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

PubMed

Harney, Michael; Yim, Wen-sau

2015-01-01

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

Regionalisation of low flow frequency curves for the Peninsular Malaysia

NASA Astrophysics Data System (ADS)

Mamun, Abdullah A.; Hashim, Alias; Daoud, Jamal I.

2010-02-01

SUMMARYRegional maps and equations for the magnitude and frequency of 1, 7 and 30-day low flows were derived and are presented in this paper. The river gauging stations of neighbouring catchments that produced similar low flow frequency curves were grouped together. As such, the Peninsular Malaysia was divided into seven low flow regions. Regional equations were developed using the multivariate regression technique. An empirical relationship was developed for mean annual minimum flow as a function of catchment area, mean annual rainfall and mean annual evaporation. The regional equations exhibited good coefficient of determination ( R2 > 0.90). Three low flow frequency curves showing the low, mean and high limits for each region were proposed based on a graphical best-fit technique. Knowing the catchment area, mean annual rainfall and evaporation in the region, design low flows of different durations can be easily estimated for the ungauged catchments. This procedure is expected to overcome the problem of data unavailability in estimating low flows in the Peninsular Malaysia.

Trajectory Control for Very Flexible Aircraft

DTIC Science & Technology

2006-10-30

aircraft are coupled with the aeroelastic equations that govern the geometrically nonlinear structural response of the vehicle. A low -order strain...nonlinear structural formulation, the finite state aerodynamic model, and the nonlinear rigid body equations together provide a low -order complete...nonlinear aircraft analysis tool. Due to the inherent flexibility of the aircraft modeling, the low order structural fre- quencies are of the same order

Estimation of low-flow statistics at ungaged sites on streams in the Lower Hudson River Basin, New York, from data in geographic information systems

USGS Publications Warehouse

Randall, Allan D.; Freehafer, Douglas A.

2017-08-02

A variety of watershed properties available in 2015 from geographic information systems were tested in regression equations to estimate two commonly used statistical indices of the low flow of streams, namely the lowest flows averaged over 7 consecutive days that have a 1 in 10 and a 1 in 2 chance of not being exceeded in any given year (7-day, 10-year and 7-day, 2-year low flows). The equations were based on streamflow measurements in 51 watersheds in the Lower Hudson River Basin of New York during the years 1958–1978, when the number of streamflow measurement sites on unregulated streams was substantially greater than in subsequent years. These low-flow indices are chiefly a function of the area of surficial sand and gravel in the watershed; more precisely, 7-day, 10-year and 7-day, 2-year low flows both increase in proportion to the area of sand and gravel deposited by glacial meltwater, whereas 7-day, 2-year low flows also increase in proportion to the area of postglacial alluvium. Both low-flow statistics are also functions of mean annual runoff (a measure of net water input to the watershed from precipitation) and area of swamps and poorly drained soils in or adjacent to surficial sand and gravel (where groundwater recharge is unlikely and riparian water loss to evapotranspiration is substantial). Small but significant refinements in estimation accuracy resulted from the inclusion of two indices of stream geometry, channel slope and length, in the regression equations. Most of the regression analysis was undertaken with the ordinary least squares method, but four equations were replicated by using weighted least squares to provide a more realistic appraisal of the precision of low-flow estimates. The most accurate estimation equations tested in this study explain nearly 84 and 87 percent of the variation in 7-day, 10-year and 7-day, 2-year low flows, respectively, with standard errors of 0.032 and 0.050 cubic feet per second per square mile. The equations use natural values of streamflow and watershed properties; logarithmic transformations yielded less accurate equations inconsistent with some conceptualized relationships.

Transport equations for low-energy solar particles in evolving interplanetary magnetic fields

NASA Technical Reports Server (NTRS)

Ng, C. K.

1988-01-01

Two new forms of a simplified Fokker-Planck equation are derived for the transport of low-energy solar energetic particles in an evolving interplanetary magnetic field, carried by a variable radial solar wind. An idealized solution suggests that the 'invariant' anisotropy direction reported by Allum et al. (1974) may be explained within the conventional theoretical framework. The equations may be used to relate studies of solar particle propagation to solar wind transients, and vice versa.

Students’ difficulties in solving linear equation problems

NASA Astrophysics Data System (ADS)

Wati, S.; Fitriana, L.; Mardiyana

2018-03-01

A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

Hawking radiation power equations for black holes

NASA Astrophysics Data System (ADS)

Mistry, Ravi; Upadhyay, Sudhaker; Ali, Ahmed Farag; Faizal, Mir

2017-10-01

We derive the Hawking radiation power equations for black holes in asymptotically flat, asymptotically Anti-de Sitter (AdS) and asymptotically de Sitter (dS) black holes. This is done by using the greybody factor for these black holes. We observe that the radiation power equation for asymptotically flat black holes, corresponding to greybody factor at low frequency, depends on both the Hawking temperature and the horizon radius. However, for the greybody factors at asymptotic frequency, it only depends on the Hawking temperature. We also obtain the power equation for asymptotically AdS black holes both below and above the critical frequency. The radiation power equation for at asymptotic frequency is same for both Schwarzschild AdS and Reissner-Nordström AdS solutions and only depends on the Hawking temperature. We also discuss the power equation for asymptotically dS black holes at low frequency, for both even or odd dimensions.

Regression equations to estimate seasonal flow duration, n-day high-flow frequency, and n-day low-flow frequency at sites in North Dakota using data through water year 2009

USGS Publications Warehouse

Williams-Sether, Tara; Gross, Tara A.

2016-02-09

Seasonal mean daily flow data from 119 U.S. Geological Survey streamflow-gaging stations in North Dakota; the surrounding states of Montana, Minnesota, and South Dakota; and the Canadian provinces of Manitoba and Saskatchewan with 10 or more years of unregulated flow record were used to develop regression equations for flow duration, n-day high flow and n-day low flow using ordinary least-squares and Tobit regression techniques. Regression equations were developed for seasonal flow durations at the 10th, 25th, 50th, 75th, and 90th percent exceedances; the 1-, 7-, and 30-day seasonal mean high flows for the 10-, 25-, and 50-year recurrence intervals; and the 1-, 7-, and 30-day seasonal mean low flows for the 2-, 5-, and 10-year recurrence intervals. Basin and climatic characteristics determined to be significant explanatory variables in one or more regression equations included drainage area, percentage of basin drainage area that drains to isolated lakes and ponds, ruggedness number, stream length, basin compactness ratio, minimum basin elevation, precipitation, slope ratio, stream slope, and soil permeability. The adjusted coefficient of determination for the n-day high-flow regression equations ranged from 55.87 to 94.53 percent. The Chi2 values for the duration regression equations ranged from 13.49 to 117.94, whereas the Chi2 values for the n-day low-flow regression equations ranged from 4.20 to 49.68.

Singular temperature dependence of the equation of state of superconductors with spin–orbit interaction in the low-temperature region

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

Ovchinnikov, Yu. N., E-mail: ovc@itp.ac.ru

The equation of state is investigated for a thin superconducting film in a longitudinal magnetic field and with strong spin-orbit interaction at the critical point. As a first step, the state with the maximal value of the magnetic field for a given value of spin–orbit interaction at T = 0 is chosen. This state is investigated in the low-temperature region. The temperature contribution to the equation of state is weakly singular.

van der Waals-Tonks-type equations of state for hard-hypersphere fluids in four and five dimensions

NASA Astrophysics Data System (ADS)

Wang, Xian-Zhi

2004-04-01

Recently, we developed accurate van der Waals-Tonks-type equations of state for hard-disk and hard-sphere fluids by using the known virial coefficients. In this paper, we derive the van der Waals-Tonks-type equations of state. We further apply these equations of state to hard-hypersphere fluids in four and five dimensions. In the low-density fluid regime, these equations of state are in good agreement with the simulation results and existing equations of state.

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

DTIC Science & Technology

2010-01-01

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

A study of cumulative fatigue damage in AISI 4130 steel

NASA Technical Reports Server (NTRS)

Jeelani, S.; Musial, M.

1986-01-01

Experimental data were obtained using AISI 4130 steel under stress ratios of -1 and 0. A study of cumulative fatigue damage using Miner's and Kramer's equations for stress ratios of -1 and 0 for low-high, low-high-mixed, high-low, and high-low-mixed stress sequences has revealed that there is a close agreement between the theoretical and experimental values of fatigue damage and fatigue life. Kramer's equation predicts less conservative and more realistic cumulative fatigue damage than the popularly used Miner's rule does.

Three-phase Power Flow Calculation of Low Voltage Distribution Network Considering Characteristics of Residents Load

NASA Astrophysics Data System (ADS)

Wang, Yaping; Lin, Shunjiang; Yang, Zhibin

2017-05-01

In the traditional three-phase power flow calculation of the low voltage distribution network, the load model is described as constant power. Since this model cannot reflect the characteristics of actual loads, the result of the traditional calculation is always different from the actual situation. In this paper, the load model in which dynamic load represented by air conditioners parallel with static load represented by lighting loads is used to describe characteristics of residents load, and the three-phase power flow calculation model is proposed. The power flow calculation model includes the power balance equations of three-phase (A,B,C), the current balance equations of phase 0, and the torque balancing equations of induction motors in air conditioners. And then an alternating iterative algorithm of induction motor torque balance equations with each node balance equations is proposed to solve the three-phase power flow model. This method is applied to an actual low voltage distribution network of residents load, and by the calculation of three different operating states of air conditioners, the result demonstrates the effectiveness of the proposed model and the algorithm.

Determination of transport wind speed in the gaussian plume diffusion equation for low-lying point sources

NASA Astrophysics Data System (ADS)

Wang, I. T.

A general method for determining the effective transport wind speed, overlineu, in the Gaussian plume equation is discussed. Physical arguments are given for using the generalized overlineu instead of the often adopted release-level wind speed with the plume diffusion equation. Simple analytical expressions for overlineu applicable to low-level point releases and a wide range of atmospheric conditions are developed. A non-linear plume kinematic equation is derived using these expressions. Crosswind-integrated SF 6 concentration data from the 1983 PNL tracer experiment are used to evaluate the proposed analytical procedures along with the usual approach of using the release-level wind speed. Results of the evaluation are briefly discussed.

Development of a Constitutive Equation for HSLA (High-Strength Low- Alloy)-100 at Cryogenic Temperatures

DTIC Science & Technology

1987-12-01

temperatur The Holloncn Power Equation and the VocE. Equation are used tý) describe the true stress;’true strain behavior to failure of individual tests...Hollomon Power Equation (a= Kcn) and the Voce Equation (c=G -[O -ao1exp[-E!A]) are used to describe the true stress / true strain behavior to failure of...6 8 A. MODIFICATIONS/ IMPROVEMENTS IN THE USE OF THE VOCE

Dynamic colloidal assembly pathways via low dimensional models

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

Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu; Thyagarajan, Raghuram

2016-05-28

Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterizedmore » by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.« less

Investment opportunity : the FPL low-cost solar dry kiln

Treesearch

George B. Harpole

1988-01-01

Two equations are presented that may be used to estimate a maximum investment limit and working capital requirements for the FPL low-cost solar dry kiln systems. The equations require data for drying cycle time, green lumber cost, and kiln-dried lumber costs. Results are intended to provide a preliminary estimate.

On thermodynamical inconsistency of isotherm equations: Gibbs's thermodynamics.

PubMed

Tóth, József

2003-06-01

It has been proven that all isotherm equations which include the expression 1-Theta contradict the exact Gibbs thermodynamics. These contradictions have been discussed in detail in the case of the Langmuir (L) equation applied to gas/solid (G/S), solid/liquid (S/L), and gas/liquid (G/L) interfaces. In G/S adsorption the L equation can theoretically be applied only at low equilibrium pressures on condition that vg > vs . vg is the molar volume of the adsorbed amount in the gas phase and vs is the same in the Gibbs phase. In S/L and G/L adsorption the L equation is practically applicable only in the domain of very low concentrations. The cause of these contradictions (inconsistencies) is that Gibbs thermodynamics takes excess adsorbed amounts into account; however, the L and other isotherm equations calculate with the absolute adsorbed amount. The two amounts may be practically equal to each other when the limiting conditions mentioned above are fulfilled. It is also discussed how these inconsistent isotherm equations can be transformed into consistent ones.

An approximate Riemann solver for real gas parabolized Navier-Stokes equations

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

Urbano, Annafederica, E-mail: annafederica.urbano@uniroma1.it; Nasuti, Francesco, E-mail: francesco.nasuti@uniroma1.it

2013-01-15

Under specific assumptions, parabolized Navier-Stokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized Navier-Stokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roe's Riemann solver is developed as the core of a Godunov type finitemore » volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roe's Riemann solver for the parabolized Navier-Stokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.« less

Accurate D-bar Reconstructions of Conductivity Images Based on a Method of Moment with Sinc Basis.

PubMed

Abbasi, Mahdi

2014-01-01

Planar D-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as Electrical impedance tomography (EIT). Recently two different methodologies are considered for the numerical solution of D-bar integrals equation, namely product integrals and multigrid. The first one involves high computational burden and the other one suffers from low convergence rate (CR). In this paper, a novel high speed moment method based using the sinc basis is introduced to solve the two-dimensional D-bar integral equation. In this method, all functions within D-bar integral equation are first expanded using the sinc basis functions. Then, the orthogonal properties of their products dissolve the integral operator of the D-bar equation and results a discrete convolution equation. That is, the new moment method leads to the equation solution without direct computation of the D-bar integral. The resulted discrete convolution equation maybe adapted to a suitable structure to be solved using fast Fourier transform. This allows us to reduce the order of computational complexity to as low as O (N (2)log N). Simulation results on solving D-bar equations arising in EIT problem show that the proposed method is accurate with an ultra-linear CR.

Hybrid radiosity-SP3 equation based bioluminescence tomography reconstruction for turbid medium with low- and non-scattering regions

NASA Astrophysics Data System (ADS)

Chen, Xueli; Zhang, Qitan; Yang, Defu; Liang, Jimin

2014-01-01

To provide an ideal solution for a specific problem of gastric cancer detection in which low-scattering regions simultaneously existed with both the non- and high-scattering regions, a novel hybrid radiosity-SP3 equation based reconstruction algorithm for bioluminescence tomography was proposed in this paper. In the algorithm, the third-order simplified spherical harmonics approximation (SP3) was combined with the radiosity equation to describe the bioluminescent light propagation in tissues, which provided acceptable accuracy for the turbid medium with both low- and non-scattering regions. The performance of the algorithm was evaluated with digital mouse based simulations and a gastric cancer-bearing mouse based in situ experiment. Primary results demonstrated the feasibility and superiority of the proposed algorithm for the turbid medium with low- and non-scattering regions.

Conservation laws and symmetries of a generalized Kawahara equation

NASA Astrophysics Data System (ADS)

Gandarias, Maria Luz; Rosa, Maria; Recio, Elena; Anco, Stephen

2017-06-01

The generalized Kawahara equation ut = a(t)uxxxxx + b(t)uxxx + c(t) f (u)ux appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which includes as a special case the usual Kawahara equation ut = αuux + βu2ux + γuxxx + μuxxxxx. A general connection between conservation laws and symmetries for the generalized Kawahara equation is derived through the Hamiltonian structure of this equation and its relationship to Noether's theorem using a potential formulation.

Miscellaneous: Various Low-Mach-Number Fluid Problems and Motions

NASA Astrophysics Data System (ADS)

Zeytounian, Radyadour Kh.

In this last chapter, we consider, first, in Sect. 7.1, mainly the asymptotic derivation of the KZK equation of nonlinear acoustics, which generalizes the well-known Burgers' unsteady one-dimensional dissipative model equation (Burgers 1948) to an equation with a diffraction and parabolic effect.

Mass and Energy: The Low-Energy Limit.

ERIC Educational Resources Information Center

Bauman, Robert P.

1994-01-01

Discusses Einstein's equation relating mass and energy highlighting these questions: (1) Can mass and energy be converted into one another? (2) What is the origin of the equation? (3) How do relativistic mass and rest mass relate? and (4) How is relativistic mass used in resulting equations? (MVL)

Estimating Glomerular Filtration Rate in Kidney Transplant Recipients: Comparing a Novel Equation With Commonly Used Equations in this Population

PubMed Central

Salvador, Cathrin L.; Hartmann, Anders; Åsberg, Anders; Bergan, Stein; Rowe, Alexander D.; Mørkrid, Lars

2017-01-01

Background Assessment of glomerular filtration rate (GFR) is important in kidney transplantation. The aim was to develop a kidney transplant specific equation for estimating GFR and evaluate against published equations commonly used for GFR estimation in these patients. Methods Adult kidney recipients (n = 594) were included, and blood samples were collected 10 weeks posttransplant. GFR was measured by 51Cr-ethylenediaminetetraacetic acid clearance. Patients were randomized into a reference group (n = 297) to generate a new equation and a test group (n = 297) for comparing it with 7 alternative equations. Results Two thirds of the test group were males. The median (2.5-97.5 percentile) age was 52 (23-75) years, cystatin C, 1.63 (1.00-3.04) mg/L; creatinine, 117 (63-220) μmol/L; and measured GFR, 51 (29-78) mL/min per 1.73 m2. We also performed external evaluation in 133 recipients without the use of trimethoprim, using iohexol clearance for measured GFR. The Modification of Diet in Renal Disease equation was the most accurate of the creatinine-equations. The new equation, estimated GFR (eGFR) = 991.15 × (1.120sex/([age0.097] × [cystatin C0.306] × [creatinine0.527]); where sex is denoted: 0, female; 1, male, demonstrating a better accuracy with a low bias as well as good precision compared with reference equations. Trimethoprim did not influence the performance of the new equation. Conclusions The new equation demonstrated superior accuracy, precision, and low bias. The Modification of Diet in Renal Disease equation was the most accurate of the creatinine-based equations. PMID:29536033

A study of cumulative fatigue damage in titanium 6Al-4V alloy

NASA Technical Reports Server (NTRS)

Jeelani, S.; Ghebremedhin, S.; Musial, M.

1986-01-01

Experimental data were obtained using titanium 6Al-4V alloy under stress ratios of -1, 0, and negative infinity. A study of cumulative fatigue damage using Miner's (1945) and Kramer's (1974) equations for stress ratios of -1 and 0 for low-high, low-high mixed, high-low, and high-low mixed stress sequences has revealed close agreement between the theoretical and experimental values of fatigue damage and fatigue life. Kramer's equation predicts less conservative and more realistic cumulative fatigue damage than does the popularly used Miner's rule.

Influencing Self-Reported Health among Rural Low-Income Women through Health Care and Social Service Utilization: A Structural Equation Model

ERIC Educational Resources Information Center

Bice-Wigington, Tiffany; Huddleston-Casas, Catherine

2012-01-01

Using structural equation modeling, this study examined the mesosystemic processes among rural low-income women, and how these processes subsequently influenced self-reported health. Acknowledging the behavioral processes inherent in utilization of health care and formal social support services, this study moved beyond a behavioral focus by…

Dark energy equation of state parameter and its evolution at low redshift

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

Tripathi, Ashutosh; Sangwan, Archana; Jassal, H.K., E-mail: ashutosh_tripathi@fudan.edu.cn, E-mail: archanakumari@iisermohali.ac.in, E-mail: hkjassal@iisermohali.ac.in

In this paper, we constrain dark energy models using a compendium of observations at low redshifts. We consider the dark energy as a barotropic fluid, with the equation of state a constant as well the case where dark energy equation of state is a function of time. The observations considered here are Supernova Type Ia data, Baryon Acoustic Oscillation data and Hubble parameter measurements. We compare constraints obtained from these data and also do a combined analysis. The combined observational constraints put strong limits on variation of dark energy density with redshift. For varying dark energy models, the range ofmore » parameters preferred by the supernova type Ia data is in tension with the other low redshift distance measurements.« less

Density enhancement mechanism of upwind schemes for low Mach number flows

NASA Astrophysics Data System (ADS)

Lin, Bo-Xi; Yan, Chao; Chen, Shu-Sheng

2018-06-01

Many all-speed Roe schemes have been proposed to improve performance in terms of low speeds. Among them, the F-Roe and T-D-Roe schemes have been found to get incorrect density fluctuation in low Mach flows, which is expected to be with the square of Mach number. Asymptotic analysis presents the mechanism of how the density fluctuation problem relates to the incorrect order of terms in the energy equation \\tilde{ρ {\\tilde{a}} {\\tilde{U}}Δ U}. It is known that changing the upwind scheme coefficients of the pressure-difference dissipation term D^P and the velocity-difference dissipation term in the momentum equation D^{ρ U} to the order of O(c^{-1}) and O(c0) can improve the level of pressure and velocity accuracy at low speeds. This paper shows that corresponding changes in energy equation can also improve the density accuracy in low speeds. We apply this modification to a recently proposed scheme, TV-MAS, to get a new scheme, TV-MAS2. Unsteady Gresho vortex flow, double shear-layer flow, low Mach number flows over the inviscid cylinder, and NACA0012 airfoil show that energy equation modification in these schemes can obtain the expected square Ma scaling of density fluctuations, which is in good agreement with corresponding asymptotic analysis. Therefore, this density correction is expected to be widely implemented into all-speed compressible flow solvers.

Capillary waves in the subcritical nonlinear Schroedinger equation

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

Kozyreff, G.

2010-01-15

We expand recent results on the nonlinear Schroedinger equation with cubic-quintic nonlinearity to show that some solutions are described by the Bernoulli equation in the presence of surface tension. As a consequence, capillary waves are predicted and found numerically at the interface between regions of large and low amplitude.

The functional equation truncation method for approximating slow invariant manifolds: a rapid method for computing intrinsic low-dimensional manifolds.

PubMed

Roussel, Marc R; Tang, Terry

2006-12-07

A slow manifold is a low-dimensional invariant manifold to which trajectories nearby are rapidly attracted on the way to the equilibrium point. The exact computation of the slow manifold simplifies the model without sacrificing accuracy on the slow time scales of the system. The Maas-Pope intrinsic low-dimensional manifold (ILDM) [Combust. Flame 88, 239 (1992)] is frequently used as an approximation to the slow manifold. This approximation is based on a linearized analysis of the differential equations and thus neglects curvature. We present here an efficient way to calculate an approximation equivalent to the ILDM. Our method, called functional equation truncation (FET), first develops a hierarchy of functional equations involving higher derivatives which can then be truncated at second-derivative terms to explicitly neglect the curvature. We prove that the ILDM and FET-approximated (FETA) manifolds are identical for the one-dimensional slow manifold of any planar system. In higher-dimensional spaces, the ILDM and FETA manifolds agree to numerical accuracy almost everywhere. Solution of the FET equations is, however, expected to generally be faster than the ILDM method.

A low diffusive Lagrange-remap scheme for the simulation of violent air-water free-surface flows

NASA Astrophysics Data System (ADS)

Bernard-Champmartin, Aude; De Vuyst, Florian

2014-10-01

In 2002, Després and Lagoutière [17] proposed a low-diffusive advection scheme for pure transport equation problems, which is particularly accurate for step-shaped solutions, and thus suited for interface tracking procedure by a color function. This has been extended by Kokh and Lagoutière [28] in the context of compressible multifluid flows using a five-equation model. In this paper, we explore a simplified variant approach for gas-liquid three-equation models. The Eulerian numerical scheme has two ingredients: a robust remapped Lagrange solver for the solution of the volume-averaged equations, and a low diffusive compressive scheme for the advection of the gas mass fraction. Numerical experiments show the performance of the computational approach on various flow reference problems: dam break, sloshing of a tank filled with water, water-water impact and finally a case of Rayleigh-Taylor instability. One of the advantages of the present interface capturing solver is its natural implementation on parallel processors or computers.

Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.; Matinelli, L.

1994-01-01

The steady state solution of the system of equations consisting of the full Navier-Stokes equations and two turbulence equations has been obtained using a multigrid strategy of unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time-stepping scheme with a stability-bound local time step, while turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positivity. Low-Reynolds-number modifications to the original two-equation model are incorporated in a manner which results in well-behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.

Emergence of nonwhite noise in Langevin dynamics with magnetic Lorentz force

NASA Astrophysics Data System (ADS)

Chun, Hyun-Myung; Durang, Xavier; Noh, Jae Dong

2018-03-01

We investigate the low mass limit of Langevin dynamics for a charged Brownian particle driven by a magnetic Lorentz force. In the low mass limit, velocity variables relaxing quickly are coarse-grained out to yield effective dynamics for position variables. Without the Lorentz force, the low mass limit is equivalent to the high friction limit. Both cases share the same Langevin equation that is obtained by setting the mass to zero. The equivalence breaks down in the presence of the Lorentz force. The low mass limit cannot be achieved by setting the mass to zero. The limit is also distinct from the large friction limit. We derive the effective equations of motion in the low mass limit. The resulting stochastic differential equation involves a nonwhite noise whose correlation matrix has antisymmetric components. We demonstrate the importance of the nonwhite noise by investigating the heat dissipation by a driven Brownian particle, where the emergent nonwhite noise has a physically measurable effect.

User’s Guide for the VTRPE (Variable Terrain Radio Parabolic Equation) Computer Model

DTIC Science & Technology

1991-10-01

propagation effects and antenna characteristics in radar system performance calculations. the radar transmission equation is oiten employed. Fol- lowing Kerr.2...electromagnetic wave equations for the complex electric and magnetic radiation fields. The model accounts for the effects of nonuniform atmospheric refractivity...mission equation, that is used in the performance prediction and analysis of radar and communication systems. Optimized fast Fourier transform (FFT

A unifying fractional wave equation for compressional and shear waves.

PubMed

Holm, Sverre; Sinkus, Ralph

2010-01-01

This study has been motivated by the observed difference in the range of the power-law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is a generalized Hooke's law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo [Geophys J. R. Astron. Soc. 13, 529-539 (1967)] and Wismer [J. Acoust. Soc. Am. 120, 3493-3502 (2006)]. In the low omegatau (low-frequency) case, this equation has an attenuation with a power-law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high omegatau (high-frequency) case, it describes attenuation with a power-law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases.

Corrigendum to ;Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows; [J. Comput. Phys. 307 (2016) 189-202

NASA Astrophysics Data System (ADS)

Kotov, D. V.; Yee, H. C.; Wray, A. A.; Sjögreen, Björn; Kritsuk, A. G.

2018-01-01

The authors regret for the typographic errors that were made in equation (4) and missing phrase after equation (4) in the article "Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows" [J. Comput. Phys. 307 (2016) 189-202].

Method for estimating low-flow characteristics of ungaged streams in Indiana

USGS Publications Warehouse

Arihood, Leslie D.; Glatfelter, Dale R.

1991-01-01

Equations for estimating the 7-day, 2-year and 7oday, 10-year low flows at sites on ungaged streams are presented. Regression analysis was used to develop equations relating basin characteristics and low-flow characteristics at 82 gaging stations. Significant basin characteristics in the equations are contributing drainage area and flow-duration ratio, which is the 20-percent flow duration divided by the 90-percent flow duration. Flow-duration ratio has been regionalized for Indiana on a plate. Ratios for use in the equations are obtained from the plate. Drainage areas are determined from maps or are obtained from reports. The predictive capability of the method was determined by tests of the equations and of the flow-duration ratios on the plate. The accuracy of the equations alone was tested by estimating the low-flow characteristics at 82 gaging stations where flow-duration ratio is already known. In this case, the standard errors of estimate for 7-day, 2-year and 7-day, 10-year low flows are 19 and 28 percent. When flow-duration ratios for the 82 gaging stations are obtained from the map, the standard errors are 46 and 61 percent. However, when stations having drainage areas of less than 10 square miles are excluded from the test, the standard errors decrease to 38 and 49 percent. Standard errors increase when stations with small basins are included, probably because some of the flow-duration ratios obtained for these small basins are incorrect. Local geology and its effect on the ratio are not adequately reflected on the plate, which shows the regional variation in flow-duration ratio. In all the tests, no bias is apparent areally, with increasing drainage area or with increasing ratio. Guidelines and limitations should be considered when using the method. The method can be applied only at sites in the northern and central physiographic zones of the State. Low-flow characteristics cannot be estimated for regulated streams unless the amount of regulation is known so that the estimated low-flow characteristic can be adjusted. The method is most accurate for sites having drainage areas ranging from 10 to 1,000 square miles and for predictions of 7-day, 10-year low flows ranging from 0.5 to 340 cubic feet per second.

Method for estimating low-flow characteristics of ungaged streams in Indiana

USGS Publications Warehouse

Arihood, L.D.; Glatfelter, D.R.

1986-01-01

Equations for estimating the 7-day, 2-yr and 7-day, 10-yr low flows at sites on ungaged streams are presented. Regression analysis was used to develop equations relating basin characteristics and low flow characteristics at 82 gaging stations. Significant basin characteristics in the equations are contributing drainage area and flow duration ratio, which is the 20% flow duration divided by the 90% flow duration. Flow duration ratio has been regionalized for Indiana on a plate. Ratios for use in the equations are obtained from this plate. Drainage areas are determined from maps or are obtained from reports. The predictive capability of the method was determined by tests of the equations and of the flow duration ratios on the plate. The accuracy of the equations alone was tested by estimating the low flow characteristics at 82 gaging stations where flow duration ratio is already known. In this case, the standard errors of estimate for 7-day, 2-yr and 7-day, 10-yr low flows are 19% and 28%. When flow duration ratios for the 82 gaging stations are obtained from the map, the standard errors are 46% and 61%. However, when stations with drainage areas < 10 sq mi are excluded from the test, the standard errors reduce to 38% and 49%. Standard errors increase when stations with small basins are included, probably because some of the flow duration ratios obtained for these small basins are incorrect. Local geology and its effect on the ratio are not adequately reflected on the plate, which shows the regional variation in flow duration ratio. In all the tests, no bias is apparent areally, with increasing drainage area or with increasing ratio. Guidelines and limitations should be considered when using the method. The method can be applied only at sites in the northern and the central physiographic zones of the state. Low flow characteristics cannot be estimated for regulated streams unless the amount of regulation is known so that the estimated low flow characteristic can be adjusted. The method is most accurate for sites with drainage areas ranging from 10 to 1,000 sq mi and for predictions of 7-day, 10-yr low flows ranging from 0.5 to 340 cu ft/sec. (Author 's abstract)

Simulation of propagation of the HPM in the low-pressure argon plasma

NASA Astrophysics Data System (ADS)

Zhigang, LI; Zhongcai, YUAN; Jiachun, WANG; Jiaming, SHI

2018-02-01

The propagation of the high-power microwave (HPM) with a frequency of 6 GHz in the low-pressure argon plasma was studied by the method of fluid approximation. The two-dimensional transmission model was built based on the wave equation, the electron drift-diffusion equations and the heavy species transport equations, which were solved by means of COMSOL Multiphysics software. The simulation results showed that the propagation characteristic of the HPM was closely related to the average electron density of the plasma. The attenuation of the transmitted wave increased nonlinearly with the electron density. Specifically, the growth of the attenuation slowed down as the electron density increased uniformly. In addition, the concrete transmission process of the HPM wave in the low-pressure argon plasma was given.

Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.; Martinelli, L.

1991-01-01

The system of equations consisting of the full Navier-Stokes equations and two turbulence equations was solved for in the steady state using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time stepping scheme with a stability bound local time step, while the turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positively. Low Reynolds number modifications to the original two equation model are incorporated in a manner which results in well behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved for, initializing all quantities with uniform freestream values, and resulting in rapid and uniform convergence rates for the flow and turbulence equations.

Stochastic layer scaling in the two-wire model for divertor tokamaks

NASA Astrophysics Data System (ADS)

Ali, Halima; Punjabi, Alkesh; Boozer, Allen

2009-06-01

The question of magnetic field structure in the vicinity of the separatrix in divertor tokamaks is studied. The authors have investigated this problem earlier in a series of papers, using various mathematical techniques. In the present paper, the two-wire model (TWM) [Reiman, A. 1996 Phys. Plasmas 3, 906] is considered. It is noted that, in the TWM, it is useful to consider an extra equation expressing magnetic flux conservation. This equation does not add any more information to the TWM, since the equation is derived from the TWM. This equation is useful for controlling the step size in the numerical integration of the TWM equations. The TWM with the extra equation is called the flux-preserving TWM. Nevertheless, the technique is apparently still plagued by numerical inaccuracies when the perturbation level is low, resulting in an incorrect scaling of the stochastic layer width. The stochastic broadening of the separatrix in the flux-preserving TWM is compared with that in the low mn (poloidal mode number m and toroidal mode number n) map (LMN) [Ali, H., Punjabi, A., Boozer, A. and Evans, T. 2004 Phys. Plasmas 11, 1908]. The flux-preserving TWM and LMN both give Boozer-Rechester 0.5 power scaling of the stochastic layer width with the amplitude of magnetic perturbation when the perturbation is sufficiently large [Boozer, A. and Rechester, A. 1978, Phys. Fluids 21, 682]. The flux-preserving TWM gives a larger stochastic layer width when the perturbation is low, while the LMN gives correct scaling in the low perturbation region. Area-preserving maps such as the LMN respect the Hamiltonian structure of field line trajectories, and have the added advantage of computational efficiency. Also, for a $1\\frac12$ degree of freedom Hamiltonian system such as field lines, maps do not give Arnold diffusion.

Detailed Design of the Rigidizable Inflatable Get-Away-Special Experiment

DTIC Science & Technology

2006-03-23

velocity determination, shown in Equation 4.1: V = ALF 2πfn + √ 2aSd (4.1) where ALF = Low Frequency Acceleration (m/s 2) fn = First Fundamental Frequency...Information The first equation in SSP 52005 is used to determine the velocity of the com- ponent to be contained: V = ALF 2πfn + √ 2aSd (C.1) where ALF = Low

Low flow of streams in the Susquehanna River basin of New York

USGS Publications Warehouse

Randall, Allan D.

2011-01-01

The principal source of streamflow during periods of low flow in the Susquehanna River basin of New York is the discharge of groundwater from sand-and-gravel deposits. Spatial variation in low flow is mostly a function of differences in three watershed properties: the amount of water that is introduced to the watershed and available for runoff, the extent of surficial sand and gravel relative to till-mantled bedrock, and the extent of wetlands. These three properties were consistently significant in regression equations that were developed to estimate several indices of low flow expressed in cubic feet per second or in cubic feet per second per square mile. The equations explain 90 to 99 percent of the spatial variation in low flow. A few equations indicate that underflow that bypasses streamflow-measurement sites through permeable sand and gravel can significantly decrease low flows. Analytical and numerical groundwater-flow models indicate that spatial extent, hydraulic conductivity and thickness, storage capacity, and topography of stratified sandand- gravel deposits affect low-flow yields from those deposits. Model-simulated discharge of groundwater to streams at low flow reaches a maximum where hydraulic-conductivity values are about 15 feet per day (in valleys 0.5 mile wide) to 60 feet per day (in valleys 1 mile wide). These hydraulic-conductivity values are much larger than those that are considered typical of till and bedrock, but smaller than values reported for productive sand-and-gravel aquifers in some valley reaches in New York. Differences in the properties of till and bedrock and in land-surface slope or relief within the Susquehanna River basin of New York apparently have little effect on low flow. Three regression equations were selected for practical application in estimating 7-day mean low flows in cubic feet per second with 10-year and 2-year recurrence intervals, and 90-percent flow duration, at ungaged sites draining more than 30 square miles; standard errors were 0.88, 1.40, and 1.95 cubic feet per second, respectively. Equations that express low flows in cubic feet per second per square mile were selected for estimating these three indices at ungaged sites draining less than 30 square miles; standard errors were 0.012, 0.018, and 0.022 cubic feet per second per square mile, respectively.

The effect of the Mihalas, Hummer, and Daeppen equation of state and the molecular opacity on the standard solar model

NASA Technical Reports Server (NTRS)

Kim, Y.-C.; Demarque, P.; Guenther, D. B.

1991-01-01

Improvements to the Yale Rotating Stellar Evolution Code (YREC) by incorporating the Mihalas-Hummer-Daeppen equation of state, an improved opacity interpolation routine, and the effects of molecular opacities, calculated at Los Alamos, have been made. the effect of each of the improvements on the standard solar model has been tested independently by computing the corresponding solar nonradial oscillation frequencies. According to these tests, the Mihalas-Hummer-Daeppen equation of state has very little effect on the model's low l p-mode oscillation spectrum compared to the model using the existing analytical equation of state implemented in YREC. On the other hand, the molecular opacity does improve the model's oscillation spectrum. The effect of molecular opacity on the computed solar oscillation frequencies is much larger than that of the Mihalas-Hummer-Daeppen equation of state. together, the two improvements to the physics reduce the discrepancy with observations by 10 microHz for the low l modes.

Regionalization of winter low-flow characteristics of Tennessee streams

USGS Publications Warehouse

Bingham, R.H.

1986-01-01

Procedures were developed for estimating winter (December-April) low flows at ungaged stream sites in Tennessee based on surface geology and drainage area size. One set of equations applies to West Tennessee streams, and another set applies to Middle and East Tennessee streams. The equations do not apply to streams where flow is significantly altered by the activities of man. Standard errors of estimate of equations for West Tennessee are 22% - 35% and for middle and East Tennessee 31% - 36%. Statistical analyses indicate that summer low-flow characteristics are the same as annual low-flow characteristics, and that winter low flows are larger than annual low flows. Streamflow-recession indexes, in days per log cycle of decrease in discharge, were used to account for effects of geology on low flow of streams. The indexes in Tennessee range from 32 days/log cycle for clay and shale to 350 days/log cycle for gravel and sand, indicating different aquifer characteristics of the geologic units that contribute to streamflows during periods of no surface runoff. Streamflow-recession rate depends primarily on transmissivity and storage characteristics of the aquifers, and the average distance from stream channels to basin divides. Geology and drainage basin size are the most significant variables affecting low flow in Tennessee streams according to regression analyses. (Author 's abstract)

External heat transfer predictions in a highly loaded transonic linear turbine guide vane cascade using an upwind biased Navier-Stokes solver

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

Gehrer, A.; Jericha, H.

External heat transfer predictions are performed for two-dimensional turbine blade cascades. The Reynolds-averaged Navier-Stokes equations with algebraic (Arnone and Pacciani, 1998), one-equation (Spalart and Allmaras, 1994), and two-equation (low-Re {kappa}-{epsilon}, Biswas and Fukuyama, 1994) turbulence closures are solved with a fully implicit time-marching finite volume method. Comparisons with measurements (Arts et al., 1990; Arts, 1994) for a highly loaded transonic turbine nozzle guide vane cascade show good agreement in some cases, but also reveal problems with transition prediction and turbulence modeling. Special attention has been focused on the low-Re {kappa}-{epsilon} model concerning the influence of the inlet boundary condition formore » the {epsilon}-equation and problems in the stagnation point region.« less

Applying new Magee equations for predicting the Oncotype Dx recurrence score.

PubMed

Sughayer, Maher; Alaaraj, Rolla; Alsughayer, Ahmad

2018-04-24

Breast cancer is one of the most prevalent cancers in women. Oncotype Dx is a multi-gene assay frequently used to predict the recurrence risk for estrogen receptor-positive early breast cancer, with values < 18 considered low risk; ≥ 18 and ≤ 30, intermediate risk; and > 30, high risk. Patients at a high risk for recurrence are more likely to benefit from chemotherapy treatment. In this study, clinicopathological parameters for 37 cases of early breast cancer with available Oncotype Dx results were used to estimate the recurrence score using the three new Magee equations. Correlation studies with Oncotype Dx results were performed. Applying the same cutoff points as Oncotype Dx, patients were categorized into low-, intermediate- and high-risk groups according to their estimated recurrence scores. Pearson correlation coefficient (R) values between estimated and actual recurrence score were 0.73, 0.66, and 0.70 for Magee equations 1, 2 and 3, respectively. The concordance values between actual and estimated recurrence scores were 57.6%, 52.9%, and 57.6% for Magee equations 1, 2 and 3, respectively. Using standard pathologic measures and immunohistochemistry scores in these three linear Magee equations, most low and high recurrence risk cases can be predicted with a strong positive correlation coefficient, high concordance and negligible two-step discordance. Magee equations are user-friendly and can be used to predict the recurrence score in early breast cancer cases.

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

USGS Publications Warehouse

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

1983-01-01

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

Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers

NASA Technical Reports Server (NTRS)

Mueller, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)

2001-01-01

A method of minimizing numerical errors, and improving nonlinear stability and accuracy associated with low Mach number computational aeroacoustics (CAA) is proposed. The method consists of two levels. From the governing equation level, we condition the Euler equations in two steps. The first step is to split the inviscid flux derivatives into a conservative and a non-conservative portion that satisfies a so called generalized energy estimate. This involves the symmetrization of the Euler equations via a transformation of variables that are functions of the physical entropy. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the second step is to reformulate the split Euler equations in perturbation form with the new unknowns as the small changes of the conservative variables with respect to their large stagnation values. From the numerical scheme level, a stable sixth-order central interior scheme with a third-order boundary schemes that satisfies the discrete analogue of the integration-by-parts procedure used in the continuous energy estimate (summation-by-parts property) is employed.

Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation

NASA Technical Reports Server (NTRS)

Suzen, Y. Bora; Huang, P. G.; Hultgren, Lennart S.; Ashpis, David E.

2001-01-01

A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, mu(sub t), with the intermittency factor, gamma. Turbulent quantities are predicted by using Menter's two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.

Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation

NASA Technical Reports Server (NTRS)

Suzen, Y. B.; Huang, P. G.; Hultgren, Lennart S.; Ashpis, David E.

2003-01-01

A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, t , with the intermittency factor, y. Turbulent quantities are predicted by using Menter s two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.

Methods for estimating selected low-flow frequency statistics and mean annual flow for ungaged locations on streams in North Georgia

USGS Publications Warehouse

Gotvald, Anthony J.

2017-01-13

The U.S. Geological Survey, in cooperation with the Georgia Department of Natural Resources, Environmental Protection Division, developed regional regression equations for estimating selected low-flow frequency and mean annual flow statistics for ungaged streams in north Georgia that are not substantially affected by regulation, diversions, or urbanization. Selected low-flow frequency statistics and basin characteristics for 56 streamgage locations within north Georgia and 75 miles beyond the State’s borders in Alabama, Tennessee, North Carolina, and South Carolina were combined to form the final dataset used in the regional regression analysis. Because some of the streamgages in the study recorded zero flow, the final regression equations were developed using weighted left-censored regression analysis to analyze the flow data in an unbiased manner, with weights based on the number of years of record. The set of equations includes the annual minimum 1- and 7-day average streamflow with the 10-year recurrence interval (referred to as 1Q10 and 7Q10), monthly 7Q10, and mean annual flow. The final regional regression equations are functions of drainage area, mean annual precipitation, and relief ratio for the selected low-flow frequency statistics and drainage area and mean annual precipitation for mean annual flow. The average standard error of estimate was 13.7 percent for the mean annual flow regression equation and ranged from 26.1 to 91.6 percent for the selected low-flow frequency equations.The equations, which are based on data from streams with little to no flow alterations, can be used to provide estimates of the natural flows for selected ungaged stream locations in the area of Georgia north of the Fall Line. The regression equations are not to be used to estimate flows for streams that have been altered by the effects of major dams, surface-water withdrawals, groundwater withdrawals (pumping wells), diversions, or wastewater discharges. The regression equations should be used only for ungaged sites with drainage areas between 1.67 and 576 square miles, mean annual precipitation between 47.6 and 81.6 inches, and relief ratios between 0.146 and 0.607; these are the ranges of the explanatory variables used to develop the equations. An attempt was made to develop regional regression equations for the area of Georgia south of the Fall Line by using the same approach used during this study for north Georgia; however, the equations resulted with high average standard errors of estimates and poorly predicted flows below 0.5 cubic foot per second, which may be attributed to the karst topography common in that area.The final regression equations developed from this study are planned to be incorporated into the U.S. Geological Survey StreamStats program. StreamStats is a Web-based geographic information system that provides users with access to an assortment of analytical tools useful for water-resources planning and management, and for engineering design applications, such as the design of bridges. The StreamStats program provides streamflow statistics and basin characteristics for U.S. Geological Survey streamgage locations and ungaged sites of interest. StreamStats also can compute basin characteristics and provide estimates of streamflow statistics for ungaged sites when users select the location of a site along any stream in Georgia.

A Computational Fluid Dynamics Study of Transitional Flows in Low-Pressure Turbines under a Wide Range of Operating Conditions

NASA Technical Reports Server (NTRS)

Suzen, Y. B.; Huang, P. G.; Ashpis, D. E.; Volino, R. J.; Corke, T. C.; Thomas, F. O.; Huang, J.; Lake, J. P.; King, P. I.

2007-01-01

A transport equation for the intermittency factor is employed to predict the transitional flows in low-pressure turbines. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, mu(sub p) with the intermittency factor, gamma. Turbulent quantities are predicted using Menter's two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model which can produce both the experimentally observed streamwise variation of intermittency and a realistic profile in the cross stream direction. The model had been previously validated against low-pressure turbine experiments with success. In this paper, the model is applied to predictions of three sets of recent low-pressure turbine experiments on the Pack B blade to further validate its predicting capabilities under various flow conditions. Comparisons of computational results with experimental data are provided. Overall, good agreement between the experimental data and computational results is obtained. The new model has been shown to have the capability of accurately predicting transitional flows under a wide range of low-pressure turbine conditions.

Colonization of a territory by a stochastic population under a strong Allee effect and a low immigration pressure

NASA Astrophysics Data System (ADS)

Be'er, Shay; Assaf, Michael; Meerson, Baruch

2015-06-01

We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for colonization. At low immigration rates, the average precolonization population size is small, thus invalidating the WKB approximation to the master equation. We circumvent this difficulty by deriving an exact zero-flux solution of the master equation and matching it with an approximate nonzero-flux solution of the pertinent Fokker-Planck equation in a small region around the critical population size. This procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization, for a wide range of immigration rates. At sufficiently high immigration rates our results agree with WKB results obtained previously. At low immigration rates the results can be very different.

Colonization of a territory by a stochastic population under a strong Allee effect and a low immigration pressure.

PubMed

Be'er, Shay; Assaf, Michael; Meerson, Baruch

2015-06-01

We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for colonization. At low immigration rates, the average precolonization population size is small, thus invalidating the WKB approximation to the master equation. We circumvent this difficulty by deriving an exact zero-flux solution of the master equation and matching it with an approximate nonzero-flux solution of the pertinent Fokker-Planck equation in a small region around the critical population size. This procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization, for a wide range of immigration rates. At sufficiently high immigration rates our results agree with WKB results obtained previously. At low immigration rates the results can be very different.

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

PubMed

Prieur, Fabrice; Vilenskiy, Gregory; Holm, Sverre

2012-10-01

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

Estimating the fuel moisture content of indicator sticks from selected weather variables

Treesearch

Theodore G. Storey

1965-01-01

Equations were developed to predict the fuel moisture content of indicator sticks from the controlling weather variables. Moisture content of ⅛-inch thick basswood slats used in the South and East could be determined with about equal precision by equation in the critical low moisture range or by weighing at fire danger stations. The most useful equation...

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…

Well-posedness of the Prandtl equation with monotonicity in Sobolev spaces

NASA Astrophysics Data System (ADS)

Chen, Dongxiang; Wang, Yuxi; Zhang, Zhifei

2018-05-01

By using the paralinearization technique, we prove the well-posedness of the Prandtl equation for monotonic data in anisotropic Sobolev space with exponential weight and low regularity. The proof is very elementary, thus is expected to provide a new possible way for the zero-viscosity limit problem of the Navier-Stokes equations with the non-slip boundary condition.

Cycle-time equations for five small tractors operating in low-volume small-diameter hardwood stands

Treesearch

Chris B. LeDoux; Neil K. Huyler; Neil K. Huyler

1992-01-01

Prediction equations for estimating cycle time were developed for five small tractors studied under various silvicultural treatments and operating conditions. The tractors studied included the Pasquali 933, a Holder A60F, a Forest Ant Forwarder (Skogsman), a Massey-Ferguson, and a Sam4 Minitarus. Skidding costs were estimated based on the cycle-time equations. Using...

The turbulent mean-flow, Reynolds-stress, and heat flux equations in mass-averaged dependent variables

NASA Technical Reports Server (NTRS)

Rubesin, M. W.; Rose, W. C.

1973-01-01

The time-dependent, turbulent mean-flow, Reynolds stress, and heat flux equations in mass-averaged dependent variables are presented. These equations are given in conservative form for both generalized orthogonal and axisymmetric coordinates. For the case of small viscosity and thermal conductivity fluctuations, these equations are considerably simpler than the general Reynolds system of dependent variables for a compressible fluid and permit a more direct extension of low speed turbulence modeling to computer codes describing high speed turbulence fields.

