. The multiple group analysis in structural equation modeling revealed a significant difference among oldest-old adults based on residential status. Conclusion The results suggest that we should not consider fatigue as merely an unpleasant physical symptom, but rather adopt a perspective that different factors such as psychosocial aspects can influence fatigue in advanced later life. PMID:22094445

Multidimensional predictors of fatigue among octogenarians and centenarians.

PubMed

Cho, Jinmyoung; Martin, Peter; Margrett, Jennifer; MacDonald, Maurice; Johnson, Mary Ann; Poon, Leonard W; Jazwinski, S M; Green, R C; Gearing, M; Woodard, J L; Tenover, J S; Siegler, I C; Rott, C; Rodgers, W L; Hausman, D; Arnold, J; Davey, A

2012-01-01

Fatigue is a common and frequently observed complaint among older adults. However, knowledge about the nature and correlates of fatigue in old age is very limited. This study examined the relationship of functional indicators, psychological and situational factors and fatigue for 210 octogenarians and centenarians from the Georgia Centenarian Study. Three indicators of functional capacity (self-rated health, instrumental activities of daily living, physical activities of daily living), two indicators of psychological well-being (positive and negative affect), two indicators of situational factors (social network and social support), and a multidimensional fatigue scale were used. Blocked multiple regression analyses were computed to examine significant factors related to fatigue. In addition, multi-group analysis in structural equation modeling was used to investigate residential differences (i.e., long-term care facilities vs. private homes) in the relationship between significant factors and fatigue. Blocked multiple regression analyses indicated that two indicators of functional capacity, self-rated health and instrumental activities of daily living, both positive and negative affect, and social support were significant predictors of fatigue among oldest-old adults. The multiple group analysis in structural equation modeling revealed a significant difference among oldest-old adults based on residential status. The results suggest that we should not consider fatigue as merely an unpleasant physical symptom, but rather adopt a perspective that different factors such as psychosocial aspects can influence fatigue in advanced later life. Copyright © 2011 S. Karger AG, Basel.

Multiple ionization of neon by soft x-rays at ultrahigh intensity

NASA Astrophysics Data System (ADS)

Guichard, R.; Richter, M.; Rost, J.-M.; Saalmann, U.; Sorokin, A. A.; Tiedtke, K.

2013-08-01

At the free-electron laser FLASH, multiple ionization of neon atoms was quantitatively investigated at photon energies of 93.0 and 90.5 eV. For ion charge states up to 6+, we compare the respective absolute photoionization yields with results from a minimal model and an elaborate description including standard sequential and direct photoionization channels. Both approaches are based on rate equations and take into account a Gaussian spatial intensity distribution of the laser beam. From the comparison we conclude that photoionization up to a charge of 5+ can be described by the minimal model which we interpret as sequential photoionization assisted by electron shake-up processes. For higher charges, the experimental ionization yields systematically exceed the elaborate rate-based prediction.

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

PubMed Central

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization. PMID:27243005

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

PubMed

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

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

A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2018-07-01

A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified KdV equation (MKdV-nMKdV). The complete integrability of this equation is confirmed by showing that it nicely possesses the Painlevé property. We obtain multiple soliton solutions for the newly developed integrable equation. Moreover, this equation enjoys a variety of solutions which include solitons, peakons, cuspons, negaton, positon, complexiton and other solutions.

A split-step method to include electron–electron collisions via Monte Carlo in multiple rate equation simulations

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

Huthmacher, Klaus; Molberg, Andreas K.; Rethfeld, Bärbel

2016-10-01

A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron–phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron–electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate howmore » electron–electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.« less

Multiple-Relaxation-Time Lattice Boltzmann Models in 3D

NASA Technical Reports Server (NTRS)

dHumieres, Dominique; Ginzburg, Irina; Krafczyk, Manfred; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

This article provides a concise exposition of the multiple-relaxation-time lattice Boltzmann equation, with examples of fifteen-velocity and nineteen-velocity models in three dimensions. Simulation of a diagonally lid-driven cavity flow in three dimensions at Re=500 and 2000 is performed. The results clearly demonstrate the superior numerical stability of the multiple-relaxation-time lattice Boltzmann equation over the popular lattice Bhatnagar-Gross-Krook equation.

Kinetic modeling of non-ideal explosives with CHEETAH

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

Fried, L E; Howard, W M; Souers, P C

1998-08-06

We report an implementation of the Wood-Kirkwood kinetic detonation model based on multi-species equations of state and multiple reaction rate laws. Finite rate laws are used for the slowest chemical reactions. Other reactions are given infinite rates and are kept in constant thermodynamic equilibrium. We model a wide range of ideal and non-ideal composite energetic materials. We find that we can replicate experimental detonation velocities to within a few per cent, while obtaining good agreement with estimated reaction zone lengths. The detonation velocity as a function of charge radius is also correctly reproduced.

Limit cycles in piecewise-affine gene network models with multiple interaction loops

NASA Astrophysics Data System (ADS)

Farcot, Etienne; Gouzé, Jean-Luc

2010-01-01

In this article, we consider piecewise affine differential equations modelling gene networks. We work with arbitrary decay rates, and under a local hypothesis expressed as an alignment condition of successive focal points. The interaction graph of the system may be rather complex (multiple intricate loops of any sign, multiple thresholds, etc.). Our main result is an alternative theorem showing that if a sequence of region is periodically visited by trajectories, then under our hypotheses, there exists either a unique stable periodic solution, or the origin attracts all trajectories in this sequence of regions. This result extends greatly our previous work on a single negative feedback loop. We give several examples and simulations illustrating different cases.

Global minimum profile error (GMPE) - a least-squares-based approach for extracting macroscopic rate coefficients for complex gas-phase chemical reactions.

PubMed

Duong, Minh V; Nguyen, Hieu T; Mai, Tam V-T; Huynh, Lam K

2018-01-03

Master equation/Rice-Ramsperger-Kassel-Marcus (ME/RRKM) has shown to be a powerful framework for modeling kinetic and dynamic behaviors of a complex gas-phase chemical system on a complicated multiple-species and multiple-channel potential energy surface (PES) for a wide range of temperatures and pressures. Derived from the ME time-resolved species profiles, the macroscopic or phenomenological rate coefficients are essential for many reaction engineering applications including those in combustion and atmospheric chemistry. Therefore, in this study, a least-squares-based approach named Global Minimum Profile Error (GMPE) was proposed and implemented in the MultiSpecies-MultiChannel (MSMC) code (Int. J. Chem. Kinet., 2015, 47, 564) to extract macroscopic rate coefficients for such a complicated system. The capability and limitations of the new approach were discussed in several well-defined test cases.

Effects of group velocity and multiplasmon resonances on the modulation of Langmuir waves in a degenerate plasma

NASA Astrophysics Data System (ADS)

Misra, Amar P.; Chatterjee, Debjani; Brodin, Gert

2017-11-01

We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully degenerate plasma. Using the Wigner-Moyal equation coupled to the Poisson equation and the multiple scale expansion technique, a modified nonlocal nonlinear Schrödinger (NLS) equation is derived which governs the evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in the NLS equation appears due to the group velocity and multiplasmon resonances, i.e., resonances induced by the simultaneous particle absorption of multiple wave quanta. We focus on the regime where the resonant velocity of electrons is larger than the Fermi velocity and thereby the linear Landau damping is forbidden. As a result, the nonlinear wave-particle resonances due to the group velocity and multiplasmon processes are the dominant mechanisms for wave-particle interaction. It is found that in contrast to classical or semiclassical plasmas, the group velocity resonance does not necessarily give rise the wave damping in the strong quantum regime where ℏ k ˜m vF with ℏ denoting the reduced Planck's constant, m the electron mass, and vF the Fermi velocity; however, the three-plasmon process plays a dominant role in the nonlinear Landau damping of wave envelopes. In this regime, the decay rate of the wave amplitude is also found to be higher compared to that in the modest quantum regime where the multiplasmon effects are forbidden.

Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms.

PubMed

Adams, Luise; Chaubey, Ekta; Weinzierl, Stefan

2017-04-07

In this Letter we exploit factorization properties of Picard-Fuchs operators to decouple differential equations for multiscale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to an ϵ form.

Construct validity of ADHD/ODD rating scales: recommendations for the evaluation of forthcoming DSM-V ADHD/ODD scales.

PubMed

Burns, G Leonard; Walsh, James A; Servera, Mateu; Lorenzo-Seva, Urbano; Cardo, Esther; Rodríguez-Fornells, Antoni

2013-01-01

Exploratory structural equation modeling (SEM) was applied to a multiple indicator (26 individual symptom ratings) by multitrait (ADHD-IN, ADHD-HI and ODD factors) by multiple source (mothers, fathers and teachers) model to test the invariance, convergent and discriminant validity of the Child and Adolescent Disruptive Behavior Inventory with 872 Thai adolescents and the ADHD Rating Scale-IV and ODD scale of the Disruptive Behavior Inventory with 1,749 Spanish children. Most of the individual ADHD/ODD symptoms showed convergent and discriminant validity with the loadings and thresholds being invariant over mothers, fathers and teachers in both samples (the three latent factor means were higher for parents than teachers). The ADHD-IN, ADHD-HI and ODD latent factors demonstrated convergent and discriminant validity between mothers and fathers within the two samples. Convergent and discriminant validity between parents and teachers for the three factors was either absent (Thai sample) or only partial (Spanish sample). The application of exploratory SEM to a multiple indicator by multitrait by multisource model should prove useful for the evaluation of the construct validity of the forthcoming DSM-V ADHD/ODD rating scales.

Analytical model for orbital debris environmental management

NASA Technical Reports Server (NTRS)

Talent, David L.

1990-01-01

A differential equation, also referred to as the PIB (particle-in-a-box) model, expressing the time rate of change of the number of objects in orbit, is developed, and its applicability is illustrated. The model can be used as a tool for the assessment of LEO environment stability, and as a starting point for the development of numerical evolutionary models. Within the context of the model, evolutionary scenarios are examined, and found to be sensitive to the growth rate. It is determined that the present environment is slightly unstable to catastrophic growth, and that the number of particles on orbit will continue to increase until approximately 2250-2350 AD, with a maximum of 2,000,000. The model is expandable to the more realistic (complex) case of multiple species in a multiple-tier system.

Parent ratings of ADHD symptoms: differential symptom functioning across Malaysian Malay and Chinese children.

PubMed

Gomez, Rapson; Vance, Alasdair

2008-08-01

This study examined differential symptom functioning (DSF) in ADHD symptoms across Malay and Chinese children in Malaysia. Malay (N=571) and Chinese (N=254) parents completed the Disruptive Behavior Rating Scale, which lists the DSM-IV ADHD symptoms. DSF was examined using the multiple indicators multiple causes (MIMIC) structural equation modeling procedure. Although DSF was found for a single inattention (IA) symptom and three hyperactivity-impulsivity (HI) symptoms, all these differences had low effect sizes. Controlling for these DSF, Chinese children had higher IA and HI latent factor scores. However the effect sizes were small. Together, these findings suggest adequate support for invariance of the ADHD symptoms across these ethno-cultural groups. The implications of the findings for cross-cultural invariance of the ADHD symptoms are discussed.

Aleatory Uncertainty and Scale Effects in Computational Damage Models for Failure and Fragmentation

DTIC Science & Technology

2014-09-01

larger specimens, small specimens have, on average, higher strengths. Equivalently, because curves for small specimens fall below those of larger...the material strength associated with each realization parameter R in Equation (7), and strength distribution curves associated with multiple...effects in brittle media [58], which applies micromorphological dimensional analysis to obtain a universal curve which closely fits rate-dependent

Primordial perturbations in multi-scalar inflation

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

Abedi, Habib; Abbassi, Amir M., E-mail: h.abedi@ut.ac.ir, E-mail: amabasi@khayam.ut.ac.ir

2017-07-01

Multiple field models of inflation exhibit new features than single field models. In this work, we study the hierarchy of parameters based on Hubble expansion rate in curved field space and derive the system of flow equations that describe their evolutions. Then we focus on obtaining derivatives of number of e-folds with respect to scalar fields during inflation and at hypersurface of the end of inflation.

Delay induced high order locking effects in semiconductor lasers

NASA Astrophysics Data System (ADS)

Kelleher, B.; Wishon, M. J.; Locquet, A.; Goulding, D.; Tykalewicz, B.; Huyet, G.; Viktorov, E. A.

2017-11-01

Multiple time scales appear in many nonlinear dynamical systems. Semiconductor lasers, in particular, provide a fertile testing ground for multiple time scale dynamics. For solitary semiconductor lasers, the two fundamental time scales are the cavity repetition rate and the relaxation oscillation frequency which is a characteristic of the field-matter interaction in the cavity. Typically, these two time scales are of very different orders, and mutual resonances do not occur. Optical feedback endows the system with a third time scale: the external cavity repetition rate. This is typically much longer than the device cavity repetition rate and suggests the possibility of resonances with the relaxation oscillations. We show that for lasers with highly damped relaxation oscillations, such resonances can be obtained and lead to spontaneous mode-locking. Two different laser types-—a quantum dot based device and a quantum well based device—are analysed experimentally yielding qualitatively identical dynamics. A rate equation model is also employed showing an excellent agreement with the experimental results.

Delay induced high order locking effects in semiconductor lasers.

PubMed

Kelleher, B; Wishon, M J; Locquet, A; Goulding, D; Tykalewicz, B; Huyet, G; Viktorov, E A

2017-11-01

Multiple time scales appear in many nonlinear dynamical systems. Semiconductor lasers, in particular, provide a fertile testing ground for multiple time scale dynamics. For solitary semiconductor lasers, the two fundamental time scales are the cavity repetition rate and the relaxation oscillation frequency which is a characteristic of the field-matter interaction in the cavity. Typically, these two time scales are of very different orders, and mutual resonances do not occur. Optical feedback endows the system with a third time scale: the external cavity repetition rate. This is typically much longer than the device cavity repetition rate and suggests the possibility of resonances with the relaxation oscillations. We show that for lasers with highly damped relaxation oscillations, such resonances can be obtained and lead to spontaneous mode-locking. Two different laser types--a quantum dot based device and a quantum well based device-are analysed experimentally yielding qualitatively identical dynamics. A rate equation model is also employed showing an excellent agreement with the experimental results.

Reference equation for prediction of a total distance during six-minute walk test using Indonesian anthropometrics.

PubMed

Nusdwinuringtyas, Nury; Widjajalaksmi; Yunus, Faisal; Alwi, Idrus

2014-04-01

to develop a reference equation for prediction of the total distance walk using Indonesian anthropometrics of sedentary healthy subjects. Subsequently, the prediction obtained was compared to those calculated by the Caucasian-based Enright prediction equation. the cross-sectional study was conducted among 123 healthy Indonesian adults with sedentary life style (58 male and 65 female subjects in an age range between 18 and 50 years). Heart rate was recorded using Polar with expectation in the sub-maximal zone (120-170 beats per minute). The subjects performed two six-minute walk tests, the first one on a 15-meter track according to the protocol developed by the investigator. The second walk was carried out on Biodex®gait trainer as gold standard. an average total distance of 547±54.24 m was found, not significantly different from the gold standard of 544.72±54.11 m (p>0.05). Multiple regression analysis was performed to develop the new equation. the reference equation for prediction of the total distance using Indonesian anthropometrics is more applicable in Indonesia.

Nonadiabatic dynamics of electron transfer in solution: Explicit and implicit solvent treatments that include multiple relaxation time scales

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

Schwerdtfeger, Christine A.; Soudackov, Alexander V.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu

2014-01-21

The development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents formore » a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a short-time inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solvent-controlled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.« less

Modeling the lake eutrophication stochastic ecosystem and the research of its stability.

PubMed

Wang, Bo; Qi, Qianqian

2018-06-01

In the reality, the lake system will be disturbed by stochastic factors including the external and internal factors. By adding the additive noise and the multiplicative noise to the right-hand sides of the model equation, the additive stochastic model and the multiplicative stochastic model are established respectively in order to reduce model errors induced by the absence of some physical processes. For both the two kinds of stochastic ecosystems, the authors studied the bifurcation characteristics with the FPK equation and the Lyapunov exponent method based on the Stratonovich-Khasminiskii stochastic average principle. Results show that, for the additive stochastic model, when control parameter (i.e., nutrient loading rate) falls into the interval [0.388644, 0.66003825], there exists bistability for the ecosystem and the additive noise intensities cannot make the bifurcation point drift. In the region of the bistability, the external stochastic disturbance which is one of the main triggers causing the lake eutrophication, may make the ecosystem unstable and induce a transition. When control parameter (nutrient loading rate) falls into the interval (0,  0.388644) and (0.66003825,  1.0), there only exists a stable equilibrium state and the additive noise intensity could not change it. For the multiplicative stochastic model, there exists more complex bifurcation performance and the multiplicative ecosystem will be broken by the multiplicative noise. Also, the multiplicative noise could reduce the extent of the bistable region, ultimately, the bistable region vanishes for sufficiently large noise. What's more, both the nutrient loading rate and the multiplicative noise will make the ecosystem have a regime shift. On the other hand, for the two kinds of stochastic ecosystems, the authors also discussed the evolution of the ecological variable in detail by using the Four-stage Runge-Kutta method of strong order γ=1.5. The numerical method was found to be capable of effectively explaining the regime shift theory and agreed with the realistic analyze. These conclusions also confirms the two paths for the system to move from one stable state to another proposed by Beisner et al. [3], which may help understand the occurrence mechanism related to the lake eutrophication from the view point of the stochastic model and mathematical analysis. Copyright © 2018 Elsevier Inc. All rights reserved.

Textbook Multigrid Efficiency for Leading Edge Stagnation

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Mineck, Raymond E.

2004-01-01

A multigrid solver is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in evaluating the discrete residuals. TME in solving the incompressible inviscid fluid equations is demonstrated for leading-edge stagnation flows. The contributions of this paper include (1) a special formulation of the boundary conditions near stagnation allowing convergence of the Newton iterations on coarse grids, (2) the boundary relaxation technique to facilitate relaxation and residual restriction near the boundaries, (3) a modified relaxation scheme to prevent initial error amplification, and (4) new general analysis techniques for multigrid solvers. Convergence of algebraic errors below the level of discretization errors is attained by a full multigrid (FMG) solver with one full approximation scheme (FAS) cycle per grid. Asymptotic convergence rates of the FAS cycles for the full system of flow equations are very fast, approaching those for scalar elliptic equations.

Textbook Multigrid Efficiency for Leading Edge Stagnation

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Mineck, Raymond E.

2004-01-01

A multigrid solver is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in evaluating the discrete residuals. TME in solving the incompressible inviscid fluid equations is demonstrated for leading- edge stagnation flows. The contributions of this paper include (1) a special formulation of the boundary conditions near stagnation allowing convergence of the Newton iterations on coarse grids, (2) the boundary relaxation technique to facilitate relaxation and residual restriction near the boundaries, (3) a modified relaxation scheme to prevent initial error amplification, and (4) new general analysis techniques for multigrid solvers. Convergence of algebraic errors below the level of discretization errors is attained by a full multigrid (FMG) solver with one full approximation scheme (F.4S) cycle per grid. Asymptotic convergence rates of the F.4S cycles for the full system of flow equations are very fast, approaching those for scalar elliptic equations.

Quantized expected returns in terms of dividend yield at the money

NASA Astrophysics Data System (ADS)

Dieng, Lamine

2011-03-01

We use the Bachelier (additive model) and the Black-Scholes (multiplicative model) as our models for the stock price movement for an investor who has entered into an America call option contract. We assume the investor to pay certain dividend yield on the expected rate of returns from buying stocks. In this work, we also assume the stock price to be initially in the out of the money state and eventually will move up through at the money state to the deep in the money state where the expected future payoffs and returns are positive for the stock holder. We call a singularity point at the money because the expected payoff vanishes at this point. Then, using martingale, supermartingale and Markov theories we obtain the Bachelier-type of the Black-Scholes and the Black-Scholes equations which we hedge in the limit where the change of the expected payoff of the call option is extremely small. Hence, by comparison we obtain the time-independent Schroedinger equation in Quantum Mechanics. We solve completely the time independent Schroedinger equation for both models to obtain the expected rate of returns and the expected payoffs for the stock holder at the money. We find the expected rate of returns to be quantized in terms of the dividend yield.

Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species

NASA Astrophysics Data System (ADS)

Chen, Xiuqing; Daus, Esther S.; Jüngel, Ansgar

2018-02-01

The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species is proved. The equations can be derived from an on-lattice random-walk model with general transition rates. In the case of linear transition rates, it extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The equations are considered in a bounded domain with homogeneous Neumann boundary conditions. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a detailed balance or weak cross-diffusion condition. The detailed balance condition is related to the symmetry of the mobility matrix, which mirrors Onsager's principle in thermodynamics. Under detailed balance (and without reaction) the entropy is nonincreasing in time, but counter-examples show that the entropy may increase initially if detailed balance does not hold.

The method of pulsed x-ray detection with a diode laser.

PubMed

Liu, Jun; Ouyang, Xiaoping; Zhang, Zhongbing; Sheng, Liang; Chen, Liang; Tan, Xinjian; Weng, Xiufeng

2016-12-01

A new class of pulsed X-ray detection methods by sensing carrier changes in a diode laser cavity has been presented and demonstrated. The proof-of-principle experiments on detecting pulsed X-ray temporal profile have been done through the diode laser with a multiple quantum well active layer. The result shows that our method can achieve the aim of detecting the temporal profile of a pulsed X-ray source. We predict that there is a minimum value for the pre-bias current of the diode laser by analyzing the carrier rate equation, which exists near the threshold current of the diode laser chip in experiments. This behaviour generally agrees with the characterizations of theoretical analysis. The relative sensitivity is estimated at about 3.3 × 10 -17 C ⋅ cm 2 . We have analyzed the time scale of about 10 ps response with both rate equation and Monte Carlo methods.

A regularization of the Burgers equation using a filtered convective velocity

NASA Astrophysics Data System (ADS)

Norgard, Greg; Mohseni, Kamran

2008-08-01

This paper examines the properties of a regularization of the Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as the convectively filtered Burgers (CFB) equation. A physical motivation behind the filtering technique is presented. An existence and uniqueness theorem for multiple dimensions and a general class of filters is proven. Multiple invariants of motion are found for the CFB equation which are shown to be shared with the viscous and inviscid Burgers equations. Traveling wave solutions are found for a general class of filters and are shown to converge to weak solutions of the inviscid Burgers equation with the correct wave speed. Numerical simulations are conducted in 1D and 2D cases where the shock behavior, shock thickness and kinetic energy decay are examined. Energy spectra are also examined and are shown to be related to the smoothness of the solutions. This approach is presented with the hope of being extended to shock regularization of compressible Euler equations.

Exploring Equity Properties in Equating Using AP® Examinations. Research Report No. 2012-4

ERIC Educational Resources Information Center

Lee, Eunjung; Lee, Won-Chan; Brennan, Robert L.

2012-01-01

In almost all high-stakes testing programs, test equating is necessary to ensure that test scores across multiple test administrations are equivalent and can be used interchangeably. Test equating becomes even more challenging in mixed-format tests, such as Advanced Placement Program® (AP®) Exams, that contain both multiple-choice and constructed…

Mesoscopic Modeling of Blood Clotting: Coagulation Cascade and Platelets Adhesion

NASA Astrophysics Data System (ADS)

Yazdani, Alireza; Li, Zhen; Karniadakis, George

2015-11-01

The process of clot formation and growth at a site on a blood vessel wall involve a number of multi-scale simultaneous processes including: multiple chemical reactions in the coagulation cascade, species transport and flow. To model these processes we have incorporated advection-diffusion-reaction (ADR) of multiple species into an extended version of Dissipative Particle Dynamics (DPD) method which is considered as a coarse-grained Molecular Dynamics method. At the continuum level this is equivalent to the Navier-Stokes equation plus one advection-diffusion equation for each specie. The chemistry of clot formation is now understood to be determined by mechanisms involving reactions among many species in dilute solution, where reaction rate constants and species diffusion coefficients in plasma are known. The role of blood particulates, i.e. red cells and platelets, in the clotting process is studied by including them separately and together in the simulations. An agonist-induced platelet activation mechanism is presented, while platelets adhesive dynamics based on a stochastic bond formation/dissociation process is included in the model.

Noise Characterization of Erbium-Doped Fiber Amplifiers and Avalanche Photodiodes in Optical Communication Systems.

NASA Astrophysics Data System (ADS)

Kahraman, Gokalp

We examine the performance of optical communication systems using erbium-doped fiber amplifiers (OFAs) and avalanche photodiodes (APDs) including nonlinear and transient effects in the former and transient effects in the latter. Transient effects become important as these amplifiers are operated at very high data rates. Nonlinear effects are important for high gain amplifiers. In most studies of noise in these devices, the temporal and nonlinear effects have been ignored. We present a quantum theory of noise in OFAs including the saturation of the atomic population inversion and the pump depletion. We study the quantum-statistical properties of pulse amplification. The generating function of the output photon number distribution (PND) is determined as a function of time during the course of the pulse with an arbitrary input PND assumed. Under stationary conditions, we determine the Kolmogorov equation obeyed by the PND. The PND at the output is determined for arbitrary input distributions. The effect of the counting time and the filter bandwidth used by the detection circuit is determined. We determine the gain, the noise figure, and the sensitivity of receivers using OFAs as preamplifiers, including the effect of backward amplified spontaneous emission (ASE). Backward ASE degrades the noise figure and the sensitivity by depleting the population inversion at the input side of the fiber and thus increasing the noise during signal amplification. We show that the sensitivity improves with the bit rate at low rates but degrades at high rates. We provide a stochastic model that describes the time dynamics in a double-carrier multiplication (DCM) APD. A discrete stochastic model for the electron/hole motion and multiplication is defined on a spatio-temporal lattice and used to derive recursive equations for the mean, the variance, and the autocorrelation of the impulse response as functions of time. The power spectral density of the photocurrent produced in response to a Poisson-distributed stream of photons of uniform rate is evaluated. A method is also developed for solving the coupled transport equations that describe the electron and hole currents in a DCM-APD of arbitrary structure.

Heat and mass transfer in vertical porous medium due to partial heating

NASA Astrophysics Data System (ADS)

Salman Ahmed N., J.; Khan, T. M. Yunus; Ahamad, N. Ameer; Kamangar, Sarfaraz

2018-05-01

The investigation of heat and mass transfer adjacent to vertical plate subjected to partial heating of plate in multiple segments is carried out. A section of the plate is heated with isothermal temperature Th and the far away condition is maintained at ambient temperature T∞.. The vertical plate is maintained at constant concentration Ch as opposed to lowest concentration at far away condition. Finite element method is used and governing equations are converted into simple form of equations using Galerkin approach. The results are discussed in terms of contour plots. Study is carried out with respect to various physical parameters. The heat and mass transfer rate found to increase with increase in Rayleigh number.

Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials

NASA Astrophysics Data System (ADS)

Doha, E.; Bhrawy, A.

2006-06-01

It is well known that spectral methods (tau, Galerkin, collocation) have a condition number of ( is the number of retained modes of polynomial approximations). This paper presents some efficient spectral algorithms, which have a condition number of , based on the Jacobi?Galerkin methods of second-order elliptic equations in one and two space variables. The key to the efficiency of these algorithms is to construct appropriate base functions, which lead to systems with specially structured matrices that can be efficiently inverted. The complexities of the algorithms are a small multiple of operations for a -dimensional domain with unknowns, while the convergence rates of the algorithms are exponentials with smooth solutions.

The rational parameterization theorem for multisite post-translational modification systems.

PubMed

Thomson, Matthew; Gunawardena, Jeremy

2009-12-21

Post-translational modification of proteins plays a central role in cellular regulation but its study has been hampered by the exponential increase in substrate modification forms ("modforms") with increasing numbers of sites. We consider here biochemical networks arising from post-translational modification under mass-action kinetics, allowing for multiple substrates, having different types of modification (phosphorylation, methylation, acetylation, etc.) on multiple sites, acted upon by multiple forward and reverse enzymes (in total number L), using general enzymatic mechanisms. These assumptions are substantially more general than in previous studies. We show that the steady-state modform concentrations constitute an algebraic variety that can be parameterized by rational functions of the L free enzyme concentrations, with coefficients which are rational functions of the rate constants. The parameterization allows steady states to be calculated by solving L algebraic equations, a dramatic reduction compared to simulating an exponentially large number of differential equations. This complexity collapse enables analysis in contexts that were previously intractable and leads to biological predictions that we review. Our results lay a foundation for the systems biology of post-translational modification and suggest deeper connections between biochemical networks and algebraic geometry.

Long-run growth rate in a random multiplicative model

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

Pirjol, Dan

2014-08-01

We consider the long-run growth rate of the average value of a random multiplicative process x{sub i+1} = a{sub i}x{sub i} where the multipliers a{sub i}=1+ρexp(σW{sub i}₋1/2 σ²t{sub i}) have Markovian dependence given by the exponential of a standard Brownian motion W{sub i}. The average value (x{sub n}) is given by the grand partition function of a one-dimensional lattice gas with two-body linear attractive interactions placed in a uniform field. We study the Lyapunov exponent λ=lim{sub n→∞}1/n log(x{sub n}), at fixed β=1/2 σ²t{sub n}n, and show that it is given by the equation of state of the lattice gas inmore » thermodynamical equilibrium. The Lyapunov exponent has discontinuous partial derivatives along a curve in the (ρ, β) plane ending at a critical point (ρ{sub C}, β{sub C}) which is related to a phase transition in the equivalent lattice gas. Using the equivalence of the lattice gas with a bosonic system, we obtain the exact solution for the equation of state in the thermodynamical limit n → ∞.« less

Advanced analysis techniques for uranium assay

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

Geist, W. H.; Ensslin, Norbert; Carrillo, L. A.

2001-01-01

Uranium has a negligible passive neutron emission rate making its assay practicable only with an active interrogation method. The active interrogation uses external neutron sources to induce fission events in the uranium in order to determine the mass. This technique requires careful calibration with standards that are representative of the items to be assayed. The samples to be measured are not always well represented by the available standards which often leads to large biases. A technique of active multiplicity counting is being developed to reduce some of these assay difficulties. Active multiplicity counting uses the measured doubles and triples countmore » rates to determine the neutron multiplication (f4) and the product of the source-sample coupling ( C ) and the 235U mass (m). Since the 35U mass always appears in the multiplicity equations as the product of Cm, the coupling needs to be determined before the mass can be known. A relationship has been developed that relates the coupling to the neutron multiplication. The relationship is based on both an analytical derivation and also on empirical observations. To determine a scaling constant present in this relationship, known standards must be used. Evaluation of experimental data revealed an improvement over the traditional calibration curve analysis method of fitting the doubles count rate to the 235Um ass. Active multiplicity assay appears to relax the requirement that the calibration standards and unknown items have the same chemical form and geometry.« less

Multi-vortex crystal lattices in Bose-Einstein condensates with a rotating trap.

PubMed

Xie, Shuangquan; Kevrekidis, Panayotis G; Kolokolnikov, Theodore

2018-05-01

We consider vortex dynamics in the context of Bose-Einstein condensates (BECs) with a rotating trap, with or without anisotropy. Starting with the Gross-Pitaevskii (GP) partial differential equation (PDE), we derive a novel reduced system of ordinary differential equations (ODEs) that describes stable configurations of multiple co-rotating vortices (vortex crystals). This description is found to be quite accurate quantitatively especially in the case of multiple vortices. In the limit of many vortices, BECs are known to form vortex crystal structures, whereby vortices tend to arrange themselves in a hexagonal-like spatial configuration. Using our asymptotic reduction, we derive the effective vortex crystal density and its radius. We also obtain an asymptotic estimate for the maximum number of vortices as a function of rotation rate. We extend considerations to the anisotropic trap case, confirming that a pair of vortices lying on the long (short) axis is linearly stable (unstable), corroborating the ODE reduction results with full PDE simulations. We then further investigate the many-vortex limit in the case of strong anisotropic potential. In this limit, the vortices tend to align themselves along the long axis, and we compute the effective one-dimensional vortex density, as well as the maximum admissible number of vortices. Detailed numerical simulations of the GP equation are used to confirm our analytical predictions.

Optimizing the Calculation of DM,CO and VC via the Single Breath Single Oxygen Tension DLCO/NO Method

PubMed Central

Coffman, Kirsten E.; Taylor, Bryan J.; Carlson, Alex R.; Wentz, Robert J.; Johnson, Bruce D.

2015-01-01

Alveolar-capillary membrane conductance (DM,CO) and pulmonary-capillary blood volume (VC) are calculated via lung diffusing capacity for carbon monoxide (DLCO) and nitric oxide (DLNO) using the single breath, single oxygen tension (single-FiO2) method. However, two calculation parameters, the reaction rate of carbon monoxide with blood (θCO) and the DM,NO/DM,CO ratio (α-ratio), are controversial. This study systematically determined optimal θCO and α-ratio values to be used in the single-FiO2 method that yielded the most similar DM,CO and VC values compared to the ‘gold-standard’ multiple-FiO2 method. Eleven healthy subjects performed single breath DLCO/DLNO maneuvers at rest and during exercise. DM,CO and VC were calculated via the single-FiO2 and multiple-FiO2 methods by implementing seven θCO equations and a range of previously reported α-ratios. The RP θCO equation (Reeves and Park, Respiration physiology 88:1–21, 1992.) and an α-ratio of 4.0–4.4 yielded DM,CO and VC values that were most similar between methods. The RP θCO equation and an experimental α-ratio should be used in future studies. PMID:26521031

Prediction of Maximal Aerobic Capacity in Severely Burned Children

PubMed Central

Porro, Laura; Rivero, Haidy G.; Gonzalez, Dante; Tan, Alai; Herndon, David N.; Suman, Oscar E.

2011-01-01

Introduction Maximal oxygen uptake (VO2 peak) is an indicator of cardiorespiratory fitness, but requires expensive equipment and a relatively high technical skill level. Purpose The aim of this study is to provide a formula for estimating VO2 peak in burned children, using information obtained without expensive equipment. Methods Children, with ≥40% total surface area burned (TBSA), underwent a modified Bruce treadmill test to asses VO2 peak at 6 months after injury. We recorded gender, age, %TBSA, %3rd degree burn, height, weight, treadmill time, maximal speed, maximal grade, and peak heart rate, and applied McHenry’s select algorithm to extract important independent variables and Robust multiple regression to establish prediction equations. Results 42 children; 7 to 17 years old were tested. Robust multiple regression model provided the equation: VO2=10.33 – 0.62 *Age (years) + 1.88 * Treadmill Time (min) + 2.3 (gender; Females = 0, Males = 1). The correlation between measured and estimated VO2 peak was R=0.80. We then validated the equation with a group of 33 burned children, which yielded a correlation between measured and estimated VO2 peak of R=0.79. Conclusions Using only a treadmill and easily gathered information, VO2 peak can be estimated in children with burns. PMID:21316155

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

PubMed

Chai, Zhenhua; Zhao, T S

2014-07-01

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

Novel approach to investigation of semiconductor MOCVD by microreactor technology

NASA Astrophysics Data System (ADS)

Konakov, S. A.; Krzhizhanovskaya, V. V.

2017-11-01

Metal-Organic Chemical Vapour Deposition is a very complex technology that requires further investigation and optimization. We propose to apply microreactors to (1) replace multiple expensive time-consuming macroscale experiments by just one microreactor deposition with many points on one substrate; (2) to derive chemical reaction rates from individual deposition profiles using theoretical analytical solution. In this paper we also present the analytical solution of a simplified equation describing the deposition rate dependency on temperature. It allows to solve an inverse problem and to obtain detailed information about chemical reaction mechanism of MOCVD process.

Multiple-grid convergence acceleration of viscous and inviscid flow computations

NASA Technical Reports Server (NTRS)

Johnson, G. M.

1983-01-01

A multiple-grid algorithm for use in efficiently obtaining steady solution to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results in substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, were obtained. Possibilities for further performance improvement are discussed.

Dietary intakes assessed by 24-h recalls in peri-urban African adolescents: validity of energy intake compared with estimated energy expenditure.

PubMed

Rankin, D; Ellis, S M; Macintyre, U E; Hanekom, S M; Wright, H H

2011-08-01

The objective of this study is to determine the relative validity of reported energy intake (EI) derived from multiple 24-h recalls against estimated energy expenditure (EE(est)). Basal metabolic rate (BMR) equations and physical activity factors were incorporated to calculate EE(est). This analysis was nested in the multidisciplinary PhysicaL Activity in the Young study with a prospective study design. Peri-urban black South African adolescents were investigated in a subsample of 131 learners (87 girls and 44 boys) from the parent study sample of 369 (211 girls and 158 boys) who had all measurements taken. Pearson correlation coefficients and Bland-Altman plots were calculated to identify the most accurate published equations to estimate BMR (P<0.05 statistically significant). EE(est) was estimated using BMR equations and estimated physical activity factors derived from Previous Day Physical Activity Recall questionnaires. After calculation of EE(est), the relative validity of reported energy intake (EI(rep)) derived from multiple 24-h recalls was tested for three data subsets using Pearson correlation coefficients. Goldberg's formula identified cut points (CPs) for under and over reporting of EI. Pearson correlation coefficients between calculated BMRs ranged from 0.97 to 0.99. Bland-Altman analyses showed acceptable agreement (two equations for each gender). One equation for each gender was used to calculate EE(est). Pearson correlation coefficients between EI(rep) and EE(est) for three data sets were weak, indicating poor agreement. CPs for physical activity groups showed under reporting in 87% boys and 95% girls. The 24-h recalls measured at five measurements over 2 years offered poor validity between EI(rep) and EE(est).

An efficient implementation of a high-order filter for a cubed-sphere spectral element model

NASA Astrophysics Data System (ADS)

Kang, Hyun-Gyu; Cheong, Hyeong-Bin

2017-03-01

A parallel-scalable, isotropic, scale-selective spatial filter was developed for the cubed-sphere spectral element model on the sphere. The filter equation is a high-order elliptic (Helmholtz) equation based on the spherical Laplacian operator, which is transformed into cubed-sphere local coordinates. The Laplacian operator is discretized on the computational domain, i.e., on each cell, by the spectral element method with Gauss-Lobatto Lagrange interpolating polynomials (GLLIPs) as the orthogonal basis functions. On the global domain, the discrete filter equation yielded a linear system represented by a highly sparse matrix. The density of this matrix increases quadratically (linearly) with the order of GLLIP (order of the filter), and the linear system is solved in only O (Ng) operations, where Ng is the total number of grid points. The solution, obtained by a row reduction method, demonstrated the typical accuracy and convergence rate of the cubed-sphere spectral element method. To achieve computational efficiency on parallel computers, the linear system was treated by an inverse matrix method (a sparse matrix-vector multiplication). The density of the inverse matrix was lowered to only a few times of the original sparse matrix without degrading the accuracy of the solution. For better computational efficiency, a local-domain high-order filter was introduced: The filter equation is applied to multiple cells, and then the central cell was only used to reconstruct the filtered field. The parallel efficiency of applying the inverse matrix method to the global- and local-domain filter was evaluated by the scalability on a distributed-memory parallel computer. The scale-selective performance of the filter was demonstrated on Earth topography. The usefulness of the filter as a hyper-viscosity for the vorticity equation was also demonstrated.

Verification and Validation of the k-kL Turbulence Model in FUN3D and CFL3D Codes

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Carlson, Jan-Renee; Rumsey, Christopher L.

2015-01-01

The implementation of the k-kL turbulence model using multiple computational uid dy- namics (CFD) codes is reported herein. The k-kL model is a two-equation turbulence model based on Abdol-Hamid's closure and Menter's modi cation to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's equation is well suited for term-by-term mod- eling and displays useful features compared to other two-equation models. An important di erence is that this formulation leads to the inclusion of higher-order velocity derivatives in the source terms of the scale equations. This can enhance the ability of the Reynolds- averaged Navier-Stokes (RANS) solvers to simulate unsteady ows. The present report documents the formulation of the model as implemented in the CFD codes Fun3D and CFL3D. Methodology, veri cation and validation examples are shown. Attached and sepa- rated ow cases are documented and compared with experimental data. The results show generally very good comparisons with canonical and experimental data, as well as matching results code-to-code. The results from this formulation are similar or better than results using the SST turbulence model.

Electrostatic ion cyclotron velocity shear instability

NASA Technical Reports Server (NTRS)

Lemons, D. S.; Winske, D.; Gary, S. P.

1992-01-01

A local electrostatic dispersion equation is derived for a shear flow perpendicular to an ambient magnetic field, which includes all kinetic effects and involves only one important parameter. The dispersion equation is cast in the form of Gordeyev integrals and is solved numerically. Numerical solutions indicate that an ion cyclotron instability is excited. The instability occurs roughly at multiples of the ion cyclotron frequency (modified by the shear), with the growth rate or the individual harmonics overlapping in the wavenumber. At large values of the shear parameter, the instability is confined to long wavelengths, but at smaller shear, a second distinct branch at shorter wavelengths also appears. The properties of the instability obtained are compared with those obtained in the nonlocal limit by Ganguli et al. (1985, 1988).

On shifted Jacobi spectral method for high-order multi-point boundary value problems

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.

2012-10-01

This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved.

Integrability of the coupled cubic-quintic complex Ginzburg-Landau equations and multiple-soliton solutions via mathematical methods

NASA Astrophysics Data System (ADS)

Selima, Ehab S.; Seadawy, Aly R.; Yao, Xiaohua; Essa, F. A.

2018-02-01

This paper is devoted to study the (1+1)-dimensional coupled cubic-quintic complex Ginzburg-Landau equations (cc-qcGLEs) with complex coefficients. This equation can be used to describe the nonlinear evolution of slowly varying envelopes of periodic spatial-temporal patterns in a convective binary fluid. Dispersion relation and properties of cc-qcGLEs are constructed. Painlevé analysis is used to check the integrability of cc-qcGLEs and to establish the Bäcklund transformation form. New traveling wave solutions and a general form of multiple-soliton solutions of cc-qcGLEs are obtained via the Bäcklund transformation and simplest equation method with Bernoulli, Riccati and Burgers’ equations as simplest equations.

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

PubMed

Chatterjee, Abhijit; Vlachos, Dionisios G

2007-07-21

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

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

PubMed

Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

2017-06-01

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

On the validity of Zeeman's classification for three dimensional competitive differential equations with linearly determined nullclines

NASA Astrophysics Data System (ADS)

Jiang, Jifa; Niu, Lei

2017-12-01

We study three dimensional competitive differential equations with linearly determined nullclines and prove that they always have 33 stable nullcline classes in total. Each class is given in terms of inequalities on the intrinsic growth rates and competitive coefficients and is independent of generating functions. The common characteristics are that every trajectory converges to an equilibrium in classes 1-25, that Hopf bifurcations do not occur within class 32, and that there is always a heteroclinic cycle in class 27. Nontrivial dynamical behaviors, such as the existence and multiplicity of limit cycles, only may occur in classes 26-33, but these nontrivial dynamical behaviors depend on generating functions. We show that Hopf bifurcation can occur within each of classes 26-31 for continuous-time Leslie/Gower system and Ricker system, the same as Lotka-Volterra system; but it only occurs in classes 26 and 27 for continuous-time Atkinson/Allen system and Gompertz system. There is an apparent distinction between Lotka-Volterra system and Leslie/Gower system, Ricker system, Atkinson/Allen system, and Gompertz system with the identical growth rate. Lotka-Volterra system with the identical growth rate has no limit cycle, but admits a center on the carrying simplex in classes 26 and 27. But Leslie/Gower system, Ricker system, Atkinson/Allen system, and Gompertz system with the identical growth rate do possess limit cycles. At last, we provide examples to show that Leslie/Gower system and Ricker system can also admit two limit cycles. This general classification greatly widens applications of Zeeman's method and makes it possible to investigate the existence and multiplicity of limit cycles, centers and stability of heteroclinic cycles for three dimensional competitive systems with linearly determined nullclines, as done in planar systems.

Electron-impact vibrational relaxation in high-temperature nitrogen

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1992-01-01

Vibrational relaxation process of N2 molecules by electron-impact is examined for the future planetary entry environments. Multiple-quantum transitions from excited states to higher/lower states are considered for the electronic ground state of the nitrogen molecule N2 (X 1Sigma-g(+)). Vibrational excitation and deexcitation rate coefficients obtained by computational quantum chemistry are incorporated into the 'diffusion model' to evaluate the time variations of vibrational number densities of each energy state and total vibrational energy. Results show a non-Boltzmann distribution of number densities at the earlier stage of relaxation, which in turn suppresses the equilibrium process but affects little the time variation of total vibrational energy. An approximate rate equation and a corresponding relaxation time from the excited states, compatible with the system of flow conservation equations, are derived. The relaxation time from the excited states indicates the weak dependency of the initial vibrational temperature. The empirical curve-fit formula for the improved e-V relaxation time is obtained.

