Volume-preserving normal forms of Hopf-zero singularity

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh

2013-10-01

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto-Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple.

On the wall-normal velocity of the compressible boundary-layer equations

NASA Technical Reports Server (NTRS)

Pruett, C. David

1991-01-01

Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x,y) plane to a computational (xi,eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability.

A descriptive study to find possible correlation between MRI findings of pituitary gland and serum prolactin level.

PubMed

Azeemuddin, Muhammad; Naqi, Rohana; Wasay, Mohammad

2013-06-01

To explore equation, if any, between findings of magnetic resonance imaging of pituitary gland and serum prolactin level. The retrospective, descriptive study was conducted at the Department of Radiology, Aga Khan University Hospital, Karachi, and related to patients' records from April 19, 2006 to April 23, 2009. Seventy patients underwent magnetic resonance imaging of brain for pituitary gland. Inclusion criteria were all patients referred with relevant clinical symptoms or deranged serum prolactin level. Patients who were claustrophobic or had a pacemaker, aneurysm clip, metallic foreign body in the orbit or with no laboratory investigation were excluded from the study. SPSS 19 was used for statistical analysis. Of the 70 patients, normal imaging was noted in 29 (41.4%) patients. Out of these, 18 (62.06%) patients had normal and 11 (37.93%) had raised serum prolactin levels. Microadenoma was found in 23 (32.8%) patients. Out of these, 10 (42.47%) had normal and 13 (56.52%) had raised prolactin levels. Macroadenoma was found in 16 (22.8 %). Out of these, 8 (50%) had normal and 8 (50%) had raised prolactin levels. Pituitary cyst was located in 2 (2.8 %) patients. Out of these, 1 (50%) had normal and 1 (50%) had raised serum prolactin levels. Magnetic resonance imaging of pituitary gland was not associated with serum prolactin levels in patients with clinical suspicion of pituitary abnormality. Therefore, regular monitoring of serum prolactin is suggested.

Local bifurcations in differential equations with state-dependent delay.

PubMed

Sieber, Jan

2017-11-01

A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.

On the use of the GRACE normal equation of inter-satellite tracking data for estimation of soil moisture and groundwater in Australia

NASA Astrophysics Data System (ADS)

Tangdamrongsub, Natthachet; Han, Shin-Chan; Decker, Mark; Yeo, In-Young; Kim, Hyungjun

2018-03-01

An accurate estimation of soil moisture and groundwater is essential for monitoring the availability of water supply in domestic and agricultural sectors. In order to improve the water storage estimates, previous studies assimilated terrestrial water storage variation (ΔTWS) derived from the Gravity Recovery and Climate Experiment (GRACE) into land surface models (LSMs). However, the GRACE-derived ΔTWS was generally computed from the high-level products (e.g. time-variable gravity fields, i.e. level 2, and land grid from the level 3 product). The gridded data products are subjected to several drawbacks such as signal attenuation and/or distortion caused by a posteriori filters and a lack of error covariance information. The post-processing of GRACE data might lead to the undesired alteration of the signal and its statistical property. This study uses the GRACE least-squares normal equation data to exploit the GRACE information rigorously and negate these limitations. Our approach combines GRACE's least-squares normal equation (obtained from ITSG-Grace2016 product) with the results from the Community Atmosphere Biosphere Land Exchange (CABLE) model to improve soil moisture and groundwater estimates. This study demonstrates, for the first time, an importance of using the GRACE raw data. The GRACE-combined (GC) approach is developed for optimal least-squares combination and the approach is applied to estimate the soil moisture and groundwater over 10 Australian river basins. The results are validated against the satellite soil moisture observation and the in situ groundwater data. Comparing to CABLE, we demonstrate the GC approach delivers evident improvement of water storage estimates, consistently from all basins, yielding better agreement on seasonal and inter-annual timescales. Significant improvement is found in groundwater storage while marginal improvement is observed in surface soil moisture estimates.

Validation of cystatin C-based equations for evaluating residual renal function in patients on continuous ambulatory peritoneal dialysis.

PubMed

Zhong, Hui; Zhang, Wei; Qin, Min; Gou, ZhongPing; Feng, Ping

2017-06-01

Residual renal function needs to be assessed frequently in patients on continuous ambulatory peritoneal dialysis (CAPD). A commonly used method is to measure creatinine (Cr) and urea clearance in urine collected over 24 h, but collection can be cumbersome and difficult to manage. A faster, simpler alternative is to measure levels of cystatin C (CysC) in serum, but the accuracy and reliability of this method is controversial. Our study aims to validate published CysC-based equations for estimating residual renal function in patients on CAPD. Residual renal function was measured by calculating average clearance of urea and Cr in 24-h urine as well as by applying CysC- or Cr-based equations published by Hoek and Yang. We then compared the performance of the equations against the 24-h urine results. In our sample of 255 patients ages 47.9 ± 15.6 years, the serum CysC level was 6.43 ± 1.13 mg/L. Serum CysC level was not significantly associated with age, gender, height, weight, body mass index, hemoglobin, intact parathyroid hormone, normalized protein catabolic rate or the presence of diabetes. In contrast, serum CysC levels did correlate with peritoneal clearance of CysC and with levels of prealbumin and high-sensitivity C-reactive protein. Residual renal function was 2.56 ± 2.07 mL/min/1.73 m 2 based on 24-h urine sampling, compared with estimates (mL/min/1.73 m 2 ) of 2.98 ± 0.66 for Hoek's equation, 2.03 ± 0.97 for Yang's CysC-based equation and 2.70 ± 1.30 for Yang's Cr-based equation. Accuracies within 30%/50% of measured residual renal function for the three equations were 29.02/48.24, 34.90/56.86 and 31.37/54.90. The three equations for estimating residual renal function showed similar limits of agreement and differed significantly from the measured value. Published CysC-based equations do not appear to be particularly reliable for patients on CAPD. Further development and validation of CysC-based equations should take into account peritoneal clearance of CysC and other relevant factors. © The Author 2016. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Analytical bound-state solutions of the Schrödinger equation for the Manning-Rosen plus Hulthén potential within SUSY quantum mechanics

NASA Astrophysics Data System (ADS)

Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

2018-01-01

In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any l≠0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

Standard Error of Linear Observed-Score Equating for the NEAT Design with Nonnormally Distributed Data

ERIC Educational Resources Information Center

Zu, Jiyun; Yuan, Ke-Hai

2012-01-01

In the nonequivalent groups with anchor test (NEAT) design, the standard error of linear observed-score equating is commonly estimated by an estimator derived assuming multivariate normality. However, real data are seldom normally distributed, causing this normal estimator to be inconsistent. A general estimator, which does not rely on the…

Boundary Layer Model for Air Pollutant Concentrations Due to Highway Traffic

ERIC Educational Resources Information Center

Ragland, Kenneth W.; Peirce, J. Jeffrey

1975-01-01

A numerical solution of the three-dimensional steady-state diffusion equation for a finite width line source is presented. The wind speed and eddy diffusivity as a function of height above the roadway are obtained. Normalized ground level and elevated concentrations near a highway are obtained for winds perpendicular, parallel, and at 45 degrees.…

Normal Theory Two-Stage ML Estimator When Data Are Missing at the Item Level

ERIC Educational Resources Information Center

Savalei, Victoria; Rhemtulla, Mijke

2017-01-01

In many modeling contexts, the variables in the model are linear composites of the raw items measured for each participant; for instance, regression and path analysis models rely on scale scores, and structural equation models often use parcels as indicators of latent constructs. Currently, no analytic estimation method exists to appropriately…

Prediction equations for maximal respiratory pressures of Brazilian adolescents.

PubMed

Mendes, Raquel E F; Campos, Tania F; Macêdo, Thalita M F; Borja, Raíssa O; Parreira, Verônica F; Mendonça, Karla M P P

2013-01-01

The literature emphasizes the need for studies to provide reference values and equations able to predict respiratory muscle strength of Brazilian subjects at different ages and from different regions of Brazil. To develop prediction equations for maximal respiratory pressures (MRP) of Brazilian adolescents. In total, 182 healthy adolescents (98 boys and 84 girls) aged between 12 and 18 years, enrolled in public and private schools in the city of Natal-RN, were evaluated using an MVD300 digital manometer (Globalmed®) according to a standardized protocol. Statistical analysis was performed using SPSS Statistics 17.0 software, with a significance level of 5%. Data normality was verified using the Kolmogorov-Smirnov test, and descriptive analysis results were expressed as the mean and standard deviation. To verify the correlation between the MRP and the independent variables (age, weight, height and sex), the Pearson correlation test was used. To obtain the prediction equations, stepwise multiple linear regression was used. The variables height, weight and sex were correlated to MRP. However, weight and sex explained part of the variability of MRP, and the regression analysis in this study indicated that these variables contributed significantly in predicting maximal inspiratory pressure, and only sex contributed significantly to maximal expiratory pressure. This study provides reference values and two models of prediction equations for maximal inspiratory and expiratory pressures and sets the necessary normal lower limits for the assessment of the respiratory muscle strength of Brazilian adolescents.

The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1984-01-01

The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner.

Interannual Variability of Sea Level in Tropical Pacific during 1993-2014

NASA Astrophysics Data System (ADS)

Zhu, X.; Greatbatch, R. J.; Claus, M.

2016-12-01

More than 40 years ago, sea level variability in the tropical Pacific was being studied using linear shallow water models driven by observed estimates of the surface wind stress. At that time, the only available sea level data was from the sparse tide gauge record. However, with the advent of satellite data, there has been a revolution in the available data coverage for sea level. Here, a linear model, consisting of the first five baroclinic normal modes, and driven by ERA-Interim monthly wind stress anomalies, is used to investigate interannual variability in tropical Pacific sea level as seen in satellite altimeter data. The model output is fitted to the altimeter data along the equator, in order to derive the vertical profile for the wind forcing, and showing that a signature from modes higher than mode six cannot be extracted from the altimeter data. It is shown that the model has considerable skill at capturing interannual sea level variability both on and off the equator. The correlation between modelled and satellite-derived sea level data exceeds 0.8 over a wide range of longitudes along the equator and readily captures the observed ENSO events. Overall, the combination of the first, second and third and fifth modes can provide a robust estimate of the interannual sea level variability, the second mode being the most dominant. A remarkable feature of both the model and the altimeter data is the presence of a pivot point in the western Pacific on the equator. We show that the westward displacement of the pivot point from the centre of the basin is partly a signature of the recharge/discharge mechanism but is also strongly influenced by the fact that most of the wind stress variance along the equator is found in the western part of the basin. We also show that the Sverdrup transport plays no role in the recharge/discharge mechanism in our model.

Weighted triangulation adjustment

USGS Publications Warehouse

Anderson, Walter L.

1969-01-01

The variation of coordinates method is employed to perform a weighted least squares adjustment of horizontal survey networks. Geodetic coordinates are required for each fixed and adjustable station. A preliminary inverse geodetic position computation is made for each observed line. Weights associated with each observed equation for direction, azimuth, and distance are applied in the formation of the normal equations in-the least squares adjustment. The number of normal equations that may be solved is twice the number of new stations and less than 150. When the normal equations are solved, shifts are produced at adjustable stations. Previously computed correction factors are applied to the shifts and a most probable geodetic position is found for each adjustable station. Pinal azimuths and distances are computed. These may be written onto magnetic tape for subsequent computation of state plane or grid coordinates. Input consists of punch cards containing project identification, program options, and position and observation information. Results listed include preliminary and final positions, residuals, observation equations, solution of the normal equations showing magnitudes of shifts, and a plot of each adjusted and fixed station. During processing, data sets containing irrecoverable errors are rejected and the type of error is listed. The computer resumes processing of additional data sets.. Other conditions cause warning-errors to be issued, and processing continues with the current data set.

Projecting diffusion along the normal bundle of a plane curve

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

Valero-Valdés, Carlos; Herrera-Guzmán, Rafael

2014-05-15

The purpose of this paper is to provide new formulas for the effective diffusion coefficient of a generalized Fick-Jacob's equation obtained by projecting the two-dimensional diffusion equation along the normal directions of an arbitrary curve on the plane.

Cross-Validation of a Recently Published Equation Predicting Energy Expenditure to Run or Walk a Mile in Normal-Weight and Overweight Adults

ERIC Educational Resources Information Center

Morris, Cody E.; Owens, Scott G.; Waddell, Dwight E.; Bass, Martha A.; Bentley, John P.; Loftin, Mark

2014-01-01

An equation published by Loftin, Waddell, Robinson, and Owens (2010) was cross-validated using ten normal-weight walkers, ten overweight walkers, and ten distance runners. Energy expenditure was measured at preferred walking (normal-weight walker and overweight walkers) or running pace (distance runners) for 5 min and corrected to a mile. Energy…

Quantum electron levels in the field of a charged black hole

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

Dokuchaev, V. I.; Eroshenko, Yu. N., E-mail: eroshenko@ms2.inr.ac.ru

2015-12-15

Stationary solutions of the Dirac equation in the metric of the charged Reissner–Nordstrom black hole are found. In the case of an extremal black hole, the normalization integral of the wave functions is finite, and the regular stationary solution is physically self-consistent. The presence of quantum electron levels under the Cauchy horizon can have an impact on the final stage of the Hawking evaporation of the black hole, as well as on the particle scattering in the field of the black hole.

Normal evaporation of binary alloys

NASA Technical Reports Server (NTRS)

Li, C. H.

1972-01-01

In the study of normal evaporation, it is assumed that the evaporating alloy is homogeneous, that the vapor is instantly removed, and that the alloy follows Raoult's law. The differential equation of normal evaporation relating the evaporating time to the final solute concentration is given and solved for several important special cases. Uses of the derived equations are exemplified with a Ni-Al alloy and some binary iron alloys. The accuracy of the predicted results are checked by analyses of actual experimental data on Fe-Ni and Ni-Cr alloys evaporated at 1600 C, and also on the vacuum purification of beryllium. These analyses suggest that the normal evaporation equations presented here give satisfactory results that are accurate to within an order of magnitude of the correct values, even for some highly concentrated solutions. Limited diffusion and the resultant surface solute depletion or enrichment appear important in the extension of this normal evaporation approach.

Modified Chapman-Enskog moment approach to diffusive phonon heat transport.

PubMed

Banach, Zbigniew; Larecki, Wieslaw

2008-12-01

A detailed treatment of the Chapman-Enskog method for a phonon gas is given within the framework of an infinite system of moment equations obtained from Callaway's model of the Boltzmann-Peierls equation. Introducing no limitations on the magnitudes of the individual components of the drift velocity or the heat flux, this method is used to derive various systems of hydrodynamic equations for the energy density and the drift velocity. For one-dimensional flow problems, assuming that normal processes dominate over resistive ones, it is found that the first three levels of the expansion (i.e., the zeroth-, first-, and second-order approximations) yield the equations of hydrodynamics which are linearly stable at all wavelengths. This result can be achieved either by examining the dispersion relations for linear plane waves or by constructing the explicit quadratic Lyapunov entropy functionals for the linear perturbation equations. The next order in the Chapman-Enskog expansion leads to equations which are unstable to some perturbations. Precisely speaking, the linearized equations of motion that describe the propagation of small disturbances in the flow have unstable plane-wave solutions in the short-wavelength limit of the dispersion relations. This poses no problem if the equations are used in their proper range of validity.

Geopotential Model Improvement Using POCM_4B Dynamic Ocean Topography Information: PGM2000A

NASA Technical Reports Server (NTRS)

Pavlis, N. K.; Chinn, D. S.; Cox, C. M.; Lemoine, Frank G.; Smith, David E. (Technical Monitor)

2000-01-01

The two-year mean (1993-1994) Dynamic Ocean Topography (DOT) field implied by the POCM_4B circulation model was used to develop normal equations for DOT, in a surface spherical harmonic representation. These normal equations were combined with normal equations from satellite tracking data, surface gravity data, and altimeter data from TOPEX/Poseidon and ERS-1. Several least-squares combination solutions were developed in this fashion, by varying parameters such as the maximum degree of the estimated DOT and the relative weights of the different data. The solutions were evaluated in terms of orbit fit residuals, GPS/Leveling-derived undulations, and independent DOT information from in situ WOCE hydrographic data. An optimal solution was developed in this fashion which was originally presented at the 1998 EGS meeting in Nice, France. This model, designated here PGM2000A, maintains the orbit and land geoid modeling performance of EGM96, while improving its marine geoid modeling capability. In addition, PGM2000A's error spectrum is considerably more realistic than those of other contemporary gravitational models and agrees well with the error spectrum of EGM96. We will present the development and evaluation of PGM2000A, with particular emphasis on the weighting of the DOT information implied by POCM_4B. We will also present an inter-comparison of PGM2000A with the GRIM5-C1 and TEG-4 models. Directions for future work and problematic areas will be identified.

Derivation of a Multiparameter Gamma Model for Analyzing the Residence-Time Distribution Function for Nonideal Flow Systems as an Alternative to the Advection-Dispersion Equation

DOE PAGES

Embry, Irucka; Roland, Victor; Agbaje, Oluropo; ...

2013-01-01

A new residence-time distribution (RTD) function has been developed and applied to quantitative dye studies as an alternative to the traditional advection-dispersion equation (AdDE). The new method is based on a jointly combined four-parameter gamma probability density function (PDF). The gamma residence-time distribution (RTD) function and its first and second moments are derived from the individual two-parameter gamma distributions of randomly distributed variables, tracer travel distance, and linear velocity, which are based on their relationship with time. The gamma RTD function was used on a steady-state, nonideal system modeled as a plug-flow reactor (PFR) in the laboratory to validate themore » effectiveness of the model. The normalized forms of the gamma RTD and the advection-dispersion equation RTD were compared with the normalized tracer RTD. The normalized gamma RTD had a lower mean-absolute deviation (MAD) (0.16) than the normalized form of the advection-dispersion equation (0.26) when compared to the normalized tracer RTD. The gamma RTD function is tied back to the actual physical site due to its randomly distributed variables. The results validate using the gamma RTD as a suitable alternative to the advection-dispersion equation for quantitative tracer studies of non-ideal flow systems.« less

Angular motion equations for a satellite with hinged flexible solar panel

NASA Astrophysics Data System (ADS)

Ovchinnikov, M. Yu.; Tkachev, S. S.; Roldugin, D. S.; Nuralieva, A. B.; Mashtakov, Y. V.

2016-11-01

Non-linear mathematical model for the satellite with hinged flexible solar panel is presented. Normal modes of flexible elements are used for motion description. Motion equations are derived using virtual work principle. A comparison of normal modes calculation between finite element method and developed model is presented.

Analytical Solutions of the Schrödinger Equation for the Manning-Rosen plus Hulthén Potential Within SUSY Quantum Mechanics

NASA Astrophysics Data System (ADS)

Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

2018-02-01

In this paper, the bound state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by implementing the novel improved scheme to surmount the centrifugal term. The energy eigenvalues and corresponding radial wave functions are defined for any l ≠ 0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods. By using these two different methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

Improved solution of the lidar equation utilizing particle counter measurements

NASA Technical Reports Server (NTRS)

Jaeger, H.; Hofmann, D. J.; Jaeger, H.; Hofmann, D. J.

1986-01-01

The extraction of particle backscattering from incoherent lidar measurements poses some problems. In the case of measurements of the stratospheric aerosol layer the solution of the lidar equation is based on two assumptions which are necessary to normalize the measured signal and to correct it with the two-way transmission of the laser pulse. Normalization and transmission are tackled by adding the information contained in aerosol particle counter measurements of the University of Wyoming to the ruby lidar measurements at Garmisch-Partenkirchen. Calculated backscattering from height levels above 25 km for the El Chichon period will be compared with lidar measurements and necessary corrections. The calculated backscatter-to-extinction ratios are compared to those, which were derived from a comparison of published extinction values to measured lidar backscattering at Garmisch. These ratios were used to calculate the Garmisch lidar returns. For the period 4 to 12 months after the El Chichon eruption a backscater-to-extinction ratio of 0.026 1/sr was applied with smaller values before and after that time.

Angular and linear fields of view of Galilean telescopes and telemicroscopes.

PubMed

Katz, Milton

2007-06-01

The calculation of the angular fields of view (FOVs) of Galilean telescopes generally necessitates the calculation of the pupils and ports. This, in turn, requires knowledge of the optical design of the telescope, in particular, the focal lengths or powers of the objective and ocular lenses. Equations for finding the FOV that obviate the need to calculate pupils and ports, or even to know the lens powers of the telescope, are presented in this article. The equations can be used to find the FOVs in image space of real Galilean telescopes of known magnification, merely by measuring the distance between the objective and ocular lenses and the diameter of the objective lens. The equations include the effects of eye pupil diameter and eye relief. Linear FOVs (LFOVs) of Galilean telemicroscopes are similarly determined. Two image space angular FOV equations were derived: (1) an equation to determine the angular FOVs of a telescope with various amounts of vignetting and eye relief; and (2) an equivalent equation for the LFOVs of telescopes fitted with lens caps for near vision. The FOV increases linearly with increasing vignetting. Increasing the eye relief results in a nonlinear decrease in the FOV, shown as a fraction of the normalized value for zero eye relief. Decrements in the FOVs with increasing eye relief as a fraction of the normalized field angle when the eye relief = 0 are shown to be constant regardless of the vignetting level. A transition of the objective lens from field stop to aperture stop occurs when the eye pupil diameter exceeds the diameter of the objective lens divided by the magnification. Equations have been derived for Galilean telescopes and telemicroscopes that make it unnecessary to find pupils and ports, or to know the powers of the lenses. They provide a direct and simple evaluation of angular and LFOVs as functions of magnification, objective lens diameter, eye pupil diameter, eye relief, and vignetting, and enable comparisons of actual telescopes.

Association between folate levels and CpG island hypermethylation in normal colorectal mucosa

PubMed Central

Wallace, Kristin; Grau, Maria V.; Levine, Joan A.; Shen, Lanlan; Hamdan, Randala; Chen, Xinli; Gui, Jiang; Haile, Robert W.; Barry, Elizabeth L.; Ahnen, Dennis; McKeown-Eyssen, Gail; Baron, John A.; Issa, Jean Pierre J.

2010-01-01

Background Gene-specific promoter methylation of several genes occurs in aging normal tissues and may predispose to tumorigenesis. In the present study, we investigate the association among blood folate levels, and dietary and lifestyle factors with CpG island methylation in normal colorectal mucosa. Methods Subjects were enrolled in a multi-center chemoprevention trial of aspirin or folic acid for the prevention of large bowel adenomas. We collected 1000 biopsies from 389 patients, 501 samples from the right colon and 499 from the rectum at the follow-up colonoscopy. We measured DNA methylation of estrogen receptor alpha (ERα) and secreted frizzled related protein-1 (SFRP1) using bisulfite pyrosequencing. We used Generalized Estimating Equations regression analysis to examine the association between methylation and selected variables. Results For both ERα and SFRP1, percent methylation was significantly higher in the rectum compared to the right colon (p = 0.001). For each 10 years of age, we observed a 1.7 % increase in methylation level for ERα and a 2.9 % increase for SFRP1 (P < 0.0001). African Americans had a significantly lower level of ERα and SFRP1 methylation compared to Caucasians and Hispanics. Higher RBC folate levels were associated with higher levels of both ERα (p=0.03) and SFRP1 methylation (p=0.01). Conclusions Our results suggest that CpG island methylation in normal colorectal mucosa is related to advancing age, race, rectal location, and RBC folate levels. These data have important implications regarding the safety of supplementary folate administration in healthy adults given the hypothesis that methylation in normal mucosa may predispose to colorectal neoplasia. PMID:21149331

TOPEX/El Nino Watch - Warm Water Pool is Thinning, Feb, 5, 1998

NASA Technical Reports Server (NTRS)

1998-01-01

This image of the Pacific Ocean was produced using sea surface height measurements taken by the U.S.-French TOPEX/Poseidon satellite. The image shows sea surface height relative to normal ocean conditions on Feb. 5, 1998 and sea surface height is an indicator of the heat content of the ocean. The area and volume of the El Nino warm water pool that is affecting global weather patterns remains extremely large, but the pool has thinned along the equator and near the coast of South America. This 'thinning' means that the warm water is not as deep as it was a few months ago. Oceanographers indicate this is a classic pattern, typical of a mature El Nino condition that they would expect to see during the ocean's gradual transition back to normal sea level. In this image, the white and red areas indicate unusual patterns of heat storage; in the white areas, the sea surface is between 14 and 32 centimeters (6 to 13 inches) above normal; in the red areas, it's about 10 centimeters (4 inches) above normal. The green areas indicate normal conditions, while purple (the western Pacific) means at least 18 centimeters (7 inches) below normal sea level. The El Nino phenomenon is thought to be triggered when the steady westward blowing trade winds weaken and even reverse direction. This change in the winds allows a large mass of warm water (the red and white area) that is normally located near Australia to move eastward along the equator until it reaches the coast of South America. The displacement of so much warm water affects evaporation, where rain clouds form and, consequently, alters the typical atmospheric jet stream patterns around the world. Using satellite imagery, buoy and ship data, and a forecasting model of the ocean-atmosphere system, the National Oceanic and Atmospheric Administration, (NOAA), has continued to issue an advisory indicating the so-called El Nino weather conditions that have impacted much of the United States and the world are expected to remain through the spring.

For more information, please visit the TOPEX/Poseidon project web page at http://topex-www.jpl.nasa.gov

Thermodynamics of an Attractive 2D Fermi Gas

NASA Astrophysics Data System (ADS)

Fenech, K.; Dyke, P.; Peppler, T.; Lingham, M. G.; Hoinka, S.; Hu, H.; Vale, C. J.

2016-01-01

Thermodynamic properties of matter are conveniently expressed as functional relations between variables known as equations of state. Here we experimentally determine the compressibility, density, and pressure equations of state for an attractive 2D Fermi gas in the normal phase as a function of temperature and interaction strength. In 2D, interacting gases exhibit qualitatively different features to those found in 3D. This is evident in the normalized density equation of state, which peaks at intermediate densities corresponding to the crossover from classical to quantum behavior.

Comparison of anthropometric-based equations for estimation of body fat percentage in a normal-weight and overweight female cohort: validation via air-displacement plethysmography.

PubMed

Temple, Derry; Denis, Romain; Walsh, Marianne C; Dicker, Patrick; Byrne, Annette T

2015-02-01

To evaluate the accuracy of the most commonly used anthropometric-based equations in the estimation of percentage body fat (%BF) in both normal-weight and overweight women using air-displacement plethysmography (ADP) as the criterion measure. A comparative study in which the equations of Durnin and Womersley (1974; DW) and Jackson, Pollock and Ward (1980) at three, four and seven sites (JPW₃, JPW₄ and JPW₇) were validated against ADP in three groups. Group 1 included all participants, group 2 included participants with a BMI <25·0 kg/m² and group 3 included participants with a BMI ≥25·0 kg/m². Human Performance Laboratory, Institute for Sport and Health, University College Dublin, Republic of Ireland. Forty-three female participants aged between 18 and 55 years. In all three groups, the %BF values estimated from the DW equation were closer to the criterion measure (i.e. ADP) than those estimated from the other equations. Of the three JPW equations, JPW₃ provided the most accurate estimation of %BF when compared with ADP in all three groups. In comparison to ADP, these findings suggest that the DW equation is the most accurate anthropometric method for the estimation of %BF in both normal-weight and overweight females.

Global fields of soil moisture and land surface evapotranspiration derived from observed precipitation and surface air temperature

NASA Technical Reports Server (NTRS)

Mintz, Y.; Walker, G. K.

1993-01-01

The global fields of normal monthly soil moisture and land surface evapotranspiration are derived with a simple water budget model that has precipitation and potential evapotranspiration as inputs. The precipitation is observed and the potential evapotranspiration is derived from the observed surface air temperature with the empirical regression equation of Thornthwaite (1954). It is shown that at locations where the net surface radiation flux has been measured, the potential evapotranspiration given by the Thornthwaite equation is in good agreement with those obtained with the radiation-based formulations of Priestley and Taylor (1972), Penman (1948), and Budyko (1956-1974), and this provides the justification for the use of the Thornthwaite equation. After deriving the global fields of soil moisture and evapotranspiration, the assumption is made that the potential evapotranspiration given by the Thornthwaite equation and by the Priestley-Taylor equation will everywhere be about the same; the inverse of the Priestley-Taylor equation is used to obtain the normal monthly global fields of net surface radiation flux minus ground heat storage. This and the derived evapotranspiration are then used in the equation for energy conservation at the surface of the earth to obtain the global fields of normal monthly sensible heat flux from the land surface to the atmosphere.

Pain and the defense response: structural equation modeling reveals a coordinated psychophysiological response to increasing painful stimulation.

PubMed

Donaldson, Gary W; Chapman, C Richard; Nakamura, Yoshi; Bradshaw, David H; Jacobson, Robert C; Chapman, Christopher N

2003-03-01

The defense response theory implies that individuals should respond to increasing levels of painful stimulation with correlated increases in affectively mediated psychophysiological responses. This paper employs structural equation modeling to infer the latent processes responsible for correlated growth in the pain report, evoked potential amplitudes, pupil dilation, and skin conductance of 92 normal volunteers who experienced 144 trials of three levels of increasingly painful electrical stimulation. The analysis assumed a two-level model of latent growth as a function of stimulus level. The first level of analysis formulated a nonlinear growth model for each response measure, and allowed intercorrelations among the parameters of these models across individuals. The second level of analysis posited latent process factors to account for these intercorrelations. The best-fitting parsimonious model suggests that two latent processes account for the correlations. One of these latent factors, the activation threshold, determines the initial threshold response, while the other, the response gradient, indicates the magnitude of the coherent increase in response with stimulus level. Collectively, these two second-order factors define the defense response, a broad construct comprising both subjective pain evaluation and physiological mechanisms.

Bias and Efficiency in Structural Equation Modeling: Maximum Likelihood versus Robust Methods

ERIC Educational Resources Information Center

Zhong, Xiaoling; Yuan, Ke-Hai

2011-01-01

In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…

Adjustment technique without explicit formation of normal equations /conjugate gradient method/

NASA Technical Reports Server (NTRS)

Saxena, N. K.

1974-01-01

For a simultaneous adjustment of a large geodetic triangulation system, a semiiterative technique is modified and used successfully. In this semiiterative technique, known as the conjugate gradient (CG) method, original observation equations are used, and thus the explicit formation of normal equations is avoided, 'huge' computer storage space being saved in the case of triangulation systems. This method is suitable even for very poorly conditioned systems where solution is obtained only after more iterations. A detailed study of the CG method for its application to large geodetic triangulation systems was done that also considered constraint equations with observation equations. It was programmed and tested on systems as small as two unknowns and three equations up to those as large as 804 unknowns and 1397 equations. When real data (573 unknowns, 965 equations) from a 1858-km-long triangulation system were used, a solution vector accurate to four decimal places was obtained in 2.96 min after 1171 iterations (i.e., 2.0 times the number of unknowns).

A quantitative description of normal AV nodal conduction curve in man.

PubMed

Teague, S; Collins, S; Wu, D; Denes, P; Rosen, K; Arzbaecher, R

1976-01-01

The AV nodal conduction curve generated by the atrial extrastimulus technique has been described only qualitatively in man, making clinical comparison of known normal curves with those of suspected AV nodal dysfunction difficult. Also, the effects of physiological and pharmacological interventions have not been quantifiable. In 50 patients with normal AV conduction as defined by normal AH (less than 130 ms), normal AV nodal effective and functional refractory periods (less than 380 and less than 500 ms), and absence of demonstrable dual AV nodal pathways, we found that conduction curves (at sinus rhythm or longest paced cycle length) can be described by an exponential equation of the form delta = Ae-Bx. In this equation, delta is the increase in AV nodal conduction time of an extrastimulus compared to that of a regular beat and x is extrastimulus interval. The natural logarithm of this equation is linear in the semilogarithmic plane, thus permitting the constants A and B to be easily determined by a least-squares regression analysis with a hand calculator.

Applicability of the Old European Respiratory Society/European Community for Steel and Coal reference equations for spirometry interpretation in Tunisian adult population.

PubMed

El Attar, Mohamed Nour; Hadj Mabrouk, Khaoula; Ben Abdelaziz, Ahmed; Abdelghani, Ahmed; Bousarssar, Mohamed; Limam, Khélifa; Maatoug, Chiraz; Bouslah, Hmida; Charrada, Ameur; Rouatbi, Sonia; Ben Saad, Helmi

2014-01-01

Tunisian pulmonary functional laboratories accept the default settings for reference equations (European Respiratory Society/European Community for Steel and Coal (ERS/ECSC1983) offered by the manufacturer even though adult Tunisian reference equations (Tunisian1995) are available. To compare the spirometric profile of Tunisian subjects, according to the two reference equations. Spirometric data were recorded from 1192 consecutive spirometry procedures in adults aged 18-60 years. Reference values and lower limits of normality (LLN) were calculated using the two reference equations. Applied definitions: large airway obstructive ventilatory defect (LAOVD): ratio between the 1st second expiratory volume and forced vital capacity (FEV1/FVC) < LLN. Small AOVD (SAOVD): FEV1/FVC > LLN and FVC > LLN and maximal midexpiratory flow < LLN. Tendency through a restrictive ventilatory defect (TRVD): FEV1 and FVC < LLN. The spirometric profile, according the two reference equations, was determined. Using Tunisian1995 reference equations, 34%, 7%, 37% and 19% of spirometry records were interpreted as normal, and as having, LAOVD, SAOVD and TRVD, respectively. Using ERS/ECSC1983 reference equations, 85%, 3%, 9% and 2% of spirometry records were interpreted as normal, and as having, LAOVD, SAOVD and TRVD, respectively. Using the ERS/ECSC1983 reference equations, misclassification was worse for LAOVD, for SAOVD and for TRVD, respectively, 68%, 94% and 89%. Our results showed that the use of the old Caucasian reference equations resulted in misinterpretation of spirometry data in a significant proportion of subjects. This could result in inappropriate diagnosis and/or management.

On the response of superpressure balloons to displacements from equilibrium density level

NASA Technical Reports Server (NTRS)

Levanon, N.; Kushnir, Y.

1976-01-01

The response of a superpressure balloon to an initial displacement from its constant-density floating level is examined. An approximate solution is obtained to the governing vertical equation of motion for constant-density superpressure balloons. This solution is used to filter out neutrally buoyant oscillations in balloon records despite the nonlinear behavior of the balloon. The graph depicting the pressure data after deconvolution between the raw pressure data and the normalized balloon wavelet shows clearly the strong filtering-out of the neutral buoyancy oscillations.

Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations

NASA Astrophysics Data System (ADS)

DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.

2008-06-01

For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Second- and third-order upwind difference schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Yang, J. Y.

1984-01-01

Second- and third-order two time-level five-point explicit upwind-difference schemes are described for the numerical solution of hyperbolic systems of conservation laws and applied to the Euler equations of inviscid gas dynamics. Nonliner smoothing techniques are used to make the schemes total variation diminishing. In the method both hyperbolicity and conservation properties of the hyperbolic conservation laws are combined in a very natural way by introducing a normalized Jacobian matrix of the hyperbolic system. Entropy satisfying shock transition operators which are consistent with the upwind differencing are locally introduced when transonic shock transition is detected. Schemes thus constructed are suitable for shockcapturing calculations. The stability and the global order of accuracy of the proposed schemes are examined. Numerical experiments for the inviscid Burgers equation and the compressible Euler equations in one and two space dimensions involving various situations of aerodynamic interest are included and compared.

Aided Electrophysiology Using Direct Audio Input: Effects of Amplification and Absolute Signal Level

PubMed Central

Billings, Curtis J.; Miller, Christi W.; Tremblay, Kelly L.

2016-01-01

Purpose This study investigated (a) the effect of amplification on cortical auditory evoked potentials (CAEPs) at different signal levels when signal-to-noise ratios (SNRs) were equated between unaided and aided conditions, and (b) the effect of absolute signal level on aided CAEPs when SNR was held constant. Method CAEPs were recorded from 13 young adults with normal hearing. A 1000-Hz pure tone was presented in unaided and aided conditions with a linear analog hearing aid. Direct audio input was used, allowing recorded hearing aid noise floor to be added to unaided conditions to equate SNRs between conditions. An additional stimulus was created through scaling the noise floor to study the effect of signal level. Results Amplification resulted in delayed N1 and P2 peak latencies relative to the unaided condition. An effect of absolute signal level (when SNR was constant) was present for aided CAEP area measures, such that larger area measures were found at higher levels. Conclusion Results of this study further demonstrate that factors in addition to SNR must also be considered before CAEPs can be used to clinically to measure aided thresholds. PMID:26953543

Free geometric adjustment of the SECOR Equatorial Network (Solution SECOR-27)

NASA Technical Reports Server (NTRS)

Mueller, I. I.; Kumar, M.; Soler, T.

1973-01-01

The basic purpose of this experiment is to compute reduced normal equations from the observational data of the SECOR Equatorial Network obtained from DMA/Topographic Center, D/Geodesy, Geosciences Div. Washington, D.C. These reduced normal equations are to be combined with reduced normal equations of other satellite networks of the National Geodetic Satellite Program to provide station coordinates from a single least square adjustment. An individual SECOR solution was also obtained and is presented in this report, using direction constraints computed from BC-4 optical data from stations collocated with SECOR stations. Due to the critical configuration present in the range observations, weighted height constraints were also applied in order to break the near coplanarity of the observing stations.

A two-level approach to VLBI terrestrial and celestial reference frames using both least-squares adjustment and Kalman filter algorithms

NASA Astrophysics Data System (ADS)

Soja, B.; Krasna, H.; Boehm, J.; Gross, R. S.; Abbondanza, C.; Chin, T. M.; Heflin, M. B.; Parker, J. W.; Wu, X.

2017-12-01

The most recent realizations of the ITRS include several innovations, two of which are especially relevant to this study. On the one hand, the IERS ITRS combination center at DGFI-TUM introduced a two-level approach with DTRF2014, consisting of a classical deterministic frame based on normal equations and an optional coordinate time series of non-tidal displacements calculated from geophysical loading models. On the other hand, the JTRF2014 by the combination center at JPL is a time series representation of the ITRF determined by Kalman filtering. Both the JTRF2014 and the second level of the DTRF2014 are thus able to take into account short-term variations in the station coordinates. In this study, based on VLBI data, we combine these two approaches, applying them to the determination of both terrestrial and celestial reference frames. Our product has two levels like DTRF2014, with the second level being a Kalman filter solution like JTRF2014. First, we compute a classical TRF and CRF in a global least-squares adjustment by stacking normal equations from 5446 VLBI sessions between 1979 and 2016 using the Vienna VLBI and Satellite Software VieVS (solution level 1). Next, we obtain coordinate residuals from the global adjustment by applying the level-1 TRF and CRF in the single-session analysis and estimating coordinate offsets. These residuals are fed into a Kalman filter and smoother, taking into account the stochastic properties of the individual stations and radio sources. The resulting coordinate time series (solution level 2) serve as an additional layer representing irregular variations not considered in the first level of our approach. Both levels of our solution are implemented in VieVS in order to test their individual and combined performance regarding the repeatabilities of estimated baseline lengths, EOP, and radio source coordinates.

Concealed renal failure and adverse drug reactions in older patients with type 2 diabetes mellitus.

PubMed

Corsonello, Andrea; Pedone, Claudio; Corica, Francesco; Mazzei, Bruno; Di Iorio, Angelo; Carbonin, Pierugo; Incalzi, Raffaele Antonelli

2005-09-01

In elderly patients serum creatinine may be normal despite decreased glomerular filtration rate (GFR). The aim of this study was to evaluate the prevalence of this "concealed" renal failure, i.e., renal failure with normal serum creatinine levels, in elderly diabetic patients, and to verify whether it is a risk factor for adverse drug reactions (ADR) to hydrosoluble drugs. We used data on 2257 hospitalized patients with type 2 diabetes mellitus enrolled in the Gruppo Italiano di Farmacovigilanza nell'Anziano study. On the basis of serum creatinine and calculated GFR, patients were grouped as follows: normal renal function (normal serum creatinine levels and normal GFR), concealed (normal serum creatinine levels and reduced GFR), or overt (increased creatinine levels and reduced GFR) renal failure. GFR was calculated using the Modification of Diet in Renal Disease (MDRD) equation. The outcome of the study was the incidence of ADR to hydrosoluble drugs during the hospital stay. The relationship between renal function and ADR was evaluated using Cox regression analysis including potential confounders. Concealed renal failure was observed in 363 (16.1%) of patients studied. Patients with concealed or overt renal failure were older, had more frequently cognitive impairment and polypharmacy, and had lower serum albumin levels than did those with normal renal function. Both concealed (hazard ratio = 1.90; 95% confidence interval, 1.04-3.48; p =.036) and overt (hazard ratio = 2.23; 95% confidence interval, 1.40-3.55; p =.001) renal failure were significantly associated with ADR to hydrosoluble drugs. The use of more than four drugs also qualified as an independent risk factor for ADRs to hydrosoluble drugs during hospital stay. Older diabetic patients should be systematically screened to ascertain the presence of concealed renal failure in an attempt to optimize the pharmacological treatment and reduce the risk of ADRs.

The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells.

PubMed

Levine, M W

1991-01-01

Simulated neural impulse trains were generated by a digital realization of the integrate-and-fire model. The variability in these impulse trains had as its origin a random noise of specified distribution. Three different distributions were used: the normal (Gaussian) distribution (no skew, normokurtic), a first-order gamma distribution (positive skew, leptokurtic), and a uniform distribution (no skew, platykurtic). Despite these differences in the distribution of the variability, the distributions of the intervals between impulses were nearly indistinguishable. These inter-impulse distributions were better fit with a hyperbolic gamma distribution than a hyperbolic normal distribution, although one might expect a better approximation for normally distributed inverse intervals. Consideration of why the inter-impulse distribution is independent of the distribution of the causative noise suggests two putative interval distributions that do not depend on the assumed noise distribution: the log normal distribution, which is predicated on the assumption that long intervals occur with the joint probability of small input values, and the random walk equation, which is the diffusion equation applied to a random walk model of the impulse generating process. Either of these equations provides a more satisfactory fit to the simulated impulse trains than the hyperbolic normal or hyperbolic gamma distributions. These equations also provide better fits to impulse trains derived from the maintained discharges of ganglion cells in the retinae of cats or goldfish. It is noted that both equations are free from the constraint that the coefficient of variation (CV) have a maximum of unity.(ABSTRACT TRUNCATED AT 250 WORDS)

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

Morgan, Nathaniel Ray; Waltz, Jacob I.

The level set method is commonly used to model dynamically evolving fronts and interfaces. In this work, we present new methods for evolving fronts with a specified velocity field or in the surface normal direction on 3D unstructured tetrahedral meshes with adaptive mesh refinement (AMR). The level set field is located at the nodes of the tetrahedral cells and is evolved using new upwind discretizations of Hamilton–Jacobi equations combined with a Runge–Kutta method for temporal integration. The level set field is periodically reinitialized to a signed distance function using an iterative approach with a new upwind gradient. We discuss themore » details of these level set and reinitialization methods. Results from a range of numerical test problems are presented.« less

Conic Sections and the Discovery of a Novel Curve Using Differential Equations

ERIC Educational Resources Information Center

de Alwis, Amal

2013-01-01

We began by observing a variety of properties related to the tangent and normal lines of three conic sections: a parabola, an ellipse, and a hyperbola. Some of these properties include specific relationships between the x- and y-intercepts of the tangent and normal lines. Using these properties, we were able to form several differential equations.…

Management of Listeria monocytogenes in fermented sausages using the Food Safety Objective concept underpinned by stochastic modeling and meta-analysis.

PubMed

Mataragas, M; Alessandria, V; Rantsiou, K; Cocolin, L

2015-08-01

In the present work, a demonstration is made on how the risk from the presence of Listeria monocytogenes in fermented sausages can be managed using the concept of Food Safety Objective (FSO) aided by stochastic modeling (Bayesian analysis and Monte Carlo simulation) and meta-analysis. For this purpose, the ICMSF equation was used, which combines the initial level (H0) of the hazard and its subsequent reduction (ΣR) and/or increase (ΣI) along the production chain. Each element of the equation was described by a distribution to investigate the effect not only of the level of the hazard, but also the effect of the accompanying variability. The distribution of each element was determined by Bayesian modeling (H0) and meta-analysis (ΣR and ΣI). The output was a normal distribution N(-5.36, 2.56) (log cfu/g) from which the percentage of the non-conforming products, i.e. the fraction above the FSO of 2 log cfu/g, was estimated at 0.202%. Different control measures were examined such as lowering initial L. monocytogenes level and inclusion of an additional killing step along the process resulting in reduction of the non-conforming products from 0.195% to 0.003% based on the mean and/or square-root change of the normal distribution, and 0.001%, respectively. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

A fictitious domain finite element method for simulations of fluid-structure interactions: The Navier-Stokes equations coupled with a moving solid

NASA Astrophysics Data System (ADS)

Court, Sébastien; Fournié, Michel

2015-05-01

The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an optimal approximation of the normal stress tensor at the interface. The dynamics of the solid is governed by the Newton's laws and the interface between the fluid and the structure is materialized by a level-set which cuts the elements of the mesh. An algorithm is proposed in order to treat the time evolution of the geometry and numerical results are presented on a classical benchmark of the motion of a disk falling in a channel.

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

PubMed Central

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

2017-01-01

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

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

PubMed

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

2017-02-13

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

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

Jibben, Zechariah Joel; Herrmann, Marcus

Here, we present a Runge-Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constantmore » with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.« less

Integration of local motion is normal in amblyopia

NASA Astrophysics Data System (ADS)

Hess, Robert F.; Mansouri, Behzad; Dakin, Steven C.; Allen, Harriet A.

2006-05-01

We investigate the global integration of local motion direction signals in amblyopia, in a task where performance is equated between normal and amblyopic eyes at the single element level. We use an equivalent noise model to derive the parameters of internal noise and number of samples, both of which we show are normal in amblyopia for this task. This result is in apparent conflict with a previous study in amblyopes showing that global motion processing is defective in global coherence tasks [Vision Res. 43, 729 (2003)]. A similar discrepancy between the normalcy of signal integration [Vision Res. 44, 2955 (2004)] and anomalous global coherence form processing has also been reported [Vision Res. 45, 449 (2005)]. We suggest that these discrepancies for form and motion processing in amblyopia point to a selective problem in separating signal from noise in the typical global coherence task.

Evaluation of Delamination Growth Characterization Methods Under Mode I Fatigue Loading

NASA Technical Reports Server (NTRS)

Murri, Gretchen B.

2012-01-01

Reliable delamination characterization data for laminated composites are needed for input to analytical models of structures to predict delamination. The double-cantilevered beam (DCB) specimen is used with laminated composites to measure fracture toughness, G(sub Ic), delamination onset strain energy release rate, and growth rate data under cyclic loading. In the current study, DCB specimens of IM7/8552 graphite/epoxy supplied by two different manufacturers were tested in static and fatigue to compare the measured characterization data from the two sources, and to evaluate a proposed ASTM standard for generating Paris Law equations. Static results were used to generate compliance calibration constants for the fatigue data, and a delamination resistance curve, G(sub IR), which was used to determine the effects of fiber-bridging on delamination growth. Specimens were tested in fatigue at a cyclic G(sub Imax) level equal to 50, 40 or 30% of G(sub Ic), to determine a delamination onset curve and delamination growth rate. The delamination onset curve equations had similar exponents and the same trends. Delamination growth rate was calculated by fitting a Paris Law to the da/dN versus G(sub Imax) data. Both a 2-point and a 7-point data reduction method were used and the Paris Law equations were compared. To determine the effects of fiber-bridging, growth rate results were normalized by the delamination resistance curve for each material and compared to the non-normalized results. Paris Law exponents were found to decrease by 31% to 37% due to normalizing the growth data. Normalizing the data also greatly reduced the amount of scatter between the different specimens. Visual data records from the fatigue testing were used to calculate individual compliance calibration constants from the fatigue data for some of the specimens. The resulting da/dN versus G(sub Imax) plots showed much improved repeatability between specimens. Gretchen

Ductility normalized-strainrange partitioning life relations for creep-fatigue life predictions

NASA Technical Reports Server (NTRS)

Halford, G. R.; Saltsman, J. F.; Hirschberg, M. H.

1977-01-01

Procedures based on Strainrange Partitioning (SRP) are presented for estimating the effects of environment and other influences on the high temperature, low cycle, creep fatigue resistance of alloys. It is proposed that the plastic and creep, ductilities determined from conventional tensile and creep rupture tests conducted in the environment of interest be used in a set of ductility normalized equations for making a first order approximation of the four SRP inelastic strainrange life relations. Different levels of sophistication in the application of the procedures are presented by means of illustrative examples with several high temperature alloys. Predictions of cyclic lives generally agree with observed lives within factors of three.

Interface equation and viscosity contrast in Hele-Shaw flow

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

Casademunt, J.; Jasnow, D.; Hernandez-Machado, A.

1992-05-20

In this paper, the authors derive an integro-differential equation for the evolution of the interface separating two immiscible viscous fluids in a Hele-Shaw cell with a channel geometry, for arbitrary viscosity contrast. The authors' equation differs from a previous one obtained by a vortex-sheet formulation of the problem, in that the normal component of the interface velocity is formally decoupled from the gauge-dependent tangential part. The result is thus a closed integral equation for the normal velocity. The authors briefly comment on the advantages of such a formulation and implement an alternative computational algorithm based on it. Preliminary numerical resultsmore » confirm a highly inefficient finger competition in the zero viscosity contrast limit.« less

Modeling electromagnetic ion cyclotron waves in the inner magnetosphere

NASA Astrophysics Data System (ADS)

Gamayunov, Konstantin; Engebretson, Mark; Zhang, Ming; Rassoul, Hamid

The evolution of He+-mode electromagnetic ion cyclotron (EMIC) waves is studied inside the geostationary orbit using our global model of ring current (RC) ions, electric field, plasmasphere, and EMIC waves. In contrast to the approach previously used by Gamayunov et al. [2009], however, we do not use the bounce-averaged wave kinetic equation but instead use a complete, non bounce-averaged, equation to model the evolution of EMIC wave power spectral density, including off-equatorial wave dynamics. The major results of our study can be summarized as follows. (1) The thermal background level for EMIC waves is too low to allow waves to grow up to the observable level during one pass between the “bi-ion latitudes” (the latitudes where the given wave frequency is equal to the O+-He+ bi-ion frequency) in conjugate hemispheres. As a consequence, quasi-field-aligned EMIC waves are not typically produced in the model if the thermal background level is used, but routinely observed in the Earth’s magnetosphere. To overcome this model-observation discrepancy we suggest a nonlinear energy cascade from the lower frequency range of ultra low frequency waves into the frequency range of EMIC wave generation as a possible mechanism supplying the needed level of seed fluctuations that guarantees growth of EMIC waves during one pass through the near equatorial region. The EMIC wave development from a suprathermal background level shows that EMIC waves are quasi-field-aligned near the equator, while they are oblique at high latitudes, and the Poynting flux is predominantly directed away from the near equatorial source region in agreement with observations. (2) An abundance of O+ strongly controls the energy of oblique He+-mode EMIC waves that propagate to the equator after their reflection at “bi-ion latitudes”, and so it controls a fraction of wave energy in the oblique normals. (3) The RC O+ not only causes damping of the He+-mode EMIC waves but also causes wave generation in the region of highly oblique wave normal angles, typically for theta > 82deg, where a growth rate gamma > 0.01 rad/s is frequently observed. The instability is driven by the loss-cone feature in the RC O+ distribution function. (4) The oblique and intense He+-mode EMIC waves generated by RC O+ in the region L ˜ 2-3 may have an implication to the energetic particle loss in the inner radiation belt. Acknowledgments: This paper is based upon work supported by the National Science Foundation under Grant Number AGS-1203516.

Compact Representations of Extended Causal Models

DTIC Science & Technology

2012-10-01

get a yet more compact representation by assuming that, by default , it is typical for the variables to obey the structural equations. Finally, in...Halpern and Hitchcock (2011), is to incorporate considerations about about defaults , typicality, and normality. “Normality” and its cognates (“normal...atypical to violate it. 17 Variables typically obey the structural equations. Thus, it is often far more efficient to assume this holds by default

Predictive equations for total lung capacity and residual volume calculated from radiographs in a random sample of the Michigan population.