Numerical investigations of low-density nozzle flow by solving the Boltzmann equation

NASA Technical Reports Server (NTRS)

Deng, Zheng-Tao; Liaw, Goang-Shin; Chou, Lynn Chen

1995-01-01

A two-dimensional finite-difference code to solve the BGK-Boltzmann equation has been developed. The solution procedure consists of three steps: (1) transforming the BGK-Boltzmann equation into two simultaneous partial differential equations by taking moments of the distribution function with respect to the molecular velocity u(sub z), with weighting factors 1 and u(sub z)(sup 2); (2) solving the transformed equations in the physical space based on the time-marching technique and the four-stage Runge-Kutta time integration, for a given discrete-ordinate. The Roe's second-order upwind difference scheme is used to discretize the convective terms and the collision terms are treated as source terms; and (3) using the newly calculated distribution functions at each point in the physical space to calculate the macroscopic flow parameters by the modified Gaussian quadrature formula. Repeating steps 2 and 3, the time-marching procedure stops when the convergent criteria is reached. A low-density nozzle flow field has been calculated by this newly developed code. The BGK Boltzmann solution and experimental data show excellent agreement. It demonstrated that numerical solutions of the BGK-Boltzmann equation are ready to be experimentally validated.

Regional regression equations for the estimation of selected monthly low-flow duration and frequency statistics at ungaged sites on streams in New Jersey

USGS Publications Warehouse

Watson, Kara M.; McHugh, Amy R.

2014-01-01

Regional regression equations were developed for estimating monthly flow-duration and monthly low-flow frequency statistics for ungaged streams in Coastal Plain and non-coastal regions of New Jersey for baseline and current land- and water-use conditions. The equations were developed to estimate 87 different streamflow statistics, which include the monthly 99-, 90-, 85-, 75-, 50-, and 25-percentile flow-durations of the minimum 1-day daily flow; the August–September 99-, 90-, and 75-percentile minimum 1-day daily flow; and the monthly 7-day, 10-year (M7D10Y) low-flow frequency. These 87 streamflow statistics were computed for 41 continuous-record streamflow-gaging stations (streamgages) with 20 or more years of record and 167 low-flow partial-record stations in New Jersey with 10 or more streamflow measurements. The regression analyses used to develop equations to estimate selected streamflow statistics were performed by testing the relation between flow-duration statistics and low-flow frequency statistics for 32 basin characteristics (physical characteristics, land use, surficial geology, and climate) at the 41 streamgages and 167 low-flow partial-record stations. The regression analyses determined drainage area, soil permeability, average April precipitation, average June precipitation, and percent storage (water bodies and wetlands) were the significant explanatory variables for estimating the selected flow-duration and low-flow frequency statistics. Streamflow estimates were computed for two land- and water-use conditions in New Jersey—land- and water-use during the baseline period of record (defined as the years a streamgage had little to no change in development and water use) and current land- and water-use conditions (1989–2008)—for each selected station using data collected through water year 2008. The baseline period of record is representative of a period when the basin was unaffected by change in development. The current period is representative of the increased development of the last 20 years (1989–2008). The two different land- and water-use conditions were used as surrogates for development to determine whether there have been changes in low-flow statistics as a result of changes in development over time. The State was divided into two low-flow regression regions, the Coastal Plain and the non-coastal region, in order to improve the accuracy of the regression equations. The left-censored parametric survival regression method was used for the analyses to account for streamgages and partial-record stations that had zero flow values for some of the statistics. The average standard error of estimate for the 348 regression equations ranged from 16 to 340 percent. These regression equations and basin characteristics are presented in the U.S. Geological Survey (USGS) StreamStats Web-based geographic information system application. This tool allows users to click on an ungaged site on a stream in New Jersey and get the estimated flow-duration and low-flow frequency statistics. Additionally, the user can click on a streamgage or partial-record station and get the “at-site” streamflow statistics. The low-flow characteristics of a stream ultimately affect the use of the stream by humans. Specific information on the low-flow characteristics of streams is essential to water managers who deal with problems related to municipal and industrial water supply, fish and wildlife conservation, and dilution of wastewater.

Turbulence Model Selection for Low Reynolds Number Flows

PubMed Central

2016-01-01

One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil’s surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Reθ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail. PMID:27104354

Determining partial differential cross sections for low-energy electron photodetachment involving conical intersections using the solution of a Lippmann-Schwinger equation constructed with standard electronic structure techniques.

PubMed

Han, Seungsuk; Yarkony, David R

2011-05-07

A method for obtaining partial differential cross sections for low energy electron photodetachment in which the electronic states of the residual molecule are strongly coupled by conical intersections is reported. The method is based on the iterative solution to a Lippmann-Schwinger equation, using a zeroth order Hamiltonian consisting of the bound nonadiabatically coupled residual molecule and a free electron. The solution to the Lippmann-Schwinger equation involves only standard electronic structure techniques and a standard three-dimensional free particle Green's function quadrature for which fast techniques exist. The transition dipole moment for electron photodetachment, is a sum of matrix elements each involving one nonorthogonal orbital obtained from the solution to the Lippmann-Schwinger equation. An expression for the electron photodetachment transition dipole matrix element in terms of Dyson orbitals, which does not make the usual orthogonality assumptions, is derived.

Turbulence Model Selection for Low Reynolds Number Flows.

PubMed

Aftab, S M A; Mohd Rafie, A S; Razak, N A; Ahmad, K A

2016-01-01

One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil's surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Reθ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail.

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

Waves in magnetized quark matter

NASA Astrophysics Data System (ADS)

Fogaça, D. A.; Sanches, S. M.; Navarra, F. S.

2018-05-01

We study wave propagation in a non-relativistic cold quark-gluon plasma immersed in a constant magnetic field. Starting from the Euler equation we derive linear wave equations and investigate their stability and causality. We use a generic form for the equation of state, the EOS derived from the MIT bag model and also a variant of the this model which includes gluon degrees of freedom. The results of this analysis may be relevant for perturbations propagating through the quark matter phase in the core of compact stars and also for perturbations propagating in the low temperature quark-gluon plasma formed in low energy heavy ion collisions, to be carried out at FAIR and NICA.

Low-density lipoprotein transport through an arterial wall under hyperthermia and hypertension conditions--An analytical solution.

PubMed

Iasiello, Marcello; Vafai, Kambiz; Andreozzi, Assunta; Bianco, Nicola

2016-01-25

An analytical solution for Low-Density Lipoprotein transport through an arterial wall under hyperthermia conditions is established in this work. A four-layer model is used to characterize the arterial wall. Transport governing equations are obtained as a combination between Staverman-Kedem-Katchalsky membrane equations and volume-averaged porous media equations. Temperature and solute transport fields are coupled by means of Ludwig-Soret effect. Results are in excellent agreement with numerical and analytical literature data under isothermal conditions, and with numerical literature data for the hyperthermia case. Effects of hypertension combined with hyperthermia, are also analyzed in this work. Copyright © 2015 Elsevier Ltd. All rights reserved.

Development and Assessment of a Computer-Based Equation of State for Equilibrium Air

DTIC Science & Technology

2013-09-01

for very low energies. However, the ideal gas EOS is appropriate for atmospheric flight at subsonic, transonic, and low supersonic flight speeds...Flow Properties About Blunt Bodies Moving at Supersonic Speeds in an Equilibrium Gas ,” NASA TR R-204, July 1964. 21. Tannehill, John C., and Mugge...changes are made. 15. Subject Terms Air, thermodynamic properties, equation of state, chemical equilibrium, real- gas 16. SECURITY CLASSIFICATION

Beam-plasma instability in the presence of low-frequency turbulence. [during type 3 solar emission

NASA Technical Reports Server (NTRS)

Goldman, M. V.; Dubois, D. F.

1982-01-01

General equations are derived for a linear beam-plasma instability in the presence of low-frequency turbulence. Within a 'quasi-linear' statistical approximation, these equations contain Langmuir wave scattering, diffusion, resonant and nonresonant anomalous absorption, and a 'plasma laser' effect. It is proposed that naturally occurring density irregularities in the solar wind may stabilize the beam-unstable Langmuir waves which occur during type III solar emissions.

Low-frequency Carbon Radio Recombination Lines. I. Calculations of Departure Coefficients

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

Salgado, F.; Morabito, L. K.; Oonk, J. B. R.

In the first paper of this series, we study the level population problem of recombining carbon ions. We focus our study on high quantum numbers, anticipating observations of carbon radio recombination lines to be carried out by the Low Frequency Array. We solve the level population equation including angular momentum levels with updated collision rates up to high principal quantum numbers. We derive departure coefficients by solving the level population equation in the hydrogenic approximation and including low-temperature dielectronic capture effects. Our results in the hydrogenic approximation agree well with those of previous works. When comparing our results including dielectronicmore » capture, we find differences that we ascribe to updates in the atomic physics (e.g., collision rates) and to the approximate solution method of the statistical equilibrium equations adopted in previous studies. A comparison with observations is discussed in an accompanying article, as radiative transfer effects need to be considered.« less

Echo power analysis and simulation of low altitude radio fuze

NASA Astrophysics Data System (ADS)

Chen, Xiaolu; Chen, Biao; Xu, Tao; Xu, Suqin

2013-01-01

The echo power from the earth gound which was received by fuze plays an important role in aerial defense missile, especially when the fuze is working in the look down mode. It is necessary to analyze and even simulate the echo power signals to enhance the missile's anti-jamming ability. In this paper, the quantity of echo power from the earth ground of low altitude radio fuze was analyzed in detail. Three boundary equations of area irradiated by electromagnetic beams were presented, which include two equidistant curve equations and one equal-Doppler curve equation. The relationship between the working mode and the critical height was analyzed. The calculating formula of echo power waveform was derived. And based on the derived formula, the correlation between the maximal echo power and the incident height was given and simulated, which would be helpful for the further researches of low altitude radio fuze.

Low shear stress gravel-bed river

USGS Publications Warehouse

Milhous, Robert T.

1997-01-01

A low stress gravel bed river is a river where the cross-sectional average dimensionless shear stress (??*) rarely exceeds 0.047. That is the case for the Gunnison River below Delta in Western Colorado. The cross-sectional average ??* in the Gunnison River has not exceeded 0.047, except at one cross section during one year, in the 87 years of record. A ??* of 0.047 is the critical ??* in the bed-load equation considered to be most applicable to gravel/cobble bed rivers (the Meyer-Peter, Mueller equation). According to this equation, there has been no bed-material movement in the Gunnison River since 1920; in fact there has been bed-material movement and this movement is biologically important. Bed-material is moved when the ??* is 0.016 or larger. Streamflows that cause a ??* of at least 0.016 maintain the aquatic habitat in a low shear stress river.

Droplet size in flow: Theoretical model and application to polymer blends

NASA Astrophysics Data System (ADS)

Fortelný, Ivan; Jůza, Josef

2017-05-01

The paper is focused on prediction of the average droplet radius, R, in flowing polymer blends where the droplet size is determined by dynamic equilibrium between the droplet breakup and coalescence. Expressions for the droplet breakup frequency in systems with low and high contents of the dispersed phase are derived using available theoretical and experimental results for model blends. Dependences of the coalescence probability, Pc, on system parameters, following from recent theories, is considered and approximate equation for Pc in a system with a low polydispersity in the droplet size is proposed. Equations for R in systems with low and high contents of the dispersed phase are derived. Combination of these equations predicts realistic dependence of R on the volume fraction of dispersed droplets, φ. Theoretical prediction of the ratio of R to the critical droplet radius at breakup agrees fairly well with experimental values for steadily mixed polymer blends.

An application of a two-equation model of turbulence to three-dimensional chemically reacting flows

NASA Technical Reports Server (NTRS)

Lee, J.

1994-01-01

A numerical study of three dimensional chemically reacting and non-reacting flowfields is conducted using a two-equation model of turbulence. A generalized flow solver using an implicit Lower-Upper (LU) diagonal decomposition numerical technique and finite-rate chemistry has been coupled with a low-Reynolds number two-equation model of turbulence. This flow solver is then used to study chemically reacting turbulent supersonic flows inside combustors with synergetic fuel injectors. The reacting and non-reacting turbulent combustor solutions obtained are compared with zero-equation turbulence model solutions and with available experimental data. The hydrogen-air chemistry is modeled using a nine-species/eighteen reaction model. A low-Reynolds number k-epsilon model was used to model the effect of turbulence because, in general, the low-Reynolds number k-epsilon models are easier to implement numerically and are far more general than algebraic models. However, low-Reynolds number k-epsilon models require a much finer near-wall grid resolution than high-Reynolds number models to resolve accurately the near-wall physics. This is especially true in complex flowfields, where the stiff nature of the near-wall turbulence must be resolved. Therefore, the limitations imposed by the near-wall characteristics and compressible model corrections need to be evaluated further. The gradient-diffusion hypothesis is used to model the effects of turbulence on the mass diffusion process. The influence of this low-Reynolds number turbulence model on the reacting flowfield predictions was studied parametrically.

Phenomenological QCD equation of state for massive neutron stars

DOE PAGES

Kojo, Toru; Powell, Philip D.; Song, Yifan; ...

2015-02-03

Here, we construct an equation of state for massive neutron stars based on quantum chromodynamics phenomenology. Our primary purpose is to delineate the relevant ingredients of equations of state that simultaneously have the required stiffness and satisfy constraints from thermodynamics and causality. These ingredients are (i) a repulsive density-density interaction, universal for all flavors, (ii) the color-magnetic interaction active from low to high densities, (iii) confining effects, which become increasingly important as the baryon density decreases, and (iv) nonperturbative gluons, which are not very sensitive to changes of the quark density. We use the following “3-window” description: At baryon densitiesmore » below about twice normal nuclear density, 2n 0, we use the Akmal-Pandharipande-Ravenhall (APR) equation of state, and at high densities, ≥(4–7)n 0, we use the three-flavor Nambu-Jona-Lasinio (NJL) model supplemented by vector and diquark interactions. In the transition density region, we smoothly interpolate the hadronic and quark equations of state in the chemical potential-pressure plane. Requiring that the equation of state approach APR at low densities, we find that the quark pressure in nonconfining models can be larger than the hadronic pressure, unlike in conventional equations of state. We show that consistent equations of state of stiffness sufficient to allow massive neutron stars are reasonably tightly constrained, suggesting that gluon dynamics remains nonperturbative even at baryon densities ~10n 0.« less

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.

Cockcroft-Gault revisited: New de-liver-ance on recommendations for use in cirrhosis.

PubMed

Scappaticci, Gianni B; Regal, Randolph E

2017-01-28

The Cockcroft-Gault (CG) equation has become perhaps the most popular practical approach for estimating renal function among health care professionals. Despite its widespread use, clinicians often overlook not only the limitations of the original serum creatinine (SCr) based equation, but also may not appreciate the validity of the many variations used to compensate for these limitations. For cirrhotic patients in particular, the underlying pathophysiology of the disease contributes to a falsely low SCr, thereby overestimating renal function with use of the CG equation in this population. We reviewed the original CG trial from 1976 along with data surrounding clinician specific alterations to the CG equation that followed through time. These alterations included different formulas for body weight in obese patients and the "rounding up" approach in patients with low SCr. Additionally, we described the pathophysiology and hemodynamic changes that occur in cirrhosis; and reviewed several studies that attempted to estimate renal function in this population. The evidence we reviewed regarding the most accurate manipulation of the original CG equation to estimate creatinine clearance (CrCl) was inconclusive. Unfortunately, the homogeneity of the patient population in the original CG trial limited its external validity. Elimination of body weight in the CG equation actually produced the estimate closest to the measure CrCl. Furthermore, "rounding up" of SCr values often underestimated CrCl. This approach could lead to suboptimal dosing of drug therapies in patients with low SCr. In cirrhotic patients, utilization of SCr based methods overestimated true renal function by about 50% in the literature we reviewed.

Gyrotropic Guiding-Center Fluid Theory for Turbulent Inhomogeneous Magnetized Plasma

DTIC Science & Technology

2006-01-01

this paper, a new fluid theory is given in the guiding-center and gyrotropic approximation which is derivable from the Vlasov-Maxwell equations . The... equations can be solved (1) by using measurements of the low-order velocity moments to specify the initial and boundary conditions. 15. SUBJECT TERMS...Vlasov-Maxwell equations Fokker-Planck operator guiding-center Inhomogeneous, gyrotropic, magnetized plasma 16. SECURITY CLASSIFICATION OF: 17

Dayside Magnetosphere-Ionosphere Coupling and Prompt Response of Low-Latitude/Equatorial Ionosphere

NASA Astrophysics Data System (ADS)

Tu, J.; Song, P.

2017-12-01

We use a newly developed numerical simulation model of the ionosphere/thermosphere to investigate magnetosphere-ionosphere coupling and response of the low-latitude/equatorial ionosphere. The simulation model adapts an inductive-dynamic approach (including self-consistent solutions of Faraday's law and retaining inertia terms in ion momentum equations), that is, based on magnetic field B and plasma velocity v (B-v paradigm), in contrast to the conventional modeling based on electric field E and current j (E-j paradigm). The most distinct feature of this model is that the magnetic field in the ionosphere is not constant but self-consistently varies, e.g., with currents, in time. The model solves self-consistently time-dependent continuity, momentum, and energy equations for multiple species of ions and neutrals including photochemistry, and Maxwell's equations. The governing equations solved in the model are a set of multifluid-collisional-Hall MHD equations which are one of unique features of our ionosphere/thermosphere model. With such an inductive-dynamic approach, all possible MHD wave modes, each of which may refract and reflect depending on the local conditions, are retained in the solutions so that the dynamic coupling between the magnetosphere and ionosphere and among different regions of the ionosphere can be self-consistently investigated. In this presentation, we show that the disturbances propagate in the Alfven speed from the magnetosphere along the magnetic field lines down to the ionosphere/thermosphere and that they experience a mode conversion to compressional mode MHD waves (particularly fast mode) in the ionosphere. Because the fast modes can propagate perpendicular to the field, they propagate from the dayside high-latitude to the nightside as compressional waves and to the dayside low-latitude/equatorial ionosphere as rarefaction waves. The apparent prompt response of the low-latitude/equatorial ionosphere, manifesting as the sudden increase of the upward flow around the equator and global antisunward convection, is the result of such coupling of the high-latitude and the low-latitude/equatorial ionosphere, and the requirement of the flow continuity, instead of mechanisms such as the penetration electric field.

Estimating Selected Streamflow Statistics Representative of 1930-2002 in West Virginia

USGS Publications Warehouse

Wiley, Jeffrey B.

2008-01-01

Regional equations and procedures were developed for estimating 1-, 3-, 7-, 14-, and 30-day 2-year; 1-, 3-, 7-, 14-, and 30-day 5-year; and 1-, 3-, 7-, 14-, and 30-day 10-year hydrologically based low-flow frequency values for unregulated streams in West Virginia. Regional equations and procedures also were developed for estimating the 1-day, 3-year and 4-day, 3-year biologically based low-flow frequency values; the U.S. Environmental Protection Agency harmonic-mean flows; and the 10-, 25-, 50-, 75-, and 90-percent flow-duration values. Regional equations were developed using ordinary least-squares regression using statistics from 117 U.S. Geological Survey continuous streamflow-gaging stations as dependent variables and basin characteristics as independent variables. Equations for three regions in West Virginia - North, South-Central, and Eastern Panhandle - were determined. Drainage area, precipitation, and longitude of the basin centroid are significant independent variables in one or more of the equations. Estimating procedures are presented for determining statistics at a gaging station, a partial-record station, and an ungaged location. Examples of some estimating procedures are presented.

A conservative, thermodynamically consistent numerical approach for low Mach number combustion. Part I: Single-level integration

NASA Astrophysics Data System (ADS)

Nonaka, Andrew; Day, Marcus S.; Bell, John B.

2018-01-01

We present a numerical approach for low Mach number combustion that conserves both mass and energy while remaining on the equation of state to a desired tolerance. We present both unconfined and confined cases, where in the latter the ambient pressure changes over time. Our overall scheme is a projection method for the velocity coupled to a multi-implicit spectral deferred corrections (SDC) approach to integrate the mass and energy equations. The iterative nature of SDC methods allows us to incorporate a series of pressure discrepancy corrections naturally that lead to additional mass and energy influx/outflux in each finite volume cell in order to satisfy the equation of state. The method is second order, and satisfies the equation of state to a desired tolerance with increasing iterations. Motivated by experimental results, we test our algorithm on hydrogen flames with detailed kinetics. We examine the morphology of thermodiffusively unstable cylindrical premixed flames in high-pressure environments for confined and unconfined cases. We also demonstrate that our algorithm maintains the equation of state for premixed methane flames and non-premixed dimethyl ether jet flames.

Rheological Analysis of Binary Eutectic Mixture of Sodium and Potassium Nitrate and the Effect of Low Concentration CuO Nanoparticle Addition to Its Viscosity.

PubMed

Lasfargues, Mathieu; Cao, Hui; Geng, Qiao; Ding, Yulong

2015-08-11

This paper is focused on the characterisation and demonstration of Newtonian behaviour of salt at both high and low shear rate for sodium and potassium nitrate eutectic mixture (60/40) ranging from 250 °C to 500 °C. Analysis of published and experimental data was carried out to correlate all the numbers into one meaningful 4th order polynomial equation. Addition of a low amount of copper oxide nanoparticles to the mixture increased viscosity of 5.0%-18.0% compared to the latter equation.

Improvement of the low frequency oscillation model for Hall thrusters

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

Wang, Chunsheng, E-mail: wangcs@hit.edu.cn; Wang, Huashan

2016-08-15

The low frequency oscillation of the discharge current in Hall thrusters is a major aspect of these devices that requires further study. While the existing model captures the ionization mechanism of the low frequency oscillation, it unfortunately fails to express the dynamic characteristics of the ion acceleration. The analysis in this paper shows this is because of the simplification of the electron equation, which affects both the electric field distribution and the ion acceleration process. Additionally, the electron density equation is revised and a new model that is based on the physical properties of ion movement is proposed.

Low frequency acoustic and electromagnetic scattering

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Maccamy, R. C.

1986-01-01

This paper deals with two classes of problems arising from acoustics and electromagnetics scattering in the low frequency stations. The first class of problem is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two dimensional body while the second one is an interior-exterior interface problem with Helmholtz equation in the exterior. Low frequency analysis show that there are two intermediate problems which solve the above problems accurate to 0(k/2/ log k) where k is the frequency. These solutions greatly differ from the zero frequency approximations. For the Dirichlet problem numerical examples are shown to verify the theoretical estimates.

Selected Streamflow Statistics and Regression Equations for Predicting Statistics at Stream Locations in Monroe County, Pennsylvania

USGS Publications Warehouse

Thompson, Ronald E.; Hoffman, Scott A.

2006-01-01

A suite of 28 streamflow statistics, ranging from extreme low to high flows, was computed for 17 continuous-record streamflow-gaging stations and predicted for 20 partial-record stations in Monroe County and contiguous counties in north-eastern Pennsylvania. The predicted statistics for the partial-record stations were based on regression analyses relating inter-mittent flow measurements made at the partial-record stations indexed to concurrent daily mean flows at continuous-record stations during base-flow conditions. The same statistics also were predicted for 134 ungaged stream locations in Monroe County on the basis of regression analyses relating the statistics to GIS-determined basin characteristics for the continuous-record station drainage areas. The prediction methodology for developing the regression equations used to estimate statistics was developed for estimating low-flow frequencies. This study and a companion study found that the methodology also has application potential for predicting intermediate- and high-flow statistics. The statistics included mean monthly flows, mean annual flow, 7-day low flows for three recurrence intervals, nine flow durations, mean annual base flow, and annual mean base flows for two recurrence intervals. Low standard errors of prediction and high coefficients of determination (R2) indicated good results in using the regression equations to predict the statistics. Regression equations for the larger flow statistics tended to have lower standard errors of prediction and higher coefficients of determination (R2) than equations for the smaller flow statistics. The report discusses the methodologies used in determining the statistics and the limitations of the statistics and the equations used to predict the statistics. Caution is indicated in using the predicted statistics for small drainage area situations. Study results constitute input needed by water-resource managers in Monroe County for planning purposes and evaluation of water-resources availability.

The validation and application of a rotor acoustic prediction computer program

NASA Technical Reports Server (NTRS)

Gallman, Judith M.

1990-01-01

An essential prerequisite to reducing the acoustic detectability of military rotorcraft is a better understanding of main rotor noise which is the major contributor to the overall noise. A simple, yet accurate, Rotor Acoustic Prediction Program (RAPP) was developed to advance the understanding of main rotor noise. This prediction program uses the Ffowcs Williams and Hawkings (FW-H) equation. The particular form of the FW-H equation used is well suited for the coupling of the measured blade surface pressure to the prediction of acoustic pressure. The FW-H equation is an inhomogeneous wave equation that is valid in all space and governs acoustic pressure generated by thin moving bodies. The nonhomogeneous terms describe mass displacement due to surface motion and forces due to local surface stresses, such as viscous stress and pressure distribution on the surface. This paper examines two of the four types of main rotor noise: BVI noise and low-frequency noise. Blade-vortex interaction noise occurs when a tip vortex, previously shed by a rotor blade, passes close enough to a rotor blade to cause large variations in the blade surface pressures. This event is most disturbing when it happens on the advancing side of the rotor disk. Low-frequency noise includes hover and low to moderate speed forward flight. For these flight conditions, the low frequency components of the acoustic signal dominate.

Final Technical Report for "Applied Mathematics Research: Simulation Based Optimization and Application to Electromagnetic Inverse Problems"

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

Haber, Eldad

2014-03-17

The focus of research was: Developing adaptive mesh for the solution of Maxwell's equations; Developing a parallel framework for time dependent inverse Maxwell's equations; Developing multilevel methods for optimization problems with inequality constraints; A new inversion code for inverse Maxwell's equations in the 0th frequency (DC resistivity); A new inversion code for inverse Maxwell's equations in low frequency regime. Although the research concentrated on electromagnetic forward and in- verse problems the results of the research was applied to the problem of image registration.

On conservation laws for a generalized Boussinesq equation

NASA Astrophysics Data System (ADS)

Anco, S.; Rosa, M.; Gandarias, M. L.

2017-07-01

In this work, we study a Boussinesq equation with a strong damping term from the point of view of the Lie theory. By using the low order conservation laws we apply the conservation laws multiplier method to the associated potential systems.

Application of a constant hole volume Sanchez-Lacombe equation of state to mixtures relevant to polymeric foaming.

PubMed

von Konigslow, Kier; Park, Chul B; Thompson, Russell B

2018-06-06

A variant of the Sanchez-Lacombe equation of state is applied to several polymers, blowing agents, and saturated mixtures of interest to the polymer foaming industry. These are low-density polyethylene-carbon dioxide and polylactide-carbon dioxide saturated mixtures as well as polystyrene-carbon dioxide-dimethyl ether and polystyrene-carbon dioxide-nitrogen ternary saturated mixtures. Good agreement is achieved between theoretically predicted and experimentally determined solubilities, both for binary and ternary mixtures. Acceptable agreement with swelling ratios is found with no free parameters. Up-to-date pure component Sanchez-Lacombe characteristic parameters are provided for carbon dioxide, dimethyl ether, low-density polyethylene, nitrogen, polylactide, linear and branched polypropylene, and polystyrene. Pure fluid low-density polyethylene and nitrogen parameters exhibit more moderate success while still providing acceptable quantitative estimations. Mixture estimations are found to have more moderate success where pure components are not as well represented. The Sanchez-Lacombe equation of state is found to correctly predict the anomalous reversal of solubility temperature dependence for low critical point fluids through the observation of this behaviour in polystyrene nitrogen mixtures.

Artificial equilibrium points in binary asteroid systems with continuous low-thrust

NASA Astrophysics Data System (ADS)

Bu, Shichao; Li, Shuang; Yang, Hongwei

2017-08-01

The positions and dynamical characteristics of artificial equilibrium points (AEPs) in the vicinity of a binary asteroid with continuous low-thrust are studied. The restricted ellipsoid-ellipsoid model of binary system is employed for the binary asteroid system. The positions of AEPs are obtained by this model. It is found that the set of the point L1 or L2 forms a shape of an ellipsoid while the set of the point L3 forms a shape like a "banana". The effect of the continuous low-thrust on the feasible region of motion is analyzed by zero velocity curves. Because of using the low-thrust, the unreachable region can become reachable. The linearized equations of motion are derived for stability's analysis. Based on the characteristic equation of the linearized equations, the stability conditions are derived. The stable regions of AEPs are investigated by a parametric analysis. The effect of the mass ratio and ellipsoid parameters on stable region is also discussed. The results show that the influence of the mass ratio on the stable regions is more significant than the parameters of ellipsoid.

Low-Visibility Visual Simulation with Real Fog

NASA Technical Reports Server (NTRS)

Chase, Wendell D.

1982-01-01

An environmental fog simulation (EFS) attachment was developed to aid in the study of natural low-visibility visual cues and subsequently used to examine the realism effect upon the aircraft simulator visual scene. A review of the basic fog equations indicated that the two major factors must be accounted for in the simulation of low visibility-one due to atmospheric attenuation and one due to veiling luminance. These factors are compared systematically by: comparing actual measurements lo those computed from the Fog equations, and comparing runway-visual-range-related visual-scene contrast values with the calculated values. These values are also compared with the simulated equivalent equations and with contrast measurements obtained from a current electronic fog synthesizer to help identify areas in which improvements are needed. These differences in technique, the measured values, the Features of both systems, a pilot opinion survey of the EFS fog, and improvements (by combining features of both systems) that are expected to significantly increase the potential as well as flexibility for producing a very high-fidelity, low-visibility visual simulation are discussed.

Low-visibility visual simulation with real fog

NASA Technical Reports Server (NTRS)

Chase, W. D.

1981-01-01

An environmental fog simulation (EFS) attachment was developed to aid in the study of natural low-visibility visual cues and subsequently used to examine the realism effect upon the aircraft simulator visual scene. A review of the basic fog equations indicated that two major factors must be accounted for in the simulation of low visibility - one due to atmospheric attenuation and one due to veiling luminance. These factors are compared systematically by (1) comparing actual measurements to those computed from the fog equations, and (2) comparing runway-visual-range-related visual-scene contrast values with the calculated values. These values are also compared with the simulated equivalent equations and with contrast measurements obtained from a current electronic fog synthesizer to help identify areas in which improvements are needed. These differences in technique, the measured values, the features of both systems, a pilot opinion survey of the EFS fog, and improvements (by combining features of both systems) that are expected to significantly increase the potential as well as flexibility for producing a very high-fidelity low-visibility visual simulation are discussed.

Theoretical Pressure Distribution, Apparent Mass, and Moment of Inertia of a Disk Pendulum Oscillating at Low Frequency. M.S. Thesis - George Washington Univ., Washington, D. C.

NASA Technical Reports Server (NTRS)

Dunning, R. S.

1973-01-01

Equations are developed which give the pressure profile, the forces and torques on a disk pendulum by means of point source wave theory from acoustics. The pressure, force and torque equations for an unbaffled disk are developed. These equations are then used to calculate the apparent mass and apparent inertia for the pendulum.

Pattern of mathematic representation ability in magnetic electricity problem

NASA Astrophysics Data System (ADS)

Hau, R. R. H.; Marwoto, P.; Putra, N. M. D.

2018-03-01

The mathematic representation ability in solving magnetic electricity problem gives information about the way students understand magnetic electricity. Students have varied mathematic representation pattern ability in solving magnetic electricity problem. This study aims to determine the pattern of students' mathematic representation ability in solving magnet electrical problems.The research method used is qualitative. The subject of this study is the fourth semester students of UNNES Physics Education Study Program. The data collection is done by giving a description test that refers to the test of mathematical representation ability and interview about field line topic and Gauss law. The result of data analysis of student's mathematical representation ability in solving magnet electric problem is categorized into high, medium and low category. The ability of mathematical representations in the high category tends to use a pattern of making known and asked symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representation in the medium category tends to use several patterns of writing the known symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representations in the low category tends to use several patterns of making known symbols, writing equations, substituting quantities into equations, performing calculations and final answer.

Master equations and the theory of stochastic path integrals

NASA Astrophysics Data System (ADS)

Weber, Markus F.; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Master equations and the theory of stochastic path integrals.

PubMed

Weber, Markus F; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Multigrid Solution of the Navier-Stokes Equations at Low Speeds with Large Temperature Variations

NASA Technical Reports Server (NTRS)

Sockol, Peter M.

2002-01-01

Multigrid methods for the Navier-Stokes equations at low speeds and large temperature variations are investigated. The compressible equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. Three implicit smoothers have been incorporated into a common multigrid procedure. Both full coarsening and semi-coarsening with directional fine-grid defect correction have been studied. The resulting methods have been tested on four 2D laminar problems over a range of Reynolds numbers on both uniform and highly stretched grids. Two of the three methods show efficient and robust performance over the entire range of conditions. In addition none of the methods have any difficulty with the large temperature variations.

Assessment of the agreement between the Framingham and DAD risk equations for estimating cardiovascular risk in adult Africans living with HIV infection: a cross-sectional study.

PubMed

Noumegni, Steve Raoul; Ama, Vicky Jocelyne Moor; Assah, Felix K; Bigna, Jean Joel; Nansseu, Jobert Richie; Kameni, Jenny Arielle M; Katte, Jean-Claude; Dehayem, Mesmin Y; Kengne, Andre Pascal; Sobngwi, Eugene

2017-01-01

The Absolute cardiovascular disease (CVD) risk evaluation using multivariable CVD risk models is increasingly advocated in people with HIV, in whom existing models remain largely untested. We assessed the agreement between the general population derived Framingham CVD risk equation and the HIV-specific Data collection on Adverse effects of anti-HIV Drugs (DAD) CVD risk equation in HIV-infected adult Cameroonians. This cross-sectional study involved 452 HIV infected adults recruited at the HIV day-care unit of the Yaoundé Central Hospital, Cameroon. The 5-year projected CVD risk was estimated for each participant using the DAD and Framingham CVD risk equations. Agreement between estimates from these equations was assessed using the spearman correlation and Cohen's kappa coefficient. The mean age of participants (80% females) was 44.4 ± 9.8 years. Most participants (88.5%) were on antiretroviral treatment with 93.3% of them receiving first-line regimen. The most frequent cardiovascular risk factors were abdominal obesity (43.1%) and dyslipidemia (33.8%). The median estimated 5-year CVD risk was 0.6% (25th-75th percentiles: 0.3-1.3) using the DAD equation and 0.7% (0.2-2.0) with the Framingham equation. The Spearman correlation between the two estimates was 0.93 ( p  < 0.001). The kappa statistic was 0.61 (95% confident interval: 0.54-0.67) for the agreement between the two equations in classifying participants across risk categories defined as low, moderate, high and very high. Most participants had a low-to-moderate estimated CVD risk, with acceptable level of agreement between the general and HIV-specific equations in ranking CVD risk.

Cardiovascular risk prediction tools for populations in Asia.

PubMed

Barzi, F; Patel, A; Gu, D; Sritara, P; Lam, T H; Rodgers, A; Woodward, M

2007-02-01

Cardiovascular risk equations are traditionally derived from the Framingham Study. The accuracy of this approach in Asian populations, where resources for risk factor measurement may be limited, is unclear. To compare "low-information" equations (derived using only age, systolic blood pressure, total cholesterol and smoking status) derived from the Framingham Study with those derived from the Asian cohorts, on the accuracy of cardiovascular risk prediction. Separate equations to predict the 8-year risk of a cardiovascular event were derived from Asian and Framingham cohorts. The performance of these equations, and a subsequently "recalibrated" Framingham equation, were evaluated among participants from independent Chinese cohorts. Six cohort studies from Japan, Korea and Singapore (Asian cohorts); six cohort studies from China; the Framingham Study from the US. 172,077 participants from the Asian cohorts; 25,682 participants from Chinese cohorts and 6053 participants from the Framingham Study. In the Chinese cohorts, 542 cardiovascular events occurred during 8 years of follow-up. Both the Asian cohorts and the Framingham equations discriminated cardiovascular risk well in the Chinese cohorts; the area under the receiver-operator characteristic curve was at least 0.75 for men and women. However, the Framingham risk equation systematically overestimated risk in the Chinese cohorts by an average of 276% among men and 102% among women. The corresponding average overestimation using the Asian cohorts equation was 11% and 10%, respectively. Recalibrating the Framingham risk equation using cardiovascular disease incidence from the non-Chinese Asian cohorts led to an overestimation of risk by an average of 4% in women and underestimation of risk by an average of 2% in men. A low-information Framingham cardiovascular risk prediction tool, which, when recalibrated with contemporary data, is likely to estimate future cardiovascular risk with similar accuracy in Asian populations as tools developed from data on local cohorts.

Low-degree Structure in Mercury's Planetary Magnetic Field

NASA Technical Reports Server (NTRS)

Anderson, Brian J.; Johnson, Catherine L.; Korth, Haje; Winslow, Reka M.; Borovsky, Joseph E.; Purucker, Michael E.; Slavin, James A.; Solomon, Sean C.; Zuber, Maria T.; McNutt, Ralph L. Jr.

2012-01-01

The structure of Mercury's internal magnetic field has been determined from analysis of orbital Magnetometer measurements by the MESSENGER spacecraft. We identified the magnetic equator on 531 low-altitude and 120 high-altitude equator crossings from the zero in the radial cylindrical magnetic field component, Beta (sub rho). The low-altitude crossings are offset 479 +/- 6 km northward, indicating an offset of the planetary dipole. The tilt of the magnetic pole relative to the planetary spin axis is less than 0.8 deg.. The high-altitude crossings yield a northward offset of the magnetic equator of 486 +/- 74 km. A field with only nonzero dipole and octupole coefficients also matches the low-altitude observations but cannot yield off-equatorial Beta (sub rho) = 0 at radial distances greater than 3520 km. We compared offset dipole and other descriptions of the field with vector field observations below 600 km for 13 longitudinally distributed, magnetically quiet orbits. An offset dipole with southward directed moment of 190 nT-R-cube (sub M) yields root-mean-square (RMS) residuals below 14 nT, whereas a field with only dipole and octupole terms tuned to match the polar field and the low-altitude magnetic equator crossings yields RMS residuals up to 68 nT. Attributing the residuals from the offset-dipole field to axial degree 3 and 4 contributions we estimate that the Gauss coefficient magnitudes for the additional terms are less than 4% and 7%, respectively, relative to the dipole. The axial alignment and prominent quadrupole are consistent with a non-convecting layer above a deep dynamo in Mercury's fluid outer core.

The integration of the motion equations of low-orbiting earth satellites using Taylor's method

NASA Astrophysics Data System (ADS)

Krivov, A. V.; Chernysheva, N. A.

1990-04-01

A method for the numerical integration of the equations of motion for a satellite is proposed, taking the earth's oblateness and atmospheric drag into account. The method is based on Taylor's representation of the solution to the corresponding polynomial system. The algorithm for choosing the integration step and error estimation is constructed. The method is realized as a subrouting package. The method is applied to a low-orbiting earth satellite and the results are compared with those obtained using Everhart's method.

Rheological Analysis of Binary Eutectic Mixture of Sodium and Potassium Nitrate and the Effect of Low Concentration CuO Nanoparticle Addition to Its Viscosity

PubMed Central

Lasfargues, Mathieu; Cao, Hui; Geng, Qiao; Ding, Yulong

2015-01-01

This paper is focused on the characterisation and demonstration of Newtonian behaviour of salt at both high and low shear rate for sodium and potassium nitrate eutectic mixture (60/40) ranging from 250 °C to 500 °C. Analysis of published and experimental data was carried out to correlate all the numbers into one meaningful 4th order polynomial equation. Addition of a low amount of copper oxide nanoparticles to the mixture increased viscosity of 5.0%–18.0% compared to the latter equation. PMID:28793498

Viscous-shock-layer analysis of hypersonic flows over long slender vehicles. Ph.D. Thesis, 1988

NASA Technical Reports Server (NTRS)

Lee, Kam-Pui; Gupta, Roop N.

1992-01-01

An efficient and accurate method for solving the viscous shock layer equations for hypersonic flows over long slender bodies is presented. The two first order equations, continuity and normal momentum, are solved simultaneously as a coupled set. The flow conditions included are from high Reynolds numbers at low altitudes to low Reynolds numbers at high altitudes. For high Reynolds number flows, both chemical nonequilibrium and perfect gas cases are analyzed with surface catalytic effects and different turbulence models, respectively. At low Reynolds number flow conditions, corrected slip models are implemented with perfect gas case. Detailed comparisons are included with other predictions and experimental data.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Roy-Steiner equations for πN scattering

NASA Astrophysics Data System (ADS)

de Elvira, J. Ruiz; Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2015-10-01

In this talk, we briefly review our ongoing collaboration to precisely determine the low-energy πN scattering amplitude by means of Roy-Steiner equations. After giving a brief overview of this system of dispersive equations and their application to πN scattering, we proceed to solve for the lower partial waves of the s-channel (πN → πN) and the t-channel l( {π π to bar NN} right) sub-problems.

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

Shock waves: The Maxwell-Cattaneo case.

PubMed

Uribe, F J

2016-03-01

Several continuum theories for shock waves give rise to a set of differential equations in which the analysis of the underlying vector field can be done using the tools of the theory of dynamical systems. We illustrate the importance of the divergences associated with the vector field by considering the ideas by Maxwell and Cattaneo and apply them to study shock waves in dilute gases. By comparing the predictions of the Maxwell-Cattaneo equations with shock wave experiments we are lead to the following conclusions: (a) For low compressions (low Mach numbers: M) the results from the Maxwell-Cattaneo equations provide profiles that are in fair agreement with the experiments, (b) as the Mach number is increased we find a range of Mach numbers (1.27 ≈ M(1) < M < M(2) ≈ 1.90) such that numerical shock wave solutions to the Maxwell-Cattaneo equations cannot be found, and (c) for greater Mach numbers (M>M_{2}) shock wave solutions can be found though they differ significantly from experiments.

Equations of motion for a spectrum-generating algebra: Lipkin Meshkov Glick model

NASA Astrophysics Data System (ADS)

Rosensteel, G.; Rowe, D. J.; Ho, S. Y.

2008-01-01

For a spectrum-generating Lie algebra, a generalized equations-of-motion scheme determines numerical values of excitation energies and algebra matrix elements. In the approach to the infinite particle number limit or, more generally, whenever the dimension of the quantum state space is very large, the equations-of-motion method may achieve results that are impractical to obtain by diagonalization of the Hamiltonian matrix. To test the method's effectiveness, we apply it to the well-known Lipkin-Meshkov-Glick (LMG) model to find its low-energy spectrum and associated generator matrix elements in the eigenenergy basis. When the dimension of the LMG representation space is 106, computation time on a notebook computer is a few minutes. For a large particle number in the LMG model, the low-energy spectrum makes a quantum phase transition from a nondegenerate harmonic vibrator to a twofold degenerate harmonic oscillator. The equations-of-motion method computes critical exponents at the transition point.

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519

Analysis of the low-flow characteristics of streams in Louisiana

USGS Publications Warehouse

Lee, Fred N.

1985-01-01

The U.S. Geological Survey, in cooperation with the Louisiana Department of Transportation and Development, Office of Public Works, used geologic maps, soils maps, precipitation data, and low-flow data to define four hydrographic regions in Louisiana having distinct low-flow characteristics. Equations were derived, using regression analyses, to estimate the 7Q2, 7Q10, and 7Q20 flow rates for basically unaltered stream basins smaller than 525 square miles. Independent variables in the equations include drainage area (square miles), mean annual precipitation index (inches), and main channel slope (feet per mile). Average standard errors of regression ranged from +44 to +61 percent. Graphs are given for estimating the 7Q2, 7Q10, and 7Q20 for stream basins for which the drainage area of the most downstream data-collection site is larger than 525 square miles. Detailed examples are given in this report for the use of the equations and graphs.

Low-Power Embedded DSP Core for Communication Systems

NASA Astrophysics Data System (ADS)

Tsao, Ya-Lan; Chen, Wei-Hao; Tan, Ming Hsuan; Lin, Maw-Ching; Jou, Shyh-Jye

2003-12-01

This paper proposes a parameterized digital signal processor (DSP) core for an embedded digital signal processing system designed to achieve demodulation/synchronization with better performance and flexibility. The features of this DSP core include parameterized data path, dual MAC unit, subword MAC, and optional function-specific blocks for accelerating communication system modulation operations. This DSP core also has a low-power structure, which includes the gray-code addressing mode, pipeline sharing, and advanced hardware looping. Users can select the parameters and special functional blocks based on the character of their applications and then generating a DSP core. The DSP core has been implemented via a cell-based design method using a synthesizable Verilog code with TSMC 0.35[InlineEquation not available: see fulltext.]m SPQM and 0.25[InlineEquation not available: see fulltext.]m 1P5M library. The equivalent gate count of the core area without memory is approximately 50 k. Moreover, the maximum operating frequency of a[InlineEquation not available: see fulltext.] version is 100 MHz (0.35[InlineEquation not available: see fulltext.]m) and 140 MHz (0.25[InlineEquation not available: see fulltext.]m).

Dispersion of capillary waves in elliptical cylindrical jets

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Dolatabadi, Ali

2011-11-01

In this work motion of a low speed liquid jet issuing from an elliptic orifice through the air is studied. Mathematical solution of viscous free-surface flow for this asymmetric geometry is simplified by using one-dimensional Cosserat (directed curve) equations which can be assumed as a low order form of Navier-Stokes equations for slender jets. Linear solution is performed and temporal and spatial dispersion equations are derived. Growth rate and phase speed of unstable and stable modes under various conditions are presented. The possibility of instability of asymmetric disturbances is studied too. With distance down the jet, major and minor axes are altered and finally jet breaks up due to capillary instability. The effect of jet velocity and viscosity and also orifice ellipticity on axis-switching and breakup is investigated.

Neoclassical toroidal plasma viscosity in the vicinity of the magnetic axis in tokamaks with broken symmetry

NASA Astrophysics Data System (ADS)

Shaing, K. C.; Lee, H.; Seol, J.; Aydemir, A. Y.

2015-08-01

Theory for neoclassical toroidal plasma viscosity in the low collisionality regime is extended to the vicinity of the magnetic axis in tokamaks with broken symmetry. The toroidal viscosity is induced by particles drifting off the perturbed magnetic surface under the influence of the symmetry breaking magnetic field. In the region away from the magnetic axis, the drift orbit dynamics is governed by the bounce averaged drift kinetic equation in the low collisionality regimes. In the vicinity of the magnetic axis, it is the drift kinetic equation, averaged over the trapped particle orbits, i.e., potato orbits, that governs the drift dynamics. The orbit averaged drift kinetic equation is derived when collision frequency is low enough for trapped particles to complete their potato trajectories. The resultant equation is solved in the 1 /ν regime to obtain transport fluxes and, thus, toroidal plasma viscosity through flux-force relation. Here, ν is the collision frequency. The viscosity does not vanish on the magnetic axis, and has the same scalings as that in the region away from magnetic axis, except that the fraction of bananas is replaced by the fraction of potatoes. It also has a weak radial dependence. Modeling of plasma flow velocity V for the case where the magnetic surfaces are broken is also discussed.

Nonquaternary Cholinesterase Reactivators.

DTIC Science & Technology

1982-08-30

c, a plot (not shown) of pKa versus Hammet substituent constant (a )42 is also linear and conforms p to equation (5) pKa - (7.63 ±0.02) - (.63 ±0.05...dissociates to the active oximate form, we have defined an effective bimolecular reactivation rate constant as in equation (6) keff ’ kb [1 + antilog(pKa...type 1 compounds generally exhibit low activity as reactivators. In terms of keff values [see equation (6)] for reactivation of ethyl methylphosphonyl

Development of Bicarbonate-Activated Peroxide as a Chemical and Biological Warfare Agent Decontaminant

DTIC Science & Technology

2006-06-30

may operate for certain substrates. The reaction of equation 1 proceeds with the intermediacy of CO2 as shown in Figure 1. Although it is well...competition between paths 5 and 6 will depend on the conditions and the nature of the substrate S. Note that figures, equations , etc. in the...1 shows the complete reaction scheme used to model the equilibration reaction at low temperature. Table 1 Kinetic equations and their

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

PubMed Central

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

2016-01-01

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

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

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

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

A method for estimating mean and low flows of streams in national forests of Montana

USGS Publications Warehouse

Parrett, Charles; Hull, J.A.

1985-01-01

Equations were developed for estimating mean annual discharge, 80-percent exceedance discharge, and 95-percent exceedance discharge for streams on national forest lands in Montana. The equations for mean annual discharge used active-channel width, drainage area and mean annual precipitation as independent variables, with active-channel width being most significant. The equations for 80-percent exceedance discharge and 95-percent exceedance discharge used only active-channel width as an independent variable. The standard error or estimate for the best equation for estimating mean annual discharge was 27 percent. The standard errors of estimate for the equations were 67 percent for estimating 80-percent exceedance discharge and 75 percent for estimating 95-percent exceedance discharge. (USGS)

Dynamic response of a collidant impacting a low pressure airbag

NASA Astrophysics Data System (ADS)

Dreher, Peter A.

There are many uses of low pressure airbags, both military and commercial. Many of these applications have been hampered by inadequate and inaccurate modeling tools. This dissertation contains the derivation of a four degree-of-freedom system of differential equations from physical laws of mass and energy conservation, force equilibrium, and the Ideal Gas Law. Kinematic equations were derived to model a cylindrical airbag as a single control volume impacted by a parallelepiped collidant. An efficient numerical procedure was devised to solve the simplified system of equations in a manner amenable to discovering design trends. The largest public airbag experiment, both in scale and scope, was designed and built to collect data on low-pressure airbag responses, otherwise unavailable in the literature. The experimental results were compared to computational simulations to validate the simplified numerical model. Experimental response trends are presented that will aid airbag designers. The two objectives of using a low pressure airbag to demonstrate the feasibility to (1) accelerate a munition to 15 feet per second velocity from a bomb bay, and (2) decelerate humans hitting trucks below the human tolerance level of 50 G's, were both met.