Application of fault factor method to fault detection and diagnosis for space shuttle main engine

NASA Astrophysics Data System (ADS)

Cha, Jihyoung; Ha, Chulsu; Ko, Sangho; Koo, Jaye

2016-09-01

This paper deals with an application of the multiple linear regression algorithm to fault detection and diagnosis for the space shuttle main engine (SSME) during a steady state. In order to develop the algorithm, the energy balance equations, which balances the relation among pressure, mass flow rate and power at various locations within the SSME, are obtained. Then using the measurement data of some important parameters of the engine, fault factors which reflects the deviation of each equation from the normal state are estimated. The probable location of each fault and the levels of severity can be obtained from the estimated fault factors. This process is numerically demonstrated for the SSME at 104% Rated Propulsion Level (RPL) by using the simulated measurement data from the mathematical models of the engine. The result of the current study is particularly important considering that the recently developed reusable Liquid Rocket Engines (LREs) have staged-combustion cycles similarly to the SSME.

A Common Mechanism for Resistance to Oxime Reactivation of Acetylcholinesterase Inhibited by Organophosphorus Compounds

DTIC Science & Technology

2013-01-01

application of the Hammett equation with the constants rph in the chemistry of organophosphorus compounds, Russ. Chem. Rev. 38 (1969) 795–811. [13...of oximes and OP compounds and the ability of oximes to reactivate OP- inhibited AChE. Multiple linear regression equations were analyzed using...phosphonate pairs, 21 oxime/ phosphoramidate pairs and 12 oxime/phosphate pairs. The best linear regression equation resulting from multiple regression anal

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7 T.

PubMed

Qin, Shanlin; Liu, Fawang; Turner, Ian W; Yu, Qiang; Yang, Qianqian; Vegh, Viktor

2017-04-01

To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain. Magn Reson Med 77:1485-1494, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Reforming the Military Health Care System

DTIC Science & Technology

1988-01-01

Population Model and its Application ," International Journal of Health Services, vol. 10, no. 4 (1980). 7. "Understanding Variations in the Use of... Financial Management (November 1986), pp. 26- 34. 21. Based on the following multiple regression equation: OP/NOR= 0.51 + 0.35x(POP/NOR)-6.84x(CIV/NORxPOP) (t...Military Beneficiary Health Care Survey 95 B Actual and Expected Admission Rates 99 C The Statistical Model of Family Use 103 D The Capitation Budgeting

Estimating Commute Distances of U.S. Army Reservists by Regional and Unit Characteristics

DTIC Science & Technology

1990-09-01

multiple regression equation is used to estimate the parameters of the commute distance distribution as a function of reserve center and market ...used to estimate the parameters of the commute distance distribution as a function of reserve center and market characteristics. The results of the...recruiting personnel to meet unit fill rates. An important objective of the USAREC is to identify market areas that will support new reserve units [Ref. 2:p

Convective heat transfer in MHD slip flow over a stretching surface in the presence of carbon nanotubes

NASA Astrophysics Data System (ADS)

Ul Haq, Rizwan; Nadeem, Sohail; Khan, Z. H.; Noor, N. F. M.

2015-01-01

In the present study, thermal conductivity and viscosity of both single-wall and multiple-wall Carbon Nanotubes (CNT) within the base fluids (water, engine oil and ethylene glycol) of similar volume have been investigated when the fluid is flowing over a stretching surface. The magnetohydrodynamic (MHD) and viscous dissipation effects are also incorporated in the present phenomena. Experimental data consists of thermo-physical properties of each base fluid and CNT have been considered. The mathematical model has been constructed and by employing similarity transformation, system of partial differential equations is rehabilitated into the system of non-linear ordinary differential equations. The results of local skin friction and local Nusselt number are plotted for each base fluid by considering both Single Wall Carbon Nanotube (SWCNT) and Multiple-Wall Carbon Nanotubes (MWCNT). The behavior of fluid flow for water based-SWCNT and MWCNT are analyzed through streamlines. Concluding remarks have been developed on behalf of the whole analysis and it is found that engine oil-based CNT have higher skin friction and heat transfer rate as compared to water and ethylene glycol-based CNT.

Diffusion of multiple species with excluded-volume effects.

PubMed

Bruna, Maria; Chapman, S Jonathan

2012-11-28

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter-species competition emerges at the population level. Each individual is described as a finite-size hard core interacting particle undergoing brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear cross-diffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excluded-volume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and self-diffusion. Simulations of the discrete system show good agreement with the analytic results.

A general multiple-compartment model for the transport of trace elements through animals

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

Assimakopoulos, P.A.; Ioannides, K.G.; Pakou, A.A.

1991-08-01

Multiple-compartment models employed in the analysis of trace element transport in animals are often based on linear differential equations which relate the rate of change of contaminant (or contaminant concentration) in each compartment to the amount of contaminant (or contaminant concentration) in every other compartment in the system. This has the serious disadvantage of mixing intrinsic physiological properties with the geometry of the animal. The basic equations on which the model presented here is developed are derived from the actual physical process under way and are capable of separating intrinsic physiological properties from geometry. It is thus expected that ratemore » coefficients determined through this model will be applicable to a wider category of physiologically similar animals. A specific application of the model for the study of contamination of sheep--or indeed for any ruminant--is presented, and the temporal evolution of contaminant concentration in the various compartments of the animal is calculated. The application of this model to a system of compartments with changing geometry is also presented.« less

A Persistent Feature of Multiple Scattering of Waves in the Time-Domain: A Tutorial

NASA Technical Reports Server (NTRS)

Lock, James A.; Mishchenko, Michael I.

2015-01-01

The equations for frequency-domain multiple scattering are derived for a scalar or electromagnetic plane wave incident on a collection of particles at known positions, and in the time-domain for a plane wave pulse incident on the same collection of particles. The calculation is carried out for five different combinations of wave types and particle types of increasing geometrical complexity. The results are used to illustrate and discuss a number of physical and mathematical characteristics of multiple scattering in the frequency- and time-domains. We argue that frequency-domain multiple scattering is a purely mathematical construct since there is no temporal sequencing information in the frequency-domain equations and since the multi-particle path information can be dispelled by writing the equations in another mathematical form. However, multiple scattering becomes a definite physical phenomenon in the time-domain when the collection of particles is illuminated by an appropriately short localized pulse.

Nonlinear convergence active vibration absorber for single and multiple frequency vibration control

NASA Astrophysics Data System (ADS)

Wang, Xi; Yang, Bintang; Guo, Shufeng; Zhao, Wenqiang

2017-12-01

This paper presents a nonlinear convergence algorithm for active dynamic undamped vibration absorber (ADUVA). The damping of absorber is ignored in this algorithm to strengthen the vibration suppressing effect and simplify the algorithm at the same time. The simulation and experimental results indicate that this nonlinear convergence ADUVA can help significantly suppress vibration caused by excitation of both single and multiple frequency. The proposed nonlinear algorithm is composed of equivalent dynamic modeling equations and frequency estimator. Both the single and multiple frequency ADUVA are mathematically imitated by the same mechanical structure with a mass body and a voice coil motor (VCM). The nonlinear convergence estimator is applied to simultaneously satisfy the requirements of fast convergence rate and small steady state frequency error, which are incompatible for linear convergence estimator. The convergence of the nonlinear algorithm is mathematically proofed, and its non-divergent characteristic is theoretically guaranteed. The vibration suppressing experiments demonstrate that the nonlinear ADUVA can accelerate the convergence rate of vibration suppressing and achieve more decrement of oscillation attenuation than the linear ADUVA.

Estimating methane emissions from landfills based on rainfall, ambient temperature, and waste composition: The CLEEN model.

PubMed

Karanjekar, Richa V; Bhatt, Arpita; Altouqui, Said; Jangikhatoonabad, Neda; Durai, Vennila; Sattler, Melanie L; Hossain, M D Sahadat; Chen, Victoria

2015-12-01

Accurately estimating landfill methane emissions is important for quantifying a landfill's greenhouse gas emissions and power generation potential. Current models, including LandGEM and IPCC, often greatly simplify treatment of factors like rainfall and ambient temperature, which can substantially impact gas production. The newly developed Capturing Landfill Emissions for Energy Needs (CLEEN) model aims to improve landfill methane generation estimates, but still require inputs that are fairly easy to obtain: waste composition, annual rainfall, and ambient temperature. To develop the model, methane generation was measured from 27 laboratory scale landfill reactors, with varying waste compositions (ranging from 0% to 100%); average rainfall rates of 2, 6, and 12 mm/day; and temperatures of 20, 30, and 37°C, according to a statistical experimental design. Refuse components considered were the major biodegradable wastes, food, paper, yard/wood, and textile, as well as inert inorganic waste. Based on the data collected, a multiple linear regression equation (R(2)=0.75) was developed to predict first-order methane generation rate constant values k as functions of waste composition, annual rainfall, and temperature. Because, laboratory methane generation rates exceed field rates, a second scale-up regression equation for k was developed using actual gas-recovery data from 11 landfills in high-income countries with conventional operation. The Capturing Landfill Emissions for Energy Needs (CLEEN) model was developed by incorporating both regression equations into the first-order decay based model for estimating methane generation rates from landfills. CLEEN model values were compared to actual field data from 6 US landfills, and to estimates from LandGEM and IPCC. For 4 of the 6 cases, CLEEN model estimates were the closest to actual. Copyright © 2015 Elsevier Ltd. All rights reserved.

Multiple attenuation to reflection seismic data using Radon filter and Wave Equation Multiple Rejection (WEMR) method

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

Erlangga, Mokhammad Puput

Separation between signal and noise, incoherent or coherent, is important in seismic data processing. Although we have processed the seismic data, the coherent noise is still mixing with the primary signal. Multiple reflections are a kind of coherent noise. In this research, we processed seismic data to attenuate multiple reflections in the both synthetic and real seismic data of Mentawai. There are several methods to attenuate multiple reflection, one of them is Radon filter method that discriminates between primary reflection and multiple reflection in the τ-p domain based on move out difference between primary reflection and multiple reflection. However, inmore » case where the move out difference is too small, the Radon filter method is not enough to attenuate the multiple reflections. The Radon filter also produces the artifacts on the gathers data. Except the Radon filter method, we also use the Wave Equation Multiple Elimination (WEMR) method to attenuate the long period multiple reflection. The WEMR method can attenuate the long period multiple reflection based on wave equation inversion. Refer to the inversion of wave equation and the magnitude of the seismic wave amplitude that observed on the free surface, we get the water bottom reflectivity which is used to eliminate the multiple reflections. The WEMR method does not depend on the move out difference to attenuate the long period multiple reflection. Therefore, the WEMR method can be applied to the seismic data which has small move out difference as the Mentawai seismic data. The small move out difference on the Mentawai seismic data is caused by the restrictiveness of far offset, which is only 705 meter. We compared the real free multiple stacking data after processing with Radon filter and WEMR process. The conclusion is the WEMR method can more attenuate the long period multiple reflection than the Radon filter method on the real (Mentawai) seismic data.« less

Asymmetrical flow field-flow fractionation coupled with multiple detections: A complementary approach in the characterization of egg yolk plasma.

PubMed

Dou, Haiyang; Li, Yueqiu; Choi, Jaeyeong; Huo, Shuying; Ding, Liang; Shen, Shigang; Lee, Seungho

2016-09-23

The capability of asymmetrical flow field-flow fractionation (AF4) coupled with UV/VIS, multiangle light scattering (MALS) and quasi-elastic light scattering (QELS) (AF4-UV-MALS-QELS) for separation and characterization of egg yolk plasma was evaluated. The accuracy of hydrodynamic radius (Rh) obtained from QELS and AF4 theory (using both simplified and full expression of AF4 retention equations) was discussed. The conformation of low density lipoprotein (LDL) and its aggregates in egg yolk plasma was discussed based on the ratio of radius of gyration (Rg) to Rh together with the results from bio-transmission electron microscopy (Bio-TEM). The results indicate that the full retention equation is more relevant than simplified version for the Rh determination at high cross flow rate. The Rh from online QELS is reliable only at a specific range of sample concentration. The effect of programmed cross flow rate (linear and exponential decay) on the analysis of egg yolk plasma was also investigated. It was found that the use of an exponentially decaying cross flow rate not only reduces the AF4 analysis time of the egg yolk plasma, but also provides better resolution than the use of either a constant or linearly decaying cross flow rate. A combination of an exponentially decaying cross flow AF4-UV-MALS-QELS and the utilization of full retention equation was proved to be a useful method for the separation and characterization of egg yolk plasma. Copyright © 2016 Elsevier B.V. All rights reserved.

Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models

NASA Astrophysics Data System (ADS)

Giona, M.; Brasiello, A.; Crescitelli, S.

2015-11-01

One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.

Multiple shooting algorithms for jump-discontinuous problems in optimal control and estimation

NASA Technical Reports Server (NTRS)

Mook, D. J.; Lew, Jiann-Shiun

1991-01-01

Multiple shooting algorithms are developed for jump-discontinuous two-point boundary value problems arising in optimal control and optimal estimation. Examples illustrating the origin of such problems are given to motivate the development of the solution algorithms. The algorithms convert the necessary conditions, consisting of differential equations and transversality conditions, into algebraic equations. The solution of the algebraic equations provides exact solutions for linear problems. The existence and uniqueness of the solution are proved.

Silanols, a New Class of Antimicrobial Agent

DTIC Science & Technology

2006-04-01

carbinols against the four bacteria was log (1/MLC) = 0.670 log P + 0.0035 ∆ν -1.836, n = 282, r = 0.96, s = 0.22. This equation and a significantly...activity relationship of antimicrobial agents by means of equations [8] based on a method proposed by Hansch and Fujita in 1964 [1]. This multiple...correlation equations between their antimicrobial activities and structural properties, log P and H-bond acidity, were created by a multiple regression

Analysis of dynamic behavior of multiple-stage planetary gear train used in wind driven generator.

PubMed

Wang, Jungang; Wang, Yong; Huo, Zhipu

2014-01-01

A dynamic model of multiple-stage planetary gear train composed of a two-stage planetary gear train and a one-stage parallel axis gear is proposed to be used in wind driven generator to analyze the influence of revolution speed and mesh error on dynamic load sharing characteristic based on the lumped parameter theory. Dynamic equation of the model is solved using numerical method to analyze the uniform load distribution of the system. It is shown that the load sharing property of the system is significantly affected by mesh error and rotational speed; load sharing coefficient and change rate of internal and external meshing of the system are of obvious difference from each other. The study provides useful theoretical guideline for the design of the multiple-stage planetary gear train of wind driven generator.

Analysis of Dynamic Behavior of Multiple-Stage Planetary Gear Train Used in Wind Driven Generator

PubMed Central

Wang, Jungang; Wang, Yong; Huo, Zhipu

2014-01-01

A dynamic model of multiple-stage planetary gear train composed of a two-stage planetary gear train and a one-stage parallel axis gear is proposed to be used in wind driven generator to analyze the influence of revolution speed and mesh error on dynamic load sharing characteristic based on the lumped parameter theory. Dynamic equation of the model is solved using numerical method to analyze the uniform load distribution of the system. It is shown that the load sharing property of the system is significantly affected by mesh error and rotational speed; load sharing coefficient and change rate of internal and external meshing of the system are of obvious difference from each other. The study provides useful theoretical guideline for the design of the multiple-stage planetary gear train of wind driven generator. PMID:24511295

Compactness and robustness: Applications in the solution of integral equations for chemical kinetics and electromagnetic scattering

NASA Astrophysics Data System (ADS)

Zhou, Yajun

This thesis employs the topological concept of compactness to deduce robust solutions to two integral equations arising from chemistry and physics: the inverse Laplace problem in chemical kinetics and the vector wave scattering problem in dielectric optics. The inverse Laplace problem occurs in the quantitative understanding of biological processes that exhibit complex kinetic behavior: different subpopulations of transition events from the "reactant" state to the "product" state follow distinct reaction rate constants, which results in a weighted superposition of exponential decay modes. Reconstruction of the rate constant distribution from kinetic data is often critical for mechanistic understandings of chemical reactions related to biological macromolecules. We devise a "phase function approach" to recover the probability distribution of rate constants from decay data in the time domain. The robustness (numerical stability) of this reconstruction algorithm builds upon the continuity of the transformations connecting the relevant function spaces that are compact metric spaces. The robust "phase function approach" not only is useful for the analysis of heterogeneous subpopulations of exponential decays within a single transition step, but also is generalizable to the kinetic analysis of complex chemical reactions that involve multiple intermediate steps. A quantitative characterization of the light scattering is central to many meteoro-logical, optical, and medical applications. We give a rigorous treatment to electromagnetic scattering on arbitrarily shaped dielectric media via the Born equation: an integral equation with a strongly singular convolution kernel that corresponds to a non-compact Green operator. By constructing a quadratic polynomial of the Green operator that cancels out the kernel singularity and satisfies the compactness criterion, we reveal the universality of a real resonance mode in dielectric optics. Meanwhile, exploiting the properties of compact operators, we outline the geometric and physical conditions that guarantee a robust solution to the light scattering problem, and devise an asymptotic solution to the Born equation of electromagnetic scattering for arbitrarily shaped dielectric in a non-perturbative manner.

Kinetic Studies that Evaluate the Solvolytic Mechanisms of Allyl and Vinyl Chloroformate Esters

PubMed Central

D’Souza, Malcolm J.; Givens, Aaron F.; Lorchak, Peter A.; Greenwood, Abigail E.; Gottschall, Stacey L.; Carter, Shannon E.; Kevill, Dennis N.

2013-01-01

At 25.0 °C the specific rates of solvolysis for allyl and vinyl chloroformates have been determined in a wide mix of pure and aqueous organic mixtures. In all the solvents studied, vinyl chloroformate was found to react significantly faster than allyl chloroformate. Multiple correlation analyses of these rates are completed using the extended (two-term) Grunwald-Winstein equation with incorporation of literature values for solvent nucleophilicity (NT) and solvent ionizing power (YCl). Both substrates were found to solvolyze by similar dual bimolecular carbonyl-addition and unimolecular ionization channels, each heavily dependent upon the solvents nucleophilicity and ionizing ability. PMID:23549265

Cognitive Load in Algebra: Element Interactivity in Solving Equations

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Chung, Siu Fung; Yeung, Alexander Seeshing

2015-01-01

Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side…

Structural instability, multiple stable states, and hysteresis in periphyton driven by phosphorus enrichment in the Everglades

USGS Publications Warehouse

Dong, Quan; McCormick, Paul V.; Sklar, Fred H.; DeAngelis, Donald L.

2002-01-01

Periphyton is a key component of the Everglades ecosystems. It is a major primary producer, providing food and habitat for a variety of organisms, contributing material to the surface soil, and regulating water chemistry. Periphyton is sensitive to the phosphorus (P) supply and P enrichment has caused dramatic changes in the native Everglades periphyton assemblages. Periphyton also affects P availability by removing P from the water column and depositing a refractory portion into sediment. A quantitative understanding of the response of periphyton assemblages to P supply and its effects on P cycling could provide critical supports to decision making in the conservation and restoration of the Everglades. We constructed a model to examine the interaction between periphyton and P dynamics. The model contains two differential equations: P uptake and periphyton growth are assumed to follow the Monod equation and are limited by a modified logistic equation. Equilibrium and stability analyses suggest that P loading is the driving force and determines the system behavior. The position and number of steady states and the stability also depend upon the rate of sloughing, through which periphyton deposits refractory P into sediment. Multiple equilibria may exist, with two stable equilibria separated by an unstable equilibrium. Due to nonlinear interplay of periphyton and P in this model, catastrophe and hysteresis are likely to occur.

Optimizing the calculation of DM,CO and VC via the single breath single oxygen tension DLCO/NO method.

PubMed

Coffman, Kirsten E; Taylor, Bryan J; Carlson, Alex R; Wentz, Robert J; Johnson, Bruce D

2016-01-15

Alveolar-capillary membrane conductance (D(M,CO)) and pulmonary-capillary blood volume (V(C)) are calculated via lung diffusing capacity for carbon monoxide (DL(CO)) and nitric oxide (DL(NO)) using the single breath, single oxygen tension (single-FiO2) method. However, two calculation parameters, the reaction rate of carbon monoxide with blood (θ(CO)) and the D(M,NO)/D(M,CO) ratio (α-ratio), are controversial. This study systematically determined optimal θ(CO) and α-ratio values to be used in the single-FiO2 method that yielded the most similar D(M,CO) and V(C) values compared to the 'gold-standard' multiple-FiO2 method. Eleven healthy subjects performed single breath DL(CO)/DL(NO) maneuvers at rest and during exercise. D(M,CO) and V(C) were calculated via the single-FiO2 and multiple-FiO2 methods by implementing seven θ(CO) equations and a range of previously reported α-ratios. The RP θ(CO) equation (Reeves, R.B., Park, H.K., 1992. Respiration Physiology 88 1-21) and an α-ratio of 4.0-4.4 yielded DM,CO and VC values that were most similar between methods. The RP θ(CO) equation and an experimental α-ratio should be used in future studies. Copyright © 2015 Elsevier B.V. All rights reserved.

Elimination of trait blocks from multiple trait mixed model equations with singular (Co)variance parameter matrices

USDA-ARS?s Scientific Manuscript database

Transformations to multiple trait mixed model equations (MME) which are intended to improve computational efficiency in best linear unbiased prediction (BLUP) and restricted maximum likelihood (REML) are described. It is shown that traits that are expected or estimated to have zero residual variance...

Estimating air drying times of lumber with multiple regression

Treesearch

William T. Simpson

2004-01-01

In this study, the applicability of a multiple regression equation for estimating air drying times of red oak, sugar maple, and ponderosa pine lumber was evaluated. The equation allows prediction of estimated air drying times from historic weather records of temperature and relative humidity at any desired location.

Prescription-induced jump distributions in multiplicative Poisson processes.

PubMed

Suweis, Samir; Porporato, Amilcare; Rinaldo, Andrea; Maritan, Amos

2011-06-01

Generalized Langevin equations (GLE) with multiplicative white Poisson noise pose the usual prescription dilemma leading to different evolution equations (master equations) for the probability distribution. Contrary to the case of multiplicative Gaussian white noise, the Stratonovich prescription does not correspond to the well-known midpoint (or any other intermediate) prescription. By introducing an inertial term in the GLE, we show that the Itô and Stratonovich prescriptions naturally arise depending on two time scales, one induced by the inertial term and the other determined by the jump event. We also show that, when the multiplicative noise is linear in the random variable, one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization, in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white Poisson noise, the features of which are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

Prescription-induced jump distributions in multiplicative Poisson processes

NASA Astrophysics Data System (ADS)

Suweis, Samir; Porporato, Amilcare; Rinaldo, Andrea; Maritan, Amos

2011-06-01

Generalized Langevin equations (GLE) with multiplicative white Poisson noise pose the usual prescription dilemma leading to different evolution equations (master equations) for the probability distribution. Contrary to the case of multiplicative Gaussian white noise, the Stratonovich prescription does not correspond to the well-known midpoint (or any other intermediate) prescription. By introducing an inertial term in the GLE, we show that the Itô and Stratonovich prescriptions naturally arise depending on two time scales, one induced by the inertial term and the other determined by the jump event. We also show that, when the multiplicative noise is linear in the random variable, one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization, in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white Poisson noise, the features of which are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

Generalized Master Equation with Non-Markovian Multichromophoric Förster Resonance Energy Transfer for Modular Exciton Densities

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

Jang, Seogjoo; Hoyer, Stephan; Fleming, Graham

2014-10-31

A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations of small length scales into dynamics over large length scales, and also provides a non-Markovian generalization and rigorous derivation of the Pauli master equation employing multichromophoric Förster resonance energy transfer rates. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic populations over coupled chromophores can be accurately describedmore » by transitions between subgroups (modules) of delocalized excitons. Application of the GME-MED to the exciton dynamics between a pair of light harvesting complexes in purple bacteria demonstrates its promise as a computationally efficient tool to investigate large scale exciton dynamics in complex environments.« less

Preconditioned implicit solvers for the Navier-Stokes equations on distributed-memory machines

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Liou, Meng-Sing; Dyson, Rodger W.

1994-01-01

The GMRES method is parallelized, and combined with local preconditioning to construct an implicit parallel solver to obtain steady-state solutions for the Navier-Stokes equations of fluid flow on distributed-memory machines. The new implicit parallel solver is designed to preserve the convergence rate of the equivalent 'serial' solver. A static domain-decomposition is used to partition the computational domain amongst the available processing nodes of the parallel machine. The SPMD (Single-Program Multiple-Data) programming model is combined with message-passing tools to develop the parallel code on a 32-node Intel Hypercube and a 512-node Intel Delta machine. The implicit parallel solver is validated for internal and external flow problems, and is found to compare identically with flow solutions obtained on a Cray Y-MP/8. A peak computational speed of 2300 MFlops/sec has been achieved on 512 nodes of the Intel Delta machine,k for a problem size of 1024 K equations (256 K grid points).

Dynamic Disorder in Quasi-Equilibrium Enzymatic Systems

PubMed Central

Chaudhury, Srabanti; Igoshin, Oleg A.

2010-01-01

Conformations and catalytic rates of enzymes fluctuate over a wide range of timescales. Despite these fluctuations, there exist some limiting cases in which the enzymatic catalytic rate follows the macroscopic rate equation such as the Michaelis-Menten law. In this paper we investigate the applicability of macroscopic rate laws for fluctuating enzyme systems in which catalytic transitions are slower than ligand binding-dissociation reactions. In this quasi-equilibrium limit, for an arbitrary reaction scheme we show that the catalytic rate has the same dependence on ligand concentrations as obtained from mass-action kinetics even in the presence of slow conformational fluctuations. These results indicate that the timescale of conformational dynamics – no matter how slow – will not affect the enzymatic rate in quasi-equilibrium limit. Our numerical results for two enzyme-catalyzed reaction schemes involving multiple substrates and inhibitors further support our general theory. PMID:20808776

Magnetotransport of multiple-band nearly antiferromagnetic metals due to hot-spot scattering

DOE PAGES

Koshelev, A. E.

2016-09-30

Multiple-band electronic structure and proximity to antiferromagnetic (AF) instability are the key properties of iron-based superconductors. In this paper, we explore the influence of scattering by the AF spin fluctuations on transport of multiple-band metals above the magnetic transition. A salient feature of scattering on the AF fluctuations is that it is strongly enhanced at the Fermi surface locations where the nesting is perfect (“hot spots” or “hot lines”). We review derivation of the collision integral for the Boltzmann equation due to AF-fluctuations scattering. In the paramagnetic state, the enhanced scattering rate near the hot lines leads to anomalous behaviormore » of electronic transport in magnetic field. We explore this behavior by analytically solving the Boltzmann transport equation with approximate transition rates. This approach accounts for return scattering events and is more accurate than the relaxation-time approximation. The magnetic-field dependences are characterized by two very different field scales: the lower scale is set by the hot-spot width and the higher scale is set by the total scattering amplitude. A conventional magnetotransport behavior is limited to magnetic fields below the lower scale. In the wide range in-between these two scales, the longitudinal conductivity has linear dependence on the magnetic field and the Hall conductivity has quadratic dependence. The linear dependence of the diagonal component reflects growth of the Fermi-surface area affected by the hot spots proportional to the magnetic field. Finally, we discuss applicability of this theoretical framework for describing of anomalous magnetotransport properties in different iron pnictides and chalcogenides in the paramagnetic state.« less

Theory of lasing in a multiple-scattering medium

NASA Astrophysics Data System (ADS)

John, Sajeev; Pang, Gendi

1996-10-01

In several recent experiments, isotropic lasing action was observed in paints that contain rhodamine 640 dye molecules in methanol solution as gain media and titania particles as optical scatterers. These so-called paint-on laser systems are extraordinary because they are highly disordered systems. The microscopic mechanism for laser activity and the coherence properties of light emission in this multiple-light-scattering medium have not yet been elucidated. In this paper we derive the emission intensity properties of a model dye system with excited singlet and triplet electronic energy levels, which is immersed in a multiple-scattering medium with transport mean free path l*. Using physically reasonable estimates for the absorption and emission cross section for the singlet and triplet manifolds, and the singlet-triplet intersystem crossing rate, we solve the nonlinear laser rate equations for the dye molecules. This leads to a diffusion equation for the light intensity in the medium with a nonlinear intensity-dependent gain coefficient. Using this model we are able to account for nearly all of the experimentally observed properties of laser paint reported so far when l*>>λ0, the emission wavelength. This includes the dependence of the peak intensity of amplified emission on the mean free path l*, the dye concentration ρ, and the pump intensity characteristics. Our model recaptures the collapse of the emission linewidth at a specific threshold pump intensity and describes how this threshold intensity varies with l*. In addition, our model predicts a dramatic increase in the peak intensity and a further lowering of the lasing threshold for the strong scattering limit l*-->λ0. This suggests a striking enhancement of the characteristics of laser paint near the photon localization threshold in a disordered medium.

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.

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

NASA Technical Reports Server (NTRS)

Barker, L. K.

1983-01-01

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

Physical Interpretation of Laboratory Friction Laws in the Context of Damage Physics

NASA Astrophysics Data System (ADS)

Rundle, J. B.; Tiampo, K. F.; Martins, J. S.; Klein, W.

2002-12-01

Frictional on sliding surfaces is ultimately related to processes of surface damage, and can be understood in the context of the physics of dynamical threshold systems. Threshold systems are known to be some of the most important nonlinear, self-organizing systems in nature, including networks of earthquake faults, neural networks, superconductors and semiconductors, and the World Wide Web, as well as political, social, and ecological systems. All of these systems have dynamics that are strongly correlated in space and time, and all typically display a multiplicity of spatial and temporal scales. Here we discuss the physics of self-organization and damage in earthquake threshold systems at the "microscopic" laboratory scale, in which consideration of results from simulations leads to dynamical equations that can be used to derive results obtained from sliding friction experiments, specifically, the empirical "rate-and-state" friction equations of Ruina. Paradoxically, in all of these dissipative systems, long-range interactions induce the existence of locally ergodic dynamics, even though the dissipation of energy is involved. The existence of dissipative effects leads to the appearance of a "leaky threshold" dynamics, equivalent to a new scaling field that controls the size of nucleation events relative to the size of the background fluctuations. The corresponding appearance of a mean field spinodal leads to a general coarse-grained equation, which expresses the balance between rate of stress supplied, and rate of stress dissipated in the processes leading to surface damage. We can use ideas from thermodynamics and kinetics of phase transitions to develop the exact form of the rate-and-state equations, giving clear physical meaning to all terms and variables. Ultimately, the self-organizing dynamics arise from the appearance of an energy landscape in these systems, which in turn arises from the strong correlations and mean field nature of the physics.

New solitary wave and multiple soliton solutions for fifth order nonlinear evolution equation with time variable coefficients

NASA Astrophysics Data System (ADS)

Jaradat, H. M.; Syam, Muhammed; Jaradat, M. M. M.; Mustafa, Zead; Moman, S.

2018-03-01

In this paper, we investigate the multiple soliton solutions and multiple singular soliton solutions of a class of the fifth order nonlinear evolution equation with variable coefficients of t using the simplified bilinear method based on a transformation method combined with the Hirota's bilinear sense. In addition, we present analysis for some parameters such as the soliton amplitude and the characteristic line. Several equation in the literature are special cases of the class which we discuss such as Caudrey-Dodd-Gibbon equation and Sawada-Kotera. Comparison with several methods in the literature, such as Helmholtz solution of the inverse variational problem, rational exponential function method, tanh method, homotopy perturbation method, exp-function method, and coth method, are made. From these comparisons, we conclude that the proposed method is efficient and our solutions are correct. It is worth mention that the proposed solution can solve many physical problems.

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…

Further Insight into the Cardiovascular Risk Calculator Controversy: The Roles of Statins, Revascularizations, and Under-Ascertainment in the Women's Health Study

PubMed Central

Cook, Nancy R.; Ridker, Paul M

2015-01-01

Importance While the Pooled Cohort Equations from the recent ACC/AHA Guideline on the Assessment of Cardiovascular Risk have over-estimated cardiovascular risk in multiple external cohorts, the reasons for the discrepancy are unclear. Objective To determine whether increased use of statins over time, incident coronary revascularization procedures, or under-ascertainment of vascular events explain over-estimation of risk in a more contemporary population. Design, Setting, and Participants 27,542 women aged 45-79 with complete ascertainment of plasma lipids and other risk factors from the Women's Health Study (WHS), a nationwide cohort of US women free of cardiovascular disease, cancer or other major illness at baseline in 1992-95. Women were followed for a median of 10 years. Main Outcomes and Measures Atherosclerotic cardiovascular disease (ASCVD), defined as any myocardial infarction, any stroke, or death due to cardiovascular cause. Results 632 women experienced an ASCVD event over follow-up. The average predicted risk from the Pooled Cohort Equations was 3.6% over 10 years, compared to an actual observed risk of 2.2%. Predicted rates were 90% higher than the observed rates in the 0-<5% and 5-<7.5% risk groups and 40% higher in the 7.5-<10% and 10%+ risk groups. Rates of statin use and revascularizations increased over follow-up time and by risk group, and in sensitivity analyses, we estimated the hypothetical rates if no women were on statins or underwent revascularization procedures. After adjustment for intervention effects of statins and revascularization as well as hypothetical confounding by indication, predicted rates remained 80% higher than observed rates in the lower two risk groups and 30% higher in the upper two risk groups. Under-ascertainment is unlikely since follow-up rates in the WHS were 97%, and overall we would need 60% more events to match the numbers predicted using the Pooled Cohort Equations. Conclusions and Relevance Neither statin use, revascularization procedures, nor under-ascertainment of events explain the discrepancy between observed rates of ASCVD in the WHS and those predicted by the ACC/AHA Pooled Cohort Equations. Other explanations include changing patterns of risk within more contemporary populations. PMID:25285455

Experimental evaluation of the extended Dytlewski-style dead time correction formalism for neutron multiplicity counting

NASA Astrophysics Data System (ADS)

Lockhart, M.; Henzlova, D.; Croft, S.; Cutler, T.; Favalli, A.; McGahee, Ch.; Parker, R.

2018-01-01

Over the past few decades, neutron multiplicity counting has played an integral role in Special Nuclear Material (SNM) characterization pertaining to nuclear safeguards. Current neutron multiplicity analysis techniques use singles, doubles, and triples count rates because a methodology to extract and dead time correct higher order count rates (i.e. quads and pents) was not fully developed. This limitation is overcome by the recent extension of a popular dead time correction method developed by Dytlewski. This extended dead time correction algorithm, named Dytlewski-Croft-Favalli(DCF), is detailed in reference Croft and Favalli (2017), which gives an extensive explanation of the theory and implications of this new development. Dead time corrected results can then be used to assay SNM by inverting a set of extended point model equations which as well have only recently been formulated. The current paper discusses and presents the experimental evaluation of practical feasibility of the DCF dead time correction algorithm to demonstrate its performance and applicability in nuclear safeguards applications. In order to test the validity and effectiveness of the dead time correction for quads and pents, 252Cf and SNM sources were measured in high efficiency neutron multiplicity counters at the Los Alamos National Laboratory (LANL) and the count rates were extracted up to the fifth order and corrected for dead time. In order to assess the DCF dead time correction, the corrected data is compared to traditional dead time correction treatment within INCC. The DCF dead time correction is found to provide adequate dead time treatment for broad range of count rates available in practical applications.

River velocities from sequential multispectral remote sensing images

NASA Astrophysics Data System (ADS)

Chen, Wei; Mied, Richard P.

2013-06-01

We address the problem of extracting surface velocities from a pair of multispectral remote sensing images over rivers using a new nonlinear multiple-tracer form of the global optimal solution (GOS). The derived velocity field is a valid solution across the image domain to the nonlinear system of equations obtained by minimizing a cost function inferred from the conservation constraint equations for multiple tracers. This is done by deriving an iteration equation for the velocity, based on the multiple-tracer displaced frame difference equations, and a local approximation to the velocity field. The number of velocity equations is greater than the number of velocity components, and thus overly constrain the solution. The iterative technique uses Gauss-Newton and Levenberg-Marquardt methods and our own algorithm of the progressive relaxation of the over-constraint. We demonstrate the nonlinear multiple-tracer GOS technique with sequential multispectral Landsat and ASTER images over a portion of the Potomac River in MD/VA, and derive a dense field of accurate velocity vectors. We compare the GOS river velocities with those from over 12 years of data at four NOAA reference stations, and find good agreement. We discuss how to find the appropriate spatial and temporal resolutions to allow optimization of the technique for specific rivers.

Quasi-Maximum Likelihood Estimation of Structural Equation Models with Multiple Interaction and Quadratic Effects

ERIC Educational Resources Information Center

Klein, Andreas G.; Muthen, Bengt O.

2007-01-01

In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly…

Testing Mediation Using Multiple Regression and Structural Equation Modeling Analyses in Secondary Data

ERIC Educational Resources Information Center

Li, Spencer D.

2011-01-01

Mediation analysis in child and adolescent development research is possible using large secondary data sets. This article provides an overview of two statistical methods commonly used to test mediated effects in secondary analysis: multiple regression and structural equation modeling (SEM). Two empirical studies are presented to illustrate the…

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C072)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C048)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

The first reference equations for the 6-minute walk distance over a 10 m course.

PubMed

Beekman, Emmylou; Mesters, Ilse; Gosselink, Rik; Klaassen, Mariska P M; Hendriks, Erik J M; Van Schayck, Onno C P; de Bie, Rob A

2014-09-01

As primary care practice space is mostly limited to 10 m, the 6-minute walk test (6MWT) over a 10 m course is a frequently used alternative to evaluate patients' performance in COPD. Considering that course length significantly affects distance walked in 6 minutes (6MWD), this study aims to develop appropriate reference equations for the 10 m 6MWT. 181 healthy subjects, aged 40-90 years, performed two standardised 6MWTs over a straight 10 m course in a cross-sectional study. Average distance achieved was 578±108 m and differed between males and females (p<0.001). Resulting sex-specific reference equations from multiple regression analysis included age, body mass index and change in heart rate, explaining 62% of the variance in 6MWD for males and 71% for females. The presented reference equations are the first to evaluate 6MWD over a 10 m course and expand the usefulness of the 6MWT. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.

Equivalent circuit model of Ge/Si separate absorption charge multiplication avalanche photodiode

NASA Astrophysics Data System (ADS)

Wang, Wei; Chen, Ting; Yan, Linshu; Bao, Xiaoyuan; Xu, Yuanyuan; Wang, Guang; Wang, Guanyu; Yuan, Jun; Li, Junfeng

2018-03-01

The equivalent circuit model of Ge/Si Separate Absorption Charge Multiplication Avalanche Photodiode (SACM-APD) is proposed. Starting from the carrier rate equations in different regions of device and considering the influences of non-uniform electric field, noise, parasitic effect and some other factors, the equivalent circuit model of SACM-APD device is established, in which the steady-state and transient current voltage characteristics can be described exactly. In addition, the proposed Ge/Si SACM APD equivalent circuit model is embedded in PSpice simulator. The important characteristics of Ge/Si SACM APD such as dark current, frequency response, shot noise are simulated, the simulation results show that the simulation with the proposed model are in good agreement with the experimental results.

A (2+1)-dimensional Korteweg-de Vries type equation in water waves: Lie symmetry analysis; multiple exp-function method; conservation laws

NASA Astrophysics Data System (ADS)

Adem, Abdullahi Rashid

2016-05-01

We consider a (2+1)-dimensional Korteweg-de Vries type equation which models the shallow-water waves, surface and internal waves. In the analysis, we use the Lie symmetry method and the multiple exp-function method. Furthermore, conservation laws are computed using the multiplier method.

Development of Multiple Regression Equations To Predict Fourth Graders' Achievement in Reading and Selected Content Areas.

ERIC Educational Resources Information Center

Hafner, Lawrence E.

A study developed a multiple regression prediction equation for each of six selected achievement variables in a popular standardized test of achievement. Subjects, 42 fourth-grade pupils randomly selected across several classes in a large elementary school in a north Florida city, were administered several standardized tests to determine predictor…

Developing above-ground woody biomass equations for open-grown, multiple-stemmed tree species: shelterbelt-grown Russian-olive

Treesearch

Xinhau Zhour; James R. Brandle; Michele M. Schoeneberger; Tala Awada

2007-01-01

Multiple-stemmed tree species are often used in agricultural settings, playing a significant role in natural resource conservation and carbon sequestration. Biomass estimation, whether for modeling growth under different climate scenarios, accounting for carbon sequestered, or inclusion in natural resource inventories, requires equations that can accurately describe...

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

NASA Astrophysics Data System (ADS)

Remizov, I. D.

2012-07-01

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.

Power-law Exponent in Multiplicative Langevin Equation with Temporally Correlated Noise

NASA Astrophysics Data System (ADS)

Morita, Satoru

2018-05-01

Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. For discrete-time systems, the power-law exponent is known to decrease as the autocorrelation time of the multiplier increases. However, for continuous-time systems, it is not yet clear how the temporal correlation affects the power-law behavior. Herein, we analytically investigated a multiplicative Langevin equation with colored noise. We show that the power-law exponent depends on the details of the multiplicative noise, in contrast to the case of discrete-time systems.

An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations

PubMed Central

Özkum, Gülcan

2013-01-01

We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior. PMID:24453914

Equatorial late-afternoon periodic TEC fluctuations observed by multiple GPS receivers

NASA Astrophysics Data System (ADS)

Tsugawa, T.; Maruyama, T.; Saito, S.; Ishii, M.

2009-12-01

We report, for the first time, equatorial periodic total electron content (TEC) fluctuations observed in the late afternoon by multiple GPS receivers. As a part of Southeast Asia low-latitude ionospheric network (SEALION), GPS receivers at Chiang Mai and Chumphon, Thailand, have been operated since 2005. We found that periodic TEC fluctuations (PTF) with the periods of 15-30 minutes are often observed at these two sites in the spring (Apr-May) late afternoon. Further investigations using multiple GPS receivers in Southeast Asia revealed that the PTFs propagate at 150-200 m/s away from the equator and their amplitudes depend on the satellite azimuth angle. Statistical study of the PTF activity at different latitudes and longitudes clarified that the PTFs are not observed at mid-latitudes, and their seasonal variations are different at different longitudes and at geomagnetically conjugate regions. These observational results indicate that the PTFs are caused by the atmospheric gravity waves (AGW) which are generated in the equatorial lower atmosphere and propagate away from the equator. Simultaneous GPS-TEC and ionosonde observations at Chumphon revealed that the day-to-day variations of PTF activities are well correlated with those of the rate of TEC change index (ROTI) and the occurrence of equatorial spread F (ESF) after the sunset, indicating the PTFs may be related with the onset of the ESF and plasma bubbles.

Multiplicity of solutions of the bi-harmonic Schrödinger equation with critical growth

NASA Astrophysics Data System (ADS)

Zhang, Jian; Lou, Zhenluo; Ji, Yanju; Shao, Wei

2018-04-01

In this paper, we study multiplicity of solutions of the critical bi-harmonic equation ɛ ^4 Δ ^2 u +V(x) u =h(x) f(u)+g(x) u^{2_*-1} in R^N, where 2_*=2N/N-4 is the critical exponent. When ɛ >0 is small, we establish the relationship between the number of solutions and the profile of V, h, g. Also, without the restriction on ɛ , we obtain a multiplicity result.

Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.

PubMed

Shah, Kamal; Khan, Rahmat Ali

2016-01-01

In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results.

Pathogenesis of renal failure in multiple myeloma: any role of contrast media?

PubMed

Mussap, Michele; Merlini, Giampaolo

2014-01-01

The spectrum of kidney disease-associated monoclonal immunoglobulin and plasma cell malignancies is remarkably broad and encompasses nearly all nephropathologic entities. Multiple myeloma with kidney impairment at presentation is a medical emergency since the recovery of kidney function is associated with survival benefits. In most cases, kidney impairment may be the first clinical manifestation of malignant plasma cell dyscrasias like multiple myeloma and light chain amyloidosis. Multiple myeloma per se cannot be considered a main risk factor for developing acute kidney injury following intravascular administration of iodinated contrast media. The risk is increased by comorbidities such as chronic kidney disease, diabetes, hypercalcemia, dehydration, and use of nephrotoxic drugs. Before the administration of contrast media, the current recommended laboratory tests for assessing kidney function are serum creatinine measurement and the estimation of glomerular filtration rate by using the CKD-EPI equation. The assessment of Bence Jones proteinuria is unnecessary for evaluating the risk of kidney failure in patients with multiple myeloma, since this test cannot be considered a surrogate biomarker of kidney function.

Pathogenesis of Renal Failure in Multiple Myeloma: Any Role of Contrast Media?