PubMed Central

Kilburn, K H; Warshaw, R H; Thornton, J C; Thornton, K; Miller, A

1992-01-01

BACKGROUND: Published predicted values for total lung capacity and residual volume are often based on a small number of subjects and derive from different populations from predicted spirometric values. Equations from the only two large studies gave smaller predicted values for total lung capacity than the smaller studies. A large number of subjects have been studied from a population which has already provided predicted values for spirometry and transfer factor for carbon monoxide. METHODS: Total lung capacity was measured from standard posteroanterior and lateral chest radiographs and forced vital capacity by spirometry in a population sample of 771 subjects. Prediction equations were developed for total lung capacity (TLC), residual volume (RV) and RV/TLC in two groups--normal and total. Subjects with signs or symptoms of cardiopulmonary disease were combined with the normal subjects and equations for all subjects were also modelled. RESULTS: Prediction equations for TLC and RV in non-smoking normal men and women were square root transformations which included height and weight but not age. They included a coefficient for duration of smoking in current smokers. The predictive equation for RV/TLC included weight, age, age and duration of smoking for current smokers and ex-smokers of both sexes. For the total population the equations took the same form but the height coefficients and constants were slightly different. CONCLUSION: These population based prediction equations for TLC, RV and RV/TLC provide reference standards in a population that has provided reference standards for spirometry and single breath transfer factor for carbon monoxide. PMID:1412094

Anisotropic elliptic optical fibers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kang, Soon Ahm

1991-01-01

The exact characteristic equation for an anisotropic elliptic optical fiber is obtained for odd and even hybrid modes in terms of infinite determinants utilizing Mathieu and modified Mathieu functions. A simplified characteristic equation is obtained by applying the weakly guiding approximation such that the difference in the refractive indices of the core and the cladding is small. The simplified characteristic equation is used to compute the normalized guide wavelength for an elliptical fiber. When the anisotropic parameter is equal to unity, the results are compared with the previous research and they are in close agreement. For a fixed value normalized cross-section area or major axis, the normalized guide wavelength lambda/lambda(sub 0) for an anisotropic elliptic fiber is small for the larger value of anisotropy. This condition indicates that more energy is carried inside of the fiber. However, the geometry and anisotropy of the fiber have a smaller effect when the normalized cross-section area is very small or very large.

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

PubMed

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

2012-01-01

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

Cancer Theory from Systems Biology Point of View

NASA Astrophysics Data System (ADS)

Wang, Gaowei; Tang, Ying; Yuan, Ruoshi; Ao, Ping

In our previous work, we have proposed a novel cancer theory, endogenous network theory, to understand mechanism underlying cancer genesis and development. Recently, we apply this theory to hepatocellular carcinoma (HCC). A core endogenous network of hepatocyte was established by integrating the current understanding of hepatocyte at molecular level. Quantitative description of the endogenous network consisted of a set of stochastic differential equations which could generate many local attractors with obvious or non-obvious biological functions. By comparing with clinical observation and experimental data, the results showed that two robust attractors from the model reproduced the main known features of normal hepatocyte and cancerous hepatocyte respectively at both modular and molecular level. In light of our theory, the genesis and progression of cancer is viewed as transition from normal attractor to HCC attractor. A set of new insights on understanding cancer genesis and progression, and on strategies for cancer prevention, cure, and care were provided.

HPC in Basin Modeling: Simulating Mechanical Compaction through Vertical Effective Stress using Level Sets

NASA Astrophysics Data System (ADS)

McGovern, S.; Kollet, S. J.; Buerger, C. M.; Schwede, R. L.; Podlaha, O. G.

2017-12-01

In the context of sedimentary basins, we present a model for the simulation of the movement of ageological formation (layers) during the evolution of the basin through sedimentation and compactionprocesses. Assuming a single phase saturated porous medium for the sedimentary layers, the modelfocuses on the tracking of the layer interfaces, through the use of the level set method, as sedimentationdrives fluid-flow and reduction of pore space by compaction. On the assumption of Terzaghi's effectivestress concept, the coupling of the pore fluid pressure to the motion of interfaces in 1-D is presented inMcGovern, et.al (2017) [1] .The current work extends the spatial domain to 3-D, though we maintain the assumption ofvertical effective stress to drive the compaction. The idealized geological evolution is conceptualized asthe motion of interfaces between rock layers, whose paths are determined by the magnitude of a speedfunction in the direction normal to the evolving layer interface. The speeds normal to the interface aredependent on the change in porosity, determined through an effective stress-based compaction law,such as the exponential Athy's law. Provided with the speeds normal to the interface, the level setmethod uses an advection equation to evolve a potential function, whose zero level set defines theinterface. Thus, the moving layer geometry influences the pore pressure distribution which couplesback to the interface speeds. The flexible construction of the speed function allows extension, in thefuture, to other terms to represent different physical processes, analogous to how the compaction rulerepresents material deformation.The 3-D model is implemented using the generic finite element method framework Deal II,which provides tools, building on p4est and interfacing to PETSc, for the massively parallel distributedsolution to the model equations [2]. Experiments are being run on the Juelich Supercomputing Center'sJureca cluster. [1] McGovern, et.al. (2017). Novel basin modelling concept for simulating deformation from mechanical compaction using level sets. Computational Geosciences, SI:ECMOR XV, 1-14.[2] Bangerth, et. al. (2011). Algorithms and data structures for massively parallel generic adaptive finite element codes. ACM Transactions on Mathematical Software (TOMS), 38(2):14.

Calculation of normal modes of the closed waveguides in general vector case

NASA Astrophysics Data System (ADS)

Malykh, M. D.; Sevastianov, L. A.; Tiutiunnik, A. A.

2018-04-01

The article is devoted to the calculation of normal modes of the closed waveguides with an arbitrary filling ɛ, μ in the system of computer algebra Sage. Maxwell equations in the cylinder are reduced to the system of two bounded Helmholtz equations, the notion of weak solution of this system is given and then this system is investigated as a system of ordinary differential equations. The normal modes of this system are an eigenvectors of a matrix pencil. We suggest to calculate the matrix elements approximately and to truncate the matrix by usual way but further to solve the truncated eigenvalue problem exactly in the field of algebraic numbers. This approach allows to keep the symmetry of the initial problem and in particular the multiplicity of the eigenvalues. In the work would be presented some results of calculations.

Planck constant as spectral parameter in integrable systems and KZB equations

NASA Astrophysics Data System (ADS)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

Effect of second to first normal stress difference ratio at the die exit on neck-in phenomenon in polymeric flat film production

NASA Astrophysics Data System (ADS)

Barborik, Tomas; Zatloukal, Martin

2017-05-01

In this study, viscoelastic modeling of the extrusion film casting process, based on the lD membrane model and modified Leonov constitutive equation, was conducted and the effect of the viscoelastic stress state at the die exit (captured here via second to first normal stress difference ratio) on the unwanted neck-in phenomenon has been analyzed for wide range of Deborah numbers and materials having different level of uniaxial and planar extensional strain hardening. Relevant experimental data for LDPE and theoretical predictions based on multimode eXtended Pom-Pom model acquired from the open literature were used for the validation purposes. It was found that firstly, the predicting capabilities of both constitutive equations for given material and processing conditions are comparable even if the single mode modified Leonov model was used and secondly, the agreement between theoretical and experimental data on neck-in is fairly good. Results of the theoretical study revealed that the viscoelastic stress state at the die exit (i.e. -N2/N1 ratio) increases the level of neck-in if uniaxial extensional strain hardening, planar to uniaxial extensional viscosity ratio and Deborah number increases. It has also been revealed that there exists threshold value for Deborah number and extensional strain hardening below which the neck-in becomes independent on the die exit stress state.

Derivation of equations of motion for multi-blade rotors employing coupled modes and including high twist capability

NASA Technical Reports Server (NTRS)

Sopher, R.

1975-01-01

The equations of motion are derived for a multiblade rotor. A high twist capability and coupled flatwise-edgewise assumed normal modes are employed instead of uncoupled flatwise - edgewise assumed normal models. The torsion mode is uncoupled. Support system models, consisting of complete helicopters in free flight, or grounded flexible supports, arbitrary rotor-induced inflow, and arbitrary vertical gust models are also used.

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

NASA Technical Reports Server (NTRS)

Barker, L. K.

1983-01-01

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

The Dirac equation and the normalization of its solutions in a closed Friedmann- Robertson-Walker universe

NASA Astrophysics Data System (ADS)

Finster, Felix; Reintjes, Moritz

2009-05-01

We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and separate the spatial and time variables. In the case of a closed universe, the spatial dependence is solved explicitly, giving rise to a discrete set of solutions. We compute the probability integral and analyze a spacetime normalization integral. This analysis allows us to introduce the fermionic projector in a closed Friedmann-Robertson-Walker geometry and to specify its global normalization as well as its local form. First author supported in part by the Deutsche Forschungsgemeinschaft.

An Integrable Approximation for the Fermi Pasta Ulam Lattice

NASA Astrophysics Data System (ADS)

Rink, Bob

This contribution presents a review of results obtained from computations of approximate equations of motion for the Fermi-Pasta-Ulam lattice. These approximate equations are obtained as a finite-dimensional Birkhoff normal form. It turns out that in many cases, the Birkhoff normal form is suitable for application of the KAM theorem. In particular, this proves Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal Birkhoff normal form computations of Nishida, the KAM theorem and discrete symmetry considerations.

Tools for Basic Statistical Analysis

NASA Technical Reports Server (NTRS)

Luz, Paul L.

2005-01-01

Statistical Analysis Toolset is a collection of eight Microsoft Excel spreadsheet programs, each of which performs calculations pertaining to an aspect of statistical analysis. These programs present input and output data in user-friendly, menu-driven formats, with automatic execution. The following types of calculations are performed: Descriptive statistics are computed for a set of data x(i) (i = 1, 2, 3 . . . ) entered by the user. Normal Distribution Estimates will calculate the statistical value that corresponds to cumulative probability values, given a sample mean and standard deviation of the normal distribution. Normal Distribution from two Data Points will extend and generate a cumulative normal distribution for the user, given two data points and their associated probability values. Two programs perform two-way analysis of variance (ANOVA) with no replication or generalized ANOVA for two factors with four levels and three repetitions. Linear Regression-ANOVA will curvefit data to the linear equation y=f(x) and will do an ANOVA to check its significance.

Harmonized Reference Ranges for Circulating Testosterone Levels in Men of Four Cohort Studies in the United States and Europe

PubMed Central

Travison, Thomas G.; Vesper, Hubert W.; Orwoll, Eric; Wu, Frederick; Kaufman, Jean Marc; Wang, Ying; Lapauw, Bruno; Fiers, Tom; Matsumoto, Alvin M.

2017-01-01

Background: Reference ranges for testosterone are essential for making a diagnosis of hypogonadism in men. Objective: To establish harmonized reference ranges for total testosterone in men that can be applied across laboratories by cross-calibrating assays to a reference method and standard. Population: The 9054 community-dwelling men in cohort studies in the United States and Europe: Framingham Heart Study; European Male Aging Study; Osteoporotic Fractures in Men Study; and Male Sibling Study of Osteoporosis. Methods: Testosterone concentrations in 100 participants in each of the four cohorts were measured using a reference method at Centers for Disease Control and Prevention (CDC). Generalized additive models and Bland-Altman analyses supported the use of normalizing equations for transformation between cohort-specific and CDC values. Normalizing equations, generated using Passing-Bablok regression, were used to generate harmonized values, which were used to derive standardized, age-specific reference ranges. Results: Harmonization procedure reduced intercohort variation between testosterone measurements in men of similar ages. In healthy nonobese men, 19 to 39 years, harmonized 2.5th, 5th, 50th, 95th, and 97.5th percentile values were 264, 303, 531, 852, and 916 ng/dL, respectively. Age-specific harmonized testosterone concentrations in nonobese men were similar across cohorts and greater than in all men. Conclusion: Harmonized normal range in a healthy nonobese population of European and American men, 19 to 39 years, is 264 to 916 ng/dL. A substantial proportion of intercohort variation in testosterone levels is due to assay differences. These data demonstrate the feasibility of generating harmonized reference ranges for testosterone that can be applied to assays, which have been calibrated to a reference method and calibrator. PMID:28324103

Elementary diagrams in nuclear and neutron matter

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

Wiringa, R.B.

1995-08-01

Variational calculations of nuclear and neutron matter are currently performed using a diagrammatic cluster expansion with the aid of nonlinear integral equations for evaluating expectation values. These are the Fermi hypernetted chain (FHNC) and single-operator chain (SOC) equations, which are a way of doing partial diagram summations to infinite order. A more complete summation can be made by adding elementary diagrams to the procedure. The simplest elementary diagrams appear at the four-body cluster level; there is one such E{sub 4} diagram in Bose systems, but 35 diagrams in Fermi systems, which gives a level of approximation called FHNC/4. We developedmore » a novel technique for evaluating these diagrams, by computing and storing 6 three-point functions, S{sub xyz}(r{sub 12}, r{sub 13}, r{sub 23}), where xyz (= ccd, cce, ddd, dde, dee, or eee) denotes the exchange character at the vertices 1, 2, and 3. All 35 Fermi E{sub 4} diagrams can be constructed from these 6 functions and other two-point functions that are already calculated. The elementary diagrams are known to be important in some systems like liquid {sup 3}He. We expect them to be small in nuclear matter at normal density, but they might become significant at higher densities appropriate for neutron star calculations. This year we programmed the FHNC/4 contributions to the energy and tested them in a number of simple model cases, including liquid {sup 3}He and Bethe`s homework problem. We get reasonable, but not exact agreement with earlier published work. In nuclear and neutron matter with the Argonne v{sub 14} interaction these contributions are indeed small corrections at normal density and grow to only 5-10 MeV/nucleon at 5 times normal density.« less

A delay differential equation model of follicle waves in women.

PubMed

Panza, Nicole M; Wright, Andrew A; Selgrade, James F

2016-01-01

This article presents a mathematical model for hormonal regulation of the menstrual cycle which predicts the occurrence of follicle waves in normally cycling women. Several follicles of ovulatory size that develop sequentially during one menstrual cycle are referred to as follicle waves. The model consists of 13 nonlinear, delay differential equations with 51 parameters. Model simulations exhibit a unique stable periodic cycle and this menstrual cycle accurately approximates blood levels of ovarian and pituitary hormones found in the biological literature. Numerical experiments illustrate that the number of follicle waves corresponds to the number of rises in pituitary follicle stimulating hormone. Modifications of the model equations result in simulations which predict the possibility of two ovulations at different times during the same menstrual cycle and, hence, the occurrence of dizygotic twins via a phenomenon referred to as superfecundation. Sensitive parameters are identified and bifurcations in model behaviour with respect to parameter changes are discussed. Studying follicle waves may be helpful for improving female fertility and for understanding some aspects of female reproductive ageing.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

The use of copulas to practical estimation of multivariate stochastic differential equation mixed effects models

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

Rupšys, P.

A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE.

3D level set methods for evolving fronts on tetrahedral meshes with adaptive mesh refinement

DOE PAGES

Morgan, Nathaniel Ray; Waltz, Jacob I.

2017-03-02

The level set method is commonly used to model dynamically evolving fronts and interfaces. In this work, we present new methods for evolving fronts with a specified velocity field or in the surface normal direction on 3D unstructured tetrahedral meshes with adaptive mesh refinement (AMR). The level set field is located at the nodes of the tetrahedral cells and is evolved using new upwind discretizations of Hamilton–Jacobi equations combined with a Runge–Kutta method for temporal integration. The level set field is periodically reinitialized to a signed distance function using an iterative approach with a new upwind gradient. We discuss themore » details of these level set and reinitialization methods. Results from a range of numerical test problems are presented.« less

Validating Reference Equations for Impulse Oscillometry in Healthy Mexican Children.

PubMed

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

2017-09-01

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

An arbitrary-order Runge–Kutta discontinuous Galerkin approach to reinitialization for banded conservative level sets

DOE PAGES

Jibben, Zechariah Joel; Herrmann, Marcus

2017-08-24

Here, we present a Runge-Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constantmore » with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.« less

Vibrational population of the A super 3 sigma sub u/+/ and B super 3 pi sub g states of N2 in normal auroras.

NASA Technical Reports Server (NTRS)

Cartwright, D. C.; Trajmar, S.; Williams, W.

1971-01-01

Use of new electron impact excitation cross sections for the six lowest triplet states (A, B, W, C, E, D) of N2, and solution of the coupled equations of statistical equilibrium to obtain the vibrational population of each electronic state. The results show that cascade from high levels of the A super 3 sigma sub u(+) state and from the W super 3 delta sub u state is significant in populating the lower vibrational levels of the B state and hence the character of its ?apparent' excitation cross sections. For the B state excited under auroral conditions, the fraction of the total population due to cascade processes exceeds 25% for all levels lower than 7 and is greater than 80% for B(v' = 0). For the A state under similar conditions, cascade from the B state contributes 50% or more of the total vibrational population for levels lower than 7, and 80% or more for levels below 4. For levels of the A state greater than 7, the A yields B transitions depopulate the levels rapidly and indicate that the Vegard-Kaplan emissions from these higher levels will be weak or totally absent in normal auroras.

Modeling Pulse Transmission in the Monterey Bay Using Parabolic Equation Methods

DTIC Science & Technology

1991-12-01

Collins 9-13 was chosen for this purpose due its energy conservation scheme , and its ability to efficiently incorporate higher order terms in its...pressure field generated by the PE model into normal modes. Additionally, this process provides increased physical understanding of mode coupling and...separation of variables (i.e. normal modes or fast field), as well as pure numerical schemes such as the parabolic equation methods, can be used. However, as

High-frequency Born synthetic seismograms based on coupled normal modes

USGS Publications Warehouse

Pollitz, Fred F.

2011-01-01

High-frequency and full waveform synthetic seismograms on a 3-D laterally heterogeneous earth model are simulated using the theory of coupled normal modes. The set of coupled integral equations that describe the 3-D response are simplified into a set of uncoupled integral equations by using the Born approximation to calculate scattered wavefields and the pure-path approximation to modulate the phase of incident and scattered wavefields. This depends upon a decomposition of the aspherical structure into smooth and rough components. The uncoupled integral equations are discretized and solved in the frequency domain, and time domain results are obtained by inverse Fourier transform. Examples show the utility of the normal mode approach to synthesize the seismic wavefields resulting from interaction with a combination of rough and smooth structural heterogeneities. This approach is applied to an ∼4 Hz shallow crustal wave propagation around the site of the San Andreas Fault Observatory at Depth (SAFOD).

A probabilistic approach to photovoltaic generator performance prediction

NASA Astrophysics Data System (ADS)

Khallat, M. A.; Rahman, S.

1986-09-01

A method for predicting the performance of a photovoltaic (PV) generator based on long term climatological data and expected cell performance is described. The equations for cell model formulation are provided. Use of the statistical model for characterizing the insolation level is discussed. The insolation data is fitted to appropriate probability distribution functions (Weibull, beta, normal). The probability distribution functions are utilized to evaluate the capacity factors of PV panels or arrays. An example is presented revealing the applicability of the procedure.

A Volume and Taper Prediction System for Bald Cypress

Treesearch

Bernard R. Parresol; James E. Hotvedt; Quang V. Cao

1987-01-01

A volume and taper prediction system based on d10 and consisting of a total volume equation, two volume ratio equations (one for diameter limits, the other for height limits), and a taper equation was developed for bald cypress using sample tree data collected in Louisiana. Normal diameter (dn), a subjective variable-...

The way from microscopic many-particle theory to macroscopic hydrodynamics.

PubMed

Haussmann, Rudolf

2016-03-23

Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena. We specify the densities of the conserved quantities as the relevant hydrodynamic variables and apply the methods of non-equilibrium statistical mechanics with projection operator techniques. As a result we obtain time-evolution equations for the hydrodynamic variables with three kinds of terms on the right-hand sides: reversible, dissipative and fluctuating terms. In their original form these equations are completely exact and contain nonlocal terms in space and time which describe nonlocal memory effects. Applying a few approximations the nonlocal properties and the memory effects are removed. As a result we find the well known hydrodynamic equations of a normal fluid with Gaussian fluctuating forces. In the following we investigate if and how the time-inversion invariance is broken and how the second law of thermodynamics comes about. Furthermore, we show that the hydrodynamic equations with fluctuating forces are equivalent to stochastic Langevin equations and the related Fokker-Planck equation. Finally, we investigate the fluctuation theorem and find a modification by an additional term.

Starvation effects on the hydrodynamic lubrication of rigid nonconformal contacts in combined rolling and normal motion

NASA Technical Reports Server (NTRS)

Ghosh, M. K.; Hamrock, B. J.; Brewe, D. E.

1986-01-01

The effect of inlet starvation on the hydrodynamic lubrication of lightly loaded rigid nonconformal contacts in combined rolling and normal motion is determined through a numerical solution of the Reynolds' equation for an isoviscous, incompressible lubricant. Starvation is effected by systematically reducing the fluid inlet level. The pressures are taken to be ambient at the inlet meniscus boundary and Reynolds' boundary condition is applied for film rupture in the exit region. Results are presented for the dynamic performance of the starved contacts in combined rolling and normal motion for both normal approach and separation. During normal approach the dynamic load ratio (i.e. ratio of dynamic to steady state load capacity) increases considerably with increase in the inlet starvation. The effect of starvation on the dynamic peak pressure ratio is relatively small. Further, it has been observed that with increasing starvation, film thickness effects become significant in the dynamic behavior of the nonconformal contacts. For significantly starved contacts the dynamic load ratio increases with increase in film thickness during normal approach and a similar reduction is observed during separation. A similar effect is noted for the dynamic peak pressure ratio.

Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics, production version (SOUSSA-P 1.1). Volume 1: Theoretical manual. [Green function

NASA Technical Reports Server (NTRS)

Morino, L.

1980-01-01

Recent developments of the Green's function method and the computer program SOUSSA (Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed and summarized. Applying the Green's function method to the fully unsteady (transient) potential equation yields an integro-differential-delay equation. With spatial discretization by the finite-element method, this equation is approximated by a set of differential-delay equations in time. Time solution by Laplace transform yields a matrix relating the velocity potential to the normal wash. Premultiplying and postmultiplying by the matrices relating generalized forces to the potential and the normal wash to the generalized coordinates one obtains the matrix of the generalized aerodynamic forces. The frequency and mode-shape dependence of this matrix makes the program SOUSSA useful for multiple frequency and repeated mode-shape evaluations.

Coupled latent differential equation with moderators: simulation and application.

PubMed

Hu, Yueqin; Boker, Steve; Neale, Michael; Klump, Kelly L

2014-03-01

Latent differential equations (LDE) use differential equations to analyze time series data. Because of the recent development of this technique, some issues critical to running an LDE model remain. In this article, the authors provide solutions to some of these issues and recommend a step-by-step procedure demonstrated on a set of empirical data, which models the interaction between ovarian hormone cycles and emotional eating. Results indicated that emotional eating is self-regulated. For instance, when people do more emotional eating than normal, they will subsequently tend to decrease their emotional eating behavior. In addition, a sudden increase will produce a stronger tendency to decrease than will a slow increase. We also found that emotional eating is coupled with the cycle of the ovarian hormone estradiol, and the peak of emotional eating occurs after the peak of estradiol. The self-reported average level of negative affect moderates the frequency of eating regulation and the coupling strength between eating and estradiol. Thus, people with a higher average level of negative affect tend to fluctuate faster in emotional eating, and their eating behavior is more strongly coupled with the hormone estradiol. Permutation tests on these empirical data supported the reliability of using LDE models to detect self-regulation and a coupling effect between two regulatory behaviors. (c) 2014 APA, all rights reserved.

Validation of Normalizations, Scaling, and Photofading Corrections for FRAP Data Analysis

PubMed Central

Kang, Minchul; Andreani, Manuel; Kenworthy, Anne K.

2015-01-01

Fluorescence Recovery After Photobleaching (FRAP) has been a versatile tool to study transport and reaction kinetics in live cells. Since the fluorescence data generated by fluorescence microscopy are in a relative scale, a wide variety of scalings and normalizations are used in quantitative FRAP analysis. Scaling and normalization are often required to account for inherent properties of diffusing biomolecules of interest or photochemical properties of the fluorescent tag such as mobile fraction or photofading during image acquisition. In some cases, scaling and normalization are also used for computational simplicity. However, to our best knowledge, the validity of those various forms of scaling and normalization has not been studied in a rigorous manner. In this study, we investigate the validity of various scalings and normalizations that have appeared in the literature to calculate mobile fractions and correct for photofading and assess their consistency with FRAP equations. As a test case, we consider linear or affine scaling of normal or anomalous diffusion FRAP equations in combination with scaling for immobile fractions. We also consider exponential scaling of either FRAP equations or FRAP data to correct for photofading. Using a combination of theoretical and experimental approaches, we show that compatible scaling schemes should be applied in the correct sequential order; otherwise, erroneous results may be obtained. We propose a hierarchical workflow to carry out FRAP data analysis and discuss the broader implications of our findings for FRAP data analysis using a variety of kinetic models. PMID:26017223

The Role of Deformation Energetics in Long-Term Tectonic Modeling

NASA Astrophysics Data System (ADS)

Ahamed, S.; Choi, E.

2017-12-01

The deformation-related energy budget is usually considered in the simplest form or even entirely omitted from the energy balance equation. We derive a full energy balance equation that accounts not only for heat energy but also for mechanical (elastic, plastic and viscous) work. The derived equation is implemented in DES3D, an unstructured finite element solver for long-term tectonic deformation. We verify the implementation by comparing numerical solutions to the corresponding semi-analytic solutions in three benchmarks extended from the classical oedometer test. We also investigate the long-term effects of deformation energetics on the evolution of large offset normal faults. We find that the models considering the full energy balance equation tend to produce more secondary faults and an elongated core complex. Our results for the normal fault system confirm that persistent inelastic deformation has a significant impact on the long-term evolution of faults, motivating further exploration of the role of the full energy balance equation in other geodynamic systems.

Normal modes of the shallow water system on the cubed sphere

NASA Astrophysics Data System (ADS)

Kang, H. G.; Cheong, H. B.; Lee, C. H.

2017-12-01

Spherical harmonics expressed as the Rossby-Haurwitz waves are the normal modes of non-divergent barotropic model. Among the normal modes in the numerical models, the most unstable mode will contaminate the numerical results, and therefore the investigation of normal mode for a given grid system and a discretiztaion method is important. The cubed-sphere grid which consists of six identical faces has been widely adopted in many atmospheric models. This grid system is non-orthogonal grid so that calculation of the normal mode is quiet challenge problem. In the present study, the normal modes of the shallow water system on the cubed sphere discretized by the spectral element method employing the Gauss-Lobatto Lagrange interpolating polynomials as orthogonal basis functions is investigated. The algebraic equations for the shallow water equation on the cubed sphere are derived, and the huge global matrix is constructed. The linear system representing the eigenvalue-eigenvector relations is solved by numerical libraries. The normal mode calculated for the several horizontal resolution and lamb parameters will be discussed and compared to the normal mode from the spherical harmonics spectral method.

GOCO05c: A New Combined Gravity Field Model Based on Full Normal Equations and Regionally Varying Weighting

NASA Astrophysics Data System (ADS)

Fecher, T.; Pail, R.; Gruber, T.

2017-05-01

GOCO05c is a gravity field model computed as a combined solution of a satellite-only model and a global data set of gravity anomalies. It is resolved up to degree and order 720. It is the first model applying regionally varying weighting. Since this causes strong correlations among all gravity field parameters, the resulting full normal equation system with a size of 2 TB had to be solved rigorously by applying high-performance computing. GOCO05c is the first combined gravity field model independent of EGM2008 that contains GOCE data of the whole mission period. The performance of GOCO05c is externally validated by GNSS-levelling comparisons, orbit tests, and computation of the mean dynamic topography, achieving at least the quality of existing high-resolution models. Results show that the additional GOCE information is highly beneficial in insufficiently observed areas, and that due to the weighting scheme of individual data the spectral and spatial consistency of the model is significantly improved. Due to usage of fill-in data in specific regions, the model cannot be used for physical interpretations in these regions.

On the Lagrangian description of unsteady boundary-layer separation. I - General theory

NASA Technical Reports Server (NTRS)

Van Dommelen, Leon L.; Cowley, Stephen J.

1990-01-01

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

NASA Technical Reports Server (NTRS)

Vandommelen, Leon L.; Cowley, Stephen J.

1989-01-01

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Impact of occult renal impairment on early and late outcomes following coronary artery bypass grafting

PubMed Central

Marui, Akira; Okabayashi, Hitoshi; Komiya, Tatsuhiko; Tanaka, Shiro; Furukawa, Yutaka; Kita, Toru; Kimura, Takeshi; Sakata, Ryuzo

2013-01-01

OBJECTIVES High serum creatinine is considered an independent risk factor for poor outcomes following coronary artery bypass grafting (CABG). However, the impact of occult renal impairment (ORI), defined as an impaired glomerular filtration rate (GFR) with a normal serum creatinine (SCr) level, remains unclear. Thus, we sought to investigate the impact of ORI on outcomes after CABG. METHODS Among patients undergoing their first percutaneous coronary intervention (PCI) or CABG enrolled in the CREDO-Kyoto Registry (a registry of first-time PCI and CABG patients in Japan), 1842 patients with normal SCr levels undergoing CABG were enrolled in the study. Patients were divided into two groups based on preoperative estimated GFR calculated by the Cockcroft–Gault equation: 1339 patients with estimated GFR of ≥60 ml/min/1.73 m2 (normal group) and 503 with estimated GFR of <60 ml/min/1.73 m2 (ORI group). RESULTS Preoperative estimated GFR differed between the groups (51.3 ± 6.6 vs 85.8 ± 23.0 ml/min/1.73 m2, P < 0.01). ORI was associated with high in-hospital mortality (3.2 vs 1.0%, P < 0.01) and need for dialysis (2.0 vs 0.2%, P < 0.01). In terms of long-term outcomes, ORI was associated with high mortality compared with the normal (hazard ratio [95% confidence interval]: 1.72 [1.16–2.54], P < 0.01) and high incidence of composite cardiovascular events (death, stroke or myocardial infarction: 1.53 [1.16–2.02], P < 0.01). CONCLUSIONS ORI was an independent risk factor for early and late death as well as cardiovascular events in patients undergoing CABG with normal SCr levels. A more accurate evaluation of renal function through a combination of SCr and estimated GFR is needed in patients with normal SCr levels. PMID:23793709

Impact of occult renal impairment on early and late outcomes following coronary artery bypass grafting.

PubMed

Marui, Akira; Okabayashi, Hitoshi; Komiya, Tatsuhiko; Tanaka, Shiro; Furukawa, Yutaka; Kita, Toru; Kimura, Takeshi; Sakata, Ryuzo

2013-10-01

High serum creatinine is considered an independent risk factor for poor outcomes following coronary artery bypass grafting (CABG). However, the impact of occult renal impairment (ORI), defined as an impaired glomerular filtration rate (GFR) with a normal serum creatinine (SCr) level, remains unclear. Thus, we sought to investigate the impact of ORI on outcomes after CABG. Among patients undergoing their first percutaneous coronary intervention (PCI) or CABG enrolled in the CREDO-Kyoto Registry (a registry of first-time PCI and CABG patients in Japan), 1842 patients with normal SCr levels undergoing CABG were enrolled in the study. Patients were divided into two groups based on preoperative estimated GFR calculated by the Cockcroft-Gault equation: 1339 patients with estimated GFR of ≥ 60 ml/min/1.73 m(2) (normal group) and 503 with estimated GFR of <60 ml/min/1.73 m(2) (ORI group). Preoperative estimated GFR differed between the groups (51.3 ± 6.6 vs 85.8 ± 23.0 ml/min/1.73 m(2), P < 0.01). ORI was associated with high in-hospital mortality (3.2 vs 1.0%, P < 0.01) and need for dialysis (2.0 vs 0.2%, P < 0.01). In terms of long-term outcomes, ORI was associated with high mortality compared with the normal (hazard ratio [95% confidence interval]: 1.72 [1.16-2.54], P < 0.01) and high incidence of composite cardiovascular events (death, stroke or myocardial infarction: 1.53 [1.16-2.02], P < 0.01). ORI was an independent risk factor for early and late death as well as cardiovascular events in patients undergoing CABG with normal SCr levels. A more accurate evaluation of renal function through a combination of SCr and estimated GFR is needed in patients with normal SCr levels.

Mathematical analysis of the normal anatomy of the aging fovea.

PubMed

Nesmith, Brooke; Gupta, Akash; Strange, Taylor; Schaal, Yuval; Schaal, Shlomit

2014-08-28

To mathematically analyze anatomical changes that occur in the normal fovea during aging. A total of 2912 spectral-domain optical coherence tomography (SD-OCT) normal foveal scans were analyzed. Subjects were healthy individuals, aged 13 to 97 years, with visual acuity ≥20/40 and without evidence of foveal pathology. Using automated symbolic regression software Eureqa (version 0.98), foveal thickness maps of 390 eyes were analyzed using several measurements: parafoveal retinal thickness at 50 μm consecutive intervals, parafoveal maximum retinal thickness at two points lateral to central foveal depression, distance between two points of maximum retinal thickness, maximal foveal slope at two intervals lateral to central foveal depression, and central length of foveal depression. A unique mathematical equation representing the mathematical analog of foveal anatomy was derived for every decade, between 10 and 100 years. The mathematical regression function for normal fovea followed first order sine curve of level 10 complexity for the second decade of life. The mathematical regression function became more complex with normal aging, up to level 43 complexity (0.085 fit; P < 0.05). Young foveas had higher symmetry (0.92 ± 0.10) along midline, whereas aged foveas had significantly less symmetry (0.76 ± 0.27, P < 0.01) along midline and steeper maximal slopes (29 ± 32°, P < 0.01). Normal foveal anatomical configuration changes with age. Normal aged foveas are less symmetric along midline with steeper slopes. Differentiating between normal aging and pathologic changes using SD-OCT scans may allow early diagnosis, follow-up, and better management of the aging population. Copyright 2014 The Association for Research in Vision and Ophthalmology, Inc.

Channel branching ratios in CH2CN- photodetachment: Rotational structure and vibrational energy redistribution in autodetachment

NASA Astrophysics Data System (ADS)

Lyle, Justin; Wedig, Olivia; Gulania, Sahil; Krylov, Anna I.; Mabbs, Richard

2017-12-01

We report photoelectron spectra of CH2CN-, recorded at photon energies between 13 460 and 15 384 cm-1, which show rapid intensity variations in particular detachment channels. The branching ratios for various spectral features reveal rotational structure associated with autodetachment from an intermediate anion state. Calculations using equation-of-motion coupled-cluster method with single and double excitations reveal the presence of two dipole-bound excited anion states (a singlet and a triplet). The computed oscillator strength for the transition to the singlet dipole-bound state provides an estimate of the autodetachment channel contribution to the total photoelectron yield. Analysis of the different spectral features allows identification of the dipole-bound and neutral vibrational levels involved in the autodetachment processes. For the most part, the autodetachment channels are consistent with the vibrational propensity rule and normal mode expectation. However, examination of the rotational structure shows that autodetachment from the ν3 (v = 1 and v = 2) levels of the dipole-bound state displays behavior counter to the normal mode expectation with the final state vibrational level belonging to a different mode.

Thyroid hormone levels and incident chronic kidney disease in euthyroid individuals: the Kangbuk Samsung Health Study.

PubMed

Zhang, Yiyi; Chang, Yoosoo; Ryu, Seungho; Cho, Juhee; Lee, Won-Young; Rhee, Eun-Jung; Kwon, Min-Jung; Pastor-Barriuso, Roberto; Rampal, Sanjay; Han, Won Kon; Shin, Hocheol; Guallar, Eliseo

2014-10-01

Overt and subclinical hypothyroidism are associated with higher levels of serum creatinine and with increased risk of chronic kidney disease (CKD). The prospective association between thyroid hormones and kidney function in euthyroid individuals,however, is largely unexplored. We conducted a prospective cohort study in 104 633 South Korean men and women who were free of CKD and proteinuria at baseline and had normal thyroid hormone levels and no history of thyroid disease or cancer. At each annual or biennial follow-up visit, thyroid-stimulating hormone (TSH), free triiodothyronine (FT3) and free thyroxin (FT4) levels were measured by radioimmunoassay. The study outcome was incident CKD, defined as an estimated glomerular filtration rate (eGFR)<60 ml/min/1.73 m2 based on the Chronic Kidney Disease Epidemiology Collaboration creatinine equation. After a median follow-up of 3.5 years, 1032 participants developed incident CKD.There was a positive association between high-normal levels of TSH and increased risk of incident CKD. In fully-adjusted models including baseline eGFR, the hazard ratio comparing the highest vs the lowest quintiles of TSH was 1.26 [95% confidence interval (CI) 1.02 to 1.55; P for linear trend=0.03]. In spline models, FT3 levels below 3 pg/ml were also associated with increased risk of incident CKD. There was no association between FT4 levels and CKD. In a large cohort of euthyroid men and women, high levels of TSH and low levels of FT3, even within the normal range, were modestly associated with an increased risk of incident CKD.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

A Maximum Likelihood Approach for Multisample Nonlinear Structural Equation Models with Missing Continuous and Dichotomous Data

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lee, Sik-Yum

2006-01-01

Structural equation models are widely appreciated in social-psychological research and other behavioral research to model relations between latent constructs and manifest variables and to control for measurement error. Most applications of SEMs are based on fully observed continuous normal data and models with a linear structural equation.…

An iterative method for the Helmholtz equation

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1983-01-01

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

Spherically symmetric Einstein-aether perfect fluid models

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

Coley, Alan A.; Latta, Joey; Leon, Genly

We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysicalmore » objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.« less

Polynomial compensation, inversion, and approximation of discrete time linear systems

NASA Technical Reports Server (NTRS)

Baram, Yoram

1987-01-01

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

A geometrically nonlinear theory of elastic plates

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Atilgan, Ali R.; Danielson, D. A.

1992-01-01

A set of kinematic and intrinsic equilibrium equations is derived for plates undergoing large deflection and rotation but with small strain. The large rotation is treated by the general finite rotation of a frame in which the material points that are originally along a normal line in the undeformed plate undergo only small displacements. Exact intrinsic virtual strain-displacement relations are derived; using a reduced 2-D strain energy function from which the warping has been systematically eliminated, a set of intrinsic equilibrium equations follows. It is demonstrated that only five equilibrium equations can be derived in this way, because the component of virtual rotation about the normal is not independent. These equations include terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories.

Colour vision in AIDS patients without HIV retinopathy.

PubMed

Sommerhalder, J; Baglivo, E; Barbey, C; Hirschel, B; Roth, A; Pelizzone, M

1998-11-01

Patients suffering from AIDS develop ocular complications, the most frequent being HIV retinopathy. It is however not clear, if functional visual impairments can be observed as early indicators of ocular complications, before clinical diagnosis of HIV retinopathy is made at fundus examination. To address this issue, we measured colour vision in a group of 49 AIDS subjects with normal clinical fundi using the 'two equation method'. This method, combining red-green Rayleigh and the blue-green Moreland metameric matches, enables more complete and quantitative assessments of colour vision than those based on pigmentary tests. Data were collected on our computer controlled colorimeter and compared to those of normal subjects. While most AIDS subjects without HIV retinopathy demonstrated normal colour vision, a significant portion of them had wider matches than normal subjects (11% for the Rayleigh equation and 16% for the Moreland equation). Furthermore, matching ranges of the Moreland equation were significantly correlated with CD4 lymphocyte counts. Patients with low CD4 values tended to produce larger matching ranges than the patients with high CD4 values. A within subject study on 17 patients confirmed this trend and showed that the patients who increased/decreased their CD4 blood counts generally improved/impaired their colour discrimination in the Moreland match. No such correlation was found between the matching ranges of the Rayleigh equation and the CD4 counts. These results show that colour discrimination is slightly reduced in some AIDS subjects, although there are no detectable ocular complications. They also suggest two different types of colour vision impairments in AIDS patients without retinopathy: one reversible process affecting colour discrimination in the blue-green range; and another irreversible process affecting colour discrimination in the red-green range.

Prognostic assessment of estimated glomerular filtration rate by the new Chronic Kidney Disease Epidemiology Collaboration equation in comparison with the Modification of Diet in Renal Disease Study equation.

PubMed

Skali, Hicham; Uno, Hajime; Levey, Andrew S; Inker, Lesley A; Pfeffer, Marc A; Solomon, Scott D

2011-09-01

Systematic reporting of estimated glomerular filtration rate (eGFR) using the Modification of Diet in Renal Disease (MDRD) Study equation is recommended for detection of chronic kidney disease and prediction of cardiovascular (CV) risk. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation is a newly developed and validated formula for eGFR that is more accurate at normal or near-normal eGFR. We aimed to assess the incremental prognostic accuracy of eGFR(CKD-EPI) versus eGFR(MDRD) in subjects at increased risk for CV disease. We performed a post hoc analysis of the VALIANT trial that enrolled 14,527 patients with acute myocardial infarction with signs and symptoms of heart failure and/or left ventricular systolic dysfunction. The eGFR(MDRD) and eGFR(CKD-EPI) were computed using age, gender, race, and baseline creatinine level. Patients were categorized according to their eGFR using each equation. To assess the incremental prognostic value of eGFR(CKD-EPI), the net reclassification improvement was calculated for the composite end point of CV death, recurrent myocardial infarction, heart failure, or stroke. Twenty-four percent of the subjects were reclassified into a different eGFR category using eGFR(CKD-EPI). The composite end point occurred in 33% of the subjects in this cohort. Based on eGFR(CKD-EPI), subjects reclassified into a higher eGFR experienced fewer events than those reclassified into a lower eGFR (21% vs 43%). In unadjusted analyses, the composite end point risk in subjects with eGFR between 75 and 90 mL/min per 1.73 m(2) was comparable with the referent group (eGFR between 90 and 105) using eGFR(MDRD) (hazard ratio 1.1, 95% CI 0.9-1.2) but was significantly higher using eGFR(CKD-EPI) (hazard ratio 1.2, 95% CI 1.1-1.4). The net reclassification improvement for eGFR(CKD-EPI) over eGFR(MDRD) was 8.7%. The CKD-EPI equation provides more accurate risk stratification than the MDRD Study equation in patients at high risk for CV disease, including identification of increased risk at mildly decreased eGFR. Copyright © 2011 Mosby, Inc. All rights reserved.

SC-GRAPPA: Self-constraint noniterative GRAPPA reconstruction with closed-form solution.

PubMed

Ding, Yu; Xue, Hui; Ahmad, Rizwan; Ting, Samuel T; Simonetti, Orlando P

2012-12-01

Parallel MRI (pMRI) reconstruction techniques are commonly used to reduce scan time by undersampling the k-space data. GRAPPA, a k-space based pMRI technique, is widely used clinically because of its robustness. In GRAPPA, the missing k-space data are estimated by solving a set of linear equations; however, this set of equations does not take advantage of the correlations within the missing k-space data. All k-space data in a neighborhood acquired from a phased-array coil are correlated. The correlation can be estimated easily as a self-constraint condition, and formulated as an extra set of linear equations to improve the performance of GRAPPA. The authors propose a modified k-space based pMRI technique called self-constraint GRAPPA (SC-GRAPPA) which combines the linear equations of GRAPPA with these extra equations to solve for the missing k-space data. Since SC-GRAPPA utilizes a least-squares solution of the linear equations, it has a closed-form solution that does not require an iterative solver. The SC-GRAPPA equation was derived by incorporating GRAPPA as a prior estimate. SC-GRAPPA was tested in a uniform phantom and two normal volunteers. MR real-time cardiac cine images with acceleration rate 5 and 6 were reconstructed using GRAPPA and SC-GRAPPA. SC-GRAPPA showed a significantly lower artifact level, and a greater than 10% overall signal-to-noise ratio (SNR) gain over GRAPPA, with more significant SNR gain observed in low-SNR regions of the images. SC-GRAPPA offers improved pMRI reconstruction, and is expected to benefit clinical imaging applications in the future.

On the existence, uniqueness, and asymptotic normality of a consistent solution of the likelihood equations for nonidentically distributed observations: Applications to missing data problems

NASA Technical Reports Server (NTRS)

Peters, C. (Principal Investigator)

1980-01-01

A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.

An efficient reliable method to estimate the vaporization enthalpy of pure substances according to the normal boiling temperature and critical properties

PubMed Central

Mehmandoust, Babak; Sanjari, Ehsan; Vatani, Mostafa

2013-01-01

The heat of vaporization of a pure substance at its normal boiling temperature is a very important property in many chemical processes. In this work, a new empirical method was developed to predict vaporization enthalpy of pure substances. This equation is a function of normal boiling temperature, critical temperature, and critical pressure. The presented model is simple to use and provides an improvement over the existing equations for 452 pure substances in wide boiling range. The results showed that the proposed correlation is more accurate than the literature methods for pure substances in a wide boiling range (20.3–722 K). PMID:25685493

An efficient reliable method to estimate the vaporization enthalpy of pure substances according to the normal boiling temperature and critical properties.

PubMed

Mehmandoust, Babak; Sanjari, Ehsan; Vatani, Mostafa

2014-03-01

The heat of vaporization of a pure substance at its normal boiling temperature is a very important property in many chemical processes. In this work, a new empirical method was developed to predict vaporization enthalpy of pure substances. This equation is a function of normal boiling temperature, critical temperature, and critical pressure. The presented model is simple to use and provides an improvement over the existing equations for 452 pure substances in wide boiling range. The results showed that the proposed correlation is more accurate than the literature methods for pure substances in a wide boiling range (20.3-722 K).

High-frequency Born synthetic seismograms based on coupled normal modes

USGS Publications Warehouse

Pollitz, F.

2011-01-01

High-frequency and full waveform synthetic seismograms on a 3-D laterally heterogeneous earth model are simulated using the theory of coupled normal modes. The set of coupled integral equations that describe the 3-D response are simplified into a set of uncoupled integral equations by using the Born approximation to calculate scattered wavefields and the pure-path approximation to modulate the phase of incident and scattered wavefields. This depends upon a decomposition of the aspherical structure into smooth and rough components. The uncoupled integral equations are discretized and solved in the frequency domain, and time domain results are obtained by inverse Fourier transform. Examples show the utility of the normal mode approach to synthesize the seismic wavefields resulting from interaction with a combination of rough and smooth structural heterogeneities. This approach is applied to an ~4 Hz shallow crustal wave propagation around the site of the San Andreas Fault Observatory at Depth (SAFOD). ?? The Author Geophysical Journal International ?? 2011 RAS.

Relationship between Burnout and Body Mass Index in Senior and Middle Managers from the Mexican Manufacturing Industry

PubMed Central

2018-01-01

This research relates Burnout Syndrome (BS) with the Body Mass Index (BMI) among middle and senior managers of the Mexican manufacturing industry. Even though BS incidence is high in the Mexican industrial population, few systematic studies have explored BS and its relationship with other health problems, such as obesity. The goal of this research is to determine the relationship between BS and the BMI in employees with normal weight, overweight, and obesity. We present three structural equation models to relate BS and the BMI. The BMI ranges were determined according to the parameters (normal weight, overweight, and obesity) proposed by the World Health Organization (WHO). The sample includes 361 employees that voluntarily answered a 31-item questionnaire. We measure the levels of BS using the Maslach Burnout Inventory–General Survey (MBI-GS) and analyze anthropometric and sociodemographic data from the participants. Then, we determine the relationships between the variables through structural equation models and estimate the direct, indirect, and total effects in the three models, which show acceptable reliability. As main findings, the normal weight model has a larger explanatory power than the overweight and obesity models. The same research hypotheses were tested and the effects of BS on the BMI differ across the three models. Such results are presented by taking into account that obesity and overweight require additional factors, such as genetic factors and personal eating habits, to be better explained. PMID:29562619

Relationship between Burnout and Body Mass Index in Senior and Middle Managers from the Mexican Manufacturing Industry.

PubMed

Armenta-Hernández, Oziely Daniela; Maldonado-Macías, Aidé; García-Alcaraz, Jorge; Avelar-Sosa, Liliana; Realyvasquez-Vargas, Arturo; Serrano-Rosa, Miguel Angel

2018-03-17

This research relates Burnout Syndrome (BS) with the Body Mass Index (BMI) among middle and senior managers of the Mexican manufacturing industry. Even though BS incidence is high in the Mexican industrial population, few systematic studies have explored BS and its relationship with other health problems, such as obesity. The goal of this research is to determine the relationship between BS and the BMI in employees with normal weight, overweight, and obesity. We present three structural equation models to relate BS and the BMI. The BMI ranges were determined according to the parameters (normal weight, overweight, and obesity) proposed by the World Health Organization (WHO). The sample includes 361 employees that voluntarily answered a 31-item questionnaire. We measure the levels of BS using the Maslach Burnout Inventory-General Survey (MBI-GS) and analyze anthropometric and sociodemographic data from the participants. Then, we determine the relationships between the variables through structural equation models and estimate the direct, indirect, and total effects in the three models, which show acceptable reliability. As main findings, the normal weight model has a larger explanatory power than the overweight and obesity models. The same research hypotheses were tested and the effects of BS on the BMI differ across the three models. Such results are presented by taking into account that obesity and overweight require additional factors, such as genetic factors and personal eating habits, to be better explained.

Equation-derived body fat percentage indicates metabolic abnormalities among normal-weight adults in a rural Chinese population.

PubMed

Liu, Xin; Zhao, Yaling; Li, Qiang; Dang, Shaonong; Yan, Hong

2017-07-08

Obesity classification using body mass index (BMI) may miss subjects with elevated body fat percentage (BF%) and related metabolic risk factors. We aimed to evaluate whether BF% calculated by equations could provide more information about metabolic risks, in addition to BMI classification, in a cross-sectional rural Chinese population. A total of 2,990 men and women aged 18-80 years were included in this study. BF% was calculated using previously validated Chinese-specific equations. Metabolic syndrome was defined according to the updated National Cholesterol Education Program Panel III criteria for Asian Americans. In total, 33.6% men and 32.9% women were overweight/obese according to BMI classification. Among those within the normal BMI range, 25.4% men and 54.7% women were indicated as overweight or obese given their elevated BF% (men: BF% ≥ 20%; women: BF% ≥ 30%). In both men and women, compared with those with normal BMI and BF% (NBB), subjects with normal BMI but elevated BF% (NBOB) were more likely to carry abnormal serum lipid profile and to have higher risks of metabolic syndrome. The multivariable adjusted odds ratios (95% confidence intervals) for metabolic syndrome were 5.45 (2.37-9.53, P < 0.001) and 5.65 (3.36-9.52, P < 0.001) for men and women, respectively. Moreover, the women with NBOB also showed higher blood pressure and serum uric acid than women with NBB. Our study suggested that high BF% based on equations may indicate adverse metabolic profiles among rural Chinese adults with a normal BMI. © 2017 Wiley Periodicals, Inc.

Using partially labeled data for normal mixture identification with application to class definition

NASA Technical Reports Server (NTRS)

Shahshahani, Behzad M.; Landgrebe, David A.

1992-01-01

The problem of estimating the parameters of a normal mixture density when, in addition to the unlabeled samples, sets of partially labeled samples are available is addressed. The density of the multidimensional feature space is modeled with a normal mixture. It is assumed that the set of components of the mixture can be partitioned into several classes and that training samples are available from each class. Since for any training sample the class of origin is known but the exact component of origin within the corresponding class is unknown, the training samples as considered to be partially labeled. The EM iterative equations are derived for estimating the parameters of the normal mixture in the presence of partially labeled samples. These equations can be used to combine the supervised and nonsupervised learning processes.