Regionalization of low-flow characteristics of Tennessee streams

USGS Publications Warehouse

Bingham, R.H.

1986-01-01

Procedures for estimating 3-day 2-year, 3-day 10-year, 3-day 20-year, and 7-day 10-year low flows at ungaged stream sites in Tennessee are based on surface geology and drainage area size. One set of equations applies to west Tennessee streams, and another set applies to central and east Tennessee streams. The equations do not apply to streams where flow is significantly altered by activities of man. Standard errors of estimate of equations for west Tennessee are 24 to 32% and for central and east Tennessee 31 to 35%. Streamflow recession indexes, in days/log cycle, are used to account for effects of geology of the drainage basin on low flow of streams. The indexes in Tennessee range from 32 days/log cycle for clay and shale to 350 days/log cycle for gravel and sand, indicating different aquifer characteristics of the geologic units that sustain streamflows during periods of no surface runoff. Streamflow recession rate depends primarily on transmissivity and storage characteristics of the aquifers, and the average distance from stream channels to basin divides. Geology and drainage basin size are the most significant variables affecting low flow in Tennessee streams according to regression analyses. (Author 's abstract)

Generation of zonal magnetic fields by low-frequency dispersive electromagnetic waves in a nonuniform dusty magnetoplasma.

PubMed

Shukla, P K

2004-04-01

It is shown that zonal magnetic fields can be parametrically excited by low-frequency dispersive driftlike compressional electromagnetic (DDCEM) modes in a nonuniform dusty magnetoplasma. For this purpose, we derive a pair of coupled equations which exhibits the nonlinear coupling between DDCEM modes and zonal magnetic fields. The coupled mode equations are Fourier analyzed to derive a nonlinear dispersion relation. The latter depicts that zonal magnetic fields are nonlinearly generated at the expense of the low-frequency DDCEM wave energy. The relevance of our investigation to the transfer of energy from short scale DDCEM waves to long scale zonal magnetic field structures in dark molecular clouds is discussed.

Coupled radial Schrödinger equations written as Dirac-type equations: application to an amplitude-phase approach

NASA Astrophysics Data System (ADS)

Thylwe, Karl-Erik; McCabe, Patrick

2012-04-01

The classical amplitude-phase method due to Milne, Wilson, Young and Wheeler in the 1930s is known to be a powerful computational tool for determining phase shifts and energy eigenvalues in cases where a sufficiently slowly varying amplitude function can be found. The key for the efficient computations is that the original single-state radial Schrödinger equation is transformed to a nonlinear equation, the Milne equation. Such an equation has solutions that may or may not oscillate, depending on boundary conditions, which then requires a robust recipe for locating the (optimal) ‘almost constant’ solutions for its use in the method. For scattering problems the solutions of the amplitude equations always approach constants as the radial distance r tends to infinity, and there is no problem locating the ‘optimal’ amplitude functions from a low-order semiclassical approximation. In the present work, the amplitude-phase approach is generalized to two coupled Schrödinger equations similar to an earlier generalization to radial Dirac equations. The original scalar amplitude then becomes a vector quantity, and the original Milne equation is generalized accordingly. Numerical applications to resonant electron-atom scattering are illustrated.

A specific prediction equation is necessary to estimate peak oxygen uptake in obese patients with metabolic syndrome.

PubMed

Debeaumont, D; Tardif, C; Folope, V; Castres, I; Lemaitre, F; Tourny, C; Dechelotte, P; Thill, C; Darmon, A; Coquart, J B

2016-06-01

The aims were to: (1) compare peak oxygen uptake ([Formula: see text]peak) predicted from four standard equations to actual [Formula: see text]peak measured from a cardiopulmonary exercise test (CPET) in obese patients with metabolic syndrome (MetS), and (2) develop a new equation to accurately estimate [Formula: see text]peak in obese women with MetS. Seventy-five obese patients with MetS performed a CPET. Anthropometric data were also collected for each participant. [Formula: see text]peak was predicted from four prediction equations (from Riddle et al., Hansen et al., Wasserman et al. or Gläser et al.) and then compared with the actual [Formula: see text]peak measured during the CPET. The accuracy of the predictions was determined with the Bland-Altman method. When accuracy was low, a new prediction equation including anthropometric variables was proposed. [Formula: see text]peak predicted from the equation of Wasserman et al. was not significantly different from actual [Formula: see text]peak in women. Moreover, a significant correlation was found between the predicted and actual values (p < 0.001, r = 0.69). In men, no significant difference was noted between actual [Formula: see text]peak and [Formula: see text]peak predicted from the prediction equation of Gläser et al., and these two values were also correlated (p = 0.03, r = 0.44). However, the LoA95% was wide, whatever the prediction equation or gender. Regression analysis suggested a new prediction equation derived from age and height for obese women with MetS. The methods of Wasserman et al. and Gläser et al. are valid to predict [Formula: see text]peak in obese women and men with MetS, respectively. However, the accuracy of the predictions was low for both methods. Consequently, a new prediction equation including age and height was developed for obese women with MetS. However, new prediction equation remains to develop in obese men with MetS.

Fluid/Structure Interaction Studies of Aircraft Using High Fidelity Equations on Parallel Computers

NASA Technical Reports Server (NTRS)

Guruswamy, Guru; VanDalsem, William (Technical Monitor)

1994-01-01

Abstract Aeroelasticity which involves strong coupling of fluids, structures and controls is an important element in designing an aircraft. Computational aeroelasticity using low fidelity methods such as the linear aerodynamic flow equations coupled with the modal structural equations are well advanced. Though these low fidelity approaches are computationally less intensive, they are not adequate for the analysis of modern aircraft such as High Speed Civil Transport (HSCT) and Advanced Subsonic Transport (AST) which can experience complex flow/structure interactions. HSCT can experience vortex induced aeroelastic oscillations whereas AST can experience transonic buffet associated structural oscillations. Both aircraft may experience a dip in the flutter speed at the transonic regime. For accurate aeroelastic computations at these complex fluid/structure interaction situations, high fidelity equations such as the Navier-Stokes for fluids and the finite-elements for structures are needed. Computations using these high fidelity equations require large computational resources both in memory and speed. Current conventional super computers have reached their limitations both in memory and speed. As a result, parallel computers have evolved to overcome the limitations of conventional computers. This paper will address the transition that is taking place in computational aeroelasticity from conventional computers to parallel computers. The paper will address special techniques needed to take advantage of the architecture of new parallel computers. Results will be illustrated from computations made on iPSC/860 and IBM SP2 computer by using ENSAERO code that directly couples the Euler/Navier-Stokes flow equations with high resolution finite-element structural equations.

An approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives

NASA Technical Reports Server (NTRS)

Korivi, V. M.; Taylor, A. C., III; Newman, P. A.; Hou, G. J.-W.; Jones, H. E.

1992-01-01

An incremental strategy is presented for iteratively solving very large systems of linear equations, which are associated with aerodynamic sensitivity derivatives for advanced CFD codes. It is shown that the left-hand side matrix operator and the well-known factorization algorithm used to solve the nonlinear flow equations can also be used to efficiently solve the linear sensitivity equations. Two airfoil problems are considered as an example: subsonic low Reynolds number laminar flow and transonic high Reynolds number turbulent flow.

Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations

NASA Technical Reports Server (NTRS)

Darmofal, David L.

1998-01-01

An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.

Simulation of rarefied low pressure RF plasma flow around the sample

NASA Astrophysics Data System (ADS)

Zheltukhin, V. S.; Shemakhin, A. Yu

2017-01-01

The paper describes a mathematical model of the flow of radio frequency plasma at low pressure. The hybrid mathematical model includes the Boltzmann equation for the neutral component of the RF plasma, the continuity and the thermal equations for the charged component. Initial and boundary conditions for the corresponding equations are described. The electron temperature in the calculations is 1-4 eV, atoms temperature in the plasma clot is (3-4) • 103 K, in the plasma jet is (3.2-10) • 102 K, the degree of ionization is 10-7-10-5, electron density is 1015-1019 m-3. For calculations plasma parameters is developed soft package on C++ program language, that uses the OpenFOAM library package. Simulations for the vacuum chamber in the presence of a sample and the free jet flow were carried out.

Methods for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma

USGS Publications Warehouse

Esralew, Rachel A.; Smith, S. Jerrod

2010-01-01

Flow statistics can be used to provide decision makers with surface-water information needed for activities such as water-supply permitting, flow regulation, and other water rights issues. Flow statistics could be needed at any location along a stream. Most often, streamflow statistics are needed at ungaged sites, where no flow data are available to compute the statistics. Methods are presented in this report for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma. Flow statistics included the (1) annual (period of record), (2) seasonal (summer-autumn and winter-spring), and (3) 12 monthly duration statistics, including the 20th, 50th, 80th, 90th, and 95th percentile flow exceedances, and the annual mean-flow (mean of daily flows for the period of record). Flow statistics were calculated from daily streamflow information collected from 235 streamflow-gaging stations throughout Oklahoma and areas in adjacent states. A drainage-area ratio method is the preferred method for estimating flow statistics at an ungaged location that is on a stream near a gage. The method generally is reliable only if the drainage-area ratio of the two sites is between 0.5 and 1.5. Regression equations that relate flow statistics to drainage-basin characteristics were developed for the purpose of estimating selected flow-duration and annual mean-flow statistics for ungaged streams that are not near gaging stations on the same stream. Regression equations were developed from flow statistics and drainage-basin characteristics for 113 unregulated gaging stations. Separate regression equations were developed by using U.S. Geological Survey streamflow-gaging stations in regions with similar drainage-basin characteristics. These equations can increase the accuracy of regression equations used for estimating flow-duration and annual mean-flow statistics at ungaged stream locations in Oklahoma. Streamflow-gaging stations were grouped by selected drainage-basin characteristics by using a k-means cluster analysis. Three regions were identified for Oklahoma on the basis of the clustering of gaging stations and a manual delineation of distinguishable hydrologic and geologic boundaries: Region 1 (western Oklahoma excluding the Oklahoma and Texas Panhandles), Region 2 (north- and south-central Oklahoma), and Region 3 (eastern and central Oklahoma). A total of 228 regression equations (225 flow-duration regressions and three annual mean-flow regressions) were developed using ordinary least-squares and left-censored (Tobit) multiple-regression techniques. These equations can be used to estimate 75 flow-duration statistics and annual mean-flow for ungaged streams in the three regions. Drainage-basin characteristics that were statistically significant independent variables in the regression analyses were (1) contributing drainage area; (2) station elevation; (3) mean drainage-basin elevation; (4) channel slope; (5) percentage of forested canopy; (6) mean drainage-basin hillslope; (7) soil permeability; and (8) mean annual, seasonal, and monthly precipitation. The accuracy of flow-duration regression equations generally decreased from high-flow exceedance (low-exceedance probability) to low-flow exceedance (high-exceedance probability) . This decrease may have happened because a greater uncertainty exists for low-flow estimates and low-flow is largely affected by localized geology that was not quantified by the drainage-basin characteristics selected. The standard errors of estimate of regression equations for Region 1 (western Oklahoma) were substantially larger than those standard errors for other regions, especially for low-flow exceedances. These errors may be a result of greater variability in low flow because of increased irrigation activities in this region. Regression equations may not be reliable for sites where the drainage-basin characteristics are outside the range of values of independent vari

Surface-slip equations for multicomponent nonequilibrium air flow

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Scott, C. D.; Moss, J. N.

1985-01-01

Equations are presented for the surface-slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds number, high-altitude flight regime of a space vehicle. The equations are obtained from closed form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities were obtained in a form which can be employed in flowfield computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate, species-concentration boundary condition for a multicomponent mixture in absence of slip.

Evaluation of Maryland abutment scour equation through selected threshold velocity methods

USGS Publications Warehouse

Benedict, S.T.

2010-01-01

The U.S. Geological Survey, in cooperation with the Maryland State Highway Administration, used field measurements of scour to evaluate the sensitivity of the Maryland abutment scour equation to the critical (or threshold) velocity variable. Four selected methods for estimating threshold velocity were applied to the Maryland abutment scour equation, and the predicted scour to the field measurements were compared. Results indicated that performance of the Maryland abutment scour equation was sensitive to the threshold velocity with some threshold velocity methods producing better estimates of predicted scour than did others. In addition, results indicated that regional stream characteristics can affect the performance of the Maryland abutment scour equation with moderate-gradient streams performing differently from low-gradient streams. On the basis of the findings of the investigation, guidance for selecting threshold velocity methods for application to the Maryland abutment scour equation are provided, and limitations are noted.

Fractal ladder models and power law wave equations

PubMed Central

Kelly, James F.; McGough, Robert J.

2009-01-01

The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters. PMID:19813816

A three operator split-step method covering a larger set of non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Zia, Haider

2017-06-01

This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

Will learning to solve one-step equations pose a challenge to 8th grade students?

NASA Astrophysics Data System (ADS)

Ngu, Bing Hiong; Phan, Huy P.

2017-08-01

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 (e.g. negative pronumeral) poses additional challenge to master equation solving skills. In an experiment, 41 8th grade students (girls = 16, boys = 25) sat for a pre-test, attended a session about equation solving, completed an acquisition phase which constituted the main intervention and were tested again in a post-test. The results showed that at post-test, students performed better on one-step equations tapping low rather than high element interactivity knowledge. In addition, students performed better on those one-step equations that contained no special features. Thus, both the degree of element interactivity and the operation with special features affect the challenge posed to 8th grade students on learning how to solve one-step equations.

Constitutive Equation with Varying Parameters for Superplastic Flow Behavior

NASA Astrophysics Data System (ADS)

Guan, Zhiping; Ren, Mingwen; Jia, Hongjie; Zhao, Po; Ma, Pinkui

2014-03-01

In this study, constitutive equations for superplastic materials with an extra large elongation were investigated through mechanical analysis. From the view of phenomenology, firstly, some traditional empirical constitutive relations were standardized by restricting some strain paths and parameter conditions, and the coefficients in these relations were strictly given new mechanical definitions. Subsequently, a new, general constitutive equation with varying parameters was theoretically deduced based on the general mechanical equation of state. The superplastic tension test data of Zn-5%Al alloy at 340 °C under strain rates, velocities, and loads were employed for building a new constitutive equation and examining its validity. Analysis results indicated that the constitutive equation with varying parameters could characterize superplastic flow behavior in practical superplastic forming with high prediction accuracy and without any restriction of strain path or deformation condition, showing good industrial or scientific interest. On the contrary, those empirical equations have low prediction capabilities due to constant parameters and poor applicability because of the limit of special strain path or parameter conditions based on strict phenomenology.

CRPropa 3.1—a low energy extension based on stochastic differential equations

NASA Astrophysics Data System (ADS)

Merten, Lukas; Becker Tjus, Julia; Fichtner, Horst; Eichmann, Björn; Sigl, Günter

2017-06-01

The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ∥ and perpendicular κ⊥ diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.

Thermospheric wind effects on the global distribution of helium in the earth's upper atmosphere. Ph.D. Thesis - Michigan Univ., Ann Arbor

NASA Technical Reports Server (NTRS)

Reber, C. A.

1973-01-01

The momentum and continuity equations for a minor gas are combined with the momentum equation for the major constituents to obtain the time dependent continuity equation for the minor species reflecting a wind field in the background gas. This equation is used to study the distributions of helium and argon at times of low, medium, and high solar activity for a variety of latitudinal-seasonal wind cells. For helium, the exospheric return flow at the higher thermospheric temperatures dominates the distribution to the extent that much larger latitudinal gradients can be maintained during periods of low solar activity than during periods of high activity. By comparison to the exospheric flow, the smoothing effect of horizontal diffusion is almost negligible. The latitudinal variation of helium observed by satellite mass spectrometers can be reproduced by the effect of a wind system of air rising in the summer hemisphere, flowing across the equator with speeds on the order of 100 to 200 m/sec, and descending in the winter hemisphere. Argon, being heavier than the mean mass in the lower thermosphere, reacts oppositely to helium in that it is enhanced in the summer hemisphere and depleted in the winter.

Ionic conduction and self-diffusion near infinitesimal concentration in lithium salt-organic solvent electrolytes

NASA Astrophysics Data System (ADS)

Aihara, Yuichi; Sugimoto, Kyoko; Price, William S.; Hayamizu, Kikuko

2000-08-01

The Debye-Hückel-Onsager and Nernst-Einstein equations, which are based on two different conceptual approaches, constitute the most widely used equations for relating ionic conduction to ionic mobility. However, both of these classical (simple) equations are predictive of ionic conductivity only at very low salt concentrations. In the present work the ionic conductivity of four organic solvent-lithium salt-based electrolytes were measured. These experimental conductivity values were then contrasted with theoretical values calculated using the translational diffusion (also known as self-diffusion or intradiffusion) coefficients of all of the species present obtained using pulsed-gradient spin-echo (1H, 19F and 7Li) nuclear magnetic resonance self-diffusion measurements. The experimental results verified the applicability of both theoretical approaches at very low salt concentrations for these particular systems as well as helping to clarify the reasons for the divergence between theory and experiment. In particular, it was found that the correspondence between the Debye-Hückel-Onsager equation and experimental values could be improved by using the measured solvent self-diffusion values to correct for salt-induced changes in the solution viscosity. The concentration dependence of the self-diffusion coefficients is discussed in terms of the Jones-Dole equation.

Extremophile Diatoms: Implications to the Drake Equation

NASA Technical Reports Server (NTRS)

Sterrenburg, Frithjof A. S.; Hoover, Richard B.

2011-01-01

Diatoms are unicellular Eukaryotes that (as a group and phylogenetically) are not strictly regarded as extremophiles , since the vast majority of diatoms are mesophilic photoautotrophs. However, among the terrestrial Eukaryotes, diatoms are by far the single group of organisms with the ability to inhabit the greatest range of hostile environments on Earth. They are the dominant eukaryotes in the polar regions; in fumaroles, hot springs and geysers; and in hypersaline and hyperalkaline lakes and pools. Cryophilic species such as Fragilaria sublinearis and Chaetoceras fragilis are able to carry out respiration at extremely low rates at low temperatures in darkness. The Drake Equation refers to the likelihood of there being intelligent life at the technological level of electromagnetic communication. However, consideration of the range of conditions suitable for the habitability of eukaryotic diatoms and prokaryotic extremophiles, the likelihood that life exists elsewhere in the cosmos becomes many orders of magnitude greater than that predicted by the classical Drake Equation. In this paper we review the characteristics of diatoms as eukaryotic extremophiles and consider the implications to adjustments needed to the Drake Equation to assess the possibility that life exists elsewhere in the Universe.

Contribution to modeling the viscosity Arrhenius-type equation for saturated pure fluids

NASA Astrophysics Data System (ADS)

Tian, Jianxiang; Zhang, Laibin

2016-09-01

Recently, Haj-Kacem et al. proposed an equation modeling the relationship between the two parameters of viscosity Arrhenius-type equations [Fluid Phase Equilibria 383, 11 (2014)]. The authors found that the two parameters are dependent upon each other in an exponential function form. In this paper, we reconsidered their ideas and calculated the two parameter values for 49 saturated pure fluids by using the experimental data in the NIST WebBook. Our conclusion is different with the ones of Haj-Kacem et al. We found that (the linearity shown by) the Arrhenius equation stands strongly only in low temperature range and that the two parameters of the Arrhenius equation are independent upon each other in the whole temperature range from the triple point to the critical point.

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

NASA Astrophysics Data System (ADS)

Barker, T.; Schaeffer, D. G.; Shearer, M.; Gray, J. M. N. T.

2017-05-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities.

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

PubMed Central

Schaeffer, D. G.; Shearer, M.; Gray, J. M. N. T.

2017-01-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities. PMID:28588402

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology.

PubMed

Barker, T; Schaeffer, D G; Shearer, M; Gray, J M N T

2017-05-01

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ ( I )-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I -dependent rheology. When the I -dependence comes from a specific friction coefficient μ ( I ), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ ( I ) satisfies certain minimal, physically natural, inequalities.

Integral Equations in Computational Electromagnetics: Formulations, Properties and Isogeometric Analysis

NASA Astrophysics Data System (ADS)

Lovell, Amy Elizabeth

Computational electromagnetics (CEM) provides numerical methods to simulate electromagnetic waves interacting with its environment. Boundary integral equation (BIE) based methods, that solve the Maxwell's equations in the homogeneous or piecewise homogeneous medium, are both efficient and accurate, especially for scattering and radiation problems. Development and analysis electromagnetic BIEs has been a very active topic in CEM research. Indeed, there are still many open problems that need to be addressed or further studied. A short and important list includes (1) closed-form or quasi-analytical solutions to time-domain integral equations, (2) catastrophic cancellations at low frequencies, (3) ill-conditioning due to high mesh density, multi-scale discretization, and growing electrical size, and (4) lack of flexibility due to re-meshing when increasing number of forward numerical simulations are involved in the electromagnetic design process. This dissertation will address those several aspects of boundary integral equations in computational electromagnetics. The first contribution of the dissertation is to construct quasi-analytical solutions to time-dependent boundary integral equations using a direct approach. Direct inverse Fourier transform of the time-harmonic solutions is not stable due to the non-existence of the inverse Fourier transform of spherical Hankel functions. Using new addition theorems for the time-domain Green's function and dyadic Green's functions, time-domain integral equations governing transient scattering problems of spherical objects are solved directly and stably for the first time. Additional, the direct time-dependent solutions, together with the newly proposed time-domain dyadic Green's functions, can enrich the time-domain spherical multipole theory. The second contribution is to create a novel method of moments (MoM) framework to solve electromagnetic boundary integral equation on subdivision surfaces. The aim is to avoid the meshing and re-meshing stages to accelerate the design process when the geometry needs to be updated. Two schemes to construct basis functions on the subdivision surface have been explored. One is to use the div-conforming basis function, and the other one is to create a rigorous iso-geometric approach based on the subdivision basis function with better smoothness properties. This new framework provides us better accuracy, more stability and high flexibility. The third contribution is a new stable integral equation formulation to avoid catastrophic cancellations due to low-frequency breakdown or dense-mesh breakdown. Many of the conventional integral equations and their associated post-processing operations suffer from numerical catastrophic cancellations, which can lead to ill-conditioning of the linear systems or serious accuracy problems. Examples includes low-frequency breakdown and dense mesh breakdown. Another instability may come from nontrivial null spaces of involving integral operators that might be related with spurious resonance or topology breakdown. This dissertation presents several sets of new boundary integral equations and studies their analytical properties. The first proposed formulation leads to the scalar boundary integral equations where only scalar unknowns are involved. Besides the requirements of gaining more stability and better conditioning in the resulting linear systems, multi-physics simulation is another driving force for new formulations. Scalar and vector potentials (rather than electromagnetic field) based formulation have been studied for this purpose. Those new contributions focus on different stages of boundary integral equations in an almost independent manner, e.g. isogeometric analysis framework can be used to solve different boundary integral equations, and the time-dependent solutions to integral equations from different formulations can be achieved through the same methodology proposed.

A near-wall four-equation turbulence model for compressible boundary layers

NASA Technical Reports Server (NTRS)

Sommer, T. P.; So, R. M. C.; Zhang, H. S.

1992-01-01

A near-wall four-equation turbulence model is developed for the calculation of high-speed compressible turbulent boundary layers. The four equations used are the k-epsilon equations and the theta(exp 2)-epsilon(sub theta) equations. These equations are used to define the turbulent diffusivities for momentum and heat fluxes, thus allowing the assumption of dynamic similarity between momentum and heat transport to be relaxed. The Favre-averaged equations of motion are solved in conjunction with the four transport equations. Calculations are compared with measurements and with another model's predictions where the assumption of the constant turbulent Prandtl number is invoked. Compressible flat plate turbulent boundary layers with both adiabatic and constant temperature wall boundary conditions are considered. Results for the range of low Mach numbers and temperature ratios investigated are essentially the same as those obtained using an identical near-wall k-epsilon model. In general, the numerical predictions are in very good agreement with measurements and there are significant improvements in the predictions of mean flow properties at high Mach numbers.

Estimates of streamflow characteristics for selected small streams, Baker River basin, Washington

USGS Publications Warehouse

Williams, John R.

1987-01-01

Regression equations were used to estimate streamflow characteristics at eight ungaged sites on small streams in the Baker River basin in the North Cascade Mountains, Washington, that could be suitable for run-of-the-river hydropower development. The regression equations were obtained by relating known streamflow characteristics at 25 gaging stations in nearby basins to several physical and climatic variables that could be easily measured in gaged or ungaged basins. The known streamflow characteristics were mean annual flows, 1-, 3-, and 7-day low flows and high flows, mean monthly flows, and flow duration. Drainage area and mean annual precipitation were not the most significant variables in all the regression equations. Variance in the low flows and the summer mean monthly flows was reduced by including an index of glacierized area within the basin as a third variable. Standard errors of estimate of the regression equations ranged from 25 to 88%, and the largest errors were associated with the low flow characteristics. Discharge measurements made at the eight sites near midmonth each month during 1981 were used to estimate monthly mean flows at the sites for that period. These measurements also were correlated with concurrent daily mean flows from eight operating gaging stations. The correlations provided estimates of mean monthly flows that compared reasonably well with those estimated by the regression analyses. (Author 's abstract)

Improved momentum-transfer theory for ion mobility. 1. Derivation of the fundamental equation.

PubMed

Siems, William F; Viehland, Larry A; Hill, Herbert H

2012-11-20

For the first time the fundamental ion mobility equation is derived by a bottom-up procedure, with N real atomic ion-atomic neutral collisions replaced by N repetitions of an average collision. Ion drift velocity is identified as the average of all pre- and postcollision velocities in the field direction. To facilitate velocity averaging, collisions are sorted into classes that "cool" and "heat" the ion. Averaging over scattering angles establishes mass-dependent relationships between pre- and postcollision velocities for the cooling and heating classes, and a combined expression for drift velocity is obtained by weighted addition according to relative frequencies of the cooling and heating encounters. At zero field this expression becomes identical to the fundamental low-field ion mobility equation. The bottom-up derivation identifies the low-field drift velocity as 3/4 of the average precollision ion velocity in the field direction and associates the passage from low-field to high-field conditions with the increasing dominance of "cooling" collisions over "heating" collisions. Most significantly, the analysis provides a direct path for generalization to fields of arbitrary strength.

A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

DOE PAGES

Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.

2016-10-21

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used tomore » compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.« less

A low dimensional dynamical system for the wall layer

NASA Technical Reports Server (NTRS)

Aubry, N.; Keefe, L. R.

1987-01-01

Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.

Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch

NASA Astrophysics Data System (ADS)

Mirus, Kevin Andrew

In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Rossler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high- dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.

Familiarity and Aptness in Metaphor Comprehension.

PubMed

Damerall, Alison Whiteford; Kellogg, Ronald T

2016-01-01

The career of metaphor hypothesis suggests that novel metaphors are understood through a search for shared features between the topic and vehicle, but with repeated exposure, the figurative meaning is understood directly as a new category is established. The categorization hypothesis argues that instead good or apt metaphors are understood through a categorization process, whether or not they are familiar. Only poor metaphors ever invoke a literal comparison. In Experiment 1, with aptness equated, we found that high familiarity speeded comprehension time over low-familiarity metaphors. In Experiment 2a, providing a literal prime failed to facilitate interpretation of low-familiarity metaphors, contrary to the career of metaphor hypothesis. In Experiment 2b, with familiarity equated, high- and low-aptness metaphors did not differ, contrary to the categorization hypothesis.

Charts for Estimating Tail-rotor Contribution to Helicopter Directional Stability and Control in Low-Speed Flight

NASA Technical Reports Server (NTRS)

Amer, Kenneth B; Gessow, Alfred

1955-01-01

Theoretically derived charts and equations are presented by which tail-rotor design studies of directional trim and control response at low forward speed can be conveniently made. The charts can also be used to obtain the main-rotor stability derivatives of thrust with respect to collective pitch and angle of attack at low forward speeds. The use of the charts and equations for tail-rotor design studies is illustrated. Comparisons between theoretical and experimental results are presented. The charts indicate, and flight tests confirm, that the region of vortex roughness which is familiar for the main rotor is also encountered by the tail rotor and that prolonged operation at the corresponding flight conditions would be difficult.

Roy-Steiner-equation analysis of pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Meißner, U.-G.; Ruiz de Elvira, J.; Hoferichter, M.; Kubis, B.

2017-03-01

Low-energy pion-nucleon scattering is relevant for many areas in nuclear and hadronic physics, ranging from the scalar couplings of the nucleon to the long-range part of two-pion-exchange potentials and three-nucleon forces in Chiral Effective Field Theory. In this talk, we show how the fruitful combination of dispersion-theoretical methods, in particular in the form of Roy-Steiner equations, with modern high-precision data on hadronic atoms allows one to determine the pion-nucleon scattering amplitudes at low energies with unprecedented accuracy. Special attention will be paid to the extraction of the pion-nucleon σ-term, and we discuss in detail the current tension with recent lattice results, as well as the determination of the low-energy constants of chiral perturbation theory.

DEVELOPMENT OF LOW-DIFFUSION FLUX-SPLITTING METHODS FOR DENSE GAS-SOLID FLOWS

EPA Science Inventory

The development of a class of low-diffusion upwinding methods for computing dense gas-solid flows is presented in this work. An artificial compressibility/low-Mach preconditioning strategy is developed for a hyperbolic two-phase flow equation system consisting of separate solids ...

Low-thrust trajectory analysis for the geosynchronous mission

NASA Technical Reports Server (NTRS)

Jasper, T. P.

1973-01-01

Methodology employed in development of a computer program designed to analyze optimal low-thrust trajectories is described, and application of the program to a Solar Electric Propulsion Stage (SEPS) geosynchronous mission is discussed. To avoid the zero inclination and eccentricity singularities which plague many small-force perturbation techniques, a special set of state variables (equinoctial) is used. Adjoint equations are derived for the minimum time problem and are also free from the singularities. Solutions to the state and adjoint equations are obtained by both orbit averaging and precision numerical integration; an evaluation of these approaches is made.

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

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

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

2016-07-15

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

Reasoning about Codata

NASA Astrophysics Data System (ADS)

Hinze, Ralf

Programmers happily use induction to prove properties of recursive programs. To show properties of corecursive programs they employ coinduction, but perhaps less enthusiastically. Coinduction is often considered a rather low-level proof method, in particular, as it departs quite radically from equational reasoning. Corecursive programs are conveniently defined using recursion equations. Suitably restricted, these equations possess unique solutions. Uniqueness gives rise to a simple and attractive proof technique, which essentially brings equational reasoning to the coworld. We illustrate the approach using two major examples: streams and infinite binary trees. Both coinductive types exhibit a rich structure: they are applicative functors or idioms, and they can be seen as memo-tables or tabulations. We show that definitions and calculations benefit immensely from this additional structure.

Magnetoresistance in organic semiconductors: Including pair correlations in the kinetic equations for hopping transport

NASA Astrophysics Data System (ADS)

Shumilin, A. V.; Kabanov, V. V.; Dediu, V. I.

2018-03-01

We derive kinetic equations for polaron hopping in organic materials that explicitly take into account the double occupation possibility and pair intersite correlations. The equations include simplified phenomenological spin dynamics and provide a self-consistent framework for the description of the bipolaron mechanism of the organic magnetoresistance. At low applied voltages, the equations can be reduced to those for an effective resistor network that generalizes the Miller-Abrahams network and includes the effect of spin relaxation on the system resistivity. Our theory discloses the close relationship between the organic magnetoresistance and the intersite correlations. Moreover, in the absence of correlations, as in an ordered system with zero Hubbard energy, the magnetoresistance vanishes.

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

NASA Astrophysics Data System (ADS)

Moix, Jeremy M.; Cao, Jianshu

2013-10-01

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems.

PubMed

Moix, Jeremy M; Cao, Jianshu

2013-10-07

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

Technical characterization of dialysis fluid flow and mass transfer rate in dialyzers with various filtration coefficients using dimensionless correlation equation.

PubMed

Fukuda, Makoto; Yoshimura, Kengo; Namekawa, Koki; Sakai, Kiyotaka

2017-06-01

The objective of the present study is to evaluate the effect of filtration coefficient and internal filtration on dialysis fluid flow and mass transfer coefficient in dialyzers using dimensionless mass transfer correlation equations. Aqueous solution of vitamin B 12 clearances were obtained for REXEED-15L as a low flux dialyzer, and APS-15EA and APS-15UA as high flux dialyzers. All the other design specifications were identical for these dialyzers except for filtration coefficient. The overall mass transfer coefficient was calculated, moreover, the exponents of Reynolds number (Re) and film mass transfer coefficient of the dialysis-side fluid (k D ) for each flow rate were derived from the Wilson plot and dimensionless correlation equation. The exponents of Re were 0.4 for the low flux dialyzer whereas 0.5 for the high flux dialyzers. Dialysis fluid of the low flux dialyzer was close to laminar flow because of its low filtration coefficient. On the other hand, dialysis fluid of the high flux dialyzers was assumed to be orthogonal flow. Higher filtration coefficient was associated with higher k D influenced by mass transfer rate through diffusion and internal filtration. Higher filtration coefficient of dialyzers and internal filtration affect orthogonal flow of dialysis fluid.

Testing continuum descriptions of low-Mach-number shock structures

NASA Technical Reports Server (NTRS)

Pham-Van-diep, Gerald C.; Erwin, Daniel A.; Muntz, E. P.

1991-01-01

Numerical experiments have been performed on normal shock waves with Monte Carlo Direct Simulations (MCDS's) to investigate the validity of continuum theories at very low Mach numbers. Results from the Navier-Stokes and the Burnett equations are compared to MCDS's for both hard-sphere and Maxwell gases. It is found that the maximum-slope shock thicknesses are described equally well (within the MCDS computational scatter) by either of the continuum formulations for Mach numbers smaller than about 1.2. For Mach numbers greater that 1.2, the Burnett predictions are more accurate than the Navier-Stokes results. Temperature-density profile separations are best described by the Burnett equations for Mach numbers greater than about 1.3. At lower Mach numbers the MCDS scatter is too great to differentiate between the two continuum theories. For all Mach numbers above one, the shock shapes are more accurately described by the Burnett equations.

Finite element modeling of electromagnetic fields and waves using NASTRAN

NASA Technical Reports Server (NTRS)

Moyer, E. Thomas, Jr.; Schroeder, Erwin

1989-01-01

The various formulations of Maxwell's equations are reviewed with emphasis on those formulations which most readily form analogies with Navier's equations. Analogies involving scalar and vector potentials and electric and magnetic field components are presented. Formulations allowing for media with dielectric and conducting properties are emphasized. It is demonstrated that many problems in electromagnetism can be solved using the NASTRAN finite element code. Several fundamental problems involving time harmonic solutions of Maxwell's equations with known analytic solutions are solved using NASTRAN to demonstrate convergence and mesh requirements. Mesh requirements are studied as a function of frequency, conductivity, and dielectric properties. Applications in both low frequency and high frequency are highlighted. The low frequency problems demonstrate the ability to solve problems involving media inhomogeneity and unbounded domains. The high frequency applications demonstrate the ability to handle problems with large boundary to wavelength ratios.

A guidance and navigation system for continuous low thrust vehicles. M.S. Thesis

NASA Technical Reports Server (NTRS)

Tse, C. J. C.

1973-01-01

A midcourse guidance and navigation system for continuous low thrust vehicles is described. A set of orbit elements, known as the equinoctial elements, are selected as the state variables. The uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time nominal trajectory is defined and the equation of motion and the measurement equation are linearized about this nominal trajectory. An exponential cost criterion is constructed and a linear feedback guidance law is derived to control the thrusting direction of the engine. Using this guidance law, the vehicle will fly in a trajectory neighboring the nominal trajectory. The extended Kalman filter is used for state estimation. Finally a short mission using this system is simulated. The results indicate that this system is very efficient for short missions.

A Robust Locally Preconditioned Semi-Coarsening Multigrid Algorithm for the 2-D Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Cain, Michael D.

1999-01-01

The goal of this thesis is to develop an efficient and robust locally preconditioned semi-coarsening multigrid algorithm for the two-dimensional Navier-Stokes equations. This thesis examines the performance of the multigrid algorithm with local preconditioning for an upwind-discretization of the Navier-Stokes equations. A block Jacobi iterative scheme is used because of its high frequency error mode damping ability. At low Mach numbers, the performance of a flux preconditioner is investigated. The flux preconditioner utilizes a new limiting technique based on local information that was developed by Siu. Full-coarsening and-semi-coarsening are examined as well as the multigrid V-cycle and full multigrid. The numerical tests were performed on a NACA 0012 airfoil at a range of Mach numbers. The tests show that semi-coarsening with flux preconditioning is the most efficient and robust combination of coarsening strategy, and iterative scheme - especially at low Mach numbers.

A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal

NASA Astrophysics Data System (ADS)

Zhou, Zhenyu; Guo, Zhichang; Zhang, Dazhi; Wu, Boying

2018-04-01

Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona-Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.

Consequences of Violated Equating Assumptions under the Equivalent Groups Design

ERIC Educational Resources Information Center

Lyren, Per-Erik; Hambleton, Ronald K.

2011-01-01

The equal ability distribution assumption associated with the equivalent groups equating design was investigated in the context of a selection test for admission to higher education. The purpose was to assess the consequences for the test-takers in terms of receiving improperly high or low scores compared to their peers, and to find strong…

Novel Methods for Electromagnetic Simulation and Design

DTIC Science & Technology

2016-08-03

The resulting discretized integral equations are compatible with fast multipoleaccelerated solvers and will form the basis for high fidelity...expansion”) which are high-order, efficient and easy to use on arbitrarily triangulated surfaces. The resulting discretized integral equations are...created a user interface compatible with both low and high order discretizations , and implemented the generalized Debye approach of [4]. The

Modulation analysis of nonlinear beam refraction at an interface in liquid crystals

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

Assanto, Gaetano; Smyth, Noel F.; Xia Wenjun

2011-09-15

A theoretical investigation of solitary wave refraction in nematic liquid crystals is undertaken. A modulation theory based on a Lagrangian formulation of the governing optical solitary wave equations is developed. The resulting low-dimensional equations are found to give solutions in excellent agreement with full numerical solutions of the governing equations, as well as with previous experimental studies. The analysis deals with a number of types of refraction from a more to a less optically dense medium, the most famous being the Goos-Haenchen shift upon total internal reflection.

Periodicity computation of generalized mathematical biology problems involving delay differential equations.

PubMed

Jasim Mohammed, M; Ibrahim, Rabha W; Ahmad, M Z

2017-03-01

In this paper, we consider a low initial population model. Our aim is to study the periodicity computation of this model by using neutral differential equations, which are recognized in various studies including biology. We generalize the neutral Rayleigh equation for the third-order by exploiting the model of fractional calculus, in particular the Riemann-Liouville differential operator. We establish the existence and uniqueness of a periodic computational outcome. The technique depends on the continuation theorem of the coincidence degree theory. Besides, an example is presented to demonstrate the finding.

Fluid equations in the presence of electron cyclotron current drive

NASA Astrophysics Data System (ADS)

Jenkins, Thomas G.; Kruger, Scott E.

2012-12-01

Two-fluid equations, which include the physics imparted by an externally applied radiofrequency source near electron cyclotron resonance, are derived in their extended magnetohydrodynamic forms using the formalism of Hegna and Callen [Phys. Plasmas 16, 112501 (2009)]. The equations are compatible with the closed fluid/drift-kinetic model developed by Ramos [Phys. Plasmas 17, 082502 (2010); 18, 102506 (2011)] for fusion-relevant regimes with low collisionality and slow dynamics, and they facilitate the development of advanced computational models for electron cyclotron current drive-induced suppression of neoclassical tearing modes.

Fluid equations in the presence of electron cyclotron current drive

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

Jenkins, Thomas G.; Kruger, Scott E.

Two-fluid equations, which include the physics imparted by an externally applied radiofrequency source near electron cyclotron resonance, are derived in their extended magnetohydrodynamic forms using the formalism of Hegna and Callen [Phys. Plasmas 16, 112501 (2009)]. The equations are compatible with the closed fluid/drift-kinetic model developed by Ramos [Phys. Plasmas 17, 082502 (2010); 18, 102506 (2011)] for fusion-relevant regimes with low collisionality and slow dynamics, and they facilitate the development of advanced computational models for electron cyclotron current drive-induced suppression of neoclassical tearing modes.

On solving the compressible Navier-Stokes equations for unsteady flows at very low Mach numbers

NASA Technical Reports Server (NTRS)

Pletcher, R. H.; Chen, K.-H.

1993-01-01

The properties of a preconditioned, coupled, strongly implicit finite difference scheme for solving the compressible Navier-Stokes equations in primitive variables are investigated for two unsteady flows at low speeds, namely the impulsively started driven cavity and the startup of pipe flow. For the shear-driven cavity flow, the computational effort was observed to be nearly independent of Mach number, especially at the low end of the range considered. This Mach number independence was also observed for steady pipe flow calculations; however, rather different conclusions were drawn for the unsteady calculations. In the pressure-driven pipe startup problem, the compressibility of the fluid began to significantly influence the physics of the flow development at quite low Mach numbers. The present scheme was observed to produce the expected characteristics of completely incompressible flow when the Mach number was set at very low values. Good agreement with incompressible results available in the literature was observed.

CRPropa 3.1—a low energy extension based on stochastic differential equations

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

Merten, Lukas; Tjus, Julia Becker; Eichmann, Björn

The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us tomore » use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ{sub ∥} and perpendicular κ{sub ⊥} diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.« less

Identification of unmeasured variables in the set of model constraints of the data reconciliation in a power unit

NASA Astrophysics Data System (ADS)

Szega, Marcin; Nowak, Grzegorz Tadeusz

2013-12-01

In generalized method of data reconciliation as equations of conditions beside substance and energy balances can be used equations which don't have precisely the status of conservation lows. Empirical coefficients in these equations are traded as unknowns' values. To this kind of equations, in application of the generalized method of data reconciliation in supercritical power unit, can be classified: steam flow capacity of a turbine for a group of stages, adiabatic internal efficiency of group of stages, equations for pressure drop in pipelines and equations for heat transfer in regeneration heat exchangers. Mathematical model of a power unit was developed in the code Thermoflex. Using this model the off-design calculation has been made in several points of loads for the power unit. Using these calculations identification of unknown values and empirical coefficients for generalized method of data reconciliation used in power unit has been made. Additional equations of conditions will be used in the generalized method of data reconciliation which will be used in optimization of measurement placement in redundant measurement system in power unit for new control systems

Linearized-moment analysis of the temperature jump and temperature defect in the Knudsen layer of a rarefied gas.

PubMed

Gu, Xiao-Jun; Emerson, David R

2014-06-01

Understanding the thermal behavior of a rarefied gas remains a fundamental problem. In the present study, we investigate the predictive capabilities of the regularized 13 and 26 moment equations. In this paper, we consider low-speed problems with small gradients, and to simplify the analysis, a linearized set of moment equations is derived to explore a classic temperature problem. Analytical solutions obtained for the linearized 26 moment equations are compared with available kinetic models and can reliably capture all qualitative trends for the temperature-jump coefficient and the associated temperature defect in the thermal Knudsen layer. In contrast, the linearized 13 moment equations lack the necessary physics to capture these effects and consistently underpredict kinetic theory. The deviation from kinetic theory for the 13 moment equations increases significantly for specular reflection of gas molecules, whereas the 26 moment equations compare well with results from kinetic theory. To improve engineering analyses, expressions for the effective thermal conductivity and Prandtl number in the Knudsen layer are derived with the linearized 26 moment equations.

Density-velocity equations with bulk modulus for computational hydro-acoustics

NASA Astrophysics Data System (ADS)

Lin, Po-Hsien; Chen, Yung-Yu; John Yu, S.-T.

2014-02-01

This paper reports a new set of model equations for Computational Hydro Acoustics (CHA). The governing equations include the continuity and the momentum equations. The definition of bulk modulus is used to relate density with pressure. For 3D flow fields, there are four equations with density and velocity components as the unknowns. The inviscid equations are proved to be hyperbolic because an arbitrary linear combination of the three Jacobian matrices is diagonalizable and has a real spectrum. The left and right eigenvector matrices are explicitly derived. Moreover, an analytical form of the Riemann invariants are derived. The model equations are indeed suitable for modeling wave propagation in low-speed, nearly incompressible air and water flows. To demonstrate the capability of the new formulation, we use the CESE method to solve the 2D equations for aeolian tones generated by air flows passing a circular cylinder at Re = 89,000, 46,000, and 22,000. Numerical results compare well with previously published data. By simply changing the value of the bulk modulus, the same code is then used to calculate three cases of water flows passing a cylinder at Re = 89,000, 67,000, and 44,000.

A Longitudinal Study on Human Outdoor Decomposition in Central Texas.

PubMed

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

2016-01-01

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

The CMC:3DPNS computer program for prediction of three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Volume 1: Theoretical

NASA Technical Reports Server (NTRS)

Baker, A. J.

1982-01-01

An order-of-magnitude analysis of the subsonic three dimensional steady time averaged Navier-Stokes equations, for semibounded aerodynamic juncture geometries, yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement of first order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. Numerical results document accuracy, convergence, and utility of the developed finite element algorithm, and the CMC:3DPNS computer code applied to an idealized wing-body juncture region. Additional results document accuracy aspects of the algorithm turbulence closure model.

A parameter study of the two-fluid solar wind

NASA Technical Reports Server (NTRS)

Sandbaek, Ornulf; Leer, Egil; Holzer, Thomas E.

1992-01-01

A two-fluid model of the solar wind was introduced by Sturrock and Hartle (1966) and Hartle and Sturrock (1968). In these studies the proton energy equation was integrated neglecting the heat conductive term. Later several authors solved the equations for the two-fluid solar wind model keeping the proton heat conductive term. Methods where the equations are integrated simultaneously outward and inward from the critical point were used. The equations were also integrated inward from a large heliocentric distance. These methods have been applied to cases with low coronal base electron densities and high base temperatures. In this paper we present a method of integrating the two-fluid solar wind equations using an iteration procedure where the equations are integrated separately and the proton flux is kept constant during the integrations. The technique is applicable for a wide range of coronal base densities and temperatures. The method is used to carry out a parameter study of the two-fluid solar wind.

Theoretical model of droplet wettability on a low-surface-energy solid under the influence of gravity.

PubMed

Yonemoto, Yukihiro; Kunugi, Tomoaki

2014-01-01

The wettability of droplets on a low surface energy solid is evaluated experimentally and theoretically. Water-ethanol binary mixture drops of several volumes are used. In the experiment, the droplet radius, height, and contact angle are measured. Analytical equations are derived that incorporate the effect of gravity for the relationships between the droplet radius and height, radius and contact angle, and radius and liquid surface energy. All the analytical equations display good agreement with the experimental data. It is found that the fundamental wetting behavior of the droplet on the low surface energy solid can be predicted by our model which gives geometrical information of the droplet such as the contact angle, droplet radius, and height from physical values of liquid and solid.

The comparison of Missouri mathematics project and teams games tournament viewed from emotional quotient eight grade student of junior school

NASA Astrophysics Data System (ADS)

Setyawan, Indra; Budiyono, Slamet, Isnandar

2017-08-01

This research was a quasi-experimental research with 2 × 3 factorial design. It aimed to determine the learning model between Missouri Mathematics Project (MMP) and Teams Games Tournament (TGT) that gave the best achievement on mathematics subject viewed from emotional quotient. The population of this research were all of Junior High School students at the 8th grade in Surakarta City, Central Java, Indonesia in academic year 2016/2017 which applied KTSP curriculum. The sample was taken by using stratified cluster random sampling. The data were collected by using methods of documentation, emotional quotient questionnaires, and mathematics achievement test. Data analysis technique used two ways analysis of variance (ANOVA) with unequal cell. According to the research findings, it could be concluded that: (1) students' mathematics achievement which were taught by using MMP is as good as emotional quotient achievement which were taught by using TGT in straight-line equation material, (2) mathematics achievement of students with high emotional quotient is better than students with medium and low emotional quotient, and mathematics achievement of students with medium emotional quotient is as good as students with low emotional quotient in straight-line equation material, (3) in each learning model, mathematics achievement of students with high emotional quotient is better than students with medium and low emotional quotient, and mathematics achievement of students with medium emotional quotient is as good as students with low emotional quotient in straight-line equation material (4) in each category of high and medium emotional quotient, student's mathematics achievement which were taught by using MMP is better than student's mathematics achievement which were taught by using TGT and in low emotional quotient student's mathematics achievement which were taught by using MMP is as good as student's mathematics achievement which were taught by using TGT in straight-line equation material.

