A hybrid 3D SEM reconstruction method optimized for complex geologic material surfaces.

PubMed

Yan, Shang; Adegbule, Aderonke; Kibbey, Tohren C G

2017-08-01

Reconstruction methods are widely used to extract three-dimensional information from scanning electron microscope (SEM) images. This paper presents a new hybrid reconstruction method that combines stereoscopic reconstruction with shape-from-shading calculations to generate highly-detailed elevation maps from SEM image pairs. The method makes use of an imaged glass sphere to determine the quantitative relationship between observed intensity and angles between the beam and surface normal, and the detector and surface normal. Two specific equations are derived to make use of image intensity information in creating the final elevation map. The equations are used together, one making use of intensities in the two images, the other making use of intensities within a single image. The method is specifically designed for SEM images captured with a single secondary electron detector, and is optimized to capture maximum detail from complex natural surfaces. The method is illustrated with a complex structured abrasive material, and a rough natural sand grain. Results show that the method is capable of capturing details such as angular surface features, varying surface roughness, and surface striations. Copyright © 2017 Elsevier Ltd. All rights reserved.

Validation and application of single breath cardiac output determinations in man

NASA Technical Reports Server (NTRS)

Loeppky, J. A.; Fletcher, E. R.; Myhre, L. G.; Luft, U. C.

1986-01-01

The results of a procedure for estimating cardiac output by a single-breath technique (Qsb), obtained in healthy males during supine rest and during exercise on a bicycle ergometer, were compared with the results on cardiac output obtained by the direct Fick method (QF). The single breath maneuver consisted of a slow exhalation to near residual volume following an inspiration somewhat deeper than normal. The Qsb calculations incorporated an equation of the CO2 dissociation curve and a 'moving spline' sequential curve-fitting technique to calculate the instantaneous R from points on the original expirogram. The resulting linear regression equation indicated a 24-percent underestimation of QF by the Qsb technique. After applying a correction, the Qsb-QF relationship was improved. A subsequent study during upright rest and exercise to 80 percent of VO2(max) in 6 subjects indicated a close linear relationship between Qsb and VO2 for all 95 values obtained, with slope and intercept close to those in published studies in which invasive cardiac output measurements were used.

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.

Fractional Dynamics of Single File Diffusion in Dusty Plasma Ring

NASA Astrophysics Data System (ADS)

Muniandy, S. V.; Chew, W. X.; Asgari, H.; Wong, C. S.; Lim, S. C.

2011-11-01

Single file diffusion (SFD) refers to the constrained motion of particles in quasi-one-dimensional channel such that the particles are unable to pass each other. Possible SFD of charged dust confined in biharmonic annular potential well with screened Coulomb interaction is investigated. Transition from normal diffusion to anomalous sub-diffusion behaviors is observed. Deviation from SFD's mean square displacement scaling behavior of 1/2-exponent may occur in strongly interacting systems. A phenomenological model based on fractional Langevin equation is proposed to account for the anomalous SFD behavior in dusty plasma ring.

Beyond SaGMRotI: Conversion to SaArb, SaSN, and SaMaxRot

USGS Publications Warehouse

Watson-Lamprey, J. A.; Boore, D.M.

2007-01-01

In the seismic design of structures, estimates of design forces are usually provided to the engineer in the form of elastic response spectra. Predictive equations for elastic response spectra are derived from empirical recordings of ground motion. The geometric mean of the two orthogonal horizontal components of motion is often used as the response value in these predictive equations, although it is not necessarily the most relevant estimate of forces within the structure. For some applications it is desirable to estimate the response value on a randomly chosen single component of ground motion, and in other applications the maximum response in a single direction is required. We give adjustment factors that allow converting the predictions of geometric-mean ground-motion predictions into either of these other two measures of seismic ground-motion intensity. In addition, we investigate the relation of the strike-normal component of ground motion to the maximum response values. We show that the strike-normal component of ground motion seldom corresponds to the maximum horizontal-component response value (in particular, at distances greater than about 3 km from faults), and that focusing on this case in exclusion of others can result in the underestimation of the maximum component. This research provides estimates of the maximum response value of a single component for all cases, not just near-fault strike-normal components. We provide modification factors that can be used to convert predictions of ground motions in terms of the geometric mean to the maximum spectral acceleration (SaMaxRot) and the random component of spectral acceleration (SaArb). Included are modification factors for both the mean and the aleatory standard deviation of the logarithm of the motions.

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.

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.

Aeroelastic Stability of Rotor Blades Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Chopra, I.; Sivaneri, N.

1982-01-01

The flutter stability of flap bending, lead-lag bending, and torsion of helicopter rotor blades in hover is investigated using a finite element formulation based on Hamilton's principle. The blade is divided into a number of finite elements. Quasi-steady strip theory is used to evaluate the aerodynamic loads. The nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The equations of motion are linearized assuming blade motion to be a small perturbation about the steady deflected shape. The normal mode method based on the coupled rotating natural modes is used to reduce the number of equations in the flutter analysis. First the formulation is applied to single-load-path blades (articulated and hingeless blades). Numerical results show very good agreement with existing results obtained using the modal approach. The second part of the application concerns multiple-load-path blades, i.e. bearingless blades. Numerical results are presented for several analytical models of the bearingless blade. Results are also obtained using an equivalent beam approach wherein a bearingless blade is modelled as a single beam with equivalent properties. Results show the equivalent beam model.

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.

Coordinates of features on the Galilean satellites

NASA Technical Reports Server (NTRS)

Davies, M. E.; Katayama, F. Y.

1980-01-01

The coordinate systems of each of the Galilean satellites are defined and coordinates of features seen in the Voyager pictures of these satellites are presented. The control nets of the satellites were computed by means of single block analytical triangulations. The normal equations were solved by the conjugate iterative method which is convenient and which converges rapidly as the initial estimates of the parameters are very good.

Diffraction of a shock wave by a compression corner; regular and single Mach reflection

NASA Technical Reports Server (NTRS)

Vijayashankar, V. S.; Kutler, P.; Anderson, D.

1976-01-01

The two dimensional, time dependent Euler equations which govern the flow field resulting from the injection of a planar shock with a compression corner are solved with initial conditions that result in either regular reflection or single Mach reflection of the incident planar shock. The Euler equations which are hyperbolic are transformed to include the self similarity of the problem. A normalization procedure is employed to align the reflected shock and the Mach stem as computational boundaries to implement the shock fitting procedure. A special floating fitting scheme is developed in conjunction with the method of characteristics to fit the slip surface. The reflected shock, the Mach stem, and the slip surface are all treated as harp discontinuities, thus, resulting in a more accurate description of the inviscid flow field. The resulting numerical solutions are compared with available experimental data and existing first-order, shock-capturing numerical solutions.

Dynamic Divisive Normalization Predicts Time-Varying Value Coding in Decision-Related Circuits

PubMed Central

LoFaro, Thomas; Webb, Ryan; Glimcher, Paul W.

2014-01-01

Normalization is a widespread neural computation, mediating divisive gain control in sensory processing and implementing a context-dependent value code in decision-related frontal and parietal cortices. Although decision-making is a dynamic process with complex temporal characteristics, most models of normalization are time-independent and little is known about the dynamic interaction of normalization and choice. Here, we show that a simple differential equation model of normalization explains the characteristic phasic-sustained pattern of cortical decision activity and predicts specific normalization dynamics: value coding during initial transients, time-varying value modulation, and delayed onset of contextual information. Empirically, we observe these predicted dynamics in saccade-related neurons in monkey lateral intraparietal cortex. Furthermore, such models naturally incorporate a time-weighted average of past activity, implementing an intrinsic reference-dependence in value coding. These results suggest that a single network mechanism can explain both transient and sustained decision activity, emphasizing the importance of a dynamic view of normalization in neural coding. PMID:25429145

Dynamics of localized structures in reaction-diffusion systems induced by delayed feedback

NASA Astrophysics Data System (ADS)

Gurevich, Svetlana V.

2013-05-01

We are interested in stability properties of a single localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to complex dynamical behavior of the system, including formation of target patterns, spontaneous motion, and spontaneous breathing as well as various complex structures, arising from combination of different oscillatory instabilities. In the case of spontaneous motion, we provide a bifurcation analysis of the delayed system and derive an order parameter equation for the position of the localized structure, explicitly describing its temporal evolution in the vicinity of the bifurcation point. This equation is a subject to a nonlinear delay differential equation, which can be transformed to the normal form of the pitchfork drift bifurcation.

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Large Angle Reorientation of a Solar Sail Using Gimballed Mass Control

NASA Astrophysics Data System (ADS)

Sperber, E.; Fu, B.; Eke, F. O.

2016-06-01

This paper proposes a control strategy for the large angle reorientation of a solar sail equipped with a gimballed mass. The algorithm consists of a first stage that manipulates the gimbal angle in order to minimize the attitude error about a single principal axis. Once certain termination conditions are reached, a regulator is employed that selects a single gimbal angle for minimizing both the residual attitude error concomitantly with the body rate. Because the force due to the specular reflection of radiation is always directed along a reflector's surface normal, this form of thrust vector control cannot generate torques about an axis normal to the plane of the sail. Thus, in order to achieve three-axis control authority a 1-2-1 or 2-1-2 sequence of rotations about principal axes is performed. The control algorithm is implemented directly in-line with the nonlinear equations of motion and key performance characteristics are identified.

Macroscopic damping model for structural dynamics with random polycrystalline configurations

NASA Astrophysics Data System (ADS)

Yang, Yantao; Cui, Junzhi; Yu, Yifan; Xiang, Meizhen

2018-06-01

In this paper the macroscopic damping model for dynamical behavior of the structures with random polycrystalline configurations at micro-nano scales is established. First, the global motion equation of a crystal is decomposed into a set of motion equations with independent single degree of freedom (SDOF) along normal discrete modes, and then damping behavior is introduced into each SDOF motion. Through the interpolation of discrete modes, the continuous representation of damping effects for the crystal is obtained. Second, from energy conservation law the expression of the damping coefficient is derived, and the approximate formula of damping coefficient is given. Next, the continuous damping coefficient for polycrystalline cluster is expressed, the continuous dynamical equation with damping term is obtained, and then the concrete damping coefficients for a polycrystalline Cu sample are shown. Finally, by using statistical two-scale homogenization method, the macroscopic homogenized dynamical equation containing damping term for the structures with random polycrystalline configurations at micro-nano scales is set up.

Adding In-Plane Flexibility to the Equations of Motion of a Single Rotor Helicopter

NASA Technical Reports Server (NTRS)

Curtiss, H. C., Jr.

2000-01-01

This report describes a way to add the effects of main rotor blade flexibility in the in- plane or lead-lag direction to a large set of non-linear equations of motion for a single rotor helicopter with rigid blades(l). Differences between the frequency of the regressing lag mode predicted by the equations of (1) and that measured in flight (2) for a UH-60 helicopter indicate that some element is missing from the analytical model of (1) which assumes rigid blades. A previous study (3) noted a similar discrepancy for the CH-53 helicopter. Using a relatively simple analytical model in (3), compared to (1), it was shown that a mechanical lag damper increases significantly the coupling between the rigid lag mode and the first flexible mode. This increased coupling due to a powerful lag damper produces an increase in the lowest lag frequency when viewed in a frame rotating with the blade. Flight test measurements normally indicate the frequency of this mode in a non-rotating or fixed frame. This report presents the additions necessary to the full equations of motion, to include main rotor blade lag flexibility. Since these additions are made to a very complex nonlinear dynamic model, in order to provide physical insight, a discussion of the results obtained from a simplified set of equations of motion is included. The reduced model illustrates the physics involved in the coupling and should indicate trends in the full model.

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.

EGSIEM: Combination of GRACE monthly gravity models on normal equation level

NASA Astrophysics Data System (ADS)

Meyer, Ulrich; Jean, Yoomin; Jäggi, Adrian; Mayer-Gürr, Torsten; Neumayer, Hans; Lemoine, Jean-Michel

2016-04-01

One of the three geodetic services to be realized in the frame of the EGSIEM project is a scientific combination service. Each associated processing center (AC) will follow a set of common processing standards but will apply its own, independent analysis method. Therefore the quality, robustness and reliability of the combined monthly gravity fields is expected to improve significantly compared to the individual solutions. The Monthly GRACE gravity fields of all ACs are combined on normal equation level. The individual normal equations are weighted depending on pairwise comparisons of the individual gravity field solutions. To derive these weights and for quality control of the individual contributions first a combination of the monthly gravity fields on solution level is performed. The concept of weighting and of the combination on normal equation level is introduced and the formats used for normal equation exchange and gravity field solutions is described. First results of the combination on normal equation level are presented and compared to the corresponding combinations on solution level. EGSIEM has an open data policy and all processing centers of GRACE gravity fields are invited to participate in the combination.