PubMed Central

Mussap, Michele; Merlini, Giampaolo

2014-01-01

The spectrum of kidney disease-associated monoclonal immunoglobulin and plasma cell malignancies is remarkably broad and encompasses nearly all nephropathologic entities. Multiple myeloma with kidney impairment at presentation is a medical emergency since the recovery of kidney function is associated with survival benefits. In most cases, kidney impairment may be the first clinical manifestation of malignant plasma cell dyscrasias like multiple myeloma and light chain amyloidosis. Multiple myeloma per se cannot be considered a main risk factor for developing acute kidney injury following intravascular administration of iodinated contrast media. The risk is increased by comorbidities such as chronic kidney disease, diabetes, hypercalcemia, dehydration, and use of nephrotoxic drugs. Before the administration of contrast media, the current recommended laboratory tests for assessing kidney function are serum creatinine measurement and the estimation of glomerular filtration rate by using the CKD-EPI equation. The assessment of Bence Jones proteinuria is unnecessary for evaluating the risk of kidney failure in patients with multiple myeloma, since this test cannot be considered a surrogate biomarker of kidney function. PMID:24877060

Kinetics of nitrous oxide production by denitrification in municipal solid waste.

PubMed

Wu, Chuanfu; Shimaoka, Takayuki; Nakayama, Hirofumi; Komiya, Teppei

2015-04-01

As one of the Nitrous Oxide (N2O) production pathways, denitrification plays an important role in regulating the emission of N2O into the atmosphere. In this study, the influences of different substrate concentrations and transient conditions on the denitrification rate and N2O-reducing activities were investigated. Results revealed that N2O production rates (i.e. denitrification rates) were stimulated by increased total organic carbon (TOC) concentration, while it was restrained under high oxygen concentrations. Moreover, the impact of nitrate concentrations on N2O production rates depended on the TOC/NO3--N ratios. All the N2O production rate data fitted well to a multiplicative Monod equation, with terms describing the influence of TOC and nitrate concentrations, and an Arrhenius-type equation. Furthermore, results demonstrated that high temperatures minimized the N2O-reducing activities in aged municipal solid waste, resulting in an accumulation of N2O. On the other hand, a transient condition caused by changing O2 concentrations may strongly influence the N2O production rates and N2O-reducing activities in solid waste. Finally, based on the results, we believe that a landfill aeration strategy properly designed to prevent rising temperatures and to cycle air injection is the key to reducing emissions of N2O during remediation of old landfills by means of in situ aeration. Copyright © 2015 Elsevier Ltd. All rights reserved.

Analytical Theory of the Destruction Terms in Dissipation Rate Transport Equations

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Zhou, Ye

1996-01-01

Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like C(epsilon 2) are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of C(epsilon 2) on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. Both the presence of this effect and the appropriate time scale in the modeled transport equation depend on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple application of these methods leads to a preliminary, dissipation rate equation for rotating buoyant turbulence.

Reusable Launch Vehicle Control in Multiple Time Scale Sliding Modes

NASA Technical Reports Server (NTRS)

Shtessel, Yuri

1999-01-01

A reusable launch vehicle control problem during ascent is addressed via multiple-time scaled continuous sliding mode control. The proposed sliding mode controller utilizes a two-loop structure and provides robust, de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of bounded external disturbances and plant uncertainties. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues placement. The dual-time scale sliding mode controller was designed for the X-33 technology demonstration sub-orbital launch vehicle in the launch mode. 6DOF simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in presence of external disturbances and vehicle inertia uncertainties. It creates possibility to operate the X-33 vehicle in an aircraft-like mode with reduced pre-launch adjustment of the control system.

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.

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...

Estimation of Glomerular Filtration Rate Based on Serum Cystatin C versus Creatinine in a Uruguayan Population

PubMed Central

Lujambio, Inés; Sottolano, Mariana; Robaina, Sebastián; Carusso, Florencia; da Rosa, Alicia; Ríos, Ana Carina; Olascoaga, Alicia; Gadola, Liliana; Noboa, Oscar; Staessen, Jan A.; Boggia, José

2014-01-01

Background. Estimation of glomerular filtration rate (eGFR) from biomarkers has evolved and multiple equations are available to estimate renal function at bedside. Methods. In a random sample of 119 Uruguayans (54.5% women; 56.2 years (mean)), we used Bland and Altman's method and Cohen's kappa statistic to assess concordance on a continuous or categorical (eGFR < 60 versus ≥60 mL/min/1.73 m2) scale between eGFRcys (reference) and eGFR derived from serum creatinine according to the Modification of Diet in Renal Disease (eGFRmdrd) or the Chronic Kidney Disease Epidemiology Collaboration equations (eGFRepi) or from both serum cystatin C and creatinine (eGFRmix). Results. In all participants, eGFRmdrd, eGFRepi, and eGFRmix were, respectively, 9.7, 11.5, and 5.6 mL/min/1.73 m2 higher (P < 0.0001) than eGFRcys. The prevalence of eGFR <60 mL/min/1.73 m2 was the highest for eGFRcys (21.8%), intermediate for eGFRmix (11.8%), and the lowest for eGFRmdrd (5.9%) and eGFRepi (3.4%). Using eGFRcys as reference, we found only fair agreement with the equations based on creatinine (Cohen's kappa statistic 0.15 to 0.23). Conclusion. Using different equations we reached clinically significant differences in the estimation of renal function. eGFRcys provides lower estimates, resulting in higher prevalence of eGFR <60 mL/min/1.73 m2. PMID:25215234

Utility of Equations to Estimate Peak Oxygen Uptake and Work Rate From a 6-Minute Walk Test in Patients With COPD in a Clinical Setting.

PubMed

Kirkham, Amy A; Pauhl, Katherine E; Elliott, Robyn M; Scott, Jen A; Doria, Silvana C; Davidson, Hanan K; Neil-Sztramko, Sarah E; Campbell, Kristin L; Camp, Pat G

2015-01-01

To determine the utility of equations that use the 6-minute walk test (6MWT) results to estimate peak oxygen uptake ((Equation is included in full-text article.)o2) and peak work rate with chronic obstructive pulmonary disease (COPD) patients in a clinical setting. This study included a systematic review to identify published equations estimating peak (Equation is included in full-text article.)o2 and peak work rate in watts in COPD patients and a retrospective chart review of data from a hospital-based pulmonary rehabilitation program. The following variables were abstracted from the records of 42 consecutively enrolled COPD patients: measured peak (Equation is included in full-text article.)o2 and peak work rate achieved during a cycle ergometer cardiopulmonary exercise test, 6MWT distance, age, sex, weight, height, forced expiratory volume in 1 second, forced vital capacity, and lung diffusion capacity. Estimated peak (Equation is included in full-text article.)o2 and peak work rate were estimated from 6MWT distance using published equations. The error associated with using estimated peak (Equation is included in full-text article.)o2 or peak work to prescribe aerobic exercise intensities of 60% and 80% was calculated. Eleven equations from 6 studies were identified. Agreement between estimated and measured values was poor to moderate (intraclass correlation coefficients = 0.11-0.63). The error associated with using estimated peak (Equation is included in full-text article.)o2 or peak work rate to prescribe exercise intensities of 60% and 80% of measured values ranged from mean differences of 12 to 35 and 16 to 47 percentage points, respectively. There is poor to moderate agreement between measured peak (Equation is included in full-text article.)o2 and peak work rate and estimations from equations that use 6MWT distance, and the use of the estimated values for prescription of aerobic exercise intensity would result in large error. Equations estimating peak (Equation is included in full-text article.)o2 and peak work rate are of low utility for prescribing exercise intensity in pulmonary rehabilitation programs.

[Combined application of multiple fluorescence in research on the degradation of fluoranthene by potassium ferrate].

PubMed

Li, Si; Yu, Dan-Ni; Ji, Fang-Ying; Zhou, Guang-Ming; He, Qiang

2012-11-01

The degradation of fluoranthene was researched by combined means of multiple fluorescence spectra, including emission, synchronous, excitation emission matrix (EEM), time-scan and photometry. The characteristics of the degradation and fluoranthene molecular changes within the degradation's process were also discussed according to the information about the degradation provided by all of the fluorescence spectra mentioned above. The equations of fluoranthene's degradation by potassium ferrate were obtained on the bases of fitting time-scan fluorescence curves at different time, and the degradation's kinetic was speculated accordingly. From the experimental results, multiple fluorescence data commonly reflected that it had same degradation rate at the same reaction time. t = 10 s, and the degradation rate is -55%, t = 25 s, -81%, t = 40 s, -91%. No new fluorescent characteristic was observed within every degradation' stage. The reaction stage during t < or = 20 s was crucial, in which the degradation process is closest to linear relationship. After this beginning stage, the linear relationship deviated gradually with the development of the degradation process. The degradation of fluoranthene by potassium ferrate was nearly in accord with the order of the first order reaction.

Multiple Linking in Equating and Random Scale Drift. Research Report. ETS RR-11-46

ERIC Educational Resources Information Center

Guo, Hongwen; Liu, Jinghua; Dorans, Neil; Feigenbaum, Miriam

2011-01-01

Maintaining score stability is crucial for an ongoing testing program that administers several tests per year over many years. One way to stall the drift of the score scale is to use an equating design with multiple links. In this study, we use the operational and experimental SAT® data collected from 44 administrations to investigate the effect…

Structural Equation Modelling of Multiple Facet Data: Extending Models for Multitrait-Multimethod Data

ERIC Educational Resources Information Center

Bechger, Timo M.; Maris, Gunter

2004-01-01

This paper is about the structural equation modelling of quantitative measures that are obtained from a multiple facet design. A facet is simply a set consisting of a finite number of elements. It is assumed that measures are obtained by combining each element of each facet. Methods and traits are two such facets, and a multitrait-multimethod…

Estimation of premorbid general fluid intelligence using traditional Chinese reading performance in Taiwanese samples.

PubMed

Chen, Ying-Jen; Ho, Meng-Yang; Chen, Kwan-Ju; Hsu, Chia-Fen; Ryu, Shan-Jin

2009-08-01

The aims of the present study were to (i) investigate if traditional Chinese word reading ability can be used for estimating premorbid general intelligence; and (ii) to provide multiple regression equations for estimating premorbid performance on Raven's Standard Progressive Matrices (RSPM), using age, years of education and Chinese Graded Word Reading Test (CGWRT) scores as predictor variables. Four hundred and twenty-six healthy volunteers (201 male, 225 female), aged 16-93 years (mean +/- SD, 41.92 +/- 18.19 years) undertook the tests individually under supervised conditions. Seventy percent of subjects were randomly allocated to the derivation group (n = 296), and the rest to the validation group (n = 130). RSPM score was positively correlated with CGWRT score and years of education. RSPM and CGWRT scores and years of education were also inversely correlated with age, but the declining trend for RSPM performance against age was steeper than that for CGWRT performance. Separate multiple regression equations were derived for estimating RSPM scores using different combinations of age, years of education, and CGWRT score for both groups. The multiple regression coefficient of each equation ranged from 0.71 to 0.80 with the standard error of estimate between 7 and 8 RSPM points. When fitting the data of one group to the equations derived from its counterpart group, the cross-validation multiple regression coefficients ranged from 0.71 to 0.79. There were no significant differences in the 'predicted-obtained' RSPM discrepancies between any equations. The regression equations derived in the present study may provide a basis for estimating premorbid RSPM performance.

Optimal analytic method for the nonlinear Hasegawa-Mima equation

NASA Astrophysics Data System (ADS)

Baxter, Mathew; Van Gorder, Robert A.; Vajravelu, Kuppalapalle

2014-05-01

The Hasegawa-Mima equation is a nonlinear partial differential equation that describes the electric potential due to a drift wave in a plasma. In the present paper, we apply the method of homotopy analysis to a slightly more general Hasegawa-Mima equation, which accounts for hyper-viscous damping or viscous dissipation. First, we outline the method for the general initial/boundary value problem over a compact rectangular spatial domain. We use a two-stage method, where both the convergence control parameter and the auxiliary linear operator are optimally selected to minimize the residual error due to the approximation. To do the latter, we consider a family of operators parameterized by a constant which gives the decay rate of the solutions. After outlining the general method, we consider a number of concrete examples in order to demonstrate the utility of this approach. The results enable us to study properties of the initial/boundary value problem for the generalized Hasegawa-Mima equation. In several cases considered, we are able to obtain solutions with extremely small residual errors after relatively few iterations are computed (residual errors on the order of 10-15 are found in multiple cases after only three iterations). The results demonstrate that selecting a parameterized auxiliary linear operator can be extremely useful for minimizing residual errors when used concurrently with the optimal homotopy analysis method, suggesting that this approach can prove useful for a number of nonlinear partial differential equations arising in physics and nonlinear mechanics.

Improving the evaluation of therapeutic interventions in multiple sclerosis: the role of new psychometric methods.

PubMed

Hobart, J; Cano, S

2009-02-01

In this monograph we examine the added value of new psychometric methods (Rasch measurement and Item Response Theory) over traditional psychometric approaches by comparing and contrasting their psychometric evaluations of existing sets of rating scale data. We have concentrated on Rasch measurement rather than Item Response Theory because we believe that it is the more advantageous method for health measurement from a conceptual, theoretical and practical perspective. Our intention is to provide an authoritative document that describes the principles of Rasch measurement and the practice of Rasch analysis in a clear, detailed, non-technical form that is accurate and accessible to clinicians and researchers in health measurement. A comparison was undertaken of traditional and new psychometric methods in five large sets of rating scale data: (1) evaluation of the Rivermead Mobility Index (RMI) in data from 666 participants in the Cannabis in Multiple Sclerosis (CAMS) study; (2) evaluation of the Multiple Sclerosis Impact Scale (MSIS-29) in data from 1725 people with multiple sclerosis; (3) evaluation of test-retest reliability of MSIS-29 in data from 150 people with multiple sclerosis; (4) examination of the use of Rasch analysis to equate scales purporting to measure the same health construct in 585 people with multiple sclerosis; and (5) comparison of relative responsiveness of the Barthel Index and Functional Independence Measure in data from 1400 people undergoing neurorehabilitation. Both Rasch measurement and Item Response Theory are conceptually and theoretically superior to traditional psychometric methods. Findings from each of the five studies show that Rasch analysis is empirically superior to traditional psychometric methods for evaluating rating scales, developing rating scales, analysing rating scale data, understanding and measuring stability and change, and understanding the health constructs we seek to quantify. There is considerable added value in using Rasch analysis rather than traditional psychometric methods in health measurement. Future research directions include the need to reproduce our findings in a range of clinical populations, detailed head-to-head comparisons of Rasch analysis and Item Response Theory, and the application of Rasch analysis to clinical practice.

Robust Scale Transformation Methods in IRT True Score Equating under Common-Item Nonequivalent Groups Design

ERIC Educational Resources Information Center

He, Yong

2013-01-01

Common test items play an important role in equating multiple test forms under the common-item nonequivalent groups design. Inconsistent item parameter estimates among common items can lead to large bias in equated scores for IRT true score equating. Current methods extensively focus on detection and elimination of outlying common items, which…

Evaluating Students' Conceptual Understanding of Balanced Equations and Stoichiometric Ratios Using a Particulate Drawing

ERIC Educational Resources Information Center

Sanger, Michael J.

2005-01-01

A total of 156 students were asked to provide free-response balanced chemical equations for a classic multiple-choice particulate-drawing question first used by Nurrenbern and Pickering. The balanced equations and the number of students providing each equation are reported in this study. The most common student errors included a confusion between…

An improved method for nonlinear parameter estimation: a case study of the Rössler model

NASA Astrophysics Data System (ADS)

He, Wen-Ping; Wang, Liu; Jiang, Yun-Di; Wan, Shi-Quan

2016-08-01

Parameter estimation is an important research topic in nonlinear dynamics. Based on the evolutionary algorithm (EA), Wang et al. (2014) present a new scheme for nonlinear parameter estimation and numerical tests indicate that the estimation precision is satisfactory. However, the convergence rate of the EA is relatively slow when multiple unknown parameters in a multidimensional dynamical system are estimated simultaneously. To solve this problem, an improved method for parameter estimation of nonlinear dynamical equations is provided in the present paper. The main idea of the improved scheme is to use all of the known time series for all of the components in some dynamical equations to estimate the parameters in single component one by one, instead of estimating all of the parameters in all of the components simultaneously. Thus, we can estimate all of the parameters stage by stage. The performance of the improved method was tested using a classic chaotic system—Rössler model. The numerical tests show that the amended parameter estimation scheme can greatly improve the searching efficiency and that there is a significant increase in the convergence rate of the EA, particularly for multiparameter estimation in multidimensional dynamical equations. Moreover, the results indicate that the accuracy of parameter estimation and the CPU time consumed by the presented method have no obvious dependence on the sample size.

Experimental evaluation of the extended Dytlewski-style dead time correction formalism for neutron multiplicity counting

DOE PAGES

Lockhart, M.; Henzlova, D.; Croft, S.; ...

2017-09-20

Over the past few decades, neutron multiplicity counting has played an integral role in Special Nuclear Material (SNM) characterization pertaining to nuclear safeguards. Current neutron multiplicity analysis techniques use singles, doubles, and triples count rates because a methodology to extract and dead time correct higher order count rates (i.e. quads and pents) was not fully developed. This limitation is overcome by the recent extension of a popular dead time correction method developed by Dytlewski. This extended dead time correction algorithm, named Dytlewski-Croft-Favalli (DCF), is detailed in reference Croft and Favalli (2017), which gives an extensive explanation of the theory andmore » implications of this new development. Dead time corrected results can then be used to assay SNM by inverting a set of extended point model equations which as well have only recently been formulated. Here, we discuss and present the experimental evaluation of practical feasibility of the DCF dead time correction algorithm to demonstrate its performance and applicability in nuclear safeguards applications. In order to test the validity and effectiveness of the dead time correction for quads and pents, 252Cf and SNM sources were measured in high efficiency neutron multiplicity counters at the Los Alamos National Laboratory (LANL) and the count rates were extracted up to the fifth order and corrected for dead time. To assess the DCF dead time correction, the corrected data is compared to traditional dead time correction treatment within INCC. In conclusion, the DCF dead time correction is found to provide adequate dead time treatment for broad range of count rates available in practical applications.« less

Experimental evaluation of the extended Dytlewski-style dead time correction formalism for neutron multiplicity counting

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

Lockhart, M.; Henzlova, D.; Croft, S.

Over the past few decades, neutron multiplicity counting has played an integral role in Special Nuclear Material (SNM) characterization pertaining to nuclear safeguards. Current neutron multiplicity analysis techniques use singles, doubles, and triples count rates because a methodology to extract and dead time correct higher order count rates (i.e. quads and pents) was not fully developed. This limitation is overcome by the recent extension of a popular dead time correction method developed by Dytlewski. This extended dead time correction algorithm, named Dytlewski-Croft-Favalli (DCF), is detailed in reference Croft and Favalli (2017), which gives an extensive explanation of the theory andmore » implications of this new development. Dead time corrected results can then be used to assay SNM by inverting a set of extended point model equations which as well have only recently been formulated. Here, we discuss and present the experimental evaluation of practical feasibility of the DCF dead time correction algorithm to demonstrate its performance and applicability in nuclear safeguards applications. In order to test the validity and effectiveness of the dead time correction for quads and pents, 252Cf and SNM sources were measured in high efficiency neutron multiplicity counters at the Los Alamos National Laboratory (LANL) and the count rates were extracted up to the fifth order and corrected for dead time. To assess the DCF dead time correction, the corrected data is compared to traditional dead time correction treatment within INCC. In conclusion, the DCF dead time correction is found to provide adequate dead time treatment for broad range of count rates available in practical applications.« less

Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez

2015-11-01

Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

The probability density function (PDF) of Lagrangian Turbulence

NASA Astrophysics Data System (ADS)

Birnir, B.

2012-12-01

The statistical theory of Lagrangian turbulence is derived from the stochastic Navier-Stokes equation. Assuming that the noise in fully-developed turbulence is a generic noise determined by the general theorems in probability, the central limit theorem and the large deviation principle, we are able to formulate and solve the Kolmogorov-Hopf equation for the invariant measure of the stochastic Navier-Stokes equations. The intermittency corrections to the scaling exponents of the structure functions require a multiplicative (multipling the fluid velocity) noise in the stochastic Navier-Stokes equation. We let this multiplicative noise, in the equation, consists of a simple (Poisson) jump process and then show how the Feynmann-Kac formula produces the log-Poissonian processes, found by She and Leveque, Waymire and Dubrulle. These log-Poissonian processes give the intermittency corrections that agree with modern direct Navier-Stokes simulations (DNS) and experiments. The probability density function (PDF) plays a key role when direct Navier-Stokes simulations or experimental results are compared to theory. The statistical theory of turbulence is determined, including the scaling of the structure functions of turbulence, by the invariant measure of the Navier-Stokes equation and the PDFs for the various statistics (one-point, two-point, N-point) can be obtained by taking the trace of the corresponding invariant measures. Hopf derived in 1952 a functional equation for the characteristic function (Fourier transform) of the invariant measure. In distinction to the nonlinear Navier-Stokes equation, this is a linear functional differential equation. The PDFs obtained from the invariant measures for the velocity differences (two-point statistics) are shown to be the four parameter generalized hyperbolic distributions, found by Barndorff-Nilsen. These PDF have heavy tails and a convex peak at the origin. A suitable projection of the Kolmogorov-Hopf equations is the differential equation determining the generalized hyperbolic distributions. Then we compare these PDFs with DNS results and experimental data.

A Brief Historical Introduction to Determinants with Applications

ERIC Educational Resources Information Center

Debnath, L.

2013-01-01

This article deals with a short historical introduction to determinants with applications to the theory of equations, geometry, multiple integrals, differential equations and linear algebra. Included are some properties of determinants with proofs, eigenvalues, eigenvectors and characteristic equations with examples of applications to simple…

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)

An iterative solver for the 3D Helmholtz equation

NASA Astrophysics Data System (ADS)

Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

2017-09-01

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

Quick and Easy Rate Equations for Multistep Reactions

ERIC Educational Resources Information Center

Savage, Phillip E.

2008-01-01

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

Representing Rate Equations for Enzyme-Catalyzed Reactions

ERIC Educational Resources Information Center

Ault, Addison

2011-01-01

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

The Dynamic Mutation Characteristics of Thermonuclear Reaction in Tokamak

PubMed Central

Li, Jing; Quan, Tingting; Zhang, Wei; Deng, Wei

2014-01-01

The stability and bifurcations of multiple limit cycles for the physical model of thermonuclear reaction in Tokamak are investigated in this paper. The one-dimensional Ginzburg-Landau type perturbed diffusion equations for the density of the plasma and the radial electric field near the plasma edge in Tokamak are established. First, the equations are transformed to the average equations with the method of multiple scales and the average equations turn to be a Z 2-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, with the bifurcations theory and method of detection function, the qualitative behavior of the unperturbed system and the number of the limit cycles of the perturbed system for certain groups of parameter are analyzed. At last, the stability of the limit cycles is studied and the physical meaning of Tokamak equations under these parameter groups is given. PMID:24892099

Speaking rate effects on locus equation slope.

PubMed

Berry, Jeff; Weismer, Gary

2013-11-01

A locus equation describes a 1st order regression fit to a scatter of vowel steady-state frequency values predicting vowel onset frequency values. Locus equation coefficients are often interpreted as indices of coarticulation. Speaking rate variations with a constant consonant-vowel form are thought to induce changes in the degree of coarticulation. In the current work, the hypothesis that locus slope is a transparent index of coarticulation is examined through the analysis of acoustic samples of large-scale, nearly continuous variations in speaking rate. Following the methodological conventions for locus equation derivation, data pooled across ten vowels yield locus equation slopes that are mostly consistent with the hypothesis that locus equations vary systematically with coarticulation. Comparable analyses between different four-vowel pools reveal variations in the locus slope range and changes in locus slope sensitivity to rate change. Analyses across rate but within vowels are substantially less consistent with the locus hypothesis. Taken together, these findings suggest that the practice of vowel pooling exerts a non-negligible influence on locus outcomes. Results are discussed within the context of articulatory accounts of locus equations and the effects of speaking rate change.

Decreasing Multicollinearity: A Method for Models with Multiplicative Functions.

ERIC Educational Resources Information Center

Smith, Kent W.; Sasaki, M. S.

1979-01-01

A method is proposed for overcoming the problem of multicollinearity in multiple regression equations where multiplicative independent terms are entered. The method is not a ridge regression solution. (JKS)

Recollections of sexual socialisation among marginalised heterosexual black men

PubMed Central

Dunlap, Eloise; Benoit, Ellen; Graves, Jennifer L.

2013-01-01

This paper describes the sexual socialisation process of marginalised, drug-using heterosexual black men, focusing primarily on the sources and content of sexual information. Analysing qualitative interview data, we discovered that the men in our sample both learn about sex and become sexually active at an early age. They most often learn about sex from the media and least often learn about sex from family members. The content of sexual information varies in specifics, but overall tends to equate sex with pleasure, encourage sexual activity with multiple partners, and emphasise using protection. Our goal is to use this data to better understand how sexual socialisation contributes to the prevalence of multiple sexual partners and high rates of HIV among heterosexual black men in order to inform future risk-reduction intervention programmes. PMID:24482611

First passage times for multiple particles with reversible target-binding kinetics

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.

2017-10-01

We investigate the first passage problem for multiple particles that diffuse towards a target, partially adsorb there, and then desorb after a finite exponentially distributed residence time. We search for the first time when m particles undergoing such reversible target-binding kinetics are found simultaneously on the target that may trigger an irreversible chemical reaction or a biophysical event. Even if the particles are independent, the finite residence time on the target yields an intricate temporal coupling between particles. We compute analytically the mean first passage time (MFPT) for two independent particles by mapping the original problem to higher-dimensional surface-mediated diffusion and solving the coupled partial differential equations. The respective effects of the adsorption and desorption rates on the MFPT are revealed and discussed.

Using Regression Equations Built from Summary Data in the Psychological Assessment of the Individual Case: Extension to Multiple Regression

ERIC Educational Resources Information Center

Crawford, John R.; Garthwaite, Paul H.; Denham, Annie K.; Chelune, Gordon J.

2012-01-01

Regression equations have many useful roles in psychological assessment. Moreover, there is a large reservoir of published data that could be used to build regression equations; these equations could then be employed to test a wide variety of hypotheses concerning the functioning of individual cases. This resource is currently underused because…

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation. Volume 2, Part 2: Appendixes B, C, D and E

NASA Technical Reports Server (NTRS)

Lowrie, J. W.; Fermelia, A. J.; Haley, D. C.; Gremban, K. D.; Vanbaalen, J.; Walsh, R. W.

1982-01-01

The derivation of the equations is presented, the rate control algorithm described, and simulation methodologies summarized. A set of dynamics equations that can be used recursively to calculate forces and torques acting at the joints of an n link manipulator given the manipulator joint rates are derived. The equations are valid for any n link manipulator system with any kind of joints connected in any sequence. The equations of motion for the class of manipulators consisting of n rigid links interconnected by rotary joints are derived. A technique is outlined for reducing the system of equations to eliminate contraint torques. The linearized dynamics equations for an n link manipulator system are derived. The general n link linearized equations are then applied to a two link configuration. The coordinated rate control algorithm used to compute individual joint rates when given end effector rates is described. A short discussion of simulation methodologies is presented.

A many-body states picture of electronic friction: The case of multiple orbitals and multiple electronic states

NASA Astrophysics Data System (ADS)

Dou, Wenjie; Subotnik, Joseph E.

2016-08-01

We present a very general form of electronic friction as present when a molecule with multiple orbitals hybridizes with a metal electrode. To develop this picture of friction, we embed the quantum-classical Liouville equation (QCLE) within a classical master equation (CME). Thus, this article extends our previous work analyzing the case of one electronic level, as we may now treat the case of multiple levels and many electronic molecular states. We show that, in the adiabatic limit, where electron transitions are much faster than nuclear motion, the QCLE-CME reduces to a Fokker-Planck equation, such that nuclei feel an average force as well as friction and a random force—as caused by their interaction with the metallic electrons. Finally, we show numerically and analytically that our frictional results agree with other published results calculated using non-equilibrium Green's functions. Numerical recipes for solving this QCLE-CME will be provided in a subsequent paper.

A many-body states picture of electronic friction: The case of multiple orbitals and multiple electronic states

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

Dou, Wenjie; Subotnik, Joseph E.

We present a very general form of electronic friction as present when a molecule with multiple orbitals hybridizes with a metal electrode. To develop this picture of friction, we embed the quantum-classical Liouville equation (QCLE) within a classical master equation (CME). Thus, this article extends our previous work analyzing the case of one electronic level, as we may now treat the case of multiple levels and many electronic molecular states. We show that, in the adiabatic limit, where electron transitions are much faster than nuclear motion, the QCLE-CME reduces to a Fokker-Planck equation, such that nuclei feel an average forcemore » as well as friction and a random force—as caused by their interaction with the metallic electrons. Finally, we show numerically and analytically that our frictional results agree with other published results calculated using non-equilibrium Green’s functions. Numerical recipes for solving this QCLE-CME will be provided in a subsequent paper.« less

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

PubMed

McIsaac, Michael; Cook, R J

2017-02-01

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

An integral equation formulation for the diffraction from convex plates and polyhedra.

PubMed

Asheim, Andreas; Svensson, U Peter

2013-06-01

A formulation of the problem of scattering from obstacles with edges is presented. The formulation is based on decomposing the field into geometrical acoustics, first-order, and multiple-order edge diffraction components. An existing secondary-source model for edge diffraction from finite edges is extended to handle multiple diffraction of all orders. It is shown that the multiple-order diffraction component can be found via the solution to an integral equation formulated on pairs of edge points. This gives what can be called an edge source signal. In a subsequent step, this edge source signal is propagated to yield a multiple-order diffracted field, taking all diffraction orders into account. Numerical experiments demonstrate accurate response for frequencies down to 0 for thin plates and a cube. No problems with irregular frequencies, as happen with the Kirchhoff-Helmholtz integral equation, are observed for this formulation. For the axisymmetric scattering from a circular disc, a highly effective symmetric formulation results, and results agree with reference solutions across the entire frequency range.

A Hybrid Method of Moment Equations and Rate Equations to Modeling Gas-Grain Chemistry

NASA Astrophysics Data System (ADS)

Pei, Y.; Herbst, E.

2011-05-01

Grain surfaces play a crucial role in catalyzing many important chemical reactions in the interstellar medium (ISM). The deterministic rate equation (RE) method has often been used to simulate the surface chemistry. But this method becomes inaccurate when the number of reacting particles per grain is typically less than one, which can occur in the ISM. In this condition, stochastic approaches such as the master equations are adopted. However, these methods have mostly been constrained to small chemical networks due to the large amounts of processor time and computer power required. In this study, we present a hybrid method consisting of the moment equation approximation to the stochastic master equation approach and deterministic rate equations to treat a gas-grain model of homogeneous cold cloud cores with time-independent physical conditions. In this model, we use the standard OSU gas phase network (version OSU2006V3) which involves 458 gas phase species and more than 4000 reactions, and treat it by deterministic rate equations. A medium-sized surface reaction network which consists of 21 species and 19 reactions accounts for the productions of stable molecules such as H_2O, CO, CO_2, H_2CO, CH_3OH, NH_3 and CH_4. These surface reactions are treated by a hybrid method of moment equations (Barzel & Biham 2007) and rate equations: when the abundance of a surface species is lower than a specific threshold, say one per grain, we use the ``stochastic" moment equations to simulate the evolution; when its abundance goes above this threshold, we use the rate equations. A continuity technique is utilized to secure a smooth transition between these two methods. We have run chemical simulations for a time up to 10^8 yr at three temperatures: 10 K, 15 K, and 20 K. The results will be compared with those generated from (1) a completely deterministic model that uses rate equations for both gas phase and grain surface chemistry, (2) the method of modified rate equations (Garrod 2008), which partially takes into account the stochastic effect for surface reactions, and (3) the master equation approach solved using a Monte Carlo technique. At 10 K and standard grain sizes, our model results agree well with the above three methods, while discrepancies appear at higher temperatures and smaller grain sizes.

Relational Priming Based on a Multiplicative Schema for Whole Numbers and Fractions.

PubMed

DeWolf, Melissa; Son, Ji Y; Bassok, Miriam; Holyoak, Keith J

2017-11-01

Why might it be (at least sometimes) beneficial for adults to process fractions componentially? Recent research has shown that college-educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study examined patterns of relational priming for problems with fractions in a task that required arithmetic computations. College students were asked to judge whether or not multiplication equations involving fractions were correct. Some equations served as structurally inverse primes for the equation that immediately followed it (e.g., 4 × 3/4 = 3 followed by 3 × 8/6 = 4). Students with relatively high math ability showed relational priming (speeded solution times to the second of two successive relationally related fraction equations) both with and without high perceptual similarity (Experiment 2). Students with relatively low math ability also showed priming, but only when the structurally inverse equation pairs were supported by high perceptual similarity between numbers (e.g., 4 × 3/4 = 3 followed by 3 × 4/3 = 4). Several additional experiments established boundary conditions on relational priming with fractions. These findings are interpreted in terms of componential processing of fractions in a relational multiplication context that takes advantage of their inherent connections to a multiplicative schema for whole numbers. Copyright © 2017 Cognitive Science Society, Inc.

Performance of bed-load transport equations relative to geomorphic significance: Predicting effective discharge and its transport rate

Treesearch

Jeffrey J. Barry; John M. Buffington; Peter Goodwin; John .G. King; William W. Emmett

2008-01-01

Previous studies assessing the accuracy of bed-load transport equations have considered equation performance statistically based on paired observations of measured and predicted bed-load transport rates. However, transport measurements were typically taken during low flows, biasing the assessment of equation performance toward low discharges, and because equation...

Flow behaviour and constitutive modelling of a ferritic stainless steel at elevated temperatures

NASA Astrophysics Data System (ADS)

Zhao, Jingwei; Jiang, Zhengyi; Zu, Guoqing; Du, Wei; Zhang, Xin; Jiang, Laizhu

2016-05-01

The flow behaviour of a ferritic stainless steel (FSS) was investigated by a Gleeble 3500 thermal-mechanical test simulator over the temperature range of 900-1100 °C and strain rate range of 1-50 s-1. Empirical and phenomenological constitutive models were established, and a comparative study was made on the predictability of them. The results indicate that the flow stress decreases with increasing the temperature and decreasing the strain rate. High strain rate may cause a drop in flow stress after a peak value due to the adiabatic heating. The Zener-Hollomon parameter depends linearly on the flow stress, and decreases with raising the temperature and reducing the strain rate. Significant deviations occur in the prediction of flow stress by the Johnson-Cook (JC) model, indicating that the JC model cannot accurately track the flow behaviour of the FSS during hot deformation. Both the multiple-linear and the Arrhenius-type models can track the flow behaviour very well under the whole hot working conditions, and have much higher accuracy in predicting the flow behaviour than that of the JC model. The multiple-linear model is recommended in the current work due to its simpler structure and less time needed for solving the equations relative to the Arrhenius-type model.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems.

PubMed

Winkelmann, Stefanie; Schütte, Christof

2017-09-21

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems

NASA Astrophysics Data System (ADS)

Winkelmann, Stefanie; Schütte, Christof

2017-09-01

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

Measuring attitude with a gradiometer

NASA Technical Reports Server (NTRS)

Sonnabend, David; Gardner, Thomas G.

1994-01-01

This paper explores using a gravity gradiometer to measure the attitude of a satellite, given that the gravity field is accurately known. Since gradiometers actually measure a combination of the gradient and attitude rate and acceleration terms, the answer is far from obvious. The paper demonstrates that it can be done and at microradian accuracy. The technique employed is dynamic estimation, based on the momentum biased Euler equations. The satellite is assumed nominally planet pointed, and subject to control, gravity gradient, and partly radom drag torques. The attitude estimator is unusual. While the standard method of feeding back measurement residuals is used, the feedback gain matrix isn't derived from Kalman theory. instead, it's chosen to minimize a measure of the terminal covariance of the error in the estimate. This depends on the gain matrix and the power spectra of all the process and measurement noises. An integration is required over multiple solutions of Lyapunov equations.

Large-displacement statistics of the rightmost particle of the one-dimensional branching Brownian motion.

PubMed

Derrida, Bernard; Meerson, Baruch; Sasorov, Pavel V

2016-04-01

Consider a one-dimensional branching Brownian motion and rescale the coordinate and time so that the rates of branching and diffusion are both equal to 1. If X_{1}(t) is the position of the rightmost particle of the branching Brownian motion at time t, the empirical velocity c of this rightmost particle is defined as c=X_{1}(t)/t. Using the Fisher-Kolmogorov-Petrovsky-Piscounov equation, we evaluate the probability distribution P(c,t) of this empirical velocity c in the long-time t limit for c>2. It is already known that, for a single seed particle, P(c,t)∼exp[-(c^{2}/4-1)t] up to a prefactor that can depend on c and t. Here we show how to determine this prefactor. The result can be easily generalized to the case of multiple seed particles and to branching random walks associated with other traveling-wave equations.

Pest persistence and eradication conditions in a deterministic model for sterile insect release.

PubMed

Gordillo, Luis F

2015-01-01

The release of sterile insects is an environment friendly pest control method used in integrated pest management programmes. Difference or differential equations based on Knipling's model often provide satisfactory qualitative descriptions of pest populations subject to sterile release at relatively high densities with large mating encounter rates, but fail otherwise. In this paper, I derive and explore numerically deterministic population models that include sterile release together with scarce mating encounters in the particular case of species with long lifespan and multiple matings. The differential equations account separately the effects of mating failure due to sterile male release and the frequency of mating encounters. When insects spatial spread is incorporated through diffusion terms, computations reveal the possibility of steady pest persistence in finite size patches. In the presence of density dependence regulation, it is observed that sterile release might contribute to induce sudden suppression of the pest population.

Equating in Small-Scale Language Testing Programs

ERIC Educational Resources Information Center

LaFlair, Geoffrey T.; Isbell, Daniel; May, L. D. Nicolas; Gutierrez Arvizu, Maria Nelly; Jamieson, Joan

2017-01-01

Language programs need multiple test forms for secure administrations and effective placement decisions, but can they have confidence that scores on alternate test forms have the same meaning? In large-scale testing programs, various equating methods are available to ensure the comparability of forms. The choice of equating method is informed by…

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.

The use of multiple imputation for the accurate measurements of individual feed intake by electronic feeders.

PubMed

Jiao, S; Tiezzi, F; Huang, Y; Gray, K A; Maltecca, C

2016-02-01

Obtaining accurate individual feed intake records is the key first step in achieving genetic progress toward more efficient nutrient utilization in pigs. Feed intake records collected by electronic feeding systems contain errors (erroneous and abnormal values exceeding certain cutoff criteria), which are due to feeder malfunction or animal-feeder interaction. In this study, we examined the use of a novel data-editing strategy involving multiple imputation to minimize the impact of errors and missing values on the quality of feed intake data collected by an electronic feeding system. Accuracy of feed intake data adjustment obtained from the conventional linear mixed model (LMM) approach was compared with 2 alternative implementations of multiple imputation by chained equation, denoted as MI (multiple imputation) and MICE (multiple imputation by chained equation). The 3 methods were compared under 3 scenarios, where 5, 10, and 20% feed intake error rates were simulated. Each of the scenarios was replicated 5 times. Accuracy of the alternative error adjustment was measured as the correlation between the true daily feed intake (DFI; daily feed intake in the testing period) or true ADFI (the mean DFI across testing period) and the adjusted DFI or adjusted ADFI. In the editing process, error cutoff criteria are used to define if a feed intake visit contains errors. To investigate the possibility that the error cutoff criteria may affect any of the 3 methods, the simulation was repeated with 2 alternative error cutoff values. Multiple imputation methods outperformed the LMM approach in all scenarios with mean accuracies of 96.7, 93.5, and 90.2% obtained with MI and 96.8, 94.4, and 90.1% obtained with MICE compared with 91.0, 82.6, and 68.7% using LMM for DFI. Similar results were obtained for ADFI. Furthermore, multiple imputation methods consistently performed better than LMM regardless of the cutoff criteria applied to define errors. In conclusion, multiple imputation is proposed as a more accurate and flexible method for error adjustments in feed intake data collected by electronic feeders.

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

PubMed Central

Dräger, Andreas; Kronfeld, Marcel; Ziller, Michael J; Supper, Jochen; Planatscher, Hannes; Magnus, Jørgen B; Oldiges, Marco; Kohlbacher, Oliver; Zell, Andreas

2009-01-01

Background To understand the dynamic behavior of cellular systems, mathematical modeling is often necessary and comprises three steps: (1) experimental measurement of participating molecules, (2) assignment of rate laws to each reaction, and (3) parameter calibration with respect to the measurements. In each of these steps the modeler is confronted with a plethora of alternative approaches, e. g., the selection of approximative rate laws in step two as specific equations are often unknown, or the choice of an estimation procedure with its specific settings in step three. This overall process with its numerous choices and the mutual influence between them makes it hard to single out the best modeling approach for a given problem. Results We investigate the modeling process using multiple kinetic equations together with various parameter optimization methods for a well-characterized example network, the biosynthesis of valine and leucine in C. glutamicum. For this purpose, we derive seven dynamic models based on generalized mass action, Michaelis-Menten and convenience kinetics as well as the stochastic Langevin equation. In addition, we introduce two modeling approaches for feedback inhibition to the mass action kinetics. The parameters of each model are estimated using eight optimization strategies. To determine the most promising modeling approaches together with the best optimization algorithms, we carry out a two-step benchmark: (1) coarse-grained comparison of the algorithms on all models and (2) fine-grained tuning of the best optimization algorithms and models. To analyze the space of the best parameters found for each model, we apply clustering, variance, and correlation analysis. Conclusion A mixed model based on the convenience rate law and the Michaelis-Menten equation, in which all reactions are assumed to be reversible, is the most suitable deterministic modeling approach followed by a reversible generalized mass action kinetics model. A Langevin model is advisable to take stochastic effects into account. To estimate the model parameters, three algorithms are particularly useful: For first attempts the settings-free Tribes algorithm yields valuable results. Particle swarm optimization and differential evolution provide significantly better results with appropriate settings. PMID:19144170

Mixed-Format Test Score Equating: Effect of Item-Type Multidimensionality, Length and Composition of Common-Item Set, and Group Ability Difference

ERIC Educational Resources Information Center

Wang, Wei

2013-01-01

Mixed-format tests containing both multiple-choice (MC) items and constructed-response (CR) items are now widely used in many testing programs. Mixed-format tests often are considered to be superior to tests containing only MC items although the use of multiple item formats leads to measurement challenges in the context of equating conducted under…

Rapid-Equilibrium Enzyme Kinetics

ERIC Educational Resources Information Center

Alberty, Robert A.

2008-01-01

Rapid-equilibrium rate equations for enzyme-catalyzed reactions are especially useful because if experimental data can be fit by these simpler rate equations, the Michaelis constants can be interpreted as equilibrium constants. However, for some reactions it is necessary to use the more complicated steady-state rate equations. Thermodynamics is…

Accurate prediction of cardiorespiratory fitness using cycle ergometry in minimally disabled persons with relapsing-remitting multiple sclerosis.

PubMed

Motl, Robert W; Fernhall, Bo

2012-03-01

To examine the accuracy of predicting peak oxygen consumption (VO(2peak)) primarily from peak work rate (WR(peak)) recorded during a maximal, incremental exercise test on a cycle ergometer among persons with relapsing-remitting multiple sclerosis (RRMS) who had minimal disability. Cross-sectional study. Clinical research laboratory. Women with RRMS (n=32) and sex-, age-, height-, and weight-matched healthy controls (n=16) completed an incremental exercise test on a cycle ergometer to volitional termination. Not applicable. Measured and predicted VO(2peak) and WR(peak). There were strong, statistically significant associations between measured and predicted VO(2peak) in the overall sample (R(2)=.89, standard error of the estimate=127.4 mL/min) and subsamples with (R(2)=.89, standard error of the estimate=131.3 mL/min) and without (R(2)=.85, standard error of the estimate=126.8 mL/min) multiple sclerosis (MS) based on the linear regression analyses. Based on the 95% confidence limits for worst-case errors, the equation predicted VO(2peak) within 10% of its true value in 95 of every 100 subjects with MS. Peak VO(2) can be accurately predicted in persons with RRMS who have minimal disability as it is in controls by using established equations and WR(peak) recorded from a maximal, incremental exercise test on a cycle ergometer. Copyright © 2012 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

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

Koshelev, A. E.