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

Why there is no Newtonian backreaction

NASA Astrophysics Data System (ADS)

Kaiser, Nick

2017-07-01

In the conventional framework for cosmological dynamics, the scalefactor a(t) is assumed to obey the 'background' Friedmann equation for a perfectly homogeneous universe while particles move according to equations of motions driven by the gravity of the density fluctuations. It has recently been suggested that the emergence of structure modifies the evolution of a(t) via Newtonian (or 'kinematic') backreaction and that this may avoid the need for dark energy. Here, we point out that the conventional system of equations is exact in Newtonian gravity and there is no approximation in the use of the homogeneous universe equation for a(t). The recently proposed modification of Rácz et al. does not reduce to Newtonian gravity in the limit of low velocities. We discuss the relation of this to the 'generalized Friedmann equation' of Buchert and Ehlers. These are quite different things; their formula describes individual regions and is obtained under the restrictive assumption that the matter behaves like a pressure-free fluid, whereas our result is exact for collisionless dynamics and is an auxiliary relation appearing in the structure equations. We use the symmetry of the general velocity autocorrelation function to show how Buchert's Q tends very rapidly to zero for large volume and that this does not simply arise 'by construction' through the adoption of periodic boundary conditions as has been claimed. We conclude that, to the extent that Newtonian gravity accurately describes the low-z universe, there is no backreaction of structure on a(t) and that the need for dark energy cannot be avoided in this way.

Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density.

PubMed

Kanagawa, Tetsuya

2015-05-01

This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.

Geostrophic balance with a full Coriolis Force: implications for low latitutde studies

NASA Technical Reports Server (NTRS)

Juarez, M. de la Torre

2002-01-01

In its standard form, geostrophic balance uses a partial representation of the Coriolis force. The resulting formation has a singularity at the equator, and violates mass and momentum conservation. When the horizontal projection of the planetary rotation vector is considered, the singularity at the equator disappears, continuity can be preserved, and quasigeostrophy can be formulated at planetary scale.

Hoph Bifurcation in Viscous, Low Speed Flows About an Airfoil with Structural Coupling

DTIC Science & Technology

1993-03-01

8 2.1 Equations of Motion ...... ..................... 8 2.2 Coordinate Transformation ....................... 13 2.3 Aerodynamic...a-frame) f - Apparent body forces applied in noninertial system fL - Explicit fourth-order numerical damping term Ai - Implicit fourth-order...resulting airfoil motion . The equations describing the airfoil motion are integrated in time using a fourth-order Runge-Kutta algorithm. The

Basis set study of classical rotor lattice dynamics.

PubMed

Witkoskie, James B; Wu, Jianlan; Cao, Jianshu

2004-03-22

The reorientational relaxation of molecular systems is important in many phenomenon and applications. In this paper, we explore the reorientational relaxation of a model Brownian rotor lattice system with short range interactions in both the high and low temperature regimes. In this study, we use a basis set expansion to capture collective motions of the system. The single particle basis set is used in the high temperature regime, while the spin wave basis is used in the low temperature regime. The equations of motion derived in this approach are analogous to the generalized Langevin equation, but the equations render flexibility by allowing nonequilibrium initial conditions. This calculation shows that the choice of projection operators in the generalized Langevin equation (GLE) approach corresponds to defining a specific inner-product space, and this inner-product space should be chosen to reveal the important physics of the problem. The basis set approach corresponds to an inner-product and projection operator that maintain the orthogonality of the spherical harmonics and provide a convenient platform for analyzing GLE expansions. The results compare favorably with numerical simulations, and the formalism is easily extended to more complex systems. (c) 2004 American Institute of Physics

Modulation of kinetic Alfvén waves in an intermediate low-beta magnetoplasma

NASA Astrophysics Data System (ADS)

Chatterjee, Debjani; Misra, A. P.

2018-05-01

We study the amplitude modulation of nonlinear kinetic Alfvén waves (KAWs) in an intermediate low-beta magnetoplasma. Starting from a set of fluid equations coupled to the Maxwell's equations, we derive a coupled set of nonlinear partial differential equations (PDEs) which govern the evolution of KAW envelopes in the plasma. The modulational instability (MI) of such KAW envelopes is then studied by a nonlinear Schrödinger equation derived from the coupled PDEs. It is shown that the KAWs can evolve into bright envelope solitons or can undergo damping depending on whether the characteristic ratio ( α ) of the Alfvén to ion-acoustic speeds remains above or below a critical value. The parameter α is also found to shift the MI domains around the k x k z plane, where k x ( k z ) is the KAW number perpendicular (parallel) to the external magnetic field. The growth rate of MI, as well as the frequency shift and the energy transfer rate, are obtained and analyzed. The results can be useful for understanding the existence and formation of bright and dark envelope solitons, or damping of KAW envelopes in space plasmas, e.g., interplanetary space, solar winds, etc.

Kinetic Alfvén solitary and rogue waves in superthermal plasmas

NASA Astrophysics Data System (ADS)

Bains, A. S.; Li, Bo; Xia, Li-Dong

2014-03-01

We investigate the small but finite amplitude solitary Kinetic Alfvén waves (KAWs) in low β plasmas with superthermal electrons modeled by a kappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equation describing the evolution of KAWs is derived by using the standard reductive perturbation method. Examining the dependence of the nonlinear and dispersion coefficients of the KdV equation on the superthermal parameter κ, plasma β, and obliqueness of propagation, we show that these parameters may change substantially the shape and size of solitary KAW pulses. Only sub-Alfvénic, compressive solitons are supported. We then extend the study to examine kinetic Alfvén rogue waves by deriving a nonlinear Schrödinger equation from the KdV equation. Rational solutions that form rogue wave envelopes are obtained. We examine how the behavior of rogue waves depends on the plasma parameters in question, finding that the rogue envelopes are lowered with increasing electron superthermality whereas the opposite is true when the plasma β increases. The findings of this study may find applications to low β plasmas in astrophysical environments where particles are superthermally distributed.

Hot Deformation Behavior of 1Cr12Ni3Mo2VN Martensitic Stainless Steel

NASA Astrophysics Data System (ADS)

He, Xiaomao; Jiang, Peng; Zhou, Leyu; Chen, Chao; Deng, Xiaochun

2017-08-01

1Cr12Ni3Mo2VN is a new type of martensitic stainless steel for the last-stage blades of large-capacity nuclear and thermal power turbines. The deformation behavior of this steel was studied by thermal compression experiments that performed on a Gleeble-3500 thermal simulator at a temperature range of 850°C to 1200°C and a strain rate of 0.01s-1 to 20s-1. When the deformation was performed at high temperature and low strain rate, a necklace type of microstructures was observed, the plastic deformation mechanism is grain boundary slip and migration, when at low temperature and lower strain rate, the slip bands were observed, the mechanism is intracrystalline slips, and when at strain rate of 20s-1, twins were observed, the mechanism are slips and twins. The Arrhenius equation was applied to describe the constitutive equation of the flow stress. The accuracy of the equation was verified by using the experimental data and the correlation coefficient R2 = 0.9786, and the equation can provide reasonable data for the design and numerical simulation of the forging process.

Skinfold Prediction Equations Fail to Provide an Accurate Estimate of Body Composition in Elite Rugby Union Athletes of Caucasian and Polynesian Ethnicity.

PubMed

Zemski, Adam J; Broad, Elizabeth M; Slater, Gary J

2018-01-01

Body composition in elite rugby union athletes is routinely assessed using surface anthropometry, which can be utilized to provide estimates of absolute body composition using regression equations. This study aims to assess the ability of available skinfold equations to estimate body composition in elite rugby union athletes who have unique physique traits and divergent ethnicity. The development of sport-specific and ethnicity-sensitive equations was also pursued. Forty-three male international Australian rugby union athletes of Caucasian and Polynesian descent underwent surface anthropometry and dual-energy X-ray absorptiometry (DXA) assessment. Body fat percent (BF%) was estimated using five previously developed equations and compared to DXA measures. Novel sport and ethnicity-sensitive prediction equations were developed using forward selection multiple regression analysis. Existing skinfold equations provided unsatisfactory estimates of BF% in elite rugby union athletes, with all equations demonstrating a 95% prediction interval in excess of 5%. The equations tended to underestimate BF% at low levels of adiposity, whilst overestimating BF% at higher levels of adiposity, regardless of ethnicity. The novel equations created explained a similar amount of variance to those previously developed (Caucasians 75%, Polynesians 90%). The use of skinfold equations, including the created equations, cannot be supported to estimate absolute body composition. Until a population-specific equation is established that can be validated to precisely estimate body composition, it is advocated to use a proven method, such as DXA, when absolute measures of lean and fat mass are desired, and raw anthropometry data routinely to derive an estimate of body composition change.

Derivation of nonlinear wave equations for ultrasound beam in nonuniform bubbly liquids

NASA Astrophysics Data System (ADS)

Kanagawa, Tetsuya; Yano, Takeru; Kawahara, Junya; Kobayashi, Kazumichi; Watanabe, Masao; Fujikawa, Shigeo

2012-09-01

Weakly nonlinear propagation of diffracted ultrasound beams in a nonuniform bubbly liquid is theoretically studied based on the method of multiple scales with the set of scaling relations of some physical parameters. It is assumed that the spatial distribution of the number density of bubbles in an initial state at rest is a slowly varying function of space coordinates and the amplitude of its variation is small compared with a mean number density. As a result, a Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with dispersion and nonuniform effects for a low frequency case and a nonlinear Schrödinger (NLS) equation with dissipation, diffraction, and nonuniform effects for a high frequency case, are derived from the basic equations of bubbly flows.

Fractional Stochastic Field Theory

NASA Astrophysics Data System (ADS)

Honkonen, Juha

2018-02-01

Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

A compressible solution of the Navier-Stokes equations for turbulent flow about an airfoil

NASA Technical Reports Server (NTRS)

Shamroth, S. J.; Gibeling, H. J.

1979-01-01

A compressible time dependent solution of the Navier-Stokes equations including a transition turbulence model is obtained for the isolated airfoil flow field problem. The equations are solved by a consistently split linearized block implicit scheme. A nonorthogonal body-fitted coordinate system is used which has maximum resolution near the airfoil surface and in the region of the airfoil leading edge. The transition turbulence model is based upon the turbulence kinetic energy equation and predicts regions of laminar, transitional, and turbulent flow. Mean flow field and turbulence field results are presented for an NACA 0012 airfoil at zero and nonzero incidence angles of Reynolds number up to one million and low subsonic Mach numbers.

A comparative study of turbulence models in predicting hypersonic inlet flows

NASA Technical Reports Server (NTRS)

Kapoor, Kamlesh

1993-01-01

A computational study has been conducted to evaluate the performance of various turbulence models. The NASA P8 inlet, which represents cruise condition of a typical hypersonic air-breathing vehicle, was selected as a test case for the study; the PARC2D code, which solves the full two dimensional Reynolds-averaged Navier-Stokes equations, was used. Results are presented for a total of six versions of zero- and two-equation turbulence models. Zero-equation models tested are the Baldwin-Lomax model, the Thomas model, and a combination of the two. Two-equation models tested are low-Reynolds number models (the Chien model and the Speziale model) and a high-Reynolds number model (the Launder and Spalding model).

A stream-gaging network analysis for the 7-day, 10-year annual low flow in New Hampshire streams

USGS Publications Warehouse

Flynn, Robert H.

2003-01-01

The 7-day, 10-year (7Q10) low-flow-frequency statistic is a widely used measure of surface-water availability in New Hampshire. Regression equations and basin-characteristic digital data sets were developed to help water-resource managers determine surface-water resources during periods of low flow in New Hampshire streams. These regression equations and data sets were developed to estimate streamflow statistics for the annual and seasonal low-flow-frequency, and period-of-record and seasonal period-of-record flow durations. generalized-least-squares (GLS) regression methods were used to develop the annual 7Q10 low-flow-frequency regression equation from 60 continuous-record stream-gaging stations in New Hampshire and in neighboring States. In the regression equation, the dependent variables were the annual 7Q10 flows at the 60 stream-gaging stations. The independent (or predictor) variables were objectively selected characteristics of the drainage basins that contribute flow to those stations. In contrast to ordinary-least-squares (OLS) regression analysis, GLS-developed estimating equations account for differences in length of record and spatial correlations among the flow-frequency statistics at the various stations.A total of 93 measurable drainage-basin characteristics were candidate independent variables. On the basis of several statistical parameters that were used to evaluate which combination of basin characteristics contribute the most to the predictive power of the equations, three drainage-basin characteristics were determined to be statistically significant predictors of the annual 7Q10: (1) total drainage area, (2) mean summer stream-gaging station precipitation from 1961 to 90, and (3) average mean annual basinwide temperature from 1961 to 1990.To evaluate the effectiveness of the stream-gaging network in providing regional streamflow data for the annual 7Q10, the computer program GLSNET (generalized-least-squares NETwork) was used to analyze the network by application of GLS regression between streamflow and the climatic and basin characteristics of the drainage basin upstream from each stream-gaging station. Improvement to the predictive ability of the regression equations developed for the network analyses is measured by the reduction in the average sampling-error variance, and can be achieved by collecting additional streamflow data at existing stations. The predictive ability of the regression equations is enhanced even further with the addition of new stations to the network. Continued data collection at unregulated stream-gaging stations with less than 14 years of record resulted in the greatest cost-weighted reduction to the average sampling-error variance of the annual 7Q10 regional regression equation. The addition of new stations in basins with underrepresented values for the independent variables of the total drainage area, average mean annual basinwide temperature, or mean summer stream-gaging station precipitation in the annual 7Q10 regression equation yielded a much greater cost-weighted reduction to the average sampling-error variance than when more data were collected at existing unregulated stations. To maximize the regional information obtained from the stream-gaging network for the annual 7Q10, ranking of the streamflow data can be used to determine whether an active station should be continued or if a new or discontinued station should be activated for streamflow data collection. Thus, this network analysis can help determine the costs and benefits of continuing the operation of a particular station or activating a new station at another location to predict the 7Q10 at ungaged stream reaches. The decision to discontinue an existing station or activate a new station, however, must also consider its contribution to other water-resource analyses such as flood management, water quality, or trends in land use or climatic change.

Technological pedagogical content knowledge of junior high school mathematics teachers in teaching linear equation

NASA Astrophysics Data System (ADS)

Wati, S.; Fitriana, L.; Mardiyana

2018-04-01

Linear equation is one of the topics in mathematics that are considered difficult. Student difficulties of understanding linear equation can be caused by lack of understanding this concept and the way of teachers teach. TPACK is a way to understand the complex relationships between teaching and content taught through the use of specific teaching approaches and supported by the right technology tools. This study aims to identify TPACK of junior high school mathematics teachers in teaching linear equation. The method used in the study was descriptive. In the first phase, a survey using a questionnaire was carried out on 45 junior high school mathematics teachers in teaching linear equation. While in the second phase, the interview involved three teachers. The analysis of data used were quantitative and qualitative technique. The result PCK revealed teachers emphasized developing procedural and conceptual knowledge through reliance on traditional in teaching linear equation. The result of TPK revealed teachers’ lower capacity to deal with the general information and communications technologies goals across the curriculum in teaching linear equation. The result indicated that PowerPoint constitutes TCK modal technological capability in teaching linear equation. The result of TPACK seems to suggest a low standard in teachers’ technological skills across a variety of mathematics education goals in teaching linear equation. This means that the ability of teachers’ TPACK in teaching linear equation still needs to be improved.

Urban Education: Its Conceptual and Functional Domains.

ERIC Educational Resources Information Center

Gordon, Edmund G.

Because of the heavy concentration of low ethnic status minorities dwelling in cities, urban education has been equated with the problems of low status persons. However, there are problems that are peculiar to education as it is influenced by urban development that go beyond the problems of special ethnic, low status minority groups. The problems…

Computation of Turbulent Heat Transfer on the Walls of a 180 Degree Turn Channel With a Low Reynolds Number Reynolds Stress Model

NASA Technical Reports Server (NTRS)

Ameri, A. A.; Rigby, D. L.; Steinthorsson, E.; Gaugler, Raymond (Technical Monitor)

2002-01-01

The Low Reynolds number version of the Stress-omega model and the two equation k-omega model of Wilcox were used for the calculation of turbulent heat transfer in a 180 degree turn simulating an internal coolant passage. The Stress-omega model was chosen for its robustness. The turbulent thermal fluxes were calculated by modifying and using the Generalized Gradient Diffusion Hypothesis. The results showed that using this Reynolds Stress model allowed better prediction of heat transfer compared to the k-omega two equation model. This improvement however required a finer grid and commensurately more CPU time.

A new variant of a scaling hypothesis and a fundamental equation of state based on it

NASA Astrophysics Data System (ADS)

Kudryavtseva, I. V.; Rykov, V. A.; Rykov, S. V.; Ustyuzhanin, E. E.

2018-01-01

This paper deals with a fundamental equation of state (FEOS) for substances. We have suggested a new method. It allows constructing FEOS that is based on the scaling theory of critical phenomena and describes thermodynamic properties related to liquid and gas phases of a substance in a wide range of the pressures and temperatures. In the framework of the methodological approach, we have provided: (i) a transition of FEOS in a virial equation of state in the low density region; (ii) a transition of FEOS in a Widom equation of state in the critical region. The method has been tested on the example of FEOS of R218. The area of applicability of FEOS is 0 < ρ/ρ c < 3.2 in the density and 133 < T < 440 K in the temperature. We have compared FEOS with some equations of state and discussed the results.

Surface-slip equations for multicomponent, nonequilibrium air flow

NASA Technical Reports Server (NTRS)

Gupta, Roop N.; Scott, Carl D.; Moss, James N.; Goglia, Gene

1985-01-01

Equations are presented for the surface slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds-number, high-altitude flight regime of a space vehicle. These are obtained from closed-form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities have been obtained in a form which can readily be employed in flow-field computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate species-concentration boundary condition for a multicomponent mixture in absence of slip.

Development of one-equation transition/turbulence models

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

Edwards, J.R.; Roy, C.J.; Blottner, F.G.

2000-01-14

This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity--transport equation for nonturbulent fluctuation growth based on that proposed by Warren and Hassan is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittency function based on the work of Dhawan and Narasimha. The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test casesmore » include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the grid-dependence of selected predictions is analyzed.« less

A new treatment of nonlocality in scattering process

NASA Astrophysics Data System (ADS)

Upadhyay, N. J.; Bhagwat, A.; Jain, B. K.

2018-01-01

Nonlocality in the scattering potential leads to an integro-differential equation. In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schrödinger equation is usually handled by approximating r,{r}{\\prime }-dependence of the nonlocal kernel. The present work proposes a novel method to solve the integro-differential equation. The method, using the mean value theorem of integral calculus, converts the nonhomogeneous term to a homogeneous term. The effective local potential in this equation turns out to be energy independent, but has relative angular momentum dependence. This method is accurate and valid for any form of nonlocality. As illustrative examples, the total and differential cross sections for neutron scattering off 12C, 56Fe and 100Mo nuclei are calculated with this method in the low energy region (up to 10 MeV) and are found to be in reasonable accord with the experiments.

Scaling properties of weakly nonlinear coefficients in the Faraday problem.

PubMed

Skeldon, A C; Porter, J

2011-07-01

Interesting and exotic surface wave patterns have regularly been observed in the Faraday experiment. Although symmetry arguments provide a qualitative explanation for the selection of some of these patterns (e.g., superlattices), quantitative analysis is hindered by mathematical difficulties inherent in a time-dependent, free-boundary Navier-Stokes problem. More tractable low viscosity approximations are available, but these do not necessarily capture the moderate viscosity regime of the most interesting experiments. Here we focus on weakly nonlinear behavior and compare the scaling results derived from symmetry arguments in the low viscosity limit with the computed coefficients of appropriate amplitude equations using both the full Navier-Stokes equations and a reduced set of partial differential equations due to Zhang and Vinãls. We find the range of viscosities over which one can expect "low viscosity" theories to hold. We also find that there is an optimal viscosity range for locating superlattice patterns experimentally-large enough that the region of parameters giving stable patterns is not impracticably small, yet not so large that crucial resonance effects are washed out. These results help explain some of the discrepancies between theory and experiment.

Low-mass neutron stars: universal relations, the nuclear symmetry energy and gravitational radiation

NASA Astrophysics Data System (ADS)

O. Silva, Hector; Berti, Emanuele; Sotani, Hajime

2016-03-01

Compact objects such as neutron stars are ideal astrophysical laboratories to test our understanding of the fundamental interactions in the regime of supranuclear densities, unachievable by terrestrial experiments. Despite recent progress, the description of matter (i.e., the equation of state) at such densities is still debatable. This translates into uncertainties in the bulk properties of neutron stars, masses and radii for instance. Here we will consider low-mass neutron stars. Such stars are expected to carry important information on nuclear matter near the nuclear saturation point. It has recently been shown that the masses and surface redshifts of low-mass neutron stars smoothly depend on simple functions of the central density and of a characteristic parameter η associated with the choice of equation of state. Here we extend these results to slowly-rotating and tidally deformed stars and obtain empirical relations for various quantities, such as the moment of inertia, quadrupole moment and ellipticity, tidal and rotational Love numbers, and rotational apsidal constants. We discuss how these relations might be used to constrain the equation of state by future observations in the electromagnetic and gravitational-wave spectra.

Unveiling the Universality of I-Love-Q Relations

NASA Astrophysics Data System (ADS)

Sham, Y.-H.; Chan, T. K.; Lin, L.-M.; Leung, P. T.

2015-01-01

The recent discovery of the universal I-Love-Q relations connecting the moment of inertia, tidal deformability, and the spin-induced quadrupole moment of compact stars is intriguing and totally unexpected. In this paper, we provide numerical evidence showing that the universality can be attributed to the incompressible limit of the I-Love-Q relations. The fact that modern equations of state are stiff, with an effective adiabatic index larger than about two, above the nuclear density range is the key to establishing the universality for neutron stars and quark stars with typical compactness from about 0.1 to 0.3. On the other hand, the I-Love-Q relations of low-mass neutron stars near the minimum mass limit depend more sensitively on the underlying equation of state because these stars are composed mainly of softer matter at low densities. However, the I-Love-Q relations for low-mass quark stars can still be represented accurately by the incompressible limit. We also study the I-Love relation connecting the moment of inertia and tidal deformability analytically in Newtonian gravity and show why the I-Love-Q relation is weakly dependent on the underlying equation of state and can be attributed to its incompressible limit.

Freeze-out of baryon number in low-scale leptogenesis

NASA Astrophysics Data System (ADS)

Eijima, S.; Shaposhnikov, M.; Timiryasov, I.

2017-11-01

Low-scale leptogenesis provides an economic and testable description of the origin of the baryon asymmetry of the Universe. In this scenario, the baryon asymmetry of the Universe is reprocessed from the lepton asymmetry by electroweak sphaleron processes. Provided that sphalerons are fast enough to maintain equilibrium, the values of the baryon and lepton asymmetries are related to each other. Usually, this relation is used to find the value of the baryon asymmetry at the time of the sphaleron freeze-out. To put in other words, the formula which is valid only when the sphalerons are fast, is applied at the moment when they are actually switched off. In this paper, we examine the validity of such a treatment. To this end, we solve the full system of kinetic equations for low-scale leptogenesis. This system includes equations describing the production of the lepton asymmetry in oscillations of right-handed neutrinos, as well as a separate kinetic equation for the baryon asymmetry. We show that for some values of the model parameters, the corrections to the standard approach are sizeable. We also present a feasible improvement to the ordinary procedure, which accounts for these corrections.

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.

Methods for estimating selected low-flow statistics and development of annual flow-duration statistics for Ohio

USGS Publications Warehouse

Koltun, G.F.; Kula, Stephanie P.

2013-01-01

This report presents the results of a study to develop methods for estimating selected low-flow statistics and for determining annual flow-duration statistics for Ohio streams. Regression techniques were used to develop equations for estimating 10-year recurrence-interval (10-percent annual-nonexceedance probability) low-flow yields, in cubic feet per second per square mile, with averaging periods of 1, 7, 30, and 90-day(s), and for estimating the yield corresponding to the long-term 80-percent duration flow. These equations, which estimate low-flow yields as a function of a streamflow-variability index, are based on previously published low-flow statistics for 79 long-term continuous-record streamgages with at least 10 years of data collected through water year 1997. When applied to the calibration dataset, average absolute percent errors for the regression equations ranged from 15.8 to 42.0 percent. The regression results have been incorporated into the U.S. Geological Survey (USGS) StreamStats application for Ohio (http://water.usgs.gov/osw/streamstats/ohio.html) in the form of a yield grid to facilitate estimation of the corresponding streamflow statistics in cubic feet per second. Logistic-regression equations also were developed and incorporated into the USGS StreamStats application for Ohio for selected low-flow statistics to help identify occurrences of zero-valued statistics. Quantiles of daily and 7-day mean streamflows were determined for annual and annual-seasonal (September–November) periods for each complete climatic year of streamflow-gaging station record for 110 selected streamflow-gaging stations with 20 or more years of record. The quantiles determined for each climatic year were the 99-, 98-, 95-, 90-, 80-, 75-, 70-, 60-, 50-, 40-, 30-, 25-, 20-, 10-, 5-, 2-, and 1-percent exceedance streamflows. Selected exceedance percentiles of the annual-exceedance percentiles were subsequently computed and tabulated to help facilitate consideration of the annual risk of exceedance or nonexceedance of annual and annual-seasonal-period flow-duration values. The quantiles are based on streamflow data collected through climatic year 2008.

PHYSICS REQUIRES A SIMPLE LOW MACH NUMBER FLOW TO BE COMPRESSIBLE

EPA Science Inventory

Radial, laminar, plane, low velocity flow represents the simplest, non-linear fluid dynamics problem. Ostensibly this apparently trivial flow could be solved using the incompressible Navier-Stokes equations, universally believed to be adequate for such problems. Most researchers ...

Effective equations and the inverse cascade theory for Kolmogorov flows

NASA Technical Reports Server (NTRS)

Weinan, E.; Shu, Chi-Wang

1992-01-01

We study the two dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

Extension of the N-point Padé approximants solution of the Eliashberg equations to T ˜ T c

NASA Astrophysics Data System (ADS)

Leavens, C. R.; Ritchie, D. S.

1985-01-01

Vidberg and Serene introduced a very useful technique for calculating the low temperature (T « T c) gap function of a superconductor which bypasses the real-frequency singular integral equations of Eliashberg. Blashke and Blocksdorf recognized and resolved a difficulty with the technique thereby extending it to higher temperatures. We present a much simpler method of doing essentially the same thing and, for a strong-coupling superconductor at a temperature near T c, compare the gap functions calculated using these methods with the accurate one computed directly from the real-frequency equations.

Using Mathematical Algorithms to Modify Glomerular Filtration Rate Estimation Equations

PubMed Central

Zhu, Bei; Wu, Jianqing; Zhu, Jin; Zhao, Weihong

2013-01-01

Background The equations provide a rapid and low-cost method of evaluating glomerular filtration rate (GFR). Previous studies indicated that the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease-Epidemiology (CKD-EPI) and MacIsaac equations need further modification for application in Chinese population. Thus, this study was designed to modify the three equations, and compare the diagnostic accuracy of the equations modified before and after. Methodology With the use of 99 mTc-DTPA renal dynamic imaging as the reference GFR (rGFR), the MDRD, CKD-EPI and MacIsaac equations were modified by two mathematical algorithms: the hill-climbing and the simulated-annealing algorithms. Results A total of 703 Chinese subjects were recruited, with the average rGFR 77.14±25.93 ml/min. The entire modification process was based on a random sample of 80% of subjects in each GFR level as a training sample set, the rest of 20% of subjects as a validation sample set. After modification, the three equations performed significant improvement in slop, intercept, correlated coefficient, root mean square error (RMSE), total deviation index (TDI), and the proportion of estimated GFR (eGFR) within 10% and 30% deviation of rGFR (P10 and P30). Of the three modified equations, the modified CKD-EPI equation showed the best accuracy. Conclusions Mathematical algorithms could be a considerable tool to modify the GFR equations. Accuracy of all the three modified equations was significantly improved in which the modified CKD-EPI equation could be the optimal one. PMID:23472113

Optimum acoustic design of free-running low speed propellers

NASA Technical Reports Server (NTRS)

Ormsbee, A. I.; Woan, C. J.

1977-01-01

A theoretical analysis is conducted concerning the effect of blade loading on the noise output of a free-running propeller in axial motion. The minimization of the mean square sound pressure at a point in space is considered, taking into account constraints on propeller thrust and torque. Attention is given to aerodynamic equations, acoustic equations, the expansion of the aerodynamic variables, and the nonlinear programming formulation.

Design of structure and simulation of the three-zone gasifier of dense layer of the inverted process

NASA Astrophysics Data System (ADS)

Zagrutdinov, R. Sh; Negutorov, V. N.; Maliykhin, D. G.; Nikishanin, M. S.; Senachin, P. K.

2017-11-01

Experts of LLC “New Energy Technologies” have developed gasifiers designs, with the implementation of the three-zone gasification method, which satisfy the following conditions: 1) the generated gas must be free from tar, soot and hydrocarbons, with a given ratio of CO/H2; 2) to use as the fuel source a wide range of low-grade low-value solid fuels, including biomass and various kinds of carbonaceous wastes; 3) have high reliability in operation, do not require qualified operating personnel, be relatively inexpensive to produce and use steam-air blowing instead of expensive steam-oxygen one; 4) the line of standard sizes should be sufficiently wide (with a single unit capacity of fuel from 1 to 50-70 MW). Two models of gas generators of the inverted gasification process with three combustion zones operating under pressure have been adopted for design: 1) gas generator with a remote combustion chamber type GOP-VKS (two-block version) and 2) a gas generator with a common combustion chamber of the GOP-OK type (single-block version), which is an almost ideal model for increasing the unit capacity. There have been worked out various schemes for the preparation of briquettes from practically the entire spectrum of low-grade fuel: high-ash and high-moisture coals, peat and biomass, including all types of waste - solid household waste, crop, livestock, poultry, etc. In the gas generators there are gasified the cylindrical briquettes with a diameter of 20-25 mm and a length of 25-35 mm. There have been developed a mathematical model and computer code for numerical simulation of synthesis gas generation processes in a gasifier of a dense layer of inverted process during a steam-air blast, including: continuity equations for the 8 gas phase components and for the solid phase; the equation of the heat balance for the entire heterogeneous system; the Darcy law equation (for porous media); equation of state for 8 components of the gas phase; equations for the rates of 3 gas-phase and 4 heterogeneous reactions; macro kinetics law of coke combustion; other equations and boundary conditions.

Predicting the crystalline and porous equations of state for secondary explosives

NASA Astrophysics Data System (ADS)

Wixom, Ryan; Damm, David

2013-06-01

Accurate simulations of energetic material response necessitate accurate unreacted equations of state at pressures much higher than even the C-J state. Unfortunately, for reactive materials, experimental data at high pressures may be unattainable, and extrapolation from low-pressure data results in unacceptable uncertainty. In addition to being low-pressure, the available data is typically limited to the porous state. The fully-dense, or crystalline, equation of state is required for building mesoscale simulations of the dynamic response of energetic materials. We have used quantum molecular dynamics to predict the Hugoniots and 300 K isotherms of crystalline PETN, HNS, CL-20 and TATB up to pressures not attainable in experiments. The porous Hugoniots for these materials were then analytically obtained and are validated by comparison with available data. Our calculations for TATB confirm the presence of a kink in the Hugoniot, and the softening of the shock response is explained in terms of a change in molecular conformation and the loss of aromaticity.

Hartman Testing of X-Ray Telescopes

NASA Technical Reports Server (NTRS)

Saha, Timo T.; Biskasch, Michael; Zhang, William W.

2013-01-01

Hartmann testing of x-ray telescopes is a simple test method to retrieve and analyze alignment errors and low-order circumferential errors of x-ray telescopes and their components. A narrow slit is scanned along the circumference of the telescope in front of the mirror and the centroids of the images are calculated. From the centroid data, alignment errors, radius variation errors, and cone-angle variation errors can be calculated. Mean cone angle, mean radial height (average radius), and the focal length of the telescope can also be estimated if the centroid data is measured at multiple focal plane locations. In this paper we present the basic equations that are used in the analysis process. These equations can be applied to full circumference or segmented x-ray telescopes. We use the Optical Surface Analysis Code (OSAC) to model a segmented x-ray telescope and show that the derived equations and accompanying analysis retrieves the alignment errors and low order circumferential errors accurately.

Techniques for estimating streamflow characteristics in the Eastern and Interior coal provinces of the United States

USGS Publications Warehouse

Wetzel, Kim L.; Bettandorff, J.M.

1986-01-01

Techniques are presented for estimating various streamflow characteristics, such as peak flows, mean monthly and annual flows, flow durations, and flow volumes, at ungaged sites on unregulated streams in the Eastern Coal region. Streamflow data and basin characteristics for 629 gaging stations were used to develop multiple-linear-regression equations. Separate equations were developed for the Eastern and Interior Coal Provinces. Drainage area is an independent variable common to all equations. Other variables needed, depending on the streamflow characteristic, are mean annual precipitation, mean basin elevation, main channel length, basin storage, main channel slope, and forest cover. A ratio of the observed 50- to 90-percent flow durations was used in the development of relations to estimate low-flow frequencies in the Eastern Coal Province. Relations to estimate low flows in the Interior Coal Province are not presented because the standard errors were greater than 0.7500 log units and were considered to be of poor reliability.

A numerical spectral approach to solve the dislocation density transport equation

NASA Astrophysics Data System (ADS)

Djaka, K. S.; Taupin, V.; Berbenni, S.; Fressengeas, C.

2015-09-01

A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme.

Development of inexpensive prosthetic feet for high-heeled shoes using simple shoe insole model.

PubMed

Meier, Margrit R; Tucker, Kerice A; Hansen, Andrew H

2014-01-01

The large majority of prosthetic feet are aimed at low-heeled shoes, with a few models allowing a heel height of up to 5 cm. However, a survey by the American Podiatric Medical Association indicates that most women wear heels over 5 cm; thus, current prosthetic feet limit most female prosthesis users in their choice. Some prosthetic foot components are heel-height adjustable; however, their plantar surface shapes do not change to match the insole shapes of the shoes with different heel heights. The aims of the study were therefore (1) to develop a model that allows prediction of insole shape for various heel height shoes in combination with different shoe sizes and (2) to develop and field-test low-cost prototypes of prosthetic feet whose insole shapes were based on the new model. An equation was developed to calculate insole shapes independent of shoe size. Field testing of prototype prosthetic feet fabricated based on the equation was successful and demonstrated the utility of the equation.

Reference Correlation of the Thermal Conductivity of Carbon Dioxide from the Triple Point to 1100 K and up to 200 MPa

PubMed Central

Huber, M. L.; Sykioti, E. A.; Assael, M. J.; Perkins, R. A.

2016-01-01

This paper contains new, representative reference equations for the thermal conductivity of carbon dioxide. The equations are based in part upon a body of experimental data that has been critically assessed for internal consistency and for agreement with theory whenever possible. In the case of the dilute-gas thermal conductivity, we incorporated recent theoretical calculations to extend the temperature range of the experimental data. Moreover, in the critical region, the experimentally observed enhancement of the thermal conductivity is well represented by theoretically based equations containing just one adjustable parameter. The correlations are applicable for the temperature range from the triple point to 1100 K and pressures up to 200 MPa. The overall uncertainty (at the 95% confidence level) of the proposed correlation varies depending on the state point from a low of 1% at very low pressures below 0.1 MPa between 300 K and 700 K, to 5% at the higher pressures of the range of validity. PMID:27064300

The large discretization step method for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

Steady-State Electrodiffusion from the Nernst-Planck Equation Coupled to Local Equilibrium Monte Carlo Simulations.

PubMed

Boda, Dezső; Gillespie, Dirk

2012-03-13

We propose a procedure to compute the steady-state transport of charged particles based on the Nernst-Planck (NP) equation of electrodiffusion. To close the NP equation and to establish a relation between the concentration and electrochemical potential profiles, we introduce the Local Equilibrium Monte Carlo (LEMC) method. In this method, Grand Canonical Monte Carlo simulations are performed using the electrochemical potential specified for the distinct volume elements. An iteration procedure that self-consistently solves the NP and flux continuity equations with LEMC is shown to converge quickly. This NP+LEMC technique can be used in systems with diffusion of charged or uncharged particles in complex three-dimensional geometries, including systems with low concentrations and small applied voltages that are difficult for other particle simulation techniques.

An analytical theory of radio-wave scattering from meteoric ionization - I. Basic equation

NASA Astrophysics Data System (ADS)

Pecina, P.

2016-01-01

We have developed an analytical theory of radio-wave scattering from ionization of meteoric origin. It is based on an integro-differential equation for the polarization vector, P, inside the meteor trail, representing an analytical solution of the set of Maxwell equations, in combination with a generalized radar equation involving an integral of the trail volume electron density, Ne, and P represented by an auxiliary vector, Q, taken over the whole trail volume. During the derivation of the final formulae, the following assumptions were applied: transversal as well as longitudinal dimensions of the meteor trail are small compared with the distances of the relevant trail point to both the transmitter and receiver and the ratio of these distances to the wavelength of the wave emitted by the radar is very large, so that the stationary-phase method can be employed for evaluation of the relevant integrals. Further, it is shown that in the case of sufficiently low electron density, Ne, corresponding to the case of underdense trails, the classical McKinley's radar equation results as a special case of the general theory. The same also applies regarding the Fresnel characteristics. Our approach is also capable of yielding solutions to the problems of the formation of Fresnel characteristics on trails having any electron density, forward scattering and scattering on trails immersed in the magnetic field. However, we have also shown that the geomagnetic field can be removed from consideration, due to its low strength. The full solution of the above integro-differential equation, valid for any electron volume densities, has been left to subsequent works dealing with this particular problem, due to its complexity.

An Equation for Moist Entropy in a Precipitating and Icy Atmosphere

NASA Technical Reports Server (NTRS)

Tao, Wei-Kuo; Simpson, Joanne; Zeng, Xiping

2003-01-01

Moist entropy is nearly conserved in adiabatic motion. It is redistributed rather than created by moist convection. Thus moist entropy and its equation, as a healthy direction, can be used to construct analytical and numerical models for the interaction between tropical convective clouds and large-scale circulations. Hence, an accurate equation of moist entropy is needed for the analysis and modeling of atmospheric convective clouds. On the basis of the consistency between the energy and the entropy equations, a complete equation of moist entropy is derived from the energy equation. The equation expresses explicitly the internal and external sources of moist entropy, including those in relation to the microphysics of clouds and precipitation. In addition, an accurate formula for the surface flux of moist entropy from the underlying surface into the air above is derived. Because moist entropy deals "easily" with the transition among three water phases, it will be used as a prognostic variable in the next generation of cloud-resolving models (e. g. a global cloud-resolving model) for low computational noise. Its equation that is derived in this paper is accurate and complete, providing a theoretical basis for using moist entropy as a prognostic variable in the long-term modeling of clouds and large-scale circulations.

The National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites

USGS Publications Warehouse

Ries(compiler), Kernell G.; With sections by Atkins, J. B.; Hummel, P.R.; Gray, Matthew J.; Dusenbury, R.; Jennings, M.E.; Kirby, W.H.; Riggs, H.C.; Sauer, V.B.; Thomas, W.O.

2007-01-01

The National Streamflow Statistics (NSS) Program is a computer program that should be useful to engineers, hydrologists, and others for planning, management, and design applications. NSS compiles all current U.S. Geological Survey (USGS) regional regression equations for estimating streamflow statistics at ungaged sites in an easy-to-use interface that operates on computers with Microsoft Windows operating systems. NSS expands on the functionality of the USGS National Flood Frequency Program, and replaces it. The regression equations included in NSS are used to transfer streamflow statistics from gaged to ungaged sites through the use of watershed and climatic characteristics as explanatory or predictor variables. Generally, the equations were developed on a statewide or metropolitan-area basis as part of cooperative study programs. Equations are available for estimating rural and urban flood-frequency statistics, such as the 1 00-year flood, for every state, for Puerto Rico, and for the island of Tutuila, American Samoa. Equations are available for estimating other statistics, such as the mean annual flow, monthly mean flows, flow-duration percentiles, and low-flow frequencies (such as the 7-day, 0-year low flow) for less than half of the states. All equations available for estimating streamflow statistics other than flood-frequency statistics assume rural (non-regulated, non-urbanized) conditions. The NSS output provides indicators of the accuracy of the estimated streamflow statistics. The indicators may include any combination of the standard error of estimate, the standard error of prediction, the equivalent years of record, or 90 percent prediction intervals, depending on what was provided by the authors of the equations. The program includes several other features that can be used only for flood-frequency estimation. These include the ability to generate flood-frequency plots, and plots of typical flood hydrographs for selected recurrence intervals, estimates of the probable maximum flood, extrapolation of the 500-year flood when an equation for estimating it is not available, and weighting techniques to improve flood-frequency estimates for gaging stations and ungaged sites on gaged streams. This report describes the regionalization techniques used to develop the equations in NSS and provides guidance on the applicability and limitations of the techniques. The report also includes a users manual and a summary of equations available for estimating basin lagtime, which is needed by the program to generate flood hydrographs. The NSS software and accompanying database, and the documentation for the regression equations included in NSS, are available on the Web at http://water.usgs.gov/software/.

Body fat measurement by bioelectrical impedance and air displacement plethysmography: a cross-validation study to design bioelectrical impedance equations in Mexican adults

PubMed Central

Macias, Nayeli; Alemán-Mateo, Heliodoro; Esparza-Romero, Julián; Valencia, Mauro E

2007-01-01

Background The study of body composition in specific populations by techniques such as bio-impedance analysis (BIA) requires validation based on standard reference methods. The aim of this study was to develop and cross-validate a predictive equation for bioelectrical impedance using air displacement plethysmography (ADP) as standard method to measure body composition in Mexican adult men and women. Methods This study included 155 male and female subjects from northern Mexico, 20–50 years of age, from low, middle, and upper income levels. Body composition was measured by ADP. Body weight (BW, kg) and height (Ht, cm) were obtained by standard anthropometric techniques. Resistance, R (ohms) and reactance, Xc (ohms) were also measured. A random-split method was used to obtain two samples: one was used to derive the equation by the "all possible regressions" procedure and was cross-validated in the other sample to test predicted versus measured values of fat-free mass (FFM). Results and Discussion The final model was: FFM (kg) = 0.7374 * (Ht2 /R) + 0.1763 * (BW) - 0.1773 * (Age) + 0.1198 * (Xc) - 2.4658. R2 was 0.97; the square root of the mean square error (SRMSE) was 1.99 kg, and the pure error (PE) was 2.96. There was no difference between FFM predicted by the new equation (48.57 ± 10.9 kg) and that measured by ADP (48.43 ± 11.3 kg). The new equation did not differ from the line of identity, had a high R2 and a low SRMSE, and showed no significant bias (0.87 ± 2.84 kg). Conclusion The new bioelectrical impedance equation based on the two-compartment model (2C) was accurate, precise, and free of bias. This equation can be used to assess body composition and nutritional status in populations similar in anthropometric and physical characteristics to this sample. PMID:17697388

Linear tearing mode stability equations for a low collisionality toroidal plasma

NASA Astrophysics Data System (ADS)

Connor, J. W.; Hastie, R. J.; Helander, P.

2009-01-01

Tearing mode stability is normally analysed using MHD or two-fluid Braginskii plasma models. However for present, or future, large hot tokamaks like JET or ITER the collisionality is such as to place them in the banana regime. Here we develop a linear stability theory for the resonant layer physics appropriate to such a regime. The outcome is a set of 'fluid' equations whose coefficients encapsulate all neoclassical physics: the neoclassical Ohm's law, enhanced ion inertia, cross-field transport of particles, heat and momentum all play a role. While earlier treatments have also addressed this type of neoclassical physics we differ in incorporating the more physically relevant 'semi-collisional fluid' regime previously considered in cylindrical geometry; semi-collisional effects tend to screen the resonant surface from the perturbed magnetic field, preventing reconnection. Furthermore we also include thermal physics, which may modify the results. While this electron description is of wide relevance and validity, the fluid treatment of the ions requires the ion banana orbit width to be less than the semi-collisional electron layer. This limits the application of the present theory to low magnetic shear—however, this is highly relevant to the sawtooth instability—or to colder ions. The outcome of the calculation is a set of one-dimensional radial differential equations of rather high order. However, various simplifications that reduce the computational task of solving these are discussed. In the collisional regime, when the set reduces to a single second-order differential equation, the theory extends previous work by Hahm et al (1988 Phys. Fluids 31 3709) to include diamagnetic-type effects arising from plasma gradients, both in Ohm's law and the ion inertia term of the vorticity equation. The more relevant semi-collisional regime pertaining to JET or ITER, is described by a pair of second-order differential equations, extending the cylindrical equations of Drake et al (1983 Phys. Fluids 26 2509) to toroidal geometry.

Discontinuous Finite Element Quasidiffusion Methods

DOE PAGES

Anistratov, Dmitriy Yurievich; Warsa, James S.

2018-05-21

Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and themore » LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.« less

Discontinuous Finite Element Quasidiffusion Methods

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

Anistratov, Dmitriy Yurievich; Warsa, James S.

Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and themore » LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.« less

Analytical evaluation of the trajectories of hypersonic projectiles launched into space

NASA Astrophysics Data System (ADS)

Stutz, John David

An equation of motion has been derived that may be solved using simple analytic functions which describes the motion of a projectile launched from the surface of the Earth into space accounting for both Newtonian gravity and aerodynamic drag. The equation of motion is based upon the Kepler equation of motion differential and variable transformations with the inclusion of a decaying angular momentum driving function and appropriate simplifying assumptions. The new equation of motion is first compared to various numerical and analytical trajectory approximations in a non-rotating Earth reference frame. The Modified Kepler solution is then corrected to include Earth rotation and compared to a rotating Earth simulation. Finally, the modified equation of motion is used to predict the apogee and trajectory of projectiles launched into space by the High Altitude Research Project from 1961 to 1967. The new equation of motion allows for the rapid equalization of projectile trajectories and intercept solutions that may be used to calculate firing solutions to enable ground launched projectiles to intercept or rendezvous with targets in low Earth orbit such as ballistic missiles.

Constitutive behavior of as-cast AA1050, AA3104, and AA5182

NASA Astrophysics Data System (ADS)

van Haaften, W. M.; Magnin, B.; Kool, W. H.; Katgerman, L.

2002-07-01

Recent thermomechanical modeling to calculate the stress field in industrially direct-chill (DC) cast-aluminum slabs has been successful, but lack of material data limits the accuracy of these calculations. Therefore, the constitutive behavior of three aluminum alloys (AA1050, AA3104, and AA5182) was determined in the as-cast condition using tensile tests at low strain rates and from room temperature to solidus temperature. The parameters of two constitutive equations, the extended Ludwik equation and a combination of the Sellars-Tegart equation with a hardening law, were determined. In order to study the effect of recovery, the constitutive behavior after prestraining at higher temperatures was also investigated. To evaluate the quantified constitutive equations, tensile tests were performed simulating the deformation and cooling history experienced by the material during casting. It is concluded that both constitutive equations perform well, but the combined hardening-Sellars-Tegart (HST) equation has temperature-independent parameters, which makes it easier to implement in a DC casting model. Further, the deformation history of the ingot should be taken into account for accurate stress calculations.

COMPRESSIBLE FLOW, ENTRAINMENT, AND MEGAPLUME

EPA Science Inventory

It is generally believed that low Mach number, i.e., low-velocity, flow may be assumed to be incompressible flow. Under steady-state conditions, an exact equation of continuity may then be used to show that such flow is non-divergent. However, a rigorous, compressible fluid-dynam...

A High Efficiency Boost Converter with MPPT Scheme for Low Voltage Thermoelectric Energy Harvesting

NASA Astrophysics Data System (ADS)

Guan, Mingjie; Wang, Kunpeng; Zhu, Qingyuan; Liao, Wei-Hsin

2016-11-01

Using thermoelectric elements to harvest energy from heat has been of great interest during the last decade. This paper presents a direct current-direct current (DC-DC) boost converter with a maximum power point tracking (MPPT) scheme for low input voltage thermoelectric energy harvesting applications. Zero current switch technique is applied in the proposed MPPT scheme. Theoretical analysis on the converter circuits is explored to derive the equations for parameters needed in the design of the boost converter. Simulations and experiments are carried out to verify the theoretical analysis and equations. A prototype of the designed converter is built using discrete components and a low-power microcontroller. The results show that the designed converter can achieve a high efficiency at low input voltage. The experimental efficiency of the designed converter is compared with a commercial converter solution. It is shown that the designed converter has a higher efficiency than the commercial solution in the considered voltage range.

A Method for Large Eddy Simulation of Acoustic Combustion Instabilities

NASA Astrophysics Data System (ADS)

Wall, Clifton; Pierce, Charles; Moin, Parviz

2002-11-01

A method for performing Large Eddy Simulation of acoustic combustion instabilities is presented. By extending the low Mach number pressure correction method to the case of compressible flow, a numerical method is developed in which the Poisson equation for pressure is replaced by a Helmholtz equation. The method avoids the acoustic CFL condition by using implicit time advancement, leading to large efficiency gains at low Mach number. The method also avoids artificial damping of acoustic waves. The numerical method is attractive for the simulation of acoustic combustion instabilities, since these flows are typically at low Mach number, and the acoustic frequencies of interest are usually low. Both of these characteristics suggest the use of larger time steps than those allowed by an acoustic CFL condition. The turbulent combustion model used is the Combined Conserved Scalar/Level Set Flamelet model of Duchamp de Lageneste and Pitsch for partially premixed combustion. Comparison of LES results to the experiments of Besson et al will be presented.

Diffusion of low-energy electrons in tissue-like liquids.