Vorticity equation for MHD fast waves in geospace environment

NASA Technical Reports Server (NTRS)

Yamauchi, M.; Lundin, R.; Lui, A. T. Y.

1993-01-01

The MHD vorticity equation is modified in order to apply it to nonlinear MHD fast waves or shocks when their extent along the magnetic field is limited. Field-aligned current (FAC) generation is also discussed on the basis of this modified vorticity equation. When the wave normal is not aligned to the finite velocity convection and the source region is spatially limited, a longitudinal polarization causes a pair of plus and minus charges inside the compressional plane waves or shocks, generating a pair of FACs. This polarization is not related to the separation between the electrons and ions caused by their difference in mass, a separation which is inherent to compressional waves. The resultant double field-aligned current structure exists both with and without the contributions from curvature drift, which is questionable in terms of its contribution to vorticity change from the viewpoint of single-particle motion.

Single- and double-photoionization cross sections of atomic nitrogen from threshold to 31 A

NASA Technical Reports Server (NTRS)

Samson, James A. R.; Angel, G. C.

1990-01-01

The relative photoionization cross section of atomic nitrogen for the production of singly and doubly charged ions has been measured from 44.3 to 275 A and from 520 to 852 A. The results have been made absolute by normalization to one-half of the molecular nitrogen cross section at short wavelengths. The smoothed atomic nitrogen cross sections sigma can be accurately represented, at short wavelengths, by the equation sigma(Mb) = 36,700 x (E exp-2.3) as a function of the photon energy E (eV), thereby allowing the cross sections to be extrapolated to the nitrogen K edge at 31 A.

Efficient spin-current injection in single-molecule magnet junctions

NASA Astrophysics Data System (ADS)

Xie, Haiqing; Xu, Fuming; Jiao, Hujun; Wang, Qiang; Liang, J.-Q.

2018-01-01

We study theoretically spin transport through a single-molecule magnet (SMM) in the sequential and cotunneling regimes, where the SMM is weakly coupled to one ferromagnetic and one normal-metallic leads. By a master-equation approach, it is found that the spin polarization injected from the ferromagnetic lead is amplified and highly polarized spin-current can be generated, due to the exchange coupling between the transport electron and the anisotropic spin of the SMM. Moreover, the spin-current polarization can be tuned by the gate or bias voltage, and thus an efficient spin injection device based on the SMM is proposed in molecular spintronics.

A new approach to the linear theory of single-species tearing in two-dimensional quasi-neutral sheets

NASA Technical Reports Server (NTRS)

Brittnacher, M.; Quest, K. B.; Karimabadi, H.

1995-01-01

We have developed the linear theory of collisionless ion tearing in a two-dimensional magnetotail equilibrium for a single resonant species. We have solved the normal mode problem for tearing instability by an algorithm that employs particle-in-cell simulation to calculate the orbit integrals in the Maxwell-Vlasov eigenmode equation. The results of our single-species tearing analysis can be applied to ion tearing where electron effects are not included. We have calculated the tearing growth rate as a function of the magnetic field component B(sub n) normal to the current sheet for thick and thin current sheets, and we show that marginal stability occurs when the normal gyrofrequency Omega(sub n) is comparable to the Harris neutral sheet growth rate. A cross-tail B(sub y) component has little effect on the growth rate for B(sub y) approximately = B(sub n). Even in the limit B(sub y) much greater than B(sub n), the mode is strongly stabilized by B(sub n). We report than random pitch angle scattering can overcome the stabilizing effect of B(sub n) and drive the growth rate up toward the Harris neutral sheet (B(sub n) = 0) value when the pitch angle diffusion rate is comparable to Omega(sub n).

SVBRDF-Invariant Shape and Reflectance Estimation from a Light-Field Camera.

PubMed

Wang, Ting-Chun; Chandraker, Manmohan; Efros, Alexei A; Ramamoorthi, Ravi

2018-03-01

Light-field cameras have recently emerged as a powerful tool for one-shot passive 3D shape capture. However, obtaining the shape of glossy objects like metals or plastics remains challenging, since standard Lambertian cues like photo-consistency cannot be easily applied. In this paper, we derive a spatially-varying (SV)BRDF-invariant theory for recovering 3D shape and reflectance from light-field cameras. Our key theoretical insight is a novel analysis of diffuse plus single-lobe SVBRDFs under a light-field setup. We show that, although direct shape recovery is not possible, an equation relating depths and normals can still be derived. Using this equation, we then propose using a polynomial (quadratic) shape prior to resolve the shape ambiguity. Once shape is estimated, we also recover the reflectance. We present extensive synthetic data on the entire MERL BRDF dataset, as well as a number of real examples to validate the theory, where we simultaneously recover shape and BRDFs from a single image taken with a Lytro Illum camera.

Dynamic divisive normalization predicts time-varying value coding in decision-related circuits.

PubMed

Louie, Kenway; LoFaro, Thomas; Webb, Ryan; Glimcher, Paul W

2014-11-26

Normalization is a widespread neural computation, mediating divisive gain control in sensory processing and implementing a context-dependent value code in decision-related frontal and parietal cortices. Although decision-making is a dynamic process with complex temporal characteristics, most models of normalization are time-independent and little is known about the dynamic interaction of normalization and choice. Here, we show that a simple differential equation model of normalization explains the characteristic phasic-sustained pattern of cortical decision activity and predicts specific normalization dynamics: value coding during initial transients, time-varying value modulation, and delayed onset of contextual information. Empirically, we observe these predicted dynamics in saccade-related neurons in monkey lateral intraparietal cortex. Furthermore, such models naturally incorporate a time-weighted average of past activity, implementing an intrinsic reference-dependence in value coding. These results suggest that a single network mechanism can explain both transient and sustained decision activity, emphasizing the importance of a dynamic view of normalization in neural coding. Copyright © 2014 the authors 0270-6474/14/3416046-12$15.00/0.

On Nonequivalence of Several Procedures of Structural Equation Modeling

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Chan, Wai

2005-01-01

The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are: the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically distribution-free procedure. When data are normally distributed and the model structure…

Single-particle potential of the Λ hyperon in nuclear matter with chiral effective field theory NLO interactions including effects of Y N N three-baryon interactions

NASA Astrophysics Data System (ADS)

Kohno, M.

2018-03-01

Adopting hyperon-nucleon and hyperon-nucleon-nucleon interactions parametrized in chiral effective field theory, single-particle potentials of the Λ and Σ hyperons are evaluated in symmetric nuclear matter and in pure neutron matter within the framework of lowest-order Bruckner theory. The chiral NLO interaction bears strong Λ N -Σ N coupling. Although the Λ potential is repulsive if the coupling is switched off, the Λ N -Σ N correlation brings about the attraction consistent with empirical data. The Σ potential is repulsive, which is also consistent with empirical information. The interesting result is that the Λ potential becomes shallower beyond normal density. This provides the possibility of solving the hyperon puzzle without introducing ad hoc assumptions. The effects of the Λ N N -Λ N N and Λ N N -Σ N N three-baryon forces are considered. These three-baryon forces are first reduced to normal-ordered effective two-baryon interactions in nuclear matter and then incorporated in the G -matrix equation. The repulsion from the Λ N N -Λ N N interaction is of the order of 5 MeV at normal density and becomes larger with increasing density. The effects of the Λ N N -Σ N N coupling compensate the repulsion at normal density. The net effect of the three-baryon interactions on the Λ single-particle potential is repulsive at higher densities.

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.

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.

Wind direction change criteria for wind turbine design

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

Cliff, W.C.

1979-01-01

A method is presented for estimating the root mean square (rms) value of the wind direction change, ..delta..theta(tau) = theta(tau + tau) - theta(tau), that occurs over the swept area of wind turbine rotor systems. An equation is also given for the rms value of the wind direction change that occurs at a single point in space, i.e., a direcion change that a wind vane would measure. Assuming a normal probability density function for the lateral wind velocity change and relating this to angular changes, equations are given for calculating the expected number of wind direction changes, larger than anmore » arbitrary value, that will occur in 1 hr as well as the expected number that will occur during the design life of a wind turbine. The equations presented are developed using a small angle approximation and are, therefore, considered appropriate for wind direction changes of less than 30/sup 0/. The equations presented are based upon neutral atmospheric boundary-layer conditions and do not include information regarding events such as tornados, hurricanes, etc.« less

Propagation of acoustic waves in a one-dimensional macroscopically inhomogeneous poroelastic material.

PubMed

Gautier, G; Kelders, L; Groby, J P; Dazel, O; De Ryck, L; Leclaire, P

2011-09-01

Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. The wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently in the case of rigid frame inhomogeneous porous materials. This paper focuses on the solution of the full wave equation in which the acoustic and the elastic properties of the poroelastic material vary in one-dimension. The reflection coefficient of a one-dimensional macroscopically inhomogeneous porous material on a rigid backing is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method at both normal and oblique incidence and to experimental measurements at normal incidence for a known two-layers porous material, considered as a single inhomogeneous layer. Finally, discussion about the absorption coefficient for various inhomogeneity profiles gives further perspectives. © 2011 Acoustical Society of America

Computing ordinary least-squares parameter estimates for the National Descriptive Model of Mercury in Fish

USGS Publications Warehouse

Donato, David I.

2013-01-01

A specialized technique is used to compute weighted ordinary least-squares (OLS) estimates of the parameters of the National Descriptive Model of Mercury in Fish (NDMMF) in less time using less computer memory than general methods. The characteristics of the NDMMF allow the two products X'X and X'y in the normal equations to be filled out in a second or two of computer time during a single pass through the N data observations. As a result, the matrix X does not have to be stored in computer memory and the computationally expensive matrix multiplications generally required to produce X'X and X'y do not have to be carried out. The normal equations may then be solved to determine the best-fit parameters in the OLS sense. The computational solution based on this specialized technique requires O(8p2+16p) bytes of computer memory for p parameters on a machine with 8-byte double-precision numbers. This publication includes a reference implementation of this technique and a Gaussian-elimination solver in preliminary custom software.

Temporal Stability of the NDVI-LAI Relationship in a Napa Valley Vineyard

NASA Technical Reports Server (NTRS)

Johnson, L. F.

2003-01-01

Remotely sensed normalized difference vegetation index (NDVI) values, derived from high-resolution satellite images, were compared with ground measurements of vineyard leaf area index (LAI) periodically during the 2001 growing season. The two variables were strongly related at six ground calibration sites on each of four occasions (r squared = 0.91 to 0.98). Linear regression equations relating the two variables did not significantly differ by observation date, and a single equation accounted for 92 percent of the variance in the combined dataset. Temporal stability of the relationship opens the possibility of transforming NDVI maps to LAI in the absence of repeated ground calibration fieldwork. In order to take advantage of this circumstance, however, steps should be taken to assure temporal consistency in spectral data values comprising the NDVI.

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) .

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.

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.

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.

A stockability equation for forest land in Siskiyou County, California.

Treesearch

Neil. McKay

1985-01-01

An equation is presented that estimates the relative stocking capacity of forest land in Siskiyou County, California, from the amount of precipitation and the presence of significant indicator plants. The equation is a toot for identifying sites incapable of supporting normal stocking. Estimated relative stocking capacity may be used to discount normal yields to levels...

Andreev bound states. Some quasiclassical reflections

NASA Astrophysics Data System (ADS)

Lin, Y.; Leggett, A. J.

2014-12-01

We discuss a very simple and essentially exactly solvable model problem which illustrates some nice features of Andreev bound states, namely, the trapping of a single Bogoliubov quasiparticle in a neutral s-wave BCS superfluid by a wide and shallow Zeeman trap. In the quasiclassical limit, the ground state is a doublet with a splitting which is proportional to the exponentially small amplitude for "normal" reflection by the edges of the trap. We comment briefly on a prima facie paradox concerning the continuity equation and conjecture a resolution to it.

Basic research and data analysis for the National Geodetic Satellite program and for the Earth Surveys program

NASA Technical Reports Server (NTRS)

1972-01-01

Current research is reported on precise and accurate descriptions of the earth's surface and gravitational field and on time variations of geophysical parameters. A new computer program was written in connection with the adjustment of the BC-4 worldwide geometric satellite triangulation net. The possibility that an increment to accuracy could be transferred from a super-control net to the basic geodetic (first-order triangulation) was investigated. Coordinates of the NA9 solution were computed and were transformed to the NAD datum, based on GEOS 1 observations. Normal equations from observational data of several different systems and constraint equations were added and a single solution was obtained for the combined systems. Transformation parameters with constraints were determined, and the impact of computers on surveying and mapping is discussed.