TOPEX/El Nino Watch - Satellite shows El Nino-related Sea Surface Height, Mar, 14, 1998

NASA Technical Reports Server (NTRS)

1998-01-01

This image of the Pacific Ocean was produced using sea surface height measurements taken by the U.S.-French TOPEX/Poseidon satellite. The image shows sea surface height relative to normal ocean conditions on Mar. 14, 1998 and sea surface height is an indicator of the heat content of the ocean. The image shows that the sea surface height along the central equatorial Pacific has returned to a near normal state. Oceanographers indicate this is a classic pattern, typical of a mature El Nino condition. Remnants of the El Nino warm water pool, shown in red and white, are situated to the north and south of the equator. These sea surface height measurements have provided scientists with a detailed view of how the 1997-98 El Nino's warm pool behaves because the TOPEX/Poseidon satellite measures the changing sea surface height with unprecedented precision. In this image, the white and red areas indicate unusual patterns of heat storage; in the white areas, the sea surface is between 14 and 32 centimeters (6 to 13 inches) above normal; in the red areas, it's about 10 centimeters (4 inches) above normal. The green areas indicate normal conditions, while purple (the western Pacific) means at least 18 centimeters (7 inches) below normal sea level. The El Nino phenomenon is thought to be triggered when the steady westward blowing trade winds weaken and even reverse direction. This change in the winds allows a large mass of warm water (the red and white area) that is normally located near Australia to move eastward along the equator until it reaches the coast of South America. The displacement of so much warm water affects evaporation, where rain clouds form and, consequently, alters the typical atmospheric jet stream patterns around the world. Using satellite imagery, buoy and ship data, and a forecasting model of the ocean-atmosphere system, the National Oceanic and Atmospheric Administration, (NOAA), has continued to issue an advisory indicating the so-called El Nino weather conditions that have impacted much of the United States and the world are expected to remain through the spring.

USAF Bioenvironmental Noise Data Handbook. Volume 155. CH-3 in-flight crew noise

NASA Astrophysics Data System (ADS)

Hille, H. K.

1982-09-01

The CH-3 is a USAF tactical combat transport helicopter. This report provides measured data defining the bioacoustic environments at flight crew/passenger locations inside this helicopter during normal flight operations. Data are reported for nine locations in a wide variety of physical and psychoacoustic measures: overall and band sound pressure levels, C weighted and A weighted sound levels, preferred speech interference level, perceived noise levels and limiting times for total daily exposure of personnel with and without standard Air Force ear protectors. Refer to Volume 1 of this handbook, USAF Bioenvironmental Noise Data handbook, Vol. 1: Organization, Content and Application, AMRL-TR-75-50(1) 1975, for discussion of the objective and design of the handbook, the types of data presented, measurement procedures, instrumentation, data processing, definitions of quantities, symbols, equations, applications, limitations, etc.

USAF Environmental Noise Data Handbook. Volume 150: C-140 in-flight crew noise

NASA Astrophysics Data System (ADS)

Hille, H. K.

1982-09-01

The C-140 is a USAF transport aircraft used for operational support. This report provides measured data defining the bioacoustic environments at flight crew/passenger locations inside this aircraft during normal flight operations. Date are reported for seven locations in a wide variety of physical and psychoacoustic measures: overall and band sound pressure levels, C-weighted and A-weighted sound levels, preferred speech interference level, perceived noise level, and limiting times for total daily exposure of personnel with and without standard Air Force ear protectors. Refer to Volume 1 of this handbook, USAF Bioenvironmental Noise Data Handbook, Vol. 1: Organization, Content and Application, AMRL-TR-75-50(1) 1975, for discussion of the objective and design of the handbook, the types of data presented, measurement procedures, instrumentation, data processing, definitions of quantities, symbols, equations, applications, limitations, etc.

Compressible Flow Toolbox

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

The Compressible Flow Toolbox is primarily a MATLAB-language implementation of a set of algorithms that solve approximately 280 linear and nonlinear classical equations for compressible flow. The toolbox is useful for analysis of one-dimensional steady flow with either constant entropy, friction, heat transfer, or Mach number greater than 1. The toolbox also contains algorithms for comparing and validating the equation-solving algorithms against solutions previously published in open literature. The classical equations solved by the Compressible Flow Toolbox are as follows: The isentropic-flow equations, The Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), The Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section), The normal-shock equations, The oblique-shock equations, and The expansion equations.

Insulin resistance and serum levels of interleukin-17 and interleukin-18 in normal pregnancy.

PubMed

Jahromi, Abdolreza Sotoodeh; Shojaei, Mohammad; Ghobadifar, Mohamed Amin

2014-06-01

We performed this study to evaluate the role of Interleukin-17 (IL-17) and Interleukin-18 (IL-18) in insulin resistance during normal pregnancy. This descriptive cross sectional study was carried out on 97 healthy pregnant women including 32, 25, and 40 individuals in the first, second, and third trimesters, respectively, and on 28 healthy non pregnant women between the autumn of 2012 and the spring of 2013. We analyzed the serum concentrations of IL-17 and IL-18 by using the enzyme linked immunosorbent assay (ELISA). Insulin resistance was measured by homeostasis model assessment of insulin resistance equation. No significant differences between the demographic data of the pregnant and non pregnant groups were observed. Insulin resistant in pregnant women was significantly higher than the controls (p=0.006). Serum IL-17 concentration was significantly different in non pregnant women and pregnant women in all gestational ages (p<0.05). Serum IL-18 level was significantly lower in subjects with first, second, and third trimesters of pregnancy in compared to non pregnant women (p<0.05). No significant correlations were found between serum IL-17 and IL-18 levels with insulin resistance (r=0.08, p=0.34 vs. r=0.01, p=0.91, respectively). Our data suggested that IL-17 and IL-18 do not appear to attribute greatly to pregnancy deduced insulin resistance during normal pregnancy.

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses.

PubMed

Guo, Xiao; Wei, Peijun

2016-03-01

The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results. Copyright © 2015 Elsevier B.V. All rights reserved.

A model for hormonal control of the menstrual cycle: structural consistency but sensitivity with regard to data.

PubMed

Selgrade, J F; Harris, L A; Pasteur, R D

2009-10-21

This study presents a 13-dimensional system of delayed differential equations which predicts serum concentrations of five hormones important for regulation of the menstrual cycle. Parameters for the system are fit to two different data sets for normally cycling women. For these best fit parameter sets, model simulations agree well with the two different data sets but one model also has an abnormal stable periodic solution, which may represent polycystic ovarian syndrome. This abnormal cycle occurs for the model in which the normal cycle has estradiol levels at the high end of the normal range. Differences in model behavior are explained by studying hysteresis curves in bifurcation diagrams with respect to sensitive model parameters. For instance, one sensitive parameter is indicative of the estradiol concentration that promotes pituitary synthesis of a large amount of luteinizing hormone, which is required for ovulation. Also, it is observed that models with greater early follicular growth rates may have a greater risk of cycling abnormally.

Generalized Langevin equation with tempered memory kernel

NASA Astrophysics Data System (ADS)

Liemert, André; Sandev, Trifce; Kantz, Holger

2017-01-01

We study a generalized Langevin equation for a free particle in presence of a truncated power-law and Mittag-Leffler memory kernel. It is shown that in presence of truncation, the particle from subdiffusive behavior in the short time limit, turns to normal diffusion in the long time limit. The case of harmonic oscillator is considered as well, and the relaxation functions and the normalized displacement correlation function are represented in an exact form. By considering external time-dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement. Additionally, the double-peak phenomenon in the imaginary part of the complex susceptibility is observed. It is obtained that the truncation parameter has a huge influence on the behavior of these quantities, and it is shown how the truncation parameter changes the critical frequencies. The normalized displacement correlation function for a fractional generalized Langevin equation is investigated as well. All the results are exact and given in terms of the three parameter Mittag-Leffler function and the Prabhakar generalized integral operator, which in the kernel contains a three parameter Mittag-Leffler function. Such kind of truncated Langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes.

Interhemispheric Propagation and Interactions of Auroral LSTIDs near the Equator

NASA Astrophysics Data System (ADS)

Pradipta, R.; Valladares, C.; Carter, B. A.; Doherty, P.

2016-12-01

In this work, we used experimental observations based on GPS total electron content (TEC) and ionosonde measurements to study some of the physics behind large-scale traveling ionospheric disturbances (LSTIDs) during the 26 September 2011 geomagnetic storm. In particular, we looked at how these LSTIDs propagate from the auroral zones all the way to the equatorial region and examined how the auroral LSTIDs from opposite hemispheres interact/interfere near the geomagnetic equator. We found that these LSTIDs had an overall propagation speed of ˜700 m/s. Furthermore, the resultant amplitude of the LSTID interference pattern was found to far exceed the sum of individual amplitudes of the incoming LSTIDs. We suspect that this peculiar intensification of auroral LSTIDs around the geomagnetic equator is facilitated by the significantly higher ceiling/canopy of the ionospheric plasma layer there. Normally, acoustic-gravity waves (AGWs) that leak upward (and thus increase in amplitude) would find a negligible level of plasma density at the topside ionosphere. However, the tip of the equatorial fountain at the geomagnetic equator constitutes a significant amount of plasma at a topside-equivalent altitude. The combination of increased AGW amplitudes and a higher plasma density at such altitude would therefore result in higher-amplitude LSTIDs in this particular region, as demonstrated in our observations and analysis.

Three dimensional steady subsonic Euler flows in bounded nozzles

NASA Astrophysics Data System (ADS)

Chen, Chao; Xie, Chunjing

The existence and uniqueness of three dimensional steady subsonic Euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the entrance are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal component of the momentum approaches the critical number, the associated flows converge to a subsonic-sonic flow. Furthermore, when the normal component of vorticity and the variation of Bernoulli function are both small, the existence and uniqueness of subsonic Euler flows with non-zero vorticity are established. The proof of these results is based on a new formulation for the Euler system, a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions, detailed study for a linear div-curl system, and delicate estimate for the transport equations.

Comparisons of Backscattering from Cylindrical Shells Described by Thin Shell and Elasticity Theories.

DTIC Science & Technology

1991-03-04

term that describes inextensional motion. The first equation represents the normal stress at the midsurface of the shell, which is equal to the...that the normal velocity at the midsurface of the shell is proportional to the normal derivative of the total pressw e. The scattered pressure ps can

3j Symbols: To Normalize or Not to Normalize?

ERIC Educational Resources Information Center

van Veenendaal, Michel

2011-01-01

The systematic use of alternative normalization constants for 3j symbols can lead to a more natural expression of quantities, such as vector products and spherical tensor operators. The redefined coupling constants directly equate tensor products to the inner and outer products without any additional square roots. The approach is extended to…

Bicarbonate can improve the prognostic value of the MELD score for critically ill patients with cirrhosis.

PubMed

Chen, Cheng-Yi; Pan, Chi-Feng; Wu, Chih-Jen; Chen, Han-Hsiang; Chen, Yu-Wei

2014-07-01

The prognosis of critically ill patients with cirrhosis is poor. Our aim was to identify an objective variable that can improve the prognostic value of the Model of End-Stage Liver Disease (MELD) score in patients who have cirrhosis and are admitted to the intensive care unit (ICU). This retrospective cohort study included 177 patients who had liver cirrhosis and were admitted to the ICU. Data pertaining to arterial blood gas-related parameters and other variables were obtained on the day of ICU admission. The overall ICU mortality rate was 36.2%. The bicarbonate (HCO3) level was found to be an independent predictor of ICU mortality (odds ratio, 2.3; 95% confidence interval [CI], 1.0-4.8; p = 0.038). A new equation was constructed (MELD-Bicarbonate) by replacing total bilirubin by HCO3 in the original MELD score. The area under the receiver operating characteristic curve for predicting ICU mortality was 0.76 (95% CI, 0.69-0.84) for the MELD-Bicarbonate equation, 0.73 (95% CI, 0.65-0.81) for the MELD score, and 0.71 (95% CI, 0.63-0.80) for the Acute Physiology and Chronic Health Evaluation II score. Bicarbonate level assessment, as an objective and reproducible laboratory test, has significant predictive value in critically ill patients with cirrhosis. In contrast, the predictive value of total bilirubin is not as prominent in this setting. The MELD-Bicarbonate equation, which included three variables (international normalized ratio, creatinine level, and HCO3 level), showed better prognostic value than the original MELD score in critically ill patients with cirrhosis.

Subthreshold resonances and resonances in the R -matrix method for binary reactions and in the Trojan horse method

NASA Astrophysics Data System (ADS)

Mukhamedzhanov, A. M.; Shubhchintak, Bertulani, C. A.

2017-08-01

In this paper we discuss the R -matrix approach to treat the subthreshold resonances for the single-level and one-channel and for the single-level and two-channel cases. In particular, the expression relating the asymptotic normalization coefficient (ANC) with the observable reduced width, when the subthreshold bound state is the only channel or coupled with an open channel, which is a resonance, is formulated. Since the ANC plays a very important role in nuclear astrophysics, these relations significantly enhance the power of the derived equations. We present the relationship between the resonance width and the ANC for the general case and consider two limiting cases: wide and narrow resonances. Different equations for the astrophysical S factors in the R -matrix approach are presented. After that we discuss the Trojan horse method (THM) formalism. The developed equations are obtained using the surface-integral formalism and the generalized R -matrix approach for the three-body resonant reactions. It is shown how the Trojan horse (TH) double-differential cross section can be expressed in terms of the on-the-energy-shell astrophysical S factor for the binary subreaction. Finally, we demonstrate how the THM can be used to calculate the astrophysical S factor for the neutron generator 13C(α ,n )16O in low-mass AGB stars. At astrophysically relevant energies this astrophysical S factor is controlled by the threshold level 1 /2+,Ex=6356 keV. Here, we reanalyzed recent TH data taking into account more accurately the three-body effects and using both assumptions that the threshold level is a subthreshold bound state or it is a resonance state.

Novel equations to estimate lean body mass in maintenance hemodialysis patients.

PubMed

Noori, Nazanin; Kovesdy, Csaba P; Bross, Rachelle; Lee, Martin; Oreopoulos, Antigone; Benner, Deborah; Mehrotra, Rajnish; Kopple, Joel D; Kalantar-Zadeh, Kamyar

2011-01-01

Lean body mass (LBM) is an important nutritional measure representing muscle mass and somatic protein in hemodialysis patients, for whom we developed and tested equations to estimate LBM. A study of diagnostic test accuracy. The development cohort included 118 hemodialysis patients with LBM measured using dual-energy x-ray absorptiometry (DEXA) and near-infrared (NIR) interactance. The validation cohort included 612 additional hemodialysis patients with LBM measured using a portable NIR interactance technique during hemodialysis. 3-month averaged serum concentrations of creatinine, albumin, and prealbumin; normalized protein nitrogen appearance; midarm muscle circumference (MAMC); handgrip strength; and subjective global assessment of nutrition. LBM measured using DEXA in the development cohort and NIR interactance in validation cohorts. In the development cohort, DEXA and NIR interactance correlated strongly (r = 0.94, P < 0.001). DEXA-measured LBM correlated with serum creatinine level, MAMC, and handgrip strength, but not with other nutritional markers. Three regression equations to estimate DEXA-measured LBM were developed based on each of these 3 surrogates and sex, height, weight, and age (and urea reduction ratio for the serum creatinine regression). In the validation cohort, the validity of the equations was tested against the NIR interactance-measured LBM. The equation estimates correlated well with NIR interactance-measured LBM (R² ≥ 0.88), although in higher LBM ranges, they tended to underestimate it. Median (95% confidence interval) differences and interquartile range for differences between equation estimates and NIR interactance-measured LBM were 3.4 (-3.2 to 12.0) and 3.0 (1.1-5.1) kg for serum creatinine and 4.0 (-2.6 to 13.6) and 3.7 (1.3-6.0) kg for MAMC, respectively. DEXA measurements were obtained on a nondialysis day, whereas NIR interactance was performed during hemodialysis treatment, with the likelihood of confounding by volume status variations. Compared with reference measures of LBM, equations using serum creatinine level, MAMC, or handgrip strength and demographic variables can estimate LBM accurately in long-term hemodialysis patients. Copyright © 2010 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.

Cystatin C a marker for renal function after exercise.

PubMed

Mingels, A; Jacobs, L; Kleijnen, V; Wodzig, W; Dieijen-Visser, M van

2009-09-01

Renal impairment is common during and after severe exercise. In clinical practice, renal function is evaluated using serum creatinine, urine parameters, and equations to estimate the Glomular Filtration Rate (GFR). However, creatinine levels may be biased by skeletal muscle damage and the GFR equations, requiring age, gender and body weight, are shown to be inadequate in normals. In the present study, we show that serum cystatin C and creatinine concentrations were elevated after marathon running in 26% and 46% of the 70 recreational male runners, respectively, possibly because of reduction in renal blood flow. The mean cystatin C increase was twice as low as compared to creatinine (21% and 41%, respectively), suggesting that cystatin C is indeed less biased by muscle damage. Future research has to reveal whether training diminishes the elevation in renal markers. Overall, cystatin C seems a more reliable method to establish renal function during and after extensive exercise. Georg Thieme Verlag KG Stuttgart.

Operational calibration of Geostationary Operational Environmental Satellite-8 and-9 imagers and sounders.

PubMed

Weinreb, M; Jamieson, M; Fulton, N; Chen, Y; Johnson, J X; Bremer, J; Smith, C; Baucom, J

1997-09-20

We describe the operational in-orbit calibration of the Geostationary Operational Environmental Satellite (GOES)-8 and-9 imagers and sounders. In the infrared channels the calibration is based on observations of space and an onboard blackbody. The calibration equation expresses radiance as a quadratic in instrument output. To suppress noise in the blackbody sequences, we filter the calibration slopes. The calibration equation also accounts for an unwanted variation of the reflectances of the instruments' scan mirrors with east-west scan position, which was not discovered until the instruments were in orbit. The visible channels are not calibrated, but the observations are provided relative to the level of space and are normalized to minimize east-west striping in the images. Users receive scaled radiances in a GOES variable format (GVAR) data stream. We describe the procedure users can apply to transform GVAR counts into radiances, temperatures, and mode-A counts.

A general low frequency acoustic radiation capability for NASTRAN

NASA Technical Reports Server (NTRS)

Everstine, G. C.; Henderson, F. M.; Schroeder, E. A.; Lipman, R. R.

1986-01-01

A new capability called NASHUA is described for calculating the radiated acoustic sound pressure field exterior to a harmonically-excited arbitrary submerged 3-D elastic structure. The surface fluid pressures and velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior fluid. After the fluid impedance is calculated, most of the required matrix operations are performed using the general matrix manipulation package (DMAP) available in NASTRAN. Far field radiated pressures are then calculated from the surface solution using the Helmholtz exterior integral equation. Other output quantities include the maximum sound pressure levels in each of the three coordinate planes, the rms and average surface pressures and normal velocities, the total radiated power and the radiation efficiency. The overall approach is illustrated and validated using known analytic solutions for submerged spherical shells subjected to both uniform and nonuniform applied loads.

Fast Legendre moment computation for template matching

NASA Astrophysics Data System (ADS)

Li, Bing C.

2017-05-01

Normalized cross correlation (NCC) based template matching is insensitive to intensity changes and it has many applications in image processing, object detection, video tracking and pattern recognition. However, normalized cross correlation implementation is computationally expensive since it involves both correlation computation and normalization implementation. In this paper, we propose Legendre moment approach for fast normalized cross correlation implementation and show that the computational cost of this proposed approach is independent of template mask sizes which is significantly faster than traditional mask size dependent approaches, especially for large mask templates. Legendre polynomials have been widely used in solving Laplace equation in electrodynamics in spherical coordinate systems, and solving Schrodinger equation in quantum mechanics. In this paper, we extend Legendre polynomials from physics to computer vision and pattern recognition fields, and demonstrate that Legendre polynomials can help to reduce the computational cost of NCC based template matching significantly.

Evaluation of bridge-scour data at selected sites in Ohio

USGS Publications Warehouse

Jackson, K.S.

1997-01-01

Scour data collected during 1989-94 were evaluated to determine whether pier scour and contraction scour occurred at 22 bridge sites in Ohio. Pier-scour depths computed from selected pier-scour prediction equations were compared with measured pier-scour depths, and the accuracy of the prediction equations were evaluated. Observed pier-scour relations were compared to relations developed through laboratory research. Mean streambed elevations were evaluated to determine the depth of contraction scour. Channel stability was assessed by use of mean streambed elevations at the approach section. Ground-penetrating radar was used at all sites to investigate the presence of historical scour. Pier scour was observed in 45 of 47 scour measurements made during floods; 84 cases of pier scour were documented, 83 at solid-wall piers and 1 at a capped-pile type pier. Estimated recurrence intervals for 27 of the 35 measured streamflows, all on unregulated streams, were less than 2 years. Seventeen pier-scour prediction equations were evaluated. The Froehlich Design equation was found to most closely meet the 'best design equation' criteria for all 84 cases of the observed data. The Larras equation was found to be the best design equation for the observed data where approach-flow attack angles were 10 degrees or less. Observed pier-scour depths and flow depths ranged from 0.5 to 6.1 feet and 3.0 to 19.8 feet, respectively. All pier-scour depths were less than 2.4 times the corresponding pier width. Selected factors were normalized by dividing by effective pier width. LOWESS curves were developed using the 84 cases of observed pier scour. Normalized scour depth increased with normalized flow depth; however, the rate of increase appeared to lessen as normalized flow depth exceeded 2.5. Normalized scour depths increased rapidly as flow intensity approached the threshold value of 1 and then decreased as flow intensities exceeded this threshold. Normalized scour depth was found to increase with Froude number, and a steeper slope was evident for Froude numbers exceeding 0.2. Normalized scour depth was found to increase with median grain size up to about 10 millimeters for bed material near the pier, then decrease for median grain sizes greater than 10 millimeters. Normalized scour depth was also found to decrease as sediment gradation of bed material near the pier increased. The observed pier-scour relations determined from the field measurements tend to support conclusions by previous researchers of streambed scour, except for the previous finding that normalized scour depth decreases consistently with increasing median grain size. Possible factors that may have influenced the observed trends in the relation between normalized scour depth and median grain size in this study are cohesion and scour measurements made at nonequilibrium conditions. LOWESS curves were developed for 45 of 84 cases of observed pier scour where approach-flow attack angles were less than or equal to 10 degrees. These curves were visually compared to LOWESS curves developed from all observations of pier scour. For three relations, differences in the trends of the LOWESS curves were of sufficient magnitude to warrant discussion. Contraction scour was observed in 4 of the 47 scour measurements and ranged from 0.8 to2.3 feet in depth. Analysis of annual mean streambed approach-section elevations indicated that approach sections were generally stable at 18 of the 22 sites. Ground-penetrating radar, a geophysical method that enables subsurface exploration of the streambed when conditions are favorable, was used at all sites to determine whether historical scour had occurred. Results of the ground-penetrating radar surveys at 20 sites in 1990 indicated the presence of historical scour surfaces at 5 sites. At four of the five sites showing evidence of possible historical scour, differences between the estimated depth of historical scour and the maximum observed scour were w

Decreased GFR estimated by MDRD or Cockcroft-Gault equation predicts incident CVD: the strong heart study.

PubMed

Shara, Nawar M; Resnick, Helaine E; Lu, Li; Xu, Jiaqiong; Vupputuri, Suma; Howard, Barbara V; Umans, Jason G

2009-01-01

Kidney function, expressed as glomerular filtration rate (GFR), is commonly estimated from serum creatinine (Scr) and, when decreased, may serve as a nonclassical risk factor for incident cardiovascular disease (CVD). The ability of estimated GFR (eGFR) to predict CVD events during 5-10 years of follow-up is assessed using data from the Strong Heart Study (SHS), a large cohort with a high prevalence of diabetes. eGFRs were calculated with the abbreviated Modification of Diet in Renal Disease study (MDRD) and the Cockcroft-Gault (CG) equations. These estimates were compared in participants with normal and abnormal Scr. The association between eGFR and incident CVD was assessed. More subjects were labeled as having low eGFR (<60 ml/min per 1.73 m2) by the MDRD or CG equation, than by Scr alone. When Scr was in the normal range, both equations labeled similar numbers of participants as having low eGFRs, although concordance between the equations was poor. However, when Scr was elevated, the MDRD equation labeled more subjects as having low eGFR. Persons with low eGFR had increased risk of CVD. The MDRD and CG equations labeled more participants as having decreased GFR than did Scr alone. Decreased eGFR was predictive of CVD in this American Indian population with a high prevalence of obesity and type 2 diabetes mellitus.

Numerical investigation of internal high-speed viscous flows using a parabolic technique

NASA Technical Reports Server (NTRS)

Anderson, O. L.; Power, G. D.

1985-01-01

A feasibility study has been conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves are present. A set of test problems with weak shock and expansion waves have been analyzed with this modified ADD method and stable and accurate solutions were demonstrated provided the streamwise step size was maintained at levels larger than the boundary layer displacement thickness. Calculations made with further reductions in step size encountered departure solutions consistent with strong interaction theory. Calculations were also performed for a flow field with a flame front in which a specific heat release was imposed to simulate a SCRAMJET combustor. In this case the flame front generated relatively thick shear layers which aggravated the departure solution problem. Qualitatively correct results were obtained for these cases using a marching technique with the convective terms in the normal momentum equation suppressed. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

Evaluation of Delamination Onset and Growth Characterization Methods under Mode I Fatigue Loading

NASA Technical Reports Server (NTRS)

Murri, Gretchen B.

2013-01-01

Double-cantilevered beam specimens of IM7/8552 graphite/epoxy from two different manufacturers were tested in static and fatigue to compare the material characterization data and to evaluate a proposed ASTM standard for generating Paris Law equations for delamination growth. Static results were used to generate compliance calibration constants for reducing the fatigue data, and a delamination resistance curve, GIR, for each material. Specimens were tested in fatigue at different initial cyclic GImax levels to determine a delamination onset curve and the delamination growth rate. The delamination onset curve equations were similar for the two sources. Delamination growth rate was calculated by plotting da/dN versus GImax on a log-log scale and fitting a Paris Law. Two different data reduction methods were used to calculate da/dN. To determine the effects of fiber-bridging, growth results were normalized by the delamination resistance curves. Paris Law exponents decreased by 31% to 37% after normalizing the data. Visual data records from the fatigue tests were used to calculate individual compliance constants from the fatigue data. The resulting da/dN versus GImax plots showed improved repeatability for each source, compared to using averaged static data. The Paris Law expressions for the two sources showed the closest agreement using the individually fit compliance data.

Sex-based comparison of limb segmentation in ostriches aged 14 months with and without tibiotarsal rotation.

PubMed

Cooper, R G; Naranowicz, H; Maliszewska, E; Tennett, A; Horbańczuk, J O

2008-09-01

The aim of this study was to propose equations to predict changes that occur over time in the angular position of the bones during motion and the angular velocity of the bones in forward motion as a consequence of tibiotarsal rotation (TTR) in ostriches aged 14 months. Twenty-four normal 14-month-old ostriches (12 cocks and 12 hens) and 20 birds with TTR (9 cocks and 11 hens) were used in the study. Daily readings of temperature, relative humidity and rainfall, the lengths of the different segments of the legs and wings, the perpendicular height from the top of the torso to ground level and the length of the erect neck were recorded. Measurements of the degree of valgus deformity in the left foot were made where applicable. TTR hens and cocks were smaller in stature than normal birds. Comparing TTR hens and cocks, the toe, claw, humerus, perpendicular height and angle of rotation were larger in cocks, indicating a larger body in cocks. Hens were more severely affected by TTR. We suggest that the equations used in this study will assist in measuring movement of ostriches and how movement is compromised by overcrowding and TTR. Birds suffering from TTR may experience an increased degree of stress due to movement restrictions in confinement.

Estimation of total body water from bioelectrical impedance spectroscopy in oncology outpatients receiving radiotherapy and agreement with three prediction equations.

PubMed

Isenring, E; Colombo, M; Cross, G; Kellett, E; Swaney, L

2009-02-01

Bioelectrical impedance spectroscopy (BIS) may be more accurate in determining total body water (TBW) than bioelectrical impedance analysis (BIA). The present study compared the agreement between three TBW prediction equations developed using BIA and BIS-derived TBW in oncology outpatients. A cross-sectional, observational study was conducted in 37 outpatients receiving radiotherapy (27 males/10 females, aged 68.3 +/- 10.2 years). TBW was estimated by BIS (TBW(BIS)) and three BIA TBW prediction equations (TBW(ca-u): underweight cancer patients; TBW(ca-n): normal-weight cancer patients; and TBW(rad): patients receiving radiotherapy). Bland-Altman analyses determined agreement between methods. BIS-derived TBW using new resistivity constants was calculated. The mean +/- SD of TBW estimated by BIS was 39.8 +/- 8.3 L, which was significantly different from the prediction equations; TBW(rad) 35.1 +/- 7.9 L, TBW(ca-u) 33.1 +/- 7.5 L and TBW(ca-n) 32.3 +/- 7.3 L, (P < 0.001). Using new resistivity constants, TBW was 36.2 +/- 8.1 L but this still differed from the equations (P < 0.001). Bias between TBW(BIS) and that predicted by the equations was in the range 4.7-7.4 L or 1.1-3.9 L using new resistivity constants. TBW estimated by BIS cannot be directly compared with oncology-specific BIA equations, suggesting that BIS cannot be used at the group level in outpatients receiving radiotherapy. There was a reduced bias with BIS using new resistivity constants; however, further research should determine any advantage of BIS over BIA in this population.

Solution of the Burnett equations for hypersonic flows near the continuum limit

NASA Technical Reports Server (NTRS)

Imlay, Scott T.

1992-01-01

The INCA code, a three-dimensional Navier-Stokes code for analysis of hypersonic flowfields, was modified to analyze the lower reaches of the continuum transition regime, where the Navier-Stokes equations become inaccurate and Monte Carlo methods become too computationally expensive. The two-dimensional Burnett equations and the three-dimensional rotational energy transport equation were added to the code and one- and two-dimensional calculations were performed. For the structure of normal shock waves, the Burnett equations give consistently better results than Navier-Stokes equations and compare reasonably well with Monte Carlo methods. For two-dimensional flow of Nitrogen past a circular cylinder the Burnett equations predict the total drag reasonably well. Care must be taken, however, not to exceed the range of validity of the Burnett equations.

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

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

2006-06-01

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

GINGA observations of Cygnus X-2.

NASA Astrophysics Data System (ADS)

Wijnands, R. A. D.; van der Klis, M.; Kuulkers, E.; Asai, K.; Hasinger, G.

1997-07-01

We have analysed all available X-ray data on the low-mass X-ray binary Cygnus X-2 obtained with the Ginga satellite. A detailed analysis of the spectral and fast timing behaviour of these 4 years of data provides new insights in the behaviour of this Z source. We confirm the previously observed recurrent patterns of behaviour in the X-ray colour-colour and hardness-intensity diagrams consisting of shifts and shape changes in the Z track. However, we find a continuous range of patterns rather than a discrete set. The source behaviour in the diagrams is correlated with overall intensity, which varied by a factor of 1.34 in the Ginga data. We find that when the overall intensity increases, the mean velocity and acceleration of the motion along the normal branch of the Z track increase, as well as the width of the normal branch in the hardness-intensity diagram. Contrary to previous results we find that, during different observations, when the source is at the same position in the normal branch of the Z track the rapid X-ray variability differs significantly. During the Kuulkers et al. (1996A&A...311..197K) ``medium'' level, a normal branch quasi-periodic oscillation is detected, which is not seen during the ``high'' overall intensity level. Also, during the high overall intensity level episodes the very-low frequency noise on the lower normal branch is very strong and steep, whereas during the medium overall intensity level episodes this noise component at the same position in the Z track is weak and less steep. The explanation of the different overall intensity levels with a precessing accretion disk is difficult to reconcile with our data. Furthermore, we found that the frequency of the horizontal branch quasi-periodic oscillation decreases when Cygnus X-2 enters the upper normal branch, giving a model dependent upper limit on the magnetic field strength at the magnetic equator of ~8.5x10^9^G. We also report five bursts, with durations between two and eight seconds, whose occurrence seems to be uncorrelated with location in the Z track, overall intensity level or orbital phase. The burst properties indicate that they are not regular type I bursts.

A coordinate free description of magnetohydrostatic equilibria

NASA Technical Reports Server (NTRS)

Martens, P. C. H.

1986-01-01

The question what geometrical restrictions are imposed on static magnetic fields by the magnetohydrostatic (MHS) equation is addressed. The general mathematical problem is therefore to determine the solutions of the MHS equations in the corona subject to an arbitrary normal component of the magnetic field at the boundary and arbitrary connectivity. What constraints the MHS equations impose on the geometry of the solutions, expressed in metric tensors, will be determined.

Serum Creatinine: Not So Simple!

PubMed

Delanaye, Pierre; Cavalier, Etienne; Pottel, Hans

2017-01-01

Measuring serum creatinine is cheap and commonly done in daily practice. However, interpretation of serum creatinine results is not always easy. In this review, we will briefly remind the physiological limitations of serum creatinine due notably to its tubular secretion and the influence of muscular mass or protein intake on its concentration. We mainly focus on the analytical limitations of serum creatinine, insisting on important concept such as reference intervals, standardization (and IDMS traceability), analytical interferences, analytical coefficient of variation (CV), biological CV and critical difference. Because the relationship between serum creatinine and glomerular filtration rate is hyperbolic, all these CVs will impact not only the precision of serum creatinine but still more the precision of different creatinine-based equations, especially in low or normal-low creatinine levels (or high or normal-high glomerular filtration rate range). © 2017 S. Karger AG, Basel.

Renormalized vibrations and normal energy transport in 1d FPU-like discrete nonlinear Schrödinger equations.

PubMed

Li, Simeng; Li, Nianbei

2018-03-28

For one-dimensional (1d) nonlinear atomic lattices, the models with on-site nonlinearities such as the Frenkel-Kontorova (FK) and ϕ 4 lattices have normal energy transport while the models with inter-site nonlinearities such as the Fermi-Pasta-Ulam-β (FPU-β) lattice exhibit anomalous energy transport. The 1d Discrete Nonlinear Schrödinger (DNLS) equations with on-site nonlinearities has been previously studied and normal energy transport has also been found. Here, we investigate the energy transport of 1d FPU-like DNLS equations with inter-site nonlinearities. Extended from the FPU-β lattice, the renormalized vibration theory is developed for the FPU-like DNLS models and the predicted renormalized vibrations are verified by direct numerical simulations same as the FPU-β lattice. However, the energy diffusion processes are explored and normal energy transport is observed for the 1d FPU-like DNLS models, which is different from their atomic lattice counterpart of FPU-β lattice. The reason might be that, unlike nonlinear atomic lattices where models with on-site nonlinearities have one less conserved quantities than the models with inter-site nonlinearities, the DNLS models with on-site or inter-site nonlinearities have the same number of conserved quantities as the result of gauge transformation.

Computerized method for automatic evaluation of lean body mass from PET/CT: comparison with predictive equations.

PubMed

Chan, Tao

2012-01-01

CT has become an established method for calculating body composition, but it requires data from the whole body, which are not typically obtained in routine PET/CT examinations. A computerized scheme that evaluates whole-body lean body mass (LBM) based on CT data from limited-whole-body coverage was developed. The LBM so obtained was compared with results from conventional predictive equations. LBM can be obtained automatically from limited-whole-body CT data by 3 means: quantification of body composition from CT images in the limited-whole-body scan, based on thresholding of CT attenuation; determination of the range of coverage based on a characteristic trend of changing composition across different levels and pattern recognition of specific features at strategic positions; and estimation of the LBM of the whole body on the basis of a predetermined relationship between proportion of fat mass and extent of coverage. This scheme was validated using 18 whole-body PET/CT examinations truncated at different lengths to emulate limited-whole-body data. LBM was also calculated using predictive equations that had been reported for use in SUV normalization. LBM derived from limited-whole-body data using the proposed method correlated strongly with LBM derived from whole-body CT data, with correlation coefficients ranging from 0.991 (shorter coverage) to 0.998 (longer coverage) and SEMs of LBM ranging from 0.14 to 0.33 kg. These were more accurate than results from different predictive equations, which ranged in correlation coefficient from 0.635 to 0.970 and in SEM from 0.64 to 2.40 kg. LBM of the whole body could be automatically estimated from CT data of limited-whole-body coverage typically acquired in PET/CT examinations. This estimation allows more accurate and consistent quantification of metabolic activity of tumors based on LBM-normalized standardized uptake value.

TOPEX/El Nino Watch - El Nino Warm Water Pool Returns to Near Normal State, Mar, 14, 1998

NASA Technical Reports Server (NTRS)

1998-01-01

This image of the Pacific Ocean was produced using sea surface height measurements taken by the U.S.-French TOPEX/Poseidon satellite. The image shows sea surface height relative to normal ocean conditions on Mar. 14, 1998 and sea surface height is an indicator of the heat content of the ocean. The image shows that the sea surface height along the central equatorial Pacific has returned to a near normal state. Oceanographers indicate this is a classic pattern, typical of a mature El Nino condition. Remnants of the El Nino warm water pool, shown in red and white, are situated to the north and south of the equator. These sea surface height measurements have provided scientists with a detailed view of how the 1997-98 El Nino's warm pool behaves because the TOPEX/Poseidon satellite measures the changing sea surface height with unprecedented precision. In this image, the white and red areas indicate unusual patterns of heat storage; in the white areas, the sea surface is between 14 and 32 centimeters (6 to 13 inches) above normal; in the red areas, it's about 10 centimeters (4 inches) above normal. The green areas indicate normal conditions, while purple (the western Pacific) means at least 18 centimeters (7 inches) below normal sea level. The El Nino phenomenon is thought to be triggered when the steady westward blowing trade winds weaken and even reverse direction. This change in the winds allows a large mass of warm water (the red and white area) that is normally located near Australia to move eastward along the equator until it reaches the coast of South America. The displacement of so much warm water affects evaporation, where rain clouds form and, consequently, alters the typical atmospheric jet stream patterns around the world. Using satellite imagery, buoy and ship data, and a forecasting model of the ocean-atmosphere system, the National Oceanic and Atmospheric Administration, (NOAA), has continued to issue an advisory indicating the so-called El Nino weather conditions that have impacted much of the United States and the world are expected to remain through the spring.

For more information, please visit the TOPEX/Poseidon project web page at http://topex-www.jpl.nasa.gov

Aspheric surface testing by irradiance transport equation

NASA Astrophysics Data System (ADS)

Shomali, Ramin; Darudi, Ahmad; Nasiri, Sadollah; Asgharsharghi Bonab, Armir

2010-10-01

In this paper a method for aspheric surface testing is presented. The method is based on solving the Irradiance Transport Equation (ITE).The accuracy of ITE normally depends on the amount of the pick to valley of the phase distribution. This subject is investigated by a simulation procedure.

Geometrically Nonlinear Transient Analysis of Laminated Composite Plates.

DTIC Science & Technology

1982-03-01

theory (CPT), in which normals to the midsurface before deformation are assumed to remain straight and normal to the midsurface after deformation (i.e...the plate are negligible when compared to the inplane stresses, and normals to the plate midsurface before deformation remain straight but not...necessarily normal to the midsurface after deformation. $ Equations of motion The plate under consideration is composed of a finite number of orthotropic

Dimensional scaling for impact cratering and perforation

NASA Technical Reports Server (NTRS)

Watts, Alan; Atkinson, Dale; Rieco, Steve

1993-01-01

This report summarizes the development of two physics-based scaling laws for describing crater depths and diameters caused by normal incidence impacts into aluminum and TFE Teflon. The report then describes equations for perforations in aluminum and TFE Teflon for normal impacts. Lastly, this report also studies the effects of non-normal incidence on cratering and perforation.

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

DTIC Science & Technology

2008-01-01

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

Environmental lead exposure accelerates progressive diabetic nephropathy in type II diabetic patients.

PubMed

Huang, Wen-Hung; Lin, Ja-Liang; Lin-Tan, Dan-Tzu; Hsu, Ching-Wei; Chen, Kuan-Hsing; Yen, Tzung-Hai

2013-01-01

Whether environmental lead exposure has a long-term effect on progressive diabetic nephropathy in type II diabetic patients remains unclear. A total of 107 type II diabetic patients with stage 3 diabetic nephropathy (estimated glomerular filtration rate (eGFR) range, 30-60 mL/min/1.73 m(2)) with normal body lead burden (BLB) (<600  μ g/72 hr in EDTA mobilization tests) and no history of exposure to lead were prospectively followed for 2 years. Patients were divided into high-normal BLB (>80  μ g) and low-normal BLB (<80  μ g) groups. The primary outcome was a 2-fold increase in the initial creatinine levels, long-term dialysis, or death. The secondary outcome was a change in eGFR over time. Forty-five patients reached the primary outcome within 2 years. Although there were no differences in baseline data and renal function, progressive nephropathy was slower in the low-normal BLB group than that in the high-normal BLB group. During the study period, we demonstrated that each 100  μ g increment in BLB and each 10  μ g increment in blood lead levels could decrease GFR by 2.2 mL/min/1.72 m(2) and 3.0 mL/min/1.72 m(2) (P = 0.005), respectively, as estimated by generalized equations. Moreover, BLB was associated with increased risk of achieving primary outcome. Environmental exposure to lead may have a long-term effect on progressive diabetic nephropathy in type II diabetic patients.

TOPEX/El Nino Watch - October 3, 1997

NASA Technical Reports Server (NTRS)

1997-01-01

This image of the Pacific Ocean was produced using sea surface height measurements taken by the U.S./French TOPEX/Poseidon satellite. The image shows sea surface height relative to normal ocean conditions on Oct. 3, 1997 as the warm water associated with El Nino (in white) spreads northward along the entire coast of North America from the equator all the way to Alaska. The warm water pool in tropical Pacific resulting from El Nino seems to have stabilized. The white and red areas indicate unusual patterns of heat storage; in the white areas, the sea surface is between 14 and 32 centimeters (6 to 13 inches) above normal; in the red areas, it's about 10 centimeters (4 inches) above normal. The surface area covered by the warm water mass is about one and one-half times the size of the continental United States. The added amount of oceanic warm water near the Americas, with a temperature between 21 and 30 C (70 to 85 F), carries the amount of heat equal to 100 times the amount of fossil fuel energy consumed by the entire U.S. population during one year. The green areas indicate normal conditions, while purple (the western Pacific) means at least 18 centimeters (7 inches) below normal sea level.

The El Nino phenomenon is thought to be triggered when the steady westward blowing trade winds weaken and even reverse direction. This change in the winds allows a large mass of warm water (the red and white area) that is normally located near Australia to move eastward along the equator until it reaches the coast of South America. The displacement of so much warm water affects evaporation, where rain clouds form and, consequently, alters the typical atmospheric jet stream patterns around the world. Using these global data, limited regional measurements from buoys and ships, and a forecasting model of the ocean-atmosphere system, the National Centers for Environmental Prediction (NCEP) of the National Oceanic and Atmospheric Administration (NOAA) has issued an advisory indicating the presence of a strong El Nino condition throughout the coming winter.

For more information, please visit the TOPEX/Poseidon project web page at http://topex-www.jpl.nasa.gov/

Detection and prognostic impact of renal dysfunction in patients with chronic heart failure and normal serum creatinine.

PubMed

Scrutinio, Domenico; Passantino, Andrea; Lagioia, Rocco; Santoro, Daniela; Cacciapaglia, Erasmo

2011-03-03

Accurate identification of renal dysfunction (RD) is crucial to risk stratification in chronic heart failure (CHF). Patients with CHF are at special risk of having RD despite normal serum creatinine (SCr), owing to a decreased Cr generation. At low levels of SCr, the equations estimating renal function are less accurate. This study was aimed to assess and compare the prognostic value of formulas estimating renal function in CHF patients with normal SCr. We studied 462 patients with systolic CHF and normal SCr. Creatinine clearance was estimated by the Cockcroft-Gault (eCrCl) and glomerular filtration rate by the 4-variable MDRD equation (eGFR); eCrCl normalized for body-surface area (eCrCl(BSA)) was calculated. The primary outcome was all-cause mortality at 2 years. Seventy five patients died. At multivariate Cox regression analysis, only eCrCl(BSA) was significantly associated with mortality (p = 0.006); eGFR (p = 0.24), eCrCl (p = 0.09) and BUN (p = 0.14) were not statistically significant predictors. The patients in the lowest eCrCl(BSA) quartile had an adjusted 2.1-fold (CI: 1.06-4.1) increased risk of mortality, compared with those in the referent quartile. Two-year survival was 70.4% in the lowest eCrCl(BSA) quartile and 89.7% in the referent quartile. Other independent predictors of mortality were ischemic etiology (RR: 2.16 [CI: 1.3-3.5], p = 0.0017), NYHA III/IV class (RR: 2.45 [CI: 1.51-3.97], p = 0.0003), LVEF <0.25 (RR: 3.38 [CI: 1.69-6.75], p = 0.014), and anemia (RR: 1.86 [CI: 1.16-2.99], p = 0.009). A sizeable proportion of CHF patients have prognostically significant RD despite normal SCr. Such patients represent a high-risk subgroup and can more accurately be identified by the CG formula corrected for BSA than the MDRD. Copyright © 2009 Elsevier B.V. All rights reserved.

Theory of the Effects of Small Gravitational Levels on Droplet Gasification

NASA Technical Reports Server (NTRS)

Beitelmal, A.; Shaw, B. D.

1995-01-01

A mathematical model taking into account small (and constant) gravitational levels is developed for vaporization of an isolated liquid droplet suspended in a stagnant atmosphere. A goal of the present analysis is to see how small gravitational levels affect droplet gasification characteristics. Attention is focused upon determining the effects on gas-phase phenomena. The conservation equations arc normalized and nondimensionalized, and a small parameter that accounts for the effects of gravity is identified. This parameter is the square of the inverse of a Froude number based on the gravitational acceleration, the droplet radius, and a characteristic gas-phase velocity at the droplet surface. Asymptotic analyses are developed in terms of this parameter. In the analyses, different spatial regions are identified. Near a droplet, gravitational effects are negligible in the first approximation, and the flowfield is spherically symmetric to the leading order. Analysis shows, however, that outer zones exist where gravitational effects cannot be neglected; it is expected that a stagnation point will be present in an outer zone that is not present when gravity is totally absent. The leading order and higher-order differential equations for each zone are derived and solved. The solutions allow the effects of gravity on vaporization rates and temperature, velocity and species fields to be determined.

Similarity of Turbulent Energy Scale Budget Equation of a Round Turbulent Jet

NASA Astrophysics Data System (ADS)

Sadeghi, Hamed; Lavoie, Philippe; Pollard, Andrew

2014-11-01

A novel extension to the similarity-based form of the transport equation for the second-order velocity structure function of <(δq) 2 > along the jet centreline (see Danaila et al., 2004) has been obtained. This new self-similar equation has the desirable benefit of requiring less extensive measurements to calculate the inhomogeneous (decay and production) terms of the transport equation. According to this equation, the normalized third-order structure function can be uniquely determined when the normalized second-order structure function, the power-law exponent of and the decay rate constants of and are available. In addition, on the basis of the current similarity analysis, the similarity assumptions in combination with power-law decay of mean velocity (U ~(x -x0) - 1) are strong enough to imply power-law decay of fluctuations ( ~(x -x0) m). The similarity solutions are then tested against new experimental data, which were taken along the centreline of a round jet at ReD = 50 , 000 . For the present set of initial conditions, exhibits a power-law behaviour with m = - 1 . 83 . This work was supported by grants from NSERC (Canada).

Evaluation and interpretation of Thematic Mapper ratios in equations for estimating corn growth parameters

NASA Technical Reports Server (NTRS)

Dardner, B. R.; Blad, B. L.; Thompson, D. R.; Henderson, K. E.

1985-01-01

Reflectance and agronomic Thematic Mapper (TM) data were analyzed to determine possible data transformations for evaluating several plant parameters of corn. Three transformation forms were used: the ratio of two TM bands, logarithms of two-band ratios, and normalized differences of two bands. Normalized differences and logarithms of two-band ratios responsed similarly in the equations for estimating the plant growth parameters evaluated in this study. Two-term equations were required to obtain the maximum predictability of percent ground cover, canopy moisture content, and total wet phytomass. Standard error of estimate values were 15-26 percent lower for two-term estimates of these parameters than for one-term estimates. The terms log(TM4/TM2) and (TM4/TM5) produced the maximum predictability for leaf area and dry green leaf weight, respectively. The middle infrared bands TM5 and TM7 are essential for maximizing predictability for all measured plant parameters except leaf area index. The estimating models were evaluated over bare soil to discriminate between equations which are statistically similar. Qualitative interpretations of the resulting prediction equations are consistent with general agronomic and remote sensing theory.

Multiple normalized solutions for a planar gauged nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Luo, Xiao

2018-06-01

We study the existence, multiplicity, quantitative property and asymptotic behavior of normalized solutions for a gauged nonlinear Schrödinger equation arising from the Chern-Simons theory Δ u + ω u +|x|^2u+ λ ( {{h^2}(| x | )}/{{{| x | ^2}}} + \\int \\limits _{| x | }^{ + ∞} {{h(s)}/s} {u^2}(s)ds) u = {| u | ^{p - 2}}u,\\quad x\\in R^2, where ω \\in R, λ >0, p>4 and h(s) = 1/2\\int \\limits _0^s {r{u^2}(r)dr} . Combining constraint minimization method and minimax principle, we prove that the problem possesses at least two normalized solutions: One is a ground state and the other is an excited state. Furthermore, the asymptotic behavior and quantitative property of the ground state are analyzed.

Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids

NASA Technical Reports Server (NTRS)

Pandya, S. A.; Chattot, JJ; Hafez, M. M.; Kutler, Paul (Technical Monitor)

1994-01-01

A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.

USAF bioenvironmental noise data handbook. Volume 157: KC-10A in-flight crew noise

NASA Astrophysics Data System (ADS)

Hille, H. K.

1982-09-01

The KC-10A is a standard USAF tanker-transport aircraft with high-speed, high altitude refueling and long range transport capability. This report provides measured data defining the bioacoustic environments at flight crew/passenger locations inside this helicopter during normal flight operations. Data are reported for 24 locations in a wide variety of physical and psychoacoustic measures: overall and band sound pressure levels, C-weighted and A-weighted sound levels, preferred speech interference level, perceived noise level, and limiting times for total daily exposure of personnel with and without standard Air Force ear protectors. Refer to Volume 1 of this handbook, USAF Bioenvironmental Noise Data Handbook, Vol. 1: Organization, Content and Application, AMRL-TR-75-50(1) 1975, for discussion of the objective and design of the handbook, the types of data presented, measurement procedures, instrumentation, data processing, definitions of quantities, symbols, equations, applications, limitations, etc.

USAF Bioenvironmental Noise Data Handbook. Volume 152: C-12A in-flight crew noise

NASA Astrophysics Data System (ADS)

Hille, H. K.

1982-09-01

The C-12A is a military version of the Beechcraft Super King Air 200. This report provides measured data defining the bioacoustic environments at flight crew/passenger locations inside this aircraft during normal flight operations. Data are reported for five locations in a wide variety of physical and psychoacoustic measures: overall and band sound pressure levels, C-weighted and A-weighted sound levels, preferred speech interference level, perceived noise level, and limiting times for total daily exposure of personnel with and without standard Air Force ear protectors. Refer to Volume 1 of this handbook, USAF Bioenvironmental Noise Data Handbook, Vol 1: Organization, Content and Application, AMRL-TR-75-50(1) 1975, for discussion of the objective and design of the handbook, the types of data presented, measurement procedures, instrumentation, data processing, definitions of quantities, symbols, equations, applications, limitations, etc.

USAF Bioenvironmental Noise Data Handbook. Volume 156. HH-1N In-flight Crew Noise

NASA Astrophysics Data System (ADS)

Hille, H. K.

1982-11-01

The HH-IN is a USAF multi-purpose utility helicopter providing support for various USAF missions. This report provides measured data defining the bioacoustic environments at flight crew locations inside this helicopter during normal flight operations. Data are reported for two locations in a wide variety of physical and psychoacoustic measures: overall and band sound pressure levels, C-weighted and A-weighted sound levels, preferred speech interference level, perceived noise level, and limiting times for total daily exposure of personnel with and without standard Air Force ear protectors. Refer to Volume 1 of this handbook, USAF Bioenvironmental Noise Data Handbook, Vol. 1: Organization, Content and Application, AMRL-TR-75-50(1) 1975, for discussion of the objective and design of the handbook, the types of data presented, measurement procedures, instrumentation, data processing, definitions of quantities, symbols, equations, applications, limitations, etc.