Multiple-band electronic structure and proximity to antiferromagnetic (AF) instability are the key properties of iron-based superconductors. In this paper, we explore the influence of scattering by the AF spin fluctuations on transport of multiple-band metals above the magnetic transition. A salient feature of scattering on the AF fluctuations is that it is strongly enhanced at the Fermi surface locations where the nesting is perfect (“hot spots” or “hot lines”). We review derivation of the collision integral for the Boltzmann equation due to AF-fluctuations scattering. In the paramagnetic state, the enhanced scattering rate near the hot lines leads to anomalous behaviormore » of electronic transport in magnetic field. We explore this behavior by analytically solving the Boltzmann transport equation with approximate transition rates. This approach accounts for return scattering events and is more accurate than the relaxation-time approximation. The magnetic-field dependences are characterized by two very different field scales: the lower scale is set by the hot-spot width and the higher scale is set by the total scattering amplitude. A conventional magnetotransport behavior is limited to magnetic fields below the lower scale. In the wide range in-between these two scales, the longitudinal conductivity has linear dependence on the magnetic field and the Hall conductivity has quadratic dependence. The linear dependence of the diagonal component reflects growth of the Fermi-surface area affected by the hot spots proportional to the magnetic field. Finally, we discuss applicability of this theoretical framework for describing of anomalous magnetotransport properties in different iron pnictides and chalcogenides in the paramagnetic state.« less

Flood characteristics of Alaskan streams

USGS Publications Warehouse

Lamke, R.D.

1979-01-01

Peak discharge data for Alaskan streams are summarized and analyzed. Multiple-regression equations relating peak discharge magnitude and frequency to climatic and physical characteristics of 260 gaged basins were determined in order to estimate average recurrence interval of floods at ungaged sites. These equations are for 1.25-, 2-, 5-, 10-, 25-, and 50-year average recurrence intervals. In this report, Alaska was divided into two regions, one having a maritime climate with fall and winter rains and floods, the other having spring and summer floods of a variety or combinations of causes. Average standard errors of the six multiple-regression equations for these two regions were 48 and 74 percent, respectively. Maximum recorded floods at more than 400 sites throughout Alaska are tabulated. Maps showing lines of equal intensity of the principal climatic variables found to be significant (mean annual precipitation and mean minimum January temperature), and location of the 260 sites used in the multiple-regression analyses are included. Little flood data have been collected in western and arctic Alaska, and the predictive equations are therefore less reliable for those areas. (Woodard-USGS)

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

NASA Astrophysics Data System (ADS)

Leskiw, Donald M.; Zhau, Junmei

2000-06-01

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

On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations

NASA Astrophysics Data System (ADS)

García, Isaac A.; Llibre, Jaume; Maza, Susanna

2018-06-01

In this work we consider real analytic functions , where , Ω is a bounded open subset of , is an interval containing the origin, are parameters, and ε is a small parameter. We study the branching of the zero-set of at multiple points when the parameter ε varies. We apply the obtained results to improve the classical averaging theory for computing T-periodic solutions of λ-families of analytic T-periodic ordinary differential equations defined on , using the displacement functions defined by these equations. We call the coefficients in the Taylor expansion of in powers of ε the averaged functions. The main contribution consists in analyzing the role that have the multiple zeros of the first non-zero averaged function. The outcome is that these multiple zeros can be of two different classes depending on whether the zeros belong or not to the analytic set defined by the real variety associated to the ideal generated by the averaged functions in the Noetheriang ring of all the real analytic functions at . We bound the maximum number of branches of isolated zeros that can bifurcate from each multiple zero z 0. Sometimes these bounds depend on the cardinalities of minimal bases of the former ideal. Several examples illustrate our results and they are compared with the classical theory, branching theory and also under the light of singularity theory of smooth maps. The examples range from polynomial vector fields to Abel differential equations and perturbed linear centers.

A feedback control model for network flow with multiple pure time delays

NASA Technical Reports Server (NTRS)

Press, J.

1972-01-01

A control model describing a network flow hindered by multiple pure time (or transport) delays is formulated. Feedbacks connect each desired output with a single control sector situated at the origin. The dynamic formulation invokes the use of differential difference equations. This causes the characteristic equation of the model to consist of transcendental functions instead of a common algebraic polynomial. A general graphical criterion is developed to evaluate the stability of such a problem. A digital computer simulation confirms the validity of such criterion. An optimal decision making process with multiple delays is presented.

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.

Modeling tracer transport in randomly heterogeneous porous media by nonlocal moment equations: Anomalous transport

NASA Astrophysics Data System (ADS)

Morales-Casique, E.; Lezama-Campos, J. L.; Guadagnini, A.; Neuman, S. P.

2013-05-01

Modeling tracer transport in geologic porous media suffers from the corrupt characterization of the spatial distribution of hydrogeologic properties of the system and the incomplete knowledge of processes governing transport at multiple scales. Representations of transport dynamics based on a Fickian model of the kind considered in the advection-dispersion equation (ADE) fail to capture (a) the temporal variation associated with the rate of spreading of a tracer, and (b) the distribution of early and late arrival times which are often observed in field and/or laboratory scenarios and are considered as the signature of anomalous transport. Elsewhere we have presented exact stochastic moment equations to model tracer transport in randomly heterogeneous aquifers. We have also developed a closure scheme which enables one to provide numerical solutions of such moment equations at different orders of approximations. The resulting (ensemble) average and variance of concentration fields were found to display a good agreement against Monte Carlo - based simulation results for mildly heterogeneous (or well-conditioned strongly heterogeneous) media. Here we explore the ability of the moment equations approach to describe the distribution of early arrival times and late time tailing effects which can be observed in Monte-Carlo based breakthrough curves (BTCs) of the (ensemble) mean concentration. We show that BTCs of mean resident concentration calculated at a fixed space location through higher-order approximations of moment equations display long tailing features of the kind which is typically associated with anomalous transport behavior and are not represented by an ADE model with constant dispersive parameter, such as the zero-order approximation.

Mean annual runoff and peak flow estimates based on channel geometry of streams in northeastern and western Montana

USGS Publications Warehouse

Parrett, Charles; Omang, R.J.; Hull, J.A.

1983-01-01

Equations for estimating mean annual runoff and peak discharge from measurements of channel geometry were developed for western and northeastern Montana. The study area was divided into two regions for the mean annual runoff analysis, and separate multiple-regression equations were developed for each region. The active-channel width was determined to be the most important independent variable in each region. The standard error of estimate for the estimating equation using active-channel width was 61 percent in the Northeast Region and 38 percent in the West region. The study area was divided into six regions for the peak discharge analysis, and multiple regression equations relating channel geometry and basin characteristics to peak discharges having recurrence intervals of 2, 5, 10, 25, 50 and 100 years were developed for each region. The standard errors of estimate for the regression equations using only channel width as an independent variable ranged from 35 to 105 percent. The standard errors improved in four regions as basin characteristics were added to the estimating equations. (USGS)

MULTISCALE MODELS OF TAXIS-DRIVEN PATTERNING IN BACTERIAL POPULATIONS

PubMed Central

XUE, CHUAN; OTHMER, HANS G.

2009-01-01

Spatially-distributed populations of various types of bacteria often display intricate spatial patterns that are thought to result from the cellular response to gradients of nutrients or other attractants. In the past decade a great deal has been learned about signal transduction, metabolism and movement in E. coli and other bacteria, but translating the individual-level behavior into population-level dynamics is still a challenging problem. However, this is a necessary step because it is computationally impractical to use a strictly cell-based model to understand patterning in growing populations, since the total number of cells may reach 1012 - 1014 in some experiments. In the past phenomenological equations such as the Patlak-Keller-Segel equations have been used in modeling the cell movement that is involved in the formation of such patterns, but the question remains as to how the microscopic behavior can be correctly described by a macroscopic equation. Significant progress has been made for bacterial species that employ a “run-and-tumble” strategy of movement, in that macroscopic equations based on simplified schemes for signal transduction and turning behavior have been derived [14, 15]. Here we extend previous work in a number of directions: (i) we allow for time-dependent signals, which extends the applicability of the equations to natural environments, (ii) we use a more general turning rate function that better describes the biological behavior, and (iii) we incorporate the effect of hydrodynamic forces that arise when cells swim in close proximity to a surface. We also develop a new approach to solving the moment equations derived from the transport equation that does not involve closure assumptions. Numerical examples show that the solution of the lowest-order macroscopic equation agrees well with the solution obtained from a Monte Carlo simulation of cell movement under a variety of temporal protocols for the signal. We also apply the method to derive equations of chemotactic movement that are governed by multiple chemotactic signals. PMID:19784399

Suppression of Growth by Multiplicative White Noise in a Parametric Resonant System

NASA Astrophysics Data System (ADS)

Ishihara, Masamichi

2015-02-01

The growth of the amplitude in a Mathieu-like equation with multiplicative white noise is studied. To obtain an approximate analytical expression for the exponent at the extremum on parametric resonance regions, a time-interval width is introduced. To determine the exponents numerically, the stochastic differential equations are solved by a symplectic numerical method. The Mathieu-like equation contains a parameter α determined by the intensity of noise and the strength of the coupling between the variable and noise; without loss of generality, only non-negative α can be considered. The exponent is shown to decrease with α, reach a minimum and increase after that. The minimum exponent is obtained analytically and numerically. As a function of α, the minimum at α≠0, occurs on the parametric resonance regions of α=0. This minimum indicates suppression of growth by multiplicative white noise.

Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.

PubMed

Cooper, F; Hyman, J M; Khare, A

2001-08-01

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable.

Dusty Pair Plasma—Wave Propagation and Diffusive Transition of Oscillations

NASA Astrophysics Data System (ADS)

Atamaniuk, Barbara; Turski, Andrzej J.

2011-11-01

The crucial point of the paper is the relation between equilibrium distributions of plasma species and the type of propagation or diffusive transition of plasma response to a disturbance. The paper contains a unified treatment of disturbance propagation (transport) in the linearized Vlasov electron-positron and fullerene pair plasmas containing charged dust impurities, based on the space-time convolution integral equations. Electron-positron-dust/ion (e-p-d/i) plasmas are rather widespread in nature. Space-time responses of multi-component linearized Vlasov plasmas on the basis of multiple integral equations are invoked. An initial-value problem for Vlasov-Poisson/Ampère equations is reduced to the one multiple integral equation and the solution is expressed in terms of forcing function and its space-time convolution with the resolvent kernel. The forcing function is responsible for the initial disturbance and the resolvent is responsible for the equilibrium velocity distributions of plasma species. By use of resolvent equations, time-reversibility, space-reflexivity and the other symmetries are revealed. The symmetries carry on physical properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing equilibrium distributions for dusty pair plasmas, we can reduce the resolvent equation to: (i) the undamped dispersive wave equations, (ii) and diffusive transport equations of oscillations.

Assisted Sonication vs Conventional Transesterification Numerical Simulation and Sensitivity Study

NASA Astrophysics Data System (ADS)

Janajreh, Isam; Noorul Hussain, Mohammed; El Samad, Tala

2015-10-01

Transeterification is known as slow reaction that can take over several hours to complete as the two immiscible liquid reactants combine to form biodiesel and the less favorable glycerol. The quest of finding the perfect catalyst, optimal operational conditions, and reactor configuration to accelerate the reaction in mere few minutes that ensures high quality biodiesel, in economically viable way is coming along with sonication. This drastic reduction is a key enabler for the development of a continuous processing that otherwise is fairly costly and low throughput using conventional method. The reaction kinetics of sonication assisted as inferred by several authors is several time faster and this work implements these rates in a high fidelity numerical simulation model. This flow model is based on Navier-Stokes equations coupled with energy equation for non-isothermal flow and the transport equations of the multiple reactive species. The model is initially validated against experimental data from previous work of the authors using an annular reactor configuration. Following the validation, comparison of the reaction rate is shown to gain more insight to the distribution of the reaction and its attained rates. The two models (conventional and sonication) then compared on the basis of their sensitivity to the methane to oil molar ratio as the most pronounced process parameter. Both the exit reactor yield and the distribution of the species are evaluated with favorable yield under sonication process. These results pave the way to build a more robust process intensified reactor having an integrated selective heterogeneous catalyst to steer the reaction. This can avoid the downstream cleaning processes, cutting reaction time, and render economic benefit to the process.

Propagation of Finite Amplitude Sound in Multiple Waveguide Modes.

NASA Astrophysics Data System (ADS)

van Doren, Thomas Walter

1993-01-01

This dissertation describes a theoretical and experimental investigation of the propagation of finite amplitude sound in multiple waveguide modes. Quasilinear analytical solutions of the full second order nonlinear wave equation, the Westervelt equation, and the KZK parabolic wave equation are obtained for the fundamental and second harmonic sound fields in a rectangular rigid-wall waveguide. It is shown that the Westervelt equation is an acceptable approximation of the full nonlinear wave equation for describing guided sound waves of finite amplitude. A system of first order equations based on both a modal and harmonic expansion of the Westervelt equation is developed for waveguides with locally reactive wall impedances. Fully nonlinear numerical solutions of the system of coupled equations are presented for waveguides formed by two parallel planes which are either both rigid, or one rigid and one pressure release. These numerical solutions are compared to finite -difference solutions of the KZK equation, and it is shown that solutions of the KZK equation are valid only at frequencies which are high compared to the cutoff frequencies of the most important modes of propagation (i.e., for which sound propagates at small grazing angles). Numerical solutions of both the Westervelt and KZK equations are compared to experiments performed in an air-filled, rigid-wall, rectangular waveguide. Solutions of the Westervelt equation are in good agreement with experiment for low source frequencies, at which sound propagates at large grazing angles, whereas solutions of the KZK equation are not valid for these cases. At higher frequencies, at which sound propagates at small grazing angles, agreement between numerical solutions of the Westervelt and KZK equations and experiment is only fair, because of problems in specifying the experimental source condition with sufficient accuracy.

[Relationship between depression symptoms and stress in occupational populations].

PubMed

Yu, Shan-fa; Yao, San-qiao; Ding, Hui; Ma, Liang-qing; Yang, Yan; Wang, Zhi-hui

2006-03-01

To explore the relationship between the depression symptoms and occupational stress in occupational populations. Depression symptoms were measured by using the center for epidemiological survey-depression scale. The occupational stress instrument were employed to investigate the stressors, personalities, social support, and coping strategies as well as the subject's age, length of service, sex, educational level and marriage status. Chi(2) test was used for analyzing the difference of depression. The multiple covariance analysis was used for testing the difference of stressors, personalities, social support, and coping strategies among the groups with different scores of depression. The variables obtained in the optional prediction equation were identified by multiple stepwise regression analysis. The incidence rate of definite depression symptoms was 40.2%. The total average score was 21.74 +/- 8.99. Henan province had the highest incidence rate of depression symptoms, 43.8%, Hebei 39.4%, and Beijing the lowest, 23.4%. The male workers had the higher incidence rate of depression symptoms, 43. 0% than female, 35.4% (P < 0.01). The older group had the lower incidence rates of depression symptoms, compared with the younger group (P < 0.01). The workers divorced or with the bereft spouse had the higher incidence rate of depression symptoms than the workers married and unmarried (P < 0.05). The workers with middle school education had the higher incidence rates of depression symptoms than those with master degree. Incidence rates in the most occupational groups were more than 30%. The significant difference was shown between the different jobs (P < 0.01). The difference of the adjusted means among three groups of different depression score were analyzed. The results showed the workers with definite depression symptoms had the higher scores than the other two groups in physical factors, role ambiguity, role conflict, job monotony, mental load, responsibility for persons, job future ambiguity, job hazards, type A behavior and work locus of control, and social support (P < 0.05, P < 0.01). The former had the lower scores than the other two groups in the scores of promotion, participation, autonomy, task identity, feedback, friendship opportunity, speed control, training adequacy, challenge, self-esteem, organizational commitment, and coping strategies. Fifteen variables entered the predictive equation of depression score explaining 33.1% of variance. There are serious mental health problems in the occupational population in our country. Stressors and personalities affect the mental health.

A multiple linear regression analysis of hot corrosion attack on a series of nickel base turbine alloys

NASA Technical Reports Server (NTRS)

Barrett, C. A.

1985-01-01

Multiple linear regression analysis was used to determine an equation for estimating hot corrosion attack for a series of Ni base cast turbine alloys. The U transform (i.e., 1/sin (% A/100) to the 1/2) was shown to give the best estimate of the dependent variable, y. A complete second degree equation is described for the centered" weight chemistries for the elements Cr, Al, Ti, Mo, W, Cb, Ta, and Co. In addition linear terms for the minor elements C, B, and Zr were added for a basic 47 term equation. The best reduced equation was determined by the stepwise selection method with essentially 13 terms. The Cr term was found to be the most important accounting for 60 percent of the explained variability hot corrosion attack.

A comparative study of serial and parallel aeroelastic computations of wings

NASA Technical Reports Server (NTRS)

Byun, Chansup; Guruswamy, Guru P.

1994-01-01

A procedure for computing the aeroelasticity of wings on parallel multiple-instruction, multiple-data (MIMD) computers is presented. In this procedure, fluids are modeled using Euler equations, and structures are modeled using modal or finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. In the present parallel procedure, each computational domain is scalable. A parallel integration scheme is used to compute aeroelastic responses by solving fluid and structural equations concurrently. The computational efficiency issues of parallel integration of both fluid and structural equations are investigated in detail. This approach, which reduces the total computational time by a factor of almost 2, is demonstrated for a typical aeroelastic wing by using various numbers of processors on the Intel iPSC/860.

Models for nearly every occasion: Part III - One box decreasing emission models.

PubMed

Hewett, Paul; Ganser, Gary H

2017-11-01

New one box "well-mixed room" decreasing emission (DE) models are introduced that allow for local exhaust or local exhaust with filtered return, as well the recirculation of a filtered (or cleaned) portion of the general room ventilation. For each control device scenario, a steady state and transient model is presented. The transient equations predict the concentration at any time t after the application of a known mass of a volatile substance to a surface, and can be used to predict the task exposure profile, the average task exposure, as well as peak and short-term exposures. The steady state equations can be used to predict the "average concentration per application" that is reached whenever the substance is repeatedly applied. Whenever the beginning and end concentrations are expected to be zero (or near zero) the steady state equations can also be used to predict the average concentration for a single task with multiple applications during the task, or even a series of such tasks. The transient equations should be used whenever these criteria cannot be met. A structured calibration procedure is proposed that utilizes a mass balance approach. Depending upon the DE model selected, one or more calibration measurements are collected. Using rearranged versions of the steady state equations, estimates of the model variables-e.g., the mass of the substance applied during each application, local exhaust capture efficiency, and the various cleaning or filtration efficiencies-can be calculated. A new procedure is proposed for estimating the emission rate constant.

Numerical analysis of single and multiple jets

NASA Astrophysics Data System (ADS)

Boussoufi, Mustapha; Sabeur-Bendehina, Amina; Ouadha, Ahmed; Morsli, Souad; El Ganaoui, Mohammed

2017-05-01

The present study aims to use the concept of entropy generation in order to study numerically the flow and the interaction of multiple jets. Several configurations of a single jet surrounded by equidistant 3, 5, 7 and 9 circumferential jets have been studied. The turbulent incompressible Navier-Stokes equations have been solved numerically using the commercial computational fluid dynamics code Fluent. The standard k-ɛ model has been selected to assess the eddy viscosity. The domain has been reduced to a quarter of the geometry due to symmetry. Results for axial and radial velocities have been compared with experimental measurements from the literature. Furthermore, additional results involving entropy generation rate have been presented and discussed. Contribution to the topical issue "Materials for Energy harvesting, conversion and storage II (ICOME 2016)", edited by Jean-Michel Nunzi, Rachid Bennacer and Mohammed El Ganaoui

Investigation of an Optimum Detection Scheme for a Star-Field Mapping System

NASA Technical Reports Server (NTRS)

Aldridge, M. D.; Credeur, L.

1970-01-01

An investigation was made to determine the optimum detection scheme for a star-field mapping system that uses coded detection resulting from starlight shining through specially arranged multiple slits of a reticle. The computer solution of equations derived from a theoretical model showed that the greatest probability of detection for a given star and background intensity occurred with the use of a single transparent slit. However, use of multiple slits improved the system's ability to reject the detection of undesirable lower intensity stars, but only by decreasing the probability of detection for lower intensity stars to be mapped. Also, it was found that the coding arrangement affected the root-mean-square star-position error and that detection is possible with error in the system's detected spin rate, though at a reduced probability.

Gas Flux and Density Surrounding a Cylindrical Aperture in the Free Molecular Flow Regime

NASA Technical Reports Server (NTRS)

Soulas, George C.

2011-01-01

The equations for rigorously calculating the particle flux and density surrounding a cylindrical aperture in the free molecular flow regime are developed and presented. The fundamental equations for particle flux and density from a reservoir and a diffusely reflecting surface will initially be developed. Assumptions will include a Maxwell-Boltzmann speed distribution, equal particle and wall temperatures, and a linear flux distribution along the cylindrical aperture walls. With this information, the equations for axial flux and density surrounding a cylindrical aperture will be developed. The cylindrical aperture will be divided into multiple volumes and regions to rigorously determine the surrounding axial flux and density, and appropriate limits of integration will be determined. The results of these equations will then be evaluated. The linear wall flux distribution assumption will be assessed. The axial flux and density surrounding a cylindrical aperture with a thickness-to-radius ratio of 1.25 will be presented. Finally, the equations determined in this study will be verified using multiple methods.

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

NASA Astrophysics Data System (ADS)

Frank, T. D.

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

Glomerular Filtration Rate in Patients with Multiple Sclerosis Undergoing Stem Cell Transplantation and Treated With Cyclophosphamide.

PubMed

Ruiz-Argüelles, Alejandro; Gastélum-Cano, Jose M; Méndez-Huerta, Mariana A; Rodríguez-Gallegos, Alma B; Ruiz-Argüelles, Guillermo J

2018-06-15

Glomerular filtration rate (GFR) is partially impaired in patients with multiple sclerosis (MS). When given chemotherapy before receiving hematopoietic stem-cell transplantation, GFR might be further deteriorated. To measure the effect of cyclophosphamide on GFR in patients with MS who undergo chemotherapy. We estimated GFR based on creatinine and cystatin C plasma concentrations in patients undergoing autologous hematopoietic stem-cell transplantation to treat their MS. Baseline GFR values were lower in the 28 patients with MS than in the 20 healthy individuals. Also, according to the Chronic Kidney Disease-Epidemiology Collaborative Group (CKD-EPI) 2012 Creat-CysC equation criteria, 4 of 28 patients were classified as having chronic kidney disease (CKD) before receiving the chemotherapy drugs. After receiving 4 × 50 mg per kg body weight cyclophosphamide, abnormal GFR results were recorded in 12 of 28 patients. Renal function must be monitored in patients with MS undergoing autologous stem-cell transplantation. Also, chemotherapy should be constrained as much as possible to prevent further deterioration of renal function.

Phase-plane analysis of the totally asymmetric simple exclusion process with binding kinetics and switching between antiparallel lanes

PubMed Central

Kuan, Hui-Shun; Betterton, Meredith D.

2016-01-01

Motor protein motion on biopolymers can be described by models related to the totally asymmetric simple exclusion process (TASEP). Inspired by experiments on the motion of kinesin-4 motors on antiparallel microtubule overlaps, we analyze a model incorporating the TASEP on two antiparallel lanes with binding kinetics and lane switching. We determine the steady-state motor density profiles using phase-plane analysis of the steady-state mean field equations and kinetic Monte Carlo simulations. We focus on the density-density phase plane, where we find an analytic solution to the mean field model. By studying the phase-space flows, we determine the model’s fixed points and their changes with parameters. Phases previously identified for the single-lane model occur for low switching rate between lanes. We predict a multiple coexistence phase due to additional fixed points that appear as the switching rate increases: switching moves motors from the higher-density to the lower-density lane, causing local jamming and creating multiple domain walls. We determine the phase diagram of the model for both symmetric and general boundary conditions. PMID:27627345

Effect of Coffee and Caffeine Ingestion on Resistance Exercise Performance.

PubMed

Richardson, Darren L; Clarke, Neil D

2016-10-01

Richardson, DL and Clarke, ND. Effect of coffee and caffeine ingestion on resistance exercise performance. J Strength Cond Res 30(10): 2892-2900, 2016-The aim of the present study was to determine the effect of ingesting caffeine dose-matched anhydrous caffeine, coffee, or decaffeinated coffee plus anhydrous caffeine during resistance exercise on performance. Nine resistance-trained men (mean ± SD: age, 24 ± 2 years; weight, 84 ± 8 kg; height, 180 ± 8 cm) completed a squat and bench press exercise protocol at 60% 1 repetition maximum until failure on 5 occasions consuming 0.15 g·kg caffeinated coffee (COF), 0.15 g·kg decaffeinated coffee (DEC), 0.15 g·kg decaffeinated coffee plus 5 mg·kg anhydrous caffeine (D + C), 5 mg·kg anhydrous caffeine (CAF), or a placebo (PLA). Felt arousal and rating of perceived exertion (RPE) were used to assess perceptual variables and heart rate (HR) to assess physiological responses between trials. There were significant differences in total weight lifted for the squat between conditions (p < 0.01; (Equation is included in full-text article.)= 0.54) with a greater amount lifted during D + C compared with DEC (p < 0.01), CAF (p ≤ 0.05), and PLA (p ≤ 0.05) conditions. Total weight lifted during the COF condition was significantly greater than that lifted under PLA (p < 0.01), although not significantly greater than the amount of weight lifted during the DEC condition (p = 0.082). No significant differences were observed in total weight lifted in the bench press protocol between conditions (p = 0.186; (Equation is included in full-text article.)= 0.17). Significant differences in HR (p < 0.01; (Equation is included in full-text article.)= 0.39) but not RPE (squat: p = 0.690; (Equation is included in full-text article.)= 0.07; bench press: p = 0.165; (Equation is included in full-text article.)= 0.18) and felt arousal (p = 0.056; (Equation is included in full-text article.)= 0.24) were observed between conditions. Coffee and decaffeinated coffee plus caffeine have the ability to improve performance during a resistance exercise protocol, although possibly not over multiple bouts.

Validating and Improving Interrill Erosion Equations

PubMed Central

Zhang, Feng-Bao; Wang, Zhan-Li; Yang, Ming-Yi

2014-01-01

Existing interrill erosion equations based on mini-plot experiments have largely ignored the effects of slope length and plot size on interrill erosion rate. This paper describes a series of simulated rainfall experiments which were conducted according to a randomized factorial design for five slope lengths (0.4, 0.8, 1.2, 1.6, and 2 m) at a width of 0.4 m, five slope gradients (17%, 27%, 36%, 47%, and 58%), and five rainfall intensities (48, 62.4, 102, 149, and 170 mm h−1) to perform a systematic validation of existing interrill erosion equations based on mini-plots. The results indicated that the existing interrill erosion equations do not adequately describe the relationships between interrill erosion rate and its influencing factors with increasing slope length and rainfall intensity. Univariate analysis of variance showed that runoff rate, rainfall intensity, slope gradient, and slope length had significant effects on interrill erosion rate and that their interactions were significant at p = 0.01. An improved interrill erosion equation was constructed by analyzing the relationships of sediment concentration with rainfall intensity, slope length, and slope gradient. In the improved interrill erosion equation, the runoff rate and slope factor are the same as in the interrill erosion equation in the Water Erosion Prediction Project (WEPP), with the weight of rainfall intensity adjusted by an exponent of 0.22 and a slope length term added with an exponent of −0.25. Using experimental data from WEPP cropland soil field interrill erodibility experiments, it has been shown that the improved interrill erosion equation describes the relationship between interrill erosion rate and runoff rate, rainfall intensity, slope gradient, and slope length reasonably well and better than existing interrill erosion equations. PMID:24516624

Observations of discrete magnetosonic waves off the magnetic equator

DOE PAGES

Zhima, Zeren; Chen, Lunjin; Fu, Huishan; ...

2015-11-23

Fast mode magnetosonic waves are typically confined close to the magnetic equator and exhibit harmonic structures at multiples of the local, equatorial proton cyclotron frequency. Here, we report observations of magnetosonic waves well off the equator at geomagnetic latitudes from -16.5°to -17.9° and L shell ~2.7–4.6. The observed waves exhibit discrete spectral structures with multiple frequency spacings. The predominant frequency spacings are ~6 and 9 Hz, neither of which is equal to the local proton cyclotron frequency. Backward ray tracing simulations show that the feature of multiple frequency spacings is caused by propagation from two spatially narrow equatorial source regionsmore » located at L ≈ 4.2 and 3.7. The equatorial proton cyclotron frequencies at those two locations match the two observed frequency spacings. Finally, our analysis provides the first observations of the harmonic nature of magnetosonic waves well away from the equatorial region and suggests that the propagation from multiple equatorial sources contributes to these off-equatorial magnetosonic emissions with varying frequency spacings.« less

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.

General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures.

PubMed

Liu, Yen; Panesi, Marco; Sahai, Amal; Vinokur, Marcel

2015-04-07

This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model's accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy relaxation model, which can only be applied to molecules, the new model is applicable to atoms, molecules, ions, and their mixtures. Numerical examples and model validations are carried out with two gas mixtures using the maximum entropy linear model: one mixture consists of nitrogen molecules undergoing internal excitation and dissociation and the other consists of nitrogen atoms undergoing internal excitation and ionization. Results show that the original hundreds to thousands of microscopic equations can be reduced to two macroscopic equations with almost perfect agreement for the total number density and total internal energy using only one or two groups. We also obtain good prediction of the microscopic state populations using 5-10 groups in the macroscopic equations.

General Model for Multicomponent Ablation Thermochemistry

NASA Technical Reports Server (NTRS)

Milos, Frank S.; Marschall, Jochen; Rasky, Daniel J. (Technical Monitor)

1994-01-01

A previous paper (AIAA 94-2042) presented equations and numerical procedures for modeling the thermochemical ablation and pyrolysis of thermal protection materials which contain multiple surface species. This work describes modifications and enhancements to the Multicomponent Ablation Thermochemistry (MAT) theory and code for application to the general case which includes surface area constraints, rate limited surface reactions, and non-thermochemical mass loss (failure). Detailed results and comparisons with data are presented for the Shuttle Orbiter reinforced carbon-carbon oxidation protection system which contains a mixture of sodium silicate (Na2SiO3), silica (SiO2), silicon carbide (SiC), and carbon (C).

Brownian motion of classical spins: Anomalous dissipation and generalized Langevin equation

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Malay; Jayannavar, A. M.

2017-10-01

In this work, we derive the Langevin equation (LE) of a classical spin interacting with a heat bath through momentum variables, starting from the fully dynamical Hamiltonian description. The derived LE with anomalous dissipation is analyzed in detail. The obtained LE is non-Markovian with multiplicative noise terms. The concomitant dissipative terms obey the fluctuation-dissipation theorem. The Markovian limit correctly produces the Kubo and Hashitsume equation. The perturbative treatment of our equations produces the Landau-Lifshitz equation and the Seshadri-Lindenberg equation. Then we derive the Fokker-Planck equation corresponding to LE and the concept of equilibrium probability distribution is analyzed.

Delivery of prazosin hydrochloride from osmotic pump system prepared by coating the core tablet with an indentation.

PubMed

Liu, Longxiao; Wang, Jinchao; Zhu, Suyan

2007-04-01

The preparation of an osmotic pump tablet was simplified by elimination of laser drilling using prazosin hydrochloride as the model drug. The osmotic pump system was obtained by coating the indented core tablet compressed by the punch with a needle. A multiple regression equation was achieved with the experimental data of core tablet formulations, and then the formulation was optimized. The influences of the indentation size of the core tablet, environmental media, and agitation rate on drug release profile were investigated. The optimal osmotic pump tablet was found to deliver prazosin hydrochloride at an approximately constant rate up to 24 hr, and independent on both release media and agitation rate. Indentation size of core tablet hardly affected drug release in the range of 0.80-1.15 mm. The method that is simplified by elimination of laser drilling may be promising for preparation of an osmotic pump tablet.

Asymptotic behavior for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions

NASA Astrophysics Data System (ADS)

Katayama, Soichiro

We consider the Cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions. Under the null condition for such systems, the global existence of small amplitude solutions is known. In this paper, we will show that the global solution is asymptotically free in the energy sense, by obtaining the asymptotic pointwise behavior of the derivatives of the solution. Nonetheless we can also show that the pointwise behavior of the solution itself may be quite different from that of the free solution. In connection with the above results, a theorem is also developed to characterize asymptotically free solutions for wave equations in arbitrary space dimensions.

A regression technique for evaluation and quantification for water quality parameters from remote sensing data

NASA Technical Reports Server (NTRS)

Whitlock, C. H.; Kuo, C. Y.

1979-01-01

The objective of this paper is to define optical physics and/or environmental conditions under which the linear multiple-regression should be applicable. An investigation of the signal-response equations is conducted and the concept is tested by application to actual remote sensing data from a laboratory experiment performed under controlled conditions. Investigation of the signal-response equations shows that the exact solution for a number of optical physics conditions is of the same form as a linearized multiple-regression equation, even if nonlinear contributions from surface reflections, atmospheric constituents, or other water pollutants are included. Limitations on achieving this type of solution are defined.

Numerical evidences for the angular momentum-mass inequality for multiple axially symmetric black holes

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

Dain, Sergio; Ortiz, Omar E.; Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba, Ciudad Universitaria

2009-07-15

We present numerical evidences for the validity of the inequality between the total mass and the total angular momentum for multiple axially symmetric (nonstationary) black holes. We use a parabolic heat flow to solve numerically the stationary axially symmetric Einstein equations. As a by-product of our method, we also give numerical evidences that there are no regular solutions of Einstein equations that describe two extreme, axially symmetric black holes in equilibrium.

Cable logging production rate equations for thinning young-growth Douglas-fir

Treesearch

Chris B. LeDoux; Lawson W. Starnes

1986-01-01

A cable logging thinning simulation model and field study data from cable thinning production studies have been assembled and converted into a set of simple equations. These equations can be used to estimate the hourly production rates of various cable thinning machines operating in the mountainous terrain of western Oregon and western Washington. The equations include...

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…

Stochastic population dynamics in spatially extended predator-prey systems

NASA Astrophysics Data System (ADS)

Dobramysl, Ulrich; Mobilia, Mauro; Pleimling, Michel; Täuber, Uwe C.

2018-02-01

Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting many-particle systems beyond rate equation approximations. Including spatial structure and stochastic noise in models for predator-prey competition invalidates the neutral Lotka-Volterra population cycles. Stochastic models yield long-lived erratic oscillations stemming from a resonant amplification mechanism. Spatially extended predator-prey systems display noise-stabilized activity fronts that generate persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively via a Doi-Peliti field theory mapping of the master equation; related tools allow detailed characterization of extinction pathways. The critical steady-state and non-equilibrium relaxation dynamics at the predator extinction threshold are governed by the directed percolation universality class. Spatial predation rate variability results in more localized clusters, enhancing both competing species’ population densities. Affixing variable interaction rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of three-species competition with ‘rock-paper-scissors’ interactions metaphorically describe cyclic dominance. These models illustrate intimate connections between population dynamics and evolutionary game theory, underscore the role of fluctuations to drive populations toward extinction, and demonstrate how space can support species diversity. Two-dimensional cyclic three-species May-Leonard models are characterized by the emergence of spiraling patterns whose properties are elucidated by a mapping onto a complex Ginzburg-Landau equation. Multiple-species extensions to general ‘food networks’ can be classified on the mean-field level, providing both fundamental understanding of ensuing cooperativity and profound insight into the rich spatio-temporal features and coarsening kinetics in the corresponding spatially extended systems. Novel space-time patterns emerge as a result of the formation of competing alliances; e.g. coarsening domains that each incorporate rock-paper-scissors competition games.

Hydrodynamic Limit of Multiple SLE

NASA Astrophysics Data System (ADS)

Hotta, Ikkei; Katori, Makoto

2018-04-01

Recently del Monaco and Schleißinger addressed an interesting problem whether one can take the limit of multiple Schramm-Loewner evolution (SLE) as the number of slits N goes to infinity. When the N slits grow from points on the real line R in a simultaneous way and go to infinity within the upper half plane H, an ordinary differential equation describing time evolution of the conformal map g_t(z) was derived in the N → ∞ limit, which is coupled with a complex Burgers equation in the inviscid limit. It is well known that the complex Burgers equation governs the hydrodynamic limit of the Dyson model defined on R studied in random matrix theory, and when all particles start from the origin, the solution of this Burgers equation is given by the Stieltjes transformation of the measure which follows a time-dependent version of Wigner's semicircle law. In the present paper, first we study the hydrodynamic limit of the multiple SLE in the case that all slits start from the origin. We show that the time-dependent version of Wigner's semicircle law determines the time evolution of the SLE hull, K_t \\subset H\\cup R, in this hydrodynamic limit. Next we consider the situation such that a half number of the slits start from a>0 and another half of slits start from -a < 0, and determine the multiple SLE in the hydrodynamic limit. After reporting these exact solutions, we will discuss the universal long-term behavior of the multiple SLE and its hull K_t in the hydrodynamic limit.

Poisson Statistics of Combinatorial Library Sampling Predict False Discovery Rates of Screening

PubMed Central

2017-01-01

Microfluidic droplet-based screening of DNA-encoded one-bead-one-compound combinatorial libraries is a miniaturized, potentially widely distributable approach to small molecule discovery. In these screens, a microfluidic circuit distributes library beads into droplets of activity assay reagent, photochemically cleaves the compound from the bead, then incubates and sorts the droplets based on assay result for subsequent DNA sequencing-based hit compound structure elucidation. Pilot experimental studies revealed that Poisson statistics describe nearly all aspects of such screens, prompting the development of simulations to understand system behavior. Monte Carlo screening simulation data showed that increasing mean library sampling (ε), mean droplet occupancy, or library hit rate all increase the false discovery rate (FDR). Compounds identified as hits on k > 1 beads (the replicate k class) were much more likely to be authentic hits than singletons (k = 1), in agreement with previous findings. Here, we explain this observation by deriving an equation for authenticity, which reduces to the product of a library sampling bias term (exponential in k) and a sampling saturation term (exponential in ε) setting a threshold that the k-dependent bias must overcome. The equation thus quantitatively describes why each hit structure’s FDR is based on its k class, and further predicts the feasibility of intentionally populating droplets with multiple library beads, assaying the micromixtures for function, and identifying the active members by statistical deconvolution. PMID:28682059

Cocirculation of infectious diseases on networks

NASA Astrophysics Data System (ADS)

Miller, Joel C.

2013-06-01

We consider multiple diseases spreading in a static configuration model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a disease-specific rate. Infection by one disease confers immediate and permanent immunity to infection by any disease. Under these assumptions, we find a simple, low-dimensional ordinary differential equations model which captures the global dynamics of the infection. The dynamics depend strongly on initial conditions. Although we motivate this Rapid Communication with infectious disease, the model may be adapted to the spread of other infectious agents such as competing political beliefs, or adoption of new technologies if these are influenced by contacts. As an example, we demonstrate how to model an infectious disease which can be prevented by a behavior change.

Implementing statistical equating for MRCP(UK) Parts 1 and 2.

PubMed

McManus, I C; Chis, Liliana; Fox, Ray; Waller, Derek; Tang, Peter

2014-09-26

The MRCP(UK) exam, in 2008 and 2010, changed the standard-setting of its Part 1 and Part 2 examinations from a hybrid Angoff/Hofstee method to statistical equating using Item Response Theory, the reference group being UK graduates. The present paper considers the implementation of the change, the question of whether the pass rate increased amongst non-UK candidates, any possible role of Differential Item Functioning (DIF), and changes in examination predictive validity after the change. Analysis of data of MRCP(UK) Part 1 exam from 2003 to 2013 and Part 2 exam from 2005 to 2013. Inspection suggested that Part 1 pass rates were stable after the introduction of statistical equating, but showed greater annual variation probably due to stronger candidates taking the examination earlier. Pass rates seemed to have increased in non-UK graduates after equating was introduced, but was not associated with any changes in DIF after statistical equating. Statistical modelling of the pass rates for non-UK graduates found that pass rates, in both Part 1 and Part 2, were increasing year on year, with the changes probably beginning before the introduction of equating. The predictive validity of Part 1 for Part 2 was higher with statistical equating than with the previous hybrid Angoff/Hofstee method, confirming the utility of IRT-based statistical equating. Statistical equating was successfully introduced into the MRCP(UK) Part 1 and Part 2 written examinations, resulting in higher predictive validity than the previous Angoff/Hofstee standard setting. Concerns about an artefactual increase in pass rates for non-UK candidates after equating were shown not to be well-founded. Most likely the changes resulted from a genuine increase in candidate ability, albeit for reasons which remain unclear, coupled with a cognitive illusion giving the impression of a step-change immediately after equating began. Statistical equating provides a robust standard-setting method, with a better theoretical foundation than judgemental techniques such as Angoff, and is more straightforward and requires far less examiner time to provide a more valid result. The present study provides a detailed case study of introducing statistical equating, and issues which may need to be considered with its introduction.

Seismic reflection imaging, accounting for primary and multiple reflections

NASA Astrophysics Data System (ADS)

Wapenaar, Kees; van der Neut, Joost; Thorbecke, Jan; Broggini, Filippo; Slob, Evert; Snieder, Roel

2015-04-01

Imaging of seismic reflection data is usually based on the assumption that the seismic response consists of primary reflections only. Multiple reflections, i.e. waves that have reflected more than once, are treated as primaries and are imaged at wrong positions. There are two classes of multiple reflections, which we will call surface-related multiples and internal multiples. Surface-related multiples are those multiples that contain at least one reflection at the earth's surface, whereas internal multiples consist of waves that have reflected only at subsurface interfaces. Surface-related multiples are the strongest, but also relatively easy to deal with because the reflecting boundary (the earth's surface) is known. Internal multiples constitute a much more difficult problem for seismic imaging, because the positions and properties of the reflecting interfaces are not known. We are developing reflection imaging methodology which deals with internal multiples. Starting with the Marchenko equation for 1D inverse scattering problems, we derived 3D Marchenko-type equations, which relate reflection data at the surface to Green's functions between virtual sources anywhere in the subsurface and receivers at the surface. Based on these equations, we derived an iterative scheme by which these Green's functions can be retrieved from the reflection data at the surface. This iterative scheme requires an estimate of the direct wave of the Green's functions in a background medium. Note that this is precisely the same information that is also required by standard reflection imaging schemes. However, unlike in standard imaging, our iterative Marchenko scheme retrieves the multiple reflections of the Green's functions from the reflection data at the surface. For this, no knowledge of the positions and properties of the reflecting interfaces is required. Once the full Green's functions are retrieved, reflection imaging can be carried out by which the primaries and multiples are mapped to their correct positions, with correct reflection amplitudes. In the presentation we will illustrate this new methodology with numerical examples and discuss its potential and limitations.

Cross-validation of resting metabolic rate prediction equations

USDA-ARS?s Scientific Manuscript database

Background: Knowledge of the resting metabolic rate (RMR) is necessary for determining individual total energy requirements. Measurement of RMR is time consuming and requires specialized equipment. Prediction equations provide an easy method to estimate RMR; however, the accuracy of these equations...

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

Ghafarian, M.; Ariaei, A., E-mail: ariaei@eng.ui.ac.ir

The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique tomore » solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube-beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results.« less

Monitoring heavy metal Cr in soil based on hyperspectral data using regression analysis

NASA Astrophysics Data System (ADS)

Zhang, Ningyu; Xu, Fuyun; Zhuang, Shidong; He, Changwei

2016-10-01

Heavy metal pollution in soils is one of the most critical problems in the global ecology and environment safety nowadays. Hyperspectral remote sensing and its application is capable of high speed, low cost, less risk and less damage, and provides a good method for detecting heavy metals in soil. This paper proposed a new idea of applying regression analysis of stepwise multiple regression between the spectral data and monitoring the amount of heavy metal Cr by sample points in soil for environmental protection. In the measurement, a FieldSpec HandHeld spectroradiometer is used to collect reflectance spectra of sample points over the wavelength range of 325-1075 nm. Then the spectral data measured by the spectroradiometer is preprocessed to reduced the influence of the external factors, and the preprocessed methods include first-order differential equation, second-order differential equation and continuum removal method. The algorithms of stepwise multiple regression are established accordingly, and the accuracy of each equation is tested. The results showed that the accuracy of first-order differential equation works best, which makes it feasible to predict the content of heavy metal Cr by using stepwise multiple regression.

Beyond the Mincer Equation: The Internal Rate of Return to Higher Education in Colombia

ERIC Educational Resources Information Center

García-Suaza, Andrés Felipe; Guataquí, Juan Carlos; Guerra, José Alberto; Maldonado, Darío

2014-01-01

In order to present an estimation of the internal rate of return (IRR) to higher education in Colombia, we take advantage of recent updates on the methodological approach towards earnings equations. In order to overcome the criticism that surrounds interpretations of the education coefficient of Mincer equations as being the rate of return to…

The Dissipation Rate Transport Equation and Subgrid-Scale Models in Rotating Turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Ye, Zhou

1997-01-01

The dissipation rate transport equation remains the most uncertain part of turbulence modeling. The difficulties arc increased when external agencies like rotation prevent straightforward dimensional analysis from determining the correct form of the modelled equation. In this work, the dissipation rate transport equation and subgrid scale models for rotating turbulence are derived from an analytical statistical theory of rotating turbulence. In the strong rotation limit, the theory predicts a turbulent steady state in which the inertial range energy spectrum scales as k(sup -2) and the turbulent time scale is the inverse rotation rate. This scaling has been derived previously by heuristic arguments.