New Equations for Calculating Principal and Fine-Structure Atomic Spectra for Single and Multi-Electron Atoms

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

Surdoval, Wayne A.; Berry, David A.; Shultz, Travis R.

A set of equations are presented for calculating atomic principal spectral lines and fine-structure energy splits for single and multi-electron atoms. Calculated results are presented and compared to the National Institute of Science and Technology database demonstrating very good accuracy. The equations do not require fitted parameters. The only experimental parameter required is the Ionization energy for the electron of interest. The equations have comparable accuracy and broader applicability than the single electron Dirac equation. Three Appendices discuss the origin of the new equations and present calculated results. New insights into the special relativistic nature of the Dirac equation andmore » its relationship to the new equations are presented.« less

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

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

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

1978-07-01

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

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…

Modeling of nonequilibrium space plasma flows

NASA Technical Reports Server (NTRS)

Gombosi, Tamas

1995-01-01

Godunov-type numerical solution of the 20 moment plasma transport equations. One of the centerpieces of our proposal was the development of a higher order Godunov-type numerical scheme to solve the gyration dominated 20 moment transport equations. In the first step we explored some fundamental analytic properties of the 20 moment transport equations for a low b plasma, including the eigenvectors and eigenvalues of propagating disturbances. The eigenvalues correspond to wave speeds, while the eigenvectors characterize the transported physical quantities. In this paper we also explored the physically meaningful parameter range of the normalized heat flow components. In the second step a new Godunov scheme type numerical method was developed to solve the coupled set of 20 moment transport equations for a quasineutral single-ion plasma. The numerical method and the first results were presented at several national and international meetings and a paper describing the method has been published in the Journal of Computational Physics. To our knowledge this is the first numerical method which is capable of producing stable time-dependent solutions to the full 20 (or 16) moment set of transport equations, including the full heat flow equation. Previous attempts resulted in unstable (oscillating) solutions of the heat flow equations. Our group invested over two man-years into the development and implementation of the new method. The present model solves the 20 moment transport equations for an ion species and thermal electrons in 8 domain extending from a collision dominated to a collisionless region (200 km to 12,000 km). This model has been applied to study O+ acceleration due to Joule heating in the lower ionosphere.

Single wall penetration equations

NASA Technical Reports Server (NTRS)

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

1991-01-01

Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

Pressure evolution equation for the particulate phase in inhomogeneous compressible disperse multiphase flows

NASA Astrophysics Data System (ADS)

Annamalai, Subramanian; Balachandar, S.; Sridharan, P.; Jackson, T. L.

2017-02-01

An analytical expression describing the unsteady pressure evolution of the dispersed phase driven by variations in the carrier phase is presented. In this article, the term "dispersed phase" represents rigid particles, droplets, or bubbles. Letting both the dispersed and continuous phases be inhomogeneous, unsteady, and compressible, the developed pressure equation describes the particle response and its eventual equilibration with that of the carrier fluid. The study involves impingement of a plane traveling wave of a given frequency and subsequent volume-averaged particle pressure calculation due to a single wave. The ambient or continuous fluid's pressure and density-weighted normal velocity are identified as the source terms governing the particle pressure. Analogous to the generalized Faxén theorem, which is applicable to the particle equation of motion, the pressure expression is also written in terms of the surface average of time-varying incoming flow properties. The surface average allows the current formulation to be generalized for any complex incident flow, including situations where the particle size is comparable to that of the incoming flow. Further, the particle pressure is also found to depend on the dispersed-to-continuous fluid density ratio and speed of sound ratio in addition to dynamic viscosities of both fluids. The model is applied to predict the unsteady pressure variation inside an aluminum particle subjected to normal shock waves. The results are compared against numerical simulations and found to be in good agreement. Furthermore, it is shown that, although the analysis is conducted in the limit of negligible flow Reynolds and Mach numbers, it can be used to compute the density and volume of the dispersed phase to reasonable accuracy. Finally, analogous to the pressure evolution expression, an equation describing the time-dependent particle radius is deduced and is shown to reduce to the Rayleigh-Plesset equation in the linear limit.

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…

Implementation of an integrated op-amp based chaotic neuron model and observation of its chaotic dynamics

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

Jung, Jinwoo; Lee, Jewon; Song, Hanjung

2011-03-15

This paper presents a fully integrated circuit implementation of an operational amplifier (op-amp) based chaotic neuron model with a bipolar output function, experimental measurements, and analyses of its chaotic behavior. The proposed chaotic neuron model integrated circuit consists of several op-amps, sample and hold circuits, a nonlinear function block for chaotic signal generation, a clock generator, a nonlinear output function, etc. Based on the HSPICE (circuit program) simulation results, approximated empirical equations for analyses were formulated. Then, the chaotic dynamical responses such as bifurcation diagrams, time series, and Lyapunov exponent were calculated using these empirical equations. In addition, we performedmore » simulations about two chaotic neuron systems with four synapses to confirm neural network connections and got normal behavior of the chaotic neuron such as internal state bifurcation diagram according to the synaptic weight variation. The proposed circuit was fabricated using a 0.8-{mu}m single poly complementary metal-oxide semiconductor technology. Measurements of the fabricated single chaotic neuron with {+-}2.5 V power supplies and a 10 kHz sampling clock frequency were carried out and compared with the simulated results.« less

Liouville master equation for multi-electron dynamics during ion-surface interactions

NASA Astrophysics Data System (ADS)

Wirtz, L.; Reinhold, C. O.; Lemell, C.; Burgdorfer, J.

2003-05-01

We present a simulation of the neutralization of highly charged ions in front of a LiF(100) surface including the close-collision regime above the surface. Our approach employs a Monte-Carlo solution of the Liouville master equation for the joint probability density of the ionic motion and the electronic population of the projectile and the target surface. It includes single as well as double particle-hole (de)excitation processes and incorporates electron correlation effects through the conditional dynamics of population strings. The input in terms of elementary one- and two-electron transfer rates is determined from CTMC calculations as well as quantum mechanical Auger calculations. For slow projectiles and normal incidence, the ionic motion depends sensitively on the interplay between image acceleration towards the surface and repulsion by an ensemble of positive hole charges in the surface (``trampoline effect"). For Ne10+ ions we find that image acceleration dominates and no collective backscattering high above the surface takes place. For grazing incidence, our simulation delineates the pathways to complete neutralization. In accordance with recent experimental observations, most ions are reflected as neutrals or even as singly charged negative particles, irrespective of the charge state of the incoming ion.

Calculation of three-dimensional compressible laminar and turbulent boundary layers. An implicit finite-difference procedure for solving the three-dimensional compressible laminar, transitional, and turbulent boundary-layer equations

NASA Technical Reports Server (NTRS)

Harris, J. E.

1975-01-01

An implicit finite-difference procedure is presented for solving the compressible three-dimensional boundary-layer equations. The method is second-order accurate, unconditionally stable (conditional stability for reverse cross flow), and efficient from the viewpoint of computer storage and processing time. The Reynolds stress terms are modeled by (1) a single-layer mixing length model and (2) a two-layer eddy viscosity model. These models, although simple in concept, accurately predicted the equilibrium turbulent flow for the conditions considered. Numerical results are compared with experimental wall and profile data for a cone at an angle of attack larger than the cone semiapex angle. These comparisons clearly indicate that the numerical procedure and turbulence models accurately predict the experimental data with as few as 21 nodal points in the plane normal to the wall boundary.

Eigenvalue equation and core-mode cutoff of weakly guiding tapered fiber as three layer optical waveguide and used as biochemical sensor.

PubMed

Linslal, C L; Mohan, P M S; Halder, A; Gangopadhyay, T K

2012-06-01

The core-mode cutoff plays a major role in evanescent field absorption based sensors. A method has been proposed to calculate the core-mode cutoff by solving the eigenvalue equations of a weakly guiding three layer optical waveguide graphically. The variation of normalized waveguide parameter (V) is also calculated with different wavelengths at core-mode cutoff. At the first step, theoretical analysis of tapered fiber parameters has been performed for core-mode cutoff. The taper angle of an adiabatic tapered fiber is also analyzed using the length-scale criterion. Secondly, single-mode tapered fiber has been developed to make a precision sensor element suitable for chemical detection. Finally, the sensor element has been used to detect absorption peak of ethylenediamine. Results are presented in which an absorption peak at 1540 nm is observed.

Effects of thermal noise on the transitional dynamics of an inextensible elastic filament in stagnation flow.

PubMed

Deng, Mingge; Grinberg, Leopold; Caswell, Bruce; Karniadakis, George Em

2015-06-28

We investigate the dynamics of a single inextensible elastic filament subject to anisotropic friction in a viscous stagnation-point flow, by employing both a continuum model represented by Langevin type stochastic partial differential equations (SPDEs) and a dissipative particle dynamics (DPD) method. Unlike previous works, the filament is free to rotate and the tension along the filament is determined by the local inextensible constraint. The kinematics of the filament is recorded and studied with normal modes analysis. The results show that the filament displays an instability induced by negative tension, which is analogous to Euler buckling of a beam. Symmetry breaking of normal modes dynamics and stretch-coil transitions are observed above the threshold of the buckling instability point. Furthermore, both temporal and spatial noise are amplified resulting from the interaction of thermal fluctuations and nonlinear filament dynamics. Specifically, the spatial noise is amplified with even normal modes being excited due to symmetry breaking, while the temporal noise is amplified with increasing time correlation length and variance.

Analytical and molecular dynamics studies on the impact loading of single-layered graphene sheet by fullerene

NASA Astrophysics Data System (ADS)

Hosseini-Hashemi, Shahrokh; Sepahi-Boroujeni, Amin; Sepahi-Boroujeni, Saeid

2018-04-01

Normal impact performance of a system including a fullerene molecule and a single-layered graphene sheet is studied in the present paper. Firstly, through a mathematical approach, a new contact law is derived to describe the overall non-bonding interaction forces of the "hollow indenter-target" system. Preliminary verifications show that the derived contact law gives a reliable picture of force field of the system which is in good agreements with the results of molecular dynamics (MD) simulations. Afterwards, equation of the transversal motion of graphene sheet is utilized on the basis of both the nonlocal theory of elasticity and the assumptions of classical plate theory. Then, to derive dynamic behavior of the system, a set including the proposed contact law and the equations of motion of both graphene sheet and fullerene molecule is solved numerically. In order to evaluate outcomes of this method, the problem is modeled by MD simulation. Despite intrinsic differences between analytical and MD methods as well as various errors arise due to transient nature of the problem, acceptable agreements are established between analytical and MD outcomes. As a result, the proposed analytical method can be reliably used to address similar impact problems. Furthermore, it is found that a single-layered graphene sheet is capable of trapping fullerenes approaching with low velocities. Otherwise, in case of rebound, the sheet effectively absorbs predominant portion of fullerene energy.

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.

Three-Dimensional Magnetohydrodynamic Modeling of the Solar Wind Including Pickup Protons and Turbulence Transport

NASA Technical Reports Server (NTRS)

Usmanov, Arcadi V.; Goldstein, Melvyn L.; Matthaeus, William H.

2012-01-01

To study the effects of interstellar pickup protons and turbulence on the structure and dynamics of the solar wind, we have developed a fully three-dimensional magnetohydrodynamic solar wind model that treats interstellar pickup protons as a separate fluid and incorporates the transport of turbulence and turbulent heating. The governing system of equations combines the mean-field equations for the solar wind plasma, magnetic field, and pickup protons and the turbulence transport equations for the turbulent energy, normalized cross-helicity, and correlation length. The model equations account for photoionization of interstellar hydrogen atoms and their charge exchange with solar wind protons, energy transfer from pickup protons to solar wind protons, and plasma heating by turbulent dissipation. Separate mass and energy equations are used for the solar wind and pickup protons, though a single momentum equation is employed under the assumption that the pickup protons are comoving with the solar wind protons.We compute the global structure of the solar wind plasma, magnetic field, and turbulence in the region from 0.3 to 100 AU for a source magnetic dipole on the Sun tilted by 0 deg - .90 deg and compare our results with Voyager 2 observations. The results computed with and without pickup protons are superposed to evaluate quantitatively the deceleration and heating effects of pickup protons, the overall compression of the magnetic field in the outer heliosphere caused by deceleration, and the weakening of corotating interaction regions by the thermal pressure of pickup protons.

Sensitivity of solar-cell performance to atmospheric variables. 2: Dissimilar cells at several locations

NASA Technical Reports Server (NTRS)

Klucher, T. M.; Hart, R. E.

1976-01-01

Several solar cells having dissimilar spectral response curves and cell construction were measured at various locations in the United States to determine sensitivity of cell performance to atmospheric water vapor and turbidity. The locations selected represent a broad range of summer atmospheric conditions, from clear and dry to turbid and humid. Cell short circuit current under direct normal incidence sunlight, the intensity, water vapor and turbidity were measured. Regression equations were developed from the limited data base in order to provide a single method of prediction of cell current sensitivity to the atmospheric variables.