PubMed

Malamut, C; Paes-Leme, P J; Paschoa, A S

1992-11-01

The spatial-energetic distribution of low-energy electrons was studied for a source located in a liquid medium simulating biological tissue. A time-independent Boltzmann equation was used to model this distribution microscopically. Ionization was treated as a perturbation to a quasi-elastic collision process between the electron and the medium. A diffusion limit was obtained by using a scale parameter, leading to a sequence of recursive partial differential equations whose solutions, associated with a macroscopic scale, were obtained by numerical approximations. As an application, electron ranges were estimated based on these solutions and then compared with values reported in the open literature based on experimental results and on Monte Carlo calculation. Local dosimetry, i.e., the energy imparted to a volume of a sphere with radius equal to the range of low-energy electrons, of low-energy electrons from internal emitters can benefit by the knowledge of the ranges estimated for biological tissue. Auger electron emitters, for example, have been the object of a number of investigations because of their radiobiological significance.

Temperature-dependent poroelastic and viscoelastic effects on microscale-modelling of seismic reflections in heavy oil reservoirs

NASA Astrophysics Data System (ADS)

Ciz, Radim; Saenger, Erik H.; Gurevich, Boris; Shapiro, Serge A.

2009-03-01

We develop a new model for elastic properties of rocks saturated with heavy oil. The heavy oil is represented by a viscoelastic material, which at low frequencies and/or high temperatures behaves as a Newtonian fluid, and at high frequencies and/or low temperatures as a nearly elastic solid. The bulk and shear moduli of a porous rock saturated with such viscoelastic material are then computed using approximate extended Gassmann equations of Ciz and Shapiro by replacing the elastic moduli of the pore filling material with complex and frequency-dependent moduli of the viscoelastic pore fill. We test the proposed model by comparing its predictions with numerical simulations based on a direct finite-difference solution of equations of dynamic viscoelasticity. The simulations are performed for the reflection coefficient from an interface between a homogeneous fluid and a porous medium. The numerical tests are performed both for an idealized porous medium consisting of alternating solid and viscoelastic layers, and for a more realistic 3-D geometry of the pore space. Both sets of numerical tests show a good agreement between the predictions of the proposed viscoelastic workflow and numerical simulations for relatively high viscosities where viscoelastic effects are important. The results confirm that application of extended Gassmann equations in conjunction with the complex and frequency-dependent moduli of viscoelastic pore filling material, such as heavy oil, provides a good approximation for the elastic moduli of rocks saturated with such material. By construction, this approximation is exactly consistent with the classical Gassmann's equation for sufficiently low frequencies or high temperature when heavy oil behaves like a fluid. For higher frequencies and/or lower temperatures, the predictions are in good agreement with the direct numerical solution of equations of dynamic viscoelasticity on the microscale. This demonstrates that the proposed methodology provides realistic estimates of elastic properties of heavy oil rocks.

Macroscopic descriptions of rarefied gases from the elimination of fast variables

NASA Astrophysics Data System (ADS)

Dellar, Paul J.

2007-10-01

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

Nonlinear stability of Gardner breathers

NASA Astrophysics Data System (ADS)

Alejo, Miguel A.

2018-01-01

We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are H2 (R) stable. Through a variational approach, we characterize Gardner breathers as minimizers of a new Lyapunov functional and we study the associated spectral problem, through (i) the analysis of the spectrum of explicit linear systems (spectral stability), and (ii) controlling degenerated directions by using low regularity conservation laws.

Computational Modeling of the Dielectric Barrier Discharge (DBD) Device for Aeronautical Applications

DTIC Science & Technology

2006-06-01

electron energy equation are solved semi-implicitly in a sequential manner. Each of the governing equations is solved by casting them onto a tridiagonal ...actuator for different device configurations and operating parameters. This will provide the Air Force with a low cost, quick turn around...Atmosphere (ATM) (20:8). Initially, the applied potential difference on the electrodes must be great enough to initiate gas breakdown. While

Compressed Semi-Discrete Central-Upwind Schemes for Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Kurganov, Alexander; Levy, Doron; Petrova, Guergana

2003-01-01

We introduce a new family of Godunov-type semi-discrete central schemes for multidimensional Hamilton-Jacobi equations. These schemes are a less dissipative generalization of the central-upwind schemes that have been recently proposed in series of works. We provide the details of the new family of methods in one, two, and three space dimensions, and then verify their expected low-dissipative property in a variety of examples.

Chemical potential, Gibbs-Duhem equation and quantum gases

NASA Astrophysics Data System (ADS)

Lee, M. Howard

2017-05-01

Thermodynamic relations like the Gibbs-Duhem are valid from the lowest to the highest temperatures. But they cannot by themselves provide any specific temperature behavior of thermodynamic functions like the chemical potential. In this work, we show that if some general conditions are attached to the Gibbs-Duhem equation, it is possible to obtain the low temperature form of the chemical potential for the ideal Fermi and Bose gases very directly.

Foundations of modelling of nonequilibrium low-temperature plasmas

NASA Astrophysics Data System (ADS)

Alves, L. L.; Bogaerts, A.; Guerra, V.; Turner, M. M.

2018-02-01

This work explains the need for plasma models, introduces arguments for choosing the type of model that better fits the purpose of each study, and presents the basics of the most common nonequilibrium low-temperature plasma models and the information available from each one, along with an extensive list of references for complementary in-depth reading. The paper presents the following models, organised according to the level of multi-dimensional description of the plasma: kinetic models, based on either a statistical particle-in-cell/Monte-Carlo approach or the solution to the Boltzmann equation (in the latter case, special focus is given to the description of the electron kinetics); multi-fluid models, based on the solution to the hydrodynamic equations; global (spatially-average) models, based on the solution to the particle and energy rate-balance equations for the main plasma species, usually including a very complete reaction chemistry; mesoscopic models for plasma-surface interaction, adopting either a deterministic approach or a stochastic dynamical Monte-Carlo approach. For each plasma model, the paper puts forward the physics context, introduces the fundamental equations, presents advantages and limitations, also from a numerical perspective, and illustrates its application with some examples. Whenever pertinent, the interconnection between models is also discussed, in view of multi-scale hybrid approaches.

Numerical Analysis of a Paraffin/Metal Foam Composite for Thermal Storage

NASA Astrophysics Data System (ADS)

Di Giorgio, P.; Iasiello, M.; Viglione, A.; Mameli, M.; Filippeschi, S.; Di Marco, P.; Andreozzi, A.; Bianco, N.

2017-01-01

In the last decade, the use of Phase Change Materials (PCMs) as passive thermal energy storage has been widely studied both analytically and experimentally. Among the PCMs, paraffins show many advantages, such as having a high latent heat, a low vapour pressure, being chemically inert, stable and non-toxic. But, their thermal conductivity is very low with a high volume change during the melting process. An efficient way to increase their poor thermal conductivity is to couple them with open cells metallic foams. This paper deals with a theoretical analysis of paraffin melting process inside an aluminum foam. A mathematical model is developed by using the volume-averaged governing equations for the porous domain, made up by the PCM embedded into the metal foam. Non-Darcian and buoyancy effects are considered in the momentum equation, while the energy equations are modelled with the Local Thermal Non-Equilibrium (LTNE) approach. The PCM liquefaction is treated with the apparent heat capacity method and the governing equations are solved with a finite-element scheme by COMSOL Multiphysics®. A new method to calculate the coupling coefficients needed for the thermal model has been developed and the results obtained have been validated comparing them to experimental data in literature.

Algorithm for Stabilizing a POD-Based Dynamical System

NASA Technical Reports Server (NTRS)

Kalb, Virginia L.

2010-01-01

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

Numerical estimation of ultrasonic production of hydrogen: Effect of ideal and real gas based models.

PubMed

Kerboua, Kaouther; Hamdaoui, Oualid

2018-01-01

Based on two different assumptions regarding the equation describing the state of the gases within an acoustic cavitation bubble, this paper studies the sonochemical production of hydrogen, through two numerical models treating the evolution of a chemical mechanism within a single bubble saturated with oxygen during an oscillation cycle in water. The first approach is built on an ideal gas model, while the second one is founded on Van der Waals equation, and the main objective was to analyze the effect of the considered state equation on the ultrasonic hydrogen production retrieved by simulation under various operating conditions. The obtained results show that even when the second approach gives higher values of temperature, pressure and total free radicals production, yield of hydrogen does not follow the same trend. When comparing the results released by both models regarding hydrogen production, it was noticed that the ratio of the molar amount of hydrogen is frequency and acoustic amplitude dependent. The use of Van der Waals equation leads to higher quantities of hydrogen under low acoustic amplitude and high frequencies, while employing ideal gas law based model gains the upper hand regarding hydrogen production at low frequencies and high acoustic amplitudes. Copyright © 2017 Elsevier B.V. All rights reserved.

Reference Values of Impulse Oscillometric Lung Function Indices in Adults of Advanced Age

PubMed Central

Schulz, Holger; Flexeder, Claudia; Behr, Jürgen; Heier, Margit; Holle, Rolf; Huber, Rudolf M.; Jörres, Rudolf A.; Nowak, Dennis; Peters, Annette; Wichmann, H.-Erich; Heinrich, Joachim; Karrasch, Stefan

2013-01-01

Background Impulse oscillometry (IOS) is a non-demanding lung function test. Its diagnostic use may be particularly useful in patients of advanced age with physical or mental limitations unable to perform spirometry. Only few reference equations are available for Caucasians, none of them covering the old age. Here, we provide reference equations up to advanced age and compare them with currently available equations. Methods IOS was performed in a population-based sample of 1990 subjects, aged 45–91 years, from KORA cohorts (Augsburg, Germany). From those, 397 never-smoking, lung healthy subjects with normal spirometry were identified and sex-specific quantile regression models with age, height and body weight as predictors for respiratory system impedance, resistance, reactance, and other parameters of IOS applied. Results Women (n = 243) showed higher resistance values than men (n = 154), while reactance at low frequencies (up to 20 Hz) was lower (p<0.05). A significant age dependency was observed for the difference between resistance values at 5 Hz and 20 Hz (R5–R20), the integrated area of low-frequency reactance (AX), and resonant frequency (Fres) in both sexes whereas reactance at 5 Hz (X5) was age dependent only in females. In the healthy subjects (n = 397), mean differences between observed values and predictions for resistance (5 Hz and 20 Hz) and reactance (5 Hz) ranged between −1% and 5% when using the present model. In contrast, differences based on the currently applied equations (Vogel & Smidt 1994) ranged between −34% and 76%. Regarding our equations the indices were beyond the limits of normal in 8.1% to 18.6% of the entire KORA cohort (n = 1990), and in 0.7% to 9.4% with the currently applied equations. Conclusions Our study provides up-to-date reference equations for IOS in Caucasians aged 45 to 85 years. We suggest the use of the present equations particularly in advanced age in order to detect airway dysfunction. PMID:23691036

Integral method for the calculation of Hawking radiation in dispersive media. I. Symmetric asymptotics.

PubMed

Robertson, Scott; Leonhardt, Ulf

2014-11-01

Hawking radiation has become experimentally testable thanks to the many analog systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion and give rise to a numerically soluble and stable ordinary differential equation only if the rest-frame dispersion relation Ω^{2}(k) is a polynomial of relatively low degree. Here we present a new method for the calculation of wave scattering in a one-dimensional medium of arbitrary dispersion. It views the wave equation as an integral equation in Fourier space, which can be solved using standard and efficient numerical techniques.

The General Fishbone Like Dispersion Relation

NASA Astrophysics Data System (ADS)

Zonca, Fulvio

2015-12-01

The following sections are included: * Introduction * Motivation and outline * Fundamental equations * The collisionless gyrokinetic equation * Vorticity equation * Quasi-neutrality condition * Perpendicular Ampère's law * Studying collective modes in burning plasmas * Ideal plasma equilibrium in the low-β limit * Approximations for the energetic population * Characteristic frequencies of particle motions * Alfvén wave frequency and wavelength orderings * Applications of the general theoretical framework * The general fishbone like dispersion relation * Properties of the fishbone like dispersion relation * Derivation of the fishbone like dispersion relation * Special cases of the fishbone like dispersion relation * Toroidal Alfvén Eigenmodes (TAE) * Alfvén Cascades * Summary and discussions * Acknowledgments * References

Estimating Locations of Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model of 7-Day, 2-Year Low Flows

USGS Publications Warehouse

Wood, Molly S.; Rea, Alan; Skinner, Kenneth D.; Hortness, Jon E.

2009-01-01

Many State and Federal agencies use information regarding the locations of streams having intermittent or perennial flow when making management and regulatory decisions. For example, the application of some Idaho water quality standards depends on whether streams are intermittent. Idaho Administrative Code defines an intermittent stream as one having a 7-day, 2-year low flow (7Q2) less than 0.1 ft3/s. However, there is a general recognition that the cartographic representation of perennial/intermittent status of streams on U.S. Geological Survey (USGS) topographic maps is not as accurate or consistent as desirable from one map to another, which makes broad management and regulatory assessments difficult and inconsistent. To help resolve this problem, the USGS has developed a methodology for predicting the locations of perennial streams based on regional generalized least-squares (GLS) regression equations for Idaho streams for the 7Q2 low-flow statistic. Using these regression equations, the 7Q2 streamflow may be estimated for naturally flowing streams in most areas in Idaho. The use of these equations in conjunction with a geographic information system (GIS) technique known as weighted flow accumulation allows for an automated and continuous estimation of 7Q2 streamflow at all points along stream reaches. The USGS has developed a GIS-based map of the locations of streams in Idaho with perennial flow based on a 7Q2 of 0.1 ft3/s and a transition zone of plus or minus 1 standard error. Idaho State cooperators plan to use this information to make regulatory and water-quality management decisions. Originally, 7Q2 equations were developed for eight regions of similar hydrologic characteristics in the study area, using long-term data from 234 streamflow-gaging stations. Equations in five of the regions were revised based on spatial patterns observed in the initial perennial streams map and unrealistic behavior of the equations in extrapolation. The standard errors of prediction for the final equations ranged from a minimum of +75.0 to -42.9 percent in the central part of the study area to a maximum of +277 to -73.5 percent in the southern part of the study area. The equations are applicable only to unregulated, naturally-flowing streams and may produce unreliable results outside the range of explanatory variables used for equation development. Extrapolation outside the range of available data was necessary, however, to predict perennial flow initiation points and transition zones along stream reaches. The map of perennial streams was evaluated by comparing predicted stream classifications with four independent datasets, including field observations by other government agencies. Overall, 81 percent of the comparison data points agreed with the USGS perennial streams model. Regions with the highest number of disagreements had a high percentage of mountainous and forested area with potential mountain front recharge zones, and regions with the highest agreements had a high percentage of low gradient, low elevation area. As a whole, the USGS model predicted a higher number of perennial streams than predictions made with the independent datasets. Some disagreements were due to poor site location coordinates, timing of the comparison site visits during unusually wet or dry years, discrepancies in classification criteria, and variable ground water contributions to flow in some areas. The Idaho Department of Environmental Quality Beneficial Use Reconnaissance Program (BURP) dataset is considered the most representative dataset for comparison because it covered a range of climate conditions and the number of sites visited were consistent from year to year during the study period. Eighty-five percent of BURP comparison data points agreed with the USGS perennial streams model. Although site-specific flow data may be needed to correctly classify streams in some areas, this information rarely is available and is not always practical to o

UNVEILING THE UNIVERSALITY OF I-LOVE-Q RELATIONS

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

Sham, Y.-H.; Lin, L.-M.; Leung, P. T.

The recent discovery of the universal I-Love-Q relations connecting the moment of inertia, tidal deformability, and the spin-induced quadrupole moment of compact stars is intriguing and totally unexpected. In this paper, we provide numerical evidence showing that the universality can be attributed to the incompressible limit of the I-Love-Q relations. The fact that modern equations of state are stiff, with an effective adiabatic index larger than about two, above the nuclear density range is the key to establishing the universality for neutron stars and quark stars with typical compactness from about 0.1 to 0.3. On the other hand, the I-Love-Qmore » relations of low-mass neutron stars near the minimum mass limit depend more sensitively on the underlying equation of state because these stars are composed mainly of softer matter at low densities. However, the I-Love-Q relations for low-mass quark stars can still be represented accurately by the incompressible limit. We also study the I-Love relation connecting the moment of inertia and tidal deformability analytically in Newtonian gravity and show why the I-Love-Q relation is weakly dependent on the underlying equation of state and can be attributed to its incompressible limit.« less

Transport synthetic acceleration with opposing reflecting boundary conditions

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

Zika, M.R.; Adams, M.L.

2000-02-01

The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iteratingmore » on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.« less

A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation.

PubMed

Gumerov, Nail A; Duraiswami, Ramani

2009-01-01

The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001 less, similarkD less, similar500 are presented and shown to perform close to theoretical expectations.

SOURCELESS STARTUP. A MACHINE CODE FOR COMPUTING LOW-SOURCE REACTOR STARTUPS

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

MacMillan, D.B.

1960-06-01

>A revision to the sourceless start-up code is presented. The code solves a system of differential equations encountered in computing the probability distribution of activity at an observed power level during reactor start-up from a very low source level. (J.R.D.)

Tsallis’ quantum q-fields

NASA Astrophysics Data System (ADS)

Plastino, A.; Rocca, M. C.

2018-05-01

We generalize several well known quantum equations to a Tsallis’ q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schródinger, q-Klein-Gordon, q-Dirac, and q-Proca equations advanced in, respectively, Phys. Rev. Lett. 106, 140601 (2011), EPL 118, 61004 (2017) and references therein. We also introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and non-Abelian instances. We show how to define the q-quantum field theories corresponding to the above equations, introduce the pertinent actions, and obtain equations of motion via the minimum action principle. These q-fields are meaningful at very high energies (TeV scale) for q = 1.15, high energies (GeV scale) for q = 1.001, and low energies (MeV scale) for q = 1.000001 [Nucl. Phys. A 955 (2016) 16 and references therein]. (See the ALICE experiment at the LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields’ logarithms.

Development of a One-Equation Transition/Turbulence Model

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

EDWARDS,JACK R.; ROY,CHRISTOPHER J.; BLOTTNER,FREDERICK G.

2000-09-26

This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity - transport equation for non-turbulent fluctuation growth based on that proposed by Warren and Hassan (Journal of Aircraft, Vol. 35, No. 5) is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittence function based on the work of Dhawan and Narasimha (Journal of Fluid Mechanics, Vol. 3, No. 4). The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow overmore » a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the spatial accuracy of selected predictions is analyzed.« less

The continuous adjoint approach to the k-ε turbulence model for shape optimization and optimal active control of turbulent flows

NASA Astrophysics Data System (ADS)

Papoutsis-Kiachagias, E. M.; Zymaris, A. S.; Kavvadias, I. S.; Papadimitriou, D. I.; Giannakoglou, K. C.

2015-03-01

The continuous adjoint to the incompressible Reynolds-averaged Navier-Stokes equations coupled with the low Reynolds number Launder-Sharma k-ε turbulence model is presented. Both shape and active flow control optimization problems in fluid mechanics are considered, aiming at minimum viscous losses. In contrast to the frequently used assumption of frozen turbulence, the adjoint to the turbulence model equations together with appropriate boundary conditions are derived, discretized and solved. This is the first time that the adjoint equations to the Launder-Sharma k-ε model have been derived. Compared to the formulation that neglects turbulence variations, the impact of additional terms and equations is evaluated. Sensitivities computed using direct differentiation and/or finite differences are used for comparative purposes. To demonstrate the need for formulating and solving the adjoint to the turbulence model equations, instead of merely relying upon the 'frozen turbulence assumption', the gain in the optimization turnaround time offered by the proposed method is quantified.

On a model of electromagnetic field propagation in ferroelectric media

NASA Astrophysics Data System (ADS)

Picard, Rainer

2007-04-01

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

Coupled dynamics in gluon mass generation and the impact of the three-gluon vertex

NASA Astrophysics Data System (ADS)

Binosi, Daniele; Papavassiliou, Joannis

2018-03-01

We present a detailed study of the subtle interplay transpiring at the level of two integral equations that are instrumental for the dynamical generation of a gluon mass in pure Yang-Mills theories. The main novelty is the joint treatment of the Schwinger-Dyson equation governing the infrared behavior of the gluon propagator and of the integral equation that controls the formation of massless bound-state excitations, whose inclusion is instrumental for obtaining massive solutions from the former equation. The self-consistency of the entire approach imposes the requirement of using a single value for the gauge coupling entering in the two key equations; its fulfilment depends crucially on the details of the three-gluon vertex, which contributes to both of them, but with different weight. In particular, the characteristic suppression of this vertex at intermediate and low energies enables the convergence of the iteration procedure to a single gauge coupling, whose value is reasonably close to that extracted from related lattice simulations.

Wave theory in rotating systems: Schrödinger equations bridge the gaps between the equatorial β-plane and the spherical earth

NASA Astrophysics Data System (ADS)

Paldor, N.

2017-12-01

The concise and elegant wave theory developed on the equatorial β-plane by Matsuno (1966, M66 hereafter) is based on the formulation of a Schrödinger equation associated with the governing Linear Rotating Shallow Water Equations (LRSWE). The theory yields explicit expressions for the dispersion relations and meridional amplitude structures of all zonally propagating waves - Rossby, Inertia-Gravity, Kelvin and Yanai. In contrast, the spherical wave theory of Longuet-Higgins (1968) is a collection of asymptotic expansions in many sub-ranges e.g. large, small (and even negative) Lamb Number; high and low frequency; low-latitudes, etc. that rests upon extensive numerical solutions of several Ordinary Differential Equations. The difference between the two theories is highlighted by their lengths. The essential elements of the former planar study are completely revealed in just 3-4 pages including the derivation of explicit formulae for the phase speeds and amplitude meridional structures. In comtrast, the latter spherical theory contains 97 pages and the results of the numerical calculations are summarized in 30 pages of tables filled with numerical values and about 31 figures, each of which containing many separate curves! In my talk I will re-visit the wave problem on a sphere by developing several Schrödinger equations that approximate the governing eigenvalue equation associated with zonally propagating waves. Each of the Schrödinger equations approximates the original second order Ordinary Differential Equation in a different range of the 3 parameters: Lamb-Number, frequency and zonal wavenumber. As in M66, each of the Schrödinger equations yields explicit expressions for the dispersion relations and meridional amplitude structure of Rossby and Inertia-Gravity waves. In addition, the analysis shows that Yanai wave exists on a sphere even tough the zonal velocity is regular everywhere there (in contrast to the β-plane where the zonal velocity is singular everywhere) and that Kelvin waves do not exist as a separate mode (but the eastward propagating n=0 Inertia-Gravity is nearly non-dispersive). References Longuet-Higgins, M. S. Phil. Trans. Roy. Soc. London; 262, 511-607; 1968 Matsuno, T.; J. Met. Soc. Japan. 44(1), 25-43; 1966

Growth, Quantitative Growth Analysis, and Applications of Graphene on γ-Al2O3 catalysts

PubMed Central

Park, Jaehyun; Lee, Joohwi; Choi, Jung-Hae; Hwang, Do Kyung; Song, Yong-Won

2015-01-01

The possibilities offered by catalytic γ-Al2O3 substrates are explored, and the mechanism governing graphene formation thereon is elucidated using both numerical simulations and experiments. The growth scheme offers metal-free synthesis at low temperature, grain-size customization, large-area uniformity of electrical properties, single-step preparation of graphene/dielectric structures, and readily detachable graphene. We quantify based on thermodynamic principles the activation energies associated with graphene nucleation/growth on γ-Al2O3, verifying the low physical and chemical barriers. Importantly, we derive a universal equation governing the adsorption-based synthesis of graphene over a wide range of temperatures in both catalytic and spontaneous growth regimes. Experimental results support the equation, highlighting the catalytic function of γ-Al2O3 at low temperatures. The synthesized graphene is manually incorporated as a ‘graphene sticker’ into an ultrafast mode-locked laser. PMID:26137994

Simultaneous Observations of Lower Band Chorus Emissions at the Equator and Microburst Precipitating Electrons in the Ionosphere

NASA Astrophysics Data System (ADS)

Mozer, F. S.; Agapitov, O. V.; Blake, J. B.; Vasko, I. Y.

2018-01-01

On 11 December 2016 at 00:12:30 UT, Van Allen Probe-B, at the equator and near midnight, and AC6-B, in the ionosphere, were on magnetic field lines whose 100 km altitude foot points were separated by 600 km. Van Allen Probe-B observed a 30 s burst of lower band chorus waves (with maximum amplitudes >1 nT) at the same time that AC6-B observed intense microburst electrons in the loss cone. One second averaged variations of the chorus intensity and the microburst electron flux were well correlated. The low-altitude electron flux expected from quasi-linear diffusion of the equatorial electrons by the equatorial chorus is in excellent agreement with the observed, 1 s averaged, low-altitude electron flux. However, the large-amplitude, <0.5 s duration, low-altitude electron pulses require nonlinear processes for their explanation.

Low-momentum ghost dressing function and the gluon mass

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

Boucaud, Ph.; Leroy, J. P.; Le Yaouanc, A.

2010-09-01

We study the low-momentum ghost propagator Dyson-Schwinger equation in the Landau gauge, assuming for the truncation a constant ghost-gluon vertex, as it is extensively done, and a simple model for a massive gluon propagator. Then, regular Dyson-Schwinger equation solutions (the zero-momentum ghost dressing function not diverging) appear to emerge, and we show the ghost propagator to be described by an asymptotic expression reliable up to the order O(q{sup 2}). That expression, depending on the gluon mass and the zero-momentum Taylor-scheme effective charge, is proven to fit pretty well some low-momentum ghost propagator data [I. L. Bogolubsky, E. M. Ilgenfritz, M.more » Muller-Preussker, and A. Sternbeck, Phys. Lett. B 676, 69 (2009); Proc. Sci., LAT2007 (2007) 290] from big-volume lattice simulations where the so-called ''simulated annealing algorithm'' is applied to fix the Landau gauge.« less

The least-squares finite element method for low-mach-number compressible viscous flows

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1994-01-01

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

Particle flows to shape and voltage surface discontinuities in the electron sheath surrounding a high voltage solar array in LEO

NASA Technical Reports Server (NTRS)

Metz, Roger N.

1991-01-01

This paper discusses the numerical modeling of electron flows from the sheath surrounding high positively biased objects in LEO (Low Earth Orbit) to regions of voltage or shape discontinuity on the biased surfaces. The sheath equations are derived from the Two-fluid, Warm Plasma Model. An equipotential corner and a plane containing strips of alternating voltage bias are treated in two dimensions. A self-consistent field solution of the sheath equations is outlined and is pursued through one cycle. The electron density field is determined by numerical solution of Poisson's equation for the electrostatic potential in the sheath using the NASCAP-LEO relation between electrostatic potential and charge density. Electron flows are calculated numerically from the electron continuity equation. Magnetic field effects are not treated.

Universal features of the equation of state of solids

NASA Technical Reports Server (NTRS)

Vinet, Pascal; Rose, James H.; Ferrante, John; Smith, John R.

1989-01-01

A study of the energetics of solids leads to the conclusion that the equation of state for all classes of solids in compression can be expressed in terms of a universal function. The form of this universal function is determined by scaling experimental compression data for measured isotherms of a wide variety of solids. The equation of state is thus known (in the absence of phase transitions), if zero-pressure volume and isothermal compression and its pressure derivative are known. The discovery described in this paper has two immediate consequences: first, despite the well known differences in the microscopic energetics of the various classes of solids, there is a single equation of state for all classes in compression; and second, a new method is provided for analyzing measured isotherms and extrapolating high-pressure data from low-pressure (e.g. acoustic) data.

Equation of state of the one- and three-dimensional Bose-Bose gases

NASA Astrophysics Data System (ADS)

Chiquillo, Emerson

2018-06-01

We calculate the equation of state of Bose-Bose gases in one and three dimensions in the framework of an effective quantum field theory. The beyond-mean-field approximation at zero temperature and the one-loop finite-temperature results are obtained performing functional integration on a local effective action. The ultraviolet divergent zero-point quantum fluctuations are removed by means of dimensional regularization. We derive the nonlinear Schrödinger equation to describe one- and three-dimensional Bose-Bose mixtures and solve it analytically in the one-dimensional scenario. This equation supports self-trapped brightlike solitonic droplets and self-trapped darklike solitons. At low temperature, we also find that the pressure and the number of particles of symmetric quantum droplets have a nontrivial dependence on the chemical potential and the difference between the intra- and the interspecies coupling constants.

Loop Integrands for Scattering Amplitudes from the Riemann Sphere

NASA Astrophysics Data System (ADS)

Geyer, Yvonne; Mason, Lionel; Monteiro, Ricardo; Tourkine, Piotr

2015-09-01

The scattering equations on the Riemann sphere give rise to remarkable formulas for tree-level gauge theory and gravity amplitudes. Adamo, Casali, and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the Riemann sphere that promises to have a wide application, based on off-shell scattering equations that depend on the loop momentum. We present new formulas, checked explicitly at low points, for supergravity and super-Yang-Mills amplitudes and for n -gon integrands at one loop. Finally, we show that the off-shell scattering equations naturally extend to arbitrary loop order, and we give a proposal for the all-loop integrands for supergravity and planar super-Yang-Mills theory.

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.

Comparative study of turbulence models in predicting hypersonic inlet flows

NASA Technical Reports Server (NTRS)

Kapoor, Kamlesh; Anderson, Bernhard H.; Shaw, Robert J.

1992-01-01

A numerical study was conducted to analyze the performance of different turbulence models when applied to the hypersonic NASA P8 inlet. Computational results from the PARC2D code, which solves the full two-dimensional Reynolds-averaged Navier-Stokes equation, were compared with experimental data. The zero-equation models considered for the study were the Baldwin-Lomax model, the Thomas model, and a combination of the Baldwin-Lomax and Thomas models; the two-equation models considered were the Chien model, the Speziale model (both low Reynolds number), and the Launder and Spalding model (high Reynolds number). The Thomas model performed best among the zero-equation models, and predicted good pressure distributions. The Chien and Speziale models compared wery well with the experimental data, and performed better than the Thomas model near the walls.

Comparative study of turbulence models in predicting hypersonic inlet flows

NASA Technical Reports Server (NTRS)

Kapoor, Kamlesh; Anderson, Bernhard H.; Shaw, Robert J.

1992-01-01

A numerical study was conducted to analyze the performance of different turbulence models when applied to the hypersonic NASA P8 inlet. Computational results from the PARC2D code, which solves the full two-dimensional Reynolds-averaged Navier-Stokes equation, were compared with experimental data. The zero-equation models considered for the study were the Baldwin-Lomax model, the Thomas model, and a combination of the Baldwin-Lomax and Thomas models; the two-equation models considered were the Chien model, the Speziale model (both low Reynolds number), and the Launder and Spalding model (high Reynolds number). The Thomas model performed best among the zero-equation models, and predicted good pressure distributions. The Chien and Speziale models compared very well with the experimental data, and performed better than the Thomas model near the walls.

Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation.

PubMed

Augustin, Moritz; Ladenbauer, Josef; Baumann, Fabian; Obermayer, Klaus

2017-06-01

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models.

Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation

PubMed Central

Baumann, Fabian; Obermayer, Klaus

2017-01-01

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models. PMID:28644841

On order and chaos in the mergers of galaxies

NASA Astrophysics Data System (ADS)

Vandervoort, Peter O.

2018-03-01

This paper describes a low-dimensional model of the merger of two galaxies. The governing equations are the complete sets of moment equations of the first and second orders derived from the collisionless Boltzmann equations representing the galaxies. The moment equations reduce to an equation governing the relative motion of the galaxies, tensor virial equations, and equations governing the kinetic energy tensors. We represent the galaxies as heterogeneous ellipsoids with Gaussian stratifications of their densities, and we represent the mean stellar motions in terms of velocity fields that sustain those densities consistently with the equation of continuity. We reduce and solve the governing equations for a head-on encounter of a dwarf galaxy with a giant galaxy. That reduction includes the effect of dynamical friction on the relative motion of the galaxies. Our criterion for chaotic behaviour is sensitivity of the motion to small changes in the initial conditions. In a survey of encounters and mergers of a dwarf galaxy with a giant galaxy, chaotic behaviour arises mainly in non-linear oscillations of the dwarf galaxy. The encounter disrupts the dwarf, excites chaotic oscillations of the dwarf, or excites regular oscillations. Dynamical friction can drive a merger to completion within a Hubble time only if the dwarf is sufficiently massive. The survey of encounters and mergers is the basis for a simple model of the evolution of a `Local Group' consisting of a giant galaxy and a population of dwarf galaxies bound to the giant as satellites on radial orbits.

Estimating residual kidney function in dialysis patients without urine collection

PubMed Central

Shafi, Tariq; Michels, Wieneke M.; Levey, Andrew S.; Inker, Lesley A.; Dekker, Friedo W.; Krediet, Raymond T.; Hoekstra, Tiny; Schwartz, George J.; Eckfeldt, John H.; Coresh, Josef

2016-01-01

Residual kidney function contributes substantially to solute clearance in dialysis patients but cannot be assessed without urine collection. We used serum filtration markers to develop dialysis-specific equations to estimate urinary urea clearance without the need for urine collection. In our development cohort, we measured 24-hour urine clearances under close supervision in 44 patients and validated these equations in 826 patients from the Netherlands Cooperative Study on the Adequacy of Dialysis. For the development and validation cohorts, median urinary urea clearance was 2.6 and 2.4 mL/min, respectively. During the 24-hour visit in the development cohort, serum β-trace protein concentrations remained in steady state but concentrations of all other markers increased. In the validation cohort, bias (median measured minus estimated clearance) was low for all equations. Precision was significantly better for β-trace protein and β2-microglobulin equations and the accuracy was significantly greater for β-trace protein, β2-microglobulin and cystatin C equations, compared with the urea plus creatinine equation. Area under the receiver operator characteristic curve for detecting measured urinary urea clearance by equation-estimated urinary urea clearance (both 2 mL/min or more) were 0.821, 0.850 and 0.796 for β-trace protein, β2-microglobulin and cystatin C equations, respectively; significantly greater than the 0.663 for the urea plus creatinine equation. Thus, residual renal function can be estimated in dialysis patients without urine collections. PMID:26924062

Estimating residual kidney function in dialysis patients without urine collection.

PubMed

Shafi, Tariq; Michels, Wieneke M; Levey, Andrew S; Inker, Lesley A; Dekker, Friedo W; Krediet, Raymond T; Hoekstra, Tiny; Schwartz, George J; Eckfeldt, John H; Coresh, Josef

2016-05-01

Residual kidney function contributes substantially to solute clearance in dialysis patients but cannot be assessed without urine collection. We used serum filtration markers to develop dialysis-specific equations to estimate urinary urea clearance without the need for urine collection. In our development cohort, we measured 24-hour urine clearances under close supervision in 44 patients and validated these equations in 826 patients from the Netherlands Cooperative Study on the Adequacy of Dialysis. For the development and validation cohorts, median urinary urea clearance was 2.6 and 2.4 ml/min, respectively. During the 24-hour visit in the development cohort, serum β-trace protein concentrations remained in steady state but concentrations of all other markers increased. In the validation cohort, bias (median measured minus estimated clearance) was low for all equations. Precision was significantly better for β-trace protein and β2-microglobulin equations and the accuracy was significantly greater for β-trace protein, β2-microglobulin, and cystatin C equations, compared with the urea plus creatinine equation. Area under the receiver operator characteristic curve for detecting measured urinary urea clearance by equation-estimated urinary urea clearance (both 2 ml/min or more) were 0.821, 0.850, and 0.796 for β-trace protein, β2-microglobulin, and cystatin C equations, respectively; significantly greater than the 0.663 for the urea plus creatinine equation. Thus, residual renal function can be estimated in dialysis patients without urine collections. Copyright © 2016 International Society of Nephrology. Published by Elsevier Inc. All rights reserved.

A family of conjugate gradient methods for large-scale nonlinear equations.

PubMed

Feng, Dexiang; Sun, Min; Wang, Xueyong

2017-01-01

In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

Holographic dark energy with varying gravitational constant in Hořava-Lifshitz cosmology

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

Setare, M.R.; Jamil, Mubasher, E-mail: rezakord@ipm.ir, E-mail: mjamil@camp.nust.edu.pk

2010-02-01

We investigate the holographic dark energy scenario with a varying gravitational constant in a flat background in the context of Hořava-Lifshitz gravity. We extract the exact differential equation determining the evolution of the dark energy density parameter, which includes G variation term. Also we discuss a cosmological implication of our work by evaluating the dark energy equation of state for low redshifts containing varying G corrections.

Fast simulation techniques for switching converters

NASA Technical Reports Server (NTRS)

King, Roger J.

1987-01-01

Techniques for simulating a switching converter are examined. The state equations for the equivalent circuits, which represent the switching converter, are presented and explained. The uses of the Newton-Raphson iteration, low ripple approximation, half-cycle symmetry, and discrete time equations to compute the interval durations are described. An example is presented in which these methods are illustrated by applying them to a parallel-loaded resonant inverter with three equivalent circuits for its continuous mode of operation.

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

ERIC Educational Resources Information Center

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

2012-01-01

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

Theory of biaxial graded-index optical fiber. M.S. Thesis

NASA Technical Reports Server (NTRS)

Kawalko, Stephen F.

1990-01-01

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

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.

Model reduction for stochastic chemical systems with abundant species.

PubMed

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2015-12-07

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. We first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently, we prove that, in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equation which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore, we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.

Computation of Separated and Unsteady Flows with One- and Two-Equation Turbulence Models

NASA Technical Reports Server (NTRS)

Ekaterinaris, John A.; Menter, Florian R.

1994-01-01

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. The two-equation turbulence models are discretized in space with an upwind-biased, second order accurate total variation diminishing scheme. One and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading edge and where natural transition was allowed to occur naturally are considered. The more recently developed field-equation turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are obtained. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading edge transitional flow region in order to capture the correct physical mechanism that leads to dynamic stall.

Constraining the equation of state of neutron stars from binary mergers.

PubMed

Takami, Kentaro; Rezzolla, Luciano; Baiotti, Luca

2014-08-29

Determining the equation of state of matter at nuclear density and hence the structure of neutron stars has been a riddle for decades. We show how the imminent detection of gravitational waves from merging neutron star binaries can be used to solve this riddle. Using a large number of accurate numerical-relativity simulations of binaries with nuclear equations of state, we find that the postmerger emission is characterized by two distinct and robust spectral features. While the high-frequency peak has already been associated with the oscillations of the hypermassive neutron star produced by the merger and depends on the equation of state, a new correlation emerges between the low-frequency peak, related to the merger process, and the total compactness of the stars in the binary. More importantly, such a correlation is essentially universal, thus providing a powerful tool to set tight constraints on the equation of state. If the mass of the binary is known from the inspiral signal, the combined use of the two frequency peaks sets four simultaneous constraints to be satisfied. Ideally, even a single detection would be sufficient to select one equation of state over the others. We test our approach with simulated data and verify it works well for all the equations of state considered.

Evaluation of Enthalpy Diagrams for NH3-H2O Absorption Refrigerator

NASA Astrophysics Data System (ADS)

Takei, Toshitaka; Saito, Kiyoshi; Kawai, Sunao

The protection of environment is becoming a grave problem nowadays and an absorption refrigerator, which does not use fleon as a refrigerant, is acquiring a close attention. Among the absorption refrigerators, a number of ammonia-water absorption refrigerators are being used in realm such as refrigeration and ice accumulation, since this type of refrigerator can produce below zero degree products. It is essential to conduct an investigation on the characteristics of ammonia-water absorption refrigerator in detail by means of computer simulation in order to realize low cost, highly efficient operation. Unfortunately, there have been number of problems in order to conduct computer simulations. Firstly, Merkel's achievements of enthalpy diagram does not give the relational equations. And secondly, although relational equation are being proposed by Ziegler, simpler equations that can be applied to computer simulation are yet to be proposed. In this research, simper equations based on Ziegler's equations have been derived to make computer simulation concerning the performance of ammonia-water absorption refrigerator possible-Both results of computer simulations using simple equations and Merkel's enthalpy diagram respectively, have been compared with the actual experimental data of one staged ammonia-water absorption refrigerator. Consequently, it is clarified that the results from Ziegler's equations agree with experimental data better than those from Merkel's enthalpy diagram.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

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

NASA Astrophysics Data System (ADS)

Umut Caglar, Mehmet; Pal, Ranadip

2010-10-01

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

Explicit Low-Thrust Guidance for Reference Orbit Targeting

NASA Technical Reports Server (NTRS)

Lam, Try; Udwadia, Firdaus E.

2013-01-01

The problem of a low-thrust spacecraft controlled to a reference orbit is addressed in this paper. A simple and explicit low-thrust guidance scheme with constrained thrust magnitude is developed by combining the fundamental equations of motion for constrained systems from analytical dynamics with a Lyapunov-based method. Examples are given for a spacecraft controlled to a reference trajectory in the circular restricted three body problem.

Persistent fluctuations in synchronization rate in globally coupled oscillators with periodic external forcing

NASA Astrophysics Data System (ADS)

Atsumi, Yu; Nakao, Hiroya

2012-05-01

A system of phase oscillators with repulsive global coupling and periodic external forcing undergoing asynchronous rotation is considered. The synchronization rate of the system can exhibit persistent fluctuations depending on parameters and initial phase distributions, and the amplitude of the fluctuations scales with the system size for uniformly random initial phase distributions. Using the Watanabe-Strogatz transformation that reduces the original system to low-dimensional macroscopic equations, we show that the fluctuations are collective dynamics of the system corresponding to low-dimensional trajectories of the reduced equations. It is argued that the amplitude of the fluctuations is determined by the inhomogeneity of the initial phase distribution, resulting in system-size scaling for the random case.

A low-complexity Reed-Solomon decoder using new key equation solver

NASA Astrophysics Data System (ADS)

Xie, Jun; Yuan, Songxin; Tu, Xiaodong; Zhang, Chongfu

2006-09-01

This paper presents a low-complexity parallel Reed-Solomon (RS) (255,239) decoder architecture using a novel pipelined variable stages recursive Modified Euclidean (ME) algorithm for optical communication. The pipelined four-parallel syndrome generator is proposed. The time multiplexing and resource sharing schemes are used in the novel recursive ME algorithm to reduce the logic gate count. The new key equation solver can be shared by two decoder macro. A new Chien search cell which doesn't need initialization is proposed in the paper. The proposed decoder can be used for 2.5Gb/s data rates device. The decoder is implemented in Altera' Stratixll device. The resource utilization is reduced about 40% comparing to the conventional method.

Low-rank approximation in the numerical modeling of the Farley-Buneman instability in ionospheric plasma

NASA Astrophysics Data System (ADS)

Dolgov, S. V.; Smirnov, A. P.; Tyrtyshnikov, E. E.

2014-04-01

We consider numerical modeling of the Farley-Buneman instability in the Earth's ionosphere plasma. The ion behavior is governed by the kinetic Vlasov equation with the BGK collisional term in the four-dimensional phase space, and since the finite difference discretization on a tensor product grid is used, this equation becomes the most computationally challenging part of the scheme. To relax the complexity and memory consumption, an adaptive model reduction using the low-rank separation of variables, namely the Tensor Train format, is employed. The approach was verified via a prototype MATLAB implementation. Numerical experiments demonstrate the possibility of efficient separation of space and velocity variables, resulting in the solution storage reduction by a factor of order tens.

Analysis for predicting adiabatic wall temperatures with single hole coolant injection into a low speed crossflow

NASA Astrophysics Data System (ADS)

Wang, C. R.; Papell, S. S.; Graham, R. W.

Assuming the local adiabatic wall temperature equals the local total temperature in a low speed coolant mixing layer, integral conservation equations with and without the boundary layer effects are formulated for the mixing layer downstream of a single coolant injection hole oriented at a 30 degree angle to the crossflow. These equations are solved numerically to determine the center line local adiabatic wall temperature and the effective coolant coverage area. Comparison of the numerical results with an existing film cooling experiment indicates that the present analysis permits a simplified but reasonably accurate prediction of the centerline effectiveness and coolant coverage area downstream of a single hole crossflow streamwise injection at 30 degree inclination angle.

Analysis for predicting adiabatic wall temperatures with single hole coolant injection into a low speed crossflow

NASA Technical Reports Server (NTRS)

Wang, C. R.; Papell, S. S.; Graham, R. W.

1981-01-01

Assuming the local adiabatic wall temperature equals the local total temperature in a low speed coolant mixing layer, integral conservation equations with and without the boundary layer effects are formulated for the mixing layer downstream of a single coolant injection hole oriented at a 30 degree angle to the crossflow. These equations are solved numerically to determine the center line local adiabatic wall temperature and the effective coolant coverage area. Comparison of the numerical results with an existing film cooling experiment indicates that the present analysis permits a simplified but reasonably accurate prediction of the centerline effectiveness and coolant coverage area downstream of a single hole crossflow streamwise injection at 30 degree inclination angle.

Analysis for predicting adiabatic wall temperatures with single hole coolant injection into a low speed crossflow

NASA Astrophysics Data System (ADS)

Wang, C. R.; Papell, S. S.; Graham, R. W.

1981-03-01

Assuming the local adiabatic wall temperature equals the local total temperature in a low speed coolant mixing layer, integral conservation equations with and without the boundary layer effects are formulated for the mixing layer downstream of a single coolant injection hole oriented at a 30 degree angle to the crossflow. These equations are solved numerically to determine the center-line local adiabatic wall temperature and the effective coolant coverage area. Comparison of the numerical results with an existing film cooling experiment indicates that the present analysis permits a simplified but reasonably accurate prediction of the centerline effectiveness and coolant coverage area downstream of a single hole crossflow streamwise injection at 30-deg inclination angle.

Analysis for predicting adiabatic wall temperatures with single hole coolant injection into a low speed crossflow

NASA Technical Reports Server (NTRS)

Wang, C. R.; Papell, S. S.; Graham, R. W.

1981-01-01

Assuming the local adiabatic wall temperature equals the local total temperature in a low speed coolant mixing layer, integral conservation equations with and without the boundary layer effects are formulated for the mixing layer downstream of a single coolant injection hole oriented at a 30 degree angle to the crossflow. These equations are solved numerically to determine the center-line local adiabatic wall temperature and the effective coolant coverage area. Comparison of the numerical results with an existing film cooling experiment indicates that the present analysis permits a simplified but reasonably accurate prediction of the centerline effectiveness and coolant coverage area downstream of a single hole crossflow streamwise injection at 30-deg inclination angle.

A guidance and navigation system for continuous low-thrust vehicles. M.S. Thesis

NASA Technical Reports Server (NTRS)

Jack-Chingtse, C.

1973-01-01

A midcourse guidance and navigation system for continuous low thrust vehicles was developed. The equinoctial elements are the state variables. Uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time trajectory is defined; equations of motion and measurements are linearized about this trajectory. An exponential cost criterion is constructed and a linear feedback quidance law is derived. An extended Kalman filter is used for state estimation. A short mission using this system is simulated. It is indicated that this system is efficient for short missions, but longer missions require accurate trajectory and ground based measurements.

Tray estimates for low reflux

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

Barna, B.A.; Ginn, R.F.

1985-05-01

In computer programs which perform shortcut calculations for multicomponent distillation, the Gilliland correlation continues to be used even though errors of up to 60% (compared with rigorous plate-to-plate calculations) were shown by Erbar and Maddox. Average absolute differences were approximately 30% for Gilliland's correlation versus 4% for the Erbar-Maddox method. The reason the Gilliland correlation continues to be used appears to be due to the availability of an equation by Eduljee which facilitates the correlation's use in computer program. A new equation is presented in this paper that represents the Erbar-Maddox correlation of trays with reflux for multicomponent distillation. Atmore » low reflux ratios, results show more trays are needed than would be estimated by Gilliland's method.« less

The acoustic power of a vibrating clamped circular plate revisited in the wide low frequency range using expansion into the radial polynomials.

PubMed

Rdzanek, Wojciech P

2016-06-01

This study deals with the classical problem of sound radiation of an excited clamped circular plate embedded into a flat rigid baffle. The system of the two coupled differential equations is solved, one for the excited and damped vibrations of the plate and the other one-the Helmholtz equation. An approach using the expansion into radial polynomials leads to results for the modal impedance coefficients useful for a comprehensive numerical analysis of sound radiation. The results obtained are accurate and efficient in a wide low frequency range and can easily be adopted for a simply supported circular plate. The fluid loading is included providing accurate results in resonance.

Evaluation of a Drag-Free Control Concept for Missions in Low Earth Orbit

NASA Technical Reports Server (NTRS)

Fleck, Melissa E.; Starin, Scott R.

2003-01-01

Atmospheric drag causes the greatest uncertainty in the equations of motion for spacecraft in Low Earth Orbit (LEO). If atmospheric drag eflects can be continuously and autonomously counteracted through the use of a drag-fee control system, drag may essentially be eliminated from the equations of motion for the spacecraft. The main perturbations on the spacecraft will then be those due to the gravitational field, which are much more easily predicted Through dynamical analysis and numerical simulation, this paper presents some potential costs and benefits associated with the fuel used during continuous drag compensation. In light of this cost-benefit analysis, simulation results are used to validate the concept of drag-free control for LEO spacecraft missions having certain characteristics.