USAF Bioenvironmental Noise Data Handbook, volume 154

NASA Astrophysics Data System (ADS)

Rau, T. H.

1982-05-01

The E-4B is a Boeing 747 aircraft modified to serve as the national emergency/HQ Strategic Air Command Airborne Command Post. This report provides measured data defining the bioacoustic environments at flight crew/passenger locations inside this aircraft during normal flight operations. Data are reported for 24 locations in a wide variety of physical and psychoacoustic measures: overall and band sound pressure levels, C-weighted and A-weighted sound levels, preferred speech interference level, perceived noise level, and limiting times for total daily exposure of personnel with and without standard Air Force ear protectors. Refer to Volume 1 of this handbook, "USAF Bioenvironmental Noise Data Handbook, Vol. 1: Organization, Content and Application", AMRL-TR-75-50(1) 1975, for discussion of the objective and design of the handbook, the types of data presented, measurement procedures, instrumentation, data processing, definitions of quantities, symbols, equations, applications, limitations, etc.

Nonlinear equations of motion for Landau resonance interactions with a whistler mode wave

NASA Technical Reports Server (NTRS)

Inan, U. S.; Tkalcevic, S.

1982-01-01

A simple set of equations is presented for the description of the cyclotron averaged motion of Landau resonant particles in a whistler mode wave propagating at an angle to the static magnetic field. A comparison is conducted of the wave magnetic field and electric field effects for the parameters of the magnetosphere, and the parameter ranges for which the wave magnetic field effects would be negligible are determined. It is shown that the effect of the wave magnetic field can be neglected for low pitch angles, high normal wave angles, and/or high normalized wave frequencies.

Stochastic modelling of non-stationary financial assets

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Contact problem on indentation of an elastic half-plane with an inhomogeneous coating by a flat punch in the presence of tangential stresses on a surface

NASA Astrophysics Data System (ADS)

Volkov, Sergei S.; Vasiliev, Andrey S.; Aizikovich, Sergei M.; Sadyrin, Evgeniy V.

2018-05-01

Indentation of an elastic half-space with functionally graded coating by a rigid flat punch is studied. The half-plane is additionally subjected to distributed tangential stresses. Tangential stresses are represented in a form of Fourier series. The problem is reduced to the solution of two dual integral equations over even and odd functions describing distribution of unknown normal contact stresses. The solutions of these dual integral equations are constructed by the bilateral asymptotic method. Approximated analytical expressions for contact normal stresses are provided.

Effect of Coannular Flow on Linearized Euler Equation Predictions of Jet Noise

NASA Technical Reports Server (NTRS)

Hixon, R.; Shih, S.-H.; Mankbadi, Reda R.

1997-01-01

An improved version of a previously validated linearized Euler equation solver is used to compute the noise generated by coannular supersonic jets. Results for a single supersonic jet are compared to the results from both a normal velocity profile and an inverted velocity profile supersonic jet.

A Robust Bayesian Approach for Structural Equation Models with Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum; Xia, Ye-Mao

2008-01-01

In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear…

Who Will Win?: Predicting the Presidential Election Using Linear Regression

ERIC Educational Resources Information Center

Lamb, John H.

2007-01-01

This article outlines a linear regression activity that engages learners, uses technology, and fosters cooperation. Students generated least-squares linear regression equations using TI-83 Plus[TM] graphing calculators, Microsoft[C] Excel, and paper-and-pencil calculations using derived normal equations to predict the 2004 presidential election.…

A Computer Model of the Cardiovascular System for Effective Learning.

ERIC Educational Resources Information Center

Rothe, Carl F.

1980-01-01

Presents a model of the cardiovascular system which solves a set of interacting, possibly nonlinear, differential equations. Figures present a schematic diagram of the model and printouts that simulate normal conditions, exercise, hemorrhage, reduced contractility. The nine interacting equations used to describe the system are described in the…

Some Properties of Estimated Scale Invariant Covariance Structures.

ERIC Educational Resources Information Center

Dijkstra, T. K.

1990-01-01

An example of scale invariance is provided via the LISREL model that is subject only to classical normalizations and zero constraints on the parameters. Scale invariance implies that the estimated covariance matrix must satisfy certain equations, and the nature of these equations depends on the fitting function used. (TJH)

Titration Calculations with Computer Algebra Software

ERIC Educational Resources Information Center

Lachance, Russ; Biaglow, Andrew

2012-01-01

This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…

Development of control systems for space shuttle vehicles. Volume 2: Appendixes

NASA Technical Reports Server (NTRS)

Stone, C. R.; Chase, T. W.; Kiziloz, B. M.; Ward, M. D.

1971-01-01

A launch phase random normal wind model is presented for delta wing, two-stage, space shuttle control system studies. Equations, data, and simulations for conventional launch studies are given as well as pitch and lateral equations and data for covariance analyses of the launch phase of MSFC vehicle B. Lateral equations and data for North American 130G and 134D are also included along with a high-altitude abort simulation.

Turbulent Fluid Motion 5: Fourier Analysis, the Spectral Form of the Continuum Equations, and Homogeneous Turbulence

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1996-01-01

Background material on Fourier analysis and on the spectral form of the continuum equations, both averaged and unaveraged, are given. The equations are applied to a number of cases of homogeneous turbulence with and without mean gradients. Spectral transfer of turbulent activity between scales of motion is studied in some detail. The effects of mean shear, heat transfer, normal strain, and buoyancy are included in the analyses.

On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Shi, Yanling; Xu, Junxiang; Xu, Xindong

2015-02-01

In this paper, one-dimensional generalized Boussinesq equation: utt - uxx + (u2 + uxx)xx = 0 with boundary conditions ux(0, t) = ux(π, t) = uxxx(0, t) = uxxx(π, t) = 0 is considered. It is proved that the equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with 2-dimensional Diophantine frequencies. The proof is based on an infinite dimensional Kolmogorov-Arnold-Moser theorem and Birkhoff normal form.

Predictive equations for respiratory muscle strength according to international and Brazilian guidelines.

PubMed

Pessoa, Isabela M B S; Houri Neto, Miguel; Montemezzo, Dayane; Silva, Luisa A M; Andrade, Armèle Dornelas De; Parreira, Verônica F

2014-01-01

The maximum static respiratory pressures, namely the maximum inspiratory pressure (MIP) and maximum expiratory pressure (MEP), reflect the strength of the respiratory muscles. These measures are simple, non-invasive, and have established diagnostic and prognostic value. This study is the first to examine the maximum respiratory pressures within the Brazilian population according to the recommendations proposed by the American Thoracic Society and European Respiratory Society (ATS/ERS) and the Brazilian Thoracic Association (SBPT). To establish reference equations, mean values, and lower limits of normality for MIP and MEP for each age group and sex, as recommended by the ATS/ERS and SBPT. We recruited 134 Brazilians living in Belo Horizonte, MG, Brazil, aged 20-89 years, with a normal pulmonary function test and a body mass index within the normal range. We used a digital manometer that operationalized the variable maximum average pressure (MIP/MEP). At least five tests were performed for both MIP and MEP to take into account a possible learning effect. We evaluated 74 women and 60 men. The equations were as follows: MIP=63.27-0.55 (age)+17.96 (gender)+0.58 (weight), r(2) of 34% and MEP= - 61.41+2.29 (age) - 0.03(age(2))+33.72 (gender)+1.40 (waist), r(2) of 49%. In clinical practice, these equations could be used to calculate the predicted values of MIP and MEP for the Brazilian population.

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

NASA Astrophysics Data System (ADS)

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

2006-03-01

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

On a Heat Exchange Problem under Sharply Changing External Conditions

NASA Astrophysics Data System (ADS)

Khishchenko, K. V.; Charakhch'yan, A. A.; Shurshalov, L. V.

2018-02-01

The heat exchange problem between carbon particles and an external environment (water) is stated and investigated based on the equations of heat conducting compressible fluid. The environment parameters are supposed to undergo large and fast variations. In the time of about 100 μs, the temperature of the environment first increases from the normal one to 2400 K, is preserved at this level for about 60 μs, and then decreases to 300 K during approximately 50 μs. At the same periods of time, the pressure of the external environment increases from the normal one to 67 GPa, is preserved at this level, and then decreases to zero. Under such external conditions, the heating of graphite particles of various sizes, their phase transition to the diamond phase, and the subsequent unloading and cooling almost to the initial values of the pressure and temperature without the reverse transition from the diamond to the graphite phase are investigated. Conclusions about the maximal size of diamond particles that can be obtained in experiments on the shock compression of the mixture of graphite with water are drawn.

Digital simulation of a communication link for Pioneer Saturn Uranus atmospheric entry probe, part 1

NASA Technical Reports Server (NTRS)

Hinrichs, C. A.

1975-01-01

A digital simulation study is presented for a candidate modulator/demodulator design in an atmospheric scintillation environment with Doppler, Doppler rate, and signal attenuation typical of the conditions of an outer planet atmospheric probe. The simulation results indicate that the mean channel error rate with and without scintillation are similar to theoretical characterizations of the link. The simulation gives information for calculating other channel statistics and generates a quantized symbol stream on magnetic tape from which error correction decoding is analyzed. Results from the magnetic tape data analyses are also included. The receiver and bit synchronizer are modeled in the simulation at the level of hardware component parameters rather than at the loop equation level and individual hardware parameters are identified. The atmospheric scintillation amplitude and phase are modeled independently. Normal and log normal amplitude processes are studied. In each case the scintillations are low pass filtered. The receiver performance is given for a range of signal to noise ratios with and without the effects of scintillation. The performance is reviewed for critical reciever parameter variations.

FEV1/FVC and FEV1 for the assessment of chronic airflow obstruction in prevalence studies: do prediction equations need revision?

PubMed

Roche, Nicolas; Dalmay, François; Perez, Thierry; Kuntz, Claude; Vergnenègre, Alain; Neukirch, Françoise; Giordanella, Jean-Pierre; Huchon, Gérard

2008-11-01

Little is known on the long-term validity of reference equations used in the calculation of FEV(1) and FEV(1)/FVC predicted values. This survey assessed the prevalence of chronic airflow obstruction in a population-based sample and how it is influenced by: (i) the definition of airflow obstruction; and (ii) equations used to calculate predicted values. Subjects aged 45 or more were recruited in health prevention centers, performed spirometry and fulfilled a standardized ECRHS-derived questionnaire. Previously diagnosed cases and risk factors were identified. Prevalence of airflow obstruction was calculated using: (i) ATS-GOLD definition (FEV(1)/FVC<0.70); and (ii) ERS definition (FEV(1)/FVC

Breastfeeding attitude, health-related quality of life and maternal obesity among multi-ethnic pregnant women: A multi-group structural equation approach.

PubMed

Lau, Ying; Htun, Tha Pyai; Lim, Peng Im; Ho-Lim, Sarah Su Tin; Chi, Claudia; Tsai, Cammy; Ong, Kai Wen; Klainin-Yobas, Piyanee

2017-02-01

Identifying the factors influencing breastfeeding attitude is significant for the implementation of effective promotion policies and counselling activities. To our best knowledge, no previous studies have modelled the relationships among breastfeeding attitude, health-related quality of life and maternal obesity among multi-ethnic pregnant women; the current study attempts to fill this research gap. This study investigated the relationships among maternal characteristics, health-related quality of life and breastfeeding attitude amidst normal weight and overweight/obese pregnant women using a multi-group structural equation modelling approach. Exploratory cross-sectional design was used. Antenatal clinics of a university-affiliated hospital PARTICIPANTS: Pregnant women were invited to participate; 708 (78.8%) agreed to participate in the study. We examined a hypothetical model on the basis of integrating the concepts of a breastfeeding decision-making model, theory of planned behaviour-based model for breastfeeding and health-related quality of life model among 708 multi-ethnic pregnant women in Singapore. The Iowa Infant Feeding Attitude Scale and Medical Outcomes Study Short Form Health Survey were used to measure breastfeeding attitude and health-related quality of life, respectively. Two structural equation models demonstrated that better health-related quality of life, higher monthly household income, planned pregnancy and previous exclusive breastfeeding experience were significantly associated with positive breastfeeding attitude among normal and overweight/obese pregnant women. Among normal weight pregnant women, those who were older with higher educational level were more likely to have positive breastfeeding attitude. Among overweight/obese pregnant women, Chinese women with confinement nanny plan were less likely to have positive breastfeeding attitude. No significant difference existed between normal weight and overweight/obese pregnant women concerning estimates of health-related quality of life on breastfeeding attitude (Critical Ratio=-0.193). The model satisfactorily fitted the data (Incremental Fit Index=0.924, Tucker-Lewis Index=0.905, Comparative Fit Index=0.921 and Root Means Square Error of Approximation=0.025). Health-related quality of life was found to affect breastfeeding attitude in multi-ethnic pregnant women. This relationship implied the importance of early culturally specific interventions to enhance health-related quality of life for improving positive breastfeeding attitude among pregnant women across different ethnic groups. Copyright © 2016 Elsevier Ltd. All rights reserved.

An improved two-dimensional depth-integrated flow equation for rough-walled fractures

NASA Astrophysics Data System (ADS)

Mallikamas, Wasin; Rajaram, Harihar

2010-08-01

We present the development of an improved 2-D flow equation for rough-walled fractures. Our improved equation accounts for the influence of midsurface tortuosity and the fact that the aperture normal to the midsurface is in general smaller than the vertical aperture. It thus improves upon the well-known Reynolds equation that is widely used for modeling flow in fractures. Unlike the Reynolds equation, our approach begins from the lubrication approximation applied in an inclined local coordinate system tangential to the fracture midsurface. The local flow equation thus obtained is rigorously transformed to an arbitrary global Cartesian coordinate system, invoking the concepts of covariant and contravariant transformations for vectors defined on surfaces. Unlike previously proposed improvements to the Reynolds equation, our improved flow equation accounts for tortuosity both along and perpendicular to a flow path. Our approach also leads to a well-defined anisotropic local transmissivity tensor relating the representations of the flux and head gradient vectors in a global Cartesian coordinate system. We show that the principal components of the transmissivity tensor and the orientation of its principal axes depend on the directional local midsurface slopes. In rough-walled fractures, the orientations of the principal axes of the local transmissivity tensor will vary from point to point. The local transmissivity tensor also incorporates the influence of the local normal aperture, which is uniquely defined at each point in the fracture. Our improved flow equation is a rigorous statement of mass conservation in any global Cartesian coordinate system. We present three examples of simple geometries to compare our flow equation to analytical solutions obtained using the exact Stokes equations: an inclined parallel plate, and circumferential and axial flows in an incomplete annulus. The effective transmissivities predicted by our flow equation agree very well with values obtained using the exact Stokes equations in all these cases. We discuss potential limitations of our depth-integrated equation, which include the neglect of convergence/divergence and the inaccuracies implicit in any depth-averaging process near sharp corners where the wall and midsurface curvatures are large.

A reference equation for maximal aerobic power for treadmill and cycle ergometer exercise testing: Analysis from the FRIEND registry.

PubMed

de Souza E Silva, Christina G; Kaminsky, Leonard A; Arena, Ross; Christle, Jeffrey W; Araújo, Claudio Gil S; Lima, Ricardo M; Ashley, Euan A; Myers, Jonathan

2018-05-01

Background Maximal oxygen uptake (VO 2 max) is a powerful predictor of health outcomes. Valid and portable reference values are integral to interpreting measured VO 2 max; however, available reference standards lack validation and are specific to exercise mode. This study was undertaken to develop and validate a single equation for normal standards for VO 2 max for the treadmill or cycle ergometer in men and women. Methods Healthy individuals ( N = 10,881; 67.8% men, 20-85 years) who performed a maximal cardiopulmonary exercise test on either a treadmill or a cycle ergometer were studied. Of these, 7617 and 3264 individuals were randomly selected for development and validation of the equation, respectively. A Brazilian sample (1619 individuals) constituted a second validation cohort. The prediction equation was determined using multiple regression analysis, and comparisons were made with the widely-used Wasserman and European equations. Results Age, sex, weight, height and exercise mode were significant predictors of VO 2 max. The regression equation was: VO 2 max (ml kg -1  min -1 ) = 45.2 - 0.35*Age - 10.9*Sex (male = 1; female = 2) - 0.15*Weight (pounds) + 0.68*Height (inches) - 0.46*Exercise Mode (treadmill = 1; bike = 2) ( R = 0.79, R 2  = 0.62, standard error of the estimate = 6.6 ml kg -1  min -1 ). Percentage predicted VO 2 max for the US and Brazilian validation cohorts were 102.8% and 95.8%, respectively. The new equation performed better than traditional equations, particularly among women and individuals ≥60 years old. Conclusion A combined equation was developed for normal standards for VO 2 max for different exercise modes derived from a US national registry. The equation provided a lower average error between measured and predicted VO 2 max than traditional equations even when applied to an independent cohort. Additional studies are needed to determine its portability.

Sensitivity of Satellite Altimetry Data Assimilation on a Naval Anti-Submarine Warfare Weapon System

DTIC Science & Technology

2004-09-01

representing the actual ocean structure than static climatology databases (Fox et. al., 2002; Chu et. al., 2004). It is expected that this 2...pressure amplitude function and ( , )P P r z= is the phase function, or eikonal . Doing this and collecting real and imaginary terms yields an equation... eikonal equation, [ ]2 2P k∇ = , (13) from which differential equations for rays can be derived (Etter, 1991). The rays are the normals to surfaces

A stochastic differential equation model of diurnal cortisol patterns

NASA Technical Reports Server (NTRS)

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

2001-01-01

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

Fibroblast proliferation alters cardiac excitation conduction and contraction: a computational study.

PubMed

Zhan, He-qing; Xia, Ling; Shou, Guo-fa; Zang, Yun-liang; Liu, Feng; Crozier, Stuart

2014-03-01

In this study, the effects of cardiac fibroblast proliferation on cardiac electric excitation conduction and mechanical contraction were investigated using a proposed integrated myocardial-fibroblastic electromechanical model. At the cellular level, models of the human ventricular myocyte and fibroblast were modified to incorporate a model of cardiac mechanical contraction and cooperativity mechanisms. Cellular electromechanical coupling was realized with a calcium buffer. At the tissue level, electrical excitation conduction was coupled to an elastic mechanics model in which the finite difference method (FDM) was used to solve electrical excitation equations, and the finite element method (FEM) was used to solve mechanics equations. The electromechanical properties of the proposed integrated model were investigated in one or two dimensions under normal and ischemic pathological conditions. Fibroblast proliferation slowed wave propagation, induced a conduction block, decreased strains in the fibroblast proliferous tissue, and increased dispersions in depolarization, repolarization, and action potential duration (APD). It also distorted the wave-front, leading to the initiation and maintenance of re-entry, and resulted in a sustained contraction in the proliferous areas. This study demonstrated the important role that fibroblast proliferation plays in modulating cardiac electromechanical behaviour and which should be considered in planning future heart-modeling studies.

Fibroblast proliferation alters cardiac excitation conduction and contraction: a computational study*

PubMed Central

Zhan, He-qing; Xia, Ling; Shou, Guo-fa; Zang, Yun-liang; Liu, Feng; Crozier, Stuart

2014-01-01

In this study, the effects of cardiac fibroblast proliferation on cardiac electric excitation conduction and mechanical contraction were investigated using a proposed integrated myocardial-fibroblastic electromechanical model. At the cellular level, models of the human ventricular myocyte and fibroblast were modified to incorporate a model of cardiac mechanical contraction and cooperativity mechanisms. Cellular electromechanical coupling was realized with a calcium buffer. At the tissue level, electrical excitation conduction was coupled to an elastic mechanics model in which the finite difference method (FDM) was used to solve electrical excitation equations, and the finite element method (FEM) was used to solve mechanics equations. The electromechanical properties of the proposed integrated model were investigated in one or two dimensions under normal and ischemic pathological conditions. Fibroblast proliferation slowed wave propagation, induced a conduction block, decreased strains in the fibroblast proliferous tissue, and increased dispersions in depolarization, repolarization, and action potential duration (APD). It also distorted the wave-front, leading to the initiation and maintenance of re-entry, and resulted in a sustained contraction in the proliferous areas. This study demonstrated the important role that fibroblast proliferation plays in modulating cardiac electromechanical behaviour and which should be considered in planning future heart-modeling studies. PMID:24599687

The Interaction of Turbulence with Parallel and Perpendicular Shocks: Theory and Observations at 1 au

NASA Astrophysics Data System (ADS)

Adhikari, L.; Zank, G. P.; Hunana, P.; Hu, Q.

2016-12-01

Shocks are thought to be responsible for the amplification of turbulence as well as for generating turbulence throughout the heliosphere. We study the interaction of turbulence with parallel and perpendicular shock waves using the six-coupled-equation turbulence transport model of Zank et al. We model a 1D stationary shock wave using a hyperbolic tangent function and the Rankine-Hugoniot conditions for both a reduced model with four coupled equations and the full model. Eight quasi-parallel and five quasi-perpendicular events in the WIND spacecraft data sets are identified, and we compute the fluctuating magnetic and kinetic energy, the energy in forward and backward propagating modes, the total turbulent energy, the normalized residual energy, and the normalized cross helicity upstream and downstream of the observed shocks. We compare the observed fitted values upstream and downstream of the shock with numerical solutions to our model equations. The comparison shows that our theoretical results are in reasonable agreement with observations for both quasi-parallel and perpendicular shocks. We find that (1) the total turbulent energy, the energy in forward and backward propagating modes, and the normalized residual energy increase across the shock, (2) the normalized cross helicity increases or decreases across the shock, and (3) the correlation length increases upstream and downstream of the shock, and slightly flattens or decreases across the shock.

THE INTERACTION OF TURBULENCE WITH PARALLEL AND PERPENDICULAR SHOCKS: THEORY AND OBSERVATIONS AT 1 au

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

Adhikari, L.; Zank, G. P.; Hunana, P.

Shocks are thought to be responsible for the amplification of turbulence as well as for generating turbulence throughout the heliosphere. We study the interaction of turbulence with parallel and perpendicular shock waves using the six-coupled-equation turbulence transport model of Zank et al. We model a 1D stationary shock wave using a hyperbolic tangent function and the Rankine–Hugoniot conditions for both a reduced model with four coupled equations and the full model. Eight quasi-parallel and five quasi-perpendicular events in the WIND spacecraft data sets are identified, and we compute the fluctuating magnetic and kinetic energy, the energy in forward and backwardmore » propagating modes, the total turbulent energy, the normalized residual energy, and the normalized cross helicity upstream and downstream of the observed shocks. We compare the observed fitted values upstream and downstream of the shock with numerical solutions to our model equations. The comparison shows that our theoretical results are in reasonable agreement with observations for both quasi-parallel and perpendicular shocks. We find that (1) the total turbulent energy, the energy in forward and backward propagating modes, and the normalized residual energy increase across the shock, (2) the normalized cross helicity increases or decreases across the shock, and (3) the correlation length increases upstream and downstream of the shock, and slightly flattens or decreases across the shock.« less

Prediction of light aircraft interior sound pressure level using the room equation

NASA Technical Reports Server (NTRS)

Atwal, M.; Bernhard, R.

1984-01-01

The room equation is investigated for predicting interior sound level. The method makes use of an acoustic power balance, by equating net power flow into the cabin volume to power dissipated within the cabin using the room equation. The sound power level transmitted through the panels was calculated by multiplying the measured space averaged transmitted intensity for each panel by its surface area. The sound pressure level was obtained by summing the mean square sound pressures radiated from each panel. The data obtained supported the room equation model in predicting the cabin interior sound pressure level.

[The implementation of computer model in research of dynamics of proliferation of cells of thyroid gland follicle].

PubMed

Abduvaliev, A A; Gil'dieva, M S; Khidirov, B N; Saĭdalieva, M; Khasanov, A A; Musaeva, Sh N; Saatov, T S

2012-04-01

The article deals with the results of computational experiments in research of dynamics of proliferation of cells of thyroid gland follicle in normal condition and in the case of malignant neoplasm. The model studies demonstrated that the chronic increase of parameter of proliferation of cells of thyroid gland follicle results in abnormal behavior of numbers of cell cenosis of thyroid gland follicle. The stationary state interrupts, the auto-oscillations occur with transition to irregular oscillations with unpredictable cell proliferation and further to the "black hole" effect. It is demonstrated that the present medical biologic experimental data and theory propositions concerning the structural functional organization of thyroid gland on cell level permit to develop mathematical models for quantitative analysis of numbers of cell cenosis of thyroid gland follicle in normal conditions. The technique of modeling of regulative mechanisms of living systems and equations of cell cenosis regulations was used

Normalized coffin-manson plot in terms of a new life function based on stress relaxation under creep-fatigue conditions

NASA Astrophysics Data System (ADS)

Jeong, Chang Yeol; Nam, Soo Woo; Lim, Jong Dae

2003-04-01

A new life prediction function based on a model formulated in terms of stress relaxation during hold time under creep-fatigue conditions is proposed. From the idea that reduction in fatigue life with hold is due to the creep effect of stress relaxation that results in additional energy dissipation in the hysteresis loop, it is suggested that the relaxed stress range may be a creep-fatigue damage function. Creep-fatigue data from the present and other investigators are used to check the validity of the proposed life prediction equation. It is shown that the data satisfy the applicability of the life relation model. Accordingly, using this life prediction model, one may realize that all the Coffin-Manson plots at various levels of hold time in strain-controlled creep-fatigue tests can be normalized to make one straight line.

Energy Cascade in Fermi-Pasta Models

NASA Astrophysics Data System (ADS)

Ponno, A.; Bambusi, D.

We show that, for long-wavelength initial conditions, the FPU dynamics is described, up to a certain time, by two KdV-like equations, which represent the resonant Hamiltonian normal form of the system. The energy cascade taking place in the system is then quantitatively characterized by arguments of dimensional analysis based on such equations.

A General Theory of Unsteady Compressible Potential Aerodynamics

NASA Technical Reports Server (NTRS)

Morino, L.

1974-01-01

The general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green function method, an integral representation for the potential is obtained for both supersonic and subsonic flow. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface, sigma, of the body. Hence, if the point P approaches the surface of the body, the representation reduces to an integro-differential equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface sigma. For the important practical case of small harmonic oscillation around a rest position, the equation reduces to a two-dimensional Fredholm integral equation of second-type. It is shown that this equation reduces properly to the lifting surface theories as well as other classical mathematical formulas. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings.

Reference breast temperature: proposal of an equation.

PubMed

Souza, Gladis Aparecida Galindo Reisemberger de; Brioschi, Marcos Leal; Vargas, José Viriato Coelho; Morais, Keli Cristiane Correia; Dalmaso Neto, Carlos; Neves, Eduardo Borba

2015-01-01

To develop an equation to estimate the breast reference temperature according to the variation of room and core body temperatures. Four asymptomatic women were evaluated for three consecutive menstrual cycles. Using thermography, the temperature of breasts and eyes was measured as indirect reference of core body and room temperatures. To analyze the thermal behavior of the breasts during the cycle, the core body and room temperatures were normalized by means of a mathematical equation. We performed 180 observations and the core temperature had the highest correlation with the breast temperature, followed by room temperature. The proposed prediction model could explain 45.3% of the breast temperature variation, with variable room temperature variable; it can be accepted as a way to estimate the reference breast temperature at different room temperatures. The average breast temperature in healthy women had a direct relation with the core and room temperature and can be estimated mathematically. It is suggested that an equation could be used in clinical practice to estimate the normal breast reference temperature in young women, regardless of the day of the cycle, therefore assisting in evaluation of anatomical studies.

Mode instability in one-dimensional anharmonic lattices: Variational equation approach

NASA Astrophysics Data System (ADS)

Yoshimura, K.

1999-03-01

The stability of normal mode oscillations has been studied in detail under the single-mode excitation condition for the Fermi-Pasta-Ulam-β lattice. Numerical experiments indicate that the mode stability depends strongly on k/N, where k is the wave number of the initially excited mode and N is the number of degrees of freedom in the system. It has been found that this feature does not change when N increases. We propose an average variational equation - approximate version of the variational equation - as a theoretical tool to facilitate a linear stability analysis. It is shown that this strong k/N dependence of the mode stability can be explained from the view point of the linear stability of the relevant orbits. We introduce a low-dimensional approximation of the average variational equation, which approximately describes the time evolution of variations in four normal mode amplitudes. The linear stability analysis based on this four-mode approximation demonstrates that the parametric instability mechanism plays a crucial role in the strong k/N dependence of the mode stability.

Self-consistent-field perturbation theory for the Schröautdinger equation

NASA Astrophysics Data System (ADS)

Goodson, David Z.

1997-06-01

A method is developed for using large-order perturbation theory to solve the systems of coupled differential equations that result from the variational solution of the Schröautdinger equation with wave functions of product form. This is a noniterative, computationally efficient way to solve self-consistent-field (SCF) equations. Possible applications include electronic structure calculations using products of functions of collective coordinates that include electron correlation, vibrational SCF calculations for coupled anharmonic oscillators with selective coupling of normal modes, and ab initio calculations of molecular vibration spectra without the Born-Oppenheimer approximation.

Birkhoff Normal Form for Some Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Bambusi, Dario

We consider the problem of extending to PDEs Birkhoff normal form theorem on Hamiltonian systems close to nonresonant elliptic equilibria. As a model problem we take the nonlinear wave equation with Dirichlet boundary conditions on [0,π] g is an analytic skewsymmetric function which vanishes for u=0 and is periodic with period 2π in the x variable. We prove, under a nonresonance condition which is fulfilled for most g's, that for any integer M there exists a canonical transformation that puts the Hamiltonian in Birkhoff normal form up to a reminder of order M. The canonical transformation is well defined in a neighbourhood of the origin of a Sobolev type phase space of sufficiently high order. Some dynamical consequences are obtained. The technique of proof is applicable to quite general semilinear equations in one space dimension.

A finite-element analysis for steady and oscillatory supersonic flows around complex configurations

NASA Technical Reports Server (NTRS)

Morino, L.; Chen, L. T.

1974-01-01

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, sigma sub i, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element, and this yields a set of linear algebraic equations. The coefficients of the equation are given by source and doublet integrals over the surface elements, sigma sub i. The results obtained using the above formulation are compared with existing analytical and experimental results.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes

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

Konor, Celal S.; Randall, David A.

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia–gravity modes on a midlatitude f plane.The results of our normal-modemore » analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.« less

Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model

DOE PAGES

Barnard, Richard C.; Frank, Martin; Krycki, Kai

2016-02-09

In this paper, we study the sensitivities of electron dose calculations with respect to stopping power and transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker–Planck approximation to the Boltzmann transport equation. Equations for the sensitivities are derived by the adjoint method. The Fokker–Planck equation and its adjoint are solved numerically in slab geometry using the spherical harmonics expansion (P N) and an Harten-Lax-van Leer finite volume method. Our method is verified by comparison to finite difference approximations of the sensitivities. Finally, we present numerical results of the sensitivities for the normalized average dose depositionmore » depth with respect to the stopping power and the transport coefficients, demonstrating the increase in relative sensitivities as beam energy decreases. In conclusion, this in turn gives estimates on the uncertainty in the normalized average deposition depth, which we present.« less

Analyzing Axial Stress and Deformation of Tubular for Steam Injection Process in Deviated Wells Based on the Varied (T, P) Fields

PubMed Central

Liu, Yunqiang; Xu, Jiuping; Wang, Shize; Qi, Bin

2013-01-01

The axial stress and deformation of high temperature high pressure deviated gas wells are studied. A new model is multiple nonlinear equation systems by comprehensive consideration of axial load of tubular string, internal and external fluid pressure, normal pressure between the tubular and well wall, and friction and viscous friction of fluid flowing. The varied temperature and pressure fields were researched by the coupled differential equations concerning mass, momentum, and energy equations instead of traditional methods. The axial load, the normal pressure, the friction, and four deformation lengths of tubular string are got ten by means of the dimensionless iterative interpolation algorithm. The basic data of the X Well, 1300 meters deep, are used for case history calculations. The results and some useful conclusions can provide technical reliability in the process of designing well testing in oil or gas wells. PMID:24163623

Numerical solutions of Navier-Stokes equations for compressible turbulent two/three dimensional flows in terminal shock region of an inlet/diffuser

NASA Technical Reports Server (NTRS)

Liu, N. S.; Shamroth, S. J.; Mcdonald, H.

1983-01-01

The multidimensional ensemble averaged compressible time dependent Navier Stokes equations in conjunction with mixing length turbulence model and shock capturing technique were used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations were carried out: (1) 2 D, steady, subsonic; (2) 2 D, steady, transonic with normal shock; (3) 2 D, steady, supersonic with terminal shock; (4) 2 D, transient process of shock development and (5) 3 D, steady, transonic with normal shock. The numerical results obtained for the 2 D and 3 D transonic shocked flows were compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes

DOE PAGES

Konor, Celal S.; Randall, David A.

2018-05-08

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia–gravity modes on a midlatitude f plane.The results of our normal-modemore » analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.« less

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations - Part 2: Quasi-geostrophic Rossby modes

NASA Astrophysics Data System (ADS)

Konor, Celal S.; Randall, David A.

2018-05-01

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia-gravity modes on a midlatitude f plane.The results of our normal-mode analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.

Dirac equation on a curved surface

NASA Astrophysics Data System (ADS)

Brandt, F. T.; Sánchez-Monroy, J. A.

2016-09-01

The dynamics of Dirac particles confined to a curved surface is examined employing the thin-layer method. We perform a perturbative expansion to first-order and split the Dirac field into normal and tangential components to the surface. In contrast to the known behavior of second order equations like Schrödinger, Maxwell and Klein-Gordon, we find that there is no geometric potential for the Dirac equation on a surface. This implies that the non-relativistic limit does not commute with the thin-layer method. Although this problem can be overcome when second-order terms are retained in the perturbative expansion, this would preclude the decoupling of the normal and tangential degrees of freedom. Therefore, we propose to introduce a first-order term which rescues the non-relativistic limit and also clarifies the effect of the intrinsic and extrinsic curvatures on the dynamics of the Dirac particles.

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering Based on the Newly Developed Self-consistent RC/EMIC Waves Model by Khazanov et al. [2006

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gallagher, D. L.; Gamayunov, K.

2007-01-01

It is well known that the effects of EMIC waves on RC ion and RB electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. Therefore, realistic characteristics of EMIC waves should be properly determined by modeling the RC-EMIC waves evolution self-consistently. Such a selfconsistent model progressively has been developing by Khaznnov et al. [2002-2006]. It solves a system of two coupled kinetic equations: one equation describes the RC ion dynamics and another equation describes the energy density evolution of EMIC waves. Using this model, we present the effectiveness of relativistic electron scattering and compare our results with previous work in this area of research.

The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes

NASA Astrophysics Data System (ADS)

Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran

2018-04-01

This paper investigates the lowest-order weak Galerkin finite element method for solving the Darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles. In this approach, the pressure is approximated by constants in element interiors and on edges. The discrete weak gradients of these constant basis functions are specified in local Raviart-Thomas spaces, specifically RT0 for triangles and unmapped RT[0] for quadrilaterals. These discrete weak gradients are used to approximate the classical gradient when solving the Darcy equation. The method produces continuous normal fluxes and is locally mass-conservative, regardless of mesh quality, and has optimal order convergence in pressure, velocity, and normal flux, when the quadrilaterals are asymptotically parallelograms. Implementation is straightforward and results in symmetric positive-definite discrete linear systems. We present numerical experiments and comparisons with other existing methods.

Plasma Modes

NASA Astrophysics Data System (ADS)

Dubin, D. H. E.

This chapter explores several aspects of the linear electrostatic normal modes of oscillation for a single-species non-neutral plasma in a Penning trap. Linearized fluid equations of motion are developed, assuming the plasma is cold but collisionless, which allow derivation of the cold plasma dielectric tensor and the electrostatic wave equation. Upper hybrid and magnetized plasma waves in an infinite uniform plasma are described. The effect of the plasma surface in a bounded plasma system is considered, and the properties of surface plasma waves are characterized. The normal modes of a cylindrical plasma column are discussed, and finally, modes of spheroidal plasmas, and finite temperature effects on the modes, are briefly described.

Rigorous Combination of GNSS and VLBI: How it Improves Earth Orientation and Reference Frames

NASA Astrophysics Data System (ADS)

Lambert, S. B.; Richard, J. Y.; Bizouard, C.; Becker, O.

2017-12-01

Current reference series (C04) of the International Earth Rotation and Reference Systems Service (IERS) are produced by a weighted combination of Earth orientation parameters (EOP) time series built up by combination centers of each technique (VLBI, GNSS, Laser ranging, DORIS). In the future, we plan to derive EOP from a rigorous combination of the normal equation systems of the four techniques.We present here the results of a rigorous combination of VLBI and GNSS pre-reduced, constraint-free, normal equations with the DYNAMO geodetic analysis software package developed and maintained by the French GRGS (Groupe de Recherche en GeÌodeÌsie Spatiale). The used normal equations are those produced separately by the IVS and IGS combination centers to which we apply our own minimal constraints.We address the usefulness of such a method with respect to the classical, a posteriori, combination method, and we show whether EOP determinations are improved.Especially, we implement external validations of the EOP series based on comparison with geophysical excitation and examination of the covariance matrices. Finally, we address the potential of the technique for the next generation celestial reference frames, which are currently determined by VLBI only.

An improved algorithm for the determination of the system paramters of a visual binary by least squares

NASA Astrophysics Data System (ADS)

Xu, Yu-Lin

The problem of computing the orbit of a visual binary from a set of observed positions is reconsidered. It is a least squares adjustment problem, if the observational errors follow a bias-free multivariate Gaussian distribution and the covariance matrix of the observations is assumed to be known. The condition equations are constructed to satisfy both the conic section equation and the area theorem, which are nonlinear in both the observations and the adjustment parameters. The traditional least squares algorithm, which employs condition equations that are solved with respect to the uncorrelated observations and either linear in the adjustment parameters or linearized by developing them in Taylor series by first-order approximation, is inadequate in our orbit problem. D.C. Brown proposed an algorithm solving a more general least squares adjustment problem in which the scalar residual function, however, is still constructed by first-order approximation. Not long ago, a completely general solution was published by W.H Jefferys, who proposed a rigorous adjustment algorithm for models in which the observations appear nonlinearly in the condition equations and may be correlated, and in which construction of the normal equations and the residual function involves no approximation. This method was successfully applied in our problem. The normal equations were first solved by Newton's scheme. Practical examples show that this converges fast if the observational errors are sufficiently small and the initial approximate solution is sufficiently accurate, and that it fails otherwise. Newton's method was modified to yield a definitive solution in the case the normal approach fails, by combination with the method of steepest descent and other sophisticated algorithms. Practical examples show that the modified Newton scheme can always lead to a final solution. The weighting of observations, the orthogonal parameters and the efficiency of a set of adjustment parameters are also considered. The definition of efficiency is revised.

Integrated design and manufacturing for the high speed civil transport (a combined aerodynamics/propulsion optimization study)

NASA Technical Reports Server (NTRS)

Baecher, Juergen; Bandte, Oliver; DeLaurentis, Dan; Lewis, Kemper; Sicilia, Jose; Soboleski, Craig

1995-01-01

This report documents the efforts of a Georgia Tech High Speed Civil Transport (HSCT) aerospace student design team in completing a design methodology demonstration under NASA's Advanced Design Program (ADP). Aerodynamic and propulsion analyses are integrated into the synthesis code FLOPS in order to improve its prediction accuracy. Executing the integrated product and process development (IPPD) methodology proposed at the Aerospace Systems Design Laboratory (ASDL), an improved sizing process is described followed by a combined aero-propulsion optimization, where the objective function, average yield per revenue passenger mile ($/RPM), is constrained by flight stability, noise, approach speed, and field length restrictions. Primary goals include successful demonstration of the application of the response surface methodolgy (RSM) to parameter design, introduction to higher fidelity disciplinary analysis than normally feasible at the conceptual and early preliminary level, and investigations of relationships between aerodynamic and propulsion design parameters and their effect on the objective function, $/RPM. A unique approach to aircraft synthesis is developed in which statistical methods, specifically design of experiments and the RSM, are used to more efficiently search the design space for optimum configurations. In particular, two uses of these techniques are demonstrated. First, response model equations are formed which represent complex analysis in the form of a regression polynomial. Next, a second regression equation is constructed, not for modeling purposes, but instead for the purpose of optimization at the system level. Such an optimization problem with the given tools normally would be difficult due to the need for hard connections between the various complex codes involved. The statistical methodology presents an alternative and is demonstrated via an example of aerodynamic modeling and planform optimization for a HSCT.

Extended symmetry analysis of generalized Burgers equations

NASA Astrophysics Data System (ADS)

Pocheketa, Oleksandr A.; Popovych, Roman O.

2017-10-01

Using enhanced classification techniques, we carry out the extended symmetry analysis of the class of generalized Burgers equations of the form ut + uux + f(t, x)uxx = 0. This enhances all the previous results on symmetries of these equations and includes the description of admissible transformations, Lie symmetries, Lie and nonclassical reductions, hidden symmetries, conservation laws, potential admissible transformations, and potential symmetries. The study is based on the fact that the class is normalized, and its equivalence group is finite-dimensional.

Exact dark soliton solutions for a family of N coupled nonlinear Schrödinger equations in optical fiber media.

PubMed

Nakkeeran, K

2001-10-01

We consider a family of N coupled nonlinear Schrödinger equations which govern the simultaneous propagation of N fields in the normal dispersion regime of an optical fiber with various important physical effects. The linear eigenvalue problem associated with the integrable form of all the equations is constructed with the help of the Ablowitz-Kaup-Newell-Segur method. Using the Hirota bilinear method, exact dark soliton solutions are explicitly derived.

Transactions of the Army Conference on Applied Mathematics and Computing (4th) Held in Ithaca, New York on 27-31 May 1986

DTIC Science & Technology

1987-02-01

positive, nonincreaslng on 0 < t < *, and m decays rapidly at Infinity. Stronger power singularities at zero (a < 0) are also...considered. In this case the wavenumber appears to power four in the differential equation, the Orr-Sommerfeld equation, and to power five in the wall...normal mode, appears to power four in the differential equation. However it is this problem that is physically realistic in which fixed real frequency

Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

NASA Astrophysics Data System (ADS)

Chang, Jing; Gao, Yixian; Li, Yong

2015-05-01

Consider the one dimensional nonlinear beam equation utt + uxxxx + mu + u3 = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form.

Model study of ATP and ADP buffering, transport of Ca(2+) and Mg(2+), and regulation of ion pumps in ventricular myocyte

NASA Technical Reports Server (NTRS)

Michailova, A.; McCulloch, A.

2001-01-01

We extended the model of the ventricular myocyte by Winslow et al. (Circ. Res 1999, 84:571-586) by incorporating equations for Ca(2+) and Mg(2+) buffering and transport by ATP and ADP and equations for MgATP regulation of ion transporters (Na(+)-K(+) pump, sarcolemmal and sarcoplasmic Ca(2+) pumps). The results indicate that, under normal conditions, Ca(2+) binding by low-affinity ATP and diffusion of CaATP may affect the amplitude and time course of intracellular Ca(2+) signals. The model also suggests that a fall in ATP/ADP ratio significantly reduces sarcoplasmic Ca(2+) content, increases diastolic Ca(2+), lowers systolic Ca(2+), increases Ca(2+) influx through L-type channels, and decreases the efficiency of the Na(+)/Ca(2+) exchanger in extruding Ca(2+) during periodic voltage-clamp stimulation. The analysis suggests that the most important reason for these changes during metabolic inhibition is the down-regulation of the sarcoplasmic Ca(2+)-ATPase pump by reduced diastolic MgATP levels. High Ca(2+) concentrations developed near the membrane might have a greater influence on Mg(2+), ATP, and ADP concentrations than that of the lower Ca(2+) concentrations in the bulk myoplasm. The model predictions are in general agreement with experimental observations measured under normal and pathological conditions.

Comparison of five equations for estimating resting energy expenditure in Chinese young, normal weight healthy adults

PubMed Central

2012-01-01

Background Most resting energy expenditure (REE) predictive equations for adults were derived from research conducted in western populations; whether they can also be used in Chinese young people is still unclear. Therefore, we conducted this study to determine the best REE predictive equation in Chinese normal weight young adults. Methods Forty-three (21 male, 22 female) healthy college students between the age of 18 and 25 years were recruited. REE was measured by the indirect calorimetry (IC) method. Harris-Benedict, World Health Organization (WHO), Owen, Mifflin and Liu’s equations were used to predictREE (REEe). REEe that was within 10% of measured REE (REEm) was defined as accurate. Student’s t test, Wilcoxon Signed Ranks Test, McNemar Test and the Bland-Altman method were used for data analysis. Results REEm was significantly lower (P < 0.05 or P < 0.01) than REEe from equations, except for Liu’s, Liu’s-s, Owen, Owen-s and Mifflin in men and Liu’s and Owen in women. REEe calculated by ideal body weight was significantly higher than REEe calculated by current body weight ( P < 0.01), the only exception being Harris-Benedict equation in men. Bland-Altman analysis showed that the Owen equation with current body weight generated the least bias. The biases of REEe from Owen with ideal body weight and Mifflin with both current and ideal weights were also lower. Conclusions Liu’s, Owen, and Mifflin equations are appropriate for the prediction of REE in young Chinese adults. However, the use of ideal body weight did not increase the accuracy of REEe. PMID:22937737

A new formula for normal tissue complication probability (NTCP) as a function of equivalent uniform dose (EUD).

PubMed

Luxton, Gary; Keall, Paul J; King, Christopher R

2008-01-07

To facilitate the use of biological outcome modeling for treatment planning, an exponential function is introduced as a simpler equivalent to the Lyman formula for calculating normal tissue complication probability (NTCP). The single parameter of the exponential function is chosen to reproduce the Lyman calculation to within approximately 0.3%, and thus enable easy conversion of data contained in empirical fits of Lyman parameters for organs at risk (OARs). Organ parameters for the new formula are given in terms of Lyman model m and TD(50), and conversely m and TD(50) are expressed in terms of the parameters of the new equation. The role of the Lyman volume-effect parameter n is unchanged from its role in the Lyman model. For a non-homogeneously irradiated OAR, an equation relates d(ref), n, v(eff) and the Niemierko equivalent uniform dose (EUD), where d(ref) and v(eff) are the reference dose and effective fractional volume of the Kutcher-Burman reduction algorithm (i.e. the LKB model). It follows in the LKB model that uniform EUD irradiation of an OAR results in the same NTCP as the original non-homogeneous distribution. The NTCP equation is therefore represented as a function of EUD. The inverse equation expresses EUD as a function of NTCP and is used to generate a table of EUD versus normal tissue complication probability for the Emami-Burman parameter fits as well as for OAR parameter sets from more recent data.

A Comparison of Normal and Elliptical Estimation Methods in Structural Equation Models.

ERIC Educational Resources Information Center

Schumacker, Randall E.; Cheevatanarak, Suchittra

Monte Carlo simulation compared chi-square statistics, parameter estimates, and root mean square error of approximation values using normal and elliptical estimation methods. Three research conditions were imposed on the simulated data: sample size, population contamination percent, and kurtosis. A Bentler-Weeks structural model established the…

Relative Performance of Rescaling and Resampling Approaches to Model Chi Square and Parameter Standard Error Estimation in Structural Equation Modeling.

ERIC Educational Resources Information Center

Nevitt, Johnathan; Hancock, Gregory R.

Though common structural equation modeling (SEM) methods are predicated upon the assumption of multivariate normality, applied researchers often find themselves with data clearly violating this assumption and without sufficient sample size to use distribution-free estimation methods. Fortunately, promising alternatives are being integrated into…

Shock-wave structure based on the Navier-Stokes-Fourier equations.

PubMed

Uribe, F J; Velasco, R M

2018-04-01

We use the Navier-Stokes-Fourier constitutive equations to study plane shock waves in dilute gases. It is shown that the experimental information on the normalized density profiles can be fit by using the so-called soft sphere model, in which the viscosity and thermal conductivity are proportional to a power of the temperature.

Shock-wave structure based on the Navier-Stokes-Fourier equations

NASA Astrophysics Data System (ADS)

Uribe, F. J.; Velasco, R. M.

2018-04-01

We use the Navier-Stokes-Fourier constitutive equations to study plane shock waves in dilute gases. It is shown that the experimental information on the normalized density profiles can be fit by using the so-called soft sphere model, in which the viscosity and thermal conductivity are proportional to a power of the temperature.

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

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Hayashi, Kentaro

2010-01-01

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

NASA Instrument Cost/Schedule Model

NASA Technical Reports Server (NTRS)

Habib-Agahi, Hamid; Mrozinski, Joe; Fox, George

2011-01-01

NASA's Office of Independent Program and Cost Evaluation (IPCE) has established a number of initiatives to improve its cost and schedule estimating capabilities. 12One of these initiatives has resulted in the JPL developed NASA Instrument Cost Model. NICM is a cost and schedule estimator that contains: A system level cost estimation tool; a subsystem level cost estimation tool; a database of cost and technical parameters of over 140 previously flown remote sensing and in-situ instruments; a schedule estimator; a set of rules to estimate cost and schedule by life cycle phases (B/C/D); and a novel tool for developing joint probability distributions for cost and schedule risk (Joint Confidence Level (JCL)). This paper describes the development and use of NICM, including the data normalization processes, data mining methods (cluster analysis, principal components analysis, regression analysis and bootstrap cross validation), the estimating equations themselves and a demonstration of the NICM tool suite.

An improved viscid/inviscid interaction procedure for transonic flow over airfoils

NASA Technical Reports Server (NTRS)

Melnik, R. E.; Chow, R. R.; Mead, H. R.; Jameson, A.

1985-01-01

A new interacting boundary layer approach for computing the viscous transonic flow over airfoils is described. The theory includes a complete treatment of viscous interaction effects induced by the wake and accounts for normal pressure gradient effects across the boundary layer near trailing edges. The method is based on systematic expansions of the full Reynolds equation of turbulent flow in the limit of Reynolds numbers, Reynolds infinity. Procedures are developed for incorporating the local trailing edge solution into the numerical solution of the coupled full potential and integral boundary layer equations. Although the theory is strictly applicable to airfoils with cusped or nearly cusped trailing edges and to turbulent boundary layers that remain fully attached to the airfoil surface, the method was successfully applied to more general airfoils and to flows with small separation zones. Comparisons of theoretical solutions with wind tunnel data indicate the present method can accurately predict the section characteristics of airfoils including the absolute levels of drag.

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

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

Sheehan, Daniel M.

2006-01-15

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

TOPEX/El Nino Watch - October 23, 1997

NASA Technical Reports Server (NTRS)

1997-01-01

This image of the Pacific Ocean was produced using sea surface height measurements taken by the U.S./French TOPEX/POSEIDON satellite. The image shows sea surface height relative to normal ocean conditions on Oct. 23, 1997 as the warm water associated with El Nino (in white) spreads northward along the entire coast of North America from the equator all the way to Alaska. The warm water pool associated with the El Nino has returned to the volume it was in mid-September after dropping to a temporary low at the beginning of October. The sea surface elevation just north of the El Nino warm pool continues to drop (purple area), enhancing the eastward flowing North Equatorial Counter Current. The intensification of this current is another tell-tale sign of the El Nino phenomenon. This flow contributes to the rise in sea level along the western coasts of the Americas that will progress towards both the north and south poles over the next several months. The white and red areas indicate unusual patterns of heat storage; in the white areas, the sea surface is between 14 and 32 centimeters (6 to 13 inches) above normal; in the red areas, it's about 10 centimeters (4 inches) above normal. The surface area covered by the warm water mass is about one and one-half times the size of the continental United States. The added amount of oceanic warm water near the Americas, with a temperature between 21-30 degrees Celsius (70- 85 degrees Fahrenheit), is about 30 times the volume of water in all the U.S. Great Lakes combined. The green areas indicate normal conditions, while purple (the western Pacific) means at least 18 centimeters (7 inches) below normal sea level.