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.

Dynamic analysis and numerical experiments for balancing of the continuous single-disc and single-span rotor-bearing system

NASA Astrophysics Data System (ADS)

Wang, Aiming; Cheng, Xiaohan; Meng, Guoying; Xia, Yun; Wo, Lei; Wang, Ziyi

2017-03-01

Identification of rotor unbalance is critical for normal operation of rotating machinery. The single-disc and single-span rotor, as the most fundamental rotor-bearing system, has attracted research attention over a long time. In this paper, the continuous single-disc and single-span rotor is modeled as a homogeneous and elastic Euler-Bernoulli beam, and the forces applied by bearings and disc on the shaft are considered as point forces. A fourth-order non-homogeneous partial differential equation set with homogeneous boundary condition is solved for analytical solution, which expresses the unbalance response as a function of position, rotor unbalance and the stiffness and damping coefficients of bearings. Based on this analytical method, a novel Measurement Point Vector Method (MPVM) is proposed to identify rotor unbalance while operating. Only a measured unbalance response registered for four selected cross-sections of the rotor-shaft under steady-state operating conditions is needed when using the method. Numerical simulation shows that the detection error of the proposed method is very small when measurement error is negligible. The proposed method provides an efficient way for rotor balancing without test runs and external excitations.

The Aeroacoustics of Supersonic Coaxial Jets

NASA Technical Reports Server (NTRS)

Dahl, Milo D.

1994-01-01

Instability waves have been established as the dominant source of mixing noise radiating into the downstream arc of a supersonic jet when the waves have phase velocities that are supersonic relative to ambient conditions. Recent theories for supersonic jet noise have used the concepts of growing and decaying linear instability waves for predicting radiated noise. This analysis is extended to the prediction of noise radiation from supersonic coaxial jets. Since the analysis requires a known mean flow and the coaxial jet mean flow is not described easily in terms of analytic functions, a numerical prediction is made for its development. The Reynolds averaged, compressible, boundary layer equations are solved using a mixing length turbulence model. Empirical correlations are developed for the effects of velocity and temperature ratios and Mach number. Both normal and inverted velocity profile coaxial jets are considered. Comparisons with measurements for both single and coaxial jets show good agreement. The results from mean flow and stability calculations are used to predict the noise radiation from coaxial jets with different operating conditions. Comparisons are made between different coaxial jets and a single equivalent jet with the same total thrust, mass flow, and exit area. Results indicate that normal velocity profile jets can have noise reductions compared to the single equivalent jet. No noise reductions are found for inverted velocity profile jets operated at the minimum noise condition compared to the single equivalent jet. However, it is inferred that changes in area ratio may provide noise reduction benefits for inverted velocity profile jets.

Effect of renal impairment on the pharmacokinetics, pharmacodynamics, and safety of apixaban.

PubMed

Chang, Ming; Yu, Zhigang; Shenker, Andrew; Wang, Jessie; Pursley, Janice; Byon, Wonkyung; Boyd, Rebecca A; LaCreta, Frank; Frost, Charles E

2016-05-01

This open-label study evaluated apixaban pharmacokinetics, pharmacodynamics, and safety in subjects with mild, moderate, or severe renal impairment and in healthy subjects following a single 10-mg oral dose. The primary analysis determined the relationship between apixaban AUC∞ and 24-hour creatinine clearance (CLcr ) as a measure of renal function. The relationships between 24-hour CLcr and iohexol clearance, estimated CLcr (Cockcroft-Gault equation), and estimated glomerular filtration rate (modification of diet in renal disease [MDRD] equation) were also assessed. Secondary objectives included assessment of safety and tolerability as well as international normalized ratio (INR) and anti-factor Xa activity as pharmacodynamic endpoints. The regression analysis showed that decreasing renal function resulted in modestly increased apixaban exposure (AUC∞ increased by 44% in severe impairment with a 24-hour CLcr of 15 mL/min, compared with subjects with normal renal function), but it did not affect Cmax or the direct relationship between apixaban plasma concentration and anti-factor Xa activity or INR. The assessment of renal function measured by iohexol clearance, Cockcroft-Gault, and MDRD was consistent with that determined by 24-hour CLcr . Apixaban was well tolerated in this study. These results suggest that dose adjustment of apixaban is not required on the basis of renal function alone. © 2015, The American College of Clinical Pharmacology.

Errors in Computing the Normalized Protein Catabolic Rate due to Use of Single-pool Urea Kinetic Modeling or to Omission of the Residual Kidney Urea Clearance.

PubMed

Daugirdas, John T

2017-07-01

The protein catabolic rate normalized to body size (PCRn) often is computed in dialysis units to obtain information about protein ingestion. However, errors can manifest when inappropriate modeling methods are used. We used a variable volume 2-pool urea kinetic model to examine the percent errors in PCRn due to use of a 1-pool urea kinetic model or after omission of residual urea clearance (Kru). When a single-pool model was used, 2 sources of errors were identified. The first, dependent on the ratio of dialyzer urea clearance to urea distribution volume (K/V), resulted in a 7% inflation of the PCRn when K/V was in the range of 6 mL/min per L. A second, larger error appeared when Kt/V values were below 1.0 and was related to underestimation of urea distribution volume (due to overestimation of effective clearance) by the single-pool model. A previously reported prediction equation for PCRn was valid, but data suggest that it should be modified using 2-pool eKt/V and V coefficients instead of single-pool values. A third source of error, this one unrelated to use of a single-pool model, namely omission of Kru, was shown to result in an underestimation of PCRn, such that each ml/minute Kru per 35 L of V caused a 5.6% underestimate in PCRn. Marked overestimation of PCRn can result due to inappropriate use of a single-pool urea kinetic model, particularly when Kt/V <1.0 (as in short daily dialysis), or after omission of residual native kidney clearance. Copyright © 2017 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.

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.

Predicting the probability of slip in gait: methodology and distribution study.

PubMed

Gragg, Jared; Yang, James

2016-01-01

The likelihood of a slip is related to the available and required friction for a certain activity, here gait. Classical slip and fall analysis presumed that a walking surface was safe if the difference between the mean available and required friction coefficients exceeded a certain threshold. Previous research was dedicated to reformulating the classical slip and fall theory to include the stochastic variation of the available and required friction when predicting the probability of slip in gait. However, when predicting the probability of a slip, previous researchers have either ignored the variation in the required friction or assumed the available and required friction to be normally distributed. Also, there are no published results that actually give the probability of slip for various combinations of required and available frictions. This study proposes a modification to the equation for predicting the probability of slip, reducing the previous equation from a double-integral to a more convenient single-integral form. Also, a simple numerical integration technique is provided to predict the probability of slip in gait: the trapezoidal method. The effect of the random variable distributions on the probability of slip is also studied. It is shown that both the required and available friction distributions cannot automatically be assumed as being normally distributed. The proposed methods allow for any combination of distributions for the available and required friction, and numerical results are compared to analytical solutions for an error analysis. The trapezoidal method is shown to be highly accurate and efficient. The probability of slip is also shown to be sensitive to the input distributions of the required and available friction. Lastly, a critical value for the probability of slip is proposed based on the number of steps taken by an average person in a single day.

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.

Noise from Supersonic Coaxial Jets. Part 1; Mean Flow Predictions

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Morris, Philip J.

1997-01-01

Recent theories for supersonic jet noise have used an instability wave noise generation model to predict radiated noise. This model requires a known mean flow that has typically been described by simple analytic functions for single jet mean flows. The mean flow of supersonic coaxial jets is not described easily in terms of analytic functions. To provide these profiles at all axial locations, a numerical scheme is developed to calculate the mean flow properties of a coaxial jet. The Reynolds-averaged, compressible, parabolic boundary layer equations are solved using a mixing length turbulence model. Empirical correlations are developed to account for the effects of velocity and temperature ratios and Mach number on the shear layer spreading. Both normal velocity profile and inverted velocity profile coaxial jets are considered. The mixing length model is modified in each case to obtain reasonable results when the two stream jet merges into a single fully developed jet. The mean flow calculations show both good qualitative and quantitative agreement with measurements in single and coaxial jet flows.

The interplay between genetic and bioelectrical signaling permits a spatial regionalisation of membrane potentials in model multicellular ensembles

PubMed Central

Cervera, Javier; Meseguer, Salvador; Mafe, Salvador

2016-01-01

The single cell-centred approach emphasises ion channels as specific proteins that determine individual properties, disregarding their contribution to multicellular outcomes. We simulate the interplay between genetic and bioelectrical signals in non-excitable cells from the local single-cell level to the long range multicellular ensemble. The single-cell genetic regulation is based on mean-field kinetic equations involving the mRNA and protein concentrations. The transcription rate factor is assumed to depend on the absolute value of the cell potential, which is dictated by the voltage-gated cell ion channels and the intercellular gap junctions. The interplay between genetic and electrical signals may allow translating single-cell states into multicellular states which provide spatio-temporal information. The model results have clear implications for biological processes: (i) bioelectric signals can override slightly different genetic pre-patterns; (ii) ensembles of cells initially at the same potential can undergo an electrical regionalisation because of persistent genetic differences between adjacent spatial regions; and (iii) shifts in the normal cell electrical balance could trigger significant changes in the genetic regulation. PMID:27731412

The interplay between genetic and bioelectrical signaling permits a spatial regionalisation of membrane potentials in model multicellular ensembles.

PubMed

Cervera, Javier; Meseguer, Salvador; Mafe, Salvador

2016-10-12

The single cell-centred approach emphasises ion channels as specific proteins that determine individual properties, disregarding their contribution to multicellular outcomes. We simulate the interplay between genetic and bioelectrical signals in non-excitable cells from the local single-cell level to the long range multicellular ensemble. The single-cell genetic regulation is based on mean-field kinetic equations involving the mRNA and protein concentrations. The transcription rate factor is assumed to depend on the absolute value of the cell potential, which is dictated by the voltage-gated cell ion channels and the intercellular gap junctions. The interplay between genetic and electrical signals may allow translating single-cell states into multicellular states which provide spatio-temporal information. The model results have clear implications for biological processes: (i) bioelectric signals can override slightly different genetic pre-patterns; (ii) ensembles of cells initially at the same potential can undergo an electrical regionalisation because of persistent genetic differences between adjacent spatial regions; and (iii) shifts in the normal cell electrical balance could trigger significant changes in the genetic regulation.

Shuttle unified navigation filter, revision 1

NASA Technical Reports Server (NTRS)

Muller, E. S., Jr.

1973-01-01

Equations designed to meet the navigation requirements of the separate shuttle mission phases are presented in a series of reports entitled, Space Shuttle GN and C Equation Document. The development of these equations is based on performance studies carried out for each particular mission phase. Although navigation equations have been documented separately for each mission phase, a single unified navigation filter design is embodied in these separate designs. The purpose of this document is to present the shuttle navigation equations in a form in which they would most likely be coded-as the single unified navigation filter used in each mission phase. This document will then serve as a single general reference for the navigation equations replacing each of the individual mission phase navigation documents (which may still be used as a description of a particular navigation phase).

Molecular motion in cell membranes: Analytic study of fence-hindered random walks

NASA Astrophysics Data System (ADS)

Kenkre, V. M.; Giuggioli, L.; Kalay, Z.

2008-05-01

A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G -protein coupled μ -opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.

Panel acoustic contribution analysis.

PubMed

Wu, Sean F; Natarajan, Logesh Kumar

2013-02-01

Formulations are derived to analyze the relative panel acoustic contributions of a vibrating structure. The essence of this analysis is to correlate the acoustic power flow from each panel to the radiated acoustic pressure at any field point. The acoustic power is obtained by integrating the normal component of the surface acoustic intensity, which is the product of the surface acoustic pressure and normal surface velocity reconstructed by using the Helmholtz equation least squares based nearfield acoustical holography, over each panel. The significance of this methodology is that it enables one to analyze and rank relative acoustic contributions of individual panels of a complex vibrating structure to acoustic radiation anywhere in the field based on a single set of the acoustic pressures measured in the near field. Moreover, this approach is valid for both interior and exterior regions. Examples of using this method to analyze and rank the relative acoustic contributions of a scaled vehicle cabin are demonstrated.

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.

THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC MODELING OF THE SOLAR WIND INCLUDING PICKUP PROTONS AND TURBULENCE TRANSPORT

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

Usmanov, Arcadi V.; Matthaeus, William H.; Goldstein, Melvyn L., E-mail: arcadi.usmanov@nasa.gov

2012-07-20

To study the effects of interstellar pickup protons and turbulence on the structure and dynamics of the solar wind, we have developed a fully three-dimensional magnetohydrodynamic solar wind model that treats interstellar pickup protons as a separate fluid and incorporates the transport of turbulence and turbulent heating. The governing system of equations combines the mean-field equations for the solar wind plasma, magnetic field, and pickup protons and the turbulence transport equations for the turbulent energy, normalized cross-helicity, and correlation length. The model equations account for photoionization of interstellar hydrogen atoms and their charge exchange with solar wind protons, energy transfermore » from pickup protons to solar wind protons, and plasma heating by turbulent dissipation. Separate mass and energy equations are used for the solar wind and pickup protons, though a single momentum equation is employed under the assumption that the pickup protons are comoving with the solar wind protons. We compute the global structure of the solar wind plasma, magnetic field, and turbulence in the region from 0.3 to 100 AU for a source magnetic dipole on the Sun tilted by 0 Degree-Sign -90 Degree-Sign and compare our results with Voyager 2 observations. The results computed with and without pickup protons are superposed to evaluate quantitatively the deceleration and heating effects of pickup protons, the overall compression of the magnetic field in the outer heliosphere caused by deceleration, and the weakening of corotating interaction regions by the thermal pressure of pickup protons.« less

Reference Equations for Static Lung Volumes and TLCO from a Population Sample in Northern Greece.

PubMed

Michailopoulos, Pavlos; Kontakiotis, Theodoros; Spyratos, Dionisios; Argyropoulou-Pataka, Paraskevi; Sichletidis, Lazaros

2015-02-14

Background: The most commonly used reference equations for the measurement of static lung volumes/capacities and transfer factor of the lung for CO (TL CO ) are based on studies around 30-40 years old with significant limitations. Objectives: Our aim was to (1) develop reference equations for static lung volumes and TL CO using the current American Thoracic Society/European Respiratory Society guidelines, and (2) compare the equations derived with those most commonly used. Methods: Healthy Caucasian subjects (234 males and 233 females) aged 18-91 years were recruited. All of them were healthy never smokers with a normal chest X-ray. Static lung volumes and TL CO were measured with a single-breath technique according to the latest guidelines. Results: Curvilinear regression prediction equations derived from the present study were compared with those that are most commonly used. Our reference equations in accordance with the latest studies show lower values for all static lung volume parameters and TL CO as well as a different way of deviation of those parameters (i.e. declining with age total lung capacity, TL CO age decline in both sex and functional residual capacity age rise in males). Conclusions: We suggest that old reference values of static lung volumes and TL CO should be updated, and our perception of deviation of some spirometric parameters should be revised. Our new reference curvilinear equations derived according to the latest guidelines could contribute to the updating by respiratory societies of old existing reference values and result in a better estimation of the lung function of contemporary populations with similar Caucasian characteristics. © 2015 S. Karger AG, Basel.

Dissolution of solid dosage form. II. Equations for the dissolution of nondisintegrating tablet under the sink condition.

PubMed

Yonezawa, Y; Shirakura, K; Otsuka, A; Sunada, H

1991-03-01

An equation for dissolution from the whole surface of a nondisintegrating single component tablet under the sink condition was derived. Also, equations for several dissolution manners of the tablet under the sink condition were derived in the postulation of the dominant dissolution rate constant which determines the dissolution manner. The applicability or validity of these equations were examined by the dissolution measurements with nondisintegrating single component tablets. About one-tenth the amount of the amount needed to saturate the solution was used to prepare a tablet, and dissolution measurements were carried out with the tablet whose flat or side surface was masked with an adhesive tape in accordance with the conditions for derivation of equations. Among the derived equations, dissolution from the whole surface of a tablet was expressed by a form similar to the cube root law equation for particles. Hence, a single component tablet compressed by the use of a suitable amount was thought to behave like a single crystal. Also, equations derived for several dissolution manners were thought to be applicable for the dissolution of a nonspherical particle and crystal concerning the crystal's habit and its dissolution property, and the extended applicability was examined by converting the crystal into a simplified or idealized form, i.e., rectangle or plate.

A statistical study of single crest phenomenon in the equatorial ionospheric anomaly region using Swarm A satellite

NASA Astrophysics Data System (ADS)

Fathy, Adel; Ghamry, Essam

2017-03-01

Though the Equatorial Ionospheric Anomaly (EIA) is represented by two crests within ±15° latitude, a single crest is also observed in the entire ionosphere. Few studies have addressed single crest phenomena. A statistical study of 2237 single crest phenomenon from the in situ electron density measurements of Swarm A satellite was investigated during December 2013-December 2015. Our analysis focused on local time, seasonal, and both geographic and geomagnetic latitudinal variations. Our results show the following observations: 1 - The maximum number of events peaks mainly in the dayside region around 0800-1200 LT and these occur mainly within the magnetic equator. 2 - The maximum amplitude of the single crests take place most prominently during equinoxes. 3 - The majority of single crests occur in the northern hemisphere. 4 - The seasonal distribution of the events shows that the summer events are located further from the magnetic equator in the northern hemisphere and shift their locations into the southern hemisphere in winter, while spring events are centered along the magnetic equator. 5 - Dayside single crest events appear close to the magnetic equator and more centered on the equator in winter season. 6 - Dawn, night and dusk side events reverse their location from northern hemisphere in summer to southern hemisphere in winter.

[Mitotic behavior of centromeres in meiosis as the fertility restoration mechanism in wheat-rye amphihaploids].

PubMed

Loginova, D B; Silkova, O G

2014-08-01

The regulation of chromosomal behavior in meiosis in partly fertile wheat-rye amphihaploids was studied using the centromere specific probes pAWRC1 and Ae. tauschii pAet6-09. Comparative analysis of the probe localization patterns in mitosis, normal meiosis in wheat Triticum aestivum L. and rye Secale cereale L., and meiosis in amphihaploids was performed. The differences in the structure of centromeres in monopolar- and bipolar- oriented chromosomes were revealed. Single dense hybridization signals were observed in the diplotene and the metaphase of the first meiotic division, while hybridization signals appeared as stretched bands with diffuse structure located across the centromere region in mitosis and the second round of meiotic division. Based upon the obtained data, we used the corresponding centromere-specific probes as a tool for the analysis of chromosomal behavior in meiosis in amphihaploids. In meiocytes with three types of chromosome behavior (reductional, equational plus reductional, and equational), dense point-like hybridization signals for the pAet6-09 probe were observed for univalents with the reductional division type and stretched bands with diffuse structure for those with the equational division type. Thus, pAet6-09 probe localization patterns suggest some structural and functional specificities of centromeres in the meiosis in wheat-rye amphihaploids that reflect special regulation of chromosomal behavior during equational division. Meiocytes with true mitotic division were also observed in anthers predominantly containing meiocytes with chromosomes undergoing equational division.

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

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

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemannmore » problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. Finally, the upwind scheme is shown to be robust and provide high-order accuracy.« less

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

DOE PAGES

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

2017-09-28

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemannmore » problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. Finally, the upwind scheme is shown to be robust and provide high-order accuracy.« less

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

NASA Astrophysics Data System (ADS)

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

2018-01-01

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw [1] how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.

Equidistant map projections of a triaxial ellipsoid with the use of reduced coordinates

NASA Astrophysics Data System (ADS)

Pędzich, Paweł

2017-12-01

The paper presents a new method of constructing equidistant map projections of a triaxial ellipsoid as a function of reduced coordinates. Equations for x and y coordinates are expressed with the use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows to use common known and widely described in literature methods of solving such integrals and functions. The main advantage of this method is the fact that the calculations of x and y coordinates are practically based on a single algorithm that is required to solve the elliptic integral of the second kind. Equations are provided for three types of map projections: cylindrical, azimuthal and pseudocylindrical. These types of projections are often used in planetary cartography for presentation of entire and polar regions of extraterrestrial objects. The paper also contains equations for the calculation of the length of a meridian and a parallel of a triaxial ellipsoid in reduced coordinates. Moreover, graticules of three coordinates systems (planetographic, planetocentric and reduced) in developed map projections are presented. The basic properties of developed map projections are also described. The obtained map projections may be applied in planetary cartography in order to create maps of extraterrestrial objects.

A local model of warped magnetized accretion discs

NASA Astrophysics Data System (ADS)

Paris, J. B.; Ogilvie, G. I.

2018-06-01

We derive expressions for the local ideal magnetohydrodynamic (MHD) equations for a warped astrophysical disc using a warped shearing box formalism. A perturbation expansion of these equations to first order in the warping amplitude leads to a linear theory for the internal local structure of magnetized warped discs in the absence of magnetorotational instability (MRI) turbulence. In the special case of an external magnetic field oriented normal to the disc surface, these equations are solved semi-analytically via a spectral method. The relatively rapid warp propagation of low-viscosity Keplerian hydrodynamic warped discs is diminished by the presence of a magnetic field. The magnetic tension adds a stiffness to the epicyclic oscillations, detuning the natural frequency from the orbital frequency and thereby removing the resonant forcing of epicyclic modes characteristic of hydrodynamic warped discs. In contrast to a single hydrodynamic resonance, we find a series of Alfvénic-epicyclic modes which may be resonantly forced by the warped geometry at critical values of the orbital shear rate q and magnetic field strength. At these critical points large internal torques are generated and anomalously rapid warp propagation occurs. As our treatment omits MRI turbulence, these results are of greatest applicability to strongly magnetized discs.

Torsional oscillations of magnetized relativistic stars

NASA Astrophysics Data System (ADS)

Messios, Neophytos; Papadopoulos, Demetrios B.; Stergioulas, Nikolaos

2001-12-01

Strong magnetic fields in relativistic stars can be a cause of crust fracturing, resulting in the excitation of global torsional oscillations. Such oscillations could become observable in gravitational waves or in high-energy radiation, thus becoming a tool for probing the equation of state of relativistic stars. As the eigenfrequency of torsional oscillation modes is affected by the presence of a strong magnetic field, we study torsional modes in magnetized relativistic stars. We derive the linearized perturbation equations that govern torsional oscillations coupled to the oscillations of a magnetic field, when variations in the metric are neglected (Cowling approximation). The oscillations are described by a single two-dimensional wave equation, which can be solved as a boundary-value problem to obtain eigenfrequencies. We find that, in the non-magnetized case, typical oscillation periods of the fundamental l=2 torsional modes can be nearly a factor of 2 larger for relativistic stars than previously computed in the Newtonian limit. For magnetized stars, we show that the influence of the magnetic field is highly dependent on the assumed magnetic field configuration, and simple estimates obtained previously in the literature cannot be used for identifying normal modes observationally.

Liouville master equation for multielectron dynamics: Neutralization of highly charged ions near a LiF surface

NASA Astrophysics Data System (ADS)

Wirtz, Ludger; Reinhold, Carlos O.; Lemell, Christoph; Burgdörfer, Joachim

2003-01-01

We present a simulation of the neutralization of highly charged ions in front of a lithium fluoride surface including the close-collision regime above the surface. The present approach employs a Monte Carlo solution of the Liouville master equation for the joint probability density of the ionic motion and the electronic population of the projectile and the target surface. It includes single as well as double particle-hole (de)excitation processes and incorporates electron correlation effects through the conditional dynamics of population strings. The input in terms of elementary one- and two-electron transfer rates is determined from classical trajectory Monte Carlo calculations as well as quantum-mechanical Auger calculations. For slow projectiles and normal incidence, the ionic motion depends sensitively on the interplay between image acceleration towards the surface and repulsion by an ensemble of positive hole charges in the surface (“trampoline effect”). For Ne10+ we find that image acceleration is dominant and no collective backscattering high above the surface takes place. For grazing incidence, our simulation delineates the pathways to complete neutralization. In accordance with recent experimental observations, most ions are reflected as neutral or even as singly charged negative particles, irrespective of the charge state of the incoming ions.

Comparison of stability and control parameters for a light, single-engine, high-winged aircraft using different flight test and parameter estimation techniques

NASA Technical Reports Server (NTRS)

Suit, W. T.; Cannaday, R. L.

1979-01-01

The longitudinal and lateral stability and control parameters for a high wing, general aviation, airplane are examined. Estimations using flight data obtained at various flight conditions within the normal range of the aircraft are presented. The estimations techniques, an output error technique (maximum likelihood) and an equation error technique (linear regression), are presented. The longitudinal static parameters are estimated from climbing, descending, and quasi steady state flight data. The lateral excitations involve a combination of rudder and ailerons. The sensitivity of the aircraft modes of motion to variations in the parameter estimates are discussed.