The nucleon as a test case to calculate vector-isovector form factors at low energies

NASA Astrophysics Data System (ADS)

Leupold, Stefan

2018-01-01

Extending a recent suggestion for hyperon form factors to the nucleon case, dispersion theory is used to relate the low-energy vector-isovector form factors of the nucleon to the pion vector form factor. The additionally required input, i.e. the pion-nucleon scattering amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the nucleons and optionally the Delta baryons. Two methods to include pion rescattering are compared: a) solving the Muskhelishvili-Omnès (MO) equation and b) using an N/D approach. It turns out that the results differ strongly from each other. Furthermore the results are compared to a fully dispersive calculation of the (subthreshold) pion-nucleon amplitudes based on Roy-Steiner (RS) equations. In full agreement with the findings from the hyperon sector it turns out that the inclusion of Delta baryons is not an option but a necessity to obtain reasonable results. The magnetic isovector form factor depends strongly on a low-energy constant of the NLO Lagrangian. If it is adjusted such that the corresponding magnetic radius is reproduced, then the results for the corresponding pion-nucleon scattering amplitude (based on the MO equation) agree very well with the RS results. Also in the electric sector the Delta degrees of freedom are needed to obtain the correct order of magnitude for the isovector charge and the corresponding electric radius. Yet quantitative agreement is not achieved. If the subtraction constant that appears in the solution of the MO equation is not taken from nucleon+Delta chiral perturbation theory but adjusted such that the electric radius is reproduced, then one obtains also in this sector a pion-nucleon scattering amplitude that agrees well with the RS results.

Study on low intensity aeration oxygenation model and optimization for shallow water

NASA Astrophysics Data System (ADS)

Chen, Xiao; Ding, Zhibin; Ding, Jian; Wang, Yi

2018-02-01

Aeration/oxygenation is an effective measure to improve self-purification capacity in shallow water treatment while high energy consumption, high noise and expensive management refrain the development and the application of this process. Based on two-film theory, the theoretical model of the three-dimensional partial differential equation of aeration in shallow water is established. In order to simplify the equation, the basic assumptions of gas-liquid mass transfer in vertical direction and concentration diffusion in horizontal direction are proposed based on engineering practice and are tested by the simulation results of gas holdup which are obtained by simulating the gas-liquid two-phase flow in aeration tank under low-intensity condition. Based on the basic assumptions and the theory of shallow permeability, the model of three-dimensional partial differential equations is simplified and the calculation model of low-intensity aeration oxygenation is obtained. The model is verified through comparing the aeration experiment. Conclusions as follows: (1)The calculation model of gas-liquid mass transfer in vertical direction and concentration diffusion in horizontal direction can reflect the process of aeration well; (2) Under low-intensity conditions, the long-term aeration and oxygenation is theoretically feasible to enhance the self-purification capacity of water bodies; (3) In the case of the same total aeration intensity, the effect of multipoint distributed aeration on the diffusion of oxygen concentration in the horizontal direction is obvious; (4) In the shallow water treatment, reducing the volume of aeration equipment with the methods of miniaturization, array, low-intensity, mobilization to overcome the high energy consumption, large size, noise and other problems can provide a good reference.

Linear analysis of auto-organization in Hebbian neural networks.

PubMed

Carlos Letelier, J; Mpodozis, J

1995-01-01

The self-organization of neurotopies where neural connections follow Hebbian dynamics is framed in terms of linear operator theory. A general and exact equation describing the time evolution of the overall synaptic strength connecting two neural laminae is derived. This linear matricial equation, which is similar to the equations used to describe oscillating systems in physics, is modified by the introduction of non-linear terms, in order to capture self-organizing (or auto-organizing) processes. The behavior of a simple and small system, that contains a non-linearity that mimics a metabolic constraint, is analyzed by computer simulations. The emergence of a simple "order" (or degree of organization) in this low-dimensionality model system is discussed.

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 3: Computer program manual

NASA Technical Reports Server (NTRS)

Schneider, J.; Boccio, J.

1972-01-01

A computer program is described capable of determining the properties of a compressible turbulent boundary layer with pressure gradient and heat transfer. The program treats the two-dimensional problem assuming perfect gas and Crocco integral energy solution. A compressibility transformation is applied to the equation for the conservation of mass and momentum, which relates this flow to a low speed constant property flow with simultaneous mass transfer and pressure gradient. The resulting system of describing equations consists of eight ordinary differential equations which are solved numerically. For Part 1, see N72-12226; for Part 2, see N72-15264.

Thermodynamically constrained correction to ab initio equations of state

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

French, Martin; Mattsson, Thomas R.

2014-07-07

We show how equations of state generated by density functional theory methods can be augmented to match experimental data without distorting the correct behavior in the high- and low-density limits. The technique is thermodynamically consistent and relies on knowledge of the density and bulk modulus at a reference state and an estimation of the critical density of the liquid phase. We apply the method to four materials representing different classes of solids: carbon, molybdenum, lithium, and lithium fluoride. It is demonstrated that the corrected equations of state for both the liquid and solid phases show a significantly reduced dependence ofmore » the exchange-correlation functional used.« less

Possible connection between the location of the cutoff in the cosmic microwave background spectrum and the equation of state of dark energy.

PubMed

Enqvist, Kari; Sloth, Martin S

2004-11-26

We investigate a possible connection between the suppression of the power at low multipoles in the cosmic microwave background (CMB) spectrum and the late time acceleration. We show that, assuming a cosmic IR/UV duality between the UV cutoff and a global infrared cutoff given by the size of the future event horizon, the equation of state of the dark energy can be related to the apparent cutoff in the CMB spectrum. The present limits on the equation of state of dark energy are shown to imply an IR cutoff in the CMB multipole interval of 9>l>8.5.

Effectiveness of the New Hampshire stream-gaging network in providing regional streamflow information

USGS Publications Warehouse

Olson, Scott A.

2003-01-01

The stream-gaging network in New Hampshire was analyzed for its effectiveness in providing regional information on peak-flood flow, mean-flow, and low-flow frequency. The data available for analysis were from stream-gaging stations in New Hampshire and selected stations in adjacent States. The principles of generalized-least-squares regression analysis were applied to develop regional regression equations that relate streamflow-frequency characteristics to watershed characteristics. Regression equations were developed for (1) the instantaneous peak flow with a 100-year recurrence interval, (2) the mean-annual flow, and (3) the 7-day, 10-year low flow. Active and discontinued stream-gaging stations with 10 or more years of flow data were used to develop the regression equations. Each stream-gaging station in the network was evaluated and ranked on the basis of how much the data from that station contributed to the cost-weighted sampling-error component of the regression equation. The potential effect of data from proposed and new stream-gaging stations on the sampling error also was evaluated. The stream-gaging network was evaluated for conditions in water year 2000 and for estimated conditions under various network strategies if an additional 5 years and 20 years of streamflow data were collected. The effectiveness of the stream-gaging network in providing regional streamflow information could be improved for all three flow characteristics with the collection of additional flow data, both temporally and spatially. With additional years of data collection, the greatest reduction in the average sampling error of the regional regression equations was found for the peak- and low-flow characteristics. In general, additional data collection at stream-gaging stations with unregulated flow, relatively short-term record (less than 20 years), and drainage areas smaller than 45 square miles contributed the largest cost-weighted reduction to the average sampling error of the regional estimating equations. The results of the network analyses can be used to prioritize the continued operation of active stations, the reactivation of discontinued stations, or the activation of new stations to maximize the regional information content provided by the stream-gaging network. Final decisions regarding altering the New Hampshire stream-gaging network would require the consideration of the many uses of the streamflow data serving local, State, and Federal interests.

A numerical solution of the Navier-Stokes equations for supercritical fluid thermodynamic analysis

NASA Technical Reports Server (NTRS)

Heinmiller, P. J.

1971-01-01

An explicit numerical solution of the compressible Navier-Stokes equations is applied to the thermodynamic analysis of supercritical oxygen in the Apollo cryogenic storage system. The wave character is retained in the conservation equations which are written in the basic fluid variables for a two-dimensional Cartesian coordinate system. Control-volume cells are employed to simplify imposition of boundary conditions and to ensure strict observance of local and global conservation principles. Non-linear real-gas thermodynamic properties responsible for the pressure collapse phenomonon in supercritical fluids are represented by tabular and empirical functions relating pressure and temperature to density and internal energy. Wall boundary conditions are adjusted at one cell face to emit a prescribed mass flowrate. Scaling principles are invoked to achieve acceptable computer execution times for very low Mach number convection problems. Detailed simulations of thermal stratification and fluid mixing occurring under low acceleration in the Apollo 12 supercritical oxygen tank are presented which model the pressure decay associated with de-stratification induced by an ordinary vehicle maneuver and heater cycle operation.

On Richardson extrapolation for low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes

NASA Astrophysics Data System (ADS)

Havasi, Ágnes; Kazemi, Ehsan

2018-04-01

In the modeling of wave propagation phenomena it is necessary to use time integration methods which are not only sufficiently accurate, but also properly describe the amplitude and phase of the propagating waves. It is not clear if amending the developed schemes by extrapolation methods to obtain a high order of accuracy preserves the qualitative properties of these schemes in the perspective of dissipation, dispersion and stability analysis. It is illustrated that the combination of various optimized schemes with Richardson extrapolation is not optimal for minimal dissipation and dispersion errors. Optimized third-order and fourth-order methods are obtained, and it is shown that the proposed methods combined with Richardson extrapolation result in fourth and fifth orders of accuracy correspondingly, while preserving optimality and stability. The numerical applications include the linear wave equation, a stiff system of reaction-diffusion equations and the nonlinear Euler equations with oscillatory initial conditions. It is demonstrated that the extrapolated third-order scheme outperforms the recently developed fourth-order diagonally implicit Runge-Kutta scheme in terms of accuracy and stability.

Multigroup Radiation-Hydrodynamics with a High-Order, Low-Order Method

DOE PAGES

Wollaber, Allan Benton; Park, HyeongKae; Lowrie, Robert Byron; ...

2016-12-09

Recent efforts at Los Alamos National Laboratory to develop a moment-based, scale-bridging [or high-order (HO)–low-order (LO)] algorithm for solving large varieties of the transport (kinetic) systems have shown promising results. A part of our ongoing effort is incorporating this methodology into the framework of the Eulerian Applications Project to achieve algorithmic acceleration of radiationhydrodynamics simulations in production software. By starting from the thermal radiative transfer equations with a simple material-motion correction, we derive a discretely consistent energy balance equation (LO equation). We demonstrate that the corresponding LO system for the Monte Carlo HO solver is closely related to the originalmore » LO system without material-motion corrections. We test the implementation on a radiative shock problem and show consistency between the energy densities and temperatures in the HO and LO solutions as well as agreement with the semianalytic solution. We also test the approach on a more challenging two-dimensional problem and demonstrate accuracy enhancements and algorithmic speedups. This paper extends a recent conference paper by including multigroup effects.« less

Parametrically excited helicopter ground resonance dynamics with high blade asymmetries

NASA Astrophysics Data System (ADS)

Sanches, L.; Michon, G.; Berlioz, A.; Alazard, D.

2012-07-01

The present work is aimed at verifying the influence of high asymmetries in the variation of in-plane lead-lag stiffness of one blade on the ground resonance phenomenon in helicopters. The periodical equations of motions are analyzed by using Floquet's Theory (FM) and the boundaries of instabilities predicted. The stability chart obtained as a function of asymmetry parameters and rotor speed reveals a complex evolution of critical zones and the existence of bifurcation points at low rotor speed values. Additionally, it is known that when treated as parametric excitations; periodic terms may cause parametric resonances in dynamic systems, some of which can become unstable. Therefore, the helicopter is later considered as a parametrically excited system and the equations are treated analytically by applying the Method of Multiple Scales (MMS). A stability analysis is used to verify the existence of unstable parametric resonances with first and second-order sets of equations. The results are compared and validated with those obtained by Floquet's Theory. Moreover, an explanation is given for the presence of unstable motion at low rotor speeds due to parametric instabilities of the second order.

Formulation of steam-methane reforming rate in Ni-YSZ porous anode of solid oxide fuel cells

NASA Astrophysics Data System (ADS)

Sugihara, Shinichi; Kawamura, Yusuke; Iwai, Hiroshi

2018-02-01

The steam-methane reforming reaction on a Ni-YSZ (yttria-stabilized zirconia) cermet was experimentally investigated under atmospheric pressure and in the temperature range from 650 to 750 °C. We examined the effects of the partial pressures of methane and steam in the supply gas on the reaction rate. The experiments were conducted with a low Ni contained Ni-YSZ cermet sheet of thickness 0.1 mm. Its porous microstructure and accompanied parameters were quantified using the FIB-SEM (focused ion beam scanning electron microscopy) technique. A power-law-type rate equation incorporating the reaction-rate-limiting conditions was obtained on the basis of the unit surface area of the Ni-pore contact surface in the cermet. The kinetics indicated a strong positive dependence on the methane partial pressure and a negative dependence on the steam partial pressure. The obtained rate equation successfully reproduced the experimental results for Ni-YSZ samples having different microstructures in the case of low methane consumption. The equation also reproduced the limiting-reaction behaviours at different temperatures.

Reference correlation of the thermal conductivity of carbon dioxide from the triple point to 1100 K and up to 200 MPa

DOE PAGES

Huber, M. L.; Sykioti, E. A.; Assael, M. J.; ...

2016-02-25

This article contains new, representative reference equations for the thermal conductivity of carbon dioxide. The equations are based in part upon a body of experimental data that has been critically assessed for internal consistency and for agreement with theory whenever possible. In the case of the dilute-gas thermal conductivity, we incorporated recent theoretical calculations to extend the temperature range of the experimental data. Moreover, in the critical region, the experimentally observed enhancement of the thermal conductivity is well represented by theoretically based equations containing just one adjustable parameter. The correlation is applicable for the temperature range from the triple pointmore » to 1100 K and pressures up to 200 MPa. Lastly, the overall uncertainty (at the 95% confidence level) of the proposed correlation varies depending on the state point from a low of 1% at very low pressures below 0.1 MPa between 300 and 700 K, to 5% at the higher pressures of the range of validity.« less

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

Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used tomore » compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.« less

Inverse scattering for an exterior Dirichlet program

NASA Technical Reports Server (NTRS)

Hariharan, S. I.

1981-01-01

Scattering due to a metallic cylinder which is in the field of a wire carrying a periodic current is considered. The location and shape of the cylinder is obtained with a far field measurement in between the wire and the cylinder. The same analysis is applicable in acoustics in the situation that the cylinder is a soft wall body and the wire is a line source. The associated direct problem in this situation is an exterior Dirichlet problem for the Helmholtz equation in two dimensions. An improved low frequency estimate for the solution of this problem using integral equation methods is presented. The far field measurements are related to the solutions of boundary integral equations in the low frequency situation. These solutions are expressed in terms of mapping function which maps the exterior of the unknown curve onto the exterior of a unit disk. The coefficients of the Laurent expansion of the conformal transformations are related to the far field coefficients. The first far field coefficient leads to the calculation of the distance between the source and the cylinder.

Modelling mass transfer during venting/soil vapour extraction: Non-aqueous phase liquid/gas mass transfer coefficient estimation

NASA Astrophysics Data System (ADS)

Esrael, D.; Kacem, M.; Benadda, B.

2017-07-01

We investigate how the simulation of the venting/soil vapour extraction (SVE) process is affected by the mass transfer coefficient, using a model comprising five partial differential equations describing gas flow and mass conservation of phases and including an expression accounting for soil saturation conditions. In doing so, we test five previously reported quations for estimating the non-aqueous phase liquid (NAPL)/gas initial mass transfer coefficient and evaluate an expression that uses a reference NAPL saturation. Four venting/SVE experiments utilizing a sand column are performed with dry and non-saturated sand at low and high flow rates, and the obtained experimental results are subsequently simulated, revealing that hydrodynamic dispersion cannot be neglected in the estimation of the mass transfer coefficient, particularly in the case of low velocities. Among the tested models, only the analytical solution of a convection-dispersion equation and the equation proposed herein are suitable for correctly modelling the experimental results, with the developed model representing the best choice for correctly simulating the experimental results and the tailing part of the extracted gas concentration curve.

On the r-mode spectrum of relativistic stars in the low-frequency approximation

NASA Astrophysics Data System (ADS)

Ruoff, Johannes; Kokkotas, Kostas D.

2001-12-01

The axial modes for non-barotropic relativistic rotating neutron stars with uniform angular velocity are studied, using the slow-rotation formalism together with the low-frequency approximation, first investigated by Kojima. The time-independent form of the equations leads to a singular eigenvalue problem, which admits a continuous spectrum. We show that for l=2, it is nevertheless also possible to find discrete mode solutions (the r modes). However, under certain conditions related to the equation of state and the compactness of the stellar model, the eigenfrequency lies inside the continuous band and the associated velocity perturbation is divergent; hence these solutions have to be discarded as being unphysical. We corroborate our results by explicitly integrating the time-dependent equations. For stellar models admitting a physical r-mode solution, it can indeed be excited by arbitrary initial data. For models admitting only an unphysical mode solution, the evolutions do not show any tendency to oscillate with the respective frequency. For higher values of l it seems that in certain cases there are no mode solutions at all.

On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas

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

Nariyuki, Y.

A multi-dimensional nonlinear evolution equation for Alfvén waves in weakly-expanding solar wind plasmas is derived by using the reductive perturbation method. The expansion of solar wind plasma parcels is modeled by an expanding box model, which includes the accelerating expansion. It is shown that the resultant equation agrees with the Wentzel-Kramers-Brillouin prediction of the low-frequency Alfvén waves in the linear limit. In the cold and one-dimensional limit, a modified derivative nonlinear Schrodinger equation is obtained. Direct numerical simulations are carried out to discuss the effect of the expansion on the modulational instability of monochromatic Alfvén waves and the propagation ofmore » Alfvén solitons. By using the instantaneous frequency, it is quantitatively shown that as far as the expansion rate is much smaller than wave frequencies, effects of the expansion are almost adiabatic. It is also confirmed that while shapes of Alfvén solitons temporally change due to the expansion, some of them can stably propagate after their collision in weakly-expanding plasmas.« less

Dual Dynamically Orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions

NASA Astrophysics Data System (ADS)

Musharbash, Eleonora; Nobile, Fabio

2018-02-01

In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational principle can be set in the constrained manifold of all S rank random fields with a prescribed value on the boundary, expressed in low rank format, with rank smaller then S. We characterize the tangent space to the constrained manifold by means of a Dual Dynamically Orthogonal (Dual DO) formulation, in which the stochastic modes are kept orthonormal and the deterministic modes satisfy suitable boundary conditions, consistent with the original problem. The Dual DO formulation is also convenient to include the incompressibility constraint, when dealing with incompressible Navier Stokes equations. We show the performance of the proposed Dual DO approximation on two numerical test cases: the classical benchmark of a laminar flow around a cylinder with random inflow velocity, and a biomedical application for simulating blood flow in realistic carotid artery reconstructed from MRI data with random inflow conditions coming from Doppler measurements.

NHANES III equations enhance early detection and mortality prediction of bronchiolitis obliterans syndrome after hematopoietic SCT

PubMed Central

Williams, KM; Hnatiuk, O; Mitchell, SA; Baird, K; Gadalla, SM; Steinberg, SM; Shelhamer, J; Carpenter, A; Avila, D; Taylor, T; Grkovic, L; Pulanic, D; Comis, LE; Blacklock-Schuver, B; Gress, RE; Pavletic, SZ

2017-01-01

Bronchiolitis obliterans syndrome (BOS) is a serious complication of chronic GVHD (cGVHD) following HSCT (hematopoietic SCT). The clinical diagnosis of BOS is based on pulmonary function test (PFT) abnormalities including: FEV1<75% predicted and obstructive FEV1/VC ratio, calculated using reference equations. We sought to determine if the frequency of clinical diagnoses and severity of BOS would be altered by using the recommended NHANES III vs older equations (Morris/Goldman/Bates, MGB) in 166 cGVHD patients, median age 48 (range: 12–67). We found that NHANES III equations significantly increased the prevalence of BOS, with an additional 11% (18/166) meeting diagnostic criteria by revealing low FEV1 (<75%) (P<0.0001), and six additional patients by obstructive ratio (vs MBG). Collectively, this led to an increase of BOS incidence from 17 (29/166) to 29% (41/166). For patients with severe BOS, (FEV1<35%), NHANES III equations correctly predicted death 71.4% vs 50% using MGB. In conclusion, the use of NHANES III equations markedly increases the proportion of cases meeting diagnostic criteria for BOS and improves prediction of survival. PMID:24419526

Development of standard weight equations for Caribbean and Gulf of Mexico amphidromous fishes

USGS Publications Warehouse

Cooney, Patrick B.; Kwak, Thomas J.

2010-01-01

We collected and compiled length and weight information from four countries and one commonwealth to develop standard weight (Ws) equations for three amphidromous fish species native to the Caribbean and Gulf of Mexico regions: mountain mullet Agonostomus monticola (N = 9,768 individuals, 52 populations), river goby Awaous banana (N = 1,847 individuals, 62 populations), and bigmouth sleeper Gobiomorus dormitor (N = 2,983 individuals, 53 populations). Linear and quadratic Ws equations for three quartiles (25%, median, 75%) are presented for these three species. The length-weight relationship from eight lentic bigmouth sleeper populations was significantly different from that of lotic populations, reflecting higher weights of juvenile fish (< 70 mm total length) in lentic environments. Thus, independent W(s) equations were developed for lotic populations of bigmouth sleepers. W(s) equations were not developed from lentic bigmouth sleeper populations alone due to the low number of applicable populations caused by life history constraints; the equation from combined lentic and lotic populations is suggested for application to lentic bigmouth sleeper populations. These morphometric relationships for amphidromous fishes may improve the ability to assess existing and potential sport fisheries and allow ecological assessment based on fish condition.

ISPATOM: A Generic Real-Time Data Processing Tool Without Programming

NASA Technical Reports Server (NTRS)

Dershowitz, Adam

2007-01-01

Information Sharing Protocol Advanced Tool of Math (ISPATOM) is an application program allowing for the streamlined generation of comps, which subscribe to streams of incoming telemetry data, perform any necessary computations on the data, then send the data to other programs for display and/or further processing in NASA mission control centers. Heretofore, the development of comps was difficult, expensive, and time-consuming: Each comp was custom written manually, in a low-level computing language, by a programmer attempting to follow requirements of flight controllers. ISPATOM enables a flight controller who is not a programmer to write a comp by simply typing in one or more equation( s) at a command line or retrieving the equation(s) from a text file. ISPATOM then subscribes to the necessary input data, performs all of necessary computations, and sends out the results. It sends out new results whenever the input data change. The use of equations in ISPATOM is no more difficult than is entering equations in a spreadsheet. The time involved in developing a comp is thus limited to the time taken to decide on the necessary equations. Thus, ISPATOM is a real-time dynamic calculator.

An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

NASA Technical Reports Server (NTRS)

Jorgenson, Philip C. E.; Pletcher, Richard H.

1994-01-01

The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

[Adherence to research reporting guidelines in biomedical journals in Latin America and the Caribbean].

PubMed

Glujovsky, Demián; Villanueva, Eleana; Reveiz, Ludovic; Murasaki, Renato

2014-10-01

To evaluate the familiarity of the editors of journals indexed in the LILACS database with the guidelines for reporting on and publishing research- promoted by the EQUATOR Network (Enhancing QUAlity and Transparency Of Health Research)-, the journals' requirements for use of the guidelines, and the editors' opinions regarding the reasons for the low rate of use. LILACS editors were surveyed by e-mail about the guidelines and their availability at the EQUATOR website, and about the requirements and difficulties in using them. Of 802 editors, 16.4% answered the survey. More than half said they were not aware of the guidelines (especially STROBE and PRISMA) and 30% were familiar with the EQUATOR Network. The first Latin American and Caribbean study on LILACS editors' familiarity with the guidelines revealed that more than half of them were not familiar either with the guidelines or the EQUATOR Network.

Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply

NASA Astrophysics Data System (ADS)

Gavrilov, S. N.; Krivtsov, A. M.; Tsvetkov, D. V.

2018-05-01

We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization procedure and derive an infinite set of linear partial differential equations for covariance variables. An exact analytic solution describing unsteady ballistic heat transfer in the crystal is obtained. It is shown that the stationary spatial profile of the kinetic temperature caused by a point source of heat supply of constant intensity is described by the Macdonald function of zero order. A comparison with the results obtained in the framework of the classical heat equation is presented. We expect that the results obtained in the paper can be verified by experiments with laser excitation of low-dimensional nanostructures.

Estimating annual suspended-sediment loads in the northern and central Appalachian Coal region

USGS Publications Warehouse

Koltun, G.F.

1985-01-01

Multiple-regression equations were developed for estimating the annual suspended-sediment load, for a given year, from small to medium-sized basins in the northern and central parts of the Appalachian coal region. The regression analysis was performed with data for land use, basin characteristics, streamflow, rainfall, and suspended-sediment load for 15 sites in the region. Two variables, the maximum mean-daily discharge occurring within the year and the annual peak discharge, explained much of the variation in the annual suspended-sediment load. Separate equations were developed employing each of these discharge variables. Standard errors for both equations are relatively large, which suggests that future predictions will probably have a low level of precision. This level of precision, however, may be acceptable for certain purposes. It is therefore left to the user to asses whether the level of precision provided by these equations is acceptable for the intended application.

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

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Nonlinear waves in electron-positron-ion plasmas including charge separation

NASA Astrophysics Data System (ADS)

Mugemana, A.; Moolla, S.; Lazarus, I. J.

2017-02-01

Nonlinear low-frequency electrostatic waves in a magnetized, three-component plasma consisting of hot electrons, hot positrons and warm ions have been investigated. The electrons and positrons are assumed to have Boltzmann density distributions while the motion of the ions are governed by fluid equations. The system is closed with the Poisson equation. This set of equations is numerically solved for the electric field. The effects of the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle are investigated. It is shown that depending on the driving electric field, ion temperature, positron density, ion drift, Mach number and propagation angle, the numerical solutions exhibit waveforms that are sinusoidal, sawtooth and spiky. The introduction of the Poisson equation increased the Mach number required to generate the waveforms but the driving electric field E 0 was reduced. The results are compared with satellite observations.

von Kármán–Howarth Equation for Hall Magnetohydrodynamics: Hybrid Simulations

NASA Astrophysics Data System (ADS)

Hellinger, Petr; Verdini, Andrea; Landi, Simone; Franci, Luca; Matteini, Lorenzo

2018-04-01

A dynamical vectorial equation for homogeneous incompressible Hall-magnetohydrodynamic (MHD) turbulence together with the exact scaling law for third-order correlation tensors, analogous to that for the incompressible MHD, is rederived and applied to the results of two-dimensional hybrid simulations of plasma turbulence. At large (MHD) scales the simulations exhibit a clear inertial range where the MHD dynamic law is valid. In the sub-ion range the cascade continues via the Hall term, but the dynamic law derived in the framework of incompressible Hall-MHD equations is obtained only in a low plasma beta simulation. For a higher beta plasma the cascade rate decreases in the sub-ion range and the change becomes more pronounced as the plasma beta increases. This break in the cascade flux can be ascribed to nonthermal (kinetic) features or to others terms in the dynamical equation that are not included in the Hall-MHD incompressible approximation.

A Computational Study of Shear Layer Receptivity

NASA Astrophysics Data System (ADS)

Barone, Matthew; Lele, Sanjiva

2002-11-01

The receptivity of two-dimensional, compressible shear layers to local and external excitation sources is examined using a computational approach. The family of base flows considered consists of a laminar supersonic stream separated from nearly quiescent fluid by a thin, rigid splitter plate with a rounded trailing edge. The linearized Euler and linearized Navier-Stokes equations are solved numerically in the frequency domain. The flow solver is based on a high order finite difference scheme, coupled with an overset mesh technique developed for computational aeroacoustics applications. Solutions are obtained for acoustic plane wave forcing near the most unstable shear layer frequency, and are compared to the existing low frequency theory. An adjoint formulation to the present problem is developed, and adjoint equation calculations are performed using the same numerical methods as for the regular equation sets. Solutions to the adjoint equations are used to shed light on the mechanisms which control the receptivity of finite-width compressible shear layers.

Kinetic theory for electrostatic waves due to transverse velocity shears

NASA Technical Reports Server (NTRS)

Ganguli, G.; Lee, Y. C.; Palmadesso, P. J.

1988-01-01

A kinetic theory in the form of an integral equation is provided to study the electrostatic oscillations in a collisionless plasma immersed in a uniform magnetic field and a nonuniform transverse electric field. In the low temperature limit the dispersion differential equation is recovered for the transverse Kelvin-Helmholtz modes for arbitrary values of K parallel, where K parallel is the component of the wave vector in the direction of the external magnetic field assumed in the z direction. For higher temperatures the ion-cyclotron-like modes described earlier in the literature by Ganguli, Lee and Plamadesso are recovered. In this article, the integral equation is reduced to a second-order differential equation and a study is made of the kinetic Kelvin-Helmholtz and ion-cyclotron-like modes that constitute the two branches of oscillation in a magnetized plasma including a transverse inhomogeneous dc electric field.

Quantum Black Hole Model and HAWKING’S Radiation

NASA Astrophysics Data System (ADS)

Berezin, Victor

The black hole model with a self-gravitating charged spherical symmetric dust thin shell as a source is considered. The Schroedinger-type equation for such a model is derived. This equation appeared to be a finite differences equation. A theory of such an equation is developed and general solution is found and investigated in details. The discrete spectrum of the bound state energy levels is obtained. All the eigenvalues appeared to be infinitely degenerate. The ground state wave functions are evaluated explicitly. The quantum black hole states are selected and investigated. It is shown that the obtained black hole mass spectrum is compatible with the existence of Hawking’s radiation in the limit of low temperatures both for large and nearly extreme Reissner-Nordstrom black holes. The above mentioned infinite degeneracy of the mass (energy) eigenvalues may appeared helpful in resolving the well known information paradox in the black hole physics.

Numerical modelling of nonlinear full-wave acoustic propagation

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

Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx

2015-10-28

The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on amore » GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.« less

Continual approach at T=0 in the mean field theory of incommensurate magnetic states in the frustrated Heisenberg ferromagnet with an easy axis anisotropy

NASA Astrophysics Data System (ADS)

Martynov, S. N.; Tugarinov, V. I.; Martynov, A. S.

2017-10-01

The algorithm of approximate solution was developed for the differential equation describing the anharmonical change of the spin orientation angle in the model of ferromagnet with the exchange competition between nearest and next nearest magnetic neighbors and the easy axis exchange anisotropy. The equation was obtained from the collinearity constraint on the discrete lattice. In the low anharmonicity approximation the equation is resulted to an autonomous form and is integrated in quadratures. The obvious dependence of the angle velocity and second derivative of angle from angle and initial condition was derived by expanding the first integral of the equation in the Taylor series in vicinity of initial condition. The ground state of the soliton solutions was calculated by a numerical minimization of the energy integral. The evaluation of the used approximation was made for a triple point of the phase diagram.

Discrete sensitivity derivatives of the Navier-Stokes equations with a parallel Krylov solver

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Taylor, Arthur C., III

1994-01-01

This paper solves an 'incremental' form of the sensitivity equations derived by differentiating the discretized thin-layer Navier Stokes equations with respect to certain design variables of interest. The equations are solved with a parallel, preconditioned Generalized Minimal RESidual (GMRES) solver on a distributed-memory architecture. The 'serial' sensitivity analysis code is parallelized by using the Single Program Multiple Data (SPMD) programming model, domain decomposition techniques, and message-passing tools. Sensitivity derivatives are computed for low and high Reynolds number flows over a NACA 1406 airfoil on a 32-processor Intel Hypercube, and found to be identical to those computed on a single-processor Cray Y-MP. It is estimated that the parallel sensitivity analysis code has to be run on 40-50 processors of the Intel Hypercube in order to match the single-processor processing time of a Cray Y-MP.

Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

NASA Astrophysics Data System (ADS)

Yu, Han; Chen, Yuqing; Hanafy, Sherif M.; Huang, Jiangping

2018-04-01

A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes the squared sum of the traveltime residuals. Even though, wave-equation traveltime inversion can partly avoid the cycle skipping problem, a good initial velocity model is required for the inversion to converge to a reasonable tomogram with different attenuation profiles. When Q model is far away from the real model, the final tomogram is very sensitive to the starting velocity model. Nevertheless, a minor or moderate perturbation of the Q model from the true one does not strongly affect the inversion if the low wavenumber information of the initial velocity model is mostly correct. These claims are validated with numerical tests on both the synthetic and field data sets.

Exact closed-form solution of the hyperbolic equation of string vibrations with material relaxation properties taken into account

NASA Astrophysics Data System (ADS)

Kudinov, I. V.; Kudinov, V. A.

2014-09-01

The differential equation of damped string vibrations was obtained with the finite speed of extension and strain propagation in the Hooke's law formula taken into account. In contrast to the well-known equations, the obtained equation contains the first and third time derivatives of the displacement and the mixed derivative with respect to the space and time variables. Separation of variables was used to obtain its exact closed-form solution, whose analysis showed that, for large values of the relaxation coefficient, the string return to the initial state after its escape from equilibrium is accompanied by high-frequency low-amplitude damped vibrations, which occur on the initial time interval only in the region of positive displacements. And in the limit, for some large values of the relaxation coefficient, the string return to the initial state occurs practically without any oscillatory process.

A Galerkin least squares approach to viscoelastic flow.

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

Rao, Rekha R.; Schunk, Peter Randall

2015-10-01

A Galerkin/least-squares stabilization technique is applied to a discrete Elastic Viscous Stress Splitting formulation of for viscoelastic flow. From this, a possible viscoelastic stabilization method is proposed. This method is tested with the flow of an Oldroyd-B fluid past a rigid cylinder, where it is found to produce inaccurate drag coefficients. Furthermore, it fails for relatively low Weissenberg number indicating it is not suited for use as a general algorithm. In addition, a decoupled approach is used as a way separating the constitutive equation from the rest of the system. A Pressure Poisson equation is used when the velocity andmore » pressure are sought to be decoupled, but this fails to produce a solution when inflow/outflow boundaries are considered. However, a coupled pressure-velocity equation with a decoupled constitutive equation is successful for the flow past a rigid cylinder and seems to be suitable as a general-use algorithm.« less

Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces: Applications to invisible cloak and ELF propagation

NASA Astrophysics Data System (ADS)

Chun, Sehun

2017-07-01

Applying the method of moving frames to Maxwell's equations yields two important advancements for scientific computing. The first is the use of upwind flux for anisotropic materials in Maxwell's equations, especially in the context of discontinuous Galerkin (DG) methods. Upwind flux has been available only to isotropic material, because of the difficulty of satisfying the Rankine-Hugoniot conditions in anisotropic media. The second is to solve numerically Maxwell's equations on curved surfaces without the metric tensor and composite meshes. For numerical validation, spectral convergences are displayed for both two-dimensional anisotropic media and isotropic spheres. In the first application, invisible two-dimensional metamaterial cloaks are simulated with a relatively coarse mesh by both the lossless Drude model and the piecewisely-parametered layered model. In the second application, extremely low frequency propagation on various surfaces such as spheres, irregular surfaces, and non-convex surfaces is demonstrated.

An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

NASA Astrophysics Data System (ADS)

Drivas, Theodore D.; Eyink, Gregory L.

2017-12-01

We prove that bounded weak solutions of the compressible Euler equations will conserve thermodynamic entropy unless the solution fields have sufficiently low space-time Besov regularity. A quantity measuring kinetic energy cascade will also vanish for such Euler solutions, unless the same singularity conditions are satisfied. It is shown furthermore that strong limits of solutions of compressible Navier-Stokes equations that are bounded and exhibit anomalous dissipation are weak Euler solutions. These inviscid limit solutions have non-negative anomalous entropy production and kinetic energy dissipation, with both vanishing when solutions are above the critical degree of Besov regularity. Stationary, planar shocks in Euclidean space with an ideal-gas equation of state provide simple examples that satisfy the conditions of our theorems and which demonstrate sharpness of our L 3-based conditions. These conditions involve space-time Besov regularity, but we show that they are satisfied by Euler solutions that possess similar space regularity uniformly in time.

Shot-noise at a Fermi-edge singularity: Non-Markovian dynamics

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

Ubbelohde, N.; Maire, N.; Haug, R. J.

2013-12-04

For an InAs quantum dot we study the current shot noise at a Fermi-edge singularity in low temperature cross-correlation measurements. In the regime of the interaction effect the strong suppression of noise observed at zero magnetic field and the sequence of enhancement and suppression in magnetic field go beyond a Markovian master equation model. Qualitative and quantitative agreement can however be achieved by a generalized master equation model taking non-Markovian dynamics into account.

Tripolar vortex formation in dense quantum plasma with ion-temperature-gradients

NASA Astrophysics Data System (ADS)

Qamar, Anisa; Ata-ur-Rahman, Mirza, Arshad M.

2012-05-01

We have derived system of nonlinear equations governing the dynamics of low-frequency electrostatic toroidal ion-temperature-gradient mode for dense quantum magnetoplasma. For some specific profiles of the equilibrium density, temperature, and ion velocity gradients, the nonlinear equations admit a stationary solution in the form of a tripolar vortex. These results are relevant to understand nonlinear structure formation in dense quantum plasmas in the presence of equilibrium ion-temperature and density gradients.

Glueball spectra from a matrix model of pure Yang-Mills theory

NASA Astrophysics Data System (ADS)

Acharyya, Nirmalendu; Balachandran, A. P.; Pandey, Mahul; Sanyal, Sambuddha; Vaidya, Sachindeo

2018-05-01

We present variational estimates for the low-lying energies of a simple matrix model that approximates SU(3) Yang-Mills theory on a three-sphere of radius R. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang-Mills coupling g as a function of R. This RG equation allows to estimate the mass of other glueball states, which we find to be in excellent agreement with lattice simulations.

On multi-graded-index soliton solutions for the Boussinesq-Burgers equations in optical communications

NASA Astrophysics Data System (ADS)

Abdel-Gawad, H. I.; Tantawy, M.

2017-02-01

Very recently, multi-solitary long waves for the homogeneous Boussinesq-Burgers equations (BBEs) were studied. Here its found that the time dependent coefficients (BBEs), shows multi-graded-index solitons waves, which are graded refractive index profile and can offer a new route for high-power lasers and transmission. They should increase data rates in low-cost telecommunications systems. Further, that (BBEs) show long periodic solitons waves in communications and television antennas.

The Effect of High-pressure Densification on Ballistic-penetration Resistance of a Soda-lime Glass

DTIC Science & Technology

2011-01-01

equation of state and the strength constitutive laws of an existing material model for glass. This was fol- lowed by a set of transient non-linear... of irreversible densification. These relations are next used to upgrade the equation of state and the strength constitutive laws of an existing...its effect on the conti- nuum-level pressure versus degree- of -compression (the negative of volumetric strain) relation, also known as the

Implicit methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Yoon, S.; Kwak, D.

1990-01-01

Numerical solutions of the Navier-Stokes equations using explicit schemes can be obtained at the expense of efficiency. Conventional implicit methods which often achieve fast convergence rates suffer high cost per iteration. A new implicit scheme based on lower-upper factorization and symmetric Gauss-Seidel relaxation offers very low cost per iteration as well as fast convergence. High efficiency is achieved by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.

USSR and Eastern Europe Scientific Abstracts, Electronics and Electrical Engineering, Number 33.

DTIC Science & Technology

1977-09-27

reduces to an infinite system of linear homogeneous algebraic equations and leads to Mathieu functions of the k-th order. The solution is convergent in...cylinder walls to be infinitesimally thin ideal conductors. The problem is reduced to a system of Fredholm linear algebraic equations of the second...EXPECTED DEVELOPMENTS OF TRANSISTORIZED LOW-NOISE MICROWAVE AMPLIFIERS Prague SDELOVACI TECHNIKA in Czech Vol 25, No 2, Feb 77 pp 47-49 TALLO, ANTON

Direct integration of the inverse Radon equation for X-ray computed tomography.

PubMed

Libin, E E; Chakhlov, S V; Trinca, D

2016-11-22

A new mathematical appoach using the inverse Radon equation for restoration of images in problems of linear two-dimensional x-ray tomography is formulated. In this approach, Fourier transformation is not used, and it gives the chance to create the practical computing algorithms having more reliable mathematical substantiation. Results of software implementation show that for especially for low number of projections, the described approach performs better than standard X-ray tomographic reconstruction algorithms.

Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II

NASA Astrophysics Data System (ADS)

Kazeykina, Anna; Muñoz, Claudio

2018-04-01

We continue our study on the Cauchy problem for the two-dimensional Novikov-Veselov (NV) equation, integrable via the inverse scattering transform for the two dimensional Schrödinger operator at a fixed energy parameter. This work is concerned with the more involved case of a positive energy parameter. For the solution of the linearized equation we derive smoothing and Strichartz estimates by combining new estimates for two different frequency regimes, extending our previous results for the negative energy case [18]. The low frequency regime, which our previous result was not able to treat, is studied in detail. At non-low frequencies we also derive improved smoothing estimates with gain of almost one derivative. Then we combine the linear estimates with a Fourier decomposition method and Xs,b spaces to obtain local well-posedness of NV at positive energy in Hs, s > 1/2. Our result implies, in particular, that at least for s > 1/2, NV does not change its behavior from semilinear to quasilinear as energy changes sign, in contrast to the closely related Kadomtsev-Petviashvili equations. As a complement to our LWP results, we also provide some new explicit solutions of NV at zero energy, generalizations of the lumps solutions, which exhibit new and nonstandard long time behavior. In particular, these solutions blow up in infinite time in L2.

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.

A Method for Large Eddy Simulation of Acoustic Combustion Instabilities

NASA Astrophysics Data System (ADS)

Wall, Clifton; Moin, Parviz

2003-11-01

A method for performing Large Eddy Simulation of acoustic combustion instabilities is presented. By extending the low Mach number pressure correction method to the case of compressible flow, a numerical method is developed in which the Poisson equation for pressure is replaced by a Helmholtz equation. The method avoids the acoustic CFL condition by using implicit time advancement, leading to large efficiency gains at low Mach number. The method also avoids artificial damping of acoustic waves. The numerical method is attractive for the simulation of acoustics combustion instabilities, since these flows are typically at low Mach number, and the acoustic frequencies of interest are usually low. Additionally, new boundary conditions based on the work of Poinsot and Lele have been developed to model the acoustic effect of a long channel upstream of the computational inlet, thus avoiding the need to include such a channel in the computational domain. The turbulent combustion model used is the Level Set model of Duchamp de Lageneste and Pitsch for premixed combustion. Comparison of LES results to the reacting experiments of Besson et al. will be presented.

Voltage control in Z-source inverter using low cost microcontroller for undergraduate approach

NASA Astrophysics Data System (ADS)

Zulkifli, Shamsul Aizam; Sewang, Mohd Rizal; Salimin, Suriana; Shah, Noor Mazliza Badrul

2017-09-01

This paper is focussing on controlling the output voltage of Z-Source Inverter (ZSI) using a low cost microcontroller with MATLAB-Simulink that has been used for interfacing the voltage control at the output of ZSI. The key advantage of this system is the ability of a low cost microcontroller to process the voltage control blocks based on the mathematical equations created in MATLAB-Simulink. The Proportional Integral (PI) control equations are been applied and then, been downloaded to the microcontroller for observing the changes on the voltage output regarding to the changes on the reference on the PI. The system has been simulated in MATLAB and been verified with the hardware setup. As the results, the Raspberry Pi and Arduino that have been used in this work are able to respond well when there is a change of ZSI output. It proofed that, by applying/introducing this method to student in undergraduate level, it will help the student to understand more on the process of the power converter combine with a control feedback function that can be applied at low cost microcontroller.

Forecasting the probability of future groundwater levels declining below specified low thresholds in the conterminous U.S.

USGS Publications Warehouse

Dudley, Robert W.; Hodgkins, Glenn A.; Dickinson, Jesse

2017-01-01

We present a logistic regression approach for forecasting the probability of future groundwater levels declining or maintaining below specific groundwater-level thresholds. We tested our approach on 102 groundwater wells in different climatic regions and aquifers of the United States that are part of the U.S. Geological Survey Groundwater Climate Response Network. We evaluated the importance of current groundwater levels, precipitation, streamflow, seasonal variability, Palmer Drought Severity Index, and atmosphere/ocean indices for developing the logistic regression equations. Several diagnostics of model fit were used to evaluate the regression equations, including testing of autocorrelation of residuals, goodness-of-fit metrics, and bootstrap validation testing. The probabilistic predictions were most successful at wells with high persistence (low month-to-month variability) in their groundwater records and at wells where the groundwater level remained below the defined low threshold for sustained periods (generally three months or longer). The model fit was weakest at wells with strong seasonal variability in levels and with shorter duration low-threshold events. We identified challenges in deriving probabilistic-forecasting models and possible approaches for addressing those challenges.

Hypervelocity atmospheric flight: Real gas flow fields

NASA Technical Reports Server (NTRS)

Howe, John T.

1990-01-01

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that were reduced to a relatively compact set of equations of a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-averaged behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equation a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. For hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates, chemical nonequilibrium is considered and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

Hypervelocity atmospheric flight: Real gas flow fields

NASA Technical Reports Server (NTRS)

Howe, John T.

1989-01-01

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that have been reduced to a relatively compact set of equations in a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-average behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equations a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. Hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates chemical nonequilibrium is considered, and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

Heart rate during basketball game play and volleyball drills accurately predicts oxygen uptake and energy expenditure.

PubMed

Scribbans, T D; Berg, K; Narazaki, K; Janssen, I; Gurd, B J

2015-09-01

There is currently little information regarding the ability of metabolic prediction equations to accurately predict oxygen uptake and exercise intensity from heart rate (HR) during intermittent sport. The purpose of the present study was to develop and, cross-validate equations appropriate for accurately predicting oxygen cost (VO2) and energy expenditure from HR during intermittent sport participation. Eleven healthy adult males (19.9±1.1yrs) were recruited to establish the relationship between %VO2peak and %HRmax during low-intensity steady state endurance (END), moderate-intensity interval (MOD) and high intensity-interval exercise (HI), as performed on a cycle ergometer. Three equations (END, MOD, and HI) for predicting %VO2peak based on %HRmax were developed. HR and VO2 were directly measured during basketball games (6 male, 20.8±1.0 yrs; 6 female, 20.0±1.3yrs) and volleyball drills (12 female; 20.8±1.0yrs). Comparisons were made between measured and predicted VO2 and energy expenditure using the 3 equations developed and 2 previously published equations. The END and MOD equations accurately predicted VO2 and energy expenditure, while the HI equation underestimated, and the previously published equations systematically overestimated VO2 and energy expenditure. Intermittent sport VO2 and energy expenditure can be accurately predicted from heart rate data using either the END (%VO2peak=%HRmax x 1.008-17.17) or MOD (%VO2peak=%HRmax x 1.2-32) equations. These 2 simple equations provide an accessible and cost-effective method for accurate estimation of exercise intensity and energy expenditure during intermittent sport.

Performance of Predictive Equations Specifically Developed to Estimate Resting Energy Expenditure in Ventilated Critically Ill Children.

PubMed

Jotterand Chaparro, Corinne; Taffé, Patrick; Moullet, Clémence; Laure Depeyre, Jocelyne; Longchamp, David; Perez, Marie-Hélène; Cotting, Jacques

2017-05-01

To determine, based on indirect calorimetry measurements, the biases of predictive equations specifically developed recently for estimating resting energy expenditure (REE) in ventilated critically ill children, or developed for healthy populations but used in critically ill children. A secondary analysis study was performed using our data on REE measured in a previous prospective study on protein and energy needs in pediatric intensive care unit. We included 75 ventilated critically ill children (median age, 21 months) in whom 407 indirect calorimetry measurements were performed. Fifteen predictive equations were used to estimate REE: the equations of White, Meyer, Mehta, Schofield, Henry, the World Health Organization, Fleisch, and Harris-Benedict and the tables of Talbot. Their differential and proportional biases (with 95% CIs) were computed and the bias plotted in graphs. The Bland-Altman method was also used. Most equations underestimated and overestimated REE between 200 and 1000 kcal/day. The equations of Mehta, Schofield, and Henry and the tables of Talbot had a bias ≤10%, but the 95% CI was large and contained values by far beyond ±10% for low REE values. Other specific equations for critically ill children had even wider biases. In ventilated critically ill children, none of the predictive equations tested met the performance criteria for the entire range of REE between 200 and 1000 kcal/day. Even the equations with the smallest bias may entail a risk of underfeeding or overfeeding, especially in the youngest children. Indirect calorimetry measurement must be preferred. Copyright © 2016 Elsevier Inc. All rights reserved.

Nonlinear theory of nonstationary low Mach number channel flows of freely cooling nearly elastic granular gases.

PubMed

Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady

2008-02-01

We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald ripening (only one hole survives at the end), and we report a particular regime where the "hole ripening" statistics exhibits a simple dynamic scaling behavior.

SIS (Superconductor-Insulator-Superconductor) Mixer Research.

DTIC Science & Technology

1988-02-01

performed in that work was unique in that it employed the complete equations of the quantum theory of mixing in the three- frequency , low -intermediate...addition, these results cast doubt upon recent reports of low - noise single-junction 5IS rec, ivers which have extremely wide bandwidths. In conjunction...have significant and widespread implications for any active arrayed device which has a very low driving power. 3. High frequency : The third objective

Computational fluid dynamics analysis and experimental study of a low measurement error temperature sensor used in climate observation.