The El Nino phenomenon is thought to be triggered when the steady westward blowing trade winds weaken and even reverse direction. This change in the winds allows a large mass of warm water (the red and white area) that is normally located near Australia to move eastward along the equator until it reaches the coast of South America. The displacement of so much warm water affects evaporation, where rain clouds form and, consequently, alters the typical atmospheric jet stream patterns around the world. Using these global data, limited regional measurements from buoys and ships, and a forecasting model of the ocean-atmosphere system, the National Centers for Environmental Prediction (NCEP) of the National Oceanic and Atmospheric Administration, (NOAA), has issued an advisory indicating the presence of a strong El Nino condition throughout the winter.

For more information, please visit the TOPEX/Poseidon project web page at http://topex-www.jpl.nasa.gov/

Determination of stress intensity factors for interface cracks under mixed-mode loading

NASA Technical Reports Server (NTRS)

Naik, Rajiv A.; Crews, John H., Jr.

1992-01-01

A simple technique was developed using conventional finite element analysis to determine stress intensity factors, K1 and K2, for interface cracks under mixed-mode loading. This technique involves the calculation of crack tip stresses using non-singular finite elements. These stresses are then combined and used in a linear regression procedure to calculate K1 and K2. The technique was demonstrated by calculating three different bimaterial combinations. For the normal loading case, the K's were within 2.6 percent of an exact solution. The normalized K's under shear loading were shown to be related to the normalized K's under normal loading. Based on these relations, a simple equation was derived for calculating K1 and K2 for mixed-mode loading from knowledge of the K's under normal loading. The equation was verified by computing the K's for a mixed-mode case with equal and normal shear loading. The correlation between exact and finite element solutions is within 3.7 percent. This study provides a simple procedure to compute K2/K1 ratio which has been used to characterize the stress state at the crack tip for various combinations of materials and loadings. Tests conducted over a range of K2/K1 ratios could be used to fully characterize interface fracture toughness.

Purfication kinetics of beryllium during vacuum induction melting

NASA Technical Reports Server (NTRS)

Mukherjee, J. L.; Gupta, K. P.; Li, C. H.

1972-01-01

The kinetics of evaporation in binary alloys were quantitatively treated. The formalism so developed works well for several systems studied. The kinetics of purification of beryllium was studied through evaporation data actually acquired during vacuum induction melting. Normal evaporation equations are shown to be generally valid and useful for understanding the kinetics of beryllium purification. The normal evaporation analysis has been extended to cover cases of limited liquid diffusion. It was shown that under steady-state evaporation, the solute concentration near the surface may be up to six orders of magnitude different from the bulk concentration. Corrections for limited liquid diffusion are definitely needed for the highly evaporative solute elements, such as Zn, Mg, and Na, for which the computed evaporation times are improved by five orders of magnitude. The commonly observed logarithmic relation between evaporation time and final concentration further supports the validity of the normal evaporation equations.

Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics.

PubMed

Glavatskiy, K S

2015-05-28

We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such that there exists an "integral of evolution" which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.

Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics

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

Glavatskiy, K. S.

We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called “mirror-image” system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such thatmore » there exists an “integral of evolution” which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.« less

Solution of the surface Euler equations for accurate three-dimensional boundary-layer analysis of aerodynamic configurations

NASA Technical Reports Server (NTRS)

Iyer, V.; Harris, J. E.

1987-01-01

The three-dimensional boundary-layer equations in the limit as the normal coordinate tends to infinity are called the surface Euler equations. The present paper describes an accurate method for generating edge conditions for three-dimensional boundary-layer codes using these equations. The inviscid pressure distribution is first interpolated to the boundary-layer grid. The surface Euler equations are then solved with this pressure field and a prescribed set of initial and boundary conditions to yield the velocities along the two surface coordinate directions. Results for typical wing and fuselage geometries are presented. The smoothness and accuracy of the edge conditions obtained are found to be superior to the conventional interpolation procedures.

No evidence for a role of the serotonin 4 receptor in five-factor personality traits: A positron emission tomography brain study.

PubMed

Stenbæk, Dea Siggaard; Dam, Vibeke Høyrup; Fisher, Patrick MacDonald; Hansen, Nanna; Hjordt, Liv Vadskjær; Frokjaer, Vibe Gedsoe

2017-01-01

Serotonin (5-HT) brain architecture appears to be implicated in normal personality traits as supported by genetic associations and studies using molecular brain imaging. However, so far, no studies have addressed potential contributions to variation in normal personality traits from in vivo serotonin 4 receptor (5-HT4R) brain availability, which has recently become possible to image with Positron Emission Tomography (PET). This is particularly relevant since availability of 5-HT4R has been shown to adapt to synaptic levels of 5-HT and thus offers information about serotonergic tone in the healthy brain. In 69 healthy participants (18 females), the associations between personality traits assessed with the five-factor NEO Personality Inventory-Revised (NEO PI-R) and regional cerebral 5-HT4R binding in neocortex, amygdala, hippocampus, and anterior cingulate cortex (ACC) were investigated using linear regression models. The associations between each of the five personality traits and a latent variable construct of global 5-HT4R levels were also evaluated using latent variable structural equation models. We found no significant associations between the five NEO personality traits and regional 5-HT4R binding (all p-values > .17) or the latent construct of global 5-HT4R levels (all p-values > .37). Our findings indicate that NEO personality traits and 5-HT4R are not related in healthy participants. Under the assumption that global 5-HT4R levels index 5-HT tone, our data also suggest that 5-HT tone per se is not directly implicated in normal personality traits.

No evidence for a role of the serotonin 4 receptor in five-factor personality traits: A positron emission tomography brain study

PubMed Central

Fisher, Patrick MacDonald; Hansen, Nanna; Hjordt, Liv Vadskjær; Frokjaer, Vibe Gedsoe

2017-01-01

Serotonin (5-HT) brain architecture appears to be implicated in normal personality traits as supported by genetic associations and studies using molecular brain imaging. However, so far, no studies have addressed potential contributions to variation in normal personality traits from in vivo serotonin 4 receptor (5-HT4R) brain availability, which has recently become possible to image with Positron Emission Tomography (PET). This is particularly relevant since availability of 5-HT4R has been shown to adapt to synaptic levels of 5-HT and thus offers information about serotonergic tone in the healthy brain. In 69 healthy participants (18 females), the associations between personality traits assessed with the five-factor NEO Personality Inventory-Revised (NEO PI-R) and regional cerebral 5-HT4R binding in neocortex, amygdala, hippocampus, and anterior cingulate cortex (ACC) were investigated using linear regression models. The associations between each of the five personality traits and a latent variable construct of global 5-HT4R levels were also evaluated using latent variable structural equation models. We found no significant associations between the five NEO personality traits and regional 5-HT4R binding (all p-values > .17) or the latent construct of global 5-HT4R levels (all p-values > .37). Our findings indicate that NEO personality traits and 5-HT4R are not related in healthy participants. Under the assumption that global 5-HT4R levels index 5-HT tone, our data also suggest that 5-HT tone per se is not directly implicated in normal personality traits. PMID:28880910

Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential

NASA Technical Reports Server (NTRS)

Campbell, Joel

2009-01-01

The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.

[Comparison of three stand-level biomass estimation methods].

PubMed

Dong, Li Hu; Li, Feng Ri

2016-12-01

At present, the forest biomass methods of regional scale attract most of attention of the researchers, and developing the stand-level biomass model is popular. Based on the forestry inventory data of larch plantation (Larix olgensis) in Jilin Province, we used non-linear seemly unrelated regression (NSUR) to estimate the parameters in two additive system of stand-level biomass equations, i.e., stand-level biomass equations including the stand variables and stand biomass equations including the biomass expansion factor (i.e., Model system 1 and Model system 2), listed the constant biomass expansion factor for larch plantation and compared the prediction accuracy of three stand-level biomass estimation methods. The results indicated that for two additive system of biomass equations, the adjusted coefficient of determination (R a 2 ) of the total and stem equations was more than 0.95, the root mean squared error (RMSE), the mean prediction error (MPE) and the mean absolute error (MAE) were smaller. The branch and foliage biomass equations were worse than total and stem biomass equations, and the adjusted coefficient of determination (R a 2 ) was less than 0.95. The prediction accuracy of a constant biomass expansion factor was relatively lower than the prediction accuracy of Model system 1 and Model system 2. Overall, although stand-level biomass equation including the biomass expansion factor belonged to the volume-derived biomass estimation method, and was different from the stand biomass equations including stand variables in essence, but the obtained prediction accuracy of the two methods was similar. The constant biomass expansion factor had the lower prediction accuracy, and was inappropriate. In addition, in order to make the model parameter estimation more effective, the established stand-level biomass equations should consider the additivity in a system of all tree component biomass and total biomass equations.

Biomechanical basis of choosing the rational mass and its distribution throughout the lower limb prosthesis segments.

PubMed

Farber, B S; Moreinis, I Sh

1995-11-01

A solution for finding a rational distribution of mass in lower limb prostheses has been considered based on the formal premise favoring the identification of the movements of a prosthetic and an intact leg. For the purpose of simplicity, and analysis has been carried out for only the swing phase, the data about the properties of moving segments being determined without integrating differential equations of motion. At the formation of equations of motion, an assumption that body segments are absolutely rigid and have constant moments of inertia and locations of the center of mass was taken into consideration. Based on independent proportions formed of combinations of the coefficients of equations of motion, a system of three equations has been formulated and solved in relation to the mass values sought: a static radius and a radius of inertia of the prosthesis complex link "shin + foot + footwear." From the six unknowns included in the equations, three values are chosen as mean values determined empirically. The solution of obtained equations results in the following conclusions: the parameters of the mass distribution in a "shin + foot + footwear" complex link depend on the amputation level and the patient's mass. These data, reported in appropriate tables, may be used in prosthetics practice. Recommendations have also been presented with regard to a prosthesic mass relative to the age of the person with amputation and a method of a balancing of prostheses aimed at the achievement of a rational distribution of masses. The analysis of obtained equations has also allowed us to make recommendations about the artificial foot mass. It has been concluded that a reasonable desire to reduce the mass of the prosthetic segments is not an end in itself, but is only the means of a rational distribution by means of balancing. It has been proved that rational prosthetic fitting results in decreased energy costs and overloads are decreased and a normalized gait.

Partial differential equations of 3D boundary layer and their numerical solutions in turbomachinery

NASA Astrophysics Data System (ADS)

Zhang, Guoqing; Hua, Yaonan; Wu, Chung-Hua

1991-08-01

This paper studies the 3D boundary layer equations (3DBLE) and their numerical solutions in turbomachinery: (1) the general form of 3DBLE in turbomachines with rotational and curvature effects are derived under the semiorthogonal coordinate system, in which the normal pressure gradient is not equal to zero; (2) the method of solution of the 3DBLE is discussed; (3) the 3D boundary layers on the rotating blade surface, IGV endwall, rotor endwall (with a relatively moving boundary) are numerically solved, and the predicted data correlates well with the measured data; and (4) the comparison is made between the numerical results of 3DBLE with and without normal pressure gradient.

Features of self-organized plasma physics in tokamaks

NASA Astrophysics Data System (ADS)

Razumova, K. A.

2018-01-01

The history of investigations the role of self-organization processes in tokamak plasma confinement is presented. It was experimentally shown that the normalized pressure profile is the same for different tokamaks. Instead of the conventional Fick equation, where the thermal flux is proportional to a pressure gradient, processes in the plasma are well described by the Dyabilanin’s energy balance equation, in which the heat flux is proportional to the difference of normalized gradients for self-consistent and real pressure profiles. The transport coefficient depends on the values of heat flux, which compensates distortion of the pressure profile with external impacts. Radiative cooling of the plasma edge decreases the heat flux and improves the confinement.

Some aspects of the stability of the plane deformation mode of filaments of finite stiffness beyond the elasticity limits

NASA Astrophysics Data System (ADS)

Shimanovskii, A. V.

A method for calculating the plane bending of elastic-plastic filaments of finite stiffness is proposed on the basis of plastic flow theory. The problem considered is shown to reduce to relations similar to Kirchhoff equations for elastic work. Expressions are obtained for determining the normalized stiffness characteristics for the cross section of a filament with plastic regions containing beam theory equations as a particular case. A study is made of the effect of the plastic region size on the position of the elastic deformation-unloading interface and on the normalized stiffness of the filament cross section. Calculation results are presented in graphic form.

CICATRIZATION OF WOUNDS

PubMed Central

Du Noüy, P. Lecomte

1916-01-01

The cicatrization of sterile wounds may be studied in the same way as an ordinary physicochemical phenomenon. It is possible, therefore, to express the law of cicatrization by a mathematical equation as soon as an accurate measure of the wound can be obtained. By means of the equation, a curve is obtained which represents the theoretical evolution of the cicatrization of a wound. This curve, being an expression of what should happen on a normal wound, healing aseptically, on a normal man, is a daily point of comparison to what appears actually on the observed wound, and allows one to study accurately the fluctuations of cicatrization on a given individual, and the action of different dressings and antiseptic substances PMID:19868053

Assessment and Calibration of Terrestrial Water Storage in North America with GRACE Level-1B Inter-satellite Residuals

NASA Astrophysics Data System (ADS)

Loomis, B.; Luthcke, S. B.

2016-12-01

The global time-variable gravity products from GRACE continue to provide unique and important measurements of vertically integrated terrestrial water storage (TWS). Despite substantial improvements in recent years to the quality of the GRACE solutions and analysis techniques, significant disagreements can still exist between various approaches to compute basin scale TWS. Applying the GRACE spherical harmonic solutions to TWS analysis requires the selection, design, and implementation of one of a wide variety of available filters. It is common to then estimate and apply a set of scale factors to these filtered solutions in an attempt to restore lost signal. The advent of global mascon solutions, such as those produced by our group at NASA GSFC, are an important advancement in time-variable gravity estimation. This method applies data-driven regularization at the normal equation level, resulting in improved estimates of regional TWS. Though mascons are a valuable product, the design of the constraint matrix, the global minimization of observation residuals, and the arc-specific parameters, all introduce the possibility that localized basin scale signals are not perfectly recovered. The precise inter-satellite ranging instrument provides the primary observation set for the GRACE gravity solutions. Recently, we have developed an approach to analyze and calibrate basin scale TWS estimates directly from the inter-satellite observation residuals. To summarize, we compute the range-acceleration residuals for two different forward models by executing separate runs of our Level-1B processing system. We then quantify the linear relationship that exists between the modeled mass and the residual differences, defining a simple differential correction procedure that is applied to the modeled signals. This new calibration procedure does not require the computationally expensive formation and inversion of normal equations, and it eliminates any influence the solution technique may have on the determined regional time series of TWS. We apply this calibration approach to sixteen drainage basins that cover North America and present new measurements of TWS determined directly from the Level-1B range-acceleration residuals. Lastly, we compare these new solutions to other GRACE solutions and independent datasets.

User Guide for Compressible Flow Toolbox Version 2.1 for Use With MATLAB(Registered Trademark); Version 7

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

This report provides a user guide for the Compressible Flow Toolbox, a collection of algorithms that solve almost 300 linear and nonlinear classical compressible flow relations. The algorithms, implemented in the popular MATLAB programming language, are useful for analysis of one-dimensional steady flow with constant entropy, friction, heat transfer, or shock discontinuities. The solutions do not include any gas dissociative effects. The toolbox also contains functions for comparing and validating the equation-solving algorithms against solutions previously published in the open literature. The classical equations solved by the Compressible Flow Toolbox are: isentropic-flow equations, Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section.), normal-shock equations, oblique-shock equations, and Prandtl-Meyer expansion equations. At the time this report was published, the Compressible Flow Toolbox was available without cost from the NASA Software Repository.

The numerical evaluation of maximum-likelihood estimates of the parameters for a mixture of normal distributions from partially identified samples

NASA Technical Reports Server (NTRS)

Walker, H. F.

1976-01-01

Likelihood equations determined by the two types of samples which are necessary conditions for a maximum-likelihood estimate were considered. These equations suggest certain successive approximations iterative procedures for obtaining maximum likelihood estimates. The procedures, which are generalized steepest ascent (deflected gradient) procedures, contain those of Hosmer as a special case.

Maximum Likelihood Methods in Treating Outliers and Symmetrically Heavy-Tailed Distributions for Nonlinear Structural Equation Models with Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum; Xia, Ye-Mao

2006-01-01

By means of more than a dozen user friendly packages, structural equation models (SEMs) are widely used in behavioral, education, social, and psychological research. As the underlying theory and methods in these packages are vulnerable to outliers and distributions with longer-than-normal tails, a fundamental problem in the field is the…

The Locus Equation as an Index of Coarticulation in Syllables Produced by Speakers with Profound Hearing Loss

ERIC Educational Resources Information Center

McCaffrey Morrison, Helen

2008-01-01

Locus equations (LEs) were derived from consonant-vowel-consonant (CVC) syllables produced by four speakers with profound hearing loss. Group data indicated that LE functions obtained for the separate CVC productions initiated by /b/, /d/, and /g/ were less well-separated in acoustic space than those obtained from speakers with normal hearing. A…

Reliable and More Powerful Methods for Power Analysis in Structural Equation Modeling

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Zhang, Zhiyong; Zhao, Yanyun

2017-01-01

The normal-distribution-based likelihood ratio statistic T[subscript ml] = nF[subscript ml] is widely used for power analysis in structural Equation modeling (SEM). In such an analysis, power and sample size are computed by assuming that T[subscript ml] follows a central chi-square distribution under H[subscript 0] and a noncentral chi-square…

Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion

PubMed Central

Grimshaw, Roger; Stepanyants, Yury; Alias, Azwani

2016-01-01

It is well known that the Ostrovsky equation with normal dispersion does not support steady solitary waves. An initial Korteweg–de Vries solitary wave decays adiabatically through the radiation of long waves and is eventually replaced by an envelope solitary wave whose carrier wave and envelope move with different velocities (phase and group velocities correspondingly). Here, we examine the same initial condition for the Ostrovsky equation with anomalous dispersion, when the wave frequency increases with wavenumber in the limit of very short waves. The essential difference is that now there exists a steady solitary wave solution (Ostrovsky soliton), which in the small-amplitude limit can be described asymptotically through the solitary wave solution of a nonlinear Schrödinger equation, based at that wavenumber where the phase and group velocities coincide. Long-time numerical simulations show that the emergence of this steady envelope solitary wave is a very robust feature. The initial Korteweg–de Vries solitary wave transforms rapidly to this envelope solitary wave in a seemingly non-adiabatic manner. The amplitude of the Ostrovsky soliton strongly correlates with the initial Korteweg–de Vries solitary wave. PMID:26997887

Reference breast temperature: proposal of an equation

PubMed Central

de Souza, Gladis Aparecida Galindo Reisemberger; Brioschi, Marcos Leal; Vargas, José Viriato Coelho; Morais, Keli Cristiane Correia; Dalmaso, Carlos; Neves, Eduardo Borba

2015-01-01

ABSTRACT Objective To develop an equation to estimate the breast reference temperature according to the variation of room and core body temperatures. Methods Four asymptomatic women were evaluated for three consecutive menstrual cycles. Using thermography, the temperature of breasts and eyes was measured as indirect reference of core body and room temperatures. To analyze the thermal behavior of the breasts during the cycle, the core body and room temperatures were normalized by means of a mathematical equation. Results We performed 180 observations and the core temperature had the highest correlation with the breast temperature, followed by room temperature. The proposed prediction model could explain 45.3% of the breast temperature variation, with variable room temperature variable; it can be accepted as a way to estimate the reference breast temperature at different room temperatures. Conclusion The average breast temperature in healthy women had a direct relation with the core and room temperature and can be estimated mathematically. It is suggested that an equation could be used in clinical practice to estimate the normal breast reference temperature in young women, regardless of the day of the cycle, therefore assisting in evaluation of anatomical studies. PMID:26761549

Structural Equation Analysis of the Wechsler Adult Intelligence Scale-Revised in a Normal Elderly Sample.

ERIC Educational Resources Information Center

Burton, D. Bradley; And Others

1994-01-01

A maximum-likelihood confirmatory factor analysis was performed by applying LISREL VII to the Wechsler Adult Intelligence Scale-Revised results of a normal elderly sample of 225 adults. Results indicate that a three-factor model fits best across all sample combinations. A mild gender effect is discussed. (SLD)

Normal versus Noncentral Chi-Square Asymptotics of Misspecified Models

ERIC Educational Resources Information Center

Chun, So Yeon; Shapiro, Alexander

2009-01-01

The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main…

A normalized model for the half-bridge series resonant converter

NASA Technical Reports Server (NTRS)

King, R.; Stuart, T. A.

1981-01-01

Closed-form steady-state equations are derived for the half-bridge series resonant converter with a rectified (dc) load. Normalized curves for various currents and voltages are then plotted as a function of the circuit parameters. Experimental results based on a 10-kHz converter are presented for comparison with the calculations.

Normal stress effects on Knudsen flow

NASA Astrophysics Data System (ADS)

Eu, Byung Chan

2018-01-01

Normal stress effects are investigated on tube flow of a single-component non-Newtonian fluid under a constant pressure gradient in a constant temperature field. The generalized hydrodynamic equations are employed, which are consistent with the laws of thermodynamics. In the cylindrical tube flow configuration, the solutions of generalized hydrodynamic equations are exactly solvable and the flow velocity is obtained in a simple one-dimensional integral quadrature. Unlike the case of flow in the absence of normal stresses, the flow develops an anomaly in that the flow in the boundary layer becomes stagnant and the thickness of such a stagnant velocity boundary layer depends on the pressure gradient, the aspect ratio of the radius to the length of the tube, and the pressure (or density and temperature) at the entrance of the tube. The volume flow rate formula through the tube is derived for the flow. It generalizes the Knudsen flow rate formula to the case of a non-Newtonian stress tensor in the presence of normal stress differences. It also reduces to the Navier-Stokes theory formula in the low shear rate limit near equilibrium.

Somigliana-Pizzetti gravity: the international gravity formula accurate to the sub-nanoGal level

NASA Astrophysics Data System (ADS)

Ardalan, A. A.; Grafarend, E. W.

2001-09-01

The Somigliana-Pizzetti gravity field (the International gravity formula), namely the gravity field of the level ellipsoid (the International Reference Ellipsoid), is derived to the sub-nanoGal accuracy level in order to fulfil the demands of modern gravimetry (absolute gravimeters, super conducting gravimeters, atomic gravimeters). Equations (53), (54) and (59) summarise Somigliana-Pizzetti gravity o({,u) as a function of Jacobi spheroidal latitude { and height u to the order ™(10m10 Gal), and o(B,H) as a function of Gauss (surface normal) ellipsoidal latitude B and height H to the order ™(10m10 Gal) as determined by GPS (`global problem solver'). Within the test area of the state of Baden-Württemberg, Somigliana-Pizzetti gravity disturbances of an average of 25.452 mGal were produced. Computer programs for an operational application of the new international gravity formula with (L,B,H) or (u,{,u) coordinate inputs to a sub-nanoGal level of accuracy are available on the Internet.

Modeling Candle Flame Behavior In Variable Gravity

NASA Technical Reports Server (NTRS)

Alsairafi, A.; Tien, J. S.; Lee, S. T.; Dietrich, D. L.; Ross, H. D.

2003-01-01

The burning of a candle, as typical non-propagating diffusion flame, has been used by a number of researchers to study the effects of electric fields on flame, spontaneous flame oscillation and flickering phenomena, and flame extinction. In normal gravity, the heat released from combustion creates buoyant convection that draws oxygen into the flame. The strength of the buoyant flow depends on the gravitational level and it is expected that the flame shape, size and candle burning rate will vary with gravity. Experimentally, there exist studies of candle burning in enhanced gravity (i.e. higher than normal earth gravity, g(sub e)), and in microgravity in drop towers and space-based facilities. There are, however, no reported experimental data on candle burning in partial gravity (g < g(sub e)). In a previous numerical model of the candle flame, buoyant forces were neglected. The treatment of momentum equation was simplified using a potential flow approximation. Although the predicted flame characteristics agreed well with the experimental results, the model cannot be extended to cases with buoyant flows. In addition, because of the use of potential flow, no-slip boundary condition is not satisfied on the wick surface. So there is some uncertainty on the accuracy of the predicted flow field. In the present modeling effort, the full Navier-Stokes momentum equations with body force term is included. This enables us to study the effect of gravity on candle flames (with zero gravity as the limiting case). In addition, we consider radiation effects in more detail by solving the radiation transfer equation. In the previous study, flame radiation is treated as a simple loss term in the energy equation. Emphasis of the present model is on the gas-phase processes. Therefore, the detailed heat and mass transfer phenomena inside the porous wick are not treated. Instead, it is assumed that a thin layer of liquid fuel coated the entire wick surface during the burning process. This is the limiting case that the mass transfer process in the wick is much faster than the evaporation process at the wick surface.

The nonlinear wave equation for higher harmonics in free-electron lasers

NASA Technical Reports Server (NTRS)

Colson, W. B.

1981-01-01

The nonlinear wave equation and self-consistent pendulum equation are generalized to describe free-electron laser operation in higher harmonics; this can significantly extend their tunable range to shorter wavelengths. The dynamics of the laser field's amplitude and phase are explored for a wide range of parameters using families of normalized gain curves applicable to both the fundamental and harmonics. The electron phase-space displays the fundamental physics driving the wave, and this picture is used to distinguish between the effects of high gain and Coulomb forces.

Numerical computation of linear instability of detonations

NASA Astrophysics Data System (ADS)

Kabanov, Dmitry; Kasimov, Aslan

2017-11-01

We propose a method to study linear stability of detonations by direct numerical computation. The linearized governing equations together with the shock-evolution equation are solved in the shock-attached frame using a high-resolution numerical algorithm. The computed results are processed by the Dynamic Mode Decomposition technique to generate dispersion relations. The method is applied to the reactive Euler equations with simple-depletion chemistry as well as more complex multistep chemistry. The results are compared with those known from normal-mode analysis. We acknowledge financial support from King Abdullah University of Science and Technology.

On the solution of integral equations with a generalized Cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

Preconditioning the Helmholtz Equation for Rigid Ducts

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1998-01-01

An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme. This scheme eliminates the large matrix storage requirements normally associated with numerical solutions to the Helmholtz equation. The solution procedure is very fast when compared to other transient and steady methods. Optimization and an error analysis of the preconditioning factors are present. For validation, the method is applied to sound propagation in a 2D semi-infinite hard wall duct.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations - Part 1: Nonhydrostatic inertia-gravity modes

NASA Astrophysics Data System (ADS)

Konor, Celal S.; Randall, David A.

2018-05-01

We have used a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the nonhydrostatic anelastic inertia-gravity modes on a midlatitude f plane. The dispersion equations are derived from the linearized anelastic equations that are discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of both horizontal grid spacing and vertical wavenumber are analyzed, and the role of nonhydrostatic effects is discussed. We also compare the results of the normal-mode analyses with numerical solutions obtained by running linearized numerical models based on the various horizontal grids. The sources and behaviors of the computational modes in the numerical simulations are also examined.Our normal-mode analyses with the Z, C, D, A, E and B grids generally confirm the conclusions of previous shallow-water studies for the cyclone-resolving scales (with low horizontal wavenumbers). We conclude that, aided by nonhydrostatic effects, the Z and C grids become overall more accurate for cloud-resolving resolutions (with high horizontal wavenumbers) than for the cyclone-resolving scales.A companion paper, Part 2, discusses the impacts of the discretization on the Rossby modes on a midlatitude β plane.

Closed system of coupling effects in generalized thermo-elastoplasticity

NASA Astrophysics Data System (ADS)

Śloderbach, Z.

2016-05-01

In this paper, the field equations of the generalized coupled thermoplasticity theory are derived using the postulates of classical thermodynamics of irreversible processses. Using the Legendre transformations two new thermodynamics potentials P and S depending upon internal thermodynamic forces Π are introduced. The most general form for all the thermodynamics potentials are assumed instead of the usually used additive form. Due to this assumption, it is possible to describe all the effects of thermomechanical couples and also the elastic-plastic coupling effects observed in such materials as rocks, soils, concretes and in some metalic materials. In this paper not only the usual postulate of existence of a dissipation qupotential (the Gyarmati postulate) is used to derive the velocity equation. The plastic flow constitutive equations have the character of non-associated flow laws even when the Gyarmati postulate is assumed. In general formulation, the plastic strain rate tensor is normal to the surface of the generalized function of plastic flow defined in the the space of internal thermodynamic forces Π but is not normal to the yield surface. However, in general formulation and after the use the Gyarmati postulate, the direction of the sum of the plastic strain rate tensor and the coupled elastic strain rate tensor is normal to the yield surface.

Trace elements in lenses of normal Wistar Kyoto rats

NASA Astrophysics Data System (ADS)

Kinoshita, Akio; Gong, Huaqing; Amemiya, Tsugio; Takaya, Kenichi; Tozu, Miyako; Ohashi, Yoshiharu

2003-01-01

Chemical analysis of the element and organic substance at the site of pathological changes due to aging is one of the approaches of cataract research. Time of flight secondary ion mass spectrometry (TOF-SIMS) microscopy is expected to analyze elements and organic substances in the lens. The purpose of the present study is to compare elements and organic substances in the lenses of normal 4-month-old rats with those of normal 15-month-old rats by means of a TOF-SIMS microscope. The present study showed that the concentration of Ca and Fe was significantly higher, and that of Na and Mg was significantly lower in 15-month-old rats than that in 4-month-old rats. No changes were found in the concentration of K. The present study also showed that the equator contained more Ca, Na and Mg than the nucleus; in contrast, the Cu concentration was higher in the nucleus than in the equator. In 15-month-old rats, Mg and Vit. A in the equator and Zn in the nucleus were significantly lower than those in 4-month-old rats. TOF-SIMS microscopy could detect elemental changes in the rat lens with age, and is expected to be useful approach of cataract studies.

Multimaterial topology optimization of contact problems using phase field regularization

NASA Astrophysics Data System (ADS)

Myśliński, Andrzej

2018-01-01

The numerical method to solve multimaterial topology optimization problems for elastic bodies in unilateral contact with Tresca friction is developed in the paper. The displacement of the elastic body in contact is governed by elliptic equation with inequality boundary conditions. The body is assumed to consists from more than two distinct isotropic elastic materials. The materials distribution function is chosen as the design variable. Since high contact stress appears during the contact phenomenon the aim of the structural optimization problem is to find such topology of the domain occupied by the body that the normal contact stress along the boundary of the body is minimized. The original cost functional is regularized using the multiphase volume constrained Ginzburg-Landau energy functional rather than the perimeter functional. The first order necessary optimality condition is recalled and used to formulate the generalized gradient flow equations of Allen-Cahn type. The optimal topology is obtained as the steady state of the phase transition governed by the generalized Allen-Cahn equation. As the interface width parameter tends to zero the transition of the phase field model to the level set model is studied. The optimization problem is solved numerically using the operator splitting approach combined with the projection gradient method. Numerical examples confirming the applicability of the proposed method are provided and discussed.

DRBEM solution of the acid-mediated tumour invasion model with time-dependent carrying capacities

NASA Astrophysics Data System (ADS)

Meral, Gülnihal

2017-07-01

It is known that the pH level of the extracellular tumour environment directly effects the progression of the tumour. In this study, the mathematical model for the acid-mediated tumour cell invasion consisting of a system of nonlinear reaction diffusion equations describing the interaction between the density of the tumour cells, normal cells and the concentration of ? protons produced by the tumour cells is solved numerically using the combined application of dual reciprocity boundary element method (DRBEM) and finite difference method. The space derivatives in the model are discretised by DRBEM using the fundamental solution of Laplace equation considering the time derivative and the nonlinearities as the nonhomogenity. The resulting systems of ordinary differential equations after the application of DRBEM are then discretised using forward difference. Because of the highly nonlinear character of the model, there arises difficulties in solving the model especially for two-dimensions and the boundary-only nature of DRBEM discretisation gives the advantage of having solutions with a lower computational cost. The proposed method is tested with different kinds of carrying capacities which also depend on time. The results of the numerical simulations are compared among each case and seen to confirm the expected behaviour of the model.

A comparative study of energy balance among housewives of Ludhiana city.

PubMed

Kaur, N; Mann, S K; Sidhu, P; Sangha, J K

1997-01-01

Energy gap is the main nutritional factor which affects work efficiency in all age groups. The low intake of food results in impaired working efficiency and a low level of vitality. Energy balance was evaluated among 30 healthy, nonpregnant, nonlactating housewives aged 29-40 years drawn from the campus of Punjab Agricultural University and its surrounding areas. The women's mean overall energy intake was 1777 +or- 31 kcal/day, 87% of the ICMR (1990) recommended allowances. Total energy expenditure was measured using a computer-based Nutriguide program of Song et al., Caltrac, FAO/WHO/UNU (1985) equations based upon body weight, and an ICMR (1990) prediction equation also based upon body weight. Statistical analysis identified a significant difference in the energy expenditure measured by all 4 methods except between the FAO/WHO/UNU and ICMR prediction equations. The overall energy balance was maximum and positive according to Caltrac at 4.5 kcal/day. The energy expenditure measured by the Nutriguide, FAO/WHO/UNU, and ICMR methods was significantly correlated to weight. Energy intake was significantly and highly correlated to energy balance in all of the 4 methods. While the subjects were overweight when compared with Life Insurance Corporation of India (1965) Standards, the women's body mass index of 23.11 kg/sq.m was within the normal range.

Shelf-life of a 2.5% sodium hypochlorite solution as determined by Arrhenius equation.

PubMed

Nicoletti, Maria Aparecida; Siqueira, Evandro Luiz; Bombana, Antonio Carlos; Oliveira, Gabriella Guimarães de

2009-01-01

Accelerated stability tests are indicated to assess, within a short time, the degree of chemical degradation that may affect an active substance, either alone or in a formula, under normal storage conditions. This method is based on increased stress conditions to accelerate the rate of chemical degradation. Based on the equation of the straight line obtained as a function of the reaction order (at 50 and 70 degrees C) and using Arrhenius equation, the speed of the reaction was calculated for the temperature of 20 degrees C (normal storage conditions). This model of accelerated stability test makes it possible to predict the chemical stability of any active substance at any given moment, as long as the method to quantify the chemical substance is available. As an example of the applicability of Arrhenius equation in accelerated stability tests, a 2.5% sodium hypochlorite solution was analyzed due to its chemical instability. Iodometric titration was used to quantify free residual chlorine in the solutions. Based on data obtained keeping this solution at 50 and 70 degrees C, using Arrhenius equation and considering 2.0% of free residual chlorine as the minimum acceptable threshold, the shelf-life was equal to 166 days at 20 degrees C. This model, however, makes it possible to calculate shelf-life at any other given temperature.

An Experimental and Computational Study on Soot Formation in a Coflow Jet Flame Under Microgravity and Normal Gravity

NASA Technical Reports Server (NTRS)

Ma, Bin; Cao, Su; Giassi, Davide; Stocker, Dennis P.; Takahashi, Fumiaki; Bennett, Beth Anne V.; Smooke, Mitchell D.; Long, Marshall B.

2014-01-01

Upon the completion of the Structure and Liftoff in Combustion Experiment (SLICE) in March 2012, a comprehensive and unique set of microgravity coflow diffusion flame data was obtained. This data covers a range of conditions from weak flames near extinction to strong, highly sooting flames, and enabled the study of gravitational effects on phenomena such as liftoff, blowout and soot formation. The microgravity experiment was carried out in the Microgravity Science Glovebox (MSG) on board the International Space Station (ISS), while the normal gravity experiment was performed at Yale utilizing a copy of the flight hardware. Computational simulations of microgravity and normal gravity flames were also carried out to facilitate understanding of the experimental observations. This paper focuses on the different sooting behaviors of CH4 coflow jet flames in microgravity and normal gravity. The unique set of data serves as an excellent test case for developing more accurate computational models.Experimentally, the flame shape and size, lift-off height, and soot temperature were determined from line-of-sight flame emission images taken with a color digital camera. Soot volume fraction was determined by performing an absolute light calibration using the incandescence from a flame-heated thermocouple. Computationally, the MC-Smooth vorticity-velocity formulation was employed to describe the chemically reacting flow, and the soot evolution was modeled by the sectional aerosol equations. The governing equations and boundary conditions were discretized on an axisymmetric computational domain by finite differences, and the resulting system of fully coupled, highly nonlinear equations was solved by a damped, modified Newtons method. The microgravity sooting flames were found to have lower soot temperatures and higher volume fraction than their normal gravity counterparts. The soot distribution tends to shift from the centerline of the flame to the wings from normal gravity to microgravity.

Erratum: ``The Luminosity Function of IRAS Point Source Catalog Redshift Survey Galaxies'' (ApJ, 587, L89 [2003])

NASA Astrophysics Data System (ADS)

Takeuchi, Tsutomu T.; Yoshikawa, Kohji; Ishii, Takako T.

2004-05-01

We have mentioned that we normalized the parameters for the luminosity function by the Hubble constant H0=100 km s-1 Mpc-1 however, for the characteristic luminosity L* we erroneously normalized it by H0=70 km s-1 Mpc-1. As a result, we have proposed wrong numerical factors for L*. In addition, there is a typographic error in the exponent of equation (6) of the published manuscript. Correct values are as follows: L*=(4.34+/-0.86)×108 h-2 [Lsolar] for equation (4), and L*=(2.50+/-0.44)×109 h-2 [Lsolar] and L*=(9.55+/-0.20)×108 h-2 [Lsolar] for equations (5) and (6), respectively. All the other parameters are correct. The errors have occurred only in the final conversion, and they do not affect our discussions and conclusions at all. We thank P. Ranalli for pointing out the errors.

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

The Equation, the Whole Equation, and Nothing but the Equation! One Approach to the Teaching of Linear Equations.

ERIC Educational Resources Information Center

Pirie, Susan E. B.; Martin, Lyndon

1997-01-01

Presents the results of a case study which looked at the mathematics classroom of one teacher trying to teach mathematics with meaning to pupils or lower ability at the secondary level. Contrasts methods of teaching linear equations to a variety of ability levels and uses the Pirie-Kieren model to account for the successful growth in understanding…

Modal content of noise generated by a coaxial jet in a pipe

NASA Technical Reports Server (NTRS)

Kerschen, E. J.; Johnston, J. P.

1978-01-01

Noise generated by air flow through a coaxial obstruction in a long, straight pipe was investigated with concentration on the modal characteristics of the noise field inside the pipe and downstream of the restriction. Two measurement techniques were developed for separation of the noise into the acoustic duct modes. The instantaneous mode separation technique uses four microphones, equally spaced in the circumferential direction, at the same axial location. The time-averaged mode separation technique uses three microphones mounted at the same axial location. A matrix operation on time-averaged data produces the modal pressure levels. This technique requires the restrictive assumption that the acoustic modes are uncorrelated with each other. The measured modal pressure spectra were converted to modal power spectra and integrated over the frequency range 200-6000 Hz. The acoustic efficiency levels (acoustic power normalized by jet kinetic energy flow), when plotted vs. jet Mach number, showed a strong dependence on the ratio of restriction diameter to pipe diameter. The acoustic energy flow analyses based on the thermodynamic energy equation and on the results of Mohring both resulted in orthogonality properties for the eigenfunctions of the radial mode shape equation. These orthogonality relationships involve the eigenvalues and derivatives of the radial mode shape functions.

Using Structural Equation Modeling to Understand Prescription Stimulant Misuse: A Test of the Theory of Triadic Influence

PubMed Central

Bavarian, Niloofar; Flay, Brian R.; Ketcham, Patricia L.; Smit, Ellen; Kodama, Cathy; Martin, Melissa; Saltz, Robert F.

2014-01-01

Objective To test a theory-driven model of health behavior to predict the illicit use of prescription stimulants (IUPS) among college students. Participants A probability sample of 554 students from one university located in California (response rate = 90.52%). Methods Students completed a paper-based survey developed with guidance from the Theory of Triadic Influence. We first assessed normality of measures and checked for multicollinearity. A single structural equation model of frequency of IUPS in college was then tested using constructs from the theory’s three streams of influence (i.e., intrapersonal, social situation/context, and sociocultural environment) and four levels of causation (i.e., ultimate causes, distal influences, proximal predictors, and immediate precursors). Results Approximately 18% of students reported engaging in IUPS during college, with frequency of use ranging from never to 40 or more times per academic term. The model tested had strong fit and the majority of paths specified within and across streams were significant at the p<.01 level. Additionally, 46% of the variance in IUPS frequency was explained by the tested model. Conclusions Results suggest the utility of the TTI as an integrative model of health behavior, specifically in predicting IUPS, and provide insight on the need for multifaceted prevention and intervention efforts. PMID:24647369

Cognitive aging on latent constructs for visual processing capacity: a novel structural equation modeling framework with causal assumptions based on a theory of visual attention.

PubMed

Nielsen, Simon; Wilms, L Inge

2014-01-01

We examined the effects of normal aging on visual cognition in a sample of 112 healthy adults aged 60-75. A testbattery was designed to capture high-level measures of visual working memory and low-level measures of visuospatial attention and memory. To answer questions of how cognitive aging affects specific aspects of visual processing capacity, we used confirmatory factor analyses in Structural Equation Modeling (SEM; Model 2), informed by functional structures that were modeled with path analyses in SEM (Model 1). The results show that aging effects were selective to measures of visual processing speed compared to visual short-term memory (VSTM) capacity (Model 2). These results are consistent with some studies reporting selective aging effects on processing speed, and inconsistent with other studies reporting aging effects on both processing speed and VSTM capacity. In the discussion we argue that this discrepancy may be mediated by differences in age ranges, and variables of demography. The study demonstrates that SEM is a sensitive method to detect cognitive aging effects even within a narrow age-range, and a useful approach to structure the relationships between measured variables, and the cognitive functional foundation they supposedly represent.

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Variational theorems for superimposed motions in elasticity, with application to beams

NASA Technical Reports Server (NTRS)

Doekmeci, M. C.

1976-01-01

Variational theorems are presented for a theory of small motions superimposed on large static deformations and governing equations for prestressed beams on the basis of 3-D theory of elastodynamics. First, the principle of virtual work is modified through Friedrichs's transformation so as to describe the initial stress problem of elastodynamics. Next, the modified principle together with a chosen displacement field is used to derive a set of 1-D macroscopic governing equations of prestressed beams. The resulting equations describe all the types of superimposed motions in elastic beams, and they include all the effects of transverse shear and normal strains, and the rotatory inertia. The instability of the governing equations is discussed briefly.

Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation

NASA Technical Reports Server (NTRS)

Spangler, Steven R.

1990-01-01

A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.

Theory of strong turbulence by renormalization

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1981-01-01

The hydrodynamical equations of turbulent motions are inhomogeneous and nonlinear in their inertia and force terms and will generate a hierarchy. A kinetic method was developed to transform the hydrodynamic equations into a master equation governing the velocity distribution, as a function of the time, the position and the velocity as an independent variable. The master equation presents the advantage of being homogeneous and having fewer nonlinear terms and is therefore simpler for the investigation of closure. After the closure by means of a cascade scaling procedure, the kinetic equation is derived and possesses a memory which represents the nonMarkovian character of turbulence. The kinetic equation is transformed back to the hydrodynamical form to yield an energy balance in the cascade form. Normal and anomalous transports are analyzed. The theory is described for incompressible, compressible and plasma turbulence. Applications of the method to problems relating to sound generation and the propagation of light in a nonfrozen turbulence are considered.

Scale-dependent behavior of scale equations.

PubMed

Kim, Pilwon

2009-09-01

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

Regional Screening Levels (RSLs) - Equations

EPA Pesticide Factsheets

Regional Screening Level RSL equations page provides quick access to the equations used in the Chemical Risk Assessment preliminary remediation goal PRG risk based concentration RBC and risk calculator for the assessment of human Health.

Determination of Resting Energy Expenditure After Severe Burn

DTIC Science & Technology

2013-02-01

increase in metab- olism after burn. However, the Society of Critical Care Medicine along with the American Society for Parenteral and Enteral... Nutrition recommended in their 2009 Guidelines that predictive equations to estimate nutritional requirements be used with cau- tion.3 Equations normally...Department of Nutritional Medicine at San Antonio Military Medical Center, the United States Army Institute of Surgical Research, Fort Sam Houston

Normalization and extension of single-collector efficiency correlation equation

NASA Astrophysics Data System (ADS)

Messina, Francesca; Marchisio, Daniele; Sethi, Rajandrea

2015-04-01

The colloidal transport and deposition are important phenomena involved in many engineering problems. In the environmental engineering field the use of micro- and nano-scale zerovalent iron (M-NZVI) is one of the most promising technologies for groundwater remediation. Colloid deposition is normally studied from a micro scale point of view and the results are then implemented in macro scale models that are used to design field-scale applications. The single collector efficiency concept predicts particles deposition onto a single grain of a complex porous medium in terms of probability that an approaching particle would be retained on the solid grain. In literature, many different approaches and equations exist to predict it, but most of them fail under specific conditions (e.g. very small or very big particle size and very low fluid velocity) because they predict efficiency values exceeding unity. By analysing particle fluxes and deposition mechanisms and performing a mass balance on the entire domain, the traditional definition of efficiency was reformulated and a novel total flux normalized correlation equation is proposed for predicting single-collector efficiency under a broad range of parameters. It has been formulated starting from a combination of Eulerian and Lagrangian numerical simulations, performed under Smoluchowski-Levich conditions, in a geometry which consists of a sphere enveloped by a control volume. In order to guarantee the independence of each term, the correlation equation is derived through a rigorous hierarchical parameter estimation process, accounting for single and mutual interacting transport mechanisms. The correlation equation provides efficiency values lower than one over a wide range of parameters and is valid both for point and finite-size particles. A reduced form is also proposed by elimination of the less relevant terms. References 1. Yao, K. M.; Habibian, M. M.; Omelia, C. R., Water and Waste Water Filtration - Concepts and Applications. Environ Sci Technol 1971, 5, (11), 1105-&. 2. Tufenkji, N., and M. Elimelech, Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media. Environmental Science & Technology 2004 38(2):529-536. 3. Boccardo, G.; Marchisio, D. L.; Sethi, R., Microscale simulation of particle deposition in porous media. J Colloid Interface Sci 2014, 417, 227-37

The roles of time and displacement in velocity-dependent volumetric strain of fault zones

USGS Publications Warehouse

Beeler, N.M.; Tullis, T.E.

1997-01-01

The relationship between measured friction??A and volumetric strain during frictional sliding was determined using a rate and state variable dependent friction constitutive equation, a common work balance relating friction and volume change, and two types of experimental faults: initially bare surfaces of Westerly granite and rock surfaces separated by a 1 mm layer of < 90 ??m Westerly granite gouge. The constitutive equation is the sum of a constant term representing the nominal resistance to sliding and two smaller terms: a rate dependent term representing the shear viscosity of the fault surface (direct effect), and a term which represents variations in the area of contact (evolution effect). The work balance relationship requires that ??A differs from the frictional resistance that leads to shear heating by the derivative of fault normal displacement with respect shear displacement, d??n ld??s. An implication of this relationship is that the rate dependence of d??n ld??s contributes to the rate dependence of ??A. Experiments show changes in sliding velocity lead to changes in both fault strength and volume. Analysis of data with the rate and state equations combined with the work balance relationship preclude the conventional interpretation of the direct effect in the rate and state variable constitutive equations. Consideration of a model bare surface fault consisting of an undeformable indentor sliding on a deformable surface reveals a serious flaw in the work balance relationship if volume change is time-dependent. For the model, at zero slip rate indentation creep under the normal load leads to time-dependent strengthening of the fault surface but, according to the work balance relationship, no work is done because compaction or dilatancy can only be induced by shearing. Additional tests on initially bare surfaces and gouges show that fault normal strain in experiments is time-dependent, consistent with the model. This time-dependent fault normal strain, which is not accounted for in the work balance relationship, explains the inconsistency between the constitutive equations and the work balance. For initially bare surface faults, all rate dependence of volume change is due to time dependence. Similar results are found for gouge. We conclude that ??A reflects the frictional resistance that results in shear heating, and no correction needs to be made for the volume changes. The result that time-dependent volume changes do not contribute to ??A is a general result and extends beyond these experiments, the simple indentor model and particular constitutive equations used to illustrate the principle.

Unpacking the Complexity of Linear Equations from a Cognitive Load Theory Perspective

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Phan, Huy P.

2016-01-01

The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…

The New Data Assimilation System at the Italian Air Force Weather Service: Design and Preliminary Results

DTIC Science & Technology

2002-09-01

weather conditions (1999 Christmas storm in Europe , January 2000 snow storm over the eastern coast of the US) can be attributed to the inaccuracies in...over the normal modes of a linearized version of the model equations. These 5 normal modes can be classified (at least for the extratropics ) based

Normals to a Parabola

ERIC Educational Resources Information Center

Srinivasan, V. K.

2013-01-01

Given a parabola in the standard form y[superscript 2] = 4ax, corresponding to three points on the parabola, such that the normals at these three points P, Q, R concur at a point M = (h, k), the equation of the circumscribing circle through the three points P, Q, and R provides a tremendous opportunity to illustrate "The Art of Algebraic…

Normal Theory Two-Stage ML Estimator When Data Are Missing at the Item Level

PubMed Central

Savalei, Victoria; Rhemtulla, Mijke

2017-01-01

In many modeling contexts, the variables in the model are linear composites of the raw items measured for each participant; for instance, regression and path analysis models rely on scale scores, and structural equation models often use parcels as indicators of latent constructs. Currently, no analytic estimation method exists to appropriately handle missing data at the item level. Item-level multiple imputation (MI), however, can handle such missing data straightforwardly. In this article, we develop an analytic approach for dealing with item-level missing data—that is, one that obtains a unique set of parameter estimates directly from the incomplete data set and does not require imputations. The proposed approach is a variant of the two-stage maximum likelihood (TSML) methodology, and it is the analytic equivalent of item-level MI. We compare the new TSML approach to three existing alternatives for handling item-level missing data: scale-level full information maximum likelihood, available-case maximum likelihood, and item-level MI. We find that the TSML approach is the best analytic approach, and its performance is similar to item-level MI. We recommend its implementation in popular software and its further study. PMID:29276371

Normal Theory Two-Stage ML Estimator When Data Are Missing at the Item Level.

PubMed

Savalei, Victoria; Rhemtulla, Mijke

2017-08-01

In many modeling contexts, the variables in the model are linear composites of the raw items measured for each participant; for instance, regression and path analysis models rely on scale scores, and structural equation models often use parcels as indicators of latent constructs. Currently, no analytic estimation method exists to appropriately handle missing data at the item level. Item-level multiple imputation (MI), however, can handle such missing data straightforwardly. In this article, we develop an analytic approach for dealing with item-level missing data-that is, one that obtains a unique set of parameter estimates directly from the incomplete data set and does not require imputations. The proposed approach is a variant of the two-stage maximum likelihood (TSML) methodology, and it is the analytic equivalent of item-level MI. We compare the new TSML approach to three existing alternatives for handling item-level missing data: scale-level full information maximum likelihood, available-case maximum likelihood, and item-level MI. We find that the TSML approach is the best analytic approach, and its performance is similar to item-level MI. We recommend its implementation in popular software and its further study.

Boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Panaras, Argyris G.

1987-01-01

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.

The limitation and applicability of Musher-Sturman equation to two dimensional lower hybrid wave collapse

NASA Technical Reports Server (NTRS)

Tam, Sunny W. Y.; Chang, Tom

1995-01-01

The existence of localized regions of intense lower hybrid waves in the auroral ionosphere recently observed by rocket and satellite experiments can be understood by the study of a non-linear two-timescale coupling process. In this Letter, we demonstrate that the leading non-linear term in the standard Musher-Sturman equation vanishes identically in strict two-dimensions (normal to the magnetic field). Instead, the new two-dimensional equation is characterized by a much weaker non-linear term which arises from the ponderomotive force perpendicular to the magnetic field, particularly that due to the ions. The old and new equations are compared by means of time-evolution calculations of wave fields. The results exhibit a remarkable difference in the evolution of the waves as governed by the two equations. Such dissimilar outcomes motivate our investigation of the limitation of Musher-Sturman equation in quasi-two-dimensions. Only within all these limits can Musher-Sturman equation adequately describe the collapse of lower hybrid waves.