The rate dependent response of a bistable chain at finite temperature

NASA Astrophysics Data System (ADS)

Benichou, Itamar; Zhang, Yaojun; Dudko, Olga K.; Givli, Sefi

2016-10-01

We study the rate dependent response of a bistable chain subjected to thermal fluctuations. The study is motivated by the fact that the behavior of this model system is prototypical to a wide range of nonlinear processes in materials physics, biology and chemistry. To account for the stochastic nature of the system response, we formulate a set of governing equations for the evolution of the probability density of meta-stable configurations. Based on this approach, we calculate the behavior for a wide range of parametric values, such as rate, temperature, overall stiffness, and number of elements in the chain. Our results suggest that fundamental characteristics of the response, such as average transition stress and hysteresis, can be captured by a simple law which folds the influence of all these factors into a single non-dimensional quantity. We also show that the applicability of analytical results previously obtained for single-well systems can be extended to systems having multiple wells by proper definition of rate and of the transition stress.

New equations improve NIR prediction of body fat among high school wrestlers.

PubMed

Oppliger, R A; Clark, R R; Nielsen, D H

2000-09-01

Methodologic study to derive prediction equations for percent body fat (%BF). To develop valid regression equations using NIR to assess body composition among high school wrestlers. Clinicians need a portable, fast, and simple field method for assessing body composition among wrestlers. Near-infrared photospectrometry (NIR) meets these criteria, but its efficacy has been challenged. Subjects were 150 high school wrestlers from 2 Midwestern states with mean +/- SD age of 16.3 +/- 1.1 yrs, weight of 69.5 +/- 11.7 kg, and height of 174.4 +/- 7.0 cm. Relative body fatness (%BF) determined from hydrostatic weighing was the criterion measure, and NIR optical density (OD) measurements at multiple sites, plus height, weight, and body mass index (BMI) were the predictor variables. Four equations were developed with multiple R2s that varied from .530 to .693, root mean squared errors varied from 2.8% BF to 3.4% BF, and prediction errors varied from 2.9% BF to 3.1% BF. The best equation used OD measurements at the biceps, triceps, and thigh sites, BMI, and age. The root mean squared error and prediction error for all 4 equations were equal to or smaller than for a skinfold equation commonly used with wrestlers. The results substantiate the validity of NIR for predicting % BF among high school wrestlers. Cross-validation of these equations is warranted.

Synthesis, Characterization, and Sensitivity Analysis of Urea Nitrate (UN)

DTIC Science & Technology

2015-04-01

of the line is the rate of the reaction for the corresponding temperature. The equations for the zero order reaction and half- life equation follow...rate law (k is rate constant; [A] is the concentration of UN) Rate = k[A]n . (1) Eq. 2 shows the half-life (t½) equation for a zero order reaction...MGMT 1 GOVT PRINTG OFC (PDF) A MALHOTRA 2 WEAPONS DEV & (PDF) INTEGRATION DIRCTRT AMRDEC RDMR WDN J NEIDERT G DRAKE

A covariant multiple scattering series for elastic projectile-target scattering

NASA Technical Reports Server (NTRS)

Gross, Franz; Maung-Maung, Khin

1989-01-01

A covariant formulation of the multiple scattering series for the optical potential is presented. The case of a scalar nucleon interacting with a spin zero isospin zero A-body target through meson exchange, is considered. It is shown that a covariant equation for the projectile-target t-matrix can be obtained which sums the ladder and crossed ladder diagrams efficiently. From this equation, a multiple scattering series for the optical potential is derived, and it is shown that in the impulse approximation, the two-body t-matrix associated with the first order optical potential is the one in which one particle is kept on mass-shell. The meaning of various terms in the multiple scattering series is given. The construction of the first-order optical potential for elastic scattering calculations is described.

Multiple-generator errors are unavoidable under model misspecification.

PubMed

Jewett, D L; Zhang, Z

1995-08-01

Model misspecification poses a major problem for dipole source localization (DSL) because it causes insidious multiple-generator errors (MulGenErrs) to occur in the fitted dipole parameters. This paper describes how and why this occurs, based upon simple algebraic considerations. MulGenErrs must occur, to some degree, in any DSL analysis of real data because there is model misspecification and mathematically the equations used for the simultaneously active generators must be of a different form than the equations for each generator active alone.

A numerical solution of Duffing's equations including the prediction of jump phenomena

NASA Technical Reports Server (NTRS)

Moyer, E. T., Jr.; Ghasghai-Abdi, E.

1987-01-01

Numerical methodology for the solution of Duffing's differential equation is presented. Algorithms for the prediction of multiple equilibrium solutions and jump phenomena are developed. In addition, a filtering algorithm for producing steady state solutions is presented. The problem of a rigidly clamped circular plate subjected to cosinusoidal pressure loading is solved using the developed algorithms (the plate is assumed to be in the geometrically nonlinear range). The results accurately predict regions of solution multiplicity and jump phenomena.

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.

The Interplay of School Readiness and Teacher Readiness for Educational Technology Integration: A Structural Equation Model

ERIC Educational Resources Information Center

Petko, Dominik; Prasse, Doreen; Cantieni, Andrea

2018-01-01

Decades of research have shown that technological change in schools depends on multiple interrelated factors. Structural equation models explaining the interplay of factors often suffer from high complexity and low coherence. To reduce complexity, a more robust structural equation model was built with data from a survey of 349 Swiss primary school…

Microscopic Simulation and Macroscopic Modeling for Thermal and Chemical Non-Equilibrium

NASA Technical Reports Server (NTRS)

Liu, Yen; Panesi, Marco; Vinokur, Marcel; Clarke, Peter

2013-01-01

This paper deals with the accurate microscopic simulation and macroscopic modeling of extreme non-equilibrium phenomena, such as encountered during hypersonic entry into a planetary atmosphere. The state-to-state microscopic equations involving internal excitation, de-excitation, dissociation, and recombination of nitrogen molecules due to collisions with nitrogen atoms are solved time-accurately. Strategies to increase the numerical efficiency are discussed. The problem is then modeled using a few macroscopic variables. The model is based on reconstructions of the state distribution function using the maximum entropy principle. The internal energy space is subdivided into multiple groups in order to better describe the non-equilibrium gases. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients. The modeling is completely physics-based, and its accuracy depends only on the assumed expression of the state distribution function and the number of groups used. The model makes no assumption at the microscopic level, and all possible collisional and radiative processes are allowed. The model is applicable to both atoms and molecules and their ions. Several limiting cases are presented to show that the model recovers the classical twotemperature models if all states are in one group and the model reduces to the microscopic equations if each group contains only one state. Numerical examples and model validations are carried out for both the uniform and linear distributions. Results show that the original over nine thousand microscopic equations can be reduced to 2 macroscopic equations using 1 to 5 groups with excellent agreement. The computer time is decreased from 18 hours to less than 1 second.

Novel Filtration Markers for GFR Estimation

PubMed Central

Inker, Lesley A.; Coresh, Josef; Levey, Andrew S.; Eckfeldt, John H.

2017-01-01

Creatinine-based glomerular filtration rate estimation (eGFRcr) has been improved and refined since the 1970s through both the Modification of Diet in Renal Disease (MDRD) Study equation in 1999 and the CKD Epidemiology Collaboration (CKD-EPI) equation in 2009, with current clinical practice dependent primarily on eGFR for accurate assessment of GFR. However, researchers and clinicians have recognized limitations of relying on creatinine as the only filtration marker, which can lead to inaccurate GFR estimates in certain populations due to the influence of non-GFR determinants of serum or plasma creatinine. Therefore, recent literature has proposed incorporation of multiple serum or plasma filtration markers into GFR estimation to improve precision and accuracy and decrease the impact of non-GFR determinants for any individual biomarker. To this end, the CKD-EPI combined creatinine-cystatin C equation (eGFRcr-cys) was developed in 2012 and demonstrated superior accuracy to equations relying on creatinine or cystatin C alone (eGFRcr or eGFRcys). Now, the focus has broadened to include additional novel filtration markers to further refine and improve GFR estimation. Beta-2-microglobulin (B2M) and beta-trace-protein (BTP) are two filtration markers with established assays that have been proposed as candidates for improving both GFR estimation and risk prediction. GFR estimating equations based on B2M and BTP have been developed and validated, with the CKD-EPI combined BTP-B2M equation (eGFRBTP-B2M) demonstrating similar performance to eGFR and eGFR. Additionally, several studies have demonstrated that both B2M and BTP are associated with outcomes in CKD patients, including cardiovascular events, ESRD and mortality. This review will primarily focus on these two biomarkers, and will highlight efforts to identify additional candidate biomarkers through metabolomics-based approaches. PMID:29333147

BDflex: A method for efficient treatment of molecular flexibility in calculating protein-ligand binding rate constants from Brownian dynamics simulations

PubMed Central

Greives, Nicholas; Zhou, Huan-Xiang

2012-01-01

A method developed by Northrup [J. Chem. Phys. 80, 1517 (1984)]10.1063/1.446900 for calculating protein-ligand binding rate constants (ka) from Brownian dynamics (BD) simulations has been widely used for rigid molecules. Application to flexible molecules is limited by the formidable computational cost to treat conformational fluctuations during the long BD simulations necessary for ka calculation. Here, we propose a new method called BDflex for ka calculation that circumvents this problem. The basic idea is to separate the whole space into an outer region and an inner region, and formulate ka as the product of kE and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}\\bar \\eta _{\\rm d}\\end{equation*} \\end{document}η¯d, which are obtained by separately solving exterior and interior problems. kE is the diffusion-controlled rate constant for the ligand in the outer region to reach the dividing surface between the outer and inner regions; in this exterior problem conformational fluctuations can be neglected. \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}\\bar \\eta _{\\rm d}\\end{equation*} \\end{document}η¯d is the probability that the ligand, starting from the dividing surface, will react at the binding site rather than escape to infinity. The crucial step in reducing the determination of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}\\bar \\eta _{\\rm d}\\end{equation*} \\end{document}η¯d to a problem confined to the inner region is a radiation boundary condition imposed on the dividing surface; the reactivity on this boundary is proportional to kE. By confining the ligand to the inner region and imposing the radiation boundary condition, we avoid multiple-crossing of the dividing surface before reaction at the binding site and hence dramatically cut down the total simulation time, making the treatment of conformational fluctuations affordable. BDflex is expected to have wide applications in problems where conformational fluctuations of the molecules are crucial for productive ligand binding, such as in cases where transient widening of a bottleneck allows the ligand to access the binding pocket, or the binding site is properly formed only after ligand entrance induces the closure of a lid. PMID:23039617

Stability of stationary inverse transport equation in diffusion scaling

NASA Astrophysics Data System (ADS)

Chen, Ke; Li, Qin; Wang, Li

2018-02-01

We consider the inverse problem of reconstructing the optical parameters for the stationary radiative transfer equation (RTE) from velocity-averaged measurement. The RTE often contains multiple scales, characterized by the magnitude of a dimensionless parameter—the Knudsen number ( \

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.

PubMed

Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio

2014-10-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations

PubMed Central

Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio

2014-01-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530

Glass dissolution as a function of pH and its implications for understanding mechanisms and future experiments

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

Strachan, Denis

For years, we have been using a certain form of the glass dissolution rate equation. In this article, I examine the assumptions that have been made and suggest that the rate equation may be more complex than originally thought. Suggestions of experiments that are needed to correct or validate the exisiting form of the rate equation are made.

Exact and Approximate Solutions for the Decades-Old Michaelis-Menten Equation: Progress-Curve Analysis through Integrated Rate Equations

ERIC Educational Resources Information Center

Golicnik, Marko

2011-01-01

The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate "V", and the Michaelis constant "K"[subscript M]) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to…

A relativistic dissipative hydrodynamic description for systems including particle number changing processes

NASA Astrophysics Data System (ADS)

El, Andrej; Muronga, Azwinndini; Xu, Zhe; Greiner, Carsten

2010-12-01

Relativistic dissipative hydrodynamic equations are extended by taking into account particle number changing processes in a gluon system, which expands in one dimension boost-invariantly. Chemical equilibration is treated by a rate equation for the particle number density based on Boltzmann equation and Grad's ansatz for the off-equilibrium particle phase space distribution. We find that not only the particle production, but also the temperature and the momentum spectra of the gluon system, obtained from the hydrodynamic calculations, are sensitive to the rates of particle number changing processes. Comparisons of the hydrodynamic calculations with the transport ones employing the parton cascade BAMPS show the inaccuracy of the rate equation at large shear viscosity to entropy density ratio. To improve the rate equation, Grad's ansatz has to be modified beyond the second moments in momentum.

A Simultaneous Equation Demand Model for Block Rates

NASA Astrophysics Data System (ADS)

Agthe, Donald E.; Billings, R. Bruce; Dobra, John L.; Raffiee, Kambiz

1986-01-01

This paper examines the problem of simultaneous-equations bias in estimation of the water demand function under an increasing block rate structure. The Hausman specification test is used to detect the presence of simultaneous-equations bias arising from correlation of the price measures with the regression error term in the results of a previously published study of water demand in Tucson, Arizona. An alternative simultaneous equation model is proposed for estimating the elasticity of demand in the presence of block rate pricing structures and availability of service charges. This model is used to reestimate the price and rate premium elasticities of demand in Tucson, Arizona for both the usual long-run static model and for a simple short-run demand model. The results from these simultaneous equation models are consistent with a priori expectations and are unbiased.

A Biochemist's View of Ecosystem Rates and their Response to Changing Temperature

NASA Astrophysics Data System (ADS)

Arcus, V. L.

2017-12-01

Enzyme kinetics lie at the heart of biochemistry and the Michaelis-Menten equation that defines the relationship between substrate and rate is over 100 years old. About 80 years ago Eyring and Polyani formulated Transistion State Theory (TST) which describes the temperature-dependence of chemical reaction rates and the precise relationship between activation energy and the rate. TST provided a robust theoretical foundation for the Arrhenius equation and together, these equations are the foundation equations for the biochemist. Can these equations provide any insights into rates at larger scales, such as organism growth rates and those rates that interest ecosystem scientists (e.g. heterotrophic respiration, gross primary production)? Let us begin by considering a microbial cell. Microbial growth (i.e. cell division) requires the coordinated kinetics of thousands of enzymes including DNA/RNA polymerases, ribosomes, biosynthetic enzymes - all under a regime of highly complex regulatory effects. There is no a priori reason to expect that Michaelis-Menten kinetics and TST will adequately describe this vastly complex process. Indeed, Lloyd and Taylor showed 23 years ago that soil respiration is not well described by the Arrhenius function. More recently, Heskel and colleagues showed that leaf respiration is also not well described by the Arrhenius function. It is the same case for rates of photosynthesis. Despite this failure of the basic equations of biochemistry to map to biological rates at greater scales, what insights can biochemistry provide to ecosystem science? As nearly all of biological metabolism is mediated through enzyme kinetics, I will begin with the Michaelis-Menten equation under regimes of low and high substrate concentrations. This simplified view can provide surprising insights into processes at larger scales. I will also consider the relationship between the activation energy and the reaction rate. Many, many ecosystem-rate papers focus on the activation energy and thus, it is important to understand this relationship. Finally, I will consider the Arrhenius and TST equations and their failure for ecosystem processes and the reasons for this failure. Understanding the failure is a first step towards a resolution to this long-standing problem in ecosystem science.

A High-Rate, Single-Crystal Model for Cyclotrimethylene Trinitramine including Phase Transformations and Plastic Slip

DOE PAGES

Addessio, Francis L.; Luscher, Darby Jon; Cawkwell, Marc Jon; ...

2017-05-14

A continuum model for the high-rate, thermo-mechanical deformation of single-crystal cyclotrimethylene trinitramine (RDX) is developed. The model includes the effects of anisotropy, large deformations, nonlinear thermo-elasticity, phase transformations, and plastic slip. A multiplicative decomposition of the deformation gradient is used. The volumetric elastic component of the deformation is accounted for through a free-energy based equation of state for the low- (α) and high-pressure (γ) polymorphs of RDX. Crystal plasticity is addressed using a phenomenological thermal activation model. The deformation gradient for the phase transformation is based on an approach that has been applied to martensitic transformations. Simulations were conducted andmore » compared to high-rate, impact loading of oriented RDX single crystals. The simulations considered multiple orientations of the crystal relative to the direction of shock loading and multiple sample thicknesses. Thirteen slip systems, which were inferred from indentation and x-ray topography, were used to model the α-polymorph. It is shown that by increasing the number of slip systems from the previously considered number of six (6) to thirteen (13) in the α-polymorph, better comparisons with data may be obtained. Simulations of impact conditions in the vicinity of the α- to γ-polymorph transformation (3.8 GPa) are considered. Eleven of the simulations, which were at pressures below the transformation value (3.0 GPa), were compared to experimental data. Comparison of the model was also made with available data for one experiment above the transformation pressure (4.4 GPa). Also, simulations are provided for a nominal pressure of 7.5 GPa to demonstrate the effect of the transformation kinetics on the deformation of a high-rate plate impact problem.« less

A High-Rate, Single-Crystal Model for Cyclotrimethylene Trinitramine including Phase Transformations and Plastic Slip

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

Addessio, Francis L.; Luscher, Darby Jon; Cawkwell, Marc Jon

A continuum model for the high-rate, thermo-mechanical deformation of single-crystal cyclotrimethylene trinitramine (RDX) is developed. The model includes the effects of anisotropy, large deformations, nonlinear thermo-elasticity, phase transformations, and plastic slip. A multiplicative decomposition of the deformation gradient is used. The volumetric elastic component of the deformation is accounted for through a free-energy based equation of state for the low- (α) and high-pressure (γ) polymorphs of RDX. Crystal plasticity is addressed using a phenomenological thermal activation model. The deformation gradient for the phase transformation is based on an approach that has been applied to martensitic transformations. Simulations were conducted andmore » compared to high-rate, impact loading of oriented RDX single crystals. The simulations considered multiple orientations of the crystal relative to the direction of shock loading and multiple sample thicknesses. Thirteen slip systems, which were inferred from indentation and x-ray topography, were used to model the α-polymorph. It is shown that by increasing the number of slip systems from the previously considered number of six (6) to thirteen (13) in the α-polymorph, better comparisons with data may be obtained. Simulations of impact conditions in the vicinity of the α- to γ-polymorph transformation (3.8 GPa) are considered. Eleven of the simulations, which were at pressures below the transformation value (3.0 GPa), were compared to experimental data. Comparison of the model was also made with available data for one experiment above the transformation pressure (4.4 GPa). Also, simulations are provided for a nominal pressure of 7.5 GPa to demonstrate the effect of the transformation kinetics on the deformation of a high-rate plate impact problem.« less

Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

PubMed Central

Vázquez, J. L.

2010-01-01

The goal of this paper is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the identification of the optimal constants in some related Hardy–Poincaré inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities, and rates for nonlinear diffusion equations. PMID:20823259

Characteristics of multiple tropopauses in the tropics

NASA Astrophysics Data System (ADS)

Mehta, Sanjay Kumar; Ratnam Madineni, Venkat; Krishna Murthy, B. V.

The characteristics of multiple tropopauses (MTs) in the tropics are studied using radiosonde data from 5 stations (Truk,Rochambeau, Singapore, Seychelles and Darwin) in the tropical belt during 1999 to 2008 and COSMIC GPS RO data during 2006-2008. In this study we emphasized the limitations of the WMO criteria for identifying the MTs and evolved an alternative criterion to effectively delineate MTs over tropical region. The current method is based on cold point tropopause (CPT) and points of inflections in the temperature profile rather than lapse rate as in WMO criteria. The points of inflection can occur both below and above the CPT. The one which occurs below the CPT is designated as the lower tropopause (LT) and those occurring above the CPT as second tropopause (ST) and third tropopause (TT) according to their heights of occurrence with CPT as the first tropopause. The percentage occurrences (25-50) of MTs are observed to be higher using the current method than by the WMO criteria (10-30). There is significant seasonal variation in the LT, CPT and ST temperatures (heights) with lower (higher) values occurring in the Northern Hemisphere winter. While the CPT temperatures are lowest at the equator the CPT heights are not highest at the equator. The occurrences of MTs are higher over equator and decrease away towards higher latitudes in the tropics. Longitudinal variation of the MTs is observed with relatively high occurrences during NH summer season over placeIndian Ocean. The equatorial minimum in the CPT temperature is broader and colder in the eastern hemisphere than the western hemisphere It is found that MTs can either occur on consecutive days in groups or on isolated days. The plausible causative mechanisms will be presented in the conference.

A reduction for spiking integrate-and-fire network dynamics ranging from homogeneity to synchrony.

PubMed

Zhang, J W; Rangan, A V

2015-04-01

In this paper we provide a general methodology for systematically reducing the dynamics of a class of integrate-and-fire networks down to an augmented 4-dimensional system of ordinary-differential-equations. The class of integrate-and-fire networks we focus on are homogeneously-structured, strongly coupled, and fluctuation-driven. Our reduction succeeds where most current firing-rate and population-dynamics models fail because we account for the emergence of 'multiple-firing-events' involving the semi-synchronous firing of many neurons. These multiple-firing-events are largely responsible for the fluctuations generated by the network and, as a result, our reduction faithfully describes many dynamic regimes ranging from homogeneous to synchronous. Our reduction is based on first principles, and provides an analyzable link between the integrate-and-fire network parameters and the relatively low-dimensional dynamics underlying the 4-dimensional augmented ODE.

Empirical modeling of environment-enhanced fatigue crack propagation in structural alloys for component life prediction

NASA Technical Reports Server (NTRS)

Richey, Edward, III

1995-01-01

This research aims to develop the methods and understanding needed to incorporate time and loading variable dependent environmental effects on fatigue crack propagation (FCP) into computerized fatigue life prediction codes such as NASA FLAGRO (NASGRO). In particular, the effect of loading frequency on FCP rates in alpha + beta titanium alloys exposed to an aqueous chloride solution is investigated. The approach couples empirical modeling of environmental FCP with corrosion fatigue experiments. Three different computer models have been developed and incorporated in the DOS executable program. UVAFAS. A multiple power law model is available, and can fit a set of fatigue data to a multiple power law equation. A model has also been developed which implements the Wei and Landes linear superposition model, as well as an interpolative model which can be utilized to interpolate trends in fatigue behavior based on changes in loading characteristics (stress ratio, frequency, and hold times).

Chronic Kidney Disease Epidemiology Collaboration versus Modification of Diet in Renal Disease equations for renal function evaluation in patients undergoing partial nephrectomy.

PubMed

Shikanov, Sergey; Clark, Melanie A; Raman, Jay D; Smith, Benjamin; Kaag, Matthew; Russo, Paul; Wheat, Jeffrey C; Wolf, J Stuart; Huang, William C; Shalhav, Arieh L; Eggener, Scott E

2010-11-01

A novel equation, the Chronic Kidney Disease Epidemiology Collaboration, has been proposed to replace the Modification of Diet in Renal Disease for estimated glomerular filtration rate due to higher accuracy, particularly in the setting of normal renal function. We compared these equations in patients with 2 functioning kidneys undergoing partial nephrectomy. We assembled a cohort of 1,158 patients from 5 institutions who underwent partial nephrectomy between 1991 and 2009. Only subjects with 2 functioning kidneys were included in the study. The end points were baseline estimated glomerular filtration rate, last followup estimated glomerular filtration rate (3 to 18 months), absolute and percent change estimated glomerular filtration rate ([absolute change/baseline] × 100%), and proportion of newly developed chronic kidney disease stage III. The agreement between the equations was evaluated using Bland-Altman plots and the McNemar test for paired observations. Mean baseline estimated glomerular filtration rate derived from the Modification of Diet in Renal Disease and Chronic Kidney Disease Epidemiology Collaboration equations were 73 and 77 ml/minute/1.73 m(2), respectively, and following surgery were 63 and 67 ml/minute/1.73 m(2), respectively. Mean percent change estimated glomerular filtration rate was -12% for both equations (p = 0.2). The proportion of patients with newly developed chronic kidney disease stage III following surgery was 32% and 25%, according to the Modification of Diet in Renal Disease and Chronic Kidney Disease Epidemiology Collaboration equations, respectively (p = 0.001). For patients with 2 functioning kidneys undergoing partial nephrectomy the Chronic Kidney Disease Epidemiology Collaboration equation provides slightly higher glomerular filtration rate estimates compared to the Modification of Diet in Renal Disease equation, with 7% fewer patients categorized as having chronic kidney disease stage III or worse. Copyright © 2010 American Urological Association Education and Research, Inc. Published by Elsevier Inc. All rights reserved.

Evaluation of the telegrapher's equation and multiple-flux theories for calculating the transmittance and reflectance of a diffuse absorbing slab.

PubMed

Kong, Steven H; Shore, Joel D

2007-03-01

We study the propagation of light through a medium containing isotropic scattering and absorption centers. With a Monte Carlo simulation serving as the benchmark solution to the radiative transfer problem of light propagating through a turbid slab, we compare the transmission and reflection density computed from the telegrapher's equation, the diffusion equation, and multiple-flux theories such as the Kubelka-Munk and four-flux theories. Results are presented for both normally incident light and diffusely incident light. We find that we can always obtain very good results from the telegrapher's equation provided that two parameters that appear in the solution are set appropriately. We also find an interesting connection between certain solutions of the telegrapher's equation and solutions of the Kubelka-Munk and four-flux theories with a small modification to how the phenomenological parameters in those theories are traditionally related to the optical scattering and absorption coefficients of the slab. Finally, we briefly explore how well the theories can be extended to the case of anisotropic scattering by multiplying the scattering coefficient by a simple correction factor.

Reference equations for the six-minute walk distance in the healthy Chinese population aged 18–59 years

PubMed Central

Zou, He; Zhu, Xiuruo; Zhang, Jia; Wang, Yi; Wu, Xiaozhen; Liu, Fang; Xie, Xiaofeng

2017-01-01

Background The six-minute walk test (6MWT) is a safe, simple, inexpensive tool for evaluating the functional exercise capacity of patients with chronic respiratory disease. However, there is a lack of standard reference equations for the six-minute walk distance (6MWD) in the healthy Chinese population aged 18–59 years. Aims The purposes of the present study were as follows: 1) to measure the anthropometric data and walking distance of a sample of healthy Chinese Han people aged 18–59 years; 2) to construct reference equations for the 6MWD; 3) to compare the measured 6MWD with previously published equations. Method The anthropometric data, demographic information, lung function, and walking distance of Chinese adults aged 18–59 years were prospectively measured using a standardized protocol. We obtained verbal consent from all the subjects before the test, and the study design was approved by the ethics committee of Wenzhou People's Hospital. The 6MWT was performed twice, and the longer distance was used for further analysis. Results A total of 643 subjects (319 females and 324 males) completed the 6MWT, and average walking distance was 601.6±55.51 m. The walking distance was compared between females and males (578±49.85 m vs. 623±52.53 m; p < 0.0001) and between physically active subjects and sedentary subjects (609.3±56.17 m vs. 592±53.23 m; p < 0.0001). Pearson’s correlation indicated that the 6MWD was significantly correlated with various demographic and the 6MWT variables, such as age, height, weight, body mass index (BMI), heart rate after the test and the difference in the heart rate before and after the test. Stepwise multiple regression analysis showed that age and height were independent predictors associated with the 6MWD. The reference equations from white, Canadian and Chilean populations tended to overestimate the walking distance in our subjects, while Brazilian and Arabian equations tended to underestimate the walking distance. There was no significant difference in the walking distance between Korean reference equations and the results of the current study. Conclusion In summary, age and height were the most significant predictors of the 6MWD, and regression equations could explain approximately 34% and 28% of the distance variance in the female and male groups, respectively. PMID:28910353

Correlated noise-based switches and stochastic resonance in a bistable genetic regulation system

NASA Astrophysics Data System (ADS)

Wang, Can-Jun; Yang, Ke-Li

2016-07-01

The correlated noise-based switches and stochastic resonance are investigated in a bistable single gene switching system driven by an additive noise (environmental fluctuations), a multiplicative noise (fluctuations of the degradation rate). The correlation between the two noise sources originates from on the lysis-lysogeny pathway system of the λ phage. The steady state probability distribution is obtained by solving the time-independent Fokker-Planck equation, and the effects of noises are analyzed. The effects of noises on the switching time between the two stable states (mean first passage time) is investigated by the numerical simulation. The stochastic resonance phenomenon is analyzed by the power amplification factor. The results show that the multiplicative noise can induce the switching from "on" → "off" of the protein production, while the additive noise and the correlation between the noise sources can induce the inverse switching "off" → "on". A nonmonotonic behaviour of the average switching time versus the multiplicative noise intensity, for different cross-correlation and additive noise intensities, is observed in the genetic system. There exist optimal values of the additive noise, multiplicative noise and cross-correlation intensities for which the weak signal can be optimal amplified.

A study of the liquid-vapor phase change of mercury based on irreversible thermodynamics.

NASA Technical Reports Server (NTRS)

Adt, R. R., Jr.; Hatsopoulos, G. N.; Bornhorst, W. J.

1972-01-01

The object of this work is to determine the transport coefficients which appear in linear irreversible-thermodynamic rate equations of a phase change. An experiment which involves the steady-state evaporation of mercury was performed to measure the principal transport coefficient appearing in the mass-rate equation and the coupling transport coefficient appearing in both the mass-rate equation and the energy-rate equation. The principal transport coefficient sigma, usually termed the 'condensation' or 'evaporation' coefficient, is found to be approximately 0.9, which is higher than that measured previously in condensation-of-mercury experiments. The experimental value of the coupling coefficient K does not agree with the value predicted from Schrage's kinetic analysis of the phase change. A modified kinetic analysis in which the Onsager reciprocal law and the conservation laws are invoked is presented which removes this discrepancy but which shows that the use of Schrage's equation for predicting mass rates of phase change is a good approximation.

Acoustic 3D modeling by the method of integral equations

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2018-02-01

This paper presents a parallel algorithm for frequency-domain acoustic modeling by the method of integral equations (IE). The algorithm is applied to seismic simulation. The IE method reduces the size of the problem but leads to a dense system matrix. A tolerable memory consumption and numerical complexity were achieved by applying an iterative solver, accompanied by an effective matrix-vector multiplication operation, based on the fast Fourier transform (FFT). We demonstrate that, the IE system matrix is better conditioned than that of the finite-difference (FD) method, and discuss its relation to a specially preconditioned FD matrix. We considered several methods of matrix-vector multiplication for the free-space and layered host models. The developed algorithm and computer code were benchmarked against the FD time-domain solution. It was demonstrated that, the method could accurately calculate the seismic field for the models with sharp material boundaries and a point source and receiver located close to the free surface. We used OpenMP to speed up the matrix-vector multiplication, while MPI was used to speed up the solution of the system equations, and also for parallelizing across multiple sources. The practical examples and efficiency tests are presented as well.

Multiple steady states in atmospheric chemistry

NASA Technical Reports Server (NTRS)

Stewart, Richard W.

1993-01-01

The equations describing the distributions and concentrations of trace species are nonlinear and may thus possess more than one solution. This paper develops methods for searching for multiple physical solutions to chemical continuity equations and applies these to subsets of equations describing tropospheric chemistry. The calculations are carried out with a box model and use two basic strategies. The first strategy is a 'search' method. This involves fixing model parameters at specified values, choosing a wide range of initial guesses at a solution, and using a Newton-Raphson technique to determine if different initial points converge to different solutions. The second strategy involves a set of techniques known as homotopy methods. These do not require an initial guess, are globally convergent, and are guaranteed, in principle, to find all solutions of the continuity equations. The first method is efficient but essentially 'hit or miss' in the sense that it cannot guarantee that all solutions which may exist will be found. The second method is computationally burdensome but can, in principle, determine all the solutions of a photochemical system. Multiple solutions have been found for models that contain a basic complement of photochemical reactions involving O(x), HO(x), NO(x), and CH4. In the present calculations, transitions occur between stable branches of a multiple solution set as a control parameter is varied. These transitions are manifestations of hysteresis phenomena in the photochemical system and may be triggered by increasing the NO flux or decreasing the CH4 flux from current mean tropospheric levels.

A new perspective on Quantum Finance using the Black-Scholes pricing model

NASA Astrophysics Data System (ADS)

Dieng, Lamine

2007-03-01

Options are known to be divided into two types, the first type is called a call option and the second type is called a put option and these options are offered to stock holders in order to hedge their positions against risky fluctuations of the stock price. It is important to mention that due to fluctuations of the stock price, options can be found sometimes deep in the money, at the money and out of the money. A deep in the money option is described when the option's holder has a positive expected payoff, at the money option is when the option's holder has a zero expected payoff and an out of the money option is when the payoff is negative. In this work, we will assume the stock price to be described by the well known Black-Scholes model or sometimes called the multiplicative model. Using Ito calculus, Martingale and supermartingale theories, we investigated the Black-Scholes pricing equation at the money (X(stock price)= K (strike price)) when the expected payoff of the options holder is zero. We also hedged the Black-Scholes pricing equation in the limit when delta is zero to obtain the non-relativistic time independent Schroedinger equation in quantum mechanics. We compared the two equations and found the diffusion constant to be a function of the stock price in contrast to the Bachelier model we have worked on earlier. We solved the Schroedinger equation and found a dependence between interest rate, volatility and strike price at the money.

A robust, finite element model for hydrostatic surface water flows

USGS Publications Warehouse

Walters, R.A.; Casulli, V.

1998-01-01

A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

Multiple Indicator Stationary Time Series Models.

ERIC Educational Resources Information Center

Sivo, Stephen A.

2001-01-01

Discusses the propriety and practical advantages of specifying multivariate time series models in the context of structural equation modeling for time series and longitudinal panel data. For time series data, the multiple indicator model specification improves on classical time series analysis. For panel data, the multiple indicator model…

A Mechanobiological model for damage-induced growth in arterial tissue with application to in-stent restenosis

NASA Astrophysics Data System (ADS)

Fereidoonnezhad, B.; Naghdabadi, R.; Sohrabpour, S.; Holzapfel, G. A.

In-stent restenosis (ISR) is one of the main drawbacks of stent implementation which limits the long-term success of the procedure. Morphological changes occurring within the arterial wall due to stent-induced mechanical injury are a major cause for activation of vascular smooth muscle cells (VSMCs), and the subsequent development of ISR. Considering the theory of volumetric mass growth and adopting a multiplicative decomposition of the deformation gradient into an elastic part and a growth part, we present a mechanobiological model for ISR. An evolution equation is developed for mass growth of the neointima, in which the activation of VSMCs due to stent-induced damage (injury) and the proliferation rate of the activated cells are considered. By introducing the mass evolution into the mass balance equation, we obtain the evolution of the growth tensor over time. The model is implemented in a finite element code and the procedure of angioplasty is simulated, whereby the features of the proposed growth model are illustrated.

Study on the Optimization and Process Modeling of the Rotary Ultrasonic Machining of Zerodur Glass-Ceramic

NASA Astrophysics Data System (ADS)

Pitts, James Daniel

Rotary ultrasonic machining (RUM), a hybrid process combining ultrasonic machining and diamond grinding, was created to increase material removal rates for the fabrication of hard and brittle workpieces. The objective of this research was to experimentally derive empirical equations for the prediction of multiple machined surface roughness parameters for helically pocketed rotary ultrasonic machined Zerodur glass-ceramic workpieces by means of a systematic statistical experimental approach. A Taguchi parametric screening design of experiments was employed to systematically determine the RUM process parameters with the largest effect on mean surface roughness. Next empirically determined equations for the seven common surface quality metrics were developed via Box-Behnken surface response experimental trials. Validation trials were conducted resulting in predicted and experimental surface roughness in varying levels of agreement. The reductions in cutting force and tool wear associated with RUM, reported by previous researchers, was experimentally verified to also extended to helical pocketing of Zerodur glass-ceramic.

No-threshold dose-response curves for nongenotoxic chemicals: Findings and applications for risk assessment

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

Sheehan, Daniel M.

2006-01-15

We tested the hypothesis that no threshold exists when estradiol acts through the same mechanism as an active endogenous estrogen. A Michaelis-Menten (MM) equation accounting for response saturation, background effects, and endogenous estrogen level fit a turtle sex-reversal data set with no threshold and estimated the endogenous dose. Additionally, 31 diverse literature dose-response data sets were analyzed by adding a term for nonhormonal background; good fits were obtained but endogenous dose estimations were not significant due to low resolving power. No thresholds were observed. Data sets were plotted using a normalized MM equation; all 178 data points were accommodated onmore » a single graph. Response rates from {approx}1% to >95% were well fit. The findings contradict the threshold assumption and low-dose safety. Calculating risk and assuming additivity of effects from multiple chemicals acting through the same mechanism rather than assuming a safe dose for nonthresholded curves is appropriate.« less

An algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equations

NASA Astrophysics Data System (ADS)

Daud, Wan Suhana Wan; Ahmad, Nazihah; Malkawi, Ghassan

2017-11-01

Sylvester matrix equations played a prominent role in various areas including control theory. Considering to any un-certainty problems that can be occurred at any time, the Sylvester matrix equation has to be adapted to the fuzzy environment. Therefore, in this study, an algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equation is constructed. The construction of the algorithm is based on the max-min arithmetic multiplication operation. Besides that, an associated arbitrary matrix equation is modified in obtaining the final solution. Finally, some numerical examples are presented to illustrate the proposed algorithm.

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.

Optimized resolved rate control of seven-degree-of-freedom Laboratory Telerobotic Manipulator (LTM) with application to three-dimensional graphics simulation

NASA Technical Reports Server (NTRS)

Barker, L. Keith; Mckinney, William S., Jr.

1989-01-01

The Laboratory Telerobotic Manipulator (LTM) is a seven-degree-of-freedom robot arm. Two of the arms were delivered to Langley Research Center for ground-based research to assess the use of redundant degree-of-freedom robot arms in space operations. Resolved-rate control equations for the LTM are derived. The equations are based on a scheme developed at the Oak Ridge National Laboratory for computing optimized joint angle rates in real time. The optimized joint angle rates actually represent a trade-off, as the hand moves, between small rates (least-squares solution) and those rates which work toward satisfying a specified performance criterion of joint angles. In singularities where the optimization scheme cannot be applied, alternate control equations are devised. The equations developed were evaluated using a real-time computer simulation to control a 3-D graphics model of the LTM.

A generic rate equation for catalysed, template-directed polymerisation.

PubMed

Hofmeyr, Jan-Hendrik S; Gqwaka, Olona P C; Rohwer, Johann M

2013-09-02

Biosynthetic networks link to growth and reproduction processes through template-directed synthesis of macromolecules such as polynucleotides and polypeptides. No rate equation exists that captures this link in a way that it can effectively be incorporated into a single computational model of the overall process. This paper describes the derivation of such a generic steady-state rate equation for catalysed, template-directed polymerisation reactions with varying monomer stoichiometry and varying chain length. The derivation is based on a classical Michaelis-Menten mechanism with template binding and an arbitrary number of chain elongation steps that produce a polymer composed of an arbitrary number of monomer types. The rate equation only requires the identity of the first dimer in the polymer sequence; for the remainder only the monomer composition needs be known. Further simplification of a term in the denominator yielded an equation requiring no positional information at all, only the monomer composition of the polymer; this equation still gave an excellent estimate of the reaction rate provided that either the monomer concentrations are at least half-saturating, or the polymer is very long. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

EFFECTS OF TURBULENCE, ECCENTRICITY DAMPING, AND MIGRATION RATE ON THE CAPTURE OF PLANETS INTO MEAN MOTION RESONANCE

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

Ketchum, Jacob A.; Adams, Fred C.; Bloch, Anthony M.

2011-01-01

Pairs of migrating extrasolar planets often lock into mean motion resonance as they drift inward. This paper studies the convergent migration of giant planets (driven by a circumstellar disk) and determines the probability that they are captured into mean motion resonance. The probability that such planets enter resonance depends on the type of resonance, the migration rate, the eccentricity damping rate, and the amplitude of the turbulent fluctuations. This problem is studied both through direct integrations of the full three-body problem and via semi-analytic model equations. In general, the probability of resonance decreases with increasing migration rate, and with increasingmore » levels of turbulence, but increases with eccentricity damping. Previous work has shown that the distributions of orbital elements (eccentricity and semimajor axis) for observed extrasolar planets can be reproduced by migration models with multiple planets. However, these results depend on resonance locking, and this study shows that entry into-and maintenance of-mean motion resonance depends sensitively on the migration rate, eccentricity damping, and turbulence.« less

Giant graviton interactions and M2-branes ending on multiple M5-branes

NASA Astrophysics Data System (ADS)

Hirano, Shinji; Sato, Yuki

2018-05-01

We study splitting and joining interactions of giant gravitons with angular momenta N 1/2 ≪ J ≪ N in the type IIB string theory on AdS 5 × S 5 by describing them as instantons in the tiny graviton matrix model introduced by Sheikh-Jabbari. At large J the instanton equation can be mapped to the four-dimensional Laplace equation and the Coulomb potential for m point charges in an n-sheeted Riemann space corresponds to the m-to- n interaction process of giant gravitons. These instantons provide the holographic dual of correlators of all semi-heavy operators and the instanton amplitudes exactly agree with the pp-wave limit of Schur polynomial correlators in N = 4 SYM computed by Corley, Jevicki and Ramgoolam. By making a slight change of variables the same instanton equation is mathematically transformed into the Basu-Harvey equation which describes the system of M2-branes ending on M5-branes. As it turns out, the solutions to the sourceless Laplace equation on an n-sheeted Riemann space correspond to n M5-branes connected by M2-branes and we find general solutions representing M2-branes ending on multiple M5-branes. Among other solutions, the n = 3 case describes an M2-branes junction ending on three M5-branes. The effective theory on the moduli space of our solutions might shed light on the low energy effective theory of multiple M5-branes.

Numerical Problem Solving Using Mathcad in Undergraduate Reaction Engineering

ERIC Educational Resources Information Center

Parulekar, Satish J.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

A Nonlinear, Multiinput, Multioutput Process Control Laboratory Experiment

ERIC Educational Resources Information Center

Young, Brent R.; van der Lee, James H.; Svrcek, William Y.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

Dilations and the Equation of a Line

ERIC Educational Resources Information Center

Yopp, David A.

2016-01-01

Students engage in proportional reasoning when they use covariance and multiple comparisons. Without rich connections to proportional reasoning, students may develop inadequate understandings of linear relationships and the equations that model them. Teachers can improve students' understanding of linear relationships by focusing on realistic…

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Multiple-Group Analysis Using the sem Package in the R System

ERIC Educational Resources Information Center

Evermann, Joerg

2010-01-01

Multiple-group analysis in covariance-based structural equation modeling (SEM) is an important technique to ensure the invariance of latent construct measurements and the validity of theoretical models across different subpopulations. However, not all SEM software packages provide multiple-group analysis capabilities. The sem package for the R…

Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers

NASA Astrophysics Data System (ADS)

Nyman, Robert A.; Walker, Benjamin T.

2018-03-01

Photons can come to thermal equilibrium at room temperature by scattering multiple times from a fluorescent dye. By confining the light and dye in a microcavity, a minimum energy is set and the photons can then show Bose-Einstein condensation. We present here the physical principles underlying photon thermalization and condensation, and review the literature on the subject. We then explore the 'small' regime where very few photons are needed for condensation. We compare thermal equilibrium results to a rate-equation model of microlasers, which includes spontaneous emission into the cavity, and we note that small systems result in ambiguity in the definition of threshold.

Discrete effect on the halfway bounce-back boundary condition of multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations.

PubMed

Cui, Shuqi; Hong, Ning; Shi, Baochang; Chai, Zhenhua

2016-04-01

In this paper, we will focus on the multiple-relaxation-time (MRT) lattice Boltzmann model for two-dimensional convection-diffusion equations (CDEs), and analyze the discrete effect on the halfway bounce-back (HBB) boundary condition (or sometimes called bounce-back boundary condition) of the MRT model where three different discrete velocity models are considered. We first present a theoretical analysis on the discrete effect of the HBB boundary condition for the simple problems with a parabolic distribution in the x or y direction, and a numerical slip proportional to the second-order of lattice spacing is observed at the boundary, which means that the MRT model has a second-order convergence rate in space. The theoretical analysis also shows that the numerical slip can be eliminated in the MRT model through tuning the free relaxation parameter corresponding to the second-order moment, while it cannot be removed in the single-relaxation-time model or the Bhatnagar-Gross-Krook model unless the relaxation parameter related to the diffusion coefficient is set to be a special value. We then perform some simulations to confirm our theoretical results, and find that the numerical results are consistent with our theoretical analysis. Finally, we would also like to point out the present analysis can be extended to other boundary conditions of lattice Boltzmann models for CDEs.