Disk in a groove with friction: An analysis of static equilibrium and indeterminacy

NASA Astrophysics Data System (ADS)

Donolato, Cesare

2018-05-01

This note studies the statics of a rigid disk placed in a V-shaped groove with frictional walls and subjected to gravity and a torque. The two-dimensional equilibrium problem is formulated in terms of the angles that contact forces form with the normal to the walls. This approach leads to a single trigonometric equation in two variables whose domain is determined by Coulomb's law of friction. The properties of solutions (existence, uniqueness, or indeterminacy) as functions of groove angle, friction coefficient and applied torque are derived by a simple geometric representation. The results modify some of the conclusions by other authors on the same problem.

Estimation of stature from radiologic anthropometry of the lumbar vertebral dimensions in Chinese.

PubMed

Zhang, Kui; Chang, Yun-feng; Fan, Fei; Deng, Zhen-hua

2015-11-01

The recent study was to assess the relationship between the radiologic anthropometry of the lumbar vertebral dimensions and stature in Chinese and to develop regression formulae to estimate stature from these dimensions. A total of 412 normal, healthy volunteers, comprising 206 males and 206 females, were recruited. The linear regression analysis were performed to assess the correlation between the stature and lengths of various segments of the lumbar vertebral column. Among the regression equations created for single variable, the predictive value was greatest for the reconstruction of stature from the lumbar segment in both sexes and subgroup analysis. When individual vertebral body was used, the heights of posterior vertebral body of L3 gave the most accurate results for male group, the heights of central vertebral body of L1 provided the most accurate results for female group and female group with age above 45 years, the heights of central vertebral body of L3 gave the most accurate results for the groups with age from 20-45 years for both sexes and the male group with age above 45 years. The heights of anterior vertebral body of L5 gave the less accurate results except for the heights of anterior vertebral body of L4 provided the less accurate result for the male group with age above 45 years. As expected, multiple regression equations were more successful than equations derived from a single variable. The research observations suggest lumbar vertebral dimensions to be useful in stature estimation among Chinese population. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

A single spacecraft method to study the spatial profiles inside the magnetopause

NASA Astrophysics Data System (ADS)

Dorville, Nicolas; Belmont, Gerard; Rezeau, Laurence; Aunai, Nicolas; Retino, Alessandro

2013-04-01

Previous magnetopause observations have revealed that the tangential magnetic field often rotates over C-shaped hodograms during the boundary crossing. Using observations of magnetopause crossings by the ESA Cluster mission and a simulation developed at LPP by Nicolas Aunai, we developed a single spacecraft method using the temporal information on the magnetic field in such crossings, complemented by the ion data. We can so obtain a 1D spatial parameter to characterize the depth in the layer and study the structure of the magnetopause as a function of this parameter. This allows using one single spacecraft magnetic data, completed by ion data at large temporal scales, to study the spatial structure of the boundary, and access scales that the particle temporal measurements of the four spacecraft do not permit. To obtain the normal direction and position, we first initialize our computations thanks to the standard MVABC method. Then we use the magnetic field data in the current layer, and suppose it is 1D, rotating in the tangential plane along an ellipse, with an angle variation essentially linear in space, with small sinusoidal perturbations. Making the assumption that the normal velocity of ions is dominated by the motion of the boundary and that the internal structure of the magnetopause is stationary over the duration of a crossing, we can compute the best normal direction and parameters of the model with CIS velocity and FGM magnetic field data, and so derive the spatial position of the spacecraft in the boundary. This method, which has been tested on the simulation data, could be applied successfully on several magnetopause crossings observed by Cluster. It directly gives a thickness and a normal direction, and permits to establish spatial profiles of all the physical quantities inside the boundary. It can be used to better understand the internal structure of the boundary, its physical properties and behavior regarding the flux conservation equations. The obtained results are compared with the results of other methods.

Effects of Thermal Noise on the Transitional Dynamics of an Inextensible Elastic Filament in Stagnation Flow

PubMed Central

Deng, Mingge; Grinberg, Leopold; Caswell, Bruce

2015-01-01

We investigate the dynamics of a single inextensible elastic filament subject to anisotropic friction in a viscous stagnation-point flow, by employing both a continuum model represented by Langevin type stochastic partial differential equations (SPDEs) and a Dissipative Particle Dynamics (DPD) method. Unlike previous works1, the filament is free to rotate and the tension along the filament is determined by the local inextensible constraint. The kinematics of the filament is recorded and studied with normal modes analysis. The results show that the filament displays an instability induced by negative tension, which is analogous to Euler buckling of a beam. Symmetry breaking of normal modes dynamics and stretch-coil transitions are observed above the threshold of the buckling instability point. Furthermore, both temporal and spatial noise are amplified resulting from the interaction of thermal fluctuations and nonlinear filament dynamics. Specifically, the spatial noise is amplified with even normal modes being excited due to symmetry breaking, while the temporal noise is amplified with increasing time correlation length and variance. PMID:26023834

Calibration and temperature correction of heat dissipation matric potential sensors

USGS Publications Warehouse

Flint, A.L.; Campbell, G.S.; Ellett, K.M.; Calissendorff, C.

2002-01-01

This paper describes how heat dissipation sensors, used to measure soil water matric potential, were analyzed to develop a normalized calibration equation and a temperature correction method. Inference of soil matric potential depends on a correlation between the variable thermal conductance of the sensor's porous ceramic and matric poten-tial. Although this correlation varies among sensors, we demonstrate a normalizing procedure that produces a single calibration relationship. Using sensors from three sources and different calibration methods, the normalized calibration resulted in a mean absolute error of 23% over a matric potential range of -0.01 to -35 MPa. Because the thermal conductivity of variably saturated porous media is temperature dependent, a temperature correction is required for application of heat dissipation sensors in field soils. A temperature correction procedure is outlined that reduces temperature dependent errors by 10 times, which reduces the matric potential measurement errors by more than 30%. The temperature dependence is well described by a thermal conductivity model that allows for the correction of measurements at any temperature to measurements at the calibration temperature.

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)

Estimation of renal function by CKD-EPI versus MDRD in a cohort of HIV-infected patients: a cross-sectional analysis.

PubMed

Cristelli, M P; Cofán, F; Rico, N; Trullàs, J C; Manzardo, C; Agüero, F; Bedini, J L; Moreno, A; Oppenheimer, F; Miro, J M

2017-02-10

Accurately determining renal function is essential for clinical management of HIV patients. Classically, it has been evaluated by estimating glomerular filtration rate (eGFR) with the MDRD-equation, but today there is evidence that the new Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation has greater diagnostic accuracy. To date, however, little information exists on patients with HIV-infection. This study aimed to evaluate eGFR by CKD-EPI vs. MDRD equations and to stratify renal function according to KDIGO guidelines. Cross-sectional, single center study including adult patients with HIV-infection. Four thousand five hundred three patients with HIV-infection (864 women; 19%) were examined. Median age was 45 years (IQR 37-52), and median baseline creatinine was 0.93 mg/dL (IQR 0.82-1.05). A similar distribution of absolute measures of eGFR was found using both formulas (p = 0.548). Baseline median eGFR was 95.2 and 90.4 mL/min/1.73 m 2 for CKD-EPI and MDRD equations (p < 0.001), respectively. Of the 4503 measurements, 4109 (91.2%) agreed, with a kappa index of 0.803. MDRD classified 7.3% of patients as "mild reduced GFR" who were classified as "normal function" with CKD-EPI. Using CKD-EPI, it was possible to identify "normal function" (>90 mL/min/1.73 m 2 ) in 73% patients and "mild reduced GFR" (60-89 mL/min/1.73 m 2 ) in 24.3% of the patients, formerly classified as >60 mL/min/1.73 m 2 with MDRD. There was good correlation between CKD-EPI and MDRD. Estimating renal function using CKD-EPI equation allowed better staging of renal function and should be considered the method of choice. CKD-EPI identified a significant proportion of patients (24%) with mild reduced GFR (60-89 mL/min/1.73 m 2 ).

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.…

Mathematical analysis of the multiband BCS gap equations in superconductivity

NASA Astrophysics Data System (ADS)

Yang, Yisong

2005-01-01

In this paper, we present a mathematical analysis for the phonon-dominated multiband isotropic and anisotropic BCS gap equations at any finite temperature T. We establish the existence of a critical temperature T so that, when TT, the only nonnegative gap solution is the zero solution, representing the normal phase. Furthermore, when T=T, we prove that the only gap solution is the zero solution and that the positive gap solution depend on the temperature T

Pore-scale modeling of saturated permeabilities in random sphere packings.

PubMed

Pan, C; Hilpert, M; Miller, C T

2001-12-01

We use two pore-scale approaches, lattice-Boltzmann (LB) and pore-network modeling, to simulate single-phase flow in simulated sphere packings that vary in porosity and sphere-size distribution. For both modeling approaches, we determine the size of the representative elementary volume with respect to the permeability. Permeabilities obtained by LB modeling agree well with Rumpf and Gupte's experiments in sphere packings for small Reynolds numbers. The LB simulations agree well with the empirical Ergun equation for intermediate but not for small Reynolds numbers. We suggest a modified form of Ergun's equation to describe both low and intermediate Reynolds number flows. The pore-network simulations agree well with predictions from the effective-medium approximation but underestimate the permeability due to the simplified representation of the porous media. Based on LB simulations in packings with log-normal sphere-size distributions, we suggest a permeability relation with respect to the porosity, as well as the mean and standard deviation of the sphere diameter.

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

Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Waag, Robert C

2010-05-01

A T-matrix formulation is presented to compute acoustic scattering from arbitrary, disjoint distributions of cylinders or spheres, each with arbitrary, uniform acoustic properties. The generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers. By employing field expansions based on orthogonal harmonic functions, continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal, analytic expressions to eliminate the need for integral equations. The effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner-object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant. Numerical results establish the validity and efficiency of the outer iteration procedure for nested objects. Two- and three-dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two-dimensional approximations to three-dimensional scattering of elevation-focused beams.

Multiple-channel guided mode resonance Brewster filter with controllable spectral separation.

PubMed

Ma, Jianyong; Cao, Hongchao; Zhou, Changhe

2014-05-01

In this work, a single-layer, multiple-channel guided mode resonance (GMR) Brewster filter with controllable spectral separation is proposed using the plane waveguide method and rigorous coupled-wave analysis. Based on the normalized eigenvalue equation, the controllability of the spectral separation is analyzed when the fill ratio of the grating layer is changed while its effective index is identical to that of the substrate. The location and the separation between resonances can be specifically controlled by modifying the fill ratio of the grating layer. In contrast to the ordinary GMR filter, where the location of the resonances is material dependent, it is demonstrated that the spectral separation for the first and second resonances can be linearly controlled by altering the fill ratio of the grating layer. In addition, the maximal shift of the second resonance is up to 5% of the first resonant wavelength using the single-layer Brewster filter.

Bubble levitation and translation under single-bubble sonoluminescence conditions.

PubMed

Matula, Thomas J

2003-08-01

Bubble levitation in an acoustic standing wave is re-examined for conditions relevant to single-bubble sonoluminescence. Unlike a previous examination [Matula et al., J. Acoust. Soc. Am. 102, 1522-1527 (1997)], the stable parameter space [Pa,R0] is accounted for in this realization. Forces such as the added mass force and drag are included, and the results are compared with a simple force balance that equates the Bjerknes force to the buoyancy force. Under normal sonoluminescence conditions, the comparison is quite favorable. A more complete accounting of the forces shows that a stably levitated bubble does undergo periodic translational motion. The asymmetries associated with translational motion are hypothesized to generate instabilities in the spherical shape of the bubble. A reduction in gravity results in reduced translational motion. It is hypothesized that such conditions may lead to increased light output from sonoluminescing bubbles.

Is there a relationship between curvature and inductance in the Josephson junction?

NASA Astrophysics Data System (ADS)

Dobrowolski, T.; Jarmoliński, A.

2018-03-01

A Josephson junction is a device made of two superconducting electrodes separated by a very thin layer of isolator or normal metal. This relatively simple device has found a variety of technical applications in the form of Superconducting Quantum Interference Devices (SQUIDs) and Single Electron Transistors (SETs). One can expect that in the near future the Josephson junction will find applications in digital electronics technology RSFQ (Rapid Single Flux Quantum) and in the more distant future in construction of quantum computers. Here we concentrate on the relation of the curvature of the Josephson junction with its inductance. We apply a simple Capacitively Shunted Junction (CSJ) model in order to find condition which guarantees consistency of this model with prediction based on the Maxwell and London equations with Landau-Ginzburg current of Cooper pairs. This condition can find direct experimental verification.

Vacillations induced by interference of stationary and traveling planetary waves

NASA Technical Reports Server (NTRS)

Salby, Murry L.; Garcia, Rolando R.