Regional Screening Levels (RSLs) - Equations (November 2017 )

EPA Pesticide Factsheets

Regional Screening Level RSL equations page provides quick access to the equations used in the Chemical Risk Assessment preliminary remediation goal PRG risk based concentration RBC and risk calculator for the assessment of human Health.

One Dimension Analytical Model of Normal Ballistic Impact on Ceramic/Metal Gradient Armor

NASA Astrophysics Data System (ADS)

Liu, Lisheng; Zhang, Qingjie; Zhai, Pengcheng; Cao, Dongfeng

2008-02-01

An analytical model of normal ballistic impact on the ceramic/metal gradient armor, which is based on modified Alekseevskii-Tate equations, has been developed. The process of gradient armour impacted by the long rod can be divided into four stages in this model. First stage is projectile's mass erosion or flowing phase, mushrooming phase and rigid phase; second one is the formation of comminuted ceramic conoid; third one is the penetration of gradient layer and last one is the penetration of metal back-up plate. The equations of third stage have been advanced by assuming the behavior of gradient layer as rigid-plastic and considering the effect of strain rate on the dynamic yield strength.

Effect on Gaseous Film Cooling of Coolant Injection Through Angled Slots and Normal Holes

NASA Technical Reports Server (NTRS)

Papell, S. Stephen

1960-01-01

A study was made to determine the effect of coolant injection angularity on gaseous film-cooling effectiveness. In the correlation of experimental data an effective injection angle was defined by a vector summation of the coolant and mainstream gas flows. The cosine of this angle was used as a parameter to empirically develop a corrective term to qualify a correlating equation presented in Technical Note D-130 that was limited to tangential injection of the coolant. Data were also obtained for coolant injection through rows of holes normal to the test plate. The slot correlating equation was adapted to fit these data by the definition of an effective slot height. An additional corrective term was then determined to correlate these data.

Exact solution of two collinear cracks normal to the boundaries of a 1D layered hexagonal piezoelectric quasicrystal

NASA Astrophysics Data System (ADS)

Zhou, Y.-B.; Li, X.-F.

2018-07-01

The electroelastic problem related to two collinear cracks of equal length and normal to the boundaries of a one-dimensional hexagonal piezoelectric quasicrystal layer is analysed. By using the finite Fourier transform, a mixed boundary value problem is solved when antiplane mechanical loading and inplane electric loading are applied. The problem is reduce to triple series equations, which are then transformed to a singular integral equation. For uniform remote loading, an exact solution is obtained in closed form, and explicit expressions for the electroelastic field are determined. The intensity factors of the electroelastic field and the energy release rate at the inner and outer crack tips are given and presented graphically.

Unsteady MHD blood flow through porous medium in a parallel plate channel

NASA Astrophysics Data System (ADS)

Latha, R.; Rushi Kumar, B.

2017-11-01

In this study, we have analyzed heat and mass transfer effects on unsteady blood flow through parallel plate channel in a saturated porous medium in the presence of a transverse magnetic field with thermal radiation. The governing higher order nonlinear PDE’S are converted to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using boundary conditions by choosing the axial flow transport and the fields of concentration and temperature apart from the normal velocity as a function of y and t. The effects of different pertinent parameters appeared in this model viz thermal radiation, Prandtl number, Heat source parameter, Hartmann number, Permeability parameter, Decay parameter on axial flow transport and the normal velocity are analyzed in detail.

One Dimension Analytical Model of Normal Ballistic Impact on Ceramic/Metal Gradient Armor

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

Liu Lisheng; Zhang Qingjie; Zhai Pengcheng

2008-02-15

An analytical model of normal ballistic impact on the ceramic/metal gradient armor, which is based on modified Alekseevskii-Tate equations, has been developed. The process of gradient armour impacted by the long rod can be divided into four stages in this model. First stage is projectile's mass erosion or flowing phase, mushrooming phase and rigid phase; second one is the formation of comminuted ceramic conoid; third one is the penetration of gradient layer and last one is the penetration of metal back-up plate. The equations of third stage have been advanced by assuming the behavior of gradient layer as rigid-plastic andmore » considering the effect of strain rate on the dynamic yield strength.« less

Quantitative cervical vertebral maturation assessment in adolescents with normal occlusion: a mixed longitudinal study.

PubMed

Chen, Li-Li; Xu, Tian-Min; Jiang, Jiu-Hui; Zhang, Xing-Zhong; Lin, Jiu-Xiang

2008-12-01

The purpose of this study was to establish a quantitative cervical vertebral maturation (CVM) system for adolescents with normal occlusion. Mixed longitudinal data were used. The subjects included 87 children and adolescents from 8 to 18 years old with normal occlusion (32 boys, 55 girls) selected from 901 candidates. Sequential lateral cephalograms and hand-wrist films were taken once a year for 6 years. The lateral cephalograms of all subjects were divided into 11 maturation groups according to the Fishman skeletal maturity indicators. The morphologic characteristics of the second, third, and fourth cervical vertebrae at 11 developmental stages were measured and analyzed. Three characteristic parameters (H4/W4, AH3/PH3, @2) were selected to determine the classification of CVM. With 3 morphologic variables, the quantitative CVM system including 4 maturational stages was established. An equation that can accurately estimate the maturation of the cervical vertebrae was established: CVM stage=-4.13+3.57xH4/W4+4.07xAH3/PH3+0.03x@2. The quantitative CVM method is an efficient, objective, and relatively simple approach to assess the level of skeletal maturation during adolescence.

Challenging the present definition of "normal" vitamin D levels obtained by a single blood test. Can we develop a formula to predict vitamin D levels in the 4 seasons from a single season's measure?

PubMed

Tandeter, Howard

2014-08-01

Publications on the health effects of vitamin D (25(OH) D) had almost triplicate in the last 10years, not only for its known "calcemic effects" (calcium, phosphor, PTH), but for the more recent findings on its "non-calcemic effects" (all-cause and cardiovascular mortality, and relation with certain types of cancer). Part of these publications deal with the definition of what is a "normal" circulating level of 25(OH) D that may distinguish between health and disease. The literature also deals with seasonal variations of vitamin D, showing levels that rise in summer and fall in winter and with DBP phenotypes and geographical location that affect seasonality of 25(OH) D measurements. Despite the knowledge of the existence of these phenomena many studies on vitamin D fail to acknowledge the time of the year the blood sample was extracted. Thus, when we compare results from different studies without defining the season that the samples were drawn, we compare incomparable figures. Furthermore, it is quite absurd to define "normal levels" as a static measure (over or under a certain value) using a single blood test when the value measured is known to change with seasons. Knowing that people have different vitamin D levels in different seasons of the year, we should ask ourselves which of these measurements should be used to define a "real" or "normal" level? Is it the lower one? Is there a "mean measure" that should be used for this matter? If yes, how do we obtain it? Do we have to make 4 seasonal measurements in each patient? Alternatively, might there be a possibility of developing a formula to help us obtain the mean from a single season's measure or one season's prediction from another season's measurement? And knowing that DBP phenotypes and geographical location affect seasonality of 25(OH) D measurements; shouldn't we include this in the equation? In this article I will discuss the hypothetical existence of an Individual Mean Annual vitamin D level that I will call the "IMAD level" and a recovery formula "RF" that may be used to calculate this mean having one single measure (in any of the 4 seasons) and to predict any season's value from another season's measurement. IMAD levels should be obtained in the two main DBP phenotypes, taking into account the geographical location of the test. Copyright © 2014 Elsevier Ltd. All rights reserved.

Quantification of cardiorespiratory fitness in healthy nonobese and obese men and women.

PubMed

Lorenzo, Santiago; Babb, Tony G

2012-04-01

The quantification and interpretation of cardiorespiratory fitness (CRF) in obesity is important for adequately assessing cardiovascular conditioning, underlying comorbidities, and properly evaluating disease risk. We retrospectively compared peak oxygen uptake (VO(2)peak) (ie, CRF) in absolute terms, and relative terms (% predicted) using three currently suggested prediction equations (Equations R, W, and G). There were 19 nonobese and 66 obese participants. Subjects underwent hydrostatic weighing and incremental cycling to exhaustion. Subject characteristics were analyzed by independent t test, and % predicted VO(2)peak by a two-way analysis of variance (group and equation) with repeated measures on one factor (equation). VO(2)peak (L/min) was not different between nonobese and obese adults (2.35 ± 0.80 [SD] vs 2.39 ± 0.68 L/min). VO(2)peak was higher (P < .02) relative to body mass and lean body mass in the nonobese (34 ± 8 mL/min/kg vs 22 ± 5 mL/min/kg, 42 ± 9 mL/min/lean body mass vs 37 ± 6 mL/min/lean body mass). Cardiorespiratory fitness assessed as % predicted was not different in the nonobese and obese (91% ± 17% predicted vs 95% ± 15% predicted) using Equation R, while using Equation W and G, CRF was lower (P < .05) but within normal limits in the obese (94 ± 15 vs 87 ± 11; 101% ± 17% predicted vs 90% ± 12% predicted, respectively), depending somewhat on sex. Traditional methods of reporting VO(2)peak do not allow adequate assessment and quantification of CRF in obese adults. Predicted VO(2)peak does allow a normalized evaluation of CRF in the obese, although care must be taken in selecting the most appropriate prediction equation, especially in women. In general, otherwise healthy obese are not grossly deconditioned as is commonly believed, although CRF may be slightly higher in nonobese subjects depending on the uniqueness of the prediction equation.

A Comparison of the Bounded Derivative and the Normal Mode Initialization Methods Using Real Data

NASA Technical Reports Server (NTRS)

Semazzi, F. H. M.; Navon, I. M.

1985-01-01

Browning et al. (1980) proposed an initialization method called the bounded derivative method (BDI). They used analytical data to test the new method. Kasahara (1982) theoretically demonstrated the equivalence between BDI and the well known nonlinear normal mode initialization method (NMI). The purposes of this study are the extension of the application of BDI to real data and comparison with NMI. The unbalanced initial state (UBD) is data of January, 1979 OOZ which were interpolated from the adjacent sigma levels of the GLAS GCM to the 300 mb surface. The global barotropic model described by Takacs and Balgovind (1983) is used. Orographic forcing is explicitly included in the model. Many comparisons are performed between various quantities. However, we only present a comparison of the time evolution at two grid points A(50 S, 90 E) and B(10 S, 20 E) which represent low and middle latitude locations. To facilitate a more complete comparison an initialization experiment based on the classical balance equation (CBE) was also included.

Prediction of light aircraft interior sound pressure level from the measured sound power flowing in to the cabin

NASA Technical Reports Server (NTRS)

Atwal, Mahabir S.; Heitman, Karen E.; Crocker, Malcolm J.

1986-01-01

The validity of the room equation of Crocker and Price (1982) for predicting the cabin interior sound pressure level was experimentally tested using a specially constructed setup for simultaneous measurements of transmitted sound intensity and interior sound pressure levels. Using measured values of the reverberation time and transmitted intensities, the equation was used to predict the space-averaged interior sound pressure level for three different fuselage conditions. The general agreement between the room equation and experimental test data is considered good enough for this equation to be used for preliminary design studies.

A pyramid scheme for three-dimensional diffusion equations on polyhedral meshes

NASA Astrophysics Data System (ADS)

Wang, Shuai; Hang, Xudeng; Yuan, Guangwei

2017-12-01

In this paper, a new cell-centered finite volume scheme is proposed for three-dimensional diffusion equations on polyhedral meshes, which is called as pyramid scheme (P-scheme). The scheme is designed for polyhedral cells with nonplanar cell-faces. The normal flux on a nonplanar cell-face is discretized on a planar face, which is determined by a simple optimization procedure. The resulted discrete form of the normal flux involves only cell-centered and cell-vertex unknowns, and is free from face-centered unknowns. In the case of hexahedral meshes with skewed nonplanar cell-faces, a quite simple expression is obtained for the discrete normal flux. Compared with the second order accurate O-scheme [31], the P-scheme is more robust and the discretization cost is reduced remarkably. Numerical results are presented to show the performance of the P-scheme on various kinds of distorted meshes. In particular, the P-scheme is shown to be second order accurate.

The exit-time problem for a Markov jump process

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

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Surface thermodynamics, surface stress, equations at surfaces and triple lines for deformable bodies.

PubMed

Olives, Juan

2010-03-03

The thermodynamics and mechanics of the surface of a deformable body are studied here, following and refining the general approach of Gibbs. It is first shown that the 'local' thermodynamic variables of the state of the surface are only the temperature, the chemical potentials and the surface strain tensor (true thermodynamic variables, for a viscoelastic solid or a viscous fluid). A new definition of the surface stress is given and the corresponding surface thermodynamics equations are presented. The mechanical equilibrium equation at the surface is then obtained. It involves the surface stress and is similar to the Cauchy equation for the volume. Its normal component is a generalization of the Laplace equation. At a (body-fluid-fluid) triple contact line, two equations are obtained, which represent: (i) the equilibrium of the forces (surface stresses) for a triple line fixed on the body; (ii) the equilibrium relative to the motion of the line with respect to the body. This last equation leads to a strong modification of Young's classical capillary equation.

Modelling of charged satellite motion in Earth's gravitational and magnetic fields

NASA Astrophysics Data System (ADS)

Abd El-Bar, S. E.; Abd El-Salam, F. A.

2018-05-01

In this work Lagrange's planetary equations for a charged satellite subjected to the Earth's gravitational and magnetic force fields are solved. The Earth's gravity, and magnetic and electric force components are obtained and expressed in terms of orbital elements. The variational equations of orbit with the considered model in Keplerian elements are derived. The solution of the problem in a fully analytical way is obtained. The temporal rate of changes of the orbital elements of the spacecraft are integrated via Lagrange's planetary equations and integrals of the normalized Keplerian motion obtained by Ahmed (Astron. J. 107(5):1900, 1994).

Chronic atrophic gastritis in association with hair mercury level.

PubMed

Xue, Zeyun; Xue, Huiping; Jiang, Jianlan; Lin, Bing; Zeng, Si; Huang, Xiaoyun; An, Jianfu

2014-11-01

The objective of this study was to explore hair mercury level in association with chronic atrophic gastritis, a precancerous stage of gastric cancer (GC), and thus provide a brand new angle of view on the timely intervention of precancerous stage of GC. We recruited 149 healthy volunteers as controls and 152 patients suffering from chronic gastritis as cases. The controls denied upper gastrointestinal discomforts, and the cases were diagnosed as chronic superficial gastritis (n=68) or chronic atrophic gastritis (n=84). We utilized Mercury Automated Analyzer (NIC MA-3000) to detect hair mercury level of both healthy controls and cases of chronic gastritis. The statistic of measurement data was expressed as mean ± standard deviation, which was analyzed using Levene variance equality test and t test. Pearson correlation analysis was employed to determine associated factors affecting hair mercury levels, and multiple stepwise regression analysis was performed to deduce regression equations. Statistical significance is considered if p value is less than 0.05. The overall hair mercury level was 0.908949 ± 0.8844490 ng/g [mean ± standard deviation (SD)] in gastritis cases and 0.460198 ± 0.2712187 ng/g (mean±SD) in healthy controls; the former level was significantly higher than the latter one (p=0.000<0.01). The hair mercury level in chronic atrophic gastritis subgroup was 1.155220 ± 0.9470246 ng/g (mean ± SD) and that in chronic superficial gastritis subgroup was 0.604732 ± 0.6942509 ng/g (mean ± SD); the former level was significantly higher than the latter level (p<0.01). The hair mercury level in chronic superficial gastritis cases was significantly higher than that in healthy controls (p<0.05). The hair mercury level in chronic atrophic gastritis cases was significantly higher than that in healthy controls (p<0.01). Stratified analysis indicated that the hair mercury level in healthy controls with eating seafood was significantly higher than that in healthy controls without eating seafood (p<0.01) and that the hair mercury level in chronic atrophic gastritis cases was significantly higher than that in chronic superficial gastritis cases (p<0.01). Pearson correlation analysis indicated that eating seafood was most correlated with hair mercury level and positively correlated in the healthy controls and that the severity of gastritis was most correlated with hair mercury level and positively correlated in the gastritis cases. Multiple stepwise regression analysis indicated that the regression equation of hair mercury level in controls could be expressed as 0.262 multiplied the value of eating seafood plus 0.434, the model that was statistically significant (p<0.01). Multiple stepwise regression analysis also indicated that the regression equation of hair mercury level in gastritis cases could be expressed as 0.305 multiplied the severity of gastritis, the model that was also statistically significant (p<0.01). The graphs of regression standardized residual for both controls and cases conformed to normal distribution. The main positively correlated factor affecting the hair mercury level is eating seafood in healthy people whereas the predominant positively correlated factor affecting the hair mercury level is the severity of gastritis in chronic gastritis patients. That is to say, the severity of chronic gastritis is positively correlated with the level of hair mercury. The incessantly increased level of hair mercury possibly reflects the development of gastritis from normal stomach to superficial gastritis and to atrophic gastritis. The detection of hair mercury is potentially a means to predict the severity of chronic gastritis and possibly to insinuate the environmental mercury threat to human health in terms of gastritis or even carcinogenesis.

A logistic regression equation for estimating the probability of a stream in Vermont having intermittent flow

USGS Publications Warehouse

Olson, Scott A.; Brouillette, Michael C.

2006-01-01

A logistic regression equation was developed for estimating the probability of a stream flowing intermittently at unregulated, rural stream sites in Vermont. These determinations can be used for a wide variety of regulatory and planning efforts at the Federal, State, regional, county and town levels, including such applications as assessing fish and wildlife habitats, wetlands classifications, recreational opportunities, water-supply potential, waste-assimilation capacities, and sediment transport. The equation will be used to create a derived product for the Vermont Hydrography Dataset having the streamflow characteristic of 'intermittent' or 'perennial.' The Vermont Hydrography Dataset is Vermont's implementation of the National Hydrography Dataset and was created at a scale of 1:5,000 based on statewide digital orthophotos. The equation was developed by relating field-verified perennial or intermittent status of a stream site during normal summer low-streamflow conditions in the summer of 2005 to selected basin characteristics of naturally flowing streams in Vermont. The database used to develop the equation included 682 stream sites with drainage areas ranging from 0.05 to 5.0 square miles. When the 682 sites were observed, 126 were intermittent (had no flow at the time of the observation) and 556 were perennial (had flowing water at the time of the observation). The results of the logistic regression analysis indicate that the probability of a stream having intermittent flow in Vermont is a function of drainage area, elevation of the site, the ratio of basin relief to basin perimeter, and the areal percentage of well- and moderately well-drained soils in the basin. Using a probability cutpoint (a lower probability indicates the site has perennial flow and a higher probability indicates the site has intermittent flow) of 0.5, the logistic regression equation correctly predicted the perennial or intermittent status of 116 test sites 85 percent of the time.

Prediction of renal crystalline size distributions in space using a PBE analytic model. 2. Effect of dietary countermeasures.

PubMed

Kassemi, Mohammad; Thompson, David

2016-09-01

An analytic Population Balance Equation model is used to assess the efficacy of citrate, pyrophosphate, and augmented fluid intake as dietary countermeasures aimed at reducing the risk of renal stone formation for astronauts. The model uses the measured biochemical profile of the astronauts as input and predicts the steady-state size distribution of the nucleating, growing, and agglomerating renal calculi subject to biochemical changes brought about by administration of these dietary countermeasures. Numerical predictions indicate that an increase in citrate levels beyond its average normal ground-based urinary values is beneficial but only to a limited extent. Unfortunately, results also indicate that any decline in the citrate levels during space travel below its normal urinary values on Earth can easily move the astronaut into the stone-forming risk category. Pyrophosphate is found to be an effective inhibitor since numerical predictions indicate that even at quite small urinary concentrations, it has the potential of shifting the maximum crystal aggregate size to a much smaller and plausibly safer range. Finally, our numerical results predict a decline in urinary volume below 1.5 liters/day can act as a dangerous promoter of renal stone development in microgravity while urinary volume levels of 2.5-3 liters/day can serve as effective space countermeasures. Copyright © 2016 the American Physiological Society.

Creep rupture of polymer-matrix composites

NASA Technical Reports Server (NTRS)

Brinson, H. F.; Morris, D. H.; Griffith, W. I.

1981-01-01

The time-dependent creep-rupture process in graphite-epoxy laminates is examined as a function of temperature and stress level. Moisture effects are not considered. An accelerated characterization method of composite-laminate viscoelastic modulus and strength properties is reviewed. It is shown that lamina-modulus master curves can be obtained using a minimum of normally performed quality-control-type testing. Lamina-strength master curves, obtained by assuming a constant-strain-failure criterion, are presented along with experimental data, and reasonably good agreement is shown to exist between the two. Various phenomenological delayed failure models are reviewed and two (the modified rate equation and the Larson-Miller parameter method) are compared to creep-rupture data with poor results.

Solving the Rational Polynomial Coefficients Based on L Curve

NASA Astrophysics Data System (ADS)

Zhou, G.; Li, X.; Yue, T.; Huang, W.; He, C.; Huang, Y.

2018-05-01

The rational polynomial coefficients (RPC) model is a generalized sensor model, which can achieve high approximation accuracy. And it is widely used in the field of photogrammetry and remote sensing. Least square method is usually used to determine the optimal parameter solution of the rational function model. However the distribution of control points is not uniform or the model is over-parameterized, which leads to the singularity of the coefficient matrix of the normal equation. So the normal equation becomes ill conditioned equation. The obtained solutions are extremely unstable and even wrong. The Tikhonov regularization can effectively improve and solve the ill conditioned equation. In this paper, we calculate pathological equations by regularization method, and determine the regularization parameters by L curve. The results of the experiments on aerial format photos show that the accuracy of the first-order RPC with the equal denominators has the highest accuracy. The high order RPC model is not necessary in the processing of dealing with frame images, as the RPC model and the projective model are almost the same. The result shows that the first-order RPC model is basically consistent with the strict sensor model of photogrammetry. Orthorectification results both the firstorder RPC model and Camera Model (ERDAS9.2 platform) are similar to each other, and the maximum residuals of X and Y are 0.8174 feet and 0.9272 feet respectively. This result shows that RPC model can be used in the aerial photographic compensation replacement sensor model.

On the properties of circular beams: normalization, Laguerre-Gauss expansion, and free-space divergence.

PubMed

Vallone, Giuseppe

2015-04-15

Circular beams were introduced as a very general solution to the paraxial wave equation carrying orbital angular momentum. Here, we study their properties by looking at their normalization and their expansion in terms of Laguerre-Gauss modes. We also study their far-field divergence and, for particular cases of the beam parameters, their possible experimental generation.

SEM with Missing Data and Unknown Population Distributions Using Two-Stage ML: Theory and Its Application

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Lu, Laura

2008-01-01

This article provides the theory and application of the 2-stage maximum likelihood (ML) procedure for structural equation modeling (SEM) with missing data. The validity of this procedure does not require the assumption of a normally distributed population. When the population is normally distributed and all missing data are missing at random…

A Bayesian Model for the Estimation of Latent Interaction and Quadratic Effects When Latent Variables Are Non-Normally Distributed

ERIC Educational Resources Information Center

Kelava, Augustin; Nagengast, Benjamin

2012-01-01

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent…

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 1: Nonhydrostatic inertia–gravity modes

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

Konor, Celal S.; Randall, David A.

We have used a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the nonhydrostatic anelastic inertia–gravity modes on a midlatitude f plane. The dispersion equations are derived from the linearized anelastic equations that are discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of both horizontal grid spacing and vertical wavenumber are analyzed, and the role of nonhydrostatic effects is discussed. We also compare the results of the normal-mode analyses with numerical solutions obtained by runningmore » linearized numerical models based on the various horizontal grids. The sources and behaviors of the computational modes in the numerical simulations are also examined.Our normal-mode analyses with the Z, C, D, A, E and B grids generally confirm the conclusions of previous shallow-water studies for the cyclone-resolving scales (with low horizontal wavenumbers). We conclude that, aided by nonhydrostatic effects, the Z and C grids become overall more accurate for cloud-resolving resolutions (with high horizontal wavenumbers) than for the cyclone-resolving scales.A companion paper, Part 2, discusses the impacts of the discretization on the Rossby modes on a midlatitude β plane.« less

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 1: Nonhydrostatic inertia–gravity modes

DOE PAGES

Konor, Celal S.; Randall, David A.

2018-05-08

We have used a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the nonhydrostatic anelastic inertia–gravity modes on a midlatitude f plane. The dispersion equations are derived from the linearized anelastic equations that are discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of both horizontal grid spacing and vertical wavenumber are analyzed, and the role of nonhydrostatic effects is discussed. We also compare the results of the normal-mode analyses with numerical solutions obtained by runningmore » linearized numerical models based on the various horizontal grids. The sources and behaviors of the computational modes in the numerical simulations are also examined.Our normal-mode analyses with the Z, C, D, A, E and B grids generally confirm the conclusions of previous shallow-water studies for the cyclone-resolving scales (with low horizontal wavenumbers). We conclude that, aided by nonhydrostatic effects, the Z and C grids become overall more accurate for cloud-resolving resolutions (with high horizontal wavenumbers) than for the cyclone-resolving scales.A companion paper, Part 2, discusses the impacts of the discretization on the Rossby modes on a midlatitude β plane.« less

[Prevalence of chronic kidney disease in hypertensive persons attended in primary care from Spain determined by application of estimating equations].

PubMed

Gómez Navarro, Rafael

2009-01-01

To study the renal function (FR) of the hypertensive patients by means of estimating equations and serum creatinine (Crp). To calculate the percentage of patients with chronic kidney disease (ERC) that present normal values of Crp. To analyze which factors collaborate in the deterioration of the FR. Descriptive cross-sectional study of patients with HTA. Crp and arterial tension (TA) were determined. The glomerular filtration rate was calculated by means of Cockroft-Gault and MDRD's formula. The years of evolution of the HTA were registered. A descriptive study of the variables and the possible dependence among them was completed, using several times linear multiple regression. 52 patients were studied (57,7% women). Average age 72,4 +/- 10,8. 32,6% (Cockcroft-Gault) or 21,5% (MDRD) were fulfilling ERC criterion. The ERC was mainly diagnosed in females. 21,4% (Cockcroft-Gault) and 9,5 % patients (MDRD) with ERC had normal Crp values. We do not find linear dependence between the numbers of TA and the FR. The TA check-up objectives do not suppose less development of ERC. In males we find linear dependence within the FR (MDRD) and the years of evolution of the HTA. The ERC is a frequent pathology in the hypertense persons. The systematical utilization of estimating equations facilitates the detection of hidden ERC in patients with normal Crp.

Discretized kinetic theory on scale-free networks

NASA Astrophysics Data System (ADS)

Bertotti, Maria Letizia; Modanese, Giovanni

2016-10-01

The network of interpersonal connections is one of the possible heterogeneous factors which affect the income distribution emerging from micro-to-macro economic models. In this paper we equip our model discussed in [1, 2] with a network structure. The model is based on a system of n differential equations of the kinetic discretized-Boltzmann kind. The network structure is incorporated in a probabilistic way, through the introduction of a link density P(α) and of correlation coefficients P(β|α), which give the conditioned probability that an individual with α links is connected to one with β links. We study the properties of the equations and give analytical results concerning the existence, normalization and positivity of the solutions. For a fixed network with P(α) = c/α q , we investigate numerically the dependence of the detailed and marginal equilibrium distributions on the initial conditions and on the exponent q. Our results are compatible with those obtained from the Bouchaud-Mezard model and from agent-based simulations, and provide additional information about the dependence of the individual income on the level of connectivity.

Intrusive Method for Uncertainty Quantification in a Multiphase Flow Solver

NASA Astrophysics Data System (ADS)

Turnquist, Brian; Owkes, Mark

2016-11-01

Uncertainty quantification (UQ) is a necessary, interesting, and often neglected aspect of fluid flow simulations. To determine the significance of uncertain initial and boundary conditions, a multiphase flow solver is being created which extends a single phase, intrusive, polynomial chaos scheme into multiphase flows. Reliably estimating the impact of input uncertainty on design criteria can help identify and minimize unwanted variability in critical areas, and has the potential to help advance knowledge in atomizing jets, jet engines, pharmaceuticals, and food processing. Use of an intrusive polynomial chaos method has been shown to significantly reduce computational cost over non-intrusive collocation methods such as Monte-Carlo. This method requires transforming the model equations into a weak form through substitution of stochastic (random) variables. Ultimately, the model deploys a stochastic Navier Stokes equation, a stochastic conservative level set approach including reinitialization, as well as stochastic normals and curvature. By implementing these approaches together in one framework, basic problems may be investigated which shed light on model expansion, uncertainty theory, and fluid flow in general. NSF Grant Number 1511325.

Optimum flight paths of turbojet aircraft

NASA Technical Reports Server (NTRS)

Miele, Angelo

1955-01-01

The climb of turbojet aircraft is analyzed and discussed including the accelerations. Three particular flight performances are examined: minimum time of climb, climb with minimum fuel consumption, and steepest climb. The theoretical results obtained from a previous study are put in a form that is suitable for application on the following simplifying assumptions: the Mach number is considered an independent variable instead of the velocity; the variations of the airplane mass due to fuel consumption are disregarded; the airplane polar is assumed to be parabolic; the path curvatures and the squares of the path angles are disregarded in the projection of the equation of motion on the normal to the path; lastly, an ideal turbojet with performance independent of the velocity is involved. The optimum Mach number for each flight condition is obtained from the solution of a sixth order equation in which the coefficients are functions of two fundamental parameters: the ratio of minimum drag in level flight to the thrust and the Mach number which represents the flight at constant altitude and maximum lift-drag ratio.

multiUQ: An intrusive uncertainty quantification tool for gas-liquid multiphase flows

NASA Astrophysics Data System (ADS)

Turnquist, Brian; Owkes, Mark

2017-11-01

Uncertainty quantification (UQ) can improve our understanding of the sensitivity of gas-liquid multiphase flows to variability about inflow conditions and fluid properties, creating a valuable tool for engineers. While non-intrusive UQ methods (e.g., Monte Carlo) are simple and robust, the cost associated with these techniques can render them unrealistic. In contrast, intrusive UQ techniques modify the governing equations by replacing deterministic variables with stochastic variables, adding complexity, but making UQ cost effective. Our numerical framework, called multiUQ, introduces an intrusive UQ approach for gas-liquid flows, leveraging a polynomial chaos expansion of the stochastic variables: density, momentum, pressure, viscosity, and surface tension. The gas-liquid interface is captured using a conservative level set approach, including a modified reinitialization equation which is robust and quadrature free. A least-squares method is leveraged to compute the stochastic interface normal and curvature needed in the continuum surface force method for surface tension. The solver is tested by applying uncertainty to one or two variables and verifying results against the Monte Carlo approach. NSF Grant #1511325.

Energetic investigation of the adsorption process of CH4, C2H6 and N2 on activated carbon: Numerical and statistical physics treatment

NASA Astrophysics Data System (ADS)

Ben Torkia, Yosra; Ben Yahia, Manel; Khalfaoui, Mohamed; Al-Muhtaseb, Shaheen A.; Ben Lamine, Abdelmottaleb

2014-01-01

The adsorption energy distribution (AED) function of a commercial activated carbon (BDH-activated carbon) was investigated. For this purpose, the integral equation is derived by using a purely analytical statistical physics treatment. The description of the heterogeneity of the adsorbent is significantly clarified by defining the parameter N(E). This parameter represents the energetic density of the spatial density of the effectively occupied sites. To solve the integral equation, a numerical method was used based on an adequate algorithm. The Langmuir model was adopted as a local adsorption isotherm. This model is developed by using the grand canonical ensemble, which allows defining the physico-chemical parameters involved in the adsorption process. The AED function is estimated by a normal Gaussian function. This method is applied to the adsorption isotherms of nitrogen, methane and ethane at different temperatures. The development of the AED using a statistical physics treatment provides an explanation of the gas molecules behaviour during the adsorption process and gives new physical interpretations at microscopic levels.

Computational Analysis of the Effect of Porosity on Shock Cell Strength at Cruise

NASA Technical Reports Server (NTRS)

Massey, Steven J.; Elmiligui, Alaa A.; Pao, S. Paul; Abdol-Hamid, Khaled S.; Hunter, Craig A.

2006-01-01

A computational flow field analysis is presented of the effect of core cowl porosity on shock cell strength for a modern separate flow nozzle at cruise conditions. The goal of this study was to identify the primary physical mechanisms by which the application of porosity can reduce shock cell strength and hence the broadband shock associated noise. The flow is simulated by solving the asymptotically steady, compressible, Reynoldsaveraged Navier-Stokes equations on a structured grid using an implicit, up-wind, flux-difference splitting finite volume scheme. The standard two-equation k - epsilon turbulence model with a linear stress representation is used with the addition of a eddy viscosity dependence on total temperature gradient normalized by local turbulence length scale. Specific issues addressed in this study were the optimal area required to weaken a shock impinging on the core cowl surface and the optimal level of porosity and placement of porous areas for reduction of the overall shock cell strength downstream. Two configurations of porosity were found to reduce downstream shock strength by approximately 50%.

Dynamical Modeling of Surface Tension

NASA Technical Reports Server (NTRS)

Brackbill, Jeremiah U.; Kothe, Douglas B.

1996-01-01

In a recent review it is said that free-surface flows 'represent some of the difficult remaining challenges in computational fluid dynamics'. There has been progress with the development of new approaches to treating interfaces, such as the level-set method and the improvement of older methods such as the VOF method. A common theme of many of the new developments has been the regularization of discontinuities at the interface. One example of this approach is the continuum surface force (CSF) formulation for surface tension, which replaces the surface stress given by Laplace's equation by an equivalent volume force. Here, we describe how CSF formulation might be made more useful. Specifically, we consider a derivation of the CSF equations from a minimization of surface energy as outlined by Jacqmin (1996). This reformulation suggests that if one eliminates the computation of curvature in terms of a unit normal vector, parasitic currents may be eliminated. For this reformulation to work, it is necessary that transition region thickness be controlled. Various means for this, in addition to the one discussed by Jacqmin (1996), are discussed.

Reference range of fetal transverse cerebellar diameter between 18 and 24 weeks of pregnancy in a Brazilian population.

PubMed

Araujo Júnior, Edward; Martins, Wellington P; Nardozza, Luciano Marcondes Machado; Pires, Claudio Rodrigues; Filho, Sebastião Marques Zanforlin

2015-02-01

To determine a reference range of fetal transverse cerebellar diameter in Brazilian population. This was a retrospective cross-sectional study with 3772 normal singleton pregnancies between 18 and 24 weeks of pregnancy. The transverse cerebellar diameter was measured on the axial plane of the fetal head at the level of the lateral ventricles, including the thalamus, cavum septum pellucidum, and third ventricle. To assess the correlation between transverse cerebellar diameter and gestational age, polynomial equations were calculated, with adjustments by the determination coefficient (R2). The mean of fetal transverse cerebellar diameter ranged from 18.49 ± 1.24 mm at 18 weeks to 25.86 ± 1.66 mm at 24 weeks of pregnancy. We observed a good correlation between transverse cerebellar diameter and gestational age, which was best represented by a linear equation: transverse cerebellar diameter: -6.21 + 1.307*gestational age (R2 = 0.707). We determined a reference range of fetal transverse cerebellar diameter for the second trimester of pregnancy in Brazilian population. © The Author(s) 2014.

Matter-antimatter asymmetry and dark matter from torsion

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

Poplawski, Nikodem J.

2011-04-15

We propose a simple scenario which explains the observed matter-antimatter imbalance and the origin of dark matter in the Universe. We use the Einstein-Cartan-Sciama-Kibble theory of gravity which naturally extends general relativity to include the intrinsic spin of matter. Spacetime torsion produced by spin generates, in the classical Dirac equation, the Hehl-Datta term which is cubic in spinor fields. We show that under a charge-conjugation transformation this term changes sign relative to the mass term. A classical Dirac spinor and its charge conjugate therefore satisfy different field equations. Fermions in the presence of torsion have higher energy levels than antifermions,more » which leads to their decay asymmetry. Such a difference is significant only at extremely high densities that existed in the very early Universe. We propose that this difference caused a mechanism, according to which heavy fermions existing in such a Universe and carrying the baryon number decayed mostly to normal matter, whereas their antiparticles decayed mostly to hidden antimatter which forms dark matter. The conserved total baryon number of the Universe remained zero.« less

Modified equations of finite-size layered plates made of orthotropic material. Comparison of the results of numerical calculations with analytical solutions

NASA Astrophysics Data System (ADS)

Volchkov, Yu. M.

2017-09-01

This paper describes the modified bending equations of layered orthotropic plates in the first approximation. The approximation of the solution of the equation of the three-dimensional theory of elasticity by the Legendre polynomial segments is used to obtain differential equations of the elastic layer. For the approximation of equilibrium equations and boundary conditions of three-dimensional theory of elasticity, several approximations of each desired function (stresses and displacements) are used. The stresses at the internal points of the plate are determined from the defining equations for the orthotropic material, averaged with respect to the plate thickness. The construction of the bending equations of layered plates for each layer is carried out with the help of the elastic layer equations and the conjugation conditions on the boundaries between layers, which are conditions for the continuity of normal stresses and displacements. The numerical solution of the problem of bending of the rectangular layered plate obtained with the help of modified equations is compared with an analytical solution. It is determined that the maximum error in determining the stresses does not exceed 3 %.

Creatinine Clearance and Estimated Glomerular Filtration Rate--When are they Interchangeable.

PubMed

Simetić, Lucija; Zibar, Lada; Drmić, Sandra; Begić, Ivana; Serić, Vatroslav

2015-09-01

Study goal was to examine which of glomerular rate equations is most suitable for prediction of creatinine clearance (CrCl). Using a retrospective review of data from 500 hospital patients we calculated glomerular filtration rate according to Cockcroft-Gault equation (C-G), Modification of Diet in Renal Disease Study equation (MDRD) and Chronic Kidney Disease Epidemiology Collaboration equation (CKD-EPI). We determined if results of these equations were compatible with CrCl, and does stage of kidney disease, body-mass index (BMI), diabetes or old age have an impact on their ability to predict creatinine clearance. All of the equations showed high correlations with CrCl, regardless of diabetes, overweight or old age. There was no significant difference (p<0.05) between diagnostic accuracy when comparing ROC plots for MDRD and CKD-EPIat CrCl cut offs of 60 ml/min/1.73 m2 and 90 ml/min/1.73 m2 when analyzing data for all patients, older patients (>65 years) and diabetics. The percentage of overweight patients (BMI > or = 25) in patients with normal CrCl and decreased GFR was 64.81% for C-G, 92.04% for MDRD and 91.36% for CKD-EPI. Large number of overweight patients with normal CrCl and decreased GFR would indicate that CrCl overestimates GFR in overweight patients. The simple correction in CrCl for obese subjects is purposed. Passing-Bablok regression showed agreement between CrCl and MDRD and CrCl and CKD-EPI only in cases of severely decreased GFR (G4 and G5 stage of chronic kidney disease). Only in these stages of chronic kidney disease can CrCl and MDRD or CrCl and CKD-EPI be used simultaneously.

Understanding Vector Fields.

ERIC Educational Resources Information Center

Curjel, C. R.

1990-01-01

Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)

Analysis of the interaction of a weak normal shock wave with a turbulent boundary layer

NASA Technical Reports Server (NTRS)

Melnik, R. E.; Grossman, B.

1974-01-01

The method of matched asymptotic expansions is used to analyze the interaction of a normal shock wave with an unseparated turbulent boundary layer on a flat surface at transonic speeds. The theory leads to a three-layer description of the interaction in the double limit of Reynolds number approaching infinity and Mach number approaching unity. The interaction involves an outer, inviscid rotational layer, a constant shear-stress wall layer, and a blending region between them. The pressure distribution is obtained from a numerical solution of the outer-layer equations by a mixed-flow relaxation procedure. An analytic solution for the skin friction is determined from the inner-layer equations. The significance of the mathematical model is discussed with reference to existing experimental data.

Large scale structure formation of the normal branch in the DGP brane world model

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

Song, Yong-Seon

2008-06-15

In this paper, we study the large scale structure formation of the normal branch in the DGP model (Dvail, Gabadadze, and Porrati brane world model) by applying the scaling method developed by Sawicki, Song, and Hu for solving the coupled perturbed equations of motion of on-brane and off-brane. There is a detectable departure of perturbed gravitational potential from the cold dark matter model with vacuum energy even at the minimal deviation of the effective equation of state w{sub eff} below -1. The modified perturbed gravitational potential weakens the integrated Sachs-Wolfe effect which is strengthened in the self-accelerating branch DGP model.more » Additionally, we discuss the validity of the scaling solution in the de Sitter limit at late times.« less

Liquid jet impingement normal to a disk in zero gravity. Ph.D. Thesis Toledo Univ.

NASA Technical Reports Server (NTRS)

Labus, T. L.

1977-01-01

The free surface shapes of circular liquid jets impinging normal to sharp-edged disks in zero gravity are determined. Zero gravity drop tower experiments yielded three distinct flow patterns that were classified in terms of the relative effects of surface tension and inertial forces. An order of magnitude analysis was conducted that indicated regions where viscous forces were not significant in the computation of free surface shapes. The free surface analysis was simplified by transforming the governing potential flow equations and boundary conditions into the inverse plane, where the stream function and velocity potential became the coordinates. The resulting nonlinear equations were solved by standard finite difference methods, and comparisons were made with the experimental data for the inertia dominated regime.

High Order Accurate Finite Difference Modeling of Seismo-Acoustic Wave Propagation in a Moving Atmosphere and a Heterogeneous Earth Model Coupled Across a Realistic Topography

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

Petersson, N. Anders; Sjogreen, Bjorn

Here, we develop a numerical method for simultaneously simulating acoustic waves in a realistic moving atmosphere and seismic waves in a heterogeneous earth model, where the motions are coupled across a realistic topography. We model acoustic wave propagation by solving the linearized Euler equations of compressible fluid mechanics. The seismic waves are modeled by the elastic wave equation in a heterogeneous anisotropic material. The motion is coupled by imposing continuity of normal velocity and normal stresses across the topographic interface. Realistic topography is resolved on a curvilinear grid that follows the interface. The governing equations are discretized using high ordermore » accurate finite difference methods that satisfy the principle of summation by parts. We apply the energy method to derive the discrete interface conditions and to show that the coupled discretization is stable. The implementation is verified by numerical experiments, and we demonstrate a simulation of coupled wave propagation in a windy atmosphere and a realistic earth model with non-planar topography.« less

High Order Accurate Finite Difference Modeling of Seismo-Acoustic Wave Propagation in a Moving Atmosphere and a Heterogeneous Earth Model Coupled Across a Realistic Topography

DOE PAGES

Petersson, N. Anders; Sjogreen, Bjorn

2017-04-18

Here, we develop a numerical method for simultaneously simulating acoustic waves in a realistic moving atmosphere and seismic waves in a heterogeneous earth model, where the motions are coupled across a realistic topography. We model acoustic wave propagation by solving the linearized Euler equations of compressible fluid mechanics. The seismic waves are modeled by the elastic wave equation in a heterogeneous anisotropic material. The motion is coupled by imposing continuity of normal velocity and normal stresses across the topographic interface. Realistic topography is resolved on a curvilinear grid that follows the interface. The governing equations are discretized using high ordermore » accurate finite difference methods that satisfy the principle of summation by parts. We apply the energy method to derive the discrete interface conditions and to show that the coupled discretization is stable. The implementation is verified by numerical experiments, and we demonstrate a simulation of coupled wave propagation in a windy atmosphere and a realistic earth model with non-planar topography.« less

Model of Energy Spectrum Parameters of Ground Level Enhancement Events in Solar Cycle 23

NASA Astrophysics Data System (ADS)

Wu, S.-S.; Qin, G.

2018-01-01

Mewaldt et al. (2012) fitted the observations of the ground level enhancement (GLE) events during solar cycle 23 to the double power law equation to obtain the four spectral parameters, the normalization constant C, low-energy power law slope γ1, high-energy power law slope γ2, and break energy E0. There are 16 GLEs from which we select 13 for study by excluding some events with complicated situation. We analyze the four parameters with conditions of the corresponding solar events. According to solar event conditions, we divide the GLEs into two groups, one with strong acceleration by interplanetary shocks and another one without strong acceleration. By fitting the four parameters with solar event conditions we obtain models of the parameters for the two groups of GLEs separately. Therefore, we establish a model of energy spectrum of solar cycle 23 GLEs, which may be used in prediction in the future.

Simulation of Jet Noise with OVERFLOW CFD Code and Kirchhoff Surface Integral

NASA Technical Reports Server (NTRS)

Kandula, M.; Caimi, R.; Voska, N. (Technical Monitor)

2002-01-01

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow field are modeled with the aid of Spalart-Allmaras one-equation turbulence model. Appropriate acoustic and outflow boundary conditions were implemented to compute time-dependent acoustic pressure in the nonlinear source-field. Based on the specification of acoustic pressure, its temporal and normal derivatives on the Kirchhoff surface, the near-field and the far-field sound pressure levels are computed via Kirchhoff surface integral, with the Kirchhoff surface chosen to enclose the nonlinear sound source region described by the CFD code. The methods are validated by a comparison of the predictions of sound pressure levels with the available data for an axisymmetric turbulent supersonic (Mach 2) perfectly expanded jet.

Simulation of Supersonic Jet Noise with the Adaptation of Overflow CFD Code and Kirchhoff Surface Integral

NASA Technical Reports Server (NTRS)

Kandula, Max; Caimi, Raoul; Steinrock, T. (Technical Monitor)

2001-01-01

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow field are modeled with the aid of Spalart-Allmaras one-equation turbulence model. Appropriate acoustic and outflow boundary conditions were implemented to compute time-dependent acoustic pressure in the nonlinear source-field. Based on the specification of acoustic pressure, its temporal and normal derivatives on the Kirchhoff surface, the near-field and the far-field sound pressure levels are computed via Kirchhoff surface integral, with the Kirchhoff surface chosen to enclose the nonlinear sound source region described by the CFD code. The methods are validated by a comparison of the predictions of sound pressure levels with the available data for an axisymmetric turbulent supersonic (Mach 2) perfectly expanded jet.

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

Kinetic Equation for an Unstable Plasma

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

Balescu, R.

1963-01-01

A kinetic equation is derived for the description of the evolution in time of the distribution of velocities in a spatially homogeneous ionized gas that, at the initial time, is able to sustain exponentially growing oscillations. This equation is expressed in terms of a functional of the distribution finction that obeys the same integral equation as in the stable case. Although the method of solution used in the stable case breaks down, the equation can still be solved in closed form under unstable conditions, and hence an explicit form of the kinetic equation is obtained. The latter contains the normalmore » collision term and a new additional term describing the stabilization of the plasma. The latter acts through friction and diffusion and brings the plasma into a state of neutral stability. From there on the system evolves toward thermal equilibrium under the action of the normal collision term as well as of an additional Fokker-Planck- like term with timedependent coefficients, which however becomes less and less efficient as the plasma approaches equilibrium.« less

Errors in calculated oncotic pressure of dog plasma.

PubMed

Gabel, J C; Scott, R L; Adair, T H; Drake, R E; Traber, D L

1980-12-01

Several equations to calculate plasma oncotic pressure (pi) from the total protein concentration (C) have been previously described. These equations were derived empirically from samples with a wide range of C obtained by diluting or concentrating normal plasma samples. To test these equations over a range of naturally occurring C, we measured C and pi of plasma samples from 40 dogs. C ranged from 5.3 to 8.7 g/dl and averaged 6.5 +/- 0.1 (mean +/- SE) and pi averaged 17.9 +/- 0.3 mmHg. The regression equation was pi = 78.14 + 1.67 C (r = 0.74). pi increased with C much less than predicted with the commonly used equations. The albumin-to-globulin concentration ratios (A/G), determined in 27 of the dogs, decreased with increasing C (A/G = 1.56-0.128 C, r = 0.62). The lower A/G at the higher C's could cause the lower than predicted increase in pi with C, because the equations were developed from data in which A/G was constant.

A diagonal algorithm for the method of pseudocompressibility. [for steady-state solution to incompressible Navier-Stokes equation

NASA Technical Reports Server (NTRS)

Rogers, S. E.; Kwak, D.; Chang, J. L. C.

1986-01-01

The method of pseudocompressibility has been shown to be an efficient method for obtaining a steady-state solution to the incompressible Navier-Stokes equations. Recent improvements to this method include the use of a diagonal scheme for the inversion of the equations at each iteration. The necessary transformations have been derived for the pseudocompressibility equations in generalized coordinates. The diagonal algorithm reduces the computing time necessary to obtain a steady-state solution by a factor of nearly three. Implicit viscous terms are maintained in the equations, and it has become possible to use fourth-order implicit dissipation. The steady-state solution is unchanged by the approximations resulting from the diagonalization of the equations. Computed results for flow over a two-dimensional backward-facing step and a three-dimensional cylinder mounted normal to a flat plate are presented for both the old and new algorithms. The accuracy and computing efficiency of these algorithms are compared.

Volatilization of organic compounds from streams

USGS Publications Warehouse

Rathburn, R.E.; Tai, D.Y.

1982-01-01

Mass-transfer coefficients for the volatilization of ethylene and propane were correlated with the hydraulic and geometric properties of seven streams, and predictive equations were developed. The equations were evaluated using a normalized root-mean-square error as the criterion of comparison. The two best equations were a two-variable equation containing the energy dissipated per unit mass per unit time and the average depth of flow and a three-variable equation containing the average velocity, the average depth of flow, and the slope of the stream. Procedures for adjusting the ethylene and propane coefficients for other organic compounds were evaluated. These procedures are based on molecular diffusivity, molecular diameter, or molecular weight. Because of limited data, none of these procedures have been extensively verified. Therefore, until additional data become available, it is suggested that the mass-transfer coefficient be assumed to be inversely proportional to the square root of the molecular weight.

The Shock and Vibration Digest. Volume 16, Number 7

DTIC Science & Technology

1984-07-01

Brayton -Moser :,. existence of classical normal modes in various classes equations has been presented (32, 33]. Two methods of problems, the concept of...and Re- "Connections between the Generalized Hamil- strained Dynamical Systems," J. Appl. Mech., ton-Lagrange and Brayton -Moser Equations," Trans...committees within the division. Short Ccourses are also offered as a part of this conference, Walter Taylor described how he used a microcom- and the

The kinked interface crack

NASA Astrophysics Data System (ADS)

Heitzer, Joerg

1992-05-01

Two methods for the numerical solution of the integral equation describing the kinked interface crack, one proposed by Erdogan et al. (1973) and the other by Theokaris and Iokimidis (1979), are examined. The method of Erdogan et al. is then used to solve the equation in order to determine the kinking angle of the interface crack. Results are presented for two material combinations, aluminum/epoxy and glass/ceramic, under uniaxial tension in the direction normal to the interface.

Time dependent Schrödinger equation for black hole evaporation: No information loss

NASA Astrophysics Data System (ADS)

Corda, Christian

2015-02-01

In 1976 S. Hawking claimed that "Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state".1 In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model, a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of a unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking's claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect 't Hooft's assumption that Schrödinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in a unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.

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.

Is the ML Chi-Square Ever Robust to Nonnormality? A Cautionary Note with Missing Data

ERIC Educational Resources Information Center

Savalei, Victoria

2008-01-01

Normal theory maximum likelihood (ML) is by far the most popular estimation and testing method used in structural equation modeling (SEM), and it is the default in most SEM programs. Even though this approach assumes multivariate normality of the data, its use can be justified on the grounds that it is fairly robust to the violations of the…

The Normals to a Parabola and the Real Roots of a Cubic

ERIC Educational Resources Information Center

Bains, Majinder S.; Thoo, J. B.