Estimation of bipolar jets from accretion discs around Kerr black holes

NASA Astrophysics Data System (ADS)

Kumar, Rajiv; Chattopadhyay, Indranil

2017-08-01

We analyse flows around a rotating black hole and obtain self-consistent accretion-ejection solutions in full general relativistic prescription. Entire energy-angular momentum parameter space is investigated in the advective regime to obtain shocked and shock-free accretion solutions. Jet equations of motion are solved along the von Zeipel surfaces computed from the post-shock disc, simultaneously with the equations of accretion disc along the equatorial plane. For a given spin parameter, the mass outflow rate increases as the shock moves closer to the black hole, but eventually decreases, maximizing at some intermediate value of shock location. Interestingly, we obtain all types of possible jet solutions, for example, steady shock solution with multiple critical points, bound solution with two critical points and smooth solution with single critical point. Multiple critical points may exist in jet solution for spin parameter as ≥ 0.5. The jet terminal speed generally increases if the accretion shock forms closer to the horizon and is higher for corotating black hole than the counter-rotating and the non-rotating one. Quantitatively speaking, shocks in jet may form for spin parameter as > 0.6 and jet shocks range between 6rg and 130rg above the equatorial plane, while the jet terminal speed vj∞ > 0.35 c if Bernoulli parameter E≥1.01 for as > 0.99.

Performance of the chronic kidney disease-epidemiology study equations for estimating glomerular filtration rate before and after nephrectomy.

PubMed

Lane, Brian R; Demirjian, Sevag; Weight, Christopher J; Larson, Benjamin T; Poggio, Emilio D; Campbell, Steven C

2010-03-01

Accurate renal function determination before and after nephrectomy is essential for proper prevention and management of chronic kidney disease due to nephron loss and ischemic injury. We compared the estimated glomerular filtration rate using several serum creatinine based formulas against the measured rate based on (125)I-iothalamate clearance to determine which most accurately reflects the rate in this setting. Of 7,611 patients treated at our institution since 1975 the measured glomerular filtration rate was selectively determined before and after nephrectomy in 268 and 157, respectively. Performance of the Cockcroft-Gault, Modification of Diet in Renal Disease Study, re-expressed Modification of Diet in Renal Disease Study and Chronic Kidney Disease-Epidemiology Study equations, each of which estimates the glomerular filtration rate, were determined using serum creatinine, age, gender, weight and body surface area. The performance of serum creatinine, reciprocal serum creatinine and the 4 formulas was compared with the measured rate using Pearson's correlation, Lin's concordance coefficient and residual plots. Median serum creatinine was 1.4 mg/dl and the median measured glomerular filtration rate was 50 ml per minute per 1.73 m(2). The correlation between serum creatinine and the measured rate was poor (-0.66) compared with that of reciprocal serum creatinine (0.78) and the 4 equations (0.82 to 0.86). The Chronic Kidney Disease-Epidemiology Study equation performed with greatest precision and accuracy, and least bias of all equations. Stage 3 or greater chronic kidney disease ((125)I-iothalamate glomerular filtration rate 60 ml per minute per 1.73 m(2) or less) was present in 44% of patients with normal serum creatinine (1.4 mg/dl or less) postoperatively. Such missed diagnoses of chronic kidney disease decreased 42% using the Chronic Kidney Disease-Epidemiology Study equation. Glomerular filtration rate estimation equations outperform serum creatinine and better identify patients with perinephrectomy compromised renal function. The newly developed, serum creatinine based, Chronic Kidney Disease-Epidemiology Study equation has sufficient accuracy to render direct glomerular filtration rate measurement unnecessary before and after nephrectomy for cause in most circumstances. 2010 American Urological Association Education and Research, Inc. Published by Elsevier Inc. All rights reserved.

Biological electric fields and rate equations for biophotons.

PubMed

Alvermann, M; Srivastava, Y N; Swain, J; Widom, A

2015-04-01

Biophoton intensities depend upon the squared modulus of the electric field. Hence, we first make some general estimates about the inherent electric fields within various biosystems. Generally, these intensities do not follow a simple exponential decay law. After a brief discussion on the inapplicability of a linear rate equation that leads to strict exponential decay, we study other, nonlinear rate equations that have been successfully used for biosystems along with their physical origins when available.

Multiple re-encounter approach to radical pair reactions and the role of nonlinear master equations.

PubMed

Clausen, Jens; Guerreschi, Gian Giacomo; Tiersch, Markus; Briegel, Hans J

2014-08-07

We formulate a multiple-encounter model of the radical pair mechanism that is based on a random coupling of the radical pair to a minimal model environment. These occasional pulse-like couplings correspond to the radical encounters and give rise to both dephasing and recombination. While this is in agreement with the original model of Haberkorn and its extensions that assume additional dephasing, we show how a nonlinear master equation may be constructed to describe the conditional evolution of the radical pairs prior to the detection of their recombination. We propose a nonlinear master equation for the evolution of an ensemble of independently evolving radical pairs whose nonlinearity depends on the record of the fluorescence signal. We also reformulate Haberkorn's original argument on the physicality of reaction operators using the terminology of quantum optics/open quantum systems. Our model allows one to describe multiple encounters within the exponential model and connects this with the master equation approach. We include hitherto neglected effects of the encounters, such as a separate dephasing in the triplet subspace, and predict potential new effects, such as Grover reflections of radical spins, that may be observed if the strength and time of the encounters can be experimentally controlled.

The Use of DNS in Turbulence Modeling

NASA Technical Reports Server (NTRS)

Mansour, Nagi N.; Merriam, Marshal (Technical Monitor)

1997-01-01

The use of Direct numerical simulations (DNS) data in developing and testing turbulence models is reviewed. The data is used to test turbulence models at all levels: algebraic, one-equation, two-equation and full Reynolds stress models were tested. Particular examples on the development of models for the dissipation rate equation are presented. Homogeneous flows are used to test new scaling arguments for the various terms in the dissipation rate equation. The channel flow data is used to develop modifications to the equation model that take into account near-wall effects. DNS of compressible flows under mean compression are used in testing new compressible modifications to the two-equation models.

Linearized theory of inhomogeneous multiple 'water-bag' plasmas

NASA Technical Reports Server (NTRS)

Bloomberg, H. W.; Berk, H. L.

1973-01-01

Equations are derived for describing the inhomogeneous equilibrium and small deviations from the equilibrium, giving particular attention to systems with trapped particles. An investigation is conducted of periodic systems with a single trapped-particle water bag, taking into account the behavior of the perturbation equations at the turning points. An outline is provided concerning a procedure for obtaining the eigenvalues. The results of stability calculations connected with the sideband effects are considered along with questions regarding the general applicability of the multiple water-bag approach in stability calculations.

Stochastic Swift-Hohenberg Equation with Degenerate Linear Multiplicative Noise

NASA Astrophysics Data System (ADS)

Hernández, Marco; Ong, Kiah Wah

2018-03-01

We study the dynamic transition of the Swift-Hohenberg equation (SHE) when linear multiplicative noise acting on a finite set of modes of the dominant linear flow is introduced. Existence of a stochastic flow and a local stochastic invariant manifold for this stochastic form of SHE are both addressed in this work. We show that the approximate reduced system corresponding to the invariant manifold undergoes a stochastic pitchfork bifurcation, and obtain numerical evidence suggesting that this picture is a good approximation for the full system as well.

Multiple periodic-soliton solutions of the (3+1)-dimensional generalised shallow water equation

NASA Astrophysics Data System (ADS)

Li, Ye-Zhou; Liu, Jian-Guo

2018-06-01

Based on the extended variable-coefficient homogeneous balance method and two new ansätz functions, we construct auto-Bäcklund transformation and multiple periodic-soliton solutions of (3 {+} 1)-dimensional generalised shallow water equations. Completely new periodic-soliton solutions including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave are obtained. In addition, cross-kink three-soliton and cross-kink four-soliton solutions are derived. Furthermore, propagation characteristics and interactions of the obtained solutions are discussed and illustrated in figures.

Schedule-induced drinking: rate of food delivery and Herrnstein's equation.

PubMed Central

Wetherington, C L

1979-01-01

Schedule-induced drinking was measured in four rats exposed to fixed-time schedules of food ranging from 30 to 480 seconds. Herrnstein's (1970, 1974) equation relating rate of a single response as a hyperbolic function of reinforcement rate provided a good fit to three measures of drinking: lick rate, ingestion rate, and relative time spent drinking. The functions relating the three measures of drinking to reinforcement rate were of similar form. Herrnstein's equation also provided a good description of some already published data on schedule-induced drinking. The fit both to the present data and to the already published data was improved somewhat by computing the measures by subtracting from the time base a latency constant representing the minimal time required to consume the food pellet and travel to the water source. The data from this study provide two correspondences between operant behavior and schedule-induced behavior: (a) conformity to Herrnstein's equation and (b) equivalence of rate and relative time measures. PMID:512568

A Comparison of Raw-to-Scale Conversion Consistency between Single- and Multiple-Linking Using a Nonequivalent Groups Anchor Test Design. Research Report. ETS RR-14-13

ERIC Educational Resources Information Center

Liu, Jinghua; Guo, Hongwen; Dorans, Neil J.

2014-01-01

Maintaining score interchangeability and scale consistency is crucial for any testing programs that administer multiple forms across years. The use of a multiple linking design, which involves equating a new form to multiple old forms and averaging the conversions, has been proposed to control scale drift. However, the use of multiple linking…

Position and force control of coordinated multiple arms

NASA Technical Reports Server (NTRS)

Hayati, Samad A.

1988-01-01

A technique is presented for controlling multiple manipulators which are holding a single object and therefore form a closed kinematic chain. The object, which may or may not be in contact with a rigid environment, is assumed to be held rigidly by n robot end-effectors. The derivation is based on setting up constraint equations which reduce the 6 x n degrees of freedom of n manipulators each having six joints. Additional constraint equations are considered when one or more degrees of freedom of the object are reduced due to external constraints. Utilizing the operational space dynamic equations, a decoupling controller is designed to control both the position and the interaction forces of the object with the environment. Simulation results for the control of a pair of two-link manipulators are presented.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Greengard, Leslie F; Waag, Robert C

2010-02-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method.

Multiple solutions to a magnetic nonlinear Choquard equation

NASA Astrophysics Data System (ADS)

Cingolani, Silvia; Clapp, Mónica; Secchi, Simone

2012-04-01

We consider the stationary nonlinear magnetic Choquard equation (- inabla+ A(x))2u + V (x)u = (1/|x|^{α}ast |u|pright) |u|^{p-2}u,quad xin{R}N where A is a real-valued vector potential, V is a real-valued scalar potential, N ≥ 3, {α in (0, N)} and 2 - ( α/ N) < p < (2 N - α)/( N-2). We assume that both A and V are compatible with the action of some group G of linear isometries of {{R}N} . We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition u(gx) = tau(g)u(x)quad{for all } g in G,x in {R}N, where {tau : G rightarrow {S}1} is a given group homomorphism into the unit complex numbers.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators

PubMed Central

Hesford, Andrew J.; Astheimer, Jeffrey P.; Greengard, Leslie F.; Waag, Robert C.

2010-01-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method. PMID:20136208

Application of Stochastic and Deterministic Approaches to Modeling Interstellar Chemistry

NASA Astrophysics Data System (ADS)

Pei, Yezhe

This work is about simulations of interstellar chemistry using the deterministic rate equation (RE) method and the stochastic moment equation (ME) method. Primordial metal-poor interstellar medium (ISM) is of our interest and the socalled “Population-II” stars could have been formed in this environment during the “Epoch of Reionization” in the baby universe. We build a gas phase model using the RE scheme to describe the ionization-powered interstellar chemistry. We demonstrate that OH replaces CO as the most abundant metal-bearing molecule in such interstellar clouds of the early universe. Grain surface reactions play an important role in the studies of astrochemistry. But the lack of an accurate yet effective simulation method still presents a challenge, especially for large, practical gas-grain system. We develop a hybrid scheme of moment equations and rate equations (HMR) for large gas-grain network to model astrochemical reactions in the interstellar clouds. Specifically, we have used a large chemical gas-grain model, with stochastic moment equations to treat the surface chemistry and deterministic rate equations to treat the gas phase chemistry, to simulate astrochemical systems as of the ISM in the Milky Way, the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC). We compare the results to those of pure rate equations and modified rate equations and present a discussion about how moment equations improve our theoretical modeling and how the abundances of the assorted species are changed by varied metallicity. We also model the observed composition of H2O, CO and CO2 ices toward Young Stellar Objects in the LMC and show that the HMR method gives a better match to the observation than the pure RE method.

A New Family of Schroder's Method and Its Variants Based on Power Means for Multiple Roots of Nonlinear Equations

ERIC Educational Resources Information Center

Kanwar, V.; Sharma, Kapil K.; Behl, Ramandeep

2010-01-01

In this article, we derive one-parameter family of Schroder's method based on Gupta et al.'s (K.C. Gupta, V. Kanwar, and S. Kumar, "A family of ellipse methods for solving non-linear equations", Int. J. Math. Educ. Sci. Technol. 40 (2009), pp. 571-575) family of ellipse methods for the solution of nonlinear equations. Further, we introduce new…

Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism

NASA Astrophysics Data System (ADS)

Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G.

2015-04-01

We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.

Exploring the impact of multiple grain sizes in numerical landscape evolution model

NASA Astrophysics Data System (ADS)

Guerit, Laure; Braun, Jean; Yuan, Xiaoping; Rouby, Delphine

2017-04-01

Numerical evolution models have been widely developed in order to understand the evolution of landscape over different time-scales, but also the response of the topography to changes in external conditions, such as tectonics or climate, or to changes in the bedrock characteristics, such as its density or its erodability. Few models have coupled the evolution of the relief in erosion to the evolution of the related area in deposition, and in addition, such models generally do not consider the role of the size of the sediments reached the depositional domain. Here, we present a preliminary work based on an enhanced version of Fastscape, a very-efficient model solving the stream power equation, which now integrates a sedimentary basin at the front of a relief, together with the integration of multiple grain sizes in the system. Several simulations were performed in order to explore the impact of several grain sizes in terms of stratigraphy in the marine basin. A simple setting is considered, with uniform uplift rate, precipitation rate, and rock properties onshore. The pros and cons of this approach are discussed with respect to similar simulations performed considering only flux.

Reusable Launch Vehicle Control In Multiple Time Scale Sliding Modes

NASA Technical Reports Server (NTRS)

Shtessel, Yuri; Hall, Charles; Jackson, Mark

2000-01-01

A reusable launch vehicle control problem during ascent is addressed via multiple-time scaled continuous sliding mode control. The proposed sliding mode controller utilizes a two-loop structure and provides robust, de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of bounded external disturbances and plant uncertainties. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues placement. Overall stability of a two-loop control system is addressed. An optimal control allocation algorithm is designed that allocates torque commands into end-effector deflection commands, which are executed by the actuators. The dual-time scale sliding mode controller was designed for the X-33 technology demonstration sub-orbital launch vehicle in the launch mode. Simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in presence of external disturbances and vehicle inertia uncertainties. This is a significant advancement in performance over that achieved with linear, gain scheduled control systems currently being used for launch vehicles.

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Detection of bifurcations in noisy coupled systems from multiple time series

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

Williamson, Mark S., E-mail: m.s.williamson@exeter.ac.uk; Lenton, Timothy M.

We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, themore » possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.« less

Detection of bifurcations in noisy coupled systems from multiple time series

NASA Astrophysics Data System (ADS)

Williamson, Mark S.; Lenton, Timothy M.

2015-03-01

We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, the possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.

On the Discrete Spectrum of the Nonstationary Schrödinger Equation and Multipole Lumps of the Kadomtsev-Petviashvili I Equation

NASA Astrophysics Data System (ADS)

Villarroel, Javier; Ablowitz, Mark J.

The discrete spectrum of the nonstationary Schrödinger equation and localized solutions of the Kadomtsev-Petviashvili-I (KPI) equation are studied via the inverse scattering transform. It is shown that there exist infinitely many real and rationally decaying potentials which correspond to a discrete spectrum whose related eigenfunctions have multiple poles in the spectral parameter. An index or winding number is asssociated with each of these solutions. The resulting localized solutions of KPI behave as collection of individual humps with nonuniform dynamics.

A mathematical model of the mevalonate cholesterol biosynthesis pathway.

PubMed

Pool, Frances; Currie, Richard; Sweby, Peter K; Salazar, José Domingo; Tindall, Marcus J

2018-04-14

We formulate, parameterise and analyse a mathematical model of the mevalonate pathway, a key pathway in the synthesis of cholesterol. Of high clinical importance, the pathway incorporates rate limiting enzymatic reactions with multiple negative feedbacks. In this work we investigate the pathway dynamics and demonstrate that rate limiting steps and negative feedbacks within it act in concert to tightly regulate intracellular cholesterol levels. Formulated using the theory of nonlinear ordinary differential equations and parameterised in the context of a hepatocyte, the governing equations are analysed numerically and analytically. Sensitivity and mathematical analysis demonstrate the importance of the two rate limiting enzymes 3-hydroxy-3-methylglutaryl-CoA reductase and squalene synthase in controlling the concentration of substrates within the pathway as well as that of cholesterol. The role of individual feedbacks, both global (between that of cholesterol and sterol regulatory element-binding protein 2; SREBP-2) and local internal (between substrates in the pathway) are investigated. We find that whilst the cholesterol SREBP-2 feedback regulates the overall system dynamics, local feedbacks activate within the pathway to tightly regulate the overall cellular cholesterol concentration. The network stability is analysed by constructing a reduced model of the full pathway and is shown to exhibit one real, stable steady-state. We close by addressing the biological question as to how farnesyl-PP levels are affected by CYP51 inhibition, and demonstrate that the regulatory mechanisms within the network work in unison to ensure they remain bounded. Copyright © 2018 Elsevier Ltd. All rights reserved.

Studies into the nature of cosmic acceleration: Dark energy or a modification to gravity on cosmological scales

NASA Astrophysics Data System (ADS)

Dossett, Jason Nicholas

Since its discovery more than a decade ago, the problem of cosmic acceleration has become one of the largest in cosmology and physics as a whole. An unknown dark energy component of the universe is often invoked to explain this observation. Mathematically, this works because inserting a cosmic fluid with a negative equation of state into Einstein's equations provides an accelerated expansion. There are, however, alternative explanations for the observed cosmic acceleration. Perhaps the most promising of the alternatives is that, on the very largest cosmological scales, general relativity needs to be extended or a new, modified gravity theory must be used. Indeed, many modified gravity models are not only able to replicate the observed accelerated expansion without dark energy, but are also more compatible with a unified theory of physics. Thus it is the goal of this dissertation to develop and study robust tests that will be able to distinguish between these alternative theories of gravity and the need for a dark energy component of the universe. We will study multiple approaches using the growth history of large-scale structure in the universe as a way to accomplish this task. These approaches include studying what is known as the growth index parameter, a parameter that describes the logarithmic growth rate of structure in the universe, which describes the rate of formation of clusters and superclusters of galaxies over the entire age of the universe. We will explore the effectiveness of this parameter to distinguish between general relativity and modifications to gravity physics given realistic expectations of results from future experiments. Next, we will explore the modified growth formalism wherein deviations from the growth expected in general relativity are parameterized via changes to the growth equations, i.e. the perturbed Einstein's equations. We will also explore the impact of spatial curvature on these tests. Finally, we will study how dark energy with some unusual properties will affect the conclusiveness of these tests.

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

Garcia, Andres

Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems canmore » be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use Langevin Molecular Dynamics (MD) simulations to assess these parameters.« less

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

A Langevin equation for the rates of currency exchange based on the Markov analysis

NASA Astrophysics Data System (ADS)

Farahpour, F.; Eskandari, Z.; Bahraminasab, A.; Jafari, G. R.; Ghasemi, F.; Sahimi, Muhammad; Reza Rahimi Tabar, M.

2007-11-01

We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D and D, representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar.

Theoretical study of low-frequency noise and amplitude – frequency characteristics of a semiconductor laser with a fiber Bragg grating

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

Kurnosov, V D; Kurnosov, K V

2013-09-30

Using the rate equations for the density of photons and charge carriers, we have studied the amplitude low-frequency noise of a fibre Bragg grating semiconductor laser. The calculations rely on two versions of the rate equation for the carriers, characterised by the presence of the optical confinement coefficient for the term, which takes into account the rate of stimulated recombination. It is shown that the relative noise intensity, which is calculated by using the rate equation for the carriers without optical confinement, agrees better with the experimental results. The calculation of the amplitude – frequency characteristics (AFCs) has shown thatmore » it is impossible to give preference to any one of these systems, since the AFCs for the two versions of the rate equations for the carriers coincide. (lasers)« less

Hierarchical imputation of systematically and sporadically missing data: An approximate Bayesian approach using chained equations.

PubMed

Jolani, Shahab

2018-03-01

In health and medical sciences, multiple imputation (MI) is now becoming popular to obtain valid inferences in the presence of missing data. However, MI of clustered data such as multicenter studies and individual participant data meta-analysis requires advanced imputation routines that preserve the hierarchical structure of data. In clustered data, a specific challenge is the presence of systematically missing data, when a variable is completely missing in some clusters, and sporadically missing data, when it is partly missing in some clusters. Unfortunately, little is known about how to perform MI when both types of missing data occur simultaneously. We develop a new class of hierarchical imputation approach based on chained equations methodology that simultaneously imputes systematically and sporadically missing data while allowing for arbitrary patterns of missingness among them. Here, we use a random effect imputation model and adopt a simplification over fully Bayesian techniques such as Gibbs sampler to directly obtain draws of parameters within each step of the chained equations. We justify through theoretical arguments and extensive simulation studies that the proposed imputation methodology has good statistical properties in terms of bias and coverage rates of parameter estimates. An illustration is given in a case study with eight individual participant datasets. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Prediction of Broadband Shock-Associated Noise Including Propagation Effects Originating NASA

NASA Technical Reports Server (NTRS)

Miller, Steven; Morris, Philip J.

2012-01-01

An acoustic analogy is developed based on the Euler equations for broadband shock-associated noise (BBSAN) that directly incorporates the vector Green s function of the linearized Euler equations and a steady Reynolds-Averaged Navier-Stokes solution (SRANS) to describe the mean flow. The vector Green s function allows the BBSAN propagation through the jet shear layer to be determined. The large-scale coherent turbulence is modeled by two-point second order velocity cross-correlations. Turbulent length and time scales are related to the turbulent kinetic energy and dissipation rate. An adjoint vector Green s function solver is implemented to determine the vector Green s function based on a locally parallel mean flow at different streamwise locations. The newly developed acoustic analogy can be simplified to one that uses the Green s function associated with the Helmholtz equation, which is consistent with a previous formulation by the authors. A large number of predictions are generated using three different nozzles over a wide range of fully-expanded jet Mach numbers and jet stagnation temperatures. These predictions are compared with experimental data from multiple jet noise experimental facilities. In addition, two models for the so-called fine-scale mixing noise are included in the comparisons. Improved BBSAN predictions are obtained relative to other models that do not include propagation effects.

A dislocation density-based continuum model of the anisotropic shock response of single crystal α-cyclotrimethylene trinitramine

NASA Astrophysics Data System (ADS)

Luscher, D. J.; Addessio, F. L.; Cawkwell, M. J.; Ramos, K. J.

2017-01-01

We have developed a model for the finite deformation thermomechanical response of α-cyclotrimethylene trinitramine (RDX). Our model accounts for nonlinear thermoelastic lattice deformation through a free energy-based equation of state developed by Cawkwell et al. (2016) in combination with temperature and pressure dependent elastic constants, as well as dislocation-mediated plastic slip on a set of slip systems motivated by experimental observation. The kinetics of crystal plasticity are modeled using the Orowan equation relating slip rate to dislocation density and the dislocation velocity developed by Austin and McDowell (2011), which naturally accounts for transition from thermally activated to dislocation drag limited regimes. Evolution of dislocation density is specified in terms of local ordinary differential equations reflecting dislocation-dislocation interactions. This paper presents details of the theory and parameterization of the model, followed by discussion of simulations of flyer plate impact experiments. Impact conditions explored within this combined simulation and experimental effort span shock pressures ranging from 1 to 3 GPa for four crystallographic orientations and multiple specimen thicknesses. Simulation results generated using this model are shown to be in strong agreement with velocimetry measurements from the corresponding plate impact experiments. Finally, simulation results are used to motivate conclusions about the nature of dislocation-mediated plasticity in RDX.

Nonlinear Diophantine equation 11 x +13 y = z 2

NASA Astrophysics Data System (ADS)

Sugandha, A.; Tripena, A.; Prabowo, A.; Sukono, F.

2018-03-01

This research aims to obtaining the solutions (if any) from the Non Linear Diophantine equation of 11 x + 13 y = z 2. There are 3 possibilities to obtain the solutions (if any) from the Non Linear Diophantine equation, namely single, multiple, and no solution. This research is conducted in two stages: (1) by utilizing simulation to obtain the solutions (if any) from the Non Linear Diophantine equation of 11 x + 13 y = z 2 and (2) by utilizing congruency theory with its characteristics proven that the Non Linear Diophantine equation has no solution for non negative whole numbers (integers) of x, y, z.

Solving a mixture of many random linear equations by tensor decomposition and alternating minimization.

DOT National Transportation Integrated Search

2016-09-01

We consider the problem of solving mixed random linear equations with k components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels (which sample...

Using Structural Equation Modeling To Fit Models Incorporating Principal Components.

ERIC Educational Resources Information Center

Dolan, Conor; Bechger, Timo; Molenaar, Peter

1999-01-01

Considers models incorporating principal components from the perspectives of structural-equation modeling. These models include the following: (1) the principal-component analysis of patterned matrices; (2) multiple analysis of variance based on principal components; and (3) multigroup principal-components analysis. Discusses fitting these models…

Multiple scattering effects with cyclical terms in active remote sensing of vegetated surface using vector radiative transfer theory

USDA-ARS?s Scientific Manuscript database

The energy transport in a vegetated (corn) surface layer is examined by solving the vector radiative transfer equation using a numerical iterative approach. This approach allows a higher order that includes the multiple scattering effects. Multiple scattering effects are important when the optical t...

Multiple scales approach to weakly nonparallel and curvature effects: Details for the novice

NASA Technical Reports Server (NTRS)

Singer, Bart A.; Choudhari, Meelan

1995-01-01

A multiple scales approach is used to approximate the effects of nonparallelism and streamwise curvature on the stability of three-dimensional disturbances in incompressible flow. The multiple scales approach is implemented with the full second-order system of equations. A detailed exposition of the source of all terms is provided.

The Relevance of Depressive Symptoms and Social Support to Disability in Women with Multiple Sclerosis or Fibromyalgia

ERIC Educational Resources Information Center

Phillips, Lorraine J.

2010-01-01

Multiple sclerosis and fibromyalgia syndrome may spur substantial disability for those affected. Using structural equation modeling, this secondary analysis examined predictors of disability in women with multiple sclerosis (n = 118) and fibromyalgia syndrome (n = 197) recruited for separate wellness studies. Greater functional limitations, lower…

A Multiple Deficit Model of Reading Disability and Attention-Deficit/Hyperactivity Disorder: Searching for Shared Cognitive Deficits

ERIC Educational Resources Information Center

McGrath, Lauren M.; Pennington, Bruce F.; Shanahan, Michelle A.; Santerre-Lemmon, Laura E.; Barnard, Holly D.; Willcutt, Erik G.; DeFries, John C.; Olson, Richard K.

2011-01-01

Background: This study tests a multiple cognitive deficit model of reading disability (RD), attention-deficit/hyperactivity disorder (ADHD), and their comorbidity. Methods: A structural equation model (SEM) of multiple cognitive risk factors and symptom outcome variables was constructed. The model included phonological awareness as a unique…

Vacuum-bag-only processing of composites

NASA Astrophysics Data System (ADS)

Thomas, Shad

Ultrasonic imaging in the C-scan mode in conjunction with the amplitude of the reflected signal was used to measure flow rates of an epoxy resin film penetrating through the thickness of single layers of woven carbon fabric. Assemblies, comprised of a single layer of fabric and film, were vacuum-bagged and ultrasonically scanned in a water tank during impregnation at 50°C, 60°C, 70°C, and 80°C. Measured flow rates were plotted versus inverse viscosity to determine the permeability in the thin film, non-saturated system. The results demonstrated that ultrasonic imaging in the C-scan mode is an effective method of measuring z-direction resin flow through a single layer of fabric. The permeability values determined in this work were consistent with permeability values reported in the literature. Capillary flow was not observed at the temperatures and times required for pressurized flow to occur. The flow rate at 65°C was predicted from the linear plot of flow rate versus inverse viscosity. The effects of fabric architecture on through-thickness flow rates during impregnation of an epoxy resin film were measured by ultrasonic imaging. Multilayered laminates comprised of woven carbon fabrics and epoxy films (prepregs) were fabricated by vacuum-bagging. Ultrasonic imaging was performed in a heated water tank (65°C) during impregnation. Impregnation rates showed a strong dependence on fabric architecture, despite similar areal densities. Impregnation rates are directly affected by inter-tow spacing and tow nesting, which depend on fabric architecture, and are indirectly affected by areal densities. A new method of predicting resin infusion rates in prepreg and resin film infusion processes was proposed. The Stokes equation was used to derive an equation to predict the impregnation rate of laminates as a function of fabric architecture. Flow rate data previously measured by ultrasound was analyzed with the new equation and the Kozeny-Carman equation. A fiber interaction parameter was determined as a function of fabric architecture. The derived equation is straight-forward to use, unlike the Kozeny-Carman equation. The results demonstrated that the newly derived equation can be used to predict the resin infusion rate of multilayer laminates.

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

A composite velocity procedure for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1982-01-01

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Kinetic Glomerular Filtration Rate Equation Can Accommodate a Changing Body Volume: Derivation and Usage of the Formula.

PubMed

Chen, Sheldon

2018-05-22

Ascertaining a patient's kidney function is more difficult to do when the serum creatinine is changing than when it is stable. To accomplish the task, various kinetic clearance equations have been developed. To date, however, none of them have allowed for ongoing changes to the creatinine's volume of distribution. These diluting or concentrating effects on the [creatinine] can greatly impact the accuracy of kidney function assessment. Described herein is a model of creatinine kinetics that also accommodates volume changes. The differential equation is solved for the kinetic glomerular filtration rate (GFR), which is helpful information to the physician. Some of the equation's discontinuities, such as from dividing by a volume rate of zero, can be resolved by using limits. Being "volume-capable," the new kinetic equation reveals how a changing volume influences the maximum rate of rise in [creatinine], a parameter that heretofore was chosen empirically. To show the advantages of incorporating volume, the new and old kinetic equations are applied to a clinical case of overzealous fluid resuscitation. Appropriately, when the volume gain's dilution of [creatinine] is taken into account, the creatinine clearance is calculated to be substantially lower. In conclusion, the kinetic GFR equation has been upgraded to handle volume changes simultaneously with [creatinine] changes. Copyright © 2018. Published by Elsevier Inc.

Kinetic equations for cylindrically symmetric plasmas including atomic coherence and Coulomb potential effects

NASA Astrophysics Data System (ADS)

Csanak, G.; Fontes, C. J.; Kilcrease, D. P.; Hakel, P.; Inal, M. K.

2017-05-01

The rate equations used to model plasma kinetics and spectroscopy are typically obtained from intuitive considerations. A few years ago, the authors (Csanak et al 2011 J. Phys. B: At. Mol. Opt. Phys. 44 215701) have shown that the population-alignment collisional-radiative (CR) model and the magnetic sublevel to magnetic sublevel rate-equation scheme can be obtained from the Fano-Ben-Reuven quantum impact approximation (QIA). Here we provide a formal derivation of the rate-equation schemes for modeling hydrogenic plasmas and highly charged ionic plasmas with cylindrical symmetry using the QIA under certain approximations. In the case of hydrogenic plasmas the ‘accidental degeneracy’ (if present) leads to some coherences among the excited states of the atom (or ion) that have to be taken into account when constructing the rate equations. In the case of highly charged plasmas the Coulomb potential can be taken into account (as suggested originally by Baranger) in defining the ‘bath particles’, which leads to a derivation of the kinetic equations where no singularity occurs. For the case of spherically symmetric plasmas, this method also provides a derivation of the standard CR equations that have been implemented in many codes to successfully model the kinetics and spectra of highly charged ions.

Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft

NASA Technical Reports Server (NTRS)

Ardema, Mark D.; Windhorst, Robert; Phillips, James

1998-01-01

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Optimization of Supersonic Transport Trajectories

NASA Technical Reports Server (NTRS)

Ardema, Mark D.; Windhorst, Robert; Phillips, James

1998-01-01

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows.

PubMed

Liang, H; Shi, B C; Guo, Z L; Chai, Z H

2014-05-01

In this paper, a phase-field-based multiple-relaxation-time lattice Boltzmann (LB) model is proposed for incompressible multiphase flow systems. In this model, one distribution function is used to solve the Chan-Hilliard equation and the other is adopted to solve the Navier-Stokes equations. Unlike previous phase-field-based LB models, a proper source term is incorporated in the interfacial evolution equation such that the Chan-Hilliard equation can be derived exactly and also a pressure distribution is designed to recover the correct hydrodynamic equations. Furthermore, the pressure and velocity fields can be calculated explicitly. A series of numerical tests, including Zalesak's disk rotation, a single vortex, a deformation field, and a static droplet, have been performed to test the accuracy and stability of the present model. The results show that, compared with the previous models, the present model is more stable and achieves an overall improvement in the accuracy of the capturing interface. In addition, compared to the single-relaxation-time LB model, the present model can effectively reduce the spurious velocity and fluctuation of the kinetic energy. Finally, as an application, the Rayleigh-Taylor instability at high Reynolds numbers is investigated.

H theorem for generalized entropic forms within a master-equation framework

NASA Astrophysics Data System (ADS)

Casas, Gabriela A.; Nobre, Fernando D.; Curado, Evaldo M. F.

2016-03-01

The H theorem is proven for generalized entropic forms, in the case of a discrete set of states. The associated probability distributions evolve in time according to a master equation, for which the corresponding transition rates depend on these entropic forms. An important equation describing the time evolution of the transition rates and probabilities in such a way as to drive the system towards an equilibrium state is found. In the particular case of Boltzmann-Gibbs entropy, it is shown that this equation is satisfied in the microcanonical ensemble only for symmetric probability transition rates, characterizing a single path to the equilibrium state. This equation fulfils the proof of the H theorem for generalized entropic forms, associated with systems characterized by complex dynamics, e.g., presenting nonsymmetric probability transition rates and more than one path towards the same equilibrium state. Some examples considering generalized entropies of the literature are discussed, showing that they should be applicable to a wide range of natural phenomena, mainly those within the realm of complex systems.

The integrated Michaelis-Menten rate equation: déjà vu or vu jàdé?

PubMed

Goličnik, Marko

2013-08-01

A recent article of Johnson and Goody (Biochemistry, 2011;50:8264-8269) described the almost-100-years-old paper of Michaelis and Menten. Johnson and Goody translated this classic article and presented the historical perspective to one of incipient enzyme-reaction data analysis, including a pioneering global fit of the integrated rate equation in its implicit form to the experimental time-course data. They reanalyzed these data, although only numerical techniques were used to solve the model equations. However, there is also the still little known algebraic rate-integration equation in a closed form that enables direct fitting of the data. Therefore, in this commentary, I briefly present the integral solution of the Michaelis-Menten rate equation, which has been largely overlooked for three decades. This solution is expressed in terms of the Lambert W function, and I demonstrate here its use for global nonlinear regression curve fitting, as carried out with the original time-course dataset of Michaelis and Menten.

Chemical purity using quantitative 1H-nuclear magnetic resonance: a hierarchical Bayesian approach for traceable calibrations

NASA Astrophysics Data System (ADS)

Toman, Blaza; Nelson, Michael A.; Lippa, Katrice A.

2016-10-01

Chemical purity assessment using quantitative 1H-nuclear magnetic resonance spectroscopy is a method based on ratio references of mass and signal intensity of the analyte species to that of chemical standards of known purity. As such, it is an example of a calculation using a known measurement equation with multiple inputs. Though multiple samples are often analyzed during purity evaluations in order to assess measurement repeatability, the uncertainty evaluation must also account for contributions from inputs to the measurement equation. Furthermore, there may be other uncertainty components inherent in the experimental design, such as independent implementation of multiple calibration standards. As such, the uncertainty evaluation is not purely bottom up (based on the measurement equation) or top down (based on the experimental design), but inherently contains elements of both. This hybrid form of uncertainty analysis is readily implemented with Bayesian statistical analysis. In this article we describe this type of analysis in detail and illustrate it using data from an evaluation of chemical purity and its uncertainty for a folic acid material.

A general equation to obtain multiple cut-off scores on a test from multinomial logistic regression.

PubMed

Bersabé, Rosa; Rivas, Teresa

2010-05-01

The authors derive a general equation to compute multiple cut-offs on a total test score in order to classify individuals into more than two ordinal categories. The equation is derived from the multinomial logistic regression (MLR) model, which is an extension of the binary logistic regression (BLR) model to accommodate polytomous outcome variables. From this analytical procedure, cut-off scores are established at the test score (the predictor variable) at which an individual is as likely to be in category j as in category j+1 of an ordinal outcome variable. The application of the complete procedure is illustrated by an example with data from an actual study on eating disorders. In this example, two cut-off scores on the Eating Attitudes Test (EAT-26) scores are obtained in order to classify individuals into three ordinal categories: asymptomatic, symptomatic and eating disorder. Diagnoses were made from the responses to a self-report (Q-EDD) that operationalises DSM-IV criteria for eating disorders. Alternatives to the MLR model to set multiple cut-off scores are discussed.

Geographic associations between lactase phenotype, multiple sclerosis, and inflammatory bowel diseases; Does obesity trump geography?

PubMed

Szilagyi, Andew; Xue, Xiaoqing

2016-11-01

Geographic patterns with diminishing rates from north to south toward the equator have been described for a number of diseases, putatively related largely to "western" lifestyle. Among these the inflammatory bowel diseases; Crohn's (CD) and Ulcerative colitis (UC) have been prominent in sharing distributions with a number of autoimmune diseases. One of the interesting associations is the epidemiologic similarity with multiple sclerosis (MS). However, in addition, at least some of these diseases also correlated inversely with lactase non persistent population (LNP) distributions. It is hypothesized that MS should also have an inverse relationship with LNP. We provide support for this by comparing published MS, CD, UC and LNP national rates to the beginning of the new millennium. Possible links among these diseases may be an evolutionary signature of new genes which may have accompanied emergence of lactase persistence millennia ago. The emergent phenotypic dichotomy also forced different assimilation responses to lactose digestion. While intestinal retention of lactase results in direct host enzymatic digestion, in LNP persons intestinal bacterial metabolism of lactose impacts on the host micro-flora. These microbial changes may play some role in altering rates of diseases including IBD and MS. However, since the late 20th century previously observed patterns are changing. Although industrialization is considered to play an important modifying role, the rising rates of obesity with an emphasis on diet, and microfloral pathogenesis, but with an independent geographic pattern may also facilitate altering rates and geographic distributions of both of these and other diseases. Copyright © 2016 Elsevier Ltd. All rights reserved.

Alternatives for the Bedside Schwartz Equation to Estimate Glomerular Filtration Rate in Children.

PubMed

Pottel, Hans; Dubourg, Laurence; Goffin, Karolien; Delanaye, Pierre

2018-01-01

The bedside Schwartz equation has long been and still is the recommended equation to estimate glomerular filtration rate (GFR) in children. However, this equation is probably best suited to estimate GFR in children with chronic kidney disease (reduced GFR) but is not optimal for children with GFR >75 mL/min/1.73 m 2 . Moreover, the Schwartz equation requires the height of the child, information that is usually not available in the clinical laboratory. This makes automatic reporting of estimated glomerular filtration rate (eGFR) along with serum creatinine impossible. As the majority of children (even children referred to nephrology clinics) have GFR >75 mL/min/1.73 m 2 , it might be interesting to evaluate possible alternatives to the bedside Schwartz equation. The pediatric form of the Full Age Spectrum (FAS) equation offers an alternative to Schwartz, allowing automatic reporting of eGFR since height is not necessary. However, when height is involved in the FAS equation, the equation is essentially equal to the Schwartz equation for children, but there are large differences for adolescents. Combining standardized biomarkers increases the prediction performance of eGFR equations for children, reaching P10 ≈ 45% and P30 ≈ 90%. There are currently good and simple alternatives to the bedside Schwartz equation, but the more complex equations combining serum creatinine, serum cystatin C, and height show the highest accuracy and precision. Copyright © 2017 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.

Optically Pumped Coherent Mechanical Oscillators: The Laser Rate Equation Theory and Experimental Verification

DTIC Science & Technology

2012-10-23

Naeini A H, Hill J T, Krause A, Groblacher S, Aspelmeyer M and Painter O 2011 Nature 478 89 [14] Siegman A E 1986 Lasers (Sausalito, CA: University... laser rate equation theory and experimental verification 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT...coherent mechanical oscillators: the laser rate equation theory and experimental verification J B Khurgin1, M W Pruessner2,3, T H Stievater2 and W S

Statistical optimization of recycled-paper enzymatic hydrolysis for simultaneous saccharification and fermentation via central composite design.

PubMed

Liu, Qing; Cheng, Ke-ke; Zhang, Jian-an; Li, Jin-ping; Wang, Ge-hua

2010-01-01

A central composite design of the response surface methodology (RSM) was employed to study the effects of temperature, enzyme concentration, and stirring rate on recycled-paper enzymatic hydrolysis. Among the three variables, temperature and enzyme concentration significantly affected the conversion efficiency of substrate, whereas stirring rate was not effective. A quadratic polynomial equation was obtained for enzymatic hydrolysis by multiple regression analysis using RSM. The results of validation experiments were coincident with the predicted model. The optimum conditions for enzymatic hydrolysis were temperature, enzyme concentration, and stirring rate of 43.1 degrees C, 20 FPU g(-1) substrate, and 145 rpm, respectively. In the subsequent simultaneous saccharification and fermentation (SSF) experiment under the optimum conditions, the highest 28.7 g ethanol l(-1) was reached in the fed-batch SSF when 5% (w/v) substrate concentration was used initially, and another 5% added after 12 h fermentation. This ethanol output corresponded to 77.7% of the theoretical yield based on the glucose content in the raw material.

Observer-based perturbation extremum seeking control with input constraints for direct-contact membrane distillation process

NASA Astrophysics Data System (ADS)

Eleiwi, Fadi; Laleg-Kirati, Taous Meriem

2018-06-01

An observer-based perturbation extremum seeking control is proposed for a direct-contact membrane distillation (DCMD) process. The process is described with a dynamic model that is based on a 2D advection-diffusion equation model which has pump flow rates as process inputs. The objective of the controller is to optimise the trade-off between the permeate mass flux and the energy consumption by the pumps inside the process. Cases of single and multiple control inputs are considered through the use of only the feed pump flow rate or both the feed and the permeate pump flow rates. A nonlinear Lyapunov-based observer is designed to provide an estimation for the temperature distribution all over the designated domain of the DCMD process. Moreover, control inputs are constrained with an anti-windup technique to be within feasible and physical ranges. Performance of the proposed structure is analysed, and simulations based on real DCMD process parameters for each control input are provided.

Perturbation solutions of combustion instability problems

NASA Technical Reports Server (NTRS)

Googerdy, A.; Peddieson, J., Jr.; Ventrice, M.

1979-01-01

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Correlation of the rates of solvolysis of α-bromoisobutyrophenone using both simple and extended forms of the Grunwald-Winstein equation and the application of correlation analysis to related studies.

PubMed

Kevill, Dennis Neil; Kim, Chang-Bae; D'Souza, Malcolm John

2018-03-01

A Grunwald-Winstein treatment of the specific rates of solvolysis of α-bromoisobutyrophenone in 100% methanol and in several aqueous ethanol, methanol, acetone, 2,2,2-trifluoroethanol (TFE), and 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) mixtures gives a good logarithmic correlation against a linear combination of N T (solvent nucleophilicity) and Y Br (solvent ionizing power) values. The l and m sensitivity values are compared to those previously reported for α-bromoacetophenone and to those obtained from parallel treatments of literature specific rate values for the solvolyses of several tertiary mesylates containing a C(=O)R group attached at the α-carbon. Kinetic data obtained earlier by Pasto and Sevenair for the solvolyses of the same substrate in 75% aqueous ethanol (by weight) in the presence of silver perchlorate and perchloric acid are analyzed using multiple regression analysis.