PubMed

Yang, Jie; Liu, Qingquan; Dai, Wei

2017-02-01

To improve the air temperature observation accuracy, a low measurement error temperature sensor is proposed. A computational fluid dynamics (CFD) method is implemented to obtain temperature errors under various environmental conditions. Then, a temperature error correction equation is obtained by fitting the CFD results using a genetic algorithm method. The low measurement error temperature sensor, a naturally ventilated radiation shield, a thermometer screen, and an aspirated temperature measurement platform are characterized in the same environment to conduct the intercomparison. The aspirated platform served as an air temperature reference. The mean temperature errors of the naturally ventilated radiation shield and the thermometer screen are 0.74 °C and 0.37 °C, respectively. In contrast, the mean temperature error of the low measurement error temperature sensor is 0.11 °C. The mean absolute error and the root mean square error between the corrected results and the measured results are 0.008 °C and 0.01 °C, respectively. The correction equation allows the temperature error of the low measurement error temperature sensor to be reduced by approximately 93.8%. The low measurement error temperature sensor proposed in this research may be helpful to provide a relatively accurate air temperature result.

XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Dennis, Graham R.; Hope, Joseph J.; Johnsson, Mattias T.

2013-01-01

XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code. Program summaryProgram title: XMDS2 Catalogue identifier: AENK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 872490 No. of bytes in distributed program, including test data, etc.: 45522370 Distribution format: tar.gz Programming language: Python and C++. Computer: Any computer with a Unix-like system, a C++ compiler and Python. Operating system: Any Unix-like system; developed under Mac OS X and GNU/Linux. RAM: Problem dependent (roughly 50 bytes per grid point) Classification: 4.3, 6.5. External routines: The external libraries required are problem-dependent. Uses FFTW3 Fourier transforms (used only for FFT-based spectral methods), dSFMT random number generation (used only for stochastic problems), MPI message-passing interface (used only for distributed problems), HDF5, GNU Scientific Library (used only for Bessel-based spectral methods) and a BLAS implementation (used only for non-FFT-based spectral methods). Nature of problem: General coupled initial-value stochastic partial differential equations. Solution method: Spectral method with method-of-lines integration Running time: Determined by the size of the problem

Collision partner selection schemes in DSMC: From micro/nano flows to hypersonic flows

NASA Astrophysics Data System (ADS)

Roohi, Ehsan; Stefanov, Stefan

2016-10-01

The motivation of this review paper is to present a detailed summary of different collision models developed in the framework of the direct simulation Monte Carlo (DSMC) method. The emphasis is put on a newly developed collision model, i.e., the Simplified Bernoulli trial (SBT), which permits efficient low-memory simulation of rarefied gas flows. The paper starts with a brief review of the governing equations of the rarefied gas dynamics including Boltzmann and Kac master equations and reiterates that the linear Kac equation reduces to a non-linear Boltzmann equation under the assumption of molecular chaos. An introduction to the DSMC method is provided, and principles of collision algorithms in the DSMC are discussed. A distinction is made between those collision models that are based on classical kinetic theory (time counter, no time counter (NTC), and nearest neighbor (NN)) and the other class that could be derived mathematically from the Kac master equation (pseudo-Poisson process, ballot box, majorant frequency, null collision, Bernoulli trials scheme and its variants). To provide a deeper insight, the derivation of both collision models, either from the principles of the kinetic theory or the Kac master equation, is provided with sufficient details. Some discussions on the importance of subcells in the DSMC collision procedure are also provided and different types of subcells are presented. The paper then focuses on the simplified version of the Bernoulli trials algorithm (SBT) and presents a detailed summary of validation of the SBT family collision schemes (SBT on transient adaptive subcells: SBT-TAS, and intelligent SBT: ISBT) in a broad spectrum of rarefied gas-flow test cases, ranging from low speed, internal micro and nano flows to external hypersonic flow, emphasizing first the accuracy of these new collision models and second, demonstrating that the SBT family scheme, if compared to other conventional and recent collision models, requires smaller number of particles per cell to obtain sufficiently accurate solutions.

Low-Dimensional Model of a Cylinder Wake

NASA Astrophysics Data System (ADS)

Luchtenburg, Mark; Cohen, Kelly; Siegel, Stefan; McLaughlin, Tom

2003-11-01

In a two-dimensional cylinder wake, self-excited oscillations in the form of periodic shedding of vortices are observed above a critical Reynolds number of about 47. These flow-induced non-linear oscillations lead to some undesirable effects associated with unsteady pressures such as fluid-structure interactions. An effective way of suppressing the self-excited flow oscillations is by the incorporation of closed-loop flow control. In this effort, a low dimensional, proper orthogonal decomposition (POD) model is based on data obtained from direct numerical simulations of the Navier Stokes equations for the two dimensional circular cylinder wake at a Reynolds number of 100. Three different conditions are examined, namely, the unforced wake experiencing steady-state vortex shedding, the transient behavior of the unforced wake at the startup of the simulation, and transient response to open-loop harmonic forcing by translation. We discuss POD mode selection and the number of modes that need to be included in the low-dimensional model. It is found that the transient dynamics need to be represented by a coupled system that includes an aperiodic mean-flow mode, an aperiodic shift mode and the periodic von Karman modes. Finally, a least squares mapping method is introduced to develop the non-linear state equations. The predictive capability of the state equations demonstrates the ability of the above approach to model the transient dynamics of the wake.

Petrophysics of low-permeability medina sandstone, northwestern Pennsylvania, Appalachian Basin

USGS Publications Warehouse

Castle, J.W.; Byrnes, A.P.

1998-01-01

Petrophysical core testing combined with geophysical log analysis of low-permeability, Lower Silurian sandstones of the Appalachian basin provides guidelines and equations for predicting gas producibility. Permeability values are predictable from the borehole logs by applying empirically derived equations based on correlation between in-situ porosity and in-situ effective gas permeability. An Archie-form equation provides reasonable accuracy of log-derived water saturations because of saturated brine salinities and low clay content in the sands. Although measured porosity and permeability average less than 6% and 0.1 mD, infrequent values as high as 18% and 1,048 mD occur. Values of effective gas permeability at irreducible water saturation (Swi) range from 60% to 99% of routine values for the highest permeability rocks to several orders of magnitude less for the lowest permeability rocks. Sandstones having porosity greater than 6% and effective gas permeability greater than 0.01 mD exhibit Swi less than 20%. With decreasing porosity, Swi sharply increases to values near 40% at 3 porosity%. Analysis of cumulative storage and flow capacity indicates zones with porosity greater than 6% generally contain over 90% of flow capacity and hold a major portion of storage capacity. For rocks with Swi < 20%, gas relative permeabilities exceed 45%. Gas relative permeability and hydrocarbon volume decrease rapidly with increasing Swi as porosity drops below 6%. At Swi above 40%, gas relative permeabilities are less than approximately 10%.

The Optimation of Crude Fiber Content of Diet for Fattening Madura Beef Cattle to Achieve Good A:P Ratio and Low Methane Production

NASA Astrophysics Data System (ADS)

Luthfi, N.; Restitrisnani, V.; Umar, M.

2018-02-01

Abtract. Methane (CH4) is one of the major greenhouse gases being reducted. This study was carried out to determine the optimum of crude fiber needed for fattening Madura beef cattle to achieve low methane production. Twenty-four male madura beef cattles with an average body weight of 206.89 ± 7.82 kg were used in this study. Cattle were fed contained 47.65 - 70.23 % Total Digestible Nutrients (TDN), 9.22 - 13.20% Crude Protein (CP), and 10.25 - 28.53% Crude Fiber (CF). Correlation analysis was used to describe the correlations among crude fiber,Methane, and Acetate:Propionate acid ratio. The result showed that crude fiber (%) had medium possitive correlation with methane and the equation was y = 0.0936x + 5.4853 with determination as much as 33.98%. The Acetate: propionate acid had positive correlation withmethane and the equation was y = 1.1121x + 3.581 with determination as much as 61.64%. Crude fiber (%) had low possitive correlation with A/P ratio and the equation was y = 0.039x + 2.4437 with determination as much as 9.56%. According to the results, it can be concluded that the optimum ofcrude fiberof diet for Madura beef cattle should be 15.38% to obtain A:P ratio of 3 or less and methane production of 6.91 MJ/d.

Development of reliable predictive heat transfer correlations for low-rank coal-fired fluid bed combustors. Final report

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

Grewal, N.S.

(1) The proposed correlation of Equation (5) is recommended to predict the maximum value of heat transfer coefficient between a horzontal tube and a gas-solid fluidized bed of small particles under the conditions given. For high temperature applications (T/sub B/ > 600/sup 0/C), the radiative component is important and was estimated following Baskakov et al. (2) The proposed correlation of Equation (8) was found reliable to predict the existing data on the maximum value of heat transfer coefficient between a horizontal tube bundle and a gas-solid fluidized bed of small particles under the conditions given. At high temperatures, the radiativemore » component was estimated from the experimental data of Baskakov et al. (3) The correlation of Equation (8) predicted the GFETC data taken during the combustion of low-rank coal very well, when the contribution due to radiation was estimated following Baskakov et al. (4) The correlations proposed by Grewal and Bansal et al. were found to predict the data taken during low-rank coal combustion within +-25%, when the contribution due to radiation was included and estimated following Baskakov et al. (5) Finally, the correlations for large particles (anti d/sub p/ > 1mm) as proposed by Glicksman and Decker, Catipovic et al., Xavier and Davidson, and Zabrodsky et al. also predicted the data for low-rank coal fluidized bed combustor quite well, when the radiative component was estimated from the data of Baskakov et al. 64 references, 19 figures, 10 tables.« less

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.

2003-01-01

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Bridging the Gap Between Stationary Homogeneous Isotropic Turbulence and Quantum Mechanics

NASA Astrophysics Data System (ADS)

Sohrab, Siavash

A statistical theory of stationary isotropic turbulence is presented with eddies possessing Gaussian velocity distribution, Maxwell-Boltzmann speed distribution in harmony with perceptions of Heisenberg, and Planck energy distribution in harmony with perceptions of Chandrasekhar and in agreement with experimental observations of Van Atta and Chen. Defining the action S = - mΦ in terms of velocity potential of atomic motion, scale-invariant Schrödinger equation is derivedfrom invariant Bernoulli equation. Thus, the gap between the problems of turbulence and quantum mechanics is closed through connections between Cauchy-Euler-Bernoulli equations of hydrodynamics, Hamilton-Jacobi equation of classical mechanics, and finally Schrödinger equation of quantum mechanics. Transitions of particle (molecular cluster cji) from a small rapidly-oscillating eddy ej (high-energy level-j) to a large slowly-oscillating eddy ei (low energy-level-i) leads to emission of a sub-particle (molecule mji) that carries away the excess energy ɛji = h (νj -νi) in harmony with Bohr theory of atomic spectra. ∖ ∖ NASA Grant No. NAG3-1863.

Computation of oscillating airfoil flows with one- and two-equation turbulence models

NASA Technical Reports Server (NTRS)

Ekaterinaris, J. A.; Menter, F. R.

1994-01-01

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.

Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Kaushik, Dinesh K.; Idres, Moumen

1997-01-01

The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.

A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

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

Chen, Luoping; Zheng, Bin; Lin, Guang

In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse meshmore » $$\\mathcal{T}_H$$ with a low level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_{P}$$) and solve linearized equations on a fine mesh $$\\mathcal{T}_h$$ using high level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_p$$). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with $$\\mathcal{T}_h$$ and $$\\mathcal{P}_p$$. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.« less

On the joint bimodality of temperature and moisture near stratocumulus cloud tops

NASA Technical Reports Server (NTRS)

Randall, D. A.

1983-01-01

The observed distributions of the thermodynamic variables near stratocumulus top are highly bimodal. Two simple models of sub-grid fractional cloudiness motivated by this observed bimodality are examined. In both models, certain low order moments of two independent, moist-conservative thermodynamic variables are assumed to be known. The first model is based on the assumption of two discrete populations of parcels: a warm-day population and a cool-moist population. If only the first and second moments are assumed to be known, the number of unknowns exceeds the number of independent equations. If the third moments are assumed to be known as well, the number of independent equations exceeds the number of unknowns. The second model is based on the assumption of a continuous joint bimodal distribution of parcels, obtained as the weighted sum of two binormal distributions. For this model, the third moments are used to obtain 9 independent nonlinear algebraic equations in 11 unknowns. Two additional equations are needed to determine the covariance within the two subpopulations. In case these two internal covariance vanish, the system of equations can be solved analytically.

On the Divergence of the Velocity Vector in Real-Gas Flow

NASA Technical Reports Server (NTRS)

Bellan, Josette

2009-01-01

A theoretical study was performed addressing the degree of applicability or inapplicability, to a real gas, of the occasionally stated belief that for an ideal gas, incompressibility is synonymous with a zero or very low Mach number. The measure of compressibility used in this study is the magnitude of the divergence of the flow velocity vector [V(bar) (raised dot) u (where u is the flow velocity)]. The study involves a mathematical derivation that begins with the governing equations of flow and involves consideration of equations of state, thermodynamics, and fluxes of heat, mass, and the affected molecular species. The derivation leads to an equation for the volume integral of (V(bar) (raised dot) u)(sup 2) that indicates contributions of several thermodynamic, hydrodynamic, and species-flux effects to compressibility and reveals differences between real and ideal gases. An analysis of the equation leads to the conclusion that for a real gas, incompressibility is not synonymous with zero or very small Mach number. Therefore, it is further concluded, the contributions to compressibility revealed by the derived equation should be taken into account in simulations of real-gas flows.

Flame-conditioned turbulence modeling for reacting flows

NASA Astrophysics Data System (ADS)

Macart, Jonathan F.; Mueller, Michael E.

2017-11-01

Conventional approaches to turbulence modeling in reacting flows rely on unconditional averaging or filtering, that is, consideration of the momentum equations only in physical space, implicitly assuming that the flame only weakly affects the turbulence, aside from a variation in density. Conversely, for scalars, which are strongly coupled to the flame structure, their evolution equations are often projected onto a reduced-order manifold, that is, conditionally averaged or filtered, on a flame variable such as a mixture fraction or progress variable. Such approaches include Conditional Moment Closure (CMC) and related variants. However, recent observations from Direct Numerical Simulation (DNS) have indicated that the flame can strongly affect turbulence in premixed combustion at low Karlovitz number. In this work, a new approach to turbulence modeling for reacting flows is investigated in which conditionally averaged or filtered equations are evolved for the momentum. The conditionally-averaged equations for the velocity and its covariances are derived, and budgets are evaluated from DNS databases of turbulent premixed planar jet flames. The most important terms in these equations are identified, and preliminary closure models are proposed.

Low-Storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Kennedy, Chistopher A.; Carpenter, Mark H.; Lewis, R. Michael

1999-01-01

The derivation of storage explicit Runge-Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier-Stokes equations via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as stability and accuracy efficiency, linear and nonlinear stability, error control reliability, step change stability, and dissipation/dispersion accuracy, subject to varying degrees of memory economization. Following van der Houwen and Wray, 16 ERK pairs are presented using from two to five registers of memory per equation, per grid point and having accuracies from third- to fifth-order. Methods have been assessed using the differential equation testing code DETEST, and with the 1D wave equation. Two of the methods have been applied to the DNS of a compressible jet as well as methane-air and hydrogen-air flames. Derived 3(2) and 4(3) pairs are competitive with existing full-storage methods. Although a substantial efficiency penalty accompanies use of two- and three-register, fifth-order methods, the best contemporary full-storage methods can be pearl), matched while still saving two to three registers of memory.

Modeling of transport phenomena in concrete porous media.

PubMed

Plecas, Ilija

2014-02-01

Two fundamental concerns must be addressed when attempting to isolate low-level waste in a disposal facility on land. The first concern is isolating the waste from water, or hydrologic isolation. The second is preventing movement of the radionuclides out of the disposal facility, or radionuclide migration. Particularly, we have investigated here the latter modified scenario. To assess the safety for disposal of radioactive waste-concrete composition, the leakage of 60Co from a waste composite into a surrounding fluid has been studied. Leakage tests were carried out by the original method, developed at the Vinča Institute. Transport phenomena involved in the leaching of a radioactive material from a cement composite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source: an equation for diffusion coupled to a first-order equation, and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-y mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Phytoplankton productivity in relation to light intensity: A simple equation

USGS Publications Warehouse

Peterson, D.H.; Perry, M.J.; Bencala, K.E.; Talbot, M.C.

1987-01-01

A simple exponential equation is used to describe photosynthetic rate as a function of light intensity for a variety of unicellular algae and higher plants where photosynthesis is proportional to (1-e-??1). The parameter ?? (=Ik-1) is derived by a simultaneous curve-fitting method, where I is incident quantum-flux density. The exponential equation is tested against a wide range of data and is found to adequately describe P vs. I curves. The errors associated with photosynthetic parameters are calculated. A simplified statistical model (Poisson) of photon capture provides a biophysical basis for the equation and for its ability to fit a range of light intensities. The exponential equation provides a non-subjective simultaneous curve fitting estimate for photosynthetic efficiency (a) which is less ambiguous than subjective methods: subjective methods assume that a linear region of the P vs. I curve is readily identifiable. Photosynthetic parameters ?? and a are used widely in aquatic studies to define photosynthesis at low quantum flux. These parameters are particularly important in estuarine environments where high suspended-material concentrations and high diffuse-light extinction coefficients are commonly encountered. ?? 1987.

A fast and well-conditioned spectral method for singular integral equations

NASA Astrophysics Data System (ADS)

Slevinsky, Richard Mikael; Olver, Sheehan

2017-03-01

We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished by utilizing low rank approximations for sparse representations of the bivariate kernels. The resulting system can be solved in O (m2 n) operations using an adaptive QR factorization, where m is the bandwidth and n is the optimal number of unknowns needed to resolve the true solution. The complexity is reduced to O (mn) operations by pre-caching the QR factorization when the same operator is used for multiple right-hand sides. Stability is proved by showing that the resulting linear operator can be diagonally preconditioned to be a compact perturbation of the identity. Applications considered include the Faraday cage, and acoustic scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation of the far- and near-field solution. The JULIA software package SingularIntegralEquations.jl implements our method with a convenient, user-friendly interface.

Development of a two-equation turbulence model for hypersonic flows. Volume 1; Evaluation of a low Reynolds number correction to the Kappa - epsilon two equation compressible turbulence model

NASA Technical Reports Server (NTRS)

Knight, Doyle D.; Becht, Robert J.

1995-01-01

The objective of the current research is the development of an improved k-epsilon two-equation compressible turbulence model for turbulent boundary layer flows experiencing strong viscous-inviscid interactions. The development of an improved model is important in the design of hypersonic vehicles such as the National Aerospace Plane (NASP) and the High Speed Civil Transport (HSCT). Improvements have been made to the low Reynolds number functions in the eddy viscosity and dissipation of solenoidal dissipation of the k-epsilon turbulence mode. These corrections offer easily applicable modifications that may be utilized for more complex geometries. The low Reynolds number corrections are functions of the turbulent Reynolds number and are therefore independent of the coordinate system. The proposed model offers advantages over some current models which are based upon the physical distance from the wall, that modify the constants of the standard model, or that make more corrections than are necessary to the governing equations. The code has been developed to solve the Favre averaged, boundary layer equations for mass, momentum, energy, turbulence kinetic energy, and dissipation of solenoidal dissipation using Keller's box scheme and the Newton spatial marching method. The code has been validated by removing the turbulent terms and comparing the solution with the Blasius solution, and by comparing the turbulent solution with an existing k-epsilon model code using wall function boundary conditions. Excellent agreement is seen between the computed solution and the Blasius solution, and between the two codes. The model has been tested for both subsonic and supersonic flat-plate turbulent boundary layer flow by comparing the computed skin friction with the Van Driest II theory and the experimental data of Weighardt; by comparing the transformed velocity profile with the data of Weighardt, and the Law of the Wall and the Law of the Wake; and by comparing the computed results of an adverse pressure gradient with the experimental data of Fernando and Smits. Good agreement is obtained with the experimental correlations for all flow conditions.

Propagation of intense short laser pulses in the atmosphere.

PubMed

Sprangle, P; Peñano, J R; Hafizi, B

2002-10-01

The propagation of short, intense laser pulses in the atmosphere is investigated theoretically and numerically. A set of three-dimensional (3D), nonlinear propagation equations is derived, which includes the effects of dispersion, nonlinear self-focusing, stimulated molecular Raman scattering, multiphoton and tunneling ionization, energy depletion due to ionization, relativistic focusing, and ponderomotively excited plasma wakefields. The instantaneous frequency spread along a laser pulse in air, which develops due to various nonlinear effects, is analyzed and discussed. Coupled equations for the power, spot size, and electron density are derived for an intense ionizing laser pulse. From these equations we obtain an equilibrium for a single optical-plasma filament, which involves a balancing between diffraction, nonlinear self-focusing, and plasma defocusing. The equilibrium is shown to require a specific distribution of power along the filament. It is found that in the presence of ionization a self-guided optical filament is not realizable. A method for generating a remote spark in the atmosphere is proposed, which utilizes the dispersive and nonlinear properties of air to cause a low-intensity chirped laser pulse to compress both longitudinally and transversely. For optimally chosen parameters, we find that the transverse and longitudinal focal lengths can be made to coincide, resulting in rapid intensity increase, ionization, and white light generation in a localized region far from the source. Coupled equations for the laser spot size and pulse duration are derived, which can describe the focusing and compression process in the low-intensity regime. More general examples involving beam focusing, compression, ionization, and white light generation near the focal region are studied by numerically solving the full set of 3D, nonlinear propagation equations.

R-mode constraints from neutron star equation of state

NASA Astrophysics Data System (ADS)

Papazoglou, M. C.; Moustakidis, C. C.

2016-03-01

The gravitational radiation has been proposed a long time before, as an explanation for the observed relatively low spin frequencies of young neutron stars and of accreting neutron stars in low-mass X-ray binaries as well. In the present work we studied the effects of the neutron star equation of state on the r-mode instability window of rotating neutron stars. Firstly, we employed a set of analytical solution of the Tolman-Oppenheimer-Volkoff equations with special emphasis on the Tolman VII solution. In particular, we tried to clarify the effects of the bulk neutron star properties (mass, radius, density distribution, crust size and elasticity) on the r-mode instability window. We found that the critical angular velocity \\varOmegac depends mainly on the neutron star radius. The effects of the gravitational mass and the mass distribution are almost negligible. Secondly, we studied the effect of the elasticity of the crust, via to the slippage factor S and also the effect of the nuclear equation of state, via the slope parameter L, on the instability window. We found that the crust effects are more pronounced, compared to those originated from the equation of state. Moreover, we proposed simple analytical expressions which relate the macroscopic quantity \\varOmegac to the radius, the parameter L and the factor {S}. We also investigated the possibility to measure the radius of a neutron star and the factor {S} with the help of accurate measures of \\varOmegac and the neutron star temperature. Finally, we studied the effects of the mutual friction on the instability window and discussed the results in comparison with previous similar studies.

[Anthropometric model for the prediction of appendicular skeletal muscle mass in Chilean older adults].

PubMed

Lera, Lydia; Albala, Cecilia; Ángel, Bárbara; Sánchez, Hugo; Picrin, Yaisy; Hormazabal, María José; Quiero, Andrea

2014-03-01

To develop a predictive model of appendicular skeletal muscle mass (ASM) based on anthropometric measurements in elderly from Santiago, Chile. 616 community dwelling, non-disabled subjects ≥ 60 years (mean 69.9 ± 5.2 years) living in Santiago, 64.6% female, participating in ALEXANDROS study. Anthropometric measurements, handgrip strength, mobility tests and DEXA were performed. Step by step linear regression models were used to associate ASM from DEXA with anthropometric variables, age and sex. The sample was divided at random into two to obtain prediction equations for both subsamples, which were mutually validated by double cross-validation. The high correlation between the values of observed and predicted MMAE in both sub-samples and the low degree of shrinkage allowed developing the final prediction equation with the total sample. The cross-validity coefficient between prediction models from the subsamples (0.941 and 0.9409) and the shrinkage (0.004 and 0.006) were similar in both equations. The final prediction model obtained from the total sample was: ASM (kg) = 0.107(weight in kg) + 0.251( knee height in cm) + 0.197 (Calf Circumference in cm) +0.047 (dynamometry in kg) - 0.034 (Hip Circumference in cm) + 3.417 (Man) - 0.020 (age years) - 7.646 (R2 = 0.89). The mean ASM obtained by the prediction equation and the DEXA measurement were similar (16.8 ± 4.0 vs 16.9 ± 3.7) and highly concordant according Bland and Altman (95% CI: -2.6 -2.7) and Lin (concordance correlation coefficient = 0.94) methods. We obtained a low cost anthropometric equation to determine the appendicular skeletal muscle mass useful for the screening of sarcopenia in older adults. Copyright AULA MEDICA EDICIONES 2014. Published by AULA MEDICA. All rights reserved.

Accuracy of a Portable Indirect Calorimeter for Measuring Resting Energy Expenditure in Individuals With Cancer.

PubMed

Purcell, Sarah A; Elliott, Sarah A; Ryan, Aoife M; Sawyer, Michael B; Prado, Carla M

2018-06-05

Determining optimal caloric intake for an individual with cancer is complicated by metabolic changes that occur, namely, alterations in resting energy expenditure (REE). There is currently no validated clinically available equation or tool to measure energy expenditure in these patients. Patients with newly diagnosed solid tumors underwent REE assessments using the FitMate GS portable indirect calorimeter and reference VMax metabolic cart; both used canopy hoods. REE was also estimated from the Harris-Benedict, Mifflin St. Jeor, and Henry equations for comparison. Data were analyzed using paired samples t-test and the Bland-Altman approach to assess group-level and individual-level agreement compared with the metabolic cart. A total 26 patients (19 males; body mass index: 27.8 ± 5.5 kg/m 2 ; age: 62 ± 10 years) participated in the study. Biases for the FitMate GS and both equations were low (ranging from -44 to -92 kcal or -2.3% to -5.1%), indicating good group-level accuracy. The FitMate GS had low bias, but the widest limits of agreement (-28.0% to 21.2%) compared with the 3 equations (Harris-Benedict: -15.8% to 11.2%; Mifflin St. Jeor: -17.1% to 6.9%; Henry: -15.4% to 11.5%). These differences were not due to volume of oxygen, BMI category, or sex. FitMate GS performed well on a group level, but its accuracy was poor on an individual level. Further research should develop better equations and validate tools to measure energy expenditure for accurate dietary recommendations for patients at nutrition risk. © 2018 American Society for Parenteral and Enteral Nutrition.

The C.L.E.A.R. Score: a new comprehensive assessment method for academic physicians in military medical centers.

PubMed

Buller, Jerome L; Tetteh, Hassan A

2012-07-01

Evaluation of medical officer performance is a critical leadership role. This study offers a comprehensive evaluation system for military physicians. The Comprehensive Assessment equation (COMPASS equation), a modified Cobb-Douglas equation, was developed to evaluate academic physicians. The COMPASS equation assesses military physicians within five comprehensive dimensions: (1) Clinical (2) Leadership, (3) Educational (4) Administrative, and (5) Research productivity excellence to yield a composite "C.L.E.A.R. Score." The COMPASS equation's fidelity was tested with a cohort of military physicians within the department of Obstetrics and Gynecology in the Capital District Region and a C.L.E.A.R. score was calculated for individual physicians. Mean C.L.E.A.R score was 53.6 +/- 28.8 (range 10.1-98.5). The responsiveness of the model was tested using two hypothetical physician models: "low-performing-faculty" and "super-faculty," and calculated C.L.E.A.R. scores were 6.3 and 153.4, respectively. The C.L.E.A.R. score appears to recognize and assess the performance excellence of military physicians. Weighting measured characteristics of the COMPASS equation can be used to promote organizational priorities. Thus, leaders of military medicine can communicate institutional priorities and inculcate them through use of the COMPASS equation to reward and recognize the activities of military medical officers that are commensurate with institutional goals.

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

PubMed

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

2017-05-20

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

A fast direct solver for boundary value problems on locally perturbed geometries

NASA Astrophysics Data System (ADS)

Zhang, Yabin; Gillman, Adrianna

2018-03-01

Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.

Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory.

PubMed

Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meissner, Ulf-G

2015-11-06

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ(1232) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

A low order flow/acoustics interaction method for the prediction of sound propagation using 3D adaptive hybrid grids

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

Kallinderis, Yannis, E-mail: kallind@otenet.gr; Vitsas, Panagiotis A.; Menounou, Penelope

2012-07-15

A low-order flow/acoustics interaction method for the prediction of sound propagation and diffraction in unsteady subsonic compressible flow using adaptive 3-D hybrid grids is investigated. The total field is decomposed into the flow field described by the Euler equations, and the acoustics part described by the Nonlinear Perturbation Equations. The method is shown capable of predicting monopole sound propagation, while employment of acoustics-guided adapted grid refinement improves the accuracy of capturing the acoustic field. Interaction of sound with solid boundaries is also examined in terms of reflection, and diffraction. Sound propagation through an unsteady flow field is examined using staticmore » and dynamic flow/acoustics coupling demonstrating the importance of the latter.« less

Implicit approximate-factorization schemes for the low-frequency transonic equation

NASA Technical Reports Server (NTRS)

Ballhaus, W. F.; Steger, J. L.

1975-01-01

Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory

NASA Astrophysics Data System (ADS)

Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meißner, Ulf-G.

2015-11-01

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ (1232 ) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

A low-parametric state equation for calculating the thermodynamic properties of substances in liquid and gaseous state

NASA Astrophysics Data System (ADS)

Kaplun, A. B.; Meshalkin, A. B.

2013-08-01

Using methods and approaches developed by the authors, a new low-parametric state equation for describing the thermal properties of normal substances is obtained that allows us to describe the thermal properties of gases, liquids, and fluids over a range of densities from the ideal gas state to the triple point, except for a critical region, with a high degree of accuracy close to that of an experiment. The caloric properties and speed of sound are calculated for argon, nitrogen, and carbon dioxide without using any caloric data except for the enthalpy of an ideal gas. It is established that the calculated values of enthalpy, heat capacity, the speed of speed of sound, etc., are in good agreement with the experimental (reliably tabulated) data.

Unsteady transonic flow analysis for low aspect ratio, pointed wings.

NASA Technical Reports Server (NTRS)

Kimble, K. R.; Ruo, S. Y.; Wu, J. M.; Liu, D. Y.

1973-01-01

Oswatitsch and Keune's parabolic method for steady transonic flow is applied and extended to thin slender wings oscillating in the sonic flow field. The parabolic constant for the wing was determined from the equivalent body of revolution. Laplace transform methods were used to derive the asymptotic equations for pressure coefficient, and the Adams-Sears iterative procedure was employed to solve the equations. A computer program was developed to find the pressure distributions, generalized force coefficients, and stability derivatives for delta, convex, and concave wing planforms.

Blow-up and symmetry of sign-changing solutions to some critical elliptic equations

NASA Astrophysics Data System (ADS)

Ben Ayed, Mohamed; El Mehdi, Khalil; Pacella, Filomena

In this paper we continue the analysis of the blow-up of low energy sign-changing solutions of semi-linear elliptic equations with critical Sobolev exponent, started in [M. Ben Ayed, K. El Mehdi, F. Pacella, Blow-up and nonexistence of sign-changing solutions to the Brezis-Nirenberg problem in dimension three, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press]. In addition we prove axial symmetry results for the same kind of solutions in a ball.

Low Altitude Near-the-Horizon Propagation: A Comparison Between RPO and M-Layer

DTIC Science & Technology

1993-12-01

scaling based on the assumption that a single mode contributes to the complete field strength (Ref. 31, output from M-Layer [Ref. 4, 5] in the over-the...PE. The parabolic equation approximation to the Maxwell wave equations is developed under the optical assumption that the operating frequency is so...profile data are specified (an array) capm zim profile data (modified index of refraction; an array) (a) RPO: from I to n/evs; M-Layer from 0 to nzlayr

Methods for estimating flow-duration curve and low-flow frequency statistics for ungaged locations on small streams in Minnesota

USGS Publications Warehouse

Ziegeweid, Jeffrey R.; Lorenz, David L.; Sanocki, Chris A.; Czuba, Christiana R.

2015-12-24

Equations developed in this study apply only to stream locations where flows are not substantially affected by regulation, diversion, or urbanization. All equations presented in this study will be incorporated into StreamStats, a web-based geographic information system tool developed by the U.S. Geological Survey. StreamStats allows users to obtain streamflow statistics, basin characteristics, and other information for user-selected locations on streams through an interactive map.

Indirect evidence for substantial damping of low-mode internal tides in the open ocean

DTIC Science & Technology

2015-09-12

see also Arbic et al., 2012; M€uller et al., 2012; Waterhouse et al., 2014] (C. B. Rocha, Mesoscale to submesoscale wavenumber spectra in Drake Passage...nominal horizontal resolution, at the equator , of 1/ 12.58. The simulations are forced by the M2 tide, the largest tidal constit- uent in the ocean, and by...2005] is given below. Thorough discussions on topographic wave drag and quadratic bottom friction and their appearance in the momentum equations can

Neutron star moments of inertia

NASA Technical Reports Server (NTRS)

Ravenhall, D. G.; Pethick, C. J.

1994-01-01

An approximation for the moment of inertia of a neutron star in terms of only its mass and radius is presented, and insight into it is obtained by examining the behavior of the relativistic structural equations. The approximation is accurate to approximately 10% for a variety of nuclear equations of state, for all except very low mass stars. It is combined with information about the neutron-star crust to obtain a simple expression (again in terms only of mass and radius) for the fractional moment of inertia of the crust.

Superconductor in a weak static gravitational field

NASA Astrophysics Data System (ADS)

Ummarino, Giovanni Alberto; Gallerati, Antonio

2017-08-01

We provide the detailed calculation of a general form for Maxwell and London equations that takes into account gravitational corrections in linear approximation. We determine the possible alteration of a static gravitational field in a superconductor making use of the time-dependent Ginzburg-Landau equations, providing also an analytic solution in the weak field condition. Finally, we compare the behavior of a high-T_ {c} superconductor with a classical low-T_ {c} superconductor, analyzing the values of the parameters that can enhance the reduction of the gravitational field.

Probabilistic Simulation for Nanocomposite Fracture

NASA Technical Reports Server (NTRS)

Chamis, Christos C.

2010-01-01

A unique probabilistic theory is described to predict the uniaxial strengths and fracture properties of nanocomposites. The simulation is based on composite micromechanics with progressive substructuring down to a nanoscale slice of a nanofiber where all the governing equations are formulated. These equations have been programmed in a computer code. That computer code is used to simulate uniaxial strengths and fracture of a nanofiber laminate. The results are presented graphically and discussed with respect to their practical significance. These results show smooth distributions from low probability to high.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

The ONR-602 experiment and investigation of particle precipitation near the equator

NASA Technical Reports Server (NTRS)

Miah, M. A.

1991-01-01

The global precipitation of radiation belt particles at low altitude was investigated, using the ONR-602 experiment on board U.S. Air Force mission S81-1. A combination of a main telescope, beginning analysis at a few MeV/nucleon, and a monitor system, giving results below 1 MeV/nucleon, was designed for measuring particle phenomena characterized by almost any energy spectrum. The monitor provides an indication of the presence of the particles at low energy, while the main telescope gives detailed flux and composition data for the higher energy events. Results of the instrument performance analysis indicate that, at the equator, the monitor telescope has the peak efficiency for particles of about 90 deg pitch angles. The large opening angle of 75 deg makes it possible to detect omnidirectional flux of quasi-trapped particles. The high-energy cosmic-ray background count is found to be very insignificant. It is demonstrated that the particle counting rates for the low-energy threshold have been almost entirely due to protons.

Damped Kadomtsev-Petviashvili Equation for Weakly Dissipative Solitons in Dense Relativistic Degenerate Plasmas

NASA Astrophysics Data System (ADS)

Ahmad, S.; Ata-ur-Rahman; Khan, S. A.; Hadi, F.

2017-12-01

We have investigated the properties of three-dimensional electrostatic ion solitary structures in highly dense collisional plasma composed of ultra-relativistically degenerate electrons and non-relativistic degenerate ions. In the limit of low ion-neutral collision rate, we have derived a damped Kadomtsev-Petviashvili (KP) equation using perturbation analysis. Supplemented by vanishing boundary conditions, the time varying solution of damped KP equation leads to a weakly dissipative compressive soliton. The real frequency behavior and linear damping of solitary pulse due to ion-neutral collisions is discussed. In the presence of weak transverse perturbations, soliton evolution with damping parameter and plasma density is delineated pointing out the extent of propagation using typical parameters of dense plasma in the interior of white dwarfs.

Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence.

PubMed

Sharma, Ati S; Moarref, Rashad; McKeon, Beverley J; Park, Jae Sung; Graham, Michael D; Willis, Ashley P

2016-02-01

We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010)]. This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence.

Nonalgebraic integrability of one reversible dynamical system of the Cremona type

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

1998-05-01

A reversible dynamical system (RDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions [the Chew-Low-type equations with crossing-symmetry matrix A(l,1)], are considered. This RDS is split into one- and two-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous three-point functional equation. Nonalgebraic integrability of RDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a nonresonant fixed point.

Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-04-15

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilizemore » the equilibrium and suppress the transition to drift-wave induced turbulence.« less

Reduced-Order Model Based Feedback Control For Modified Hasegawa-Wakatani Model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-01-28

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modi ed Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in ow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then a modelbased feedback controller is designed for the reduced order model using linear quadratic regulators (LQR). Finally, a linear quadratic gaussian (LQG) controller, which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHWmore » equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.« less

Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence

NASA Astrophysics Data System (ADS)

Sharma, Ati S.; Moarref, Rashad; McKeon, Beverley J.; Park, Jae Sung; Graham, Michael D.; Willis, Ashley P.

2016-02-01

We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010), 10.1017/S002211201000176X]. This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence.

Exact Lyapunov exponent of the harmonic magnon modes of one-dimensional Heisenberg-Mattis spin glasses

NASA Astrophysics Data System (ADS)

Sepehrinia, Reza; Niry, M. D.; Bozorg, B.; Tabar, M. Reza Rahimi; Sahimi, Muhammad

2008-03-01

A mapping is developed between the linearized equation of motion for the dynamics of the transverse modes at T=0 of the Heisenberg-Mattis model of one-dimensional (1D) spin glasses and the (discretized) random wave equation. The mapping is used to derive an exact expression for the Lyapunov exponent (LE) of the magnon modes of spin glasses and to show that it follows anomalous scaling at low magnon frequencies. In addition, through numerical simulations, the differences between the LE and the density of states of the wave equation in a discrete 1D model of randomly disordered media (those with a finite correlation length) and that of continuous media (with a zero correlation length) are demonstrated and emphasized.

Gaseous Viscous Peeling of Linearly Elastic Substrates

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2017-11-01

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the governing nonlinear evolution equation describes the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the evolution equation and enable solution by self-similarity. During the peeling process the flow-field transitions between the different limits and the respective approximate solutions. The sequence of limits occurring during the propagation dynamics can be related to the thickness of the prewetting layer of the configuration at rest, yielding an approximate description of the entire peeling dynamics. The results are validated by numerical solutions of the evolution equation. Israel Science Foundation 818/13.

An adaptive grid algorithm for one-dimensional nonlinear equations

NASA Technical Reports Server (NTRS)

Gutierrez, William E.; Hills, Richard G.

1990-01-01

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme.

Mathematical Analysis of the Solidification Behavior of Plain Steel Based on Solute- and Heat-Transfer Equations in the Liquid-Solid Zone

NASA Astrophysics Data System (ADS)

Fujimura, Toshio; Takeshita, Kunimasa; Suzuki, Ryosuke O.

2018-04-01

An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions ( e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman's solution are consistent in the low carbon range. A conventional numerical heat analysis ( i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.

Model reduction for stochastic chemical systems with abundant species

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

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2015-12-07

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. We first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently, we prove that, in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equationmore » which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore, we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.« less

I-Love-Q to the extreme

NASA Astrophysics Data System (ADS)

Silva, Hector O.; Yunes, Nicolás

2018-01-01

Certain bulk properties of neutron stars, in particular their moment of inertia, rotational quadrupole moment and tidal Love number, when properly normalized, are related to one another in a nearly equation of state independent way. The goal of this paper is to test these relations with extreme equations of state at supranuclear densities constrained to satisfy only a handful of generic, physically sensible conditions. By requiring that the equation of state be (i) barotropic and (ii) its associated speed of sound be real, we construct a piecewise function that matches a tabulated equation of state at low densities, while matching a stiff equation of state parametrized by its sound speed in the high-density region. We show that the I-Love-Q relations hold to 1 percent with this class of equations of state, even in the extreme case where the speed of sound becomes superluminal and independently of the transition density. We also find further support for the interpretation of the I-Love-Q relations as an emergent symmetry due to the nearly constant eccentricity of isodensity contours inside the star. These results reinforce the robustness of the I-Love-Q relations against our current incomplete picture of physics at supranuclear densities, while strengthening our confidence in the applicability of these relations in neutron star astrophysics.

An Ab Initio and Kinetic Monte Carlo Simulation Study of Lithium Ion Diffusion on Graphene

PubMed Central

Zhong, Kehua; Yang, Yanmin; Xu, Guigui; Zhang, Jian-Min; Huang, Zhigao

2017-01-01

The Li+ diffusion coefficients in Li+-adsorbed graphene systems were determined by combining first-principle calculations based on density functional theory with Kinetic Monte Carlo simulations. The calculated results indicate that the interactions between Li ions have a very important influence on lithium diffusion. Based on energy barriers directly obtained from first-principle calculations for single-Li+ and two-Li+ adsorbed systems, a new equation predicting energy barriers with more than two Li ions was deduced. Furthermore, it is found that the temperature dependence of Li+ diffusion coefficients fits well to the Arrhenius equation, rather than meeting the equation from electrochemical impedance spectroscopy applied to estimate experimental diffusion coefficients. Moreover, the calculated results also reveal that Li+ concentration dependence of diffusion coefficients roughly fits to the equation from electrochemical impedance spectroscopy in a low concentration region; however, it seriously deviates from the equation in a high concentration region. So, the equation from electrochemical impedance spectroscopy technique could not be simply used to estimate the Li+ diffusion coefficient for all Li+-adsorbed graphene systems with various Li+ concentrations. Our work suggests that interactions between Li ions, and among Li ion and host atoms will influence the Li+ diffusion, which determines that the Li+ intercalation dependence of Li+ diffusion coefficient should be changed and complex. PMID:28773122

Advancements in engineering turbulence modeling

NASA Technical Reports Server (NTRS)

Shih, T.-H.

1991-01-01

Some new developments in two-equation models and second order closure models are presented. Two-equation models (k-epsilon models) have been widely used in computational fluid dynamics (CFD) for engineering problems. Most of low-Reynolds number two-equation models contain some wall-distance damping functions to account for the effect of wall on turbulence. However, this often causes the confusion and difficulties in computing flows with complex geometry and also needs an ad hoc treatment near the separation and reattachment points. A set of modified two-equation models is proposed to remove the aforementioned shortcomings. The calculations using various two-equation models are compared with direct numerical simulations of channel flow and flat boundary layers. Development of a second order closure model is also discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All the existing models poorly predict the normal stresses near the wall and fail to predict the 3-D effect of mean flow on the turbulence (e.g. decrease in the shear stress caused by the cross flow in the boundary layer). The newly developed second order near-wall turbulence model is described and is capable of capturing the near-wall behavior of turbulence as well as the effect of 3-D mean flow on the turbulence.

A stability analysis of the power-law steady state of marine size spectra.

PubMed

Datta, Samik; Delius, Gustav W; Law, Richard; Plank, Michael J

2011-10-01

This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick-von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick-von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems.

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

PubMed

Cid, Jaime A; von Davier, Alina A

2015-05-01

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

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

PubMed

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

2018-02-01

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

Improving estimates of streamflow characteristics by using Landsat-1 imagery

USGS Publications Warehouse

Hollyday, Este F.

1976-01-01

Imagery from the first Earth Resources Technology Satellite (renamed Landsat-1) was used to discriminate physical features of drainage basins in an effort to improve equations used to estimate streamflow characteristics at gaged and ungaged sites. Records of 20 gaged basins in the Delmarva Peninsula of Maryland, Delaware, and Virginia were analyzed for 40 statistical streamflow characteristics. Equations relating these characteristics to basin characteristics were obtained by a technique of multiple linear regression. A control group of equations contains basin characteristics derived from maps. An experimental group of equations contains basin characteristics derived from maps and imagery. Characteristics from imagery were forest, riparian (streambank) vegetation, water, and combined agricultural and urban land use. These basin characteristics were isolated photographically by techniques of film-density discrimination. The area of each characteristic in each basin was measured photometrically. Comparison of equations in the control group with corresponding equations in the experimental group reveals that for 12 out of 40 equations the standard error of estimate was reduced by more than 10 percent. As an example, the standard error of estimate of the equation for the 5-year recurrence-interval flood peak was reduced from 46 to 32 percent. Similarly, the standard error of the equation for the mean monthly flow for September was reduced from 32 to 24 percent, the standard error for the 7-day, 2-year recurrence low flow was reduced from 136 to 102 percent, and the standard error for the 3-day, 2-year flood volume was reduced from 30 to 12 percent. It is concluded that data from Landsat imagery can substantially improve the accuracy of estimates of some streamflow characteristics at sites in the Delmarva Peninsula.

Pupillary Responses to Robotic and Human Emotions: The Uncanny Valley and Media Equation Confirmed.

PubMed

Reuten, Anne; van Dam, Maureen; Naber, Marnix

2018-01-01

Physiological responses during human-robots interaction are useful alternatives to subjective measures of uncanny feelings for nearly humanlike robots (uncanny valley) and comparable emotional responses between humans and robots (media equation). However, no studies have employed the easily accessible measure of pupillometry to confirm the uncanny valley and media equation hypotheses, evidence in favor of the existence of these hypotheses in interaction with emotional robots is scarce, and previous studies have not controlled for low level image statistics across robot appearances. We therefore recorded pupil size of 40 participants that viewed and rated pictures of robotic and human faces that expressed a variety of basic emotions. The robotic faces varied along the dimension of human likeness from cartoonish to humanlike. We strictly controlled for confounding factors by removing backgrounds, hair, and color, and by equalizing low level image statistics. After the presentation phase, participants indicated to what extent the robots appeared uncanny and humanlike, and whether they could imagine social interaction with the robots in real life situations. The results show that robots rated as nearly humanlike scored higher on uncanniness, scored lower on imagined social interaction, evoked weaker pupil dilations, and their emotional expressions were more difficult to recognize. Pupils dilated most strongly to negative expressions and the pattern of pupil responses across emotions was highly similar between robot and human stimuli. These results highlight the usefulness of pupillometry in emotion studies and robot design by confirming the uncanny valley and media equation hypotheses.

Predictive beyond-mean-field rate equations for multisite lattice–gas models of catalytic surface reactions: CO oxidation on Pd(100)

DOE PAGES

Liu, Da -Jiang; Zahariev, Federico; Gordon, Mark S.; ...

2016-11-29

Tailored multisite lattice–gas (msLG) models are developed for CO oxidation on Pd(100) at low-pressures. These models include multiple adsorption site types and superlattice adlayer ordering due to short-range exclusion for highly mobile reactant adspecies. However, they are simplified to neglect longer-range weaker adspecies interactions, so that the key energetic parameters are the CO desorption barrier and the reaction barrier. We discuss existing density functional theory results for these energies and present additional analysis for CO adsorption. After also including an appropriate nontrivial specification of the dynamics of adsorption onto mixed reactant adlayers, we develop rate equations for the reaction kinetics.more » Our formulation goes beyond traditional mean-field (MF) Langmuirian treatments by accounting for multiple adsorption sites and for the strong spatial correlations associated with superlattice ordering. Specifically, we utilize factorization approximations based on appropriate site motifs, and also Padé resummation of exact low-coverage expansions for sticking coefficients. Our beyond-MF rate equations are successful in accurately predicting key aspects of reactive steady-state behavior, and thus expand the utility of rate equation formulations in surface chemistry. This is confirmed by comparison with precise kinetic Monte Carlo simulation results. Furthermore, we not only assess bistability and criticality observed for CO oxidation but also find more complex multistability associated with symmetry-breaking transitions in high-coverage CO adlayers.« less

Assimilation of Sea Surface Temperature in a doubly, two-way nested primitive equation model of the Ligurian Sea

NASA Astrophysics Data System (ADS)

Barth, A.; Alvera-Azcarate, A.; Rixen, M.; Beckers, J.-M.; Testut, C.-E.; Brankart, J.-M.; Brasseur, P.