2007-01-01

The geometric problem of finding the number of normals to the parabola y = x[squared] through a given point is equivalent to the algebraic problem of finding the number of distinct real roots of a cubic equation. Apollonius solved the former problem, and Cardano gave a solution to the latter. The two problems are bridged by Neil's (semi-cubical)…

The Effect of Multicollinearity and the Violation of the Assumption of Normality on the Testing of Hypotheses in Regression Analysis.

ERIC Educational Resources Information Center

Vasu, Ellen S.; Elmore, Patricia B.

The effects of the violation of the assumption of normality coupled with the condition of multicollinearity upon the outcome of testing the hypothesis Beta equals zero in the two-predictor regression equation is investigated. A monte carlo approach was utilized in which three differenct distributions were sampled for two sample sizes over…

The Effect of Prolonged Glucosamine Usage on HbA1c Levels and New-Onset Diabetes Mellitus in Overweight and Obese Middle-Aged Women.

PubMed

Gommans, Yvonne M M; Runhaar, Jos; Jacobs, Marloes L; Bierma-Zeinstra, Sita M A

2017-06-01

The aim of the present study was to evaluate the effect of a 2.5-year glucosamine sulfate intervention on hemoglobin A1c (HbA1c) levels and the incidence of new-onset diabetes mellitus over 6.5 years in middle-aged women with a body mass index ≥27 kg/m 2 . In total, 407 women were randomized into either oral crystalline glucosamine sulfate or placebo. At baseline, 1 year, 2.5 years, and 6.5 years, a blood sample for the HbA1c level was drawn and questionnaires were taken. After 6.5 years there were missing data for some variables, therefore, multiple imputation was used. With the imputed data, a generalized estimating equation was performed to analyze the effect of glucosamine sulfate usage over 6.5 years. Finally, these analyses were rerun for the 2 subgroups of participants with and without high HbA1c level (≥42 mmol/mol) at baseline. There was no significant effect of a 2.5-year glucosamine sulfate intervention on mean HbA1c level or on obtaining a high HbA1c level or new-onset diabetes mellitus over 6.5 years. The subgroup analyses of participants with and without high HbA1c level at baseline were also not statistically significant. However, participants with a high HbA1c level at baseline had higher odds ratios compared with the participants with a normal HbA1c at baseline. There was no effect of glucosamine sulfate on mean HbA1c level nor on obtaining a high HbA1c level or new-onset diabetes mellitus over 6.5 years, especially in participants with a normal HbA1c level at baseline. Copyright © 2016 Elsevier Inc. All rights reserved.

Research on influence of different cover to the characteristic of FBG reflectance spectrum in vacuum thermal environment

NASA Astrophysics Data System (ADS)

Pei, Yifei; Zhang, Jingchuan; Zhang, Luosha; Liu, Yang; Zhang, Lina; Chen, Shiyu

2018-01-01

To satisfy the application of fiber grating sensor technology in high vacuum thermal environment, two different kinds of sleeve compactly single model fiber covered by acrylate and polyimide are researched. Influence of the cover to the characteristic of FBG reflectance spectrum in high vacuum thermal environment is analyzed and verified. First, transmission characteristic of single model fiber in high vacuum thermal environment is analyzed by solve the equation of heat conduction. Then, experimental program of influence on FBG reflection spectrum characteristics is designed and a hardware-in-the-loop detection platform is set up. Finally, the influence of temperature and vacuum on the reflection peak power of FBG in different coating single-mode transmission fiber under high vacuum thermal environment is studied and verified. Experimental results indicate that: when vacuum varied from normal pressure to 10-4Pa level and then return to normal pressure, temperature of two different coating single-mode transmission fiber dropped to -196 ° from room temperature and then returned to room temperature, after 224 hours, the peak power of the FBG reflectance spectrum did not change. It provided the theoretical and experimental basis for the application of optical fiber sensing technology in high vacuum (pressure about 10-4Pa level) and thermal environment (-196 ° 25 ° temperature cycle) .

Investigation of the Dirac Equation by Using the Conformable Fractional Derivative

NASA Astrophysics Data System (ADS)

Mozaffari, F. S.; Hassanabadi, H.; Sobhani, H.; Chung, W. S.

2018-05-01

In this paper,the Dirac equation is constructed using the conformable fractional derivative so that in its limit for the fractional parameter, the normal version is recovered. Then, the Cornell potential is considered as the interaction of the system. In this case, the wave function and the energy eigenvalue equation are derived with the aim of the bi-confluent Heun functions. use of the conformable fractional derivative is proven to lead to a branching treatment for the energy of the system. Such a treatment is obvious for small values of the fractional parameter, and a united value as the fractional parameter approaches unity.

Chorus Source Locations from VLF Poynting Flux Measurements with the Polar Spacecraft

NASA Technical Reports Server (NTRS)

LeDocq, M. J.; Gurnett, D. A.; Hospodarsky, G. B.

1998-01-01

Previous studies have used indirect evidence to argue that whistler-mode chorus emissions are generated near the magnetic equator. In this paper a spatial survey of wave normals and Poynting vectors computed from three-component electric and magnetic field measurements is used to show that chorus is generated very close to the magnetic equator. One surprising result is that there are almost no chorus emissions propagating toward the magnetic equator, such as might be expected from high-latitude magnetospheric reflections. The absence of a reflected component indicates that the chorus is reabsorbed, probably by Landau damping, before returning to the magnetic equatorial plane.

A nonperturbative approximation for the moderate Reynolds number Navier–Stokes equations

PubMed Central

Roper, Marcus; Brenner, Michael P.

2009-01-01

The nonlinearity of the Navier–Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier–Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes. PMID:19211800

A nonperturbative approximation for the moderate Reynolds number Navier-Stokes equations.

PubMed

Roper, Marcus; Brenner, Michael P

2009-03-03

The nonlinearity of the Navier-Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier-Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes.

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

Designing scattering-free isotropic index profiles using phase-amplitude equations

NASA Astrophysics Data System (ADS)

King, C. G.; Horsley, S. A. R.; Philbin, T. G.

2018-05-01

The Helmholtz equation can be written as coupled equations for the amplitude and phase. By considering spatial phase distributions corresponding to reflectionless wave propagation in the plane and solving for the amplitude in terms of this phase, we designed two-dimensional graded-index media which do not scatter light. We give two illustrative examples, the first of which is a periodic grating for which diffraction is completely suppressed at a single frequency at normal incidence to the periodicity. The second example is a medium which behaves as a "beam shifter" at a single frequency; acting to laterally shift a plane wave, or sufficiently wide beam, without reflection.

Solving the incompressible surface Navier-Stokes equation by surface finite elements

NASA Astrophysics Data System (ADS)

Reuther, Sebastian; Voigt, Axel

2018-01-01

We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g (S ) . The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding R3, penalization of the normal component, a Chorin projection method, and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincaré-Hopf theorem on n-tori.

Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis.

PubMed

Faye, Grégory; Rankin, James; Chossat, Pascal

2013-05-01

The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.

Reply to "Comment on 'Defocusing complex short-pulse equation and its multi-dark-soliton solution' ".

PubMed

Feng, Bao-Feng; Ling, Liming; Zhu, Zuonong

2017-08-01

Our paper [Phys. Rev. E 93, 052227 (2016)PREHBM2470-004510.1103/PhysRevE.93.052227], proposing an integrable model for the propagation of ultrashort pulses, has recently received a Comment by Youssoufa et al. [Phys. Rev. E 96, 026201 (2017)10.1103/PhysRevE.96.026201] about a possible flaw in its derivation. We point out that their claim is incorrect since we have stated explicitly that a term is neglected to derive our model equation in our paper. Furthermore, the integrable model is validated by comparing with the normalized Maxwell equation and other known integrable models. Moreover, we show that a similar approximation has to be performed in deriving the same integrable equation as explained in the Comment.

Simplified Design Method for Tension Fasteners

NASA Astrophysics Data System (ADS)

Olmstead, Jim; Barker, Paul; Vandersluis, Jonathan

2012-07-01

Tension fastened joints design has traditionally been an iterative tradeoff between separation and strength requirements. This paper presents equations for the maximum external load that a fastened joint can support and the optimal preload to achieve this load. The equations, based on linear joint theory, account for separation and strength safety factors and variations in joint geometry, materials, preload, load-plane factor and thermal loading. The strength-normalized versions of the equations are applicable to any fastener and can be plotted to create a "Fastener Design Space", FDS. Any combination of preload and tension that falls within the FDS represents a safe joint design. The equation for the FDS apex represents the optimal preload and load capacity of a set of joints. The method can be used for preliminary design or to evaluate multiple pre-existing joints.

Prescribing the mixed scalar curvature of a foliated Riemann-Cartan manifold

NASA Astrophysics Data System (ADS)

Rovenski, Vladimir Y.; Zelenko, Leonid

2018-03-01

The mixed scalar curvature is the simplest curvature invariant of a foliated Riemannian manifold. We explore the problem of prescribing the leafwise constant mixed scalar curvature of a foliated Riemann-Cartan manifold by conformal change of the structure in tangent and normal to the leaves directions. Under certain geometrical assumptions and in two special cases: along a compact leaf and for a closed fibered manifold, we reduce the problem to solution of a nonlinear leafwise elliptic equation for the conformal factor. We are looking for its solutions that are stable stationary solutions of the associated parabolic equation. Our main tool is using of majorizing and minorizing nonlinear heat equations with constant coefficients and application of comparison theorems for solutions of Cauchy's problem for parabolic equations.

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

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1987-01-01

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

Electron-Impact Excitation Cross Sections for Modeling Non-Equilibrium Gas

NASA Technical Reports Server (NTRS)

Huo, Winifred M.; Liu, Yen; Panesi, Marco; Munafo, Alessandro; Wray, Alan; Carbon, Duane F.

2015-01-01

In order to provide a database for modeling hypersonic entry in a partially ionized gas under non-equilibrium, the electron-impact excitation cross sections of atoms have been calculated using perturbation theory. The energy levels covered in the calculation are retrieved from the level list in the HyperRad code. The downstream flow-field is determined by solving a set of continuity equations for each component. The individual structure of each energy level is included. These equations are then complemented by the Euler system of equations. Finally, the radiation field is modeled by solving the radiative transfer equation.

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

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

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

2015-02-15

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

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

NASA Astrophysics Data System (ADS)

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

2015-02-01

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

a Recursive Approach to Compute Normal Forms

NASA Astrophysics Data System (ADS)

HSU, L.; MIN, L. J.; FAVRETTO, L.

2001-06-01

Normal forms are instrumental in the analysis of dynamical systems described by ordinary differential equations, particularly when singularities close to a bifurcation are to be characterized. However, the computation of a normal form up to an arbitrary order is numerically hard. This paper focuses on the computer programming of some recursive formulas developed earlier to compute higher order normal forms. A computer program to reduce the system to its normal form on a center manifold is developed using the Maple symbolic language. However, it should be stressed that the program relies essentially on recursive numerical computations, while symbolic calculations are used only for minor tasks. Some strategies are proposed to save computation time. Examples are presented to illustrate the application of the program to obtain high order normalization or to handle systems with large dimension.

The Acceleration of Charged Particles at a Spherical Shock Moving through an Irregular Magnetic Field

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

Giacalone, J.

We investigate the physics of charged-particle acceleration at spherical shocks moving into a uniform plasma containing a turbulent magnetic field with a uniform mean. This has applications to particle acceleration at astrophysical shocks, most notably, to supernovae blast waves. We numerically integrate the equations of motion of a large number of test protons moving under the influence of electric and magnetic fields determined from a kinematically defined plasma flow associated with a radially propagating blast wave. Distribution functions are determined from the positions and velocities of the protons. The unshocked plasma contains a magnetic field with a uniform mean andmore » an irregular component having a Kolmogorov-like power spectrum. The field inside the blast wave is determined from Maxwell’s equations. The angle between the average magnetic field and unit normal to the shock varies with position along its surface. It is quasi-perpendicular to the unit normal near the sphere’s equator, and quasi-parallel to it near the poles. We find that the highest intensities of particles, accelerated by the shock, are at the poles of the blast wave. The particles “collect” at the poles as they approximately adhere to magnetic field lines that move poleward from their initial encounter with the shock at the equator, as the shock expands. The field lines at the poles have been connected to the shock the longest. We also find that the highest-energy protons are initially accelerated near the equator or near the quasi-perpendicular portion of the shock, where the acceleration is more rapid.« less

Characterizing functional lung heterogeneity in COPD using reference equations for CT scan-measured lobar volumes.

PubMed

Come, Carolyn E; Diaz, Alejandro A; Curran-Everett, Douglas; Muralidhar, Nivedita; Hersh, Craig P; Zach, Jordan A; Schroeder, Joyce; Lynch, David A; Celli, Bartolome; Washko, George R

2013-06-01

CT scanning is increasingly used to characterize COPD. Although it is possible to obtain CT scan-measured lung lobe volumes, normal ranges remain unknown. Using COPDGene data, we developed reference equations for lobar volumes at maximal inflation (total lung capacity [TLC]) and relaxed exhalation (approximating functional residual capacity [FRC]). Linear regression was used to develop race-specific (non-Hispanic white [NHW], African American) reference equations for lobar volumes. Covariates included height and sex. Models were developed in a derivation cohort of 469 subjects with normal pulmonary function and validated in 546 similar subjects. These cohorts were combined to produce final prediction equations, which were applied to 2,191 subjects with old GOLD (Global Initiative for Chronic Obstructive Lung Disease) stage II to IV COPD. In the derivation cohort, women had smaller lobar volumes than men. Height positively correlated with lobar volumes. Adjusting for height, NHWs had larger total lung and lobar volumes at TLC than African Americans; at FRC, NHWs only had larger lower lobes. Age and weight had no effect on lobar volumes at TLC but had small effects at FRC. In subjects with COPD at TLC, upper lobes exceeded 100% of predicted values in GOLD II disease; lower lobes were only inflated to this degree in subjects with GOLD IV disease. At FRC, gas trapping was severe irrespective of disease severity and appeared uniform across the lobes. Reference equations for lobar volumes may be useful in assessing regional lung dysfunction and how it changes in response to pharmacologic therapies and surgical or endoscopic lung volume reduction.

Arterial blood gas reference values for sea level and an altitude of 1,400 meters.

PubMed

Crapo, R O; Jensen, R L; Hegewald, M; Tashkin, D P

1999-11-01

Blood gas measurements were collected on healthy lifetime nonsmokers at sea level (n = 96) and at an altitude of 1,400 meters (n = 243) to establish reference equations. At each study site, arterial blood samples were analyzed in duplicate on two separate blood gas analyzers and CO-oximeters. Arterial blood gas variables included Pa(O(2)), Pa(CO(2)), pH, and calculated alveolar-arterial PO(2) difference (AaPO(2)). CO-oximeter variables were Hb, COHb, MetHb, and Sa(O(2)). Subjects were 18 to 81 yr of age with 166 male and 173 female. Outlier data were excluded from multiple regression analysis, and reference equations were fitted to the data in two ways: (1) best fit using linear, squared, and cross-product terms; (2) simple equations, including only the variables that explained at least 3% of the variance. Two sets of equations were created: (1) using only the sea level data and (2) using the combined data with barometric pressure as an independent variable. Comparisons with earlier studies revealed small but significant differences; the decline in Pa(O(2)) with age at each altitude was consistent with most previous studies. At sea level, the equation that included barometric pressure predicted Pa(O(2)) slightly better than the sea level specific equation. The inclusion of barometric pressure in the equations allows better prediction of blood gas reference values at sea level and at altitudes as high as 1,400 meters.

A Study of Qualitative and Geometric Knowledge in Reasoning about Motion. Revision.

DTIC Science & Technology

1981-02-01

cpartinen of I)cfcnsc under Office of Naval Research contract N00014-80-C-0505 Acce’ Tin For F T" D/ c.,, i ’" d es -t A Stud’ of Qualitatise and...UNIT-VECTOR: ((number> (number>) UNtIT-NORMAL: ((number> (number>) PERPLNDtCULAR-EQUATIONS: ((equations>) PARABOLA REGION TYPE: PARABOLA TYPE: REGION...constraints. The mapping between domain objects and Metric Diagram elements is simple: Ball -> Point Surface -> Segment Trajectory -> Segment, Parabola

Simplified conversions between specific conductance and salinity units for use with data from monitoring stations

USGS Publications Warehouse

Schemel, Laurence E.

2001-01-01

This article presents a simplified conversion to salinity units for use with specific conductance data from monitoring stations that have been normalized to a standard temperature of 25 °C and an equation for the reverse calculation. Although these previously undocumented methods have been shared with many IEP agencies over the last two decades, the sources of the equations and data are identified here so that the original literature can be accessed.

Direct perturbation theory for the dark soliton solution to the nonlinear Schroedinger equation with normal dispersion

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

Yu Jialu; Yang Chunnuan; Cai Hao

2007-04-15

After finding the basic solutions of the linearized nonlinear Schroedinger equation by the method of separation of variables, the perturbation theory for the dark soliton solution is constructed by linear Green's function theory. In application to the self-induced Raman scattering, the adiabatic corrections to the soliton's parameters are obtained and the remaining correction term is given as a pure integral with respect to the continuous spectral parameter.

Oscillations of manometric tubular springs with rigid end

NASA Astrophysics Data System (ADS)

Cherentsov, D. A.; Pirogov, S. P.; Dorofeev, S. M.; Ryabova, Y. S.

2018-05-01

The paper presents a mathematical model of attenuating oscillations of manometric tubular springs (MTS) taking into account the rigid tip. The dynamic MTS model is presented in the form of a thin-walled curved rod oscillating in the plane of curvature of the central axis. Equations for MTS oscillations are obtained in accordance with the d’Alembert principle in projections onto the normal and tangential. The Bubnov-Galerkin method is used to solve the equations obtained.

Distributed Blowing and Suction for the Purpose of Streak Control in a Boundary Layer Subjected to a Favorable Pressure Gradient

NASA Technical Reports Server (NTRS)

Forgoston, Eric; Tumin, Anatoli; Ashpis, David E.

2005-01-01

An analysis of the optimal control by blowing and suction in order to generate stream- wise velocity streaks is presented. The problem is examined using an iterative process that employs the Parabolized Stability Equations for an incompressible uid along with its adjoint equations. In particular, distributions of blowing and suction are computed for both the normal and tangential velocity perturbations for various choices of parameters.

BPHZ renormalization in configuration space for the A4-model

NASA Astrophysics Data System (ADS)

Pottel, Steffen

2018-02-01

Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann identity is shown for a normal product, which is quadratic in the field operator. The realization of the equation of motion is computed for the interacting field and the relation to parametric differential equations is indicated.

A collocation--Galerkin finite element model of cardiac action potential propagation.

PubMed

Rogers, J M; McCulloch, A D

1994-08-01

A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.

Recalibrated Equations for Determining Effect of Oil Filtration on Rolling Bearing Life

NASA Technical Reports Server (NTRS)

Needelman, William M.; Zaretsky, Erwin V.

2014-01-01

In 1991, Needelman and Zaretsky presented a set of empirically derived equations for bearing fatigue life (adjustment) factors (LFs) as a function of oil filter ratings. These equations for life factors were incorporated into the reference book, "STLE Life Factors for Rolling Bearings." These equations were normalized (LF = 1) to a 10-micrometer filter rating at Beta(sub x) = 200 (normal cleanliness) as it was then defined. Over the past 20 years, these life factors based on oil filtration have been used in conjunction with ANSI/ABMA standards and bearing computer codes to predict rolling bearing life. Also, additional experimental studies have been made by other investigators into the relationship between rolling bearing life and the size, number, and type of particle contamination. During this time period filter ratings have also been revised and improved, and they now use particle counting calibrated to a new National Institute of Standards and Technology (NIST) reference material, NIST SRM 2806, 1997. This paper reviews the relevant bearing life studies and describes the new filter ratings. New filter ratings, Beta(sub x(c)) = 200 and Beta(sub x(c)) = 1000, are benchmarked to old filter ratings, Beta(sub x) = 200, and vice versa. Two separate sets of filter LF values were derived based on the new filter ratings for roller bearings and ball bearings, respectively. Filter LFs can be calculated for the new filter ratings.

Energy Levels in Quantum Wells.

NASA Astrophysics Data System (ADS)

Zang, Jan Xin

Normalized analytical equations for eigenstates of an arbitrary one-dimensional configuration of square potentials in a well have been derived. The general formulation is used to evaluate the energy levels of a particle in a very deep potential well containing seven internal barriers. The configuration can be considered as a finite superlattice sample or as a simplified model for a sample with only several atom layers. The results are shown in graphical forms as functions of the height and width of the potential barriers and as functions of the ratio of the effective mass in barrier to the mass in well. The formation of energy bands and surface eigenstates from eigenstates of a deep single well, the coming close of two energy bands and a surface state which are separate ordinarily, and mixing of the wave function of a surface state with the bulk energy bands are seen. Then the normalized derivation is extended to study the effect of a uniform electric field applied across a one-dimensional well containing an internal configuration of square potentials The general formulation is used to calculate the electric field dependence of the energy levels of a deep well with five internal barriers. Typical results are shown in graphical forms as functions of the barrier height, barrier width, barrier effective mass and the field strength. The formation of Stark ladders and surface states from the eigenstates of a single deep well in an electric field, the localization process of wave functions with changing barrier height, width, and field strength and their anticrossing behaviors are seen. The energy levels of a hydrogenic impurity in a uniform medium and in a uniform magnetic field are calculated with variational methods. The energy eigenvalues for the eigenstates with major quantum number less than or equal to 3 are obtained. The results are consistent with previous results. Furthermore, the energy levels of a hydrogenic impurity at the bottom of a one-dimensional parabolic quantum well with a magnetic field normal to the plane of the well are calculated with the finite-basis-set variational method. The limit of small radial distance and the limit of great radial distance are considered to choose a set of proper basis functions. It is found that the energy levels increase with increasing parabolic parameter alpha and increase with increasing normalized magnetic field strength gamma except those levels with magnetic quantum number m < 0 at small gamma.

A computer program for calculating the perfect gas inviscid flow field about blunt axisymmetric bodies at an angle of attack of 0 deg

NASA Technical Reports Server (NTRS)

Zoby, E. V.; Graves, R. A., Jr.

1973-01-01

A method for the rapid calculation of the inviscid shock layer about blunt axisymmetric bodies at an angle of attack of 0 deg has been developed. The procedure is of an inverse nature, that is, a shock wave is assumed and calculations proceed along rays normal to the shock. The solution is iterated until the given body is computed. The flow field solution procedure is programed at the Langley Research Center for the Control Data 6600 computer. The geometries specified in the program are sphores, ellipsoids, paraboloids, and hyperboloids which may conical afterbodies. The normal momentum equation is replaced with an approximate algebraic expression. This simplification significantly reduces machine computation time. Comparisons of the present results with shock shapes and surface pressure distributions obtained by the more exact methods indicate that the program provides reasonably accurate results for smooth bodies in axisymmetric flow. However, further research is required to establish the proper approximate form of the normal momentum equation for the two-dimensional case.

Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants

NASA Astrophysics Data System (ADS)

Bernhoff, Niclas

2018-05-01

An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. Unlike for the Boltzmann equation, for DVMs there can appear extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and hence, without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but also for binary mixtures and recently extensively for multicomponent mixtures. In this paper, we address ways of constructing normal DVMs for polyatomic molecules (here represented by that each molecule has an internal energy, to account for non-translational energies, which can change during collisions), under the assumption that the set of allowed internal energies are finite. We present general algorithms for constructing such models, but we also give concrete examples of such constructions. This approach can also be combined with similar constructions of multicomponent mixtures to obtain multicomponent mixtures with polyatomic molecules, which is also briefly outlined. Then also, chemical reactions can be added.

Vibrational Modes of Oblate Clouds of Charge

NASA Astrophysics Data System (ADS)

Jenkins, Thomas; Spencer, Ross L.

2000-10-01

When a nonneutral plasma confined in a Penning trap is allowed time to expand, its shape at global thermal equilibrium is that of a thin oblate spheroid [D. L. Paulson et al., Phys. Plasmas 5, 345 (1998)]. Oscillations similar to those of a drumhead can be externally induced in such a plasma. Although a theory developed by Dubin predicts the frequencies of the various normal modes of oscillation [Phys. Rev. Lett. 66, 2076 (1991)], this theory assumes that the plasma has zero temperature and is confined by an ideal quadrupole electric field. Neither of these conditions is strictly true in experiments [C. S. Weimer et al., Phys. Rev. A 49, 3842 (1994)] where physical properties of the plasma are deduced from measurements of these frequencies, causing the measurements and ideal theory to differ by about 20%. We reformulate the problem of the normal oscillatory modes as a principal-value integral eigenvalue equation, including finite-temperature and non-ideal confinement effects. The equation is solved numerically to obtain the plasma's normal mode frequencies and shapes; reasonable agreement with experiment is obtained.

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

Quantification of Cardiorespiratory Fitness in Healthy Nonobese and Obese Men and Women

PubMed Central

Lorenzo, Santiago

2012-01-01

Background: The quantification and interpretation of cardiorespiratory fitness (CRF) in obesity is important for adequately assessing cardiovascular conditioning, underlying comorbidities, and properly evaluating disease risk. We retrospectively compared peak oxygen uptake (V˙o2peak) (ie, CRF) in absolute terms, and relative terms (% predicted) using three currently suggested prediction equations (Equations R, W, and G). Methods: There were 19 nonobese and 66 obese participants. Subjects underwent hydrostatic weighing and incremental cycling to exhaustion. Subject characteristics were analyzed by independent t test, and % predicted V˙o2peak by a two-way analysis of variance (group and equation) with repeated measures on one factor (equation). Results: V˙o2peak (L/min) was not different between nonobese and obese adults (2.35 ± 0.80 [SD] vs 2.39 ± 0.68 L/min). V˙o2peak was higher (P < .02) relative to body mass and lean body mass in the nonobese (34 ± 8 mL/min/kg vs 22 ± 5 mL/min/kg, 42 ± 9 mL/min/lean body mass vs 37 ± 6 mL/min/lean body mass). Cardiorespiratory fitness assessed as % predicted was not different in the nonobese and obese (91% ± 17% predicted vs 95% ± 15% predicted) using Equation R, while using Equation W and G, CRF was lower (P < .05) but within normal limits in the obese (94 ± 15 vs 87 ± 11; 101% ± 17% predicted vs 90% ± 12% predicted, respectively), depending somewhat on sex. Conclusions: Traditional methods of reporting V˙o2peak do not allow adequate assessment and quantification of CRF in obese adults. Predicted V˙o2peak does allow a normalized evaluation of CRF in the obese, although care must be taken in selecting the most appropriate prediction equation, especially in women. In general, otherwise healthy obese are not grossly deconditioned as is commonly believed, although CRF may be slightly higher in nonobese subjects depending on the uniqueness of the prediction equation. PMID:21940772

Dark and antidark solitons in the modified nonlinear Schrödinger equation accounting for the self-steepening effect.

PubMed

Li, Min; Tian, Bo; Liu, Wen-Jun; Zhang, Hai-Qiang; Wang, Pan

2010-04-01

In this paper, the modified nonlinear Schrödinger equation is investigated, which describes the femtosecond optical pulse propagation in a monomodal optical fiber. Based on the Wadati-Konno-Ichikawa system, another type of Lax pair and infinitely many conservation laws are derived. Dark and antidark soliton solutions in the normal dispersion regime are obtained by means of the Hirota method. Parametric regions for the existence of the dark and antidark soliton solutions are given. Asymptotic analysis of the two-soliton solution shows that collisions between two solitons (two antidark solitons, two dark solitons, and dark and antidark solitons) are elastic. In addition, collision between dark and antidark solitons reveals that dark and antidark solitons can co-exist on the same background in the normal dispersion regime.

Fractional calculus and morphogen gradient formation

NASA Astrophysics Data System (ADS)

Yuste, Santos Bravo; Abad, Enrique; Lindenberg, Katja

2012-12-01

Some microscopic models for reactive systems where the reaction kinetics is limited by subdiffusion are described by means of reaction-subdiffusion equations where fractional derivatives play a key role. In particular, we consider subdiffusive particles described by means of a Continuous Time Random Walk (CTRW) model subject to a linear (first-order) death process. The resulting fractional equation is employed to study the developmental biology key problem of morphogen gradient formation for the case in which the morphogens are subdiffusive. If the morphogen degradation rate (reactivity) is constant, we find exponentially decreasing stationary concentration profiles, which are similar to the profiles found when the morphogens diffuse normally. However, for the case in which the degradation rate decays exponentially with the distance to the morphogen source, we find that the morphogen profiles are qualitatively different from the profiles obtained when the morphogens diffuse normally.

A finite element formulation for supersonic flows around complex configurations

NASA Technical Reports Server (NTRS)

Morino, L.

1974-01-01

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element are assumed to be constant and equal to its value at the centroid of the element. This yields a set of linear algebraic equations whose coefficients are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented.

Elementary solutions of coupled model equations in the kinetic theory of gases

NASA Technical Reports Server (NTRS)

Kriese, J. T.; Siewert, C. E.; Chang, T. S.

1974-01-01

The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.

How to derive biological information from the value of the normalization constant in allometric equations.

PubMed

Kaitaniemi, Pekka

2008-04-09

Allometric equations are widely used in many branches of biological science. The potential information content of the normalization constant b in allometric equations of the form Y = bX(a) has, however, remained largely neglected. To demonstrate the potential for utilizing this information, I generated a large number of artificial datasets that resembled those that are frequently encountered in biological studies, i.e., relatively small samples including measurement error or uncontrolled variation. The value of X was allowed to vary randomly within the limits describing different data ranges, and a was set to a fixed theoretical value. The constant b was set to a range of values describing the effect of a continuous environmental variable. In addition, a normally distributed random error was added to the values of both X and Y. Two different approaches were then used to model the data. The traditional approach estimated both a and b using a regression model, whereas an alternative approach set the exponent a at its theoretical value and only estimated the value of b. Both approaches produced virtually the same model fit with less than 0.3% difference in the coefficient of determination. Only the alternative approach was able to precisely reproduce the effect of the environmental variable, which was largely lost among noise variation when using the traditional approach. The results show how the value of b can be used as a source of valuable biological information if an appropriate regression model is selected.

NIMROD: a program for inference via a normal approximation of the posterior in models with random effects based on ordinary differential equations.

PubMed

Prague, Mélanie; Commenges, Daniel; Guedj, Jérémie; Drylewicz, Julia; Thiébaut, Rodolphe

2013-08-01

Models based on ordinary differential equations (ODE) are widespread tools for describing dynamical systems. In biomedical sciences, data from each subject can be sparse making difficult to precisely estimate individual parameters by standard non-linear regression but information can often be gained from between-subjects variability. This makes natural the use of mixed-effects models to estimate population parameters. Although the maximum likelihood approach is a valuable option, identifiability issues favour Bayesian approaches which can incorporate prior knowledge in a flexible way. However, the combination of difficulties coming from the ODE system and from the presence of random effects raises a major numerical challenge. Computations can be simplified by making a normal approximation of the posterior to find the maximum of the posterior distribution (MAP). Here we present the NIMROD program (normal approximation inference in models with random effects based on ordinary differential equations) devoted to the MAP estimation in ODE models. We describe the specific implemented features such as convergence criteria and an approximation of the leave-one-out cross-validation to assess the model quality of fit. In pharmacokinetics models, first, we evaluate the properties of this algorithm and compare it with FOCE and MCMC algorithms in simulations. Then, we illustrate NIMROD use on Amprenavir pharmacokinetics data from the PUZZLE clinical trial in HIV infected patients. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Correlation of cystatin C and creatinine based estimates of renal function in children with hydronephrosis.

PubMed

Momtaz, Hossein-Emad; Dehghan, Arash; Karimian, Mohammad

2016-01-01

The use of a simple and accurate glomerular filtration rate (GFR) estimating method aiming minute assessment of renal function can be of great clinical importance. This study aimed to determine the association of a GFR estimating by equation that includes only cystatin C (Gentian equation) to equation that include only creatinine (Schwartz equation) among children. A total of 31 children aged from 1 day to 5 years with the final diagnosis of unilateral or bilateral hydronephrosis referred to Besat hospital in Hamadan, between March 2010 and February 2011 were consecutively enrolled. Schwartz and Gentian equations were employed to determine GFR based on plasma creatinine and cystatin C levels, respectively. The proportion of GFR based on Schwartz equation was 70.19± 24.86 ml/min/1.73 m(2), while the level of this parameter based on Gentian method and using cystatin C was 86.97 ± 21.57 ml/min/1.73 m(2). The Pearson correlation coefficient analysis showed a strong direct association between the two levels of GFR measured by Schwartz equation based on serum creatinine level and Gentian method and using cystatin C (r = 0.594, P < 0.001). The linear association between GFR values measured with the two methods included cystatin C based GFR = 50.8+ 0.515 × Schwartz GFR. The correlation between GFR values measured by using serum creatinine and serum cystatin C measurements remained meaningful even after adjustment for patients' gender and age (r = 0.724, P < 0.001). The equation developed based on cystatin C level is comparable with another equation, based on serum creatinine (Schwartz formula) to estimate GFR in children.

A practical weighting function for harbor porpoise underwater sound level measurements.

PubMed

Terhune, John M

2013-09-01

Harbor porpoise (Phocoena phocoena) are subject to underwater noise disturbance from anthropogenic sources, especially shipping. The underwater audiograms of harbor porpoise were used to create a frequency weighting function, dBht(Phocoena phocoena), to permit estimation of the broadband perceived amplitudes of ambient and shipping noise. An equation was fit to the 0.02-20 kHz range of unmasked detection thresholds and normalizing to 0 dB at 20 kHz; dB = 46.4-35.6 log(kHz). The weighting function de-emphasizes the low frequency components of noise. Harbor porpoise hearing is less sensitive to low frequency shipping noise and, except at high amplitudes, estimating potential noise impacts using linear measurements will be misleading.

NMA Analysis Center

NASA Technical Reports Server (NTRS)

Kierulf, Halfdan Pascal; Andersen, Per Helge

2013-01-01

The Norwegian Mapping Authority (NMA) has during the last few years had a close cooperation with Norwegian Defence Research Establishment (FFI) in the analysis of space geodetic data using the GEOSAT software. In 2012 NMA has taken over the full responsibility for the GEOSAT software. This implies that FFI stopped being an IVS Associate Analysis Center in 2012. NMA has been an IVS Associate Analysis Center since 28 October 2010. NMA's contributions to the IVS as an Analysis Centers focus primarily on routine production of session-by-session unconstrained and consistent normal equations by GEOSAT as input to the IVS combined solution. After the recent improvements, we expect that VLBI results produced with GEOSAT will be consistent with results from the other VLBI Analysis Centers to a satisfactory level.

Comments on compressible effects on Alfven normal modes in nonuniform plasmas

NASA Technical Reports Server (NTRS)

Mok, Y.; Einaudi, G.

1990-01-01

The paper discusses the regime of validity of the theory of dissipative Alfven normal modes presented by Mok and Einaudi (1985) and Einaudi and Mok (1985), which was based on the incompressible closure of the system of ideal MHD equations. Some simple extensions of the earlier results to the compressible case are described. In addition, certain misunderstandings of this work, which have appeared in other papers, are clarified.

Prediction of renal crystalline size distributions in space using a PBE analytic model. 1. Effect of microgravity-induced biochemical alterations.

PubMed

Kassemi, Mohammad; Thompson, David

2016-09-01

An analytical Population Balance Equation model is developed and used to assess the risk of critical renal stone formation for astronauts during future space missions. The model uses the renal biochemical profile of the subject as input and predicts the steady-state size distribution of the nucleating, growing, and agglomerating calcium oxalate crystals during their transit through the kidney. The model is verified through comparison with published results of several crystallization experiments. Numerical results indicate that the model is successful in clearly distinguishing between 1-G normal and 1-G recurrent stone-former subjects based solely on their published 24-h urine biochemical profiles. Numerical case studies further show that the predicted renal calculi size distribution for a microgravity astronaut is closer to that of a recurrent stone former on Earth rather than to a normal subject in 1 G. This interestingly implies that the increase in renal stone risk level in microgravity is relatively more significant for a normal person than a stone former. However, numerical predictions still underscore that the stone-former subject carries by far the highest absolute risk of critical stone formation during space travel. Copyright © 2016 the American Physiological Society.

Altitude-related hypoxia: risk assessment and management for passengers on commerical aircraft.

PubMed

Mortazavi, Amir; Eisenberg, Mark J; Langleben, David; Ernst, Pierre; Schiff, Renee L

2003-09-01

Individuals with pulmonary and cardiac disorders are particularly at risk of developing hypoxemia at altitude. Our objective is to describe the normal and maladaptive physiological responses to altitude-related hypoxia, to review existing methods and guidelines for preflight assessment of air travelers, and to provide recommendations for treatment of hypoxia at altitude. Falling partial pressure of oxygen with altitude results in a number of physiologic adaptations including hyperventilation, pulmonary vasoconstriction, altered ventilation/perfusion matching, and increased sympathetic tone. According to three guideline statements, the arterial pressure of oxygen (PaO2) should be maintained above 50 to 55 mm Hg at all altitudes. General indicators such as oxygen saturation and sea level blood gases may be useful in predicting altitude hypoxia. More specialized techniques for estimation of altitude PaO2, such as regression equations, hypoxia challenge testing, and hypobaric chamber exposure have also been examined. A regression equation using sea level PaO2 and spirometric parameters can be used to estimate PaO2 at altitude. Hypoxia challenge testing, performed by exposing subjects to lower inspired FIO2 at sea level may be more precise. Hypobaric chamber exposure, the gold standard, mimics lower barometric pressure, but is mainly used in research. Oxygen supplementation during air travel is needed for individuals with an estimated PaO2 (8000 ft) below 50 mmHg. There are a number of guidelines for the pre-flight assessment of patients with pulmonary and/or cardiac diseases. However, these data are based on small studies in patients with a limited group of diseases.

Stationary Random Metrics on Hierarchical Graphs Via {(min,+)}-type Recursive Distributional Equations

NASA Astrophysics Data System (ADS)

Khristoforov, Mikhail; Kleptsyn, Victor; Triestino, Michele

2016-07-01

This paper is inspired by the problem of understanding in a mathematical sense the Liouville quantum gravity on surfaces. Here we show how to define a stationary random metric on self-similar spaces which are the limit of nice finite graphs: these are the so-called hierarchical graphs. They possess a well-defined level structure and any level is built using a simple recursion. Stopping the construction at any finite level, we have a discrete random metric space when we set the edges to have random length (using a multiplicative cascade with fixed law {m}). We introduce a tool, the cut-off process, by means of which one finds that renormalizing the sequence of metrics by an exponential factor, they converge in law to a non-trivial metric on the limit space. Such limit law is stationary, in the sense that glueing together a certain number of copies of the random limit space, according to the combinatorics of the brick graph, the obtained random metric has the same law when rescaled by a random factor of law {m} . In other words, the stationary random metric is the solution of a distributional equation. When the measure m has continuous positive density on {mathbf{R}+}, the stationary law is unique up to rescaling and any other distribution tends to a rescaled stationary law under the iterations of the hierarchical transformation. We also investigate topological and geometric properties of the random space when m is log-normal, detecting a phase transition influenced by the branching random walk associated to the multiplicative cascade.

Modified Van der Waals equation and law of corresponding states

NASA Astrophysics Data System (ADS)

Zhong, Wei; Xiao, Changming; Zhu, Yongkai

2017-04-01

It is well known that the Van der Waals equation is a modification of the ideal gas law, yet it can be used to describe both gas and liquid, and some important messages can be obtained from this state equation. However, the Van der Waals equation is not a precise state equation, and it does not give a good description of the law of corresponding states. In this paper, we expand the Van der Waals equation into its Taylor's series form, and then modify the fourth order expansion by changing the constant Virial coefficients into their analogous ones. Via this way, a more precise result about the law of corresponding states has been obtained, and the law of corresponding states can then be expressed as: in terms of the reduced variables, all fluids should obey the same equation with the analogous Virial coefficients. In addition, the system of 3 He with quantum effects has also been taken into consideration with our modified Van der Waals equation, and it is found that, for a normal system without quantum effect, the modification on ideal gas law from the Van der Waals equation is more significant than the real case, however, for a system with quantum effect, this modification is less significant than the real case, thus a factor is introduced in this paper to weaken or strengthen the modification of the Van der Waals equation, respectively.

Spatiotemporal optical dark X solitary waves.

PubMed

Baronio, Fabio; Chen, Shihua; Onorato, Miguel; Trillo, Stefano; Wabnitz, Stefan; Kodama, Yuji

2016-12-01

We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schrödinger equation (NLSE), which rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between the NLSE and a well-known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics.

Comparison between Smoluchowski and Boltzmann approaches for self-propelled rods.

PubMed

Bertin, Eric; Baskaran, Aparna; Chaté, Hugues; Marchetti, M Cristina

2015-10-01

Considering systems of self-propelled polar particles with nematic interactions ("rods"), we compare the continuum equations describing the evolution of polar and nematic order parameters, derived either from Smoluchowski or Boltzmann equations. Our main goal is to understand the discrepancies between the continuum equations obtained so far in both frameworks. We first show that, in the simple case of point-like particles with only alignment interactions, the continuum equations obtained have the same structure in both cases. We further study, in the Smoluchowski framework, the case where an interaction force is added on top of the aligning torque. This clarifies the origin of the additional terms obtained in previous works. Our observations lead us to emphasize the need for a more involved closure scheme than the standard normal form of the distribution when dealing with active systems.

Numerical solutions of incompressible Navier-Stokes equations using modified Bernoulli's law

NASA Astrophysics Data System (ADS)

Shatalov, A.; Hafez, M.

2003-11-01

Simulations of incompressible flows are important for many practical applications in aeronautics and beyond, particularly in the high Reynolds number regime. The present formulation is based on Helmholtz velocity decomposition where the velocity is presented as the gradient of a potential plus a rotational component. Substituting in the continuity equation yields a Poisson equation for the potential which is solved with a zero normal derivative at solid surfaces. The momentum equation is used to update the rotational component with no slip/no penetration surface boundary conditions. The pressure is related to the potential function through a special relation which is a generalization of Bernoulli's law, with a viscous term included. Results of calculations for two- and three-dimensional problems prove that the present formulation is a valid approach, with some possible benefits compared to existing methods.

Large amplitude flexural vibration of thin elastic flat plates and shells

NASA Technical Reports Server (NTRS)

Pandalia, K. A. V.

1972-01-01

The general equations governing the large amplitude flexural vibration of any thin elastic shell using curvilinear orthogonal coordinates are derived and consist of two coupled, nonlinear, partial differential equations in the normal displacement w and the stress function F. From these equations, the governing equations for the case of shells of revolution or flat plates can be readily obtained as special cases. The material of the shell or plate is isotropic and homogeneous and Hooke's law for the two-dimensional case is valid. It is suggested that the difference between the hardening type of nonlinearity in the case of flat plates and straight beams and the softening type of nonlinearity in the case of shells and rings can, in general, be traced to the amount of curvature present in the underformed median surface of the structure concerned.

TOPEX/El Nino Watch - Satellite Shows Pacific Running Hot and Cold, September 12, 1998

NASA Technical Reports Server (NTRS)

1998-01-01

This image of the Pacific Ocean was produced using sea-surface height measurements taken by the U.S.-French TOPEX/Poseidon satellite. The image shows sea surface height relative to normal ocean conditions on September 12, 1998; these sea surface heights are an indicator of the changing amount of heat stored in the ocean. The tropical Pacific Ocean continues to exhibit the complicated characteristics of both a lingering El Nino, and a possibly waning La Nina situation. This image shows that the rapid cooling of the central tropical Pacific has slowed and this area of low sea level (shown in purple) has decreased slightly since last month. It is still uncertain, scientists say, that this cold pool will evolve into a long-lasting La Nina situation. Remnants of the El Nino warm water pool, shown here in red and white, are still lingering to the north and south of the equator. The coexistence of these two contrasting conditions indicates that the ocean and the climate system remain in transition. These strong patterns have remained in the climate system for many months and will continue to influence weather conditions around the world in the coming fall and winter. The satellite's sea-surface height measurements have provided scientists with a detailed view of the 1997-98 El Nino because the TOPEX/Poseidon satellite measures the changing sea-surface height with unprecedented precision. The purple areas are about 18 centimeters (7 inches) below normal, creating a deficit in the heat supply to the surface waters. The white areas show the sea surface is between 14 and 32 centimeters (6 to 13 inches) above normal; in the red areas, it's about 10 centimeters (4 inches) above normal. The green areas indicate normal conditions. The purple areas are 14 to 18 centimeters (6 to 7 inches) below normal and the blue areas are 5 to 13 centimeters (2 to 5 inches) below normal. The El Nino phenomenon is thought to be triggered when the steady westward blowing trade winds weaken and even reverse direction. This change in the winds allows a large mass of warm water (the red and white area) that is normally located near Australia to move eastward along the equator until it reaches the coast of South America. The displacement of so much warm water affects evaporation, where rain clouds form and, consequently, alters the typical atmospheric jet stream patterns around the world. A La Nina situation is essentially the opposite of an El Nino condition, but during La Nina the trade winds are stronger than normal and the cold water that normally exists along the coast of South America extends to the central equatorial Pacific. A La Nina situation also changes global weather patterns, and is associated with less moisture in the air resulting in less rain along the west coasts of North and South America.

For more information, please visit the TOPEX/Poseidon project web page at http://topex-www.jpl.nasa.gov

[Improvement of reproducibility in capillary electrophoretic characterization of rhubarb by normalization of migration time].

PubMed

Zhang, Hongyi; Ge, Lijuan; Chen, Hui; Jing, Cong; Shi, Zhihong

2009-07-01

The principle of the normalization of migration time and its application on the traditional Chinese medicine (TCM) analysis by capillary electrophoresis (CE) are presented. It is the core of the normalization of migration time that the fluctuation of apparent migration velocity for each component at different runs is attributed to the difference of electroosmotic flow velocity. To transform migration time (t) to normalized migration time, one peak or two peaks in the original electropherogram are selected as internal peak. The normalization of migration time is therefore classified into two types based on the number of selected internal peaks, one-peak and two-peak approaches. The migration times processed by one-peak normalization and by two-peak normalization are conducted by the following equations, respectively: (t'(i))(j) = 1/ [1/(t(i))(j) - [1/(t(istd))(j) - 1/(t(istd))1

Finite volume solution of the compressible boundary-layer equations

NASA Technical Reports Server (NTRS)

Loyd, B.; Murman, E. M.

1986-01-01

A box-type finite volume discretization is applied to the integral form of the compressible boundary layer equations. Boundary layer scaling is introduced through the grid construction: streamwise grid lines follow eta = y/h = const., where y is the normal coordinate and h(x) is a scale factor proportional to the boundary layer thickness. With this grid, similarity can be applied explicity to calculate initial conditions. The finite volume method preserves the physical transparency of the integral equations in the discrete approximation. The resulting scheme is accurate, efficient, and conceptually simple. Computations for similar and non-similar flows show excellent agreement with tabulated results, solutions computed with Keller's Box scheme, and experimental data.

Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

NASA Astrophysics Data System (ADS)

Thirukkanesh, S.; Ragel, F. C.

2014-04-01

We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.

Investigation of high-speed free shear flows using improved pressure-strain correlated Reynolds stress turbulence model

NASA Technical Reports Server (NTRS)

Tiwari, S. N.; Lakshmanan, B.

1993-01-01

A high-speed shear layer is studied using compressibility corrected Reynolds stress turbulence model which employs newly developed model for pressure-strain correlation. MacCormack explicit prediction-corrector method is used for solving the governing equations and the turbulence transport equations. The stiffness arising due to source terms in the turbulence equations is handled by a semi-implicit numerical technique. Results obtained using the new model show a sharper reduction in growth rate with increasing convective Mach number. Some improvements were also noted in the prediction of the normalized streamwise stress and Reynolds shear stress. The computed results are in good agreement with the experimental data.

Direct perturbation theory for the dark soliton solution to the nonlinear Schrödinger equation with normal dispersion.

PubMed

Yu, Jia-Lu; Yang, Chun-Nuan; Cai, Hao; Huang, Nian-Ning

2007-04-01

After finding the basic solutions of the linearized nonlinear Schrödinger equation by the method of separation of variables, the perturbation theory for the dark soliton solution is constructed by linear Green's function theory. In application to the self-induced Raman scattering, the adiabatic corrections to the soliton's parameters are obtained and the remaining correction term is given as a pure integral with respect to the continuous spectral parameter.

A Solution to the Fundamental Linear Fractional Order Differential Equation

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations

NASA Technical Reports Server (NTRS)

Osher, Stanley

1989-01-01

Simple inequalities for the Riemann problem for a Hamilton-Jacobi equation in N space dimension when neither the initial data nor the Hamiltonian need be convex (or concave) are presented. The initial data is globally continuous, affine in each orthant, with a possible jump in normal derivative across each coordinate plane, x sub i = 0. The inequalities become equalities wherever a maxmin equals a minmax and thus an exact closed form solution to this problem is then obtained.

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

ERIC Educational Resources Information Center

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

2017-01-01

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

Automatic segementation of histological structures in normal and neoplastic mammary gland tissue sections

NASA Astrophysics Data System (ADS)

Fernandez-Gonzalez, Rodrigo; Deschamps, Thomas; Idica, Adam; Malladi, Ravikanth; Ortiz de Solorzano, Carlos

2003-07-01

In this paper we present a scheme for real time segmentation of histological structures in microscopic images of normal and neoplastic mammary gland sections. Paraffin embedded or frozen tissue blocks are sliced, and sections are stained with hematoxylin and eosin (H&E). The sections are then imaged using conventional bright field microscopy. The background of the images is corrected by arithmetic manipulation using a "phantom." Then we use the fast marching method with a speed function that depends on the brightness gradient of the image to obtain a preliminary approximation to the boundaries of the structures of interest within a region of interest (ROI) of the entire section manually selected by the user. We use the result of the fast marching method as the initial condition for the level set motion equation. We run this last method for a few steps and obtain the final result of the segmentation. These results can be connected from section to section to build a three-dimensional reconstruction of the entire tissue block that we are studying.

One-dimensional flows of an imperfect diatomic gas

NASA Technical Reports Server (NTRS)

1959-01-01

With the assumptions that Berthelot's equation of state accounts for molecular size and intermolecular force effects, and that changes in the vibrational heat capacities are given by a Planck term, expressions are developed for analyzing one-dimensional flows of a diatomic gas. The special cases of flow through normal and oblique shocks in free air at sea level are investigated. It is found that up to a Mach number 10 pressure ratio across a normal shock differs by less than 6 percent from its ideal gas value; whereas at Mach numbers above 4 the temperature rise is considerable below and hence the density rise is well above that predicted assuming ideal gas behavior. It is further shown that only the caloric imperfection in air has an appreciable effect on the pressures developed in the shock process considered. The effects of gaseous imperfections on oblique shock-flows are studied from the standpoint of their influence on the life and pressure drag of a flat plate operating at Mach numbers of 10 and 20. The influence is found to be small. (author)

Method of sections in analytical calculations of pneumatic tires

NASA Astrophysics Data System (ADS)

Tarasov, V. N.; Boyarkina, I. V.

2018-01-01

Analytical calculations in the pneumatic tire theory are more preferable in comparison with experimental methods. The method of section of a pneumatic tire shell allows to obtain equations of intensities of internal forces in carcass elements and bead rings. Analytical dependencies of intensity of distributed forces have been obtained in tire equator points, on side walls (poles) and pneumatic tire bead rings. Along with planes in the capacity of secant surfaces cylindrical surfaces are used for the first time together with secant planes. The tire capacity equation has been obtained using the method of section, by means of which a contact body is cut off from the tire carcass along the contact perimeter by the surface which is normal to the bearing surface. It has been established that the Laplace equation for the solution of tasks of this class of pneumatic tires contains two unknown values that requires the generation of additional equations. The developed computational schemes of pneumatic tire sections and new equations allow to accelerate the pneumatic tire structure improvement process during engineering.