On uniformly valid high-frequency far-field asymptotic solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Mcaninch, G. L.

1986-01-01

An asymptotic, large wave number approximation for the Helmholtz equation is derived. The theory is an extension of the geometric acoustic theory, and provides corrections to that theory in the form of multiplicative functions which satisfy parabolic equations. A simple example is used both to illustrate failure of the geometric theory for large propagation distances, and to show the improvement obtained by use of the new theory.

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.

Multiple determinants of transfer of evaluative function after conditioning with free-operant schedules of reinforcement.

PubMed

Dack, Charlotte; Reed, Phil; McHugh, Louise

2010-11-01

The aim of the four present experiments was to explore how different schedules of reinforcement influence schedule-induced behavior, their impact on evaluative ratings given to conditioned stimuli associated with each schedule through evaluative conditioning, and the transfer of these evaluations through derived stimulus networks. Experiment 1 compared two contrasting response reinforcement rules (variable ratio [VR], variable interval [VI]). Experiment 2 varied the response to reinforcement rule between two schedules but equated the outcome to response rate (differential reinforcement of high rate [DRH] vs. VR). Experiment 3 compared molar and molecular aspects of contingencies of reinforcement (tandem VIVR vs. tandem VRVI). Finally, Experiment 4 employed schedules that induced low rates of responding to determine whether, under these circumstances, responses were more sensitive to the molecular aspects of a schedule (differential reinforcement of low rate [DRL] vs. VI). The findings suggest that the transfer of evaluative functions is determined mainly by differences in response rate between the schedules and the molar aspects of the schedules. However, when neither schedule was based on a strong response reinforcement rule, the transfer of evaluative judgments came under the control of the molecular aspects of the schedule.

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

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

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

NASA Astrophysics Data System (ADS)

Paeng, Seong-Hun

2015-02-01

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

Validity of bioelectrical impedance measurement in predicting fat-free mass of Chinese children and adolescents.

PubMed

Wang, Lin; Hui, Stanley Sai-chuen; Wong, Stephen Heung-sang

2014-11-15

The current study aimed to examine the validity of various published bioelectrical impedance analysis (BIA) equations in estimating FFM among Chinese children and adolescents and to develop BIA equations for the estimation of fat-free mass (FFM) appropriate for Chinese children and adolescents. A total of 255 healthy Chinese children and adolescents aged 9 to 19 years old (127 males and 128 females) from Tianjin, China, participated in the BIA measurement at 50 kHz between the hand and the foot. The criterion measure of FFM was also employed using dual-energy X-ray absorptiometry (DEXA). FFM estimated from 24 published BIA equations was cross-validated against the criterion measure from DEXA. Multiple linear regression was conducted to examine alternative BIA equation for the studied population. FFM estimated from the 24 published BIA equations yielded high correlations with the directly measured FFM from DEXA. However, none of the 24 equations was statistically equivalent with the DEXA-measured FFM. Using multiple linear regression and cross-validation against DEXA measurement, an alternative prediction equation was determined as follows: FFM (kg)=1.613+0.742×height (cm)2/impedance (Ω)+0.151×body weight (kg); R2=0.95; SEE=2.45 kg; CV=6.5, 93.7% of the residuals of all the participants fell within the 95% limits of agreement. BIA was highly correlated with FFM in Chinese children and adolescents. When the new developed BIA equations are applied, BIA can provide a practical and valid measurement of body composition in Chinese children and adolescents.

Validity of Bioelectrical Impedance Measurement in Predicting Fat-Free Mass of Chinese Children and Adolescents

PubMed Central

Wang, Lin; Hui, Stanley Sai-chuen; Wong, Stephen Heung-sang

2014-01-01

Background The current study aimed to examine the validity of various published bioelectrical impedance analysis (BIA) equations in estimating FFM among Chinese children and adolescents and to develop BIA equations for the estimation of fat-free mass (FFM) appropriate for Chinese children and adolescents. Material/Methods A total of 255 healthy Chinese children and adolescents aged 9 to 19 years old (127 males and 128 females) from Tianjin, China, participated in the BIA measurement at 50 kHz between the hand and the foot. The criterion measure of FFM was also employed using dual-energy X-ray absorptiometry (DEXA). FFM estimated from 24 published BIA equations was cross-validated against the criterion measure from DEXA. Multiple linear regression was conducted to examine alternative BIA equation for the studied population. Results FFM estimated from the 24 published BIA equations yielded high correlations with the directly measured FFM from DEXA. However, none of the 24 equations was statistically equivalent with the DEXA-measured FFM. Using multiple linear regression and cross-validation against DEXA measurement, an alternative prediction equation was determined as follows: FFM (kg)=1.613+0.742×height (cm)2/impedance (Ω)+0.151×body weight (kg); R2=0.95; SEE=2.45kg; CV=6.5, 93.7% of the residuals of all the participants fell within the 95% limits of agreement. Conclusions BIA was highly correlated with FFM in Chinese children and adolescents. When the new developed BIA equations are applied, BIA can provide a practical and valid measurement of body composition in Chinese children and adolescents. PMID:25398209

CTE method and interaction solutions for the Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Ren, Bo

2017-02-01

The consistent tanh expansion method is applied to the Kadomtsev-Petviashvili equation. The interaction solutions among one soliton and other types of solitary waves, such as multiple resonant soliton solutions and cnoidal waves, are explicitly given. Some special concrete interaction solutions are discussed both in analytical and graphical ways.

Teaching Algebraic Equations to Middle School Students with Intellectual Disabilities

ERIC Educational Resources Information Center

Baker, Joshua N.; Rivera, Christopher J.; Morgan, Joseph John; Reese, Noelle

2015-01-01

The purpose of this study was to replicate similar instructional techniques of Jimenez, Browder, and Courtade (2008) using a single-subject multiple-probe across participants design to investigate the effects of task analytic instruction coupled with semi-concrete representations to teach linear algebraic equations to middle school students with…

Will Learning to Solve One-Step Equations Pose a Challenge to 8th Grade Students?

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Phan, Huy P.

2017-01-01

Assimilating multiple interactive elements simultaneously in working memory to allow understanding to occur, while solving an equation, would impose a high cognitive load. "Element interactivity" arises from the interaction between elements within and across operational and relational lines. Moreover, operating with special features…

How Students Process Equations in Solving Quantitative Synthesis Problems? Role of Mathematical Complexity in Students' Mathematical Performance

ERIC Educational Resources Information Center

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

2017-01-01

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,…

Determining Sample Size for Accurate Estimation of the Squared Multiple Correlation Coefficient.

ERIC Educational Resources Information Center

Algina, James; Olejnik, Stephen

2000-01-01

Discusses determining sample size for estimation of the squared multiple correlation coefficient and presents regression equations that permit determination of the sample size for estimating this parameter for up to 20 predictor variables. (SLD)

Non-equilibrium reaction rates in chemical kinetic equations

NASA Astrophysics Data System (ADS)

Gorbachev, Yuriy

2018-05-01

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

Taguchi method for partial differential equations with application in tumor growth.

PubMed

Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena

2014-01-01

The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Determination of dryout localization using a five-equation model of annular flow for boiling in minichannels

NASA Astrophysics Data System (ADS)

Wajs, Jan; Mikielewicz, Dariusz

2017-03-01

Detailed studies have suggested that the critical heat flux in the form of dryout in minichannels occurs when the combined effects of entrainment, deposition, and evaporation of the film make the film flow rate go gradually and smoothly to zero. Most approaches so far used the mass balance equation for the liquid film with appropriate formulations for the rate of deposition and entrainment respectively. It must be acknowledged that any discrepancy in determination of deposition and entrainment rates, together with cross-correlations between them, leads to the loss of accuracy of model predictions. Conservation equations relating the primary parameters are established for the liquid film and vapor core. The model consists of three mass balance equations, for liquid in the film as well as two-phase core and the gas phase itself. These equations are supplemented by the corresponding momentum equations for liquid in the film and the two-phase core. Applicability of the model has been tested on some experimental data.

The Aerodynamics of Axisymmetric Blunt Bodies Flying at Angle of Attack

NASA Technical Reports Server (NTRS)

Schoenenberger, Mark; Kutty, Prasad; Queen, Eric; Karlgaard, Chris

2014-01-01

The Mars Science Laboratory entry capsule is used as an example to demonstrate how a blunt body of revolution must be treated as asymmetric in some respects when flying at a non-zero trim angle of attack. A brief description of the axisymmetric moment equations are provided before solving a system of equations describing the lateral-directional moment equations for a blunt body trimming at an angle of attack. Simplifying assumptions are made which allow the solution to the equations to be rearranged to relate the roll and yaw stability with sideslip angle to the frequency of oscillation of the vehicle body rates. The equations show that for a blunt body the roll and yaw rates are in phase and proportional to each other. The ratio of the rates is determined by the static stability coefficients and mass properties about those axes. A trajectory simulation is used to validate the static yaw stability parameter identification equation and a simple method of identifying the oscillation frequency from the body rates. The approach is shown to successfully extract the modeled yaw stability coefficient along a simulated Mars entry in agreement with data earlier analysis of MSL flight data.

Quasi-periodic solutions to nonlinear beam equations on compact Lie groups with a multiplicative potential

NASA Astrophysics Data System (ADS)

Chen, Bochao; Gao, Yixian; Jiang, Shan; Li, Yong

2018-06-01

The goal of this work is to study the existence of quasi-periodic solutions to nonlinear beam equations with a multiplicative potential. The nonlinearity is required to only finitely differentiable and the frequency is along a pre-assigned direction. The result holds on any compact Lie group or homogeneous manifold with respect to a compact Lie group, which includes standard torus Td, special orthogonal group SO (d), special unitary group SU (d), spheres Sd and the real and complex Grassmannians. The proof is based on a differentiable Nash-Moser iteration scheme.

Planned versus actual outcomes as a result of animal feeding operation decisions for managing phosphorus.

PubMed

Cabot, Perry E; Nowak, Pete

2005-01-01

The paper explores how decisions made on animal feeding operations (AFOs) influence the management of manure and phosphorus. Variability among these decisions from operation to operation and from field to field can influence the validity of nutrient loss risk assessments. These assessments are based on assumptions that the decision outcomes regarding manure distribution will occur as they are planned. The discrepancy between planned versus actual outcomes in phosphorus management was explored on nine AFOs managing a contiguous set of 210 fields in south-central Wisconsin. A total of 2611 soil samples were collected and multiple interviews conducted to assign phosphorus index (PI) ratings to the fields. Spearman's rank correlation coefficients (r(S)) indicated that PI ratings were less sensitive to soil test phosphorus (STP) levels (r(S) = 0.378), universal soil loss equation (USLE) (r(S) = 0.261), ratings for chemical fertilizer application (r(S) = 0.185), and runoff class (r(S) = -0.089), and more sensitive to ratings for manure application (r(S) = 0.854). One-way ANOVA indicated that mean field STP levels were more homogenous than field PI ratings between AFOs. Kolmogorov-Smirnov (K-S) tests displayed several nonsignificant comparisons for cumulative distribution functions, S(x), of mean STP levels on AFO fields. On the other hand, the K-S tests of S(x) for PI ratings indicated that the majority of these S(x) functions were significantly different between AFOs at or greater than the 0.05 significance level. Interviews suggested multiple reasons for divergence between planned and actual outcomes in managing phosphorus, and that this divergence arises at the strategic, tactical, and operational levels of decision-making.

Implementation of Kane's Method for a Spacecraft Composed of Multiple Rigid Bodies

NASA Technical Reports Server (NTRS)

Stoneking, Eric T.

2013-01-01

Equations of motion are derived for a general spacecraft composed of rigid bodies connected via rotary (spherical or gimballed) joints in a tree topology. Several supporting concepts are developed in depth. Basis dyads aid in the transition from basis-free vector equations to component-wise equations. Joint partials allow abstraction of 1-DOF, 2-DOF, 3-DOF gimballed and spherical rotational joints to a common notation. The basic building block consisting of an "inner" body and an "outer" body connected by a joint enables efficient organization of arbitrary tree structures. Kane's equation is recast in a form which facilitates systematic assembly of large systems of equations, and exposes a relationship of Kane's equation to Newton and Euler's equations which is obscured by the usual presentation. The resulting system of dynamic equations is of minimum dimension, and is suitable for numerical solution by computer. Implementation is ·discussed, and illustrative simulation results are presented.

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

USGS Publications Warehouse

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

2009-01-01

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

Multiple model cardinalized probability hypothesis density filter

NASA Astrophysics Data System (ADS)

Georgescu, Ramona; Willett, Peter

2011-09-01

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

Measuring dynamic infiltration rates during rainfall of fluctuating intensity: an approach using affine Horton equations.

NASA Astrophysics Data System (ADS)

Dunkerley, David

2017-04-01

It is important to develop methods for determining infiltrability and infiltration rates under conditions of fluctuating rainfall intensity, since rainfall intensity rarely remains constant. During rain of fluctuating intensity, ponding deepens and dissipates, and the drivers of soil infiltration, including sorptivity, fluctuate in value. This has been explored on dryland soils in the field, using small plots and rainfall simulation, involving repeated changes in intensity as well as short and long hiatuses in rainfall. The field area was the Fowlers Gap Arid Zone Research Station, in western NSW, Australia. The field experiments used multiple 60 minute design rainfall events that all had the same total depth and average rainfall intensity, but which included intensity bursts at various positions within the event. These were based on the character of local rainfall events in the field area. Infiltration was found from plot runoff rates measured every 2 minutes, and rainfall intensities that were adjusted by computer-controlled pumps at 1 second intervals. Data were analysed by fitting a family of affine Horton equations, all having the same final infiltrability (about 6-7 mm/h) but having initial infiltrabilities and exponential decay constants that were permitted to recover during periods of very low intensity rain, or rainfall hiatuses. Results show that the terms in the Horton equation, f0, fc, and Kf, can all be estimated from field data of the kind collected. This is a considerable advance over 'steady-state' rainfall simulation methods, which typically only allow the estimation of the final infiltrability fc. This may rarely be reached owing to the occurrence of short rainfall events, or to changing intensity under natural rainfall, that prohibits the establishment of steady-state infiltration and runoff. Importantly, this method allows a focus on the recovery of infiltrability during periods of reduced rainfall intensity. Recovery of infiltrability is shown to proceed at rates of up to 1 mm/h per minute of hiatus time, or by 20 mm/h during a 20 minute period of low rainfall intensity.

Comparison of Different Shrinkage Formulas in Estimating Population Multiple Correlation Coefficients.

ERIC Educational Resources Information Center

Carter, David S.

1979-01-01

There are a variety of formulas for reducing the positive bias which occurs in estimating R squared in multiple regression or correlation equations. Five different formulas are evaluated in a Monte Carlo study, and recommendations are made. (JKS)

Accounting for Multiple Births in Neonatal and Perinatal Trials: Systematic Review and Case Study

PubMed Central

Hibbs, Anna Maria; Black, Dennis; Palermo, Lisa; Cnaan, Avital; Luan, Xianqun; Truog, William E; Walsh, Michele C; Ballard, Roberta A

2010-01-01

Objectives To determine the prevalence in the neonatal literature of statistical approaches accounting for the unique clustering patterns of multiple births. To explore the sensitivity of an actual trial to several analytic approaches to multiples. Methods A systematic review of recent perinatal trials assessed the prevalence of studies accounting for clustering of multiples. The NO CLD trial served as a case study of the sensitivity of the outcome to several statistical strategies. We calculated odds ratios using non-clustered (logistic regression) and clustered (generalized estimating equations, multiple outputation) analyses. Results In the systematic review, most studies did not describe the randomization of twins and did not account for clustering. Of those studies that did, exclusion of multiples and generalized estimating equations were the most common strategies. The NO CLD study included 84 infants with a sibling enrolled in the study. Multiples were more likely than singletons to be white and were born to older mothers (p<0.01). Analyses that accounted for clustering were statistically significant; analyses assuming independence were not. Conclusions The statistical approach to multiples can influence the odds ratio and width of confidence intervals, thereby affecting the interpretation of a study outcome. A minority of perinatal studies address this issue. PMID:19969305

Accounting for multiple births in neonatal and perinatal trials: systematic review and case study.

PubMed

Hibbs, Anna Maria; Black, Dennis; Palermo, Lisa; Cnaan, Avital; Luan, Xianqun; Truog, William E; Walsh, Michele C; Ballard, Roberta A

2010-02-01

To determine the prevalence in the neonatal literature of statistical approaches accounting for the unique clustering patterns of multiple births and to explore the sensitivity of an actual trial to several analytic approaches to multiples. A systematic review of recent perinatal trials assessed the prevalence of studies accounting for clustering of multiples. The Nitric Oxide to Prevent Chronic Lung Disease (NO CLD) trial served as a case study of the sensitivity of the outcome to several statistical strategies. We calculated odds ratios using nonclustered (logistic regression) and clustered (generalized estimating equations, multiple outputation) analyses. In the systematic review, most studies did not describe the random assignment of twins and did not account for clustering. Of those studies that did, exclusion of multiples and generalized estimating equations were the most common strategies. The NO CLD study included 84 infants with a sibling enrolled in the study. Multiples were more likely than singletons to be white and were born to older mothers (P < .01). Analyses that accounted for clustering were statistically significant; analyses assuming independence were not. The statistical approach to multiples can influence the odds ratio and width of confidence intervals, thereby affecting the interpretation of a study outcome. A minority of perinatal studies address this issue. Copyright 2010 Mosby, Inc. All rights reserved.

Spectral sensitivity of the photointrinsic iris in the red-eared slider turtle (Trachemys scripta elegans).

PubMed

Sipe, Grayson O; Dearworth, James R; Selvarajah, Brian P; Blaum, Justin F; Littlefield, Tory E; Fink, Deborah A; Casey, Corinne N; McDougal, David H

2011-01-01

Our goal in this study was to examine the red-eared slider turtle for a photomechanical response (PMR) and define its spectral sensitivity. Pupils of enucleated eyes constricted to light by ∼11%, which was one-third the response measured in alert behaving turtles at ∼33%. Rates of constriction in enucleated eyes that were measured by time constants (1.44-3.70 min) were similar to those measured in turtles at 1.97 min. Dilation recovery rates during dark adaptation for enucleated eyes were predicted using line equations and computed times for reaching maximum sizes between 26 and 44 min. Times were comparable to the measures in turtles where maximum pupil size occurred within 40 min and possessed a time constant of 12.78 min. Hill equations were used to derive irradiance threshold values from enucleated hemisected eyes and then plot a spectral sensitivity curve. The analysis of the slopes and maximum responses revealed contribution from at least two different photopigments, one with a peak at 410 nm and another with a peak at 480 nm. Fits by template equations suggest that contractions are triggered by multiple photopigments in the iris including an opsin-based visual pigment and some other novel photopigment, or a cryptochrome with an absorbance spectrum significantly different from that used in our model. In addition to being regulated by retinal feedback via parasympathetic nervous pathways, the results support that the iris musculature is photointrinsically responsive. In the turtle, the control of its direct pupillary light response (dPLR) includes photoreceptive mechanisms occurring both in its iris and in its retina. Copyright © 2010 Elsevier Ltd. All rights reserved.

Assessment of the effect of visual impairment on mortality through multiple health pathways: structural equation modeling.

PubMed

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

2008-08-01

To estimate the direct effects of self-reported visual impairment (VI) on health, disability, and mortality and to estimate the indirect effects of VI on mortality through health and disability mediators. The National Health Interview Survey (NHIS) is a population-based annual survey designed to be representative of the U.S. civilian noninstitutionalized population. The National Death Index of 135,581 NHIS adult participants, 18 years of age and older, from 1986 to 1996 provided the mortality linkage through 2002. A generalized linear structural equation model (GSEM) with latent variable was used to estimate the results of a system of equations with various outcomes. Standard errors and test statistics were corrected for weighting, clustering, and stratification. VI affects mortality, when direct adjustment was made for the covariates. Severe VI increases the hazard rate by a factor of 1.28 (95% CI: 1.07-1.53) compared with no VI, and some VI increases the hazard by a factor of 1.13 (95% CI: 1.07-1.20). VI also affects mortality indirectly through self-rated health and disability. The total effects (direct effects plus mediated effects) on the hazard of mortality of severe VI and some VI relative to no VI are hazard ratio (HR) 1.54 (95% CI: 1.28-1.86) and HR 1.23 (95% CI: 1.16-1.31), respectively. In addition to the direct link between VI and mortality, the effects of VI on general health and disability contribute to an increased risk of death. Ignoring the latter may lead to an underestimation of the substantive impact of VI on mortality.

Model for predicting peak expiratory flow rate of Nigerian workers in a cement factory in Itori, Ogun State, Nigeria.

PubMed

Ismaila, Salami Olasunkanmi; Akanbi, Olusegun Gabriel; Olaoniye, Wasiu

2015-01-01

The main aim of the study was to propose a model for predicting the peak expiratory flow rate (PEFR) of Nigerian workers in a cement factory. Sixty randomly selected non-smoker and healthy workers (30 in production sections, 30 in the administrative section of the factory) participated in the study. Their physical characteristics and PEFR were measured. Multiple correlations using SPSS version 16.0 were performed on the data. The values of PEFR, using the obtained model, were compared with the measured values using a two-tailed t test. There were positive correlations among age, height and PEFR. A prediction equation for PEFR based on age, height, weight and years of exposure (experience) was obtained with R² = .843 (p < 0.001). The developed model will be useful for the management in determining PEFR of workers in the cement industry for possible medical attention.

[Optimization of one-step pelletization technology of Biqiu granules by Plackett-Burman design and Box-Behnken response surface methodology].

PubMed

Zhang, Yan-jun; Liu, Li-li; Hu, Jun-hua; Wu, Yun; Chao, En-xiang; Xiao, Wei

2015-11-01

First with the qualified rate of granules as the evaluation index, significant influencing factors were firstly screened by Plackett-Burman design. Then, with the qualified rate and moisture content as the evaluation indexes, significant factors that affect one-step pelletization technology were further optimized by Box-Behnken design; experimental data were imitated by multiple regression and second-order polynomial equation; and response surface method was used for predictive analysis of optimal technology. The best conditions were as follows: inlet air temperature of 85 degrees C, sample introduction speed of 33 r x min(-1), density of concrete 1. 10. One-step pelletization technology of Biqiu granules by Plackett-Burman design and Box-Behnken response surface methodology was stable and feasible with good predictability, which provided reliable basis for the industrialized production of Biqiu granules.

Nonlinear stability of non-stationary cross-flow vortices in compressible boundary layers

NASA Technical Reports Server (NTRS)

Gajjar, J. S. B.

1995-01-01

The nonlinear evolution of long wavelength non-stationary cross-flow vortices in a compressible boundary layer is investigated and the work extends that of Gajjar (1994) to flows involving multiple critical layers. The basic flow profile considered in this paper is that appropriate for a fully three-dimensional boundary layer with O(1) Mach number and with wall heating or cooling. The governing equations for the evolution of the cross-flow vortex are obtained and some special cases are discussed. One special case includes linear theory where exact analytic expressions for the growth rate of the vortices are obtained. Another special case is a generalization of the Bassom & Gajjar (1988) results for neutral waves to compressible flows. The viscous correction to the growth rate is derived and it is shown how the unsteady nonlinear critical layer structure merges with that for a Haberman type of viscous critical layer.

Multifractal analysis of time series generated by discrete Ito equations

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

Telesca, Luciano; Czechowski, Zbigniew; Lovallo, Michele

2015-06-15

In this study, we show that discrete Ito equations with short-tail Gaussian marginal distribution function generate multifractal time series. The multifractality is due to the nonlinear correlations, which are hidden in Markov processes and are generated by the interrelation between the drift and the multiplicative stochastic forces in the Ito equation. A link between the range of the generalized Hurst exponents and the mean of the squares of all averaged net forces is suggested.

Evaluation of atomic pressure in the multiple time-step integration algorithm.

PubMed

Andoh, Yoshimichi; Yoshii, Noriyuki; Yamada, Atsushi; Okazaki, Susumu

2017-04-15

In molecular dynamics (MD) calculations, reduction in calculation time per MD loop is essential. A multiple time-step (MTS) integration algorithm, the RESPA (Tuckerman and Berne, J. Chem. Phys. 1992, 97, 1990-2001), enables reductions in calculation time by decreasing the frequency of time-consuming long-range interaction calculations. However, the RESPA MTS algorithm involves uncertainties in evaluating the atomic interaction-based pressure (i.e., atomic pressure) of systems with and without holonomic constraints. It is not clear which intermediate forces and constraint forces in the MTS integration procedure should be used to calculate the atomic pressure. In this article, we propose a series of equations to evaluate the atomic pressure in the RESPA MTS integration procedure on the basis of its equivalence to the Velocity-Verlet integration procedure with a single time step (STS). The equations guarantee time-reversibility even for the system with holonomic constrants. Furthermore, we generalize the equations to both (i) arbitrary number of inner time steps and (ii) arbitrary number of force components (RESPA levels). The atomic pressure calculated by our equations with the MTS integration shows excellent agreement with the reference value with the STS, whereas pressures calculated using the conventional ad hoc equations deviated from it. Our equations can be extended straightforwardly to the MTS integration algorithm for the isothermal NVT and isothermal-isobaric NPT ensembles. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Effects of Recovery Behavior and Strain-Rate Dependence of Stress-Strain Curve on Prediction Accuracy of Thermal Stress Analysis During Casting

NASA Astrophysics Data System (ADS)

Motoyama, Yuichi; Shiga, Hidetoshi; Sato, Takeshi; Kambe, Hiroshi; Yoshida, Makoto

2017-06-01

Recovery behavior (recovery) and strain-rate dependence of the stress-strain curve (strain-rate dependence) are incorporated into constitutive equations of alloys to predict residual stress and thermal stress during casting. Nevertheless, few studies have systematically investigated the effects of these metallurgical phenomena on the prediction accuracy of thermal stress in a casting. This study compares the thermal stress analysis results with in situ thermal stress measurement results of an Al-Si-Cu specimen during casting. The results underscore the importance for the alloy constitutive equation of incorporating strain-rate dependence to predict thermal stress that develops at high temperatures where the alloy shows strong strain-rate dependence of the stress-strain curve. However, the prediction accuracy of the thermal stress developed at low temperatures did not improve by considering the strain-rate dependence. Incorporating recovery into the constitutive equation improved the accuracy of the simulated thermal stress at low temperatures. Results of comparison implied that the constitutive equation should include strain-rate dependence to simulate defects that develop from thermal stress at high temperatures, such as hot tearing and hot cracking. Recovery should be incorporated into the alloy constitutive equation to predict the casting residual stress and deformation caused by the thermal stress developed mainly in the low temperature range.

An efficient, explicit finite-rate algorithm to compute flows in chemical nonequilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

An explicit finite-rate code was developed to compute hypersonic viscous chemically reacting flows about three-dimensional bodies. Equations describing the finite-rate chemical reactions were fully coupled to the gas dynamic equations using a new coupling technique. The new technique maintains stability in the explicit finite-rate formulation while permitting relatively large global time steps.

Bilinear approach to Kuperschmidt super-KdV type equations

NASA Astrophysics Data System (ADS)

Babalic, Corina N.; Carstea, A. S.

2018-06-01

Hirota bilinear form and soliton solutions for the super-KdV (Korteweg–de Vries) equation of Kuperschmidt (Kuper–KdV) are given. It is shown that even though the collision of supersolitons is more complicated than in the case of the supersymmetric KdV equation of Manin–Radul, the asymptotic effect of the interaction is simpler. As a physical application it is shown that the well-known FPU problem, having a phonon-mediated interaction of some internal degrees of freedom expressed through Grassmann fields, transforms to the Kuper–KdV equation in a multiple-scale approach.

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations

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

Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C., E-mail: waymire@math.oregonstate.edu

2015-07-15

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturallymore » arise as a result of this investigation.« less

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations.

PubMed

Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C

2015-07-01

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.

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.

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.

Using the Multiplicative Schwarz Alternating Algorithm (MSAA) for Solving the Large Linear System of Equations Related to Global Gravity Field Recovery up to Degree and Order 120

NASA Astrophysics Data System (ADS)

Safari, A.; Sharifi, M. A.; Amjadiparvar, B.

2010-05-01

The GRACE mission has substantiated the low-low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high-low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair is the mostly used observable for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. In this paper, mathematical formulae for LOS acceleration difference observations have been derived and the corresponding linear system of equations has been set up for spherical harmonic up to degree and order 120. The total number of unknowns is 14641. Such a linear equation system can be solved with iterative solvers or direct solvers. However, the runtime of direct methods or that of iterative solvers without a suitable preconditioner increases tremendously. This is the reason why we need a more sophisticated method to solve the linear system of problems with a large number of unknowns. Multiplicative variant of the Schwarz alternating algorithm is a domain decomposition method, which allows it to split the normal matrix of the system into several smaller overlaped submatrices. In each iteration step the multiplicative variant of the Schwarz alternating algorithm solves linear systems with the matrices obtained from the splitting successively. It reduces both runtime and memory requirements drastically. In this paper we propose the Multiplicative Schwarz Alternating Algorithm (MSAA) for solving the large linear system of gravity field recovery. The proposed algorithm has been tested on the International Association of Geodesy (IAG)-simulated data of the GRACE mission. The achieved results indicate the validity and efficiency of the proposed algorithm in solving the linear system of equations from accuracy and runtime points of view. Keywords: Gravity field recovery, Multiplicative Schwarz Alternating Algorithm, Low-Low Satellite-to-Satellite Tracking

Malignant testicular tumour incidence and mortality trends

PubMed Central

Wojtyła-Buciora, Paulina; Więckowska, Barbara; Krzywinska-Wiewiorowska, Małgorzata; Gromadecka-Sutkiewicz, Małgorzata

2016-01-01

Aim of the study In Poland testicular tumours are the most frequent cancer among men aged 20–44 years. Testicular tumour incidence since the 1980s and 1990s has been diversified geographically, with an increased risk of mortality in Wielkopolska Province, which was highlighted at the turn of the 1980s and 1990s. The aim of the study was the comparative analysis of the tendencies in incidence and death rates due to malignant testicular tumours observed among men in Poland and in Wielkopolska Province. Material and methods Data from the National Cancer Registry were used for calculations. The incidence/mortality rates among men due to malignant testicular cancer as well as the tendencies in incidence/death ratio observed in Poland and Wielkopolska were established based on regression equation. The analysis was deepened by adopting the multiple linear regression model. A p-value < 0.05 was arbitrarily adopted as the criterion of statistical significance, and for multiple comparisons it was modified according to the Bonferroni adjustment to a value of p < 0.0028. Calculations were performed with the use of PQStat v1.4.8 package. Results The incidence of malignant testicular neoplasms observed among men in Poland and in Wielkopolska Province indicated a significant rising tendency. The multiple linear regression model confirmed that the year variable is a strong incidence forecast factor only within the territory of Poland. A corresponding analysis of mortality rates among men in Poland and in Wielkopolska Province did not show any statistically significant correlations. Conclusions Late diagnosis of Polish patients calls for undertaking appropriate educational activities that would facilitate earlier reporting of the patients, thus increasing their chances for recovery. Introducing preventive examinations in the regions of increased risk of testicular tumour may allow earlier diagnosis. PMID:27095941

Hybrid colored noise process with space-dependent switching rates

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.; Lawley, Sean D.

2017-07-01

A fundamental issue in the theory of continuous stochastic process is the interpretation of multiplicative white noise, which is often referred to as the Itô-Stratonovich dilemma. From a physical perspective, this reflects the need to introduce additional constraints in order to specify the nature of the noise, whereas from a mathematical perspective it reflects an ambiguity in the formulation of stochastic differential equations (SDEs). Recently, we have identified a mechanism for obtaining an Itô SDE based on a form of temporal disorder. Motivated by switching processes in molecular biology, we considered a Brownian particle that randomly switches between two distinct conformational states with different diffusivities. In each state, the particle undergoes normal diffusion (additive noise) so there is no ambiguity in the interpretation of the noise. However, if the switching rates depend on position, then in the fast switching limit one obtains Brownian motion with a space-dependent diffusivity of the Itô form. In this paper, we extend our theory to include colored additive noise. We show that the nature of the effective multiplicative noise process obtained by taking both the white-noise limit (κ →0 ) and fast switching limit (ɛ →0 ) depends on the order the two limits are taken. If the white-noise limit is taken first, then we obtain Itô, and if the fast switching limit is taken first, then we obtain Stratonovich. Moreover, the form of the effective diffusion coefficient differs in the two cases. The latter result holds even in the case of space-independent transition rates, where one obtains additive noise processes with different diffusion coefficients. Finally, we show that yet another form of multiplicative noise is obtained in the simultaneous limit ɛ ,κ →0 with ɛ /κ2 fixed.

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

Chemical vapor deposition fluid flow simulation modelling tool

NASA Technical Reports Server (NTRS)

Bullister, Edward T.

1992-01-01

Accurate numerical simulation of chemical vapor deposition (CVD) processes requires a general purpose computational fluid dynamics package combined with specialized capabilities for high temperature chemistry. In this report, we describe the implementation of these specialized capabilities in the spectral element code NEKTON. The thermal expansion of the gases involved is shown to be accurately approximated by the low Mach number perturbation expansion of the incompressible Navier-Stokes equations. The radiative heat transfer between multiple interacting radiating surfaces is shown to be tractable using the method of Gebhart. The disparate rates of reaction and diffusion in CVD processes are calculated via a point-implicit time integration scheme. We demonstrate the use above capabilities on prototypical CVD applications.

Control law synthesis and optimization software for large order aeroservoelastic systems

NASA Technical Reports Server (NTRS)

Mukhopadhyay, V.; Pototzky, A.; Noll, Thomas

1989-01-01

A flexible aircraft or space structure with active control is typically modeled by a large-order state space system of equations in order to accurately represent the rigid and flexible body modes, unsteady aerodynamic forces, actuator dynamics and gust spectra. The control law of this multi-input/multi-output (MIMO) system is expected to satisfy multiple design requirements on the dynamic loads, responses, actuator deflection and rate limitations, as well as maintain certain stability margins, yet should be simple enough to be implemented on an onboard digital microprocessor. A software package for performing an analog or digital control law synthesis for such a system, using optimal control theory and constrained optimization techniques is described.

External noise-induced transitions in a current-biased Josephson junction

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

Huang, Qiongwei; Xue, Changfeng, E-mail: cfxue@163.com; Tang, Jiashi

We investigate noise-induced transitions in a current-biased and weakly damped Josephson junction in the presence of multiplicative noise. By using the stochastic averaging procedure, the averaged amplitude equation describing dynamic evolution near a constant phase difference is derived. Numerical results show that a stochastic Hopf bifurcation between an absorbing and an oscillatory state occurs. This means the external controllable noise triggers a transition into the non-zero junction voltage state. With the increase of noise intensity, the stationary probability distribution peak shifts and is characterised by increased width and reduced height. And the different transition rates are shown for large andmore » small bias currents.« less

Leak rates in sealed cells.

NASA Technical Reports Server (NTRS)

Frank, H. A.; Uchiyama, A. A.

1973-01-01

Water vapor loss rates were determined from simulated and imperfectly sealed alkaline cells in the vacuum environment. The observed rates were found to be in agreement with a semi-empirical equation employed in vacuum technology. Results thereby give support for using this equation for the prediction of loss rates of battery gases and vapors to the aerospace environment. On this basis it was shown how the equation can be applied to the solution of many heretofore unresolved questions regarding leaks in batteries. Among these are the maximum permissible leak size consistent with a given cell life or conversely the maximum life consistent with a given leak size. It was also shown that loss rates of these cells in the terrestrial environment are several orders of magnitude less than the corresponding loss rates in the aerospace environment.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Depoliticizing Minority Admissions through Predicted Graduation Equations. AIR Forum 1982 Paper.

ERIC Educational Resources Information Center

Sanford, Timothy R.

The way that the University of North Carolina, Chapel Hill, has tried to depoliticize minority admissions through the use of predicted graduation equations that are race specific is examined. Multiple regression and discriminant analyses were used with nine independent variables (primarily academic) to predict graduation status of 1974 entering…

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…

Balancing the Readiness Equation in Early Childhood Education Reform

ERIC Educational Resources Information Center

Brown, Christopher P.

2010-01-01

As policy-makers continue to implement early childhood education reforms that frame the field as a mechanism that is to ready children for elementary school success, questions arise as to how the multiple variables in the readiness equation, such as the child, family, and program, are affected by these policies. The instrumental case study…

Toward the Development of a Model to Estimate the Readability of Credentialing-Examination Materials

ERIC Educational Resources Information Center

Badgett, Barbara A.

2010-01-01

The purpose of this study was to develop a set of procedures to establish readability, including an equation, that accommodates the multiple-choice item format and occupational-specific language related to credentialing examinations. The procedures and equation should be appropriate for learning materials, examination materials, and occupational…

Fitting Meta-Analytic Structural Equation Models with Complex Datasets

ERIC Educational Resources Information Center

Wilson, Sandra Jo; Polanin, Joshua R.; Lipsey, Mark W.

2016-01-01

A modification of the first stage of the standard procedure for two-stage meta-analytic structural equation modeling for use with large complex datasets is presented. This modification addresses two common problems that arise in such meta-analyses: (a) primary studies that provide multiple measures of the same construct and (b) the correlation…

Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves

NASA Astrophysics Data System (ADS)

Tobita, Miwa; Omura, Yoshiharu

2018-03-01

We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.

Gyrokinetic theory for particle and energy transport in fusion plasmas

NASA Astrophysics Data System (ADS)

Falessi, Matteo Valerio; Zonca, Fulvio

2018-03-01

A set of equations is derived describing the macroscopic transport of particles and energy in a thermonuclear plasma on the energy confinement time. The equations thus derived allow studying collisional and turbulent transport self-consistently, retaining the effect of magnetic field geometry without postulating any scale separation between the reference state and fluctuations. Previously, assuming scale separation, transport equations have been derived from kinetic equations by means of multiple-scale perturbation analysis and spatio-temporal averaging. In this work, the evolution equations for the moments of the distribution function are obtained following the standard approach; meanwhile, gyrokinetic theory has been used to explicitly express the fluctuation induced fluxes. In this way, equations for the transport of particles and energy up to the transport time scale can be derived using standard first order gyrokinetics.

Near-wall modelling of compressible turbulent flows

NASA Technical Reports Server (NTRS)

So, Ronald M. C.

1990-01-01

Work was carried out to formulate near-wall models for the equations governing the transport of the temperature-variance and its dissipation rate. With these equations properly modeled, a foundation is laid for their extension together with the heat-flux equations to compressible flows. This extension is carried out in a manner similar to that used to extend the incompressible near-wall Reynolds-stress models to compressible flows. The methodology used to accomplish the extension of the near-wall Reynolds-stress models is examined and the actual extension of the models for the Reynolds-stress equations and the near-wall dissipation-rate equation to compressible flows is given. Then the formulation of the near-wall models for the equations governing the transport of the temperature variance and its dissipation rate is discussed. Finally, a sample calculation of a flat plate compressible turbulent boundary-layer flow with adiabatic wall boundary condition and a free-stream Mach number of 2.5 using a two-equation near-wall closure is presented. The results show that the near-wall two-equation closure formulated for compressible flows is quite valid and the calculated properties are in good agreement with measurements. Furthermore, the near-wall behavior of the turbulence statistics and structure parameters is consistent with that found in incompressible flows.

The Identities Hidden in the Matching Laws, and Their Uses

ERIC Educational Resources Information Center

Thorne, David R.

2010-01-01

Various theoretical equations have been proposed to predict response rate as a function of the rate of reinforcement. If both the rate and probability of reinforcement are considered, a simple identity, defining equation, or "law" holds. This identity places algebraic constraints on the allowable forms of our mathematical models and can help…

Connecting Related Rates and Differential Equations

ERIC Educational Resources Information Center

Brandt, Keith

2012-01-01

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

High Strain Rate Deformation Modeling of a Polymer Matrix Composite. Part 1; Matrix Constitutive Equations

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Stouffer, Donald C.

1998-01-01

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.

Exact PDF equations and closure approximations for advective-reactive transport

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

Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

2013-06-01

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recentlymore » proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.« less

Efficient reporting of the estimated glomerular filtration rate without height in pediatric patients with cancer.

PubMed

Jeong, Tae-Dong; Cho, Eun-Jung; Lee, Woochang; Chun, Sail; Hong, Ki-Sook; Min, Won-Ki

2017-10-26

The updated bedside Schwartz equation requires constant, serum creatinine concentration and height measurements to calculate the estimated glomerular filtration rate (eGFR) in pediatric patients. Unlike the serum creatinine levels, obtaining height information from the laboratory information system (LIS) is not always possible in a clinical laboratory. Recently, the height-independent eGFR equation, the full age spectrum (FAS) equation, has been introduced. We evaluated the performance of height-independent eGFR equation in Korean children with cancer. A total of 250 children who underwent chromium-51-ethylenediamine tetra acetic-acid (51Cr-EDTA)-based glomerular filtration rate (GFR) measurements were enrolled. The 51Cr-EDTA GFR was used as the reference GFR. The bias (eGFR - measured GFR), precision (root mean square error [RMSE]) and accuracy (P30) of the FAS equations were compared to those of the updated Schwartz equation. P30 was defined as the percentage of patients whose eGFR was within ±30% of the measured GFR. The FAS equation showed significantly lower bias (mL/min/1.73 m2) than the updated Schwartz equation (4.2 vs. 8.7, p<0.001). The RMSE and P30 were: updated Schwartz of 43.8 and 64.4%, respectively, and FAS of 42.7 and 66.8%, respectively. The height-independent eGFR-FAS equation was less biased and as accurate as the updated Schwartz equation in Korean children. The use of the height-independent eGFR equation will allow for efficient reporting of eGFR through the LIS in clinical laboratories.

Effects of work-family-school role conflicts and role-related social support on burnout in Registered Nurses: a structural equation modelling approach.

PubMed

Goong, Hwasoo; Xu, Lijuan; Li, Chun-Yu

2016-11-01

To examine the effects of work-family-school role conflicts and role-related social support (RRSS) on burnout of nurses pursuing an advanced degree. A predictive correlational cross-sectional study design was used. Nurses were found to be a high-risk group for burnout, even more so among nurses pursuing an advanced degree. When nurses with a professional career marry and decide to become students, inter-role conflicts and burnout are possible outcomes of the resulting multiple roles. Using convenience sampling, data were collected from October 2011-May 2012. A questionnaire about work-family-school role conflicts, RRSS, burnout and general information was completed by 286 nurses pursuing an advanced degree at 12 hospitals in Korea. Data were analysed using SPSS and structural equation modelling with the Analysis of Moment Structures program. The proposed model provided a good fit to the obtained data. Work-family-school role conflicts and social support exerted significant effects on burnout. Role-related social support was found to play a partial mediating role between work-family-school role conflicts and burnout. The findings of this study imply that RRSS significantly directly and indirectly influences burnout among the nurses pursuing an advanced degree. It is necessary for nursing managers to consider implementing family- and school-friendly policies (e.g. flexible work schedules) to help nurses to manage their multiple roles and thereby decrease their burnout rate. © 2016 John Wiley & Sons Ltd.

Multi-specie isothermal flow calculations of widely-spaced co-axial jets in a confined sudden expansion, with the central jet dominant

NASA Astrophysics Data System (ADS)

Sturgess, G. J.; Syed, S. A.

1982-06-01

A numerical simulation is made of the flow in the Wright Aeronautical Propulsion Laboratory diffusion flame research combustor operating with a strong central jet of carbon dioxide in a weak and removed co-axial jet of air. The simulation is based on a finite difference solution of the time-average, steady-state, elliptic form of the Reynolds equations. Closure for these equations is provided by a two-equation turbulence model. Comparisons between measurements and predictions are made for centerline axial velocities and radial profiles of CO2 concentration. Earlier findings for a single specie, constant density, single jet flow that a large expansion ratio confined jet behaves initially as if it were unconfined, are confirmed for the multiple-specie, variable density, multiple-jet system. The lack of universality in the turbulence model constants and the turbulent Schmidt/Prandtl number is discussed.

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

NASA Astrophysics Data System (ADS)

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

2006-06-01

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

Fast computation of radiation pressure force exerted by multiple laser beams on red blood cell-like particles

NASA Astrophysics Data System (ADS)

Gou, Ming-Jiang; Yang, Ming-Lin; Sheng, Xin-Qing

2016-10-01

Mature red blood cells (RBC) do not contain huge complex nuclei and organelles, makes them can be approximately regarded as homogeneous medium particles. To compute the radiation pressure force (RPF) exerted by multiple laser beams on this kind of arbitrary shaped homogenous nano-particles, a fast electromagnetic optics method is demonstrated. In general, based on the Maxwell's equations, the matrix equation formed by the method of moment (MOM) has many right hand sides (RHS's) corresponding to the different laser beams. In order to accelerate computing the matrix equation, the algorithm conducts low-rank decomposition on the excitation matrix consisting of all RHS's to figure out the so-called skeleton laser beams by interpolative decomposition (ID). After the solutions corresponding to the skeletons are obtained, the desired responses can be reconstructed efficiently. Some numerical results are performed to validate the developed method.