1987-01-01

The interference pattern produced when a traveling planetary wave propagates over a stationary forced wave is explored, examining the interference signature in a variety of diagnostics. The wave field is first restricted to a diatomic spectrum consisting of two components: a single stationary wave and a single monochromatic traveling wave. A simple barotropic normal mode propagating over a simple stationary plane wave is considered, and closed form solutions are obtained. The wave fields are then restricted spatially, providing more realistic structures without sacrificing the advantages of an analytical solution. Both stationary and traveling wave fields are calculated numerically with the linearized Primitive Equations in a realistic basic state. The mean flow reaction to the fluctuating eddy forcing which results from interference is derived. Synoptic geopotential behavior corresponding to the combined wave and mean flow fields is presented, and the synoptic signature in potential vorticity on isentropic surfaces is examined.

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.

Octanol reduces end-plate channel lifetime

PubMed Central

Gage, Peter W.; McBurney, Robert N.; Van Helden, Dirk

1978-01-01

1. Post-synaptic effects of n-octanol at concentrations of 0·1-1 mM were examined in toad sartorius muscles by use of extracellular and voltage-clamp techniques. 2. Octanol depressed the amplitude and duration of miniature end-plate currents and hence depressed neuromuscular transmission. 3. The decay of miniature end-plate currents remained exponential in octanol solutions even when the time constant of decay (τD) was decreased by 80-90%. 4. The lifetime of end-plate channels, obtained by analysis of acetylcholine noise, was also decreased by octanol. The average lifetime measured from noise spectra agreed reasonably well with the time constant of decay of miniature end-plate currents, both in control solution and in octanol solutions. 5. Octanol caused a reduction in the conductance of end-plate channels. Single channel conductance was on average about 25 pS in control solution and 20 pS in octanol. 6. In most cells the normal voltage sensitivity of the decay of miniature end-plate currents was retained in octanol solutions. The lifetime of end-plate channels measured from acetylcholine noise also remained voltage-sensitive in octanol solutions. In some experiments in which channel lifetime was exceptionally reduced the voltage sensitivity was less than normal. 7. In octanol solutions, τD was still very sensitive to temperature changes in most cells although in some the temperature sensitivity of τD was clearly reduced. Changes in τD with temperature could generally be fitted by the Arrhenius equation suggesting that a single step reaction controlled the decay of currents both in control and in octanol solutions. In some cells in which τD became less than 0·3 ms, the relationship between τD and temperature became inconsistent with the Arrhenius equation. 8. As the decay of end-plate currents in octanol solutions remains exponential, and the voltage and temperature sensitivity can be unchanged even when τD is significantly reduced, it seems likely that octanol decreases τD by increasing the rate of the reaction which normally controls the lifetime of end-plate channels. PMID:203674

Identifying mechanical property parameters of planetary soil using in-situ data obtained from exploration rovers

NASA Astrophysics Data System (ADS)

Ding, Liang; Gao, Haibo; Liu, Zhen; Deng, Zongquan; Liu, Guangjun

2015-12-01

Identifying the mechanical property parameters of planetary soil based on terramechanics models using in-situ data obtained from autonomous planetary exploration rovers is both an important scientific goal and essential for control strategy optimization and high-fidelity simulations of rovers. However, identifying all the terrain parameters is a challenging task because of the nonlinear and coupling nature of the involved functions. Three parameter identification methods are presented in this paper to serve different purposes based on an improved terramechanics model that takes into account the effects of slip, wheel lugs, etc. Parameter sensitivity and coupling of the equations are analyzed, and the parameters are grouped according to their sensitivity to the normal force, resistance moment and drawbar pull. An iterative identification method using the original integral model is developed first. In order to realize real-time identification, the model is then simplified by linearizing the normal and shearing stresses to derive decoupled closed-form analytical equations. Each equation contains one or two groups of soil parameters, making step-by-step identification of all the unknowns feasible. Experiments were performed using six different types of single-wheels as well as a four-wheeled rover moving on planetary soil simulant. All the unknown model parameters were identified using the measured data and compared with the values obtained by conventional experiments. It is verified that the proposed iterative identification method provides improved accuracy, making it suitable for scientific studies of soil properties, whereas the step-by-step identification methods based on simplified models require less calculation time, making them more suitable for real-time applications. The models have less than 10% margin of error comparing with the measured results when predicting the interaction forces and moments using the corresponding identified parameters.

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

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

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.

Regulation of landslide motion by dilatancy and pore pressure feedback

USGS Publications Warehouse

Iverson, R.M.

2005-01-01

A new mathematical model clarifies how diverse styles and rates of landslide motion can result from regulation of Coulomb friction by dilation or contraction of water-saturated basal shear zones. Normalization of the model equations shows that feedback due to coupling between landslide motion, shear zone volume change, and pore pressure change depends on a single dimensionless parameter ??, which, in turn, depends on the dilatancy angle ?? and the intrinsic timescales for pore pressure generation and dissipation. If shear zone soil contracts during slope failure, then ?? 0, and negative feedback permits slow, steady landslide motion to occur while positive pore pressure is supplied by rain infiltration. Steady state slip velocities v0 obey v0 = -(K/??) p*e, where K is the hydraulic conductivity and p*e is the normalized (dimensionless) negative pore pressure generated by dilation. If rain infiltration and attendant pore pressure growth continue unabated, however, their influence ultimately overwhelms the stabilizing influence of negative p*e. Then, unbounded landslide acceleration occurs, accentuated by an instability that develops if ?? diminishes as landslide motion proceeds. Nonetheless, numerical solutions of the model equations show that slow, nearly steady motion of a clay-rich landslide may persist for many months as a result of negative pore pressure feedback that regulates basal Coulomb friction. Similarly stabilized motion is less likely to occur in sand-rich landslides that are characterized by weaker negative feedback.

A comparison of radiometric correction techniques in the evaluation of the relationship between LST and NDVI in Landsat imagery.

PubMed

Tan, Kok Chooi; Lim, Hwee San; Matjafri, Mohd Zubir; Abdullah, Khiruddin

2012-06-01

Atmospheric corrections for multi-temporal optical satellite images are necessary, especially in change detection analyses, such as normalized difference vegetation index (NDVI) rationing. Abrupt change detection analysis using remote-sensing techniques requires radiometric congruity and atmospheric correction to monitor terrestrial surfaces over time. Two atmospheric correction methods were used for this study: relative radiometric normalization and the simplified method for atmospheric correction (SMAC) in the solar spectrum. A multi-temporal data set consisting of two sets of Landsat images from the period between 1991 and 2002 of Penang Island, Malaysia, was used to compare NDVI maps, which were generated using the proposed atmospheric correction methods. Land surface temperature (LST) was retrieved using ATCOR3_T in PCI Geomatica 10.1 image processing software. Linear regression analysis was utilized to analyze the relationship between NDVI and LST. This study reveals that both of the proposed atmospheric correction methods yielded high accuracy through examination of the linear correlation coefficients. To check for the accuracy of the equation obtained through linear regression analysis for every single satellite image, 20 points were randomly chosen. The results showed that the SMAC method yielded a constant value (in terms of error) to predict the NDVI value from linear regression analysis-derived equation. The errors (average) from both proposed atmospheric correction methods were less than 10%.

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.

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.

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

ERIC Educational Resources Information Center

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

2010-01-01

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

Shock Equation of State of Multi-Phase Epoxy-Based Composite (Al-MnO2-Epoxy)

DTIC Science & Technology

2010-10-01

single stage light gas gun , two...using three different loading techniques— single stage light gas gun , two stage light gas gun , and explosive loading—with multiple diagnostic...wave speed. B. Single stage gas gun loading experiments Four gas gun -driven equation of state experiments were conducted at NSWC-Indian Head using

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.

Propagation of quasifracture in viscoelastic media under low-cycle repeated stressing

NASA Technical Reports Server (NTRS)

Liu, X. P.; Hsiao, C. C.

1985-01-01

The propagation of a craze as quasifracture under repeated cyclic stressing in polymeric systems has been under intensive investigation recently. Based upon a time-dependent crazing theory, the governing differential equation describing the propagation of a single craze as quasifracture in an infinite viscoelastic plate has been solved for sinusoidal stresses. Numerical methods have been employed to obtain the normalized craze length as a function of time. The computed results indicate that the length of a quasifracture may decelerate and decrease indicating that its velocity can reverse. This behavior may be consistent with the observed and much discussed craze healing and the enclosure model in fatigue and fracture of solids.

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.

Axisymmetric ideal MHD stellar wind flow

NASA Technical Reports Server (NTRS)

Heinemann, M.; Olbert, S.

1978-01-01

The ideal MHD equations are reduced to a single equation under the assumption of axisymmetric flow. A variational principle from which the equation is derivable is given. The characteristics of the equation are briefly discussed. The equation is used to rederive the theorem of Gussenhoven and Carovillano.

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.

A new cytogenetic mechanism for bacterial endosymbiont-induced parthenogenesis in Hymenoptera

PubMed Central

Adachi-Hagimori, Tetsuya; Miura, Kazuki; Stouthamer, Richard

2008-01-01

Vertically transmitted endosymbiotic bacteria, such as Wolbachia, Cardinium and Rickettsia, modify host reproduction in several ways to facilitate their own spread. One such modification results in parthenogenesis induction, where males, which are unable to transmit the bacteria, are not produced. In Hymenoptera, the mechanism of diploidization due to Wolbachia infection, known as gamete duplication, is a post-meiotic modification. During gamete duplication, the meiotic mechanism is normal, but in the first mitosis the anaphase is aborted. The two haploid sets of chromosomes do not separate and thus result in a single nucleus containing two identical sets of haploid chromosomes. Here, we outline an alternative cytogenetic mechanism for bacterial endosymbiont-induced parthenogenesis in Hymenoptera. During female gamete formation in Rickettsia-infected Neochrysocharis formosa (Westwood) parasitoids, meiotic cells undergo only a single equational division followed by the expulsion of a single polar body. This absence of meiotic recombination and reduction corresponds well with a non-segregation pattern in the offspring of heterozygous females. We conclude that diploidy in N. formosa is maintained through a functionally apomictic cloning mechanism that differs entirely from the mechanism induced by Wolbachia. PMID:18713719

A theoretical analysis of fluid flow and energy transport in hydrothermal systems

USGS Publications Warehouse

Faust, Charles R.; Mercer, James W.

1977-01-01

A mathematical derivation for fluid flow and energy transport in hydrothermal systems is presented. Specifically, the mathematical model describes the three-dimensional flow of both single- and two-phase, single-component water and the transport of heat in porous media. The derivation begins with the point balance equations for mass, momentum, and energy. These equations are then averaged over a finite volume to obtain the macroscopic balance equations for a porous medium. The macroscopic equations are combined by appropriate constitutive relationships to form two similified partial differential equations posed in terms of fluid pressure and enthalpy. A two-dimensional formulation of the simplified equations is also derived by partial integration in the vertical dimension. (Woodard-USGS)

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

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.

Inflow performance relationship for perforated wells producing from solution gas drive reservoir

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

Sukarno, P.; Tobing, E.L.

1995-10-01

The IPR curve equations, which are available today, are developed for open hole wells. In the application of Nodal System Analysis in perforated wells, an accurate calculation of pressure loss in the perforation is very important. Nowadays, the equation which is widely used is Blount, Jones and Glaze equation, to estimate pressure loss across perforation. This equation is derived for single phase flow, either oil or gas, therefore it is not suitable for two-phase production wells. In this paper, an IPR curve equation for perforated wells, producing from solution gas drive reservoir, is introduced. The equation has been developed usingmore » two phase single well simulator combine to two phase flow in perforation equation, derived by Perez and Kelkar. A wide range of reservoir rock and fluid properties and perforation geometry are used to develop the equation statistically.« less

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.

Lump solutions of the BKP equation

NASA Astrophysics Data System (ADS)

Gilson, C. R.; Nimmo, J. J. C.

1990-07-01

Rational solutions of the BKP equation which decay to zero in all directions in the plane are obtained. These solutions are analogous to the lump solutions of the KPI equation. Properties of the single lump solution are described and the form of the N-lump solution is given. It is shown that single lump solutions are only non-singular for spectral parameters lying in certain regions of the complex plane.

Impact of kerogen heterogeneity on sorption of organic pollutants. 2. Sorption equilibria

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

Yang, C.; Yu, Z.Q.; Xiao, B.H.