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

NASA Astrophysics Data System (ADS)

Lv, Qiuyu; Liao, Xiaofeng

2018-03-01

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

Interactive calculation procedure for supersonic flows. Ph.D. Thesis - Case Western Reserve Univ., 1976. Final Report

NASA Technical Reports Server (NTRS)

Tassa, Y.; Anderson, B. H.; Reshotko, E.

1977-01-01

An interactive procedure was developed for supersonic viscous flows that can be used for either two-dimensional or axisymmetric configurations. The procedure is directed to supersonic internal flows as well as those supersonic external flows that require consideration of mutual interaction between the outer flow and the boundary layer flow. The flow field is divided into two regions: an inner region which is highly viscous and mostly subsonic and an outer region where the flow is supersonic and in which viscous effects are small but not negligible. For the outer region a numerical solution is obtained by applying the method of characteristics to a system of equations which includes viscous and conduction transport terms only normal to the streamlines. The inner region is treated by a system of equations of the boundary layer type that includes higher order effects such as longitudinal and transverse curvature and normal pressure gradients. These equations are coupled and solved simultaneously in the physical coordinates by using an implicit finite difference scheme. This system can also be used to calculate laminar and turbulent boundary layers using a scalar eddy viscosity concept.

Theoretical and Experimental Analysis of an Induction Planar Actuator with Different Secondaries—A Planar Driver Application for Metallic Surface Inspection

PubMed Central

Treviso, Felipe; Silveira, Marilia A.; Flores Filho, Aly F.; Dorrell, David G.

2016-01-01

This paper presents a study on an induction planar actuator concept. The device uses the same principles as a linear induction motor in which the interaction between a travelling magnetic field and a conducting surface produces eddy currents that leads to the generation of a thrust force and can result in movement over a metallic surface. This can benefit the inspection of metallic surfaces based on the driving platform provided by the induction planar actuator. Equations of the magnetic and electric fields are presented and, by means of these equations, the forces involved were calculated. The behaviour of thrust and normal forces was analysed through the equations and by numerical models, and compared with the results obtained by measurements on a device prototype built in the laboratory as part of the study. With relation to the surface under inspection that forms the secondary, three cases were analysed: (1) a double-layered secondary formed by aluminium and ferromagnetic slabs; (2) a single aluminium layer and (3) a single ferromagnetic layer. Theoretical and measured values of thrust and normal forces showed good correlation. PMID:27007377

Effects of Sampling and Spatio/Temporal Granularity in Traffic Monitoring on Anomaly Detectability

NASA Astrophysics Data System (ADS)

Ishibashi, Keisuke; Kawahara, Ryoichi; Mori, Tatsuya; Kondoh, Tsuyoshi; Asano, Shoichiro

We quantitatively evaluate how sampling and spatio/temporal granularity in traffic monitoring affect the detectability of anomalous traffic. Those parameters also affect the monitoring burden, so network operators face a trade-off between the monitoring burden and detectability and need to know which are the optimal paramter values. We derive equations to calculate the false positive ratio and false negative ratio for given values of the sampling rate, granularity, statistics of normal traffic, and volume of anomalies to be detected. Specifically, assuming that the normal traffic has a Gaussian distribution, which is parameterized by its mean and standard deviation, we analyze how sampling and monitoring granularity change these distribution parameters. This analysis is based on observation of the backbone traffic, which exhibits spatially uncorrelated and temporally long-range dependence. Then we derive the equations for detectability. With those equations, we can answer the practical questions that arise in actual network operations: what sampling rate to set to find the given volume of anomaly, or, if the sampling is too high for actual operation, what granularity is optimal to find the anomaly for a given lower limit of sampling rate.

Analysis of the dynamic response of a supersonic inlet to flow-field perturbations upstream of the normal shock

NASA Technical Reports Server (NTRS)

Cole, G. L.; Willoh, R. G.

1975-01-01

A linearized mathematical analysis is presented for determining the response of normal shock position and subsonic duct pressures to flow-field perturbations upstream of the normal shock in mixed-compression supersonic inlets. The inlet duct cross-sectional area variation is approximated by constant-area sections; this approximation results in one-dimensional wave equations. A movable normal shock separates the supersonic and subsonic flow regions, and a choked exit is assumed for the inlet exit condition. The analysis leads to a closed-form matrix solution for the shock position and pressure transfer functions. Analytical frequency response results are compared with experimental data and a method of characteristics solution.

From shunting inhibition to dynamic normalization: Attentional selection and decision-making in brief visual displays.

PubMed

Smith, Philip L; Sewell, David K; Lilburn, Simon D

2015-11-01

Normalization models of visual sensitivity assume that the response of a visual mechanism is scaled divisively by the sum of the activity in the excitatory and inhibitory mechanisms in its neighborhood. Normalization models of attention assume that the weighting of excitatory and inhibitory mechanisms is modulated by attention. Such models have provided explanations of the effects of attention in both behavioral and single-cell recording studies. We show how normalization models can be obtained as the asymptotic solutions of shunting differential equations, in which stimulus inputs and the activity in the mechanism control growth rates multiplicatively rather than additively. The value of the shunting equation approach is that it characterizes the entire time course of the response, not just its asymptotic strength. We describe two models of attention based on shunting dynamics, the integrated system model of Smith and Ratcliff (2009) and the competitive interaction theory of Smith and Sewell (2013). These models assume that attention, stimulus salience, and the observer's strategy for the task jointly determine the selection of stimuli into visual short-term memory (VSTM) and the way in which stimulus representations are weighted. The quality of the VSTM representation determines the speed and accuracy of the decision. The models provide a unified account of a variety of attentional phenomena found in psychophysical tasks using single-element and multi-element displays. Our results show the generality and utility of the normalization approach to modeling attention. Copyright © 2014 Elsevier B.V. All rights reserved.

Analysis of ¹³¹I therapy and correlation factors of Graves' disease patients: a 4-year retrospective study.

PubMed

Zheng, Wei; Jian, Tan; Guizhi, Zhang; Zhaowei, Meng; Renfei, Wang

2012-01-01

To analyze the correlation therapeutic effects of first sufficiency ¹³¹I therapy in Graves' disease patients and improve its one-time curative ratio. Seven hundred and sixty-six patients (age range 12-77 years, mean 40.46 ± 13.12 years), including 237 men (range 12-77 years, 40.98 ± 12.64 years) and 529 women (range 14-75 years, 40.22 ± 13.34 years), who received the first I treatment were studied. The relevant examinations were performed before ¹³¹I therapy: the maximal radioactive iodine uptake of thyroid (RAIUmax), the effective half-life (EHL), the ultrasound of thyroid to calculate its weight, thyroid imaging with single-photon emission computed tomography and serum-free triiodothyronine (FT₃), free thyroxine (FT₄), sensitive thyroid-stimulating hormone (sTSH), anti-thyrotrophin receptor antibody (TRAb), thyroid-stimulating immunoglobulin, thyroglobulin antibody (TgAb), and anti-thyroid microsome antibody (TMAb). After the ¹³¹I dosage was determined, all the patients took ¹³¹I once orally. The ¹³¹I dosage range was 74-592 MBq (221.63 ± 100.64 MBq). A clinical and laboratory assessment was performed at 1, 3, 6, and 12 months after ¹³¹I therapy. Patients were divided into the clinically recovered group (symptoms and signs disappeared, free thyroid hormone levels were within or below the normal range, and sTSH was within or above the normal range) and the clinically unhealed group (symptoms and signs disappeared partially, free thyroid hormone levels were still above the normal range or within the normal range for a time and then increased again, and sTSH was constantly below the normal range). Data were analyzed by the unpaired t-test, the independent samples t-test, the χ² test, logistic regression, and Pearson bivariate correlation. The one-time curative ratio of ¹³¹I therapy was 78.7% (including euthyroidism and hypothyroidism). Multiplicity in healing patients fit the logistic regression equation. The accuracy of discrimination of the equation was 79.5%. The influential factors of ¹³¹I therapy were age, RAIUmax, EHL, TRAb, and TgAb. RAIUmax and EHL were the protecting factors. Age, TRAb, and TgAb were the risk factors. TRAb influenced the one-time curative ratio between patients with negative and positive TRAb, which was higher in men (2.836 times) than in women (1.438 times). ¹³¹I therapy is an effective intervention for Graves' disease. The higher the RAIUmax and (or) the longer the EHL, the higher the possibility of a one-time cure. Elder patients or patients with a positive TRAb and (or) TgAb have a lower possibility of a one-time cure. Women with a positive TRAb should be administered an increased ¹³¹I dose to improve the curative effect.

Universal equation for estimating ideal body weight and body weight at any BMI1

PubMed Central

Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B

2016-01-01

Background: Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. Objective: For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. Design: With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Results: Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5–0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Conclusions: Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. PMID:27030535

Universal equation for estimating ideal body weight and body weight at any BMI.

PubMed

Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B

2016-05-01

Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5-0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. © 2016 American Society for Nutrition.

MHD Modeling of the Solar Wind with Turbulence Transport and Heating

NASA Technical Reports Server (NTRS)

Goldstein, M. L.; Usmanov, A. V.; Matthaeus, W. H.; Breech, B.

2009-01-01

We have developed a magnetohydrodynamic model that describes the global axisymmetric steady-state structure of the solar wind near solar minimum with account for transport of small-scale turbulence associated heating. The Reynolds-averaged mass, momentum, induction, and energy equations for the large-scale solar wind flow are solved simultaneously with the turbulence transport equations in the region from 0.3 to 100 AU. The large-scale equations include subgrid-scale terms due to turbulence and the turbulence (small-scale) equations describe the effects of transport and (phenomenologically) dissipation of the MHD turbulence based on a few statistical parameters (turbulence energy, normalized cross-helicity, and correlation scale). The coupled set of equations is integrated numerically for a source dipole field on the Sun by a time-relaxation method in the corotating frame of reference. We present results on the plasma, magnetic field, and turbulence distributions throughout the heliosphere and on the role of the turbulence in the large-scale structure and temperature distribution in the solar wind.

Progressive wave expansions and open boundary problems

NASA Technical Reports Server (NTRS)

Hagstrom, T.; Hariharan, S. I.

1995-01-01

In this paper we construct progressive wave expansions and asymptotic boundary conditions for wave-like equations in exterior domains, including applications to electromagnetics, compressible flows and aero-acoustics. The development of the conditions will be discussed in two parts. The first part will include derivations of asymptotic conditions based on the well-known progressive wave expansions for the two-dimensional wave equations. A key feature in the derivations is that the resulting family of boundary conditions involves a single derivative in the direction normal to the open boundary. These conditions are easy to implement and an application in electromagnetics will be presented. The second part of the paper will discuss the theory for hyperbolic systems in two dimensions. Here, the focus will be to obtain the expansions in a general way and to use them to derive a class of boundary conditions that involve only time derivatives or time and tangential derivatives. Maxwell's equations and the compressible Euler equations are used as examples. Simulations with the linearized Euler equations are presented to validate the theory.

Simulation of subwavelength metallic gratings using a new implementation of the recursive convolution finite-difference time-domain algorithm.

PubMed

Banerjee, Saswatee; Hoshino, Tetsuya; Cole, James B

2008-08-01

We introduce a new implementation of the finite-difference time-domain (FDTD) algorithm with recursive convolution (RC) for first-order Drude metals. We implemented RC for both Maxwell's equations for light polarized in the plane of incidence (TM mode) and the wave equation for light polarized normal to the plane of incidence (TE mode). We computed the Drude parameters at each wavelength using the measured value of the dielectric constant as a function of the spatial and temporal discretization to ensure both the accuracy of the material model and algorithm stability. For the TE mode, where Maxwell's equations reduce to the wave equation (even in a region of nonuniform permittivity) we introduced a wave equation formulation of RC-FDTD. This greatly reduces the computational cost. We used our methods to compute the diffraction characteristics of metallic gratings in the visible wavelength band and compared our results with frequency-domain calculations.

Perfectly Matched Layer for Linearized Euler Equations in Open and Ducted Domains

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Auriault, Laurent; Cambuli, Francesco

1998-01-01

Recently, perfectly matched layer (PML) as an absorbing boundary condition has widespread applications. The idea was first introduced by Berenger for electromagnetic waves computations. In this paper, it is shown that the PML equations for the linearized Euler equations support unstable solutions when the mean flow has a component normal to the layer. To suppress such unstable solutions so as to render the PML concept useful for this class of problems, it is proposed that artificial selective damping terms be added to the discretized PML equations. It is demonstrated that with a proper choice of artificial mesh Reynolds number, the PML equations can be made stable. Numerical examples are provided to illustrate that the stabilized PML performs well as an absorbing boundary condition. In a ducted environment, the wave mode are dispersive. It will be shown that the group velocity and phase velocity of these modes can have opposite signs. This results in a confined environment, PML may not be suitable as an absorbing boundary condition.

Analytical and Experimental Random Vibration of Nonlinear Aeroelastic Structures.

DTIC Science & Technology

1987-01-28

firstorder differential equations. In view of the system complexi- ty an attempt s made to close the infinite hierarchy by using a Gaussian scheme. This sc...year of this project-. When the first normal mode is externally excited by a band-limited random excitation, the system mean square response is found...governed mainly by the internal detuning parameter and the system damping ratios. The results are completely different when the second normal mode is

Empirical prediction of peak pressure levels in anthropogenic impulsive noise. Part I: Airgun arrays signals.

PubMed

Galindo-Romero, Marta; Lippert, Tristan; Gavrilov, Alexander

2015-12-01

This paper presents an empirical linear equation to predict peak pressure level of anthropogenic impulsive signals based on its correlation with the sound exposure level. The regression coefficients are shown to be weakly dependent on the environmental characteristics but governed by the source type and parameters. The equation can be applied to values of the sound exposure level predicted with a numerical model, which provides a significant improvement in the prediction of the peak pressure level. Part I presents the analysis for airgun arrays signals, and Part II considers the application of the empirical equation to offshore impact piling noise.

Generalized graphs and unitary irrational central charge in the superconformal master equation

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

Halpern, M.B.; Obers, N.A.

1991-12-01

For each magic basis of Lie {ital g}, it is known that the Virasoro master equation on affine {ital g} contains a generalized graph theory of conformal level-families. In this paper, it is found that the superconformal master equation on affine {ital g}{times}SO(dim {ital g}) similarly contains a generalized graph theory of superconformal level-families for each magic basis of {ital g}. The superconformal level-families satisfy linear equations on the generalized graphs, and the first exact unitary irrational solutions of the superconformal master equation are obtained on the sine-area graphs of {ital g}=SU({ital n}), including the simplest unitary irrational central chargesmore » {ital c}=6{ital nx}/({ital nx}+8 sin{sup 2}(rs{pi}/n)) yet observed in the program.« less

Determination of rolling resistance coefficient based on normal tyre stiffness

NASA Astrophysics Data System (ADS)

Rykov, S. P.; Tarasuyk, V. N.; Koval, V. S.; Ovchinnikova, N. I.; Fedotov, A. I.; Fedotov, K. V.

2018-03-01

The purpose of the article is to develop analytical dependence of wheel rolling resistance coefficient based on the mathematical description of normal tyre stiffness. The article uses the methods of non-holonomic mechanics and plane section methods. The article shows that the abscissa of gravity center of tyre stiffness expansion by the length of the contact area is the shift of normal road response. It can be used for determining rolling resistance coefficient. When determining rolling resistance coefficient using ellipsis and power function equations, one can reduce labor costs for testing and increase assessment accuracy.

Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1993-01-01

The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.

Importance of Ambipolar Electric Field in the Ion Loss from Mars- Results from a Multi-fluid MHD Model with the Electron Pressure Equation Included

NASA Astrophysics Data System (ADS)

Ma, Y.; Dong, C.; van der Holst, B.; Nagy, A. F.; Bougher, S. W.; Toth, G.; Cravens, T.; Yelle, R. V.; Jakosky, B. M.

2017-12-01

The multi-fluid (MF) magnetohydrodynamic (MHD) model of Mars is further improved by solving an additional electron pressure equation. Through the electron pressure equation, the electron temperature is calculated based on the effects from various electrons related heating and cooling processes (e.g. photo-electron heating, electron-neutral collision and electron-ion collision), and thus the improved model is able to calculate the electron temperature and the electron pressure force self-consistently. Electron thermal conductivity is also considered in the calculation. Model results of a normal case with electron pressure equation included (MFPe) are compared in detail to an identical case using the regular MF model to identify the effect of the improved physics. We found that when the electron pressure equation is included, the general interaction patterns are similar to that of the case with no electron pressure equation. The model with electron pressure equation predicts that electron temperature is much larger than the ion temperature in the ionosphere, consistent with both Viking and MAVEN observations. The inclusion of electron pressure equation significantly increases the total escape fluxes predicted by the model, indicating the importance of the ambipolar electric field(electron pressure gradient) in driving the ion loss from Mars.

Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory.

PubMed

Bardhan, Jaydeep P

2008-10-14

The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms.

Weight of fitness deviation governs strict physical chaos in replicator dynamics.

PubMed

Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar

2018-03-01

Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions-fixed points, periodic orbits, and chaotic trajectories-are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

Source positions from VLBI combined solution

NASA Astrophysics Data System (ADS)

Bachmann, S.; Thaller, D.; Engelhardt, G.

2014-12-01

The IVS Combination Center at BKG is primarily responsible for combined Earth Orientation Parameter (EOP) products and the generation of a terrestrial reference frame based on VLBI observations (VTRF). The procedure is based on the combination of normal equations provided by six IVS Analysis Centers (AC). Since more and more ACs also provide source positions in the normal equations - beside EOPs and station coordinates - an estimation of these parameters is possible and should be investigated. In the past, the International Celestial Reference Frame (ICRF) was not generated as a combined solution from several individual solutions, but was based on a single solution provided by one AC. The presentation will give an overview on the combination strategy and the possibilities for combined source position determination. This includes comparisons with existing catalogs, quality estimation and possibilities of rigorous combination of EOP, TRF and CRF in one combination process.

A field theoretic generalization of Hajicek and Kuchar's quantization scheme in 3+1 canonical quantum gravity

NASA Astrophysics Data System (ADS)

Melas, Evangelos

2011-07-01

The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited as a generalization of a previous work. A proposal, consisting of a specific re-normalization Assumption and an accompanying Requirement, which has been put forward in the 2+1 case is now generalized to 3+1 dimensions. This enables the canonical quantization of these geometries through a generalization of Kuchař's quantization scheme in the case of infinite degrees of freedom. The resulting Wheeler-deWitt equation is based on a re-normalized manifold parameterized by three smooth scalar functionals. The entire space of solutions to this equation is analytically given, a fact that is entirely new to the present case. This is made possible by exploiting the freedom left by the imposition of the Requirement and contained in the third functional.

Nonlinear longitudinal resonance interaction of energetic charged particles and VLF waves in the magnetosphere

NASA Technical Reports Server (NTRS)

Tkalcevic, S.

1982-01-01

The longitudinal resonance of waves and energetic electrons in the Earth's magnetosphere, and the possible role this resonance may play in generating various magnetospheric phenomena are studied. The derivation of time-averaged nonlinear equations of motion for energetic particles longitudinally resonant with a whistler mode wave propagating with nonzero wave normal is considered. It is shown that the wave magnetic forces can be neglected at lower particle pitch angles, while they become equal to or larger than the wave electric forces for alpha 20 deg. The time-averaged equations of motion were used in test particle simulation which were done for a wide range of wave amplitudes, wave normals, particle pitch angles, particle parallel velocities, and in an inhomogeneous medium such as the magnetosphere. It was found that there are two classes of particles, trapped and untrapped, and that the scattering and energy exchange for those two groups exhibit significantly different behavior.

Study on moisture absorption and sweat discharge of honeycomb polyester fiber

NASA Astrophysics Data System (ADS)

Feng, Aifen; Zhang, Yongjiu

2015-07-01

The moisture absorption and liberation properties of honeycomb polyester fiber were studied in order to understand its moisture absorption and sweat discharge. Through testing moisture absorption and liberation regains of honeycomb polyester fiber and normal polyester fiber in standard atmospheric conditions, their moisture absorption and liberation curves were depicted, and the regression equations of moisture regains to time during their reaching the balance of moisture absorption and moisture liberation were obtained according to the curves. Their moisture absorption and liberation rate curves were analyzed and the regression equations of the rates to time were obtained. The results shows that the moisture regain of honeycomb polyester fiber is much bigger than the normal polyester fiber's, and the initial moisture absorption and moisture liberation rates of the former are much higher than the latter's, so that the moisture absorbance and sweat discharge of honeycomb polyester fiber are excellent.

Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos.

PubMed

Basko, D M

2014-02-01

We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.

Improved Conjugate Gradient Bundle Adjustment of Dunhuang Wall Painting Images

NASA Astrophysics Data System (ADS)

Hu, K.; Huang, X.; You, H.

2017-09-01

Bundle adjustment with additional parameters is identified as a critical step for precise orthoimage generation and 3D reconstruction of Dunhuang wall paintings. Due to the introduction of self-calibration parameters and quasi-planar constraints, the structure of coefficient matrix of the reduced normal equation is banded-bordered, making the solving process of bundle adjustment complex. In this paper, Conjugate Gradient Bundle Adjustment (CGBA) method is deduced by calculus of variations. A preconditioning method based on improved incomplete Cholesky factorization is adopt to reduce the condition number of coefficient matrix, as well as to accelerate the iteration rate of CGBA. Both theoretical analysis and experimental results comparison with conventional method indicate that, the proposed method can effectively conquer the ill-conditioned problem of normal equation and improve the calculation efficiency of bundle adjustment with additional parameters considerably, while maintaining the actual accuracy.

A finite-element analysis for steady and oscillatory subsonic flow around complex configurations

NASA Technical Reports Server (NTRS)

Chen, L. T.; Suciu, E. O.; Morino, L.

1974-01-01

The problem of potential subsonic flow around complex configurations is considered. The solution is given of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element. The coefficients of the equation are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented. The results obtained with the above formulation are compared with existing analytical and experimental results.

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.

Flow Glottogram and Subglottal Pressure Relationship in Singers and Untrained Voices.

PubMed

Sundberg, Johan

2018-01-01

This article combines results from three earlier investigations of the glottal voice source during phonation at varying degrees of vocal loudness (1) in five classically trained baritone singers (Sundberg et al., 1999), (2) in 15 female and 14 male untrained voices (Sundberg et al., 2005), and (3) in voices rated as hyperfunctional by an expert panel (Millgård et al., 2015). Voice source data were obtained by inverse filtering. Associated subglottal pressures were estimated from oral pressure during the occlusion for the consonant /p/. Five flow glottogram parameters, (1) maximum flow declination rate (MFDR), (2) peak-to-peak pulse amplitude, (3) level difference between the first and the second harmonics of the voice source, (4) closed quotient, and (5) normalized amplitude quotient, were averaged across the singer subjects and related to associated MFDR values. Strong, quantitative relations, expressed as equations, are found between subglottal pressure and MFDR and between MFDR and each of the other flow glottogram parameters. The values for the untrained voices, as well as those for the voices rated as hyperfunctional, deviate systematically from the values derived from the equations. Copyright © 2018 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

Iterative absolute electroanalytical approach to characterization of bulk redox conducting systems.

PubMed

Lewera, Adam; Miecznikowski, Krzysztof; Chojak, Malgorzata; Makowski, Oktawian; Golimowski, Jerzy; Kulesza, Pawel J

2004-05-15

A novel electroanalytical approach is proposed here, and it is demonstrated with the direct and simultaneous determination of two unknowns: the concentration of redox sites and the apparent diffusion coefficient for charge propagation in a single crystal of dodecatungstophosphoric acid. This Keggin-type polyoxometalate serves as a model bulk redox conducting inorganic material for solid-state voltammetry. The system has been investigated using an ultramicrodisk working electrode in the absence of external liquid supporting electrolyte. The analytical method requires numerical solution of the combination of two equations in which the first one describes current (or charge) in a well-defined (either spherical or linear) diffusional regime and the second general equation describes chronoamperometric (or normal pulse voltammetric current) under mixed (linear-spherical) conditions. The iterative approach is based on successive approximations through calculation and minimizing the least-squares error function. The method is fairly universal, and in principle, it can be extended to the investigation of other bulk systems including sol-gel processed materials, redox melts, and solutions on condition that they are electroactive and well behaved, they contain redox centers at sufficiently high level, and a number of electrons for the redox reaction considered is known.

Theory of equilibria of elastic 2-braids with interstrand interaction

NASA Astrophysics Data System (ADS)

Starostin, E. L.; van der Heijden, G. H. M.

2014-03-01

Motivated by continuum models for DNA supercoiling we formulate a theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. No assumption is made on the shape of the contact curve. The theory is developed in terms of a moving frame of directors attached to one of the strands. The other strand is tracked by including in this frame the normalised closest-approach chord connecting the two strands. The kinematic constant-distance constraint is formulated at strain level through the introduction of what we call braid strains. As a result the total potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Hard contact models are used to obtain the normal contact pressure between strands that has to be non-negative for a physically realisable solution without the need for external devices such as clamps or glue to keep the strands together. The theory is first illustrated by a number of problems that can be solved analytically and then applied to several new problems that have not hitherto been treated.

Undergraduate paramedic students cannot do drug calculations.

PubMed

Eastwood, Kathryn; Boyle, Malcolm J; Williams, Brett

2012-01-01

Previous investigation of drug calculation skills of qualified paramedics has highlighted poor mathematical ability with no published studies having been undertaken on undergraduate paramedics. There are three major error classifications. Conceptual errors involve an inability to formulate an equation from information given, arithmetical errors involve an inability to operate a given equation, and finally computation errors are simple errors of addition, subtraction, division and multiplication. The objective of this study was to determine if undergraduate paramedics at a large Australia university could accurately perform common drug calculations and basic mathematical equations normally required in the workplace. A cross-sectional study methodology using a paper-based questionnaire was administered to undergraduate paramedic students to collect demographical data, student attitudes regarding their drug calculation performance, and answers to a series of basic mathematical and drug calculation questions. Ethics approval was granted. The mean score of correct answers was 39.5% with one student scoring 100%, 3.3% of students (n=3) scoring greater than 90%, and 63% (n=58) scoring 50% or less, despite 62% (n=57) of the students stating they 'did not have any drug calculations issues'. On average those who completed a minimum of year 12 Specialist Maths achieved scores over 50%. Conceptual errors made up 48.5%, arithmetical 31.1% and computational 17.4%. This study suggests undergraduate paramedics have deficiencies in performing accurate calculations, with conceptual errors indicating a fundamental lack of mathematical understanding. The results suggest an unacceptable level of mathematical competence to practice safely in the unpredictable prehospital environment.

Quasiclassical description of a superconductor with a spin density wave

NASA Astrophysics Data System (ADS)

Moor, A.; Volkov, A. F.; Efetov, K. B.

2011-04-01

We derive equations for the quasiclassical Green’s functions ǧ within a simple model of a two-band superconductor with a spin density wave (SDW). The elements of the matrix ǧ are the retarded, advanced, and Keldysh functions, each of which is an 8×8 matrix in the Gor’kov-Nambu, the spin, and the band space. In equilibrium, these equations are a generalization of the Eilenberger equation. On the basis of the derived equations, we analyze the Knight shift, the proximity, and the dc Josephson effects in the superconductors under consideration. The Knight shift is shown to depend on the orientation of the external magnetic field with respect to the direction of the vector of the magnetization of the SDW. The proximity effect is analyzed for an interface between a superconductor with the SDW and a normal metal. The function describing both superconducting and magnetic correlations is shown to penetrate the normal metal or a metal with the SDW due to the proximity effect. The dc Josephson current in an SSDW/N/SSDW junction is also calculated as a function of the phase difference φ. It is shown that in our model, the Josephson current does not depend on the mutual orientation of the magnetic moments in the superconductors SSDW and is proportional to sinφ. The dissipationless spin current jsp depends on the angle α between the magnetization vectors in the same way (jsp~sinα) and is not zero above the superconducting transition temperature.

Generalized time evolution of the homogeneous cooling state of a granular gas with positive and negative coefficient of normal restitution

NASA Astrophysics Data System (ADS)

Khalil, Nagi

2018-04-01

The homogeneous cooling state (HCS) of a granular gas described by the inelastic Boltzmann equation is reconsidered. As usual, particles are taken as inelastic hard disks or spheres, but now the coefficient of normal restitution α is allowed to take negative values , which is a simple way of modeling more complicated inelastic interactions. The distribution function of the HCS is studied at the long-time limit, as well as intermediate times. At the long-time limit, the relevant information of the HCS is given by a scaling distribution function , where the time dependence occurs through a dimensionless velocity c. For , remains close to the Gaussian distribution in the thermal region, its cumulants and exponential tails being well described by the first Sonine approximation. In contrast, for , the distribution function becomes multimodal, its maxima located at , and its observable tails algebraic. The latter is a consequence of an unbalanced relaxation–dissipation competition, and is analytically demonstrated for , thanks to a reduction of the Boltzmann equation to a Fokker–Plank-like equation. Finally, a generalized scaling solution to the Boltzmann equation is also found . Apart from the time dependence occurring through the dimensionless velocity, depends on time through a new parameter β measuring the departure of the HCS from its long-time limit. It is shown that describes the time evolution of the HCS for almost all times. The relevance of the new scaling is also discussed.

Step-by-step design of a single phase 3.3 kV/200 a resistive type superconducting fault current limiter (R-SFCL) and cryostat

NASA Astrophysics Data System (ADS)

Kar, Soumen; Rao, V. V.

2018-07-01

In our first attempt to design a single phase R-SFCL in India, we have chosen the typical rating of a medium voltage level (3.3 kVrms, 200 Arms, 1Φ) R-SFCL. The step-by-step design procedure for the R-SFCL involves conductor selection, time dependent electro-thermal simulations and recovery time optimization after fault removal. In the numerical analysis, effective fault limitation for a fault current of 5 kA for the medium voltage level R-SFCL are simulated. Maximum normal state resistance and maximum temperature rise in the SFCL coil during current limitation are estimated using one-dimensional energy balance equation. Further, a cryogenic system is conceptually designed for aforesaid MV level R-SFCL by considering inner and outer vessel materials, wall-thickness and thermal insulation which can be used for R-SFCL system. Finally, the total thermal load is calculated for the designed R-SFCL cryostat to select a suitable cryo-refrigerator for LN2 re-condensation.

A Simple, Analytical Model of Collisionless Magnetic Reconnection in a Pair Plasma

NASA Technical Reports Server (NTRS)

Hesse, Michael; Zenitani, Seiji; Kuznetova, Masha; Klimas, Alex

2011-01-01

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region, and to impart thermal energy to the plasma by means of quasi-viscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative, procedure. The solutions show expected features such as dominance of enthalpy flux in the reconnection outflow, as well as combination of adiabatic and quasi-viscous heating. Furthermore, the model predicts a maximum reconnection electric field of E(sup *)=0.4, normalized to the parameters at the inflow edge of the diffusion region.

Online gaming for learning optimal team strategies in real time

NASA Astrophysics Data System (ADS)

Hudas, Gregory; Lewis, F. L.; Vamvoudakis, K. G.

2010-04-01

This paper first presents an overall view for dynamical decision-making in teams, both cooperative and competitive. Strategies for team decision problems, including optimal control, zero-sum 2-player games (H-infinity control) and so on are normally solved for off-line by solving associated matrix equations such as the Riccati equation. However, using that approach, players cannot change their objectives online in real time without calling for a completely new off-line solution for the new strategies. Therefore, in this paper we give a method for learning optimal team strategies online in real time as team dynamical play unfolds. In the linear quadratic regulator case, for instance, the method learns the Riccati equation solution online without ever solving the Riccati equation. This allows for truly dynamical team decisions where objective functions can change in real time and the system dynamics can be time-varying.

Large eddy simulation of incompressible turbulent channel flow

NASA Technical Reports Server (NTRS)

Moin, P.; Reynolds, W. C.; Ferziger, J. H.

1978-01-01

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

A simple, analytical model of collisionless magnetic reconnection in a pair plasma

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

Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha

2009-10-15

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region and to impart thermal energy to the plasma by means of quasiviscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative procedure. The solutions show expected features such as dominance of enthalpymore » flux in the reconnection outflow, as well as combination of adiabatic and quasiviscous heating. Furthermore, the model predicts a maximum reconnection electric field of E{sup *}=0.4, normalized to the parameters at the inflow edge of the diffusion region.« less

Searching fundamental information in ordinary differential equations. Nondimensionalization technique.

PubMed

Sánchez Pérez, J F; Conesa, M; Alhama, I; Alhama, F; Cánovas, M

2017-01-01

Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.

Validation of cardiac output using real-time measurement of oxygen consumption during cardiac catheterization in children under 3 years of age.

PubMed

Seckeler, Michael D; Hirsch, Russel; Beekman, Robert H; Goldstein, Bryan H

2014-01-01

To validate a method for determination of cardiac index (CI) using real-time measurement of oxygen consumption (VO2 ) in young children undergoing cardiac catheterization. Retrospective review comparing thermodilution cardiac index (TDCI) to CI calculated by the Fick equation using real-time measured VO2 (RT-VO2 ) and VO2 derived from 2 published predictive equations. Paired t-test and Bland-Altman analysis were used to compare TDCI to Fick CI. A survey to ascertain pediatric cardiac catheterization practices regarding VO2 determination was also conducted. Quaternary care children's hospital cardiac catheterization laboratory. Children <3 years old with structurally normal hearts undergoing cardiac catheterization under general anesthesia with at least one set of contemporaneous TDCI and RT-VO2 measurements. Thirty-six paired measurements of TDCI and RT-VO2 were made in 27 patients over a 2-year period. Indications for catheterization included congenital diaphragmatic hernia postrepair (n = 13), heart disease post-orthotopic heart transplant (n = 13), and suspected cardiomyopathy (n = 1). Mean age was 21.5 ± 8 months; median weight was 9.9 kg (IQR 8.57, 12.2). RT-VO2 was higher than VO2 predicted by the LaFarge equation (190 ± 31 vs. 173.8 ± 12.8 mL/min/m(2), P < .001), but there was no difference between TDCI and Fick CI calculated using VO2 from any method. Bland-Altman analysis showed excellent agreement between TDCI and Fick CI using RT-VO2 and VO2 predicted by the Lundell equation; Fick CI using VO2 predicted by the LaFarge equation showed fair agreement with TDCI. In children <3 years with a structurally normal heart, RT-VO2 generates highly accurate determinations of Fick CI as compared with TDCI. Additionally, in this population, VO2 derived from the LaFarge and Lundell equations generates accurate Fick CI compared with TDCI. Future studies are needed to identify factors associated with inaccurate VO2 generated from these predictive equations. © 2013 Wiley Periodicals, Inc.

Level-Specific Evaluation of Model Fit in Multilevel Structural Equation Modeling

ERIC Educational Resources Information Center

Ryu, Ehri; West, Stephen G.

2009-01-01

In multilevel structural equation modeling, the "standard" approach to evaluating the goodness of model fit has a potential limitation in detecting the lack of fit at the higher level. Level-specific model fit evaluation can address this limitation and is more informative in locating the source of lack of model fit. We proposed level-specific test…

The use of normal forms for analysing nonlinear mechanical vibrations

PubMed Central

Neild, Simon A.; Champneys, Alan R.; Wagg, David J.; Hill, Thomas L.; Cammarano, Andrea

2015-01-01

A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled. It is shown how this method can be placed within the context of the general theory of normal forms provided the damping and forcing terms are treated as unfolding parameters. The approach is contrasted to the alternative theory of nonlinear normal modes (NNMs) which is argued to be problematic in the presence of damping. The efficacy of the normal form method is illustrated on a model of the vibration of a taut cable, which is geometrically nonlinear. It is shown how the method is able to accurately predict NNM shapes and their bifurcations. PMID:26303917

Optimal level of continuous positive airway pressure: auto-adjusting titration versus titration with a predictive equation.

PubMed

Choi, Ji Ho; Jun, Young Joon; Oh, Jeong In; Jung, Jong Yoon; Hwang, Gyu Ho; Kwon, Soon Young; Lee, Heung Man; Kim, Tae Hoon; Lee, Sang Hag; Lee, Seung Hoon

2013-05-01

The aims of the present study were twofold. We sought to compare two methods of titrating the level of continuous positive airway pressure (CPAP) - auto-adjusting titration and titration using a predictive equation - with full-night manual titration used as the benchmark. We also investigated the reliability of the two methods in patients with obstructive sleep apnea syndrome (OSAS). Twenty consecutive adult patients with OSAS who had successful, full-night manual and auto-adjusting CPAP titration participated in this study. The titration pressure level was calculated with a previously developed predictive equation based on body mass index and apnea-hypopnea index. The mean titration pressure levels obtained with the manual, auto-adjusting, and predictive equation methods were 9.0 +/- 3.6, 9.4 +/- 3.0, and 8.1 +/- 1.6 cm H2O,respectively. There was a significant difference in the concordance within the range of +/- 2 cm H2O (p = 0.019) between both the auto-adjusting titration and the titration using the predictive equation compared to the full-night manual titration. However, there was no significant difference in the concordance within the range of +/- 1 cm H2O (p > 0.999). When compared to full-night manual titration as the standard method, auto-adjusting titration appears to be more reliable than using a predictive equation for determining the optimal CPAP level in patients with OSAS.

Derivation of a generalized Schrödinger equation from the theory of scale relativity

NASA Astrophysics Data System (ADS)

Chavanis, Pierre-Henri

2017-06-01

Using Nottale's theory of scale relativity relying on a fractal space-time, we derive a generalized Schrödinger equation taking into account the interaction of the system with the external environment. This equation describes the irreversible evolution of the system towards a static quantum state. We first interpret the scale-covariant equation of dynamics stemming from Nottale's theory as a hydrodynamic viscous Burgers equation for a potential flow involving a complex velocity field and an imaginary viscosity. We show that the Schrödinger equation can be directly obtained from this equation by performing a Cole-Hopf transformation equivalent to the WKB transformation. We then introduce a friction force proportional and opposite to the complex velocity in the scale-covariant equation of dynamics in a way that preserves the local conservation of the normalization condition. We find that the resulting generalized Schrödinger equation, or the corresponding fluid equations obtained from the Madelung transformation, involve not only a damping term but also an effective thermal term. The friction coefficient and the temperature are related to the real and imaginary parts of the complex friction coefficient in the scale-covariant equation of dynamics. This may be viewed as a form of fluctuation-dissipation theorem. We show that our generalized Schrödinger equation satisfies an H-theorem for the quantum Boltzmann free energy. As a result, the probability distribution relaxes towards an equilibrium state which can be viewed as a Boltzmann distribution including a quantum potential. We propose to apply this generalized Schrödinger equation to dark matter halos in the Universe, possibly made of self-gravitating Bose-Einstein condensates.

Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations

PubMed Central

Zhou, Shenggao; Sun, Hui; Cheng, Li-Tien; Dzubiella, Joachim; McCammon, J. Andrew

2016-01-01

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach. PMID:27497546

Navier-Stokes solution on the CYBER-203 by a pseudospectral technique

NASA Technical Reports Server (NTRS)

Lambiotte, J. J.; Hussaini, M. Y.; Bokhari, S.; Orszag, S. A.

1983-01-01

A three-level, time-split, mixed spectral/finite difference method for the numerical solution of the three-dimensional, compressible Navier-Stokes equations has been developed and implemented on the Control Data Corporation (CDC) CYBER-203. This method uses a spectral representation for the flow variables in the streamwise and spanwise coordinates, and central differences in the normal direction. The five dependent variables are interleaved one horizontal plane at a time and the array of their values at the grid points of each horizontal plane is a typical vector in the computation. The code is organized so as to require, per time step, a single forward-backward pass through the entire data base. The one-and two-dimensional Fast Fourier Transforms are performed using software especially developed for the CYBER-203.

Nonlinear subdiffusive fractional equations and the aggregation phenomenon.

PubMed

Fedotov, Sergei

2013-09-01

In this article we address the problem of the nonlinear interaction of subdiffusive particles. We introduce the random walk model in which statistical characteristics of a random walker such as escape rate and jump distribution depend on the mean density of particles. We derive a set of nonlinear subdiffusive fractional master equations and consider their diffusion approximations. We show that these equations describe the transition from an intermediate subdiffusive regime to asymptotically normal advection-diffusion transport regime. This transition is governed by nonlinear tempering parameter that generalizes the standard linear tempering. We illustrate the general results through the use of the examples from cell and population biology. We find that a nonuniform anomalous exponent has a strong influence on the aggregation phenomenon.

Asymptotic approximations to posterior distributions via conditional moment equations

USGS Publications Warehouse

Yee, J.L.; Johnson, W.O.; Samaniego, F.J.

2002-01-01

We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations that arise naturally in the development. Asymptotic covariance matrices flow naturally from the work of Arnold & Press (1989) and involve the conditional asymptotic covariance matrices and first derivative matrices for conditional mean functions. When the fixed point equations admit an analytical solution, explicit formulae are subsequently obtained for the covariance structure of the joint limiting distribution, which may shed light on the use of the given statistical model. Two illustrations are given. ?? 2002 Biometrika Trust.

NASA Trapezoidal Wing Simulation Using Stress-w and One- and Two-Equation Turbulence Models

NASA Technical Reports Server (NTRS)

Rodio, J. J.; Xiao, X; Hassan, H. A.; Rumsey, C. L.

2014-01-01

The Wilcox 2006 stress-omega model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley code CFL3D and used to study a variety of 2-D and 3-D configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than experiment, similar to results of a two-equation model.

Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Hixon, Ray; Mankbadi, Reda R.

2003-01-01

An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

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.

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

NASA Astrophysics Data System (ADS)

Varga, Peter; Grafarend, Erik; Engels, Johannes

2017-03-01

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

Reconstructing the vibro-acoustic quantities on a highly non-spherical surface using the Helmholtz equation least squares method.

PubMed

Natarajan, Logesh Kumar; Wu, Sean F

2012-06-01

This paper presents helpful guidelines and strategies for reconstructing the vibro-acoustic quantities on a highly non-spherical surface by using the Helmholtz equation least squares (HELS). This study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces. The key is to select the optimal origin of the coordinate system behind the planar surface, choose a target structural wavelength to be reconstructed, set an appropriate stand-off distance and microphone spacing, use a hybrid regularization scheme to determine the optimal number of the expansion functions, etc. The reconstructed vibro-acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface. Results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength, and produce much more satisfactory results than a straight application of the original HELS formulations. Experiment validations on a baffled, square plate were conducted inside a fully anechoic chamber.

Wormhole potentials and throats from quasi-normal modes

NASA Astrophysics Data System (ADS)

Völkel, Sebastian H.; Kokkotas, Kostas D.

2018-05-01

Exotic compact objects refer to a wide class of black hole alternatives or effective models to describe phenomenologically quantum gravitational effects on the horizon scale. In this work we show how the knowledge of the quasi-normal mode spectrum of non-rotating wormhole models can be used to reconstruct the effective potential that appears in perturbation equations. From this it is further possible to obtain the parameters that characterize the specific wormhole model, which in this paper was chosen to be the one by Damour and Solodukhin. We also address the question whether one can distinguish such type of wormholes from ultra compact stars, if only the quasi-normal mode spectrum is known. We have proven that this is not possible by using the trapped modes only, but requires additional information. The inverse method presented here is an extension of work that has previously been developed and applied to the oscillation spectra of ultra compact stars and gravastars. However, it is not limited to the study of exotic compact objects, but applicable to symmetric double barrier potentials that appear in one-dimensional wave equations. Therefore we think it can be of interest for other fields too.

Alfven Simple Waves

NASA Astrophysics Data System (ADS)

Webb, G. M.; Zank, G. P.; Burrows, R.

2009-12-01

Multi-dimensional Alfvén simple waves in magnetohydrodynamics (MHD) are investigated using Boillat's formalism. For simple wave solutions, all physical variables (the gas density, pressure, fluid velocity, entropy, and magnetic field induction in the MHD case) depend on a single phase function ǎrphi which is a function of the space and time variables. The simple wave ansatz requires that the wave normal and the normal speed of the wave front depend only on the phase function ǎrphi. This leads to an implicit equation for the phase function, and a generalisation of the concept of a plane wave. We obtain examples of Alfvén simple waves, based on the right eigenvector solutions for the Alfvén mode. The Alfvén mode solutions have six integrals, namely that the entropy, density, magnetic pressure and the group velocity (the sum of the Alfvén and fluid velocity) are constant throughout the wave. The eigen-equations require that the rate of change of the magnetic induction B with ǎrphi throughout the wave is perpendicular to both the wave normal n and B. Methods to construct simple wave solutions based on specifying either a solution ansatz for n(ǎrphi) or B(ǎrphi) are developed.

Modeling Emerging Solar Cell Materials and Devices

NASA Astrophysics Data System (ADS)

Thongprong, Non

Organic photovoltaics (OPVs) and perovskite solar cells are emerging classes of solar cell that are promising for clean energy alternatives to fossil fuels. Understanding fundamental physics of these materials is crucial for improving their energy conversion efficiencies and promoting them to practical applications. Current density-voltage (JV) curves; which are important indicators of OPV efficiency, have direct connections to many fundamental properties of solar cells. They can be described by the Shockley diode equation, resulting in fitting parameters; series and parallel resistance (Rs and Rp), diode saturation current ( J0) and ideality factor (n). However, the Shockley equation was developed specifically for inorganic p-n junction diodes, so it lacks physical meanings when it is applied to OPVs. Hence, the puRposes of this work are to understand the fundamental physics of OPVs and to develop new diode equations in the same form as the Shockley equation that are based on OPV physics. We develop a numerical drift-diffusion simulation model to study bilayer OPVs, which will be called the drift-diffusion for bilayer interface (DD-BI) model. The model solves Poisson, drift-diffusion and current-continuity equations self-consistently for charge densities and potential profiles of a bilayer device with an organic heterojunction interface described by the GWWF model. We also derive new diode equations that have JV curves consistent with the DD-BI model and thus will be called self-consistent diode (SCD) equations. Using the DD-BI and the SCD model allows us to understand working principles of bilayer OPVs and physical definitions of the Shockley parameters. Due to low carrier mobilities in OPVs, space charge accumulation is common especially near the interface and electrodes. Hence, quasi-Fermi levels (i.e. chemical potentials), which depend on charge densities, are modified around the interface, resulting in a splitting of quasi-Fermi levels that works as a driving potential for the heterojunction diode. This brings about the meaning of R s as the resistance that gives rise to the diode voltage equal to the interface quasi-Fermi level splitting instead of the voltage between the electrodes. Quasi-Fermi levels that drop near the electrodes because of unmatched electrode work functions or due to charge injection can also increase Rs. Furthermore, we are able to study dissociation and recombination rates of bound charge pairs across the interface (i.e. polaron pairs or PPs) and arrive at the physical meaning of Rp as recombination resistance of PPs. In the dark, PP density is very low, so Rp is possibly caused by a tunneling leakage current at the interface. Ideality factors are parameters that depend on the split of quasi-Fermi levels and the ratio of recombination rate to recombination rate at equilibrium. Even though they are related to trap characteristics as normally understood, their relations are complicated and careful inte Rpretations of fitted ideality factors are needed. Our models are successfully applied to actual devices, and useful physics can be deduced, for example differences between the Shockley parameters under dark and illumination conditions. Another puRpose of this thesis is to study electronic properties of CsSnBr3 perovskite and processes of growing the perovskite film using an epitaxy technique. Calculation results using density functional theory reveal that a CsSnBr3 film that is grown on a NaCl(100) substrate can undergo a phase transition to CsSn 2Br5, which is a wide-bandgap semiconductor material. Actual mechanisms of the transition and the interface between CsSnBr3 and CsSn2Br5are interesting for future studies.

Modified Hartree-Fock-Bogoliubov theory at finite temperature

NASA Astrophysics Data System (ADS)

Dinh Dang, Nguyen; Arima, Akito

2003-07-01

The modified Hartree-Fock-Bogoliubov (MHFB) theory at finite temperature is derived, which conserves the unitarity relation of the particle-density matrix. This is achieved by constructing a modified-quasiparticle-density matrix, where the fluctuation of the quasiparticle number is microscopically built in. This matrix can be directly obtained from the usual quasiparticle-density matrix by applying the secondary Bogoliubov transformation, which includes the quasiparticle-occupation number. It is shown that, in the limit of constant pairing parameter, the MHFB theory yields the previously obtained modified BCS (MBCS) equations. It is also proved that the modified quasiparticle-random-phase approximation, which is based on the MBCS quasiparticle excitations, conserves the Ikeda sum rule. The numerical calculations of the pairing gap, heat capacity, level density, and level-density parameter within the MBCS theory are carried out for 120Sn. The results show that the superfluid-normal phase transition is completely washed out. The applicability of the MBCS up to a temperature as high as T˜5 MeV is analyzed in detail.

A protocol guided by transpulmonary thermodilution and lactate levels for resuscitation of patients with severe burns.

PubMed

Berger, Mette M; Que, Yok Ai

2013-11-11

Over-resuscitation is deleterious in many critically ill conditions, including major burns. For more than 15 years, several strategies to reduce fluid administration in burns during the initial resuscitation phase have been proposed, but no single or simple parameter has shown superiority. Fluid administration guided by invasive hemodynamic parameters usually resulted in over-resuscitation. As reported in the previous issue of Critical Care, Sánchez-Sánchez and colleagues analyzed the performance of a 'permissive hypovolemia' protocol guided by invasive hemodynamic parameters (PiCCO, Pulsion Medical Systems, Munich, Germany) and vital signs in a prospective cohort over a 3-year period. The authors' results confirm that resuscitation can be achieved with below-normal levels of preload but at the price of a fluid administration greater than predicted by the Parkland formula (2 to 4 mL/kg per% burn). The classic approach based on an adapted Parkland equation may still be the simplest until further studies identify the optimal bundle of resuscitation goals.

USAF Bioenvironmental Noise Data Handbook. Volume 160: KC-10A aircraft, near and far-field noise

NASA Astrophysics Data System (ADS)

Powell, R. G.

1982-09-01

The USAF KC-10A aircraft is an advanced tanker/cargo aircraft powered by three CF6-50C2 turbofan engines. This report provides measured and extrapolated data defining the bioacoustic environments produced by this aircraft operating on a concrete runup pad for eight engine/power configurations. Near-field data are reported for one location in a wide variety of physical and psychoacoustic measures: overall and band sound pressure levels, C-weighted and A-weighted sound levels, preferred speech interference levels, perceived noise levels, and limiting times for total daily exposure of personnel with and without standard Air Force ear protectors. Far-field data measured at 15 locations are normalized to standard meteorological conditions and extrapolated from 75-8000 meters to derive sets of equal-value contours for these same seven acoustic measures as functions of angle and distance from the source. Refer to Volume 1 of this handbook, USAF Bioenvironmental Noise Data Handbook, Vol 1: Organization, Content and Application, AMRL-TR-75-50(1) 1975, for discussion of the objective and design of the handbook, the types of data presented, measurement procedures, instrumentation, data processing, definitions of quantities, symbols, equations, applications, limitations, etc.

Rotor dynamic simulation and system identification methods for application to vacuum whirl data

NASA Technical Reports Server (NTRS)

Berman, A.; Giansante, N.; Flannelly, W. G.

1980-01-01

Methods of using rotor vacuum whirl data to improve the ability to model helicopter rotors were developed. The work consisted of the formulation of the equations of motion of elastic blades on a hub using a Galerkin method; the development of a general computer program for simulation of these equations; the study and implementation of a procedure for determining physical parameters based on measured data; and the application of a method for computing the normal modes and natural frequencies based on test data.

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

NASA Astrophysics Data System (ADS)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.

Applied Computational Electromagnetics Society Journal, Volume 7, Number 2, Winter 1992,

DTIC Science & Technology

1992-01-01

Rensselaer Polytechnic Institute University of Utah Las Cruces. NM USA -’roy. NY USA ,. Salt Lake City. UT T SA J.R. James A. Konrad D.V. Land RMCS Cranfleld...and found a strong correspondence between the two. Figures la -b show the equation and solution residuals as functions of iteration for small...I I I I I I I I I 4510 Is 31 25 16 35 .0 45 12 Figure la : Normalized solution and equation residuals as functions of iteration for a small sphere