Inverse atmospheric radiative transfer problems - A nonlinear minimization search method of solution. [aerosol pollution monitoring

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1976-01-01

The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.

Multiple concurrent recursive least squares identification with application to on-line spacecraft mass-property identification

NASA Technical Reports Server (NTRS)

Wilson, Edward (Inventor)

2006-01-01

The present invention is a method for identifying unknown parameters in a system having a set of governing equations describing its behavior that cannot be put into regression form with the unknown parameters linearly represented. In this method, the vector of unknown parameters is segmented into a plurality of groups where each individual group of unknown parameters may be isolated linearly by manipulation of said equations. Multiple concurrent and independent recursive least squares identification of each said group run, treating other unknown parameters appearing in their regression equation as if they were known perfectly, with said values provided by recursive least squares estimation from the other groups, thereby enabling the use of fast, compact, efficient linear algorithms to solve problems that would otherwise require nonlinear solution approaches. This invention is presented with application to identification of mass and thruster properties for a thruster-controlled spacecraft.

Multiple-reflection model of human skin and estimation of pigment concentrations

NASA Astrophysics Data System (ADS)

Ohtsuki, Rie; Tominaga, Shoji; Tanno, Osamu

2012-07-01

We describe a new method for estimating the concentrations of pigments in the human skin using surface spectral reflectance. We derive an equation that expresses the surface spectral reflectance of the human skin. First, we propose an optical model of the human skin that accounts for the stratum corneum. We also consider the difference between the scattering coefficient of the epidermis and that of the dermis. We then derive an equation by applying the Kubelka-Munk theory to an optical model of the human skin. Unlike a model developed in a recent study, the present equation considers pigments as well as multiple reflections and the thicknesses of the skin layers as factors that affect the color of the human skin. In two experiments, we estimate the pigment concentrations using the measured surface spectral reflectances. Finally, we confirm the feasibility of the concentrations estimated by the proposed method by evaluating the estimated pigment concentrations in the skin.

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.

Analysis of Binary Adherence Data in the Setting of Polypharmacy: A Comparison of Different Approaches

PubMed Central

Esserman, Denise A.; Moore, Charity G.; Roth, Mary T.

2009-01-01

Older community dwelling adults often take multiple medications for numerous chronic diseases. Non-adherence to these medications can have a large public health impact. Therefore, the measurement and modeling of medication adherence in the setting of polypharmacy is an important area of research. We apply a variety of different modeling techniques (standard linear regression; weighted linear regression; adjusted linear regression; naïve logistic regression; beta-binomial (BB) regression; generalized estimating equations (GEE)) to binary medication adherence data from a study in a North Carolina based population of older adults, where each medication an individual was taking was classified as adherent or non-adherent. In addition, through simulation we compare these different methods based on Type I error rates, bias, power, empirical 95% coverage, and goodness of fit. We find that estimation and inference using GEE is robust to a wide variety of scenarios and we recommend using this in the setting of polypharmacy when adherence is dichotomously measured for multiple medications per person. PMID:20414358

Similarity indices of meteo-climatic gauging stations: definition and comparison.

PubMed

Barca, Emanuele; Bruno, Delia Evelina; Passarella, Giuseppe

2016-07-01

Space-time dependencies among monitoring network stations have been investigated to detect and quantify similarity relationships among gauging stations. In this work, besides the well-known rank correlation index, two new similarity indices have been defined and applied to compute the similarity matrix related to the Apulian meteo-climatic monitoring network. The similarity matrices can be applied to address reliably the issue of missing data in space-time series. In order to establish the effectiveness of the similarity indices, a simulation test was then designed and performed with the aim of estimating missing monthly rainfall rates in a suitably selected gauging station. The results of the simulation allowed us to evaluate the effectiveness of the proposed similarity indices. Finally, the multiple imputation by chained equations method was used as a benchmark to have an absolute yardstick for comparing the outcomes of the test. In conclusion, the new proposed multiplicative similarity index resulted at least as reliable as the selected benchmark.

Electron kinetic effects in atmosphere breakdown by an intense electromagnetic pulse.

PubMed

Solovyev, A A; Terekhin, V A; Tikhonchuk, V T; Altgilbers, L L

1999-12-01

A physical model is proposed for description of electron kinetics driven by a powerful electromagnetic pulse in the Earth's atmosphere. The model is based on a numerical solution to the Boltzmann kinetic equation for two groups of electrons. Slow electrons (with energies below a few keV) are described in a two-term approximation assuming a weak anisotropy of the electron distribution function. Fast electrons (with energies above a few keV) are described by a modified macroparticle method, taking into account the electron acceleration in the electric field, energy losses in the continuous deceleration approximation, and the multiple pitch angle scattering. The model is applied to a problem of the electric discharge in a nitrogen, which is preionized by an external gamma-ray source. It is shown that the runaway electrons have an important effect on the energy distribution of free electrons, and on the avalanche ionization rate. This mechanism might explain the observation of multiple lightning discharges observed in the Ivy-Mike thermonuclear test in the early 1950's.

Transient well flow in leaky multiple-aquifer systems

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1985-10-01

A previously developed eigenvalue analysis approach to groundwater flow in leaky multiple aquifers is used to derive exact solutions for transient well flow problems in leaky and confined systems comprising any number of aquifers. Equations are presented for the drawdown distribution in systems of infinite extent, caused by wells penetrating one or more of the aquifers completely and discharging each layer at a constant rate. Since the solution obtained may be regarded as a combined analytical-numerical technique, a type of one-dimensional modelling can be applied to find approximate solutions for several complicating conditions. Numerical evaluations are presented as time-drawdown curves and include effects of storage in the aquitard, unconfined conditions, partially penetrating wells and stratified aquifers. The outcome of calculations for relatively simple systems compares very well with published corresponding results. The proposed multilayer solution can be a valuable tool in aquifer test evaluation, as it provides the analytical expression required to enable the application of existing computer methods to the determination of aquifer characteristics.

Globally coupled stochastic two-state oscillators: fluctuations due to finite numbers.

PubMed

Pinto, Italo'Ivo Lima Dias; Escaff, Daniel; Harbola, Upendra; Rosas, Alexandre; Lindenberg, Katja

2014-05-01

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Itô calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N → ∞ and t → ∞ (t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Globally coupled stochastic two-state oscillators: Fluctuations due to finite numbers

NASA Astrophysics Data System (ADS)

Pinto, Italo'Ivo Lima Dias; Escaff, Daniel; Harbola, Upendra; Rosas, Alexandre; Lindenberg, Katja

2014-05-01

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Itô calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N →∞ and t →∞ (t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Fully coupled simulation of multiple hydraulic fractures to propagate simultaneously from a perforated horizontal wellbore

NASA Astrophysics Data System (ADS)

Zeng, Qinglei; Liu, Zhanli; Wang, Tao; Gao, Yue; Zhuang, Zhuo

2018-02-01

In hydraulic fracturing process in shale rock, multiple fractures perpendicular to a horizontal wellbore are usually driven to propagate simultaneously by the pumping operation. In this paper, a numerical method is developed for the propagation of multiple hydraulic fractures (HFs) by fully coupling the deformation and fracturing of solid formation, fluid flow in fractures, fluid partitioning through a horizontal wellbore and perforation entry loss effect. The extended finite element method (XFEM) is adopted to model arbitrary growth of the fractures. Newton's iteration is proposed to solve these fully coupled nonlinear equations, which is more efficient comparing to the widely adopted fixed-point iteration in the literatures and avoids the need to impose fluid pressure boundary condition when solving flow equations. A secant iterative method based on the stress intensity factor (SIF) is proposed to capture different propagation velocities of multiple fractures. The numerical results are compared with theoretical solutions in literatures to verify the accuracy of the method. The simultaneous propagation of multiple HFs is simulated by the newly proposed algorithm. The coupled influences of propagation regime, stress interaction, wellbore pressure loss and perforation entry loss on simultaneous propagation of multiple HFs are investigated.

Multilevel Monte Carlo simulation of Coulomb collisions

DOE PAGES

Rosin, M. S.; Ricketson, L. F.; Dimits, A. M.; ...

2014-05-29

We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau–Fokker–Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy ε , the computational cost of the method is O(ε –2) or (ε –2(lnε) 2), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(ε –3) for direct simulation Monte Carlomore » or binary collision methods. We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Lévy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for ε=10 –5. Lastly, we discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.« less

Intermittency in small-scale turbulence: a velocity gradient approach

NASA Astrophysics Data System (ADS)

Meneveau, Charles; Johnson, Perry

2017-11-01

Intermittency of small-scale motions is an ubiquitous facet of turbulent flows, and predicting this phenomenon based on reduced models derived from first principles remains an important open problem. Here, a multiple-time scale stochastic model is introduced for the Lagrangian evolution of the full velocity gradient tensor in fluid turbulence at arbitrarily high Reynolds numbers. This low-dimensional model differs fundamentally from prior shell models and other empirically-motivated models of intermittency because the nonlinear gradient self-stretching and rotation A2 term vital to the energy cascade and intermittency development is represented exactly from the Navier-Stokes equations. With only one adjustable parameter needed to determine the model's effective Reynolds number, numerical solutions of the resulting set of stochastic differential equations show that the model predicts anomalous scaling for moments of the velocity gradient components and negative derivative skewness. It also predicts signature topological features of the velocity gradient tensor such as vorticity alignment trends with the eigen-directions of the strain-rate. This research was made possible by a graduate Fellowship from the National Science Foundation and by a Grant from The Gulf of Mexico Research Initiative.

On the Constitutive Model of Nitrogen-Containing Austenitic Stainless Steel 316LN at Elevated Temperature

PubMed Central

Zhang, Lei; Feng, Xiao; Wang, Xin; Liu, Changyong

2014-01-01

The nitrogen-containing austenitic stainless steel 316LN has been chosen as the material for nuclear main-pipe, which is one of the key parts in 3rd generation nuclear power plants. In this research, a constitutive model of nitrogen-containing austenitic stainless steel is developed. The true stress-true strain curves obtained from isothermal hot compression tests over a wide range of temperatures (900–1250°C) and strain rates (10−3–10 s−1), were employed to study the dynamic deformational behavior of and recrystallization in 316LN steels. The constitutive model is developed through multiple linear regressions performed on the experimental data and based on an Arrhenius-type equation and Zener-Hollomon theory. The influence of strain was incorporated in the developed constitutive equation by considering the effect of strain on the various material constants. The reliability and accuracy of the model is verified through the comparison of predicted flow stress curves and experimental curves. Possible reasons for deviation are also discussed based on the characteristics of modeling process. PMID:25375345

Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces

NASA Astrophysics Data System (ADS)

Fasondini, Marco; Fornberg, Bengt; Weideman, J. A. C.

2017-09-01

We extend the numerical pole field solver (Fornberg and Weideman (2011) [12]) to enable the computation of the multivalued Painlevé transcendents, which are the solutions to the third, fifth and sixth Painlevé equations, on their Riemann surfaces. We display, for the first time, solutions to these equations on multiple Riemann sheets. We also provide numerical evidence for the existence of solutions to the sixth Painlevé equation that have pole-free sectors, known as tronquée solutions.

Entrainment in the master equation.

PubMed

Margaliot, Michael; Grüne, Lars; Kriecherbauer, Thomas

2018-04-01

The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biological systems or periodic traffic lights in a model of vehicular traffic. Using tools from systems and control theory, we prove that under mild technical conditions every solution of the master equation converges to a periodic solution with the same period as the rates. In other words, the master equation entrains (or phase locks) to periodic excitations. We describe two applications of our theoretical results to important models from statistical mechanics and epidemiology.

Entrainment in the master equation

PubMed Central

Grüne, Lars; Kriecherbauer, Thomas

2018-01-01

The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biological systems or periodic traffic lights in a model of vehicular traffic. Using tools from systems and control theory, we prove that under mild technical conditions every solution of the master equation converges to a periodic solution with the same period as the rates. In other words, the master equation entrains (or phase locks) to periodic excitations. We describe two applications of our theoretical results to important models from statistical mechanics and epidemiology. PMID:29765669

A Study of Two-Equation Turbulence Models on the Elliptic Streamline Flow

NASA Technical Reports Server (NTRS)

Blaisdell, Gregory A.; Qin, Jim H.; Shariff, Karim; Rai, Man Mohan (Technical Monitor)

1995-01-01

Several two-equation turbulence models are compared to data from direct numerical simulations (DNS) of the homogeneous elliptic streamline flow, which combines rotation and strain. The models considered include standard two-equation models and models with corrections for rotational effects. Most of the rotational corrections modify the dissipation rate equation to account for the reduced dissipation rate in rotating turbulent flows, however, the DNS data shows that the production term in the turbulent kinetic energy equation is not modeled correctly by these models. Nonlinear relations for the Reynolds stresses are considered as a means of modifying the production term. Implications for the modeling of turbulent vortices will be discussed.

A rotor optimization using regression analysis

NASA Technical Reports Server (NTRS)

Giansante, N.

1984-01-01

The design and development of helicopter rotors is subject to the many design variables and their interactions that effect rotor operation. Until recently, selection of rotor design variables to achieve specified rotor operational qualities has been a costly, time consuming, repetitive task. For the past several years, Kaman Aerospace Corporation has successfully applied multiple linear regression analysis, coupled with optimization and sensitivity procedures, in the analytical design of rotor systems. It is concluded that approximating equations can be developed rapidly for a multiplicity of objective and constraint functions and optimizations can be performed in a rapid and cost effective manner; the number and/or range of design variables can be increased by expanding the data base and developing approximating functions to reflect the expanded design space; the order of the approximating equations can be expanded easily to improve correlation between analyzer results and the approximating equations; gradients of the approximating equations can be calculated easily and these gradients are smooth functions reducing the risk of numerical problems in the optimization; the use of approximating functions allows the problem to be started easily and rapidly from various initial designs to enhance the probability of finding a global optimum; and the approximating equations are independent of the analysis or optimization codes used.

Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review.

PubMed

Frankenfield, David; Roth-Yousey, Lori; Compher, Charlene

2005-05-01

An assessment of energy needs is a necessary component in the development and evaluation of a nutrition care plan. The metabolic rate can be measured or estimated by equations, but estimation is by far the more common method. However, predictive equations might generate errors large enough to impact outcome. Therefore, a systematic review of the literature was undertaken to document the accuracy of predictive equations preliminary to deciding on the imperative to measure metabolic rate. As part of a larger project to determine the role of indirect calorimetry in clinical practice, an evidence team identified published articles that examined the validity of various predictive equations for resting metabolic rate (RMR) in nonobese and obese people and also in individuals of various ethnic and age groups. Articles were accepted based on defined criteria and abstracted using evidence analysis tools developed by the American Dietetic Association. Because these equations are applied by dietetics practitioners to individuals, a key inclusion criterion was research reports of individual data. The evidence was systematically evaluated, and a conclusion statement and grade were developed. Four prediction equations were identified as the most commonly used in clinical practice (Harris-Benedict, Mifflin-St Jeor, Owen, and World Health Organization/Food and Agriculture Organization/United Nations University [WHO/FAO/UNU]). Of these equations, the Mifflin-St Jeor equation was the most reliable, predicting RMR within 10% of measured in more nonobese and obese individuals than any other equation, and it also had the narrowest error range. No validation work concentrating on individual errors was found for the WHO/FAO/UNU equation. Older adults and US-residing ethnic minorities were underrepresented both in the development of predictive equations and in validation studies. The Mifflin-St Jeor equation is more likely than the other equations tested to estimate RMR to within 10% of that measured, but noteworthy errors and limitations exist when it is applied to individuals and possibly when it is generalized to certain age and ethnic groups. RMR estimation errors would be eliminated by valid measurement of RMR with indirect calorimetry, using an evidence-based protocol to minimize measurement error. The Expert Panel advises clinical judgment regarding when to accept estimated RMR using predictive equations in any given individual. Indirect calorimetry may be an important tool when, in the judgment of the clinician, the predictive methods fail an individual in a clinically relevant way. For members of groups that are greatly underrepresented by existing validation studies of predictive equations, a high level of suspicion regarding the accuracy of the equations is warranted.

Predicting hearing thresholds and occupational hearing loss with multiple-frequency auditory steady-state responses.

PubMed

Hsu, Ruey-Fen; Ho, Chi-Kung; Lu, Sheng-Nan; Chen, Shun-Sheng

2010-10-01

An objective investigation is needed to verify the existence and severity of hearing impairments resulting from work-related, noise-induced hearing loss in arbitration of medicolegal aspects. We investigated the accuracy of multiple-frequency auditory steady-state responses (Mf-ASSRs) between subjects with sensorineural hearing loss (SNHL) with and without occupational noise exposure. Cross-sectional study. Tertiary referral medical centre. Pure-tone audiometry and Mf-ASSRs were recorded in 88 subjects (34 patients had occupational noise-induced hearing loss [NIHL], 36 patients had SNHL without noise exposure, and 18 volunteers were normal controls). Inter- and intragroup comparisons were made. A predicting equation was derived using multiple linear regression analysis. ASSRs and pure-tone thresholds (PTTs) showed a strong correlation for all subjects (r = .77 ≈ .94). The relationship is demonstrated by the equationThe differences between the ASSR and PTT were significantly higher for the NIHL group than for the subjects with non-noise-induced SNHL (p < .001). Mf-ASSR is a promising tool for objectively evaluating hearing thresholds. Predictive value may be lower in subjects with occupational hearing loss. Regardless of carrier frequencies, the severity of hearing loss affects the steady-state response. Moreover, the ASSR may assist in detecting noise-induced injury of the auditory pathway. A multiple linear regression equation to accurately predict thresholds was shown that takes into consideration all effect factors.

Calculation of afterbody flows with a composite velocity formulation

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rubin, S. G.; Khosla, P. K.

1983-01-01

A recently developed technique for numerical solution of the Navier-Stokes equations for subsonic, laminar flows is investigated. It is extended here to allow for the computation of transonic and turbulent flows. The basic approach involves a multiplicative composite of the appropriate velocity representations for the inviscid and viscous flow regions. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli equation for the pressure, while the continuity equation reduces to the familiar potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary layers. The velocity components are computed with a coupled strongly implicity procedure. For transonic flows the artificial compressibility method is used to treat supersonic regions. Calculations are made for both laminar and turbulent flows over axisymmetric afterbody configurations. Present results compare favorably with other numerical solutions and/or experimental data.

Multiple Representations and Connections with the Sierpinski Triangle

ERIC Educational Resources Information Center

Kirwan, J. Vince; Tobias, Jennifer M.

2014-01-01

To understand multiple representations in algebra, students must be able to describe relationships through a variety of formats, such as graphs, tables, pictures, and equations. NCTM indicates that varied representations are "essential elements in supporting students' understanding of mathematical concepts and relationships" (NCTM…

Regression-based pediatric norms for the brief visuospatial memory test: revised and the symbol digit modalities test.

PubMed

Smerbeck, A M; Parrish, J; Yeh, E A; Hoogs, M; Krupp, Lauren B; Weinstock-Guttman, B; Benedict, R H B

2011-04-01

The Brief Visuospatial Memory Test - Revised (BVMTR) and the Symbol Digit Modalities Test (SDMT) oral-only administration are known to be sensitive to cerebral disease in adult samples, but pediatric norms are not available. A demographically balanced sample of healthy control children (N = 92) ages 6-17 was tested with the BVMTR and SDMT. Multiple regression analysis (MRA) was used to develop demographically controlled normative equations. This analysis provided equations that were then used to construct demographically adjusted z-scores for the BVMTR Trial 1, Trial 2, Trial 3, Total Learning, and Delayed Recall indices, as well as the SDMT total correct score. To demonstrate the utility of this approach, a comparison group of children with acute disseminated encephalomyelitis (ADEM) or multiple sclerosis (MS) were also assessed. We find that these visual processing tests discriminate neurological patients from controls. As the tests are validated in adult multiple sclerosis, they are likely to be useful in monitoring pediatric onset multiple sclerosis patients as they transition into adulthood.

Local discretization method for overdamped Brownian motion on a potential with multiple deep wells.

PubMed

Nguyen, P T T; Challis, K J; Jack, M W

2016-11-01

We present a general method for transforming the continuous diffusion equation describing overdamped Brownian motion on a time-independent potential with multiple deep wells to a discrete master equation. The method is based on an expansion in localized basis states of local metastable potentials that match the full potential in the region of each potential well. Unlike previous basis methods for discretizing Brownian motion on a potential, this approach is valid for periodic potentials with varying multiple deep wells per period and can also be applied to nonperiodic systems. We apply the method to a range of potentials and find that potential wells that are deep compared to five times the thermal energy can be associated with a discrete localized state while shallower wells are better incorporated into the local metastable potentials of neighboring deep potential wells.

Local discretization method for overdamped Brownian motion on a potential with multiple deep wells

NASA Astrophysics Data System (ADS)

Nguyen, P. T. T.; Challis, K. J.; Jack, M. W.

2016-11-01

We present a general method for transforming the continuous diffusion equation describing overdamped Brownian motion on a time-independent potential with multiple deep wells to a discrete master equation. The method is based on an expansion in localized basis states of local metastable potentials that match the full potential in the region of each potential well. Unlike previous basis methods for discretizing Brownian motion on a potential, this approach is valid for periodic potentials with varying multiple deep wells per period and can also be applied to nonperiodic systems. We apply the method to a range of potentials and find that potential wells that are deep compared to five times the thermal energy can be associated with a discrete localized state while shallower wells are better incorporated into the local metastable potentials of neighboring deep potential wells.

Computational simulations of frictional losses in pipe networks confirmed in experimental apparatusses designed by honors students

NASA Astrophysics Data System (ADS)

Pohlman, Nicholas A.; Hynes, Eric; Kutz, April

2015-11-01

Lectures in introductory fluid mechanics at NIU are a combination of students with standard enrollment and students seeking honors credit for an enriching experience. Most honors students dread the additional homework problems or an extra paper assigned by the instructor. During the past three years, honors students of my class have instead collaborated to design wet-lab experiments for their peers to predict variable volume flow rates of open reservoirs driven by gravity. Rather than learn extra, the honors students learn the Bernoulli head-loss equation earlier to design appropriate systems for an experimental wet lab. Prior designs incorporated minor loss features such as sudden contraction or multiple unions and valves. The honors students from Spring 2015 expanded the repertoire of available options by developing large scale set-ups with multiple pipe networks that could be combined together to test the flexibility of the student team's computational programs. The engagement of bridging the theory with practice was appreciated by all of the students such that multiple teams were able to predict performance within 4% accuracy. The challenges, schedules, and cost estimates of incorporating the experimental lab into an introductory fluid mechanics course will be reported.

Prolongation structures of nonlinear evolution equations. II

NASA Technical Reports Server (NTRS)

Estabrook, F. B.; Wahlquist, H. D.

1976-01-01

The prolongation structure of a closed ideal of exterior differential forms is further discussed, and its use illustrated by application to an ideal (in six dimensions) representing the cubically nonlinear Schroedinger equation. The prolongation structure in this case is explicitly given, and recurrence relations derived which support the conjecture that the structure is open - i.e., does not terminate as a set of structure relations of a finite-dimensional Lie group. We introduce the use of multiple pseudopotentials to generate multiple Baecklund transformation, and derive the double Baecklund transformation. This symmetric transformation concisely expresses the (usually conjectured) theorem of permutability, which must consequently apply to all solutions irrespective of asymptotic constraints.

Multidimensional computer simulation of Stirling cycle engines

NASA Technical Reports Server (NTRS)

Hall, C. A.; Porsching, T. A.; Medley, J.; Tew, R. C.

1990-01-01

The computer code ALGAE (algorithms for the gas equations) treats incompressible, thermally expandable, or locally compressible flows in complicated two-dimensional flow regions. The solution method, finite differencing schemes, and basic modeling of the field equations in ALGAE are applicable to engineering design settings of the type found in Stirling cycle engines. The use of ALGAE to model multiple components of the space power research engine (SPRE) is reported. Videotape computer simulations of the transient behavior of the working gas (helium) in the heater-regenerator-cooler complex of the SPRE demonstrate the usefulness of such a program in providing information on thermal and hydraulic phenomena in multiple component sections of the SPRE.

A multiple scales approach to sound generation by vibrating bodies

NASA Technical Reports Server (NTRS)

Geer, James F.; Pope, Dennis S.

1992-01-01

The problem of determining the acoustic field in an inviscid, isentropic fluid generated by a solid body whose surface executes prescribed vibrations is formulated and solved as a multiple scales perturbation problem, using the Mach number M based on the maximum surface velocity as the perturbation parameter. Following the idea of multiple scales, new 'slow' spacial scales are introduced, which are defined as the usual physical spacial scale multiplied by powers of M. The governing nonlinear differential equations lead to a sequence of linear problems for the perturbation coefficient functions. However, it is shown that the higher order perturbation functions obtained in this manner will dominate the lower order solutions unless their dependence on the slow spacial scales is chosen in a certain manner. In particular, it is shown that the perturbation functions must satisfy an equation similar to Burgers' equation, with a slow spacial scale playing the role of the time-like variable. The method is illustrated by a simple one-dimenstional example, as well as by three different cases of a vibrating sphere. The results are compared with solutions obtained by purely numerical methods and some insights provided by the perturbation approach are discussed.

Renal function assessment in atrial fibrillation: Usefulness of chronic kidney disease epidemiology collaboration vs re-expressed 4 variable modification of diet in renal disease.

PubMed

Abumuaileq, Rami Riziq-Yousef; Abu-Assi, Emad; López-López, Andrea; Raposeiras-Roubin, Sergio; Rodríguez-Mañero, Moisés; Martínez-Sande, Luis; García-Seara, Francisco Javier; Fernandez-López, Xesus Alberte; González-Juanatey, Jose Ramón

2015-10-26

To compare the performance of the re-expressed Modification of Diet in Renal Disease equation vs the new Chronic Kidney Disease Epidemiology Collaboration equation in patients with non-valvular atrial fibrillation. We studied 911 consecutive patients with non-valvular atrial fibrillation on vitamin-K antagonist. The performance of the re-expressed Modification of Diet in Renal Disease equation vs the new Chronic Kidney Disease Epidemiology Collaboration equation in patients with non-valvular atrial fibrillation with respect to either a composite endpoint of major bleeding, thromboembolic events and all-cause mortality or each individual component of the composite endpoint was assessed using continuous and categorical ≥ 60, 59-30, and < 30 mL/min per 1.73 m(2) estimated glomerular filtration rate. During 10 ± 3 mo, the composite endpoint occurred in 98 (10.8%) patients: 30 patients developed major bleeding, 18 had thromboembolic events, and 60 died. The new equation provided lower prevalence of renal dysfunction < 60 mL/min per 1.73 m(2) (32.9%), compared with the re-expressed equation (34.1%). Estimated glomerular filtration rate from both equations was independent predictor of composite endpoint (HR = 0.98 and 0.97 for the re-expressed and the new equation, respectively; P < 0.0001) and all-cause mortality (HR = 0.98 for both equations, P < 0.01). Strong association with thromboembolic events was observed only when estimated glomerular filtration rate was < 30 mL/min per 1.73 m(2): HR is 5.1 for the re-expressed equation, and HR = 5.0 for the new equation. No significant association with major bleeding was observed for both equations. The new equation reduced the prevalence of renal dysfunction. Both equations performed similarly in predicting major adverse outcomes.

On the validity of the Arrhenius equation for electron attachment rate coefficients.

PubMed

Fabrikant, Ilya I; Hotop, Hartmut

2008-03-28

The validity of the Arrhenius equation for dissociative electron attachment rate coefficients is investigated. A general analysis allows us to obtain estimates of the upper temperature bound for the range of validity of the Arrhenius equation in the endothermic case and both lower and upper bounds in the exothermic case with a reaction barrier. The results of the general discussion are illustrated by numerical examples whereby the rate coefficient, as a function of temperature for dissociative electron attachment, is calculated using the resonance R-matrix theory. In the endothermic case, the activation energy in the Arrhenius equation is close to the threshold energy, whereas in the case of exothermic reactions with an intermediate barrier, the activation energy is found to be substantially lower than the barrier height.

Psychometric Evaluation of the Altered States of Consciousness Rating Scale (OAV)

PubMed Central

Studerus, Erich; Gamma, Alex; Vollenweider, Franz X.

2010-01-01

Background The OAV questionnaire has been developed to integrate research on altered states of consciousness (ASC). It measures three primary and one secondary dimensions of ASC that are hypothesized to be invariant across ASC induction methods. The OAV rating scale has been in use for more than 20 years and applied internationally in a broad range of research fields, yet its factorial structure has never been tested by structural equation modeling techniques and its psychometric properties have never been examined in large samples of experimentally induced ASC. Methodology/Principal Findings The present study conducted a psychometric evaluation of the OAV in a sample of psilocybin (n = 327), ketamine (n = 162), and MDMA (n = 102) induced ASC that was obtained by pooling data from 43 experimental studies. The factorial structure was examined by confirmatory factor analysis, exploratory structural equation modeling, hierarchical item clustering (ICLUST), and multiple indicators multiple causes (MIMIC) modeling. The originally proposed model did not fit the data well even if zero-constraints on non-target factor loadings and residual correlations were relaxed. Furthermore, ICLUST suggested that the “oceanic boundlessness” and “visionary restructuralization” factors could be combined on a high level of the construct hierarchy. However, because these factors were multidimensional, we extracted and examined 11 new lower order factors. MIMIC modeling indicated that these factors were highly measurement invariant across drugs, settings, questionnaire versions, and sexes. The new factors were also demonstrated to have improved homogeneities, satisfactory reliabilities, discriminant and convergent validities, and to differentiate well among the three drug groups. Conclusions/Significance The original scales of the OAV were shown to be multidimensional constructs. Eleven new lower order scales were constructed and demonstrated to have desirable psychometric properties. The new lower order scales are most likely better suited to assess drug induced ASC. PMID:20824211

Flows, scaling, and the control of moment hierarchies for stochastic chemical reaction networks

NASA Astrophysics Data System (ADS)

Smith, Eric; Krishnamurthy, Supriya

2017-12-01

Stochastic chemical reaction networks (CRNs) are complex systems that combine the features of concurrent transformation of multiple variables in each elementary reaction event and nonlinear relations between states and their rates of change. Most general results concerning CRNs are limited to restricted cases where a topological characteristic known as deficiency takes a value 0 or 1, implying uniqueness and positivity of steady states and surprising, low-information forms for their associated probability distributions. Here we derive equations of motion for fluctuation moments at all orders for stochastic CRNs at general deficiency. We show, for the standard base case of proportional sampling without replacement (which underlies the mass-action rate law), that the generator of the stochastic process acts on the hierarchy of factorial moments with a finite representation. Whereas simulation of high-order moments for many-particle systems is costly, this representation reduces the solution of moment hierarchies to a complexity comparable to solving a heat equation. At steady states, moment hierarchies for finite CRNs interpolate between low-order and high-order scaling regimes, which may be approximated separately by distributions similar to those for deficiency-zero networks and connected through matched asymptotic expansions. In CRNs with multiple stable or metastable steady states, boundedness of high-order moments provides the starting condition for recursive solution downward to low-order moments, reversing the order usually used to solve moment hierarchies. A basis for a subset of network flows defined by having the same mean-regressing property as the flows in deficiency-zero networks gives the leading contribution to low-order moments in CRNs at general deficiency, in a 1 /n expansion in large particle numbers. Our results give a physical picture of the different informational roles of mean-regressing and non-mean-regressing flows and clarify the dynamical meaning of deficiency not only for first-moment conditions but for all orders in fluctuations.

Illite Dissolution Rates and Equation (100 to 280 dec C)

DOE Data Explorer

Carroll, Susan

2014-10-17

The objective of this suite of experiments was to develop a useful kinetic dissolution expression for illite applicable over an expanded range of solution pH and temperature conditions representative of subsurface conditions in natural and/or engineered geothermal reservoirs. Using our new data, the resulting rate equation is dependent on both pH and temperature and utilizes two specific dissolution mechanisms (a “neutral” and a “basic” mechanism). The form of this rate equation should be easily incorporated into most existing reactive transport codes for to predict rock-water interactions in EGS shear zones.

The Integration of Teacher's Pedagogical Content Knowledge Components in Teaching Linear Equation

ERIC Educational Resources Information Center

Yusof, Yusminah Mohd.; Effandi, Zakaria

2015-01-01

This qualitative research aimed to explore the integration of the components of pedagogical content knowledge (PCK) in teaching Linear Equation with one unknown. For the purpose of the study, a single local case study with multiple participants was used. The selection of the participants was made based on various criteria: having more than 5 years…

Calculating Dynamics Of Helicopters And Slung Loads

NASA Technical Reports Server (NTRS)

Cicolani, Luigi; Kanning, Gerd

1991-01-01

General equations derived for numerical simulations of motions of multiple-lift, slung-load systems consisting of two or more lifting helicopters and loads slung from them by various combinations of spreader bars, cables, nets, and attaching hardware. Equations readily programmable for efficient computation of motions and lend themselves well to analysis and design of control strategies for stabilization and coordination.

Shock Equation of State of Multi-Phase Epoxy-Based Composite (Al-MnO2-Epoxy)

DTIC Science & Technology

2010-10-01

single stage light gas gun , two...using three different loading techniques— single stage light gas gun , two stage light gas gun , and explosive loading—with multiple diagnostic...wave speed. B. Single stage gas gun loading experiments Four gas gun -driven equation of state experiments were conducted at NSWC-Indian Head using

Site conditions related to erosion on logging roads

Treesearch

R. M. Rice; J. D. McCashion

1985-01-01

Synopsis - Data collected from 299 road segments in northwestern California were used to develop and test a procedure for estimating and managing road-related erosion. Site conditions and the design of each segment were described by 30 variables. Equations developed using 149 of the road segments were tested on the other 150. The best multiple regression equation...

Reporting Multiple-Group Mean and Covariance Structure across Occasions with Structural Equation Modeling

ERIC Educational Resources Information Center

Okech, David

2012-01-01

Objectives: Using baseline and second wave data, the study evaluated the measurement and structural properties of parenting stress, personal mastery, and economic strain with N = 381 lower income parents who decided to join and those who did not join in a child development savings account program. Methods: Structural equation modeling mean and…

Use of Item Parceling in Structural Equation Modeling with Missing Data

ERIC Educational Resources Information Center

Orcan, Fatih

2013-01-01

Parceling is referred to as a procedure for computing sums or average scores across multiple items. Parcels instead of individual items are then used as indicators of latent factors in the structural equation modeling analysis (Bandalos 2002, 2008; Little et al., 2002; Yang, Nay, & Hoyle, 2010). Item parceling may be applied to alleviate some…

Asymptotic Standard Errors of Observed-Score Equating with Polytomous IRT Models

ERIC Educational Resources Information Center

Andersson, Björn

2016-01-01

In observed-score equipercentile equating, the goal is to make scores on two scales or tests measuring the same construct comparable by matching the percentiles of the respective score distributions. If the tests consist of different items with multiple categories for each item, a suitable model for the responses is a polytomous item response…

The Importance of Prior Knowledge when Comparing Examples: Influences on Conceptual and Procedural Knowledge of Equation Solving

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Star, Jon R.; Durkin, Kelley

2009-01-01

Comparing multiple examples typically supports learning and transfer in laboratory studies and is considered a key feature of high-quality mathematics instruction. This experimental study investigated the importance of prior knowledge in learning from comparison. Seventh- and 8th-grade students (N = 236) learned to solve equations by comparing…

Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations

NASA Astrophysics Data System (ADS)

Blanchet, Steve; Di Bari, Pasquale; Jones, David A.; Marzola, Luca

2013-01-01

Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N1-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.

[Prevalence of chronic kidney disease in hypertensive persons attended in primary care from Spain determined by application of estimating equations].

PubMed

Gómez Navarro, Rafael

2009-01-01

To study the renal function (FR) of the hypertensive patients by means of estimating equations and serum creatinine (Crp). To calculate the percentage of patients with chronic kidney disease (ERC) that present normal values of Crp. To analyze which factors collaborate in the deterioration of the FR. Descriptive cross-sectional study of patients with HTA. Crp and arterial tension (TA) were determined. The glomerular filtration rate was calculated by means of Cockroft-Gault and MDRD's formula. The years of evolution of the HTA were registered. A descriptive study of the variables and the possible dependence among them was completed, using several times linear multiple regression. 52 patients were studied (57,7% women). Average age 72,4 +/- 10,8. 32,6% (Cockcroft-Gault) or 21,5% (MDRD) were fulfilling ERC criterion. The ERC was mainly diagnosed in females. 21,4% (Cockcroft-Gault) and 9,5 % patients (MDRD) with ERC had normal Crp values. We do not find linear dependence between the numbers of TA and the FR. The TA check-up objectives do not suppose less development of ERC. In males we find linear dependence within the FR (MDRD) and the years of evolution of the HTA. The ERC is a frequent pathology in the hypertense persons. The systematical utilization of estimating equations facilitates the detection of hidden ERC in patients with normal Crp.

Efficient Iterative Methods Applied to the Solution of Transonic Flows

NASA Astrophysics Data System (ADS)

Wissink, Andrew M.; Lyrintzis, Anastasios S.; Chronopoulos, Anthony T.

1996-02-01

We investigate the use of an inexact Newton's method to solve the potential equations in the transonic regime. As a test case, we solve the two-dimensional steady transonic small disturbance equation. Approximate factorization/ADI techniques have traditionally been employed for implicit solutions of this nonlinear equation. Instead, we apply Newton's method using an exact analytical determination of the Jacobian with preconditioned conjugate gradient-like iterative solvers for solution of the linear systems in each Newton iteration. Two iterative solvers are tested; a block s-step version of the classical Orthomin(k) algorithm called orthogonal s-step Orthomin (OSOmin) and the well-known GMRES method. The preconditioner is a vectorizable and parallelizable version of incomplete LU (ILU) factorization. Efficiency of the Newton-Iterative method on vector and parallel computer architectures is the main issue addressed. In vectorized tests on a single processor of the Cray C-90, the performance of Newton-OSOmin is superior to Newton-GMRES and a more traditional monotone AF/ADI method (MAF) for a variety of transonic Mach numbers and mesh sizes. Newton-GMRES is superior to MAF for some cases. The parallel performance of the Newton method is also found to be very good on multiple processors of the Cray C-90 and on the massively parallel thinking machine CM-5, where very fast execution rates (up to 9 Gflops) are found for large problems.

A dislocation density-based continuum model of the anisotropic shock response of single crystal α-cyclotrimethylene trinitramine

DOE PAGES

Luscher, Darby Jon; Addessio, Francis L.; Cawkwell, Marc Jon; ...

2017-01-01

Here, we have developed a model for the finite deformation thermomechanical response of α-cyclotrimethylene trinitramine (RDX). Our model accounts for nonlinear thermoelastic lattice deformation through a free energy-based equation of state developed by Cawkwell et al. (2016) in combination with temperature and pressure dependent elastic constants, as well as dislocation-mediated plastic slip on a set of slip systems motivated by experimental observation. The kinetics of crystal plasticity are modeled using the Orowan equation relating slip rate to dislocation density and the dislocation velocity developed by Austin and McDowell (2011), which naturally accounts for transition from thermally activated to dislocation dragmore » limited regimes. Evolution of dislocation density is specified in terms of local ordinary differential equations reflecting dislocation–dislocation interactions. This paper presents details of the theory and parameterization of the model, followed by discussion of simulations of flyer plate impact experiments. Impact conditions explored within this combined simulation and experimental effort span shock pressures ranging from 1 to 3 GPa for four crystallographic orientations and multiple specimen thicknesses. Simulation results generated using this model are shown to be in strong agreement with velocimetry measurements from the corresponding plate impact experiments. Finally, simulation results are used to motivate conclusions about the nature of dislocation-mediated plasticity in RDX.« less

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

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

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« less

Lower Bounds for Possible Singular Solutions for the Navier-Stokes and Euler Equations Revisited

NASA Astrophysics Data System (ADS)

Cortissoz, Jean C.; Montero, Julio A.

2018-03-01

In this paper we give optimal lower bounds for the blow-up rate of the \\dot{H}s( T^3) -norm, 1/25/2.

D3-Equivariant coupled advertising oscillators model

NASA Astrophysics Data System (ADS)

Zhang, Chunrui; Zheng, Huifeng

2011-04-01

A ring of three coupled advertising oscillators with delay is considered. Using the symmetric functional differential equation theories, the multiple Hopf bifurcations of the equilibrium at the origin are demonstrated. The existence of multiple branches of bifurcating periodic solution is obtained. Numerical simulation supports our analysis results.

General Nature of Multicollinearity in Multiple Regression Analysis.

ERIC Educational Resources Information Center

Liu, Richard

1981-01-01

Discusses multiple regression, a very popular statistical technique in the field of education. One of the basic assumptions in regression analysis requires that independent variables in the equation should not be highly correlated. The problem of multicollinearity and some of the solutions to it are discussed. (Author)

Flexibility in Problem Solving: The Case of Equation Solving

ERIC Educational Resources Information Center

Star, Jon R.; Rittle-Johnson, Bethany

2008-01-01

A key learning outcome in problem-solving domains is the development of flexible knowledge, where learners know multiple strategies and adaptively choose efficient strategies. Two interventions hypothesized to improve flexibility in problem solving were experimentally evaluated: prompts to discover multiple strategies and direct instruction on…

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

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

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

Cross-validation of recent and longstanding resting metabolic rate prediction equations

USDA-ARS?s Scientific Manuscript database

Resting metabolic rate (RMR) measurement is time consuming and requires specialized equipment. Prediction equations provide an easy method to estimate RMR; however, their accuracy likely varies across individuals. Understanding the factors that influence predicted RMR accuracy at the individual lev...

Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

NASA Astrophysics Data System (ADS)

Rubin, M. B.; Cardiff, P.

2017-11-01

Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

Theoretical basis, experimental design, and computerized simulation of synergism and antagonism in drug combination studies.

PubMed

Chou, Ting-Chao

2006-09-01

The median-effect equation derived from the mass-action law principle at equilibrium-steady state via mathematical induction and deduction for different reaction sequences and mechanisms and different types of inhibition has been shown to be the unified theory for the Michaelis-Menten equation, Hill equation, Henderson-Hasselbalch equation, and Scatchard equation. It is shown that dose and effect are interchangeable via defined parameters. This general equation for the single drug effect has been extended to the multiple drug effect equation for n drugs. These equations provide the theoretical basis for the combination index (CI)-isobologram equation that allows quantitative determination of drug interactions, where CI < 1, = 1, and > 1 indicate synergism, additive effect, and antagonism, respectively. Based on these algorithms, computer software has been developed to allow automated simulation of synergism and antagonism at all dose or effect levels. It displays the dose-effect curve, median-effect plot, combination index plot, isobologram, dose-reduction index plot, and polygonogram for in vitro or in vivo studies. This theoretical development, experimental design, and computerized data analysis have facilitated dose-effect analysis for single drug evaluation or carcinogen and radiation risk assessment, as well as for drug or other entity combinations in a vast field of disciplines of biomedical sciences. In this review, selected examples of applications are given, and step-by-step examples of experimental designs and real data analysis are also illustrated. The merging of the mass-action law principle with mathematical induction-deduction has been proven to be a unique and effective scientific method for general theory development. The median-effect principle and its mass-action law based computer software are gaining increased applications in biomedical sciences, from how to effectively evaluate a single compound or entity to how to beneficially use multiple drugs or modalities in combination therapies.

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

PubMed

Goličnik, Marko

2011-01-01

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

Effects of Example Variability and Prior Knowledge in How Students Learn to Solve Equations

ERIC Educational Resources Information Center

Guo, Jian-Peng; Yang, Ling-Yan; Ding, Yi

2014-01-01

Researchers have consistently demonstrated that multiple examples are better than one example in facilitating learning because the comparison evoked by multiple examples supports learning and transfer. However, research outcomes are unclear regarding the effects of example variability and prior knowledge on learning from comparing multiple…

A Critical Technical Review of Six Hazard Assessment Models

DTIC Science & Technology

1975-12-01

temperature is 3000K. Vi The equation describing flame length is taken from a paper of Hawthorne, Weddell, and Hottel [3] who obtained the equation by...should be noted that the flame length given by equation (6.1) in AMSHAH is independent of the flow rate; flame length independence of flow rate does not...experiments and analyses upon which the formula for flame length is based are for jets issuing from circular orifices. Substantial departures from this