2009-08-15

Phenanthrene and naphthalene sorption isotherms were measured for three different series of kerogen materials using completely mixed batch reactors. Sorption isotherms were nonlinear for each sorbate-sorbent system, and the Freundlich isotherm equation fit the sorption data well. The Freundlich isotherm linearity parameter n ranged from 0.192 to 0.729 for phenanthrene and from 0.389 to 0.731 for naphthalene. The n values correlated linearly with rigidity and aromaticity of the kerogen matrix, but the single-point, organic carbon-normalized distribution coefficients varied dramatically among the tested sorbents. A dual-mode sorption equation consisting of a linear partitioning domain and a Langmuir adsorption domain adequately quantifiedmore » the overall sorption equilibrium for each sorbent-sorbate system. Both models fit the data well, with r{sup 2} values of 0.965 to 0.996 for the Freundlich model and 0.963 to 0.997 for the dual-mode model for the phenanthrene sorption isotherms. The dual-mode model fitting results showed that as the rigidity and aromaticity of the kerogen matrix increased, the contribution of the linear partitioning domain to the overall sorption equilibrium decreased, whereas the contribution of the Langmuir adsorption domain increased. The present study suggested that kerogen materials found in soils and sediments should not be treated as a single, unified, carbonaceous sorbent phase.« less

Interaction with the lower ionosphere of electromagnetic pulses from lightning - Heating, attachment, and ionization

NASA Technical Reports Server (NTRS)

Taranenko, Y. N.; Inan, U. S.; Bell, T. F.

1993-01-01

A Boltzmann formulation of the electron distribution function and Maxwell's equations for the EM fields are used to simulate the interaction of lightning radiated EM pulses with the lower ionosphere. Ionization and dissociative attachment induced by the heated electrons cause significant changes in the local electron density, N(e). Due to 'slow' field changes of typical lightning EM pulses over time scales of tens of microsec, the distribution function follows the quasi-equilibrium solution of the Boltzmann equation in the altitude range of interest (70 to 100 km). The EM pulse is simulated as a planar 100 microsec long single period oscillation of a 10 kHz wave injected at 70 km. Under nighttime conditions, individual pulses of intensity 10-20 V/m (normalized to 100 km horizontal distance) produce changes in N(e) of 1-30 percent while a sequence of pulses leads to strong modification of N(e) at altitudes less than 95 km. The N(e) changes produce a 'sharpening' of the lower ionospheric boundary by causing a reduction in electron density at 75-85 km (due to attachment) and a substantial increase at 85-95 km (due to ionization) (e.g., the scale height decreases by a factor of about 2 at about 85 km for a single 20 V/m EM pulse). No substantial N(e) changes occur during daytime.

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.

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).

Orientation of chain molecules in ionotropic gels: a Brownian dynamics model

NASA Astrophysics Data System (ADS)

Woelki, Stefan; Kohler, Hans-Helmut

2003-09-01

As is known from birefringence measurements, polysaccharide molecules of ionotropic gels are preferentially orientated normal to the direction of gel growth. In this paper the orientation effect is investigated by means of an off-lattice Brownian dynamics model simulating the gel formation process. The model describes the integration of a single coarse grained phantom chain into the growing gel. The equations of motion of the chain are derived. The computer simulations show that, during the process of integration, the chain is contracting normal to the direction of gel growth. A scaling relation is obtained for the degree of contraction as a function of the length parameters of the chain, the velocity of the gel formation front and the rate constant of the crosslinking reaction. It is shown that the scaling relation, if applied to the example of ionotropic copper alginate gel, leads to reasonable predictions of the time course of the degree of contraction of the alginate chains.

Linear tearing mode stability equations for a low collisionality toroidal plasma

NASA Astrophysics Data System (ADS)

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

2009-01-01

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

Dynamic modeling of normal faults of the 2016 Central Italy earthquake sequence

NASA Astrophysics Data System (ADS)

Aochi, Hideo

2017-04-01

The earthquake sequence of the Central Italy in 2016 are characterized mainly by the Mw6.0 24th August, Mw5.9 26th October and Mw6.4 30th October as well as two Mw5.4 earthquakes (24th August, 26th October) (catalogue INGV). They all show normal faulting mechanisms corresponding to the Apennines's tectonics. They are aligned briefly along NNW-SSE axis, and they may not be on a single continuous fault plane. Therefore, dynamic rupture modeling of sequences should be carried out supposing co-planar normal multiple segments. We apply a Boundary Domain Method (BDM, Goto and Bielak, GJI, 2008) coupling a boundary integral equation method and a domain-based method, namely a finite difference method in this study. The Mw6.0 24th August earthquake is modeled. We use the basic information of hypocenter position, focal mechanism and potential ruptured dimension from the INGV catalogue and Tinti et al., GRL, 2016), and begin with a simple condition (homogeneous boundary condition). From our preliminary simulations, it is shown that a uniformly extended rupture model does not fit the near-field ground motions and localized heterogeneity would be required.

Alfvén simple waves

NASA Astrophysics Data System (ADS)

Webb, G. M.; Zank, G. P.; Burrows, R. H.; Ratkiewicz, R. E.

2011-02-01

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 ϕ, 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 ϕ. This leads to an implicit equation for the phase function and a generalization 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 eigenequations require that the rate of change of the magnetic induction B with ϕ 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(ϕ) or B(ϕ) are developed.

Echocardiographic measurements of the aorta in normal children and young adults.

PubMed

Kaldararova, M; Balazova, E; Tittel, P; Stankovicova, I; Brucknerova, I; Masura, J

2007-01-01

To be able to determine aortic valve and ascending aorta pathology, especially aortic root dilatation, it is important to establish normal aortic dimensions. The aim of the study was to measure the dimensions of the aorta in normal healthy children and young adults in Slovakia. 702 healthy subjects, from newborns to 20 years of age, were examined at our institution. The study was carried out prospectively, by a single observer, using digitized two-dimensional (2D), Doppler and M-mode echocardiography. The aorta was measured at 3 sites: 1. aortic valve annulus, 2. sinuses of Valsalva, 3. sinotubular junction. Patients were divided into 28 groups according to their body surface area (BSA)--from 0.15 to 2.0 m2. All data were statistically evaluated (mean value, 5th and 95th percentile for all BSA groups) and regression equations were calculated for each parameter. All 3 measured aortic parameters correlated closely. Measures of correlation (R-squared) for aortic parameters with the square root of BSA were high: 0.89 for aortic valve annulus, 0.86 for sinuses of Valsalva and 0.86 for sinotubular junction (Tab. 3, Fig. 7, Ref 13). Full Text (Free, PDF) www.bmj.sk

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.

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.

Elaboration of the α-model derived from the BCS theory of superconductivity

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

Johnston, David C.

2013-10-14

The single-band α-model of superconductivity (Padamsee et al 1973 J. Low Temp. Phys. 12 387) is a popular model that was adapted from the single-band Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity mainly to allow fits to electronic heat capacity versus temperature T data that deviate from the BCS prediction. The model assumes that the normalized superconducting order parameter Δ(T)/Δ(0) and therefore the normalized London penetration depth λL(T)/λL(0) are the same as in BCS theory, calculated using the BCS value αBCS ≈ 1.764 of α ≡ Δ(0)/kBTc, where kB is The single-band α-model of superconductivity (Padamsee et al 1973 J. Low Temp.more » Phys. 12 387) is a popular model that was adapted from the single-band Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity mainly to allow fits to electronic heat capacity versus temperature T data that deviate from the BCS prediction. The model assumes that the normalized superconducting order parameter Δ(T)/Δ(0) and therefore the normalized London penetration depth λL(T)/λL(0) are the same as in BCS theory, calculated using the BCS value αBCS ≈ 1.764 of α ≡ Δ(0)/kBTc, where kB is Boltzmann's constant and Tc is the superconducting transition temperature. On the other hand, to calculate the electronic free energy, entropy, heat capacity and thermodynamic critical field versus T, the α-model takes α to be an adjustable parameter. Here we write the BCS equations and limiting behaviors for the superconducting state thermodynamic properties explicitly in terms of α, as needed for calculations within the α-model, and present plots of the results versus T and α that are compared with the respective BCS predictions. Mechanisms such as gap anisotropy and strong coupling that can cause deviations of the thermodynamics from the BCS predictions, especially the heat capacity jump at Tc, are considered. Extensions of the α-model that have appeared in the literature, such as the two-band model, are also discussed. Tables of values of Δ(T)/Δ(0), the normalized London parameter Λ(T)/Λ(0) and λL(T)/λL(0) calculated from the BCS theory using α = αBCS are provided, which are the same in the α-model by assumption. Tables of values of the entropy, heat capacity and thermodynamic critical field versus T for seven values of α, including αBCS, are also presented.« less

Marching iterative methods for the parabolized and thin layer Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Israeli, M.

1985-01-01

Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.

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.

Local Linear Observed-Score Equating

ERIC Educational Resources Information Center

Wiberg, Marie; van der Linden, Wim J.

2011-01-01

Two methods of local linear observed-score equating for use with anchor-test and single-group designs are introduced. In an empirical study, the two methods were compared with the current traditional linear methods for observed-score equating. As a criterion, the bias in the equated scores relative to true equating based on Lord's (1980)…

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

NASA Technical Reports Server (NTRS)

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

1966-01-01

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

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.

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.

Ballistic Limit Equation for Single Wall Titanium

NASA Technical Reports Server (NTRS)

Ratliff, J. M.; Christiansen, Eric L.; Bryant, C.

2009-01-01

Hypervelocity impact tests and hydrocode simulations were used to determine the ballistic limit equation (BLE) for perforation of a titanium wall, as a function of wall thickness. Two titanium alloys were considered, and separate BLEs were derived for each. Tested wall thicknesses ranged from 0.5mm to 2.0mm. The single-wall damage equation of Cour-Palais [ref. 1] was used to analyze the Ti wall's shielding effectiveness. It was concluded that the Cour-Palais single-wall equation produced a non-conservative prediction of the ballistic limit for the Ti shield. The inaccurate prediction was not a particularly surprising result; the Cour-Palais single-wall BLE contains shield material properties as parameters, but it was formulated only from tests of different aluminum alloys. Single-wall Ti shield tests were run (thicknesses of 2.0 mm, 1.5 mm, 1.0 mm, and 0.5 mm) on Ti 15-3-3-3 material custom cut from rod stock. Hypervelocity impact (HVI) tests were used to establish the failure threshold empirically, using the additional constraint that the damage scales with impact energy, as was indicated by hydrocode simulations. The criterion for shield failure was defined as no detached spall from the shield back surface during HVI. Based on the test results, which confirmed an approximately energy-dependent shield effectiveness, the Cour-Palais equation was modified.

Analytic approach to photoelectron transport.

NASA Technical Reports Server (NTRS)

Stolarski, R. S.

1972-01-01

The equation governing the transport of photoelectrons in the ionosphere is shown to be equivalent to the equation of radiative transfer. In the single-energy approximation this equation is solved in closed form by the method of discrete ordinates for isotropic scattering and for a single-constituent atmosphere. The results include prediction of the angular distribution of photoelectrons at all altitudes and, in particular, the angular distribution of the escape flux. The implications of these solutions in real atmosphere calculations are discussed.

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.

An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes

DOE PAGES

Taitano, William; Chacon, Luis; Simakov, Andrei Nikolaevich

2016-04-25

In this paper, we propose an adaptive velocity-space discretization scheme for the multi-species, multidimensional Rosenbluth–Fokker–Planck (RFP) equation, which is exactly mass-, momentum-, and energy-conserving. Unlike most earlier studies, our approach normalizes the velocity-space coordinate to the temporally varying individual plasma species' local thermal velocity, v th (t), and explicitly considers the resulting inertial terms in the Fokker–Planck equation. Our conservation strategy employs nonlinear constraints to enforce discretely the conservation properties of these inertial terms and the Fokker–Planck collision operator. To deal with situations of extreme thermal velocity disparities among different species, we employ an asymptotic v th -ratio-based expansion ofmore » the Rosenbluth potentials that only requires the computation of several velocity-space integrals. Numerical examples demonstrate the favorable efficiency and accuracy properties of the scheme. Specifically, we show that the combined use of the velocity-grid adaptivity and asymptotic expansions delivers many orders-of-magnitude savings in mesh resolution requirements compared to a single, static uniform mesh.« less

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.

Langevin equation with fluctuating diffusivity: A two-state model

NASA Astrophysics Data System (ADS)

Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji

2016-07-01

Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.

On the Debye-Hückel effect of electric screening

NASA Astrophysics Data System (ADS)

Campos, L. M. B. C.; Lau, F. J. P.

2014-07-01

The paper considers non-linear self-consistent electric potential equation (Sec. I), due to a cloud made of a single species of electric charges, satisfying a Boltzmann distribution law (Sec. II). Exact solutions are obtained in a simple logarithmic form, in three cases: (Sec. III) spherical radial symmetry; (Sec. IV) plane parallel symmetry; (Sec. V) a special case of azimuthal-cylindrical symmetry. All these solutions, and their transformations (Sec. VI), involve the Debye-Hückel radius