2003-04-01

The GHER 3D primitive equation model is implemented with three different resolutions: a low resolution model (1/4^o) covering the whole Mediterranean Sea, an intermediate resolution model (1/20^o) of the Liguro-Provençal basin and a high resolution model (1/60^o) simulating the fine mesoscale structures in the Ligurian Sea. Boundary conditions and the averaged fields (feedback) are exchanged between two successive nesting levels. The model of the Ligurian Sea is also coupled with the assimilation package SESAM. It allows to assimilate satellite data and in situ observations using the local adaptative SEEK (Singular Evolutive Extended Kalman) filter. Instead of evolving the error space by the numerically expensive Lyapunov equation, a simplified algebraic equation depending on the misfit between observation and model forecast is used. Starting from the 1st January 1998 the low and intermediate resolution models are spun up for 18 months. The initial conditions for the Ligurian Sea are interpolated from the intermediate resolution model. The three models are then integrated until August 1999. During this period AVHRR Sea Surface Temperature of the Ligurian Sea is assimilated. The results are validated by using CTD and XBT profiles of the SIRENA cruise from the SACLANT Center. The overall objective of this study is pre-operational. It should help to identify limitations and weaknesses of forecasting methods and to suggest improvements of existing operational models.

Pupillary Responses to Robotic and Human Emotions: The Uncanny Valley and Media Equation Confirmed

PubMed Central

Reuten, Anne; van Dam, Maureen; Naber, Marnix

2018-01-01

Physiological responses during human–robots interaction are useful alternatives to subjective measures of uncanny feelings for nearly humanlike robots (uncanny valley) and comparable emotional responses between humans and robots (media equation). However, no studies have employed the easily accessible measure of pupillometry to confirm the uncanny valley and media equation hypotheses, evidence in favor of the existence of these hypotheses in interaction with emotional robots is scarce, and previous studies have not controlled for low level image statistics across robot appearances. We therefore recorded pupil size of 40 participants that viewed and rated pictures of robotic and human faces that expressed a variety of basic emotions. The robotic faces varied along the dimension of human likeness from cartoonish to humanlike. We strictly controlled for confounding factors by removing backgrounds, hair, and color, and by equalizing low level image statistics. After the presentation phase, participants indicated to what extent the robots appeared uncanny and humanlike, and whether they could imagine social interaction with the robots in real life situations. The results show that robots rated as nearly humanlike scored higher on uncanniness, scored lower on imagined social interaction, evoked weaker pupil dilations, and their emotional expressions were more difficult to recognize. Pupils dilated most strongly to negative expressions and the pattern of pupil responses across emotions was highly similar between robot and human stimuli. These results highlight the usefulness of pupillometry in emotion studies and robot design by confirming the uncanny valley and media equation hypotheses. PMID:29875722

Effects of a parallel electric field and the geomagnetic field in the topside ionosphere on auroral and photoelectron energy distributions

NASA Technical Reports Server (NTRS)

Min, Q.-L.; Lummerzheim, D.; Rees, M. H.; Stamnes, K.

1993-01-01

The consequences of electric field acceleration and an inhomogeneous magnetic field on auroral electron energy distributions in the topside ionosphere are investigated. The one-dimensional, steady state electron transport equation includes elastic and inelastic collisions, an inhomogeneous magnetic field, and a field-aligned electric field. The case of a self-consistent polarization electric field is considered first. The self-consistent field is derived by solving the continuity equation for all ions of importance, including diffusion of O(+) and H(+), and the electron and ion energy equations to derive the electron and ion temperatures. The system of coupled electron transport, continuity, and energy equations is solved numerically. Recognizing observations of parallel electric fields of larger magnitude than the baseline case of the polarization field, the effect of two model fields on the electron distribution function is investigated. In one case the field is increased from the polarization field magnitude at 300 km to a maximum at the upper boundary of 800 km, and in another case a uniform field is added to the polarization field. Substantial perturbations of the low energy portion of the electron flux are produced: an upward directed electric field accelerates the downward directed flux of low-energy secondary electrons and decelerates the upward directed component. Above about 400 km the inhomogeneous magnetic field produces anisotropies in the angular distribution of the electron flux. The effects of the perturbed energy distributions on auroral spectral emission features are noted.

Effects of a Parallel Electric Field and the Geomagnetic Field in the Topside Ionosphere on Auroral and Photoelectron Energy Distributions

NASA Technical Reports Server (NTRS)

Min, Q.-L.; Lummerzheim, D.; Rees, M. H.; Stamnes, K.

1993-01-01

The consequences of electric field acceleration and an inhomogencous magnetic field on auroral electron energy distributions in the topside ionosphere are investigated. The one- dimensional, steady state electron transport equation includes elastic and inelastic collisions, an inhomogencous magnetic field, and a field-aligned electric field. The case of a self-consistent polarization electric field is considered first. The self-consistent field is derived by solving the continuity equation for all ions of importance, including diffusion of 0(+) and H(+), and the electron and ion energy equations to derive the electron and ion temperatures. The system of coupled electron transport, continuity, and energy equations is solved numerically. Recognizing observations of parallel electric fields of larger magnitude than the baseline case of the polarization field, the effect of two model fields on the electron distribution function in investigated. In one case the field is increased from the polarization field magnitude at 300 km to a maximum at the upper boundary of 800 km, and in another case a uniform field is added to the polarization field. Substantial perturbations of the low energy portion of the electron flux are produced: an upward directed electric field accelerates the downward directed flux of low-energy secondary electrons and decelerates the upward directed component. Above about 400 km the inhomogencous magnetic field produces anisotropies in the angular distribution of the electron flux. The effects of the perturbed energy distributions on auroral spectral emission features are noted.

Optimisation of an idealised primitive equation ocean model using stochastic parameterization

NASA Astrophysics Data System (ADS)

Cooper, Fenwick C.

2017-05-01

Using a simple parameterization, an idealised low resolution (biharmonic viscosity coefficient of 5 × 1012 m4s-1 , 128 × 128 grid) primitive equation baroclinic ocean gyre model is optimised to have a much more accurate climatological mean, variance and response to forcing, in all model variables, with respect to a high resolution (biharmonic viscosity coefficient of 8 × 1010 m4s-1 , 512 × 512 grid) equivalent. For example, the change in the climatological mean due to a small change in the boundary conditions is more accurate in the model with parameterization. Both the low resolution and high resolution models are strongly chaotic. We also find that long timescales in the model temperature auto-correlation at depth are controlled by the vertical temperature diffusion parameter and time mean vertical advection and are caused by short timescale random forcing near the surface. This paper extends earlier work that considered a shallow water barotropic gyre. Here the analysis is extended to a more turbulent multi-layer primitive equation model that includes temperature as a prognostic variable. The parameterization consists of a constant forcing, applied to the velocity and temperature equations at each grid point, which is optimised to obtain a model with an accurate climatological mean, and a linear stochastic forcing, that is optimised to also obtain an accurate climatological variance and 5 day lag auto-covariance. A linear relaxation (nudging) is not used. Conservation of energy and momentum is discussed in an appendix.

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

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

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2017-03-29

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Helium atmospheric pressure plasma jets touching dielectric and metal surfaces

NASA Astrophysics Data System (ADS)

Norberg, Seth A.; Johnsen, Eric; Kushner, Mark J.

2015-07-01

Atmospheric pressure plasma jets (APPJs) are being investigated in the context plasma medicine and biotechnology applications, and surface functionalization. The composition of the surface being treated ranges from plastics, liquids, and biological tissue, to metals. The dielectric constant of these materials ranges from as low as 1.5 for plastics to near 80 for liquids, and essentially infinite for metals. The electrical properties of the surface are not independent variables as the permittivity of the material being treated has an effect on the dynamics of the incident APPJ. In this paper, results are discussed from a computational investigation of the interaction of an APPJ incident onto materials of varying permittivity, and their impact on the discharge dynamics of the plasma jet. The computer model used in this investigation solves Poisson's equation, transport equations for charged and neutral species, the electron energy equation, and the Navier-Stokes equations for the neutral gas flow. The APPJ is sustained in He/O2 = 99.8/0.2 flowing into humid air, and is directed onto dielectric surfaces in contact with ground with dielectric constants ranging from 2 to 80, and a grounded metal surface. Low values of relative permittivity encourage propagation of the electric field into the treated material and formation and propagation of a surface ionization wave. High values of relative permittivity promote the restrike of the ionization wave and the formation of a conduction channel between the plasma discharge and the treated surface. The distribution of space charge surrounding the APPJ is discussed.

Kaluza-Klein two-brane-worlds cosmology at low energy

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

Feranie, S.; Arianto; Zen, Freddy P.

2010-04-15

We study two (4+n)-dimensional branes embedded in (5+n)-dimensional spacetime. Using the gradient expansion approximation, we find that the effective theory is described by (4+n)-dimensional scalar-tensor gravity with a specific coupling function. Based on this theory we investigate the Kaluza-Klein two-brane-worlds cosmology at low energy, in both the static and the nonstatic internal dimensions. In the case of the static internal dimensions, the effective gravitational constant in the induced Friedmann equation depends on the equations of state of the brane matter, and the dark radiation term naturally appears. In the nonstatic case we take a relation between the external and internalmore » scale factors of the form b(t)=a{sup {gamma}(t)} in which the brane world evolves with two scale factors. In this case, the induced Friedmann equation on the brane is modified in the effective gravitational constant and the term proportional to a{sup -4{beta}.} For dark radiation, we find {gamma}=-2/(1+n). Finally, we discuss the issue of conformal frames which naturally arises with scalar-tensor theories. We find that the static internal dimensions in the Jordan frame may become nonstatic in the Einstein frame.« less

The Kondo problem. II. Crossover from asymptotic freedom to infrared slavery

NASA Astrophysics Data System (ADS)

Schlottmann, P.

1982-04-01

In the preceding paper we transformed the s-d Hamiltonian onto a resonance level with a large perturbation and derived the scaling equations for the vertices, the invariant coupling, and the resonance width. The scaling equations are integrated under the assumption that the energy dependence of the resonance width can be neglected. The transcendental equation obtained in this way for the renormalized resonance width is solved in the relevant limits and allows a calculation of the static and dynamical susceptibility. At high temperatures the perturbation expansion for the relaxation rate and the susceptibility is reproduced up to third order in Jρ. At low temperatures the lifetime and χ0 remain finite and vary according to a Fermi-liquid theory. The approximation scheme interpolates in this way between the asymptotic freedom and the infrared slavery, yielding a smooth crossover. The present results are in quantitative agreement with previous ones obtained with the relaxation-kernel method by Götze and Schlottmann. The advantages and drawbacks of the method are discussed. The calculation of the dynamical susceptibility is extended to nonzero external magnetic fields. The quasielastic peak of χ''(ω)ω is suppressed at low temperatures and large magnetic fields and shoulders develop at ω=+/-B.

Constitutive Equation and Hot Compression Deformation Behavior of Homogenized Al–7.5Zn–1.5Mg–0.2Cu–0.2Zr Alloy

PubMed Central

He, Jianliang; Zhang, Datong; Zhang, Weiweng; Qiu, Cheng; Zhang, Wen

2017-01-01

The deformation behavior of homogenized Al–7.5Zn–1.5Mg–0.2Cu–0.2Zr alloy has been studied by a set of isothermal hot compression tests, which were carried out over the temperature ranging from 350 °C to 450 °C and the strain rate ranging from 0.001 s−1 to 10 s−1 on Gleeble-3500 thermal simulation machine. The associated microstructure was studied using electron back scattered diffraction (EBSD) and transmission electron microscopy (TEM). The results showed that the flow stress is sensitive to strain rate and deformation temperature. The shape of true stress-strain curves obtained at a low strain rate (≤0.1 s−1) conditions shows the characteristic of dynamic recrystallization (DRX). Two Arrhenius-typed constitutive equation without and with strain compensation were established based on the true stress-strain curves. Constitutive equation with strain compensation has more precise predictability. The main softening mechanism of the studied alloy is dynamic recovery (DRV) accompanied with DRX, particularly at deformation conditions, with low Zener-Holloman parameters. PMID:29057825

Linear and nonlinear response of a rotating tokamak plasma to a resonant error-field

NASA Astrophysics Data System (ADS)

Fitzpatrick, Richard

2014-09-01

An in-depth investigation of the effect of a resonant error-field on a rotating, quasi-cylindrical, tokamak plasma is preformed within the context of constant-ψ, resistive-magnetohydrodynamical theory. General expressions for the response of the plasma at the rational surface to the error-field are derived in both the linear and nonlinear regimes, and the extents of these regimes mapped out in parameter space. Torque-balance equations are also obtained in both regimes. These equations are used to determine the steady-state plasma rotation at the rational surface in the presence of the error-field. It is found that, provided the intrinsic plasma rotation is sufficiently large, the torque-balance equations possess dynamically stable low-rotation and high-rotation solution branches, separated by a forbidden band of dynamically unstable solutions. Moreover, bifurcations between the two stable solution branches are triggered as the amplitude of the error-field is varied. A low- to high-rotation bifurcation is invariably associated with a significant reduction in the width of the magnetic island chain driven at the rational surface, and vice versa. General expressions for the bifurcation thresholds are derived and their domains of validity mapped out in parameter space.

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Resonant-Triad Interaction

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented using the generalized scaling of Lee. It is shown that resonant-triads can interact nonlinearly within the common critical layer when their (fundamental) Strouhal numbers are different by a factor whose magnitude is of the order of the growth rate multiplied by the wavenumber of the instability wave. Since the growth rates of the instability modes become larger and the critical layers become thicker as the instability waves propagate downstream, the frequency-detuned resonant-triads that grow independently of each other in the upstream region can interact nonlinearly in the later downstream stage. In the final stage of the non-equilibrium critical-layer evolution, a wide range of instability waves with the scaled frequencies differing by almost an Order of (l) can nonlinearly interact. Low-frequency modes are also generated by the nonlinear interaction between oblique waves in the critical layer. The system of partial differential critical-layer equations along with the jump equations are presented here. The amplitude equations with their numerical solutions are given in Part 2. The nonlinearly generated low-frequency components are also investigated in Part 2.

One-dimensional Lagrangian implicit hydrodynamic algorithm for Inertial Confinement Fusion applications

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

Ramis, Rafael, E-mail: rafael.ramis@upm.es

A new one-dimensional hydrodynamic algorithm, specifically developed for Inertial Confinement Fusion (ICF) applications, is presented. The scheme uses a fully conservative Lagrangian formulation in planar, cylindrical, and spherically symmetric geometries, and supports arbitrary equations of state with separate ion and electron components. Fluid equations are discretized on a staggered grid and stabilized by means of an artificial viscosity formulation. The space discretized equations are advanced in time using an implicit algorithm. The method includes several numerical parameters that can be adjusted locally. In regions with low Courant–Friedrichs–Lewy (CFL) number, where stability is not an issue, they can be adjusted tomore » optimize the accuracy. In typical problems, the truncation error can be reduced by a factor between 2 to 10 in comparison with conventional explicit algorithms. On the other hand, in regions with high CFL numbers, the parameters can be set to guarantee unconditional stability. The method can be integrated into complex ICF codes. This is demonstrated through several examples covering a wide range of situations: from thermonuclear ignition physics, where alpha particles are managed as an additional species, to low intensity laser–matter interaction, where liquid–vapor phase transitions occur.« less

Tensile properties and flow behavior analysis of modified 9Cr-1Mo steel clad tube material

NASA Astrophysics Data System (ADS)

Singh, Kanwarjeet; Latha, S.; Nandagopal, M.; Mathew, M. D.; Laha, K.; Jayakumar, T.

2014-11-01

The tensile properties and flow behavior of modified 9Cr-1Mo steel clad tube have been investigated in the framework of various constitutive equations for a wide range of temperatures (300-923 K) and strain rates (3 × 10-3 s-1, 3 × 10-4 s-1 and 3 × 10-5 s-1). The tensile flow behavior of modified 9Cr-1Mo steel clad tube was most accurately described by Voce equation. The variation of instantaneous work hardening rate (θ = dσ/dε) and σθ with stress (σ) indicated two stage behavior characterized by rapid decrease at low stresses (transient stage) followed by a gradual decrease in high stresses (Stage III). The variation of work hardening parameters and work hardening rate in terms of θ vs. σ and σθ vs. σ with temperature exhibited three distinct regimes. Rapid decrease in flow stress and work hardening parameters and rapid shift of θ vs. σ and σθ vs. σ towards low stresses with increase in temperature indicated dynamic recovery at high temperatures. Tensile properties of the material have been best predicted from Voce equation.

Modeling of nonequilibrium space plasma flows

NASA Technical Reports Server (NTRS)

Gombosi, Tamas

1995-01-01

Godunov-type numerical solution of the 20 moment plasma transport equations. One of the centerpieces of our proposal was the development of a higher order Godunov-type numerical scheme to solve the gyration dominated 20 moment transport equations. In the first step we explored some fundamental analytic properties of the 20 moment transport equations for a low b plasma, including the eigenvectors and eigenvalues of propagating disturbances. The eigenvalues correspond to wave speeds, while the eigenvectors characterize the transported physical quantities. In this paper we also explored the physically meaningful parameter range of the normalized heat flow components. In the second step a new Godunov scheme type numerical method was developed to solve the coupled set of 20 moment transport equations for a quasineutral single-ion plasma. The numerical method and the first results were presented at several national and international meetings and a paper describing the method has been published in the Journal of Computational Physics. To our knowledge this is the first numerical method which is capable of producing stable time-dependent solutions to the full 20 (or 16) moment set of transport equations, including the full heat flow equation. Previous attempts resulted in unstable (oscillating) solutions of the heat flow equations. Our group invested over two man-years into the development and implementation of the new method. The present model solves the 20 moment transport equations for an ion species and thermal electrons in 8 domain extending from a collision dominated to a collisionless region (200 km to 12,000 km). This model has been applied to study O+ acceleration due to Joule heating in the lower ionosphere.

Analytical estimates of radial segregation in Bridgman growth from low-level steady and periodic accelerations

NASA Astrophysics Data System (ADS)

Naumann, Robert J.; Baugher, Charles

1992-08-01

Estimates of the convective flows driven by horizontal temperature gradients in the vertical Bridgman configuration are made for dilute systems subject to the low level accelerations typical of the residual accelerations experienced by a spacecraft in low Earth orbit. The estimates are made by solving the Navier-Stokes momentum equation in one dimension. The mass transport equation is then solved in two dimensions using a first-order perturbation method. This approach is valid provided the convective velocities are small compared to the growth velocity which generally requires a reduced gravity environment. If this condition is satisfied, there will be no circulating cells, and hence no convective transport along the vertical axis. However, the variations in the vertical velocity with radius will give rise to radial segregation. The approximate analytical model developed here can predict the degree of radial segregation for a variety of material and processing parameters to an accuracy well within a factor of two as compared against numerical computations of the full set of Navier-Stokes equations for steady accelerations. It has the advantage of providing more insight into the complex interplay of the processing parameters and how they affect the solute distribution in the grown crystal. This could be extremely valuable in the design of low-gravity experiments in which the intent is to control radial segregation. Also, the analysis can be extended to consider transient and periodic accelerations, which is difficult and costly to do numerically. Surprisingly, it was found that the relative radial segregation falls as the inverse cube of the frequency for periodic accelerations whose periods are short compared with the characteristic diffusion time.

Formation of the Aerosol of Space Origin in Earth's Atmosphere

NASA Technical Reports Server (NTRS)

Kozak, P. M.; Kruchynenko, V. G.

2011-01-01

The problem of formation of the aerosol of space origin in Earth s atmosphere is examined. Meteoroids of the mass range of 10-18-10-8 g are considered as a source of its origin. The lower bound of the mass range is chosen according to the data presented in literature, the upper bound is determined in accordance with the theory of Whipple s micrometeorites. Basing on the classical equations of deceleration and heating for small meteor bodies we have determined the maximal temperatures of the particles, and altitudes at which they reach critically low velocities, which can be called as velocities of stopping . As a condition for the transformation of a space particle into an aerosol one we have used the condition of non-reaching melting temperature of the meteoroid. The simplified equation of deceleration without earth gravity and barometric formula for the atmosphere density are used. In the equation of heat balance the energy loss for heating is neglected. The analytical solution of the simplified equations is used for the analysis.

Spinor description of D = 5 massless low-spin gauge fields

NASA Astrophysics Data System (ADS)

Uvarov, D. V.

2016-07-01

Spinor description for the curvatures of D = 5 Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence of sources symmetric curvature spinors with 2s indices obey first-order equations that in the linearized limit reduce to Dirac-type equations for massless free fields. These equations allow for a higher-spin generalization similarly to 4d case. Their solution in the form of the integral over Lorentz-harmonic variables parametrizing coset manifold {SO}(1,4)/({SO}(1,1)× {ISO}(3)) isomorphic to the three-sphere is considered. Superparticle model that contains such Lorentz harmonics as dynamical variables, as well as harmonics parametrizing the two-sphere {SU}(2)/U(1) is proposed. The states in its spectrum are given by the functions on S 3 that upon integrating over the Lorentz harmonics reproduce on-shell symmetric curvature spinors for various supermultiplets of D = 5 space-time supersymmetry.

Coupled equations of electromagnetic waves in nonlinear metamaterial waveguides.

PubMed

Azari, Mina; Hatami, Mohsen; Meygoli, Vahid; Yousefi, Elham

2016-11-01

Over the past decades, scientists have presented ways to manipulate the macroscopic properties of a material at levels unachieved before, and called them metamaterials. This research can be considered an important step forward in electromagnetics and optics. In this study, higher-order nonlinear coupled equations in a special kind of metamaterial waveguides (a planar waveguide with metamaterial core) will be derived from both electric and magnetic components of the transverse electric mode of electromagnetic pulse propagation. On the other hand, achieving the refractive index in this research is worthwhile. It is also shown that the coupled equations are not symmetric with respect to the electric and magnetic fields, unlike these kinds of equations in fiber optics and dielectric waveguides. Simulations on the propagation of a fundamental soliton pulse in a nonlinear metamaterial waveguide near the resonance frequency (a little lower than the magnetic resonant frequency) are performed to study its behavior. These pulses are recommended to practice in optical communications in controlled switching by external voltage, even in low power.

Steady-state and transient analysis of a squeeze film damper bearing for rotor stability

NASA Technical Reports Server (NTRS)

Barrett, L. E.; Gunter, E. J.

1975-01-01

A study of the steady-state and transient response of the squeeze film damper bearing is presented. Both the steady-state and transient equations for the hydrodynamic bearing forces are derived. The bearing equivalent stiffness and damping coefficients are determined by steady-state equations. These coefficients are used to find the bearing configuration which will provide the optimum support characteristics based on a stability analysis of the rotor-bearing system. The transient analysis of rotor-bearing systems is performed by coupling the bearing and journal equations and integrating forward in time. The effects of unbalance, cavitation, and retainer springs are included in the analysis. Methods of determining the stability of a rotor-bearing system under the influence of aerodynamic forces and internal shaft friction are discussed with emphasis on solving the system characteristic frequency equation and on producing stability maps. It is shown that for optimum stability and low force transmissability the squeeze bearing should operate at an eccentricity ratio epsilon 0.4.

Extension of the BMCSL equation of state for hard spheres to the metastable disordered region: Application to the SAFT approach

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

Paricaud, P.

2015-07-28

A simple modification of the Boublík-Mansoori-Carnahan-Starling-Leland equation of state is proposed for an application to the metastable disordered region. The new model has a positive pole at the jamming limit and can accurately describe the molecular simulation data of pure hard in the stable fluid region and along the metastable branch. The new model has also been applied to binary mixtures hard spheres, and an excellent description of the fluid and metastable branches can be obtained by adjusting the jamming packing fraction. The new model for hard sphere mixtures can be used as the repulsive term of equations of statemore » for real fluids. In this case, the modified equations of state give very similar predictions of thermodynamic properties as the original models, and one can remove the multiple liquid density roots observed for some versions of the Statistical Associating Fluid Theory (SAFT) at low temperature without any modification of the dispersion term.« less

A stabilized element-based finite volume method for poroelastic problems

NASA Astrophysics Data System (ADS)

Honório, Hermínio T.; Maliska, Clovis R.; Ferronato, Massimiliano; Janna, Carlo

2018-07-01

The coupled equations of Biot's poroelasticity, consisting of stress equilibrium and fluid mass balance in deforming porous media, are numerically solved. The governing partial differential equations are discretized by an Element-based Finite Volume Method (EbFVM), which can be used in three dimensional unstructured grids composed of elements of different types. One of the difficulties for solving these equations is the numerical pressure instability that can arise when undrained conditions take place. In this paper, a stabilization technique is developed to overcome this problem by employing an interpolation function for displacements that considers also the pressure gradient effect. The interpolation function is obtained by the so-called Physical Influence Scheme (PIS), typically employed for solving incompressible fluid flows governed by the Navier-Stokes equations. Classical problems with analytical solutions, as well as three-dimensional realistic cases are addressed. The results reveal that the proposed stabilization technique is able to eliminate the spurious pressure instabilities arising under undrained conditions at a low computational cost.

Wilsonian Renormalization Group and the Lippmann-Schwinger Equation with a Multitude of Cutoff Parameters

NASA Astrophysics Data System (ADS)

Epelbaum, E.; Gegelia, J.; Meißner, Ulf-G.

2018-03-01

The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an illustration, a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained. The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed. Supported in part by BMBF under Grant No. 05P2015 - NUSTAR R&D), DFG and NSFC through Funds Provided to the Sino- German CRC 110 “Symmetries and the Emergence of Structure in QCD”, National Natural Science Foundation of China under Grant No. 11621131001, DFG Grant No. TRR110, the Georgian Shota Rustaveli National Science Foundation (grant FR/417/6-100/14) and the CAS President’s International Fellowship Initiative (PIFI) under Grant No. 2017VMA0025

Calculation of Thermally-Induced Displacements in Spherically Domed Ion Engine Grids

NASA Technical Reports Server (NTRS)

Soulas, George C.

2006-01-01

An analytical method for predicting the thermally-induced normal and tangential displacements of spherically domed ion optics grids under an axisymmetric thermal loading is presented. A fixed edge support that could be thermally expanded is used for this analysis. Equations for the displacements both normal and tangential to the surface of the spherical shell are derived. A simplified equation for the displacement at the center of the spherical dome is also derived. The effects of plate perforation on displacements and stresses are determined by modeling the perforated plate as an equivalent solid plate with modified, or effective, material properties. Analytical model results are compared to the results from a finite element model. For the solid shell, comparisons showed that the analytical model produces results that closely match the finite element model results. The simplified equation for the normal displacement of the spherical dome center is also found to accurately predict this displacement. For the perforated shells, the analytical solution and simplified equation produce accurate results for materials with low thermal expansion coefficients.

Phase structure of NJL model with weak renormalization group

NASA Astrophysics Data System (ADS)

Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi

2018-06-01

We analyze the chiral phase structure of the Nambu-Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V (σ ; t) is given as a partial differential equation, where σ : = ψ bar ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V (σ ; t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

A macroscopic plasma Lagrangian and its application to wave interactions and resonances

NASA Technical Reports Server (NTRS)

Peng, Y. K. M.

1974-01-01

The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.

4-wave dynamics in kinetic wave turbulence

NASA Astrophysics Data System (ADS)

Chibbaro, Sergio; Dematteis, Giovanni; Rondoni, Lamberto

2018-01-01

A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function Z is obtained within an ;interaction representation; and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for Z. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the N-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. Some of the main results which are developed here in detail have been tested numerically in a recent work.

Regulation of the High-Affinity NO3− Uptake System by NRT1.1-Mediated NO3− Demand Signaling in Arabidopsis[W

PubMed Central

Krouk, Gabriel; Tillard, Pascal; Gojon, Alain

2006-01-01

The NRT2.1 gene of Arabidopsis thaliana encodes a major component of the root high-affinity \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document} transport system (HATS) that plays a crucial role in \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document} uptake by the plant. Although NRT2.1 was known to be induced by \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document} and feedback repressed by reduced nitrogen (N) metabolites, NRT2.1 is surprisingly up-regulated when \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document} concentration decreases to a low level (<0.5 mm) in media containing a high concentration of \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NH}}_{4}^{+}\\end{equation*}\\end{document} or Gln (≥1 mm). The NRT3.1 gene, encoding another key component of the HATS, displays the same response pattern. This revealed that both NRT2.1 and NRT3.1 are coordinately down-regulated by high external \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document} availability through a mechanism independent from that involving N metabolites. We show here that repression of both genes by high \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document} is specifically mediated by the NRT1.1 \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document} transporter. This mechanism warrants that either NRT1.1 or NRT2.1 is active in taking up \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document} in the presence of a reduced N source. Under low \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}/{\\mathrm{high\\hspace{.167em}NH}}_{4}^{+}\\end{equation*}\\end{document} provision, NRT1.1-mediated repression of NRT2.1/NRT3.1 is relieved, which allows reactivation of the HATS. Analysis of atnrt2.1 mutants showed that this constitutes a crucial adaptive response against \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NH}}_{4}^{+}\\end{equation*}\\end{document} toxicity because \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document} taken up by the HATS in this situation prevents the detrimental effects of pure \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NH}}_{4}^{+}\\end{equation*}\\end{document} nutrition. It is thus hypothesized that NRT1.1-mediated regulation of NRT2.1/NRT3.1 is a mechanism aiming to satisfy a specific \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document} demand of the plant in relation to the various specific roles that \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document} plays, in addition to being a N source. A new model is proposed for regulation of the HATS, involving both feedback repression by N metabolites and NRT1.1-mediated repression by high \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{NO}}_{3}^{-}\\end{equation*}\\end{document}. PMID:16998085

Obliquely propagating low frequency electromagnetic shock waves in two dimensional quantum magnetoplasmas

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

Masood, W.

2009-04-15

Linear and nonlinear propagation characteristics of low frequency magnetoacoustic waves in quantum magnetoplasmas are studied employing the quantum magnetohydrodynamic model. In this regard, a quantum Kadomtsev-Petviashvili-Burgers (KPB) equation is derived using the small amplitude expansion method. The dissipation is introduced by taking into account the kinematic viscosity among the plasma constituents. Furthermore, the solution of KPB equation is presented using the tangent hyperbolic (tanh) method. The variation in the fast and slow magnetoacoustic shock profiles with the quantum Bohm potential via increasing number density, obliqueness angle {theta}, magnetic field, and the resistivity are also investigated. It is observed that themore » aforementioned plasma parameters significantly modify the propagation characteristics of nonlinear magnetoacoustic shock waves in quantum magnetoplasmas. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.« less

Treatment of late time instabilities in finite-difference EMP scattering codes

NASA Astrophysics Data System (ADS)

Simpson, L. T.; Holland, R.; Arman, S.

1982-12-01

Constraints applicable to a finite difference mesh for solution of Maxwell's equations are defined. The equations are applied in the time domain for computing electromagnetic coupling to complex structures, e.g., rectangular, cylindrical, or spherical. In a spatially varying grid, the amplitude growth of high frequency waves becomes exponential through multiple reflections from the outer boundary in cases of late-time solution. The exponential growth of the numerical noise exceeds the value of the real signal. The correction technique employs an absorbing surface and a radiating boundary, along with tailored selection of the grid mesh size. High frequency noise is removed through use of a low-pass digital filter, a linear least squares fit is made to thy low frequency filtered response, and the original, filtered, and fitted data are merged to preserve the high frequency early-time response.

Disease elimination and re-emergence in differential-equation models.

PubMed

Greenhalgh, Scott; Galvani, Alison P; Medlock, Jan

2015-12-21

Traditional differential equation models of disease transmission are often used to predict disease trajectories and evaluate the effectiveness of alternative intervention strategies. However, such models cannot account explicitly for probabilistic events, such as those that dominate dynamics when disease prevalence is low during the elimination and re-emergence phases of an outbreak. To account for the dynamics at low prevalence, i.e. the elimination and risk of disease re-emergence, without the added analytical and computational complexity of a stochastic model, we develop a novel application of control theory. We apply our approach to analyze historical data of measles elimination and re-emergence in Iceland from 1923 to 1938, predicting the temporal trajectory of local measles elimination and re-emerge as a result of disease migration from Copenhagen, Denmark. Copyright © 2015 Elsevier Ltd. All rights reserved.

Effect of electron-electron scattering on the conductance of a quantum wire studied with the Boltzman transport equation

NASA Astrophysics Data System (ADS)

Lyo, S. K.; Huang, Danhong

2006-05-01

Electron-electron scattering conserves total momentum and does not dissipate momentum directly in a low-density system where the umklapp process is forbidden. However, it can still affect the conductance through the energy relaxation of the electrons. We show here that this effect can be studied with arbitrary accuracy in a multisublevel one-dimensional (1D) single quantum wire system in the presence of roughness and phonon scattering using a formally exact solution of the Boltzmann transport equation. The intrasubband electron-electron scattering is found to yield no net effect on the transport of electrons in 1D with only one sublevel occupied. For a system with a multilevel occupation, however, we find a significant effect of intersublevel electron-electron scattering on the temperature and density dependence of the resistance at low temperatures.

Transport tensors in perfectly aligned low-density fluids: Self-diffusion and thermal conductivity

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

Singh, G. S.; Kumar, B.

2001-06-01

The modified Taxman equation for the kinetic theory of low-density fluids composed of rigid aspherical molecules possessing internal degrees of freedom is generalized to obtain the transport tensors in a fluid of aligned molecules. The theory takes care of the shape of the particles exactly but the solution has been obtained only for the case of perfectly aligned hard spheroids within the framework of the first Sonine polynomial approximation. The expressions for the thermal-conductivity components have been obtained for the first time whereas the self-diffusion components obtained here turn out to be exactly the same as those derived by Kumarmore » and Masters [Mol. Phys. >81, 491 (1994)] through the solution of the Lorentz-Boltzmann equation. All our expressions yield correct results in the hard-sphere limit.« less

Propagation of Ion Solitary Pulses in Dense Astrophysical Electron-Positron-Ion Magnetoplasmas

NASA Astrophysics Data System (ADS)

Ata-Ur-Rahman; A. Khan, S.; Qamar, A.

2015-12-01

In this paper, we theoretically investigate the existence and propagation of low amplitude nonlinear ion waves in a dense plasma under the influence of a strong magnetic field. The plasma consists of ultra-relativistic and degenerate electrons and positrons and non-degenerate cold ions. Firstly, the appearance of two distinct linear modes and their evolution is studied by deriving a dispersion equation with the aid of Fourier analysis. Secondly, the dynamics of low amplitude ion solitary structures is investigated via a Korteweg-de Vries equation derived by employing a reductive perturbation method. The effects of various plasma parameters like positron concentration, strength of magnetic field, obliqueness of field, etc., are discussed in detail. At the end, analytical results are supplemented through numerical analysis by using typical representative parameters consistent with degenerate and ultra-relativistic magnetoplasmas of astrophysical regimes.

Time-domain wavefield reconstruction inversion

NASA Astrophysics Data System (ADS)

Li, Zhen-Chun; Lin, Yu-Zhao; Zhang, Kai; Li, Yuan-Yuan; Yu, Zhen-Nan

2017-12-01

Wavefield reconstruction inversion (WRI) is an improved full waveform inversion theory that has been proposed in recent years. WRI method expands the searching space by introducing the wave equation into the objective function and reconstructing the wavefield to update model parameters, thereby improving the computing efficiency and mitigating the influence of the local minimum. However, frequency-domain WRI is difficult to apply to real seismic data because of the high computational memory demand and requirement of time-frequency transformation with additional computational costs. In this paper, wavefield reconstruction inversion theory is extended into the time domain, the augmented wave equation of WRI is derived in the time domain, and the model gradient is modified according to the numerical test with anomalies. The examples of synthetic data illustrate the accuracy of time-domain WRI and the low dependency of WRI on low-frequency information.

Comparative atmosphere structure experiment

NASA Technical Reports Server (NTRS)

Sommer, S.

1974-01-01

Atmospheric structure of outer planets as determined by pressure, temperature, and accelerometers is reviewed and results obtained from the PAET earth entry are given. In order to describe atmospheric structure, entry is divided into two regimes, high and low speed. Acceleration is then measured: from these measurements density is determined as a function of time. The equations of motion are integrated to determine velocity, flight path angle, and altitude as a function of time. Density is then determined as a function of altitude from the previous determinations of density and altitude as a function of time. Hydrostatic equilibrium was assumed to determine pressure as a function of altitude. Finally the equation of space applied to determine temperature as a function of altitude, if the mean molecular weight is known. The mean molecular weight is obtained independently from either the low speed experiment or from the composition experiments.

Investigation of Low-Reynolds-Number Rocket Nozzle Design Using PNS-Based Optimization Procedure

NASA Technical Reports Server (NTRS)

Hussaini, M. Moin; Korte, John J.

1996-01-01

An optimization approach to rocket nozzle design, based on computational fluid dynamics (CFD) methodology, is investigated for low-Reynolds-number cases. This study is undertaken to determine the benefits of this approach over those of classical design processes such as Rao's method. A CFD-based optimization procedure, using the parabolized Navier-Stokes (PNS) equations, is used to design conical and contoured axisymmetric nozzles. The advantage of this procedure is that it accounts for viscosity during the design process; other processes make an approximated boundary-layer correction after an inviscid design is created. Results showed significant improvement in the nozzle thrust coefficient over that of the baseline case; however, the unusual nozzle design necessitates further investigation of the accuracy of the PNS equations for modeling expanding flows with thick laminar boundary layers.

The nonlocal electron kinetics for a low-pressure glow discharge dusty plasma

NASA Astrophysics Data System (ADS)

Liang, Yonggan; Wang, Ying; Li, Hui; Tian, Ruihuan; Yuan, Chengxun; Kudryavtsev, A. A.; Rabadanov, K. M.; Wu, Jian; Zhou, Zhongxiang; Tian, Hao

2018-05-01

The nonlocal electron kinetic model based on the Boltzmann equation is developed in low-pressure argon glow discharge dusty plasmas. The additional electron-dust elastic and inelastic collision processes are considered when solving the kinetic equation numerically. The orbital motion limited theory and collision enhanced collection approximation are employed to calculate the dust surface potential. The electron energy distribution function (EEDF), effective electron temperature Teff, and dust surface potential are investigated under different plasma and dust conditions by solving the Boltzmann and the dust charging current balance equations self-consistently. A comparison of the calculation results obtained from nonlocal and local kinetic models is made. It is shown that the appearance of dust particles leads to a deviation of the EEDF from its original profile for both nonlocal and local kinetic models. With the increase in dust density and size, the effective electron temperature and dust surface potential decrease due to the high-energy electron loss on the dust surface. Meanwhile, the nonlocal and local results differ much from each other under the same calculation condition. It is concluded that, for low-pressure (PR ≤ 1 cm*Torr) glow discharge dusty plasmas, the existence of dust particles will amplify the difference of local and nonlocal EEDFs, which makes the local kinetic model more improper to determine the main parameters of the positive column. The nonlocal kinetic model should be used for the calculation of the EEDFs and dusty plasma parameters.

Quiet Time Depression of the Equatorial Electrojet and Dynamics of the F-layer Ionosphere

NASA Astrophysics Data System (ADS)

Khadka, S.; Valladares, C. E.; Doherty, P.

2017-12-01

The depression of the equatorial electrojet (EEJ) is marked by a westward current due to streaming movement of laterally limited (±3°) charged particles in the ionospheric E region during the day along the magnetic equator. It is a complex low-latitude phenomenon and driven by various sources of electric fields associated with global neutral wind, solar tidal force, Interplanetary magnetic Field (IMF), etc. This unique physical property of the equatorial ionosphere holds a great promise for sorting out the governing mechanism of the dayside ionospheric electrodynamics and the onset of the enigmatic plasma structures in the ionospheric layers. Present study provides an overview of the special sequence of the longitudinal, seasonal, and occurrence rate variability of the depression of the EEJ, including its temporal variation, using data from an excellent chain of magnetic and ionospheric observatories along the low-latitude regions. A case and statistical study of the geomagnetically quiet time depression of EEJ strengths is presented using a pair of magnetometers, one located at the dip equator and another off the dip equator (±6° to ±9° away) in the American low-latitude regions. The significance of the variability of the depression of the EEJ current observed in the scenario of vertical drifts, sporadic E-layer, the equatorial F region plasma fountain, and height of the peak ionization in the F-layer, as well as GPS-TEC distributions, will be investigated.

Equation of state and shock compression of carbon-hydrogen and other ablator materials

NASA Astrophysics Data System (ADS)

Zhang, S.; Militzer, B.; Whitley, H.

2017-12-01

Dynamic compression experiments in planetary interior studies and fusion sciences often implement carbon-hydrogen or other low-Z elements or compounds as ablators. Accurate quantum simulations of these materials enables theoretical investigation of the equation of state (EOS) over temperatures and pressures that are difficult to access experimentally, and can help guide the design of targets for future experiments. In this work, we use path integral Monte Carlo and density functional molecular dynamics to calculate the equation of state of a series of hydrocarbons and other low-Z materials (B, B4C, and BN). For the hydrocarbon with C:H=1:1, we predict the pressure-compression profile to agree remarkably with experiments at low pressures. At high pressures, we find the Hugoniot curve displays a single compression maximum of 4.7 that corresponds to K-shell ionization. This is slightly higher than that of glow-discharge polymers but both occur at the same pressure (0.47 Gbar). We study the linear mixing approximation for the EOS of hydrocarbons and demonstrate its validity at stellar core conditions. We examine the sensitivity of the fusion yield to the EOS of these candidate ablator materials in radiation-hydrodynamic simulations of a direct-drive implosion. We also make detailed comparisons of the EOS and atomic and electronic structure of C and BN, which is useful for systematic improvement of existing EOS models. Prepared by LLNL under Contract DE-AC52-07NA27344.

Preconditioned conjugate-gradient methods for low-speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations is integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the Lower-Upper Successive Symmetric Over-Relaxation iterative scheme is more efficient than a preconditioner based on Incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional Line Gauss-Seidel Relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Preconditioned Conjugate Gradient methods for low speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Revisiting low-fidelity two-fluid models for gas-solids transport

NASA Astrophysics Data System (ADS)

Adeleke, Najeem; Adewumi, Michael; Ityokumbul, Thaddeus

2016-08-01

Two-phase gas-solids transport models are widely utilized for process design and automation in a broad range of industrial applications. Some of these applications include proppant transport in gaseous fracking fluids, air/gas drilling hydraulics, coal-gasification reactors and food processing units. Systems automation and real time process optimization stand to benefit a great deal from availability of efficient and accurate theoretical models for operations data processing. However, modeling two-phase pneumatic transport systems accurately requires a comprehensive understanding of gas-solids flow behavior. In this study we discuss the prevailing flow conditions and present a low-fidelity two-fluid model equation for particulate transport. The model equations are formulated in a manner that ensures the physical flux term remains conservative despite the inclusion of solids normal stress through the empirical formula for modulus of elasticity. A new set of Roe-Pike averages are presented for the resulting strictly hyperbolic flux term in the system of equations, which was used to develop a Roe-type approximate Riemann solver. The resulting scheme is stable regardless of the choice of flux-limiter. The model is evaluated by the prediction of experimental results from both pneumatic riser and air-drilling hydraulics systems. We demonstrate the effect and impact of numerical formulation and choice of numerical scheme on model predictions. We illustrate the capability of a low-fidelity one-dimensional two-fluid model in predicting relevant flow parameters in two-phase particulate systems accurately even under flow regimes involving counter-current flow.

Low Academic Competence in First Grade as a Risk Factor for Depressive Cognitions and Symptoms in Middle School

ERIC Educational Resources Information Center

Herman, Keith C.; Lambert, Sharon F.; Reinke, Wendy M.; Ialongo, Nicholas S.

2008-01-01

The present study investigated the role of low academic competence in the emergence of depressive cognitions and symptoms. Structural equation modeling was conducted on a longitudinal sample of African American boys (n = 253) and girls (n = 221). Results supported the hypothesized path models from academic competence in 1st grade to depressive…

Binding in pair potentials of liquid simple metals from nonlocality in electronic kinetic energy

NASA Technical Reports Server (NTRS)

Perrot, F.; March, N. H.

1990-01-01

The paper presents an explicit expression for the pair potential in liquid simple metals from low-order density-gradient theory when the superposition of single-center displaced charges is employed. Numerical results are presented for the gradient expansion pair interaction in liquid Na and Be. The low-order density-gradient equation for the pair potential is presented.

Balancing the One-to-One Equation: Equity and Access in Three Laptop Programs

ERIC Educational Resources Information Center

Warschauer, Mark; Zheng, Binbin; Niiya, Melissa; Cotten, Shelia; Farkas, George

2014-01-01

Seeking to improve teaching and learning and to narrow gaps between students of high and low socioeconomic status, many school districts in the United States are implementing one-to-one laptop programs. In this comparative case study, we examine one-to-one laptop programs in Colorado, California, and Alabama, all of which deployed low-cost netbook…

Managing fish habitat for flow and temperature extremes ...

EPA Pesticide Factsheets

Summer low flows and stream temperature maxima are key drivers affecting the sustainability of fish populations. Thus, it is critical to understand both the natural templates of spatiotemporal variability, how these are shifting due to anthropogenic influences of development and climate change, and how these impacts can be moderated by natural and constructed green infrastructure. Low flow statistics of New England streams have been characterized using a combination of regression equations to describe long-term averages as a function of indicators of hydrologic regime (rain- versus snow-dominated), precipitation, evapotranspiration or temperature, surface water storage, baseflow recession rates, and impervious cover. Difference equations have been constructed to describe interannual variation in low flow as a function of changing air temperature, precipitation, and ocean-atmospheric teleconnection indices. Spatial statistical network models have been applied to explore fine-scale variability of thermal regimes along stream networks in New England as a function of variables describing natural and altered energy inputs, groundwater contributions, and retention time. Low flows exacerbate temperature impacts by reducing thermal inertia of streams to energy inputs. Based on these models, we can construct scenarios of fish habitat suitability using current and projected future climate and the potential for preservation and restoration of historic habitat regimes th

Integrated Fault Diagnosis Algorithm for Motor Sensors of In-Wheel Independent Drive Electric Vehicles.

PubMed

Jeon, Namju; Lee, Hyeongcheol

2016-12-12

An integrated fault-diagnosis algorithm for a motor sensor of in-wheel independent drive electric vehicles is presented. This paper proposes a method that integrates the high- and low-level fault diagnoses to improve the robustness and performance of the system. For the high-level fault diagnosis of vehicle dynamics, a planar two-track non-linear model is first selected, and the longitudinal and lateral forces are calculated. To ensure redundancy of the system, correlation between the sensor and residual in the vehicle dynamics is analyzed to detect and separate the fault of the drive motor system of each wheel. To diagnose the motor system for low-level faults, the state equation of an interior permanent magnet synchronous motor is developed, and a parity equation is used to diagnose the fault of the electric current and position sensors. The validity of the high-level fault-diagnosis algorithm is verified using Carsim and Matlab/Simulink co-simulation. The low-level fault diagnosis is verified through Matlab/Simulink simulation and experiments. Finally, according to the residuals of the high- and low-level fault diagnoses, fault-detection flags are defined. On the basis of this information, an integrated fault-diagnosis strategy is proposed.

Parametric reduced models for the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Harlim, John; Li, Xiantao

2015-05-01

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

Properties of wavelet discretization of Black-Scholes equation

NASA Astrophysics Data System (ADS)

Finěk, Václav

2017-07-01

Using wavelet methods, the continuous problem is transformed into a well-conditioned discrete problem. And once a non-symmetric problem is given, squaring yields a symmetric positive definite formulation. However squaring usually makes the condition number of discrete problems substantially worse. This note is concerned with a wavelet based numerical solution of the Black-Scholes equation for pricing European options. We show here that in wavelet coordinates a symmetric part of the discretized equation dominates over an unsymmetric part in the standard economic environment with low interest rates. It provides some justification for using a fractional step method with implicit treatment of the symmetric part of the weak form of the Black-Scholes operator and with explicit treatment of its unsymmetric part. Then a well-conditioned discrete problem is obtained.

Theoretical study of interactions of BSA protein in a NaCl aqueous solution

NASA Astrophysics Data System (ADS)

Pellicane, Giuseppe; Cavero, Miguel

2013-03-01

Bovine Serum Albumine (BSA) aqueous solutions in the presence of NaCl are investigated for different protein concentrations and low to intermediate ionic strengths. Protein interactions are modeled via a charge-screened colloidal model, in which the range of the potential is determined by the Debye-Hückel constant. We use Monte Carlo computer simulations to calculate the structure factor, and assume an oblate ellipsoidal form factor for BSA. The theoretical scattered intensities are found in good agreement with the experimental small angle X-ray scattering intensities available in the literature. The performance of well-known integral equation closures to the Ornstein-Zernike equation, namely the mean spherical approximation, the Percus-Yevick, and the hypernetted chain equations, is also assessed with respect to computer simulation.

Hawking radiation in a d-dimensional static spherically symmetric black hole surrounded by quintessence

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

Chen Songbai; Wang Bin; Su Rukeng

2008-06-15

We present a solution of Einstein equations with quintessential matter surrounding a d-dimensional black hole, whose asymptotic structures are determined by the state of the quintessential matter. We examine the thermodynamics of this black hole and find that the mass of the black hole depends on the equation of state of the quintessence, while the first law is universal. Investigating the Hawking radiation in this black hole background, we observe that the Hawking radiation dominates on the brane in the low-energy regime. For different asymptotic structures caused by the equation of state of the quintessential matter surrounding the black hole,more » we learn that the influences by the state parameter of the quintessence on Hawking radiation are different.« less

Parametric reduced models for the nonlinear Schrödinger equation.

PubMed

Harlim, John; Li, Xiantao

2015-05-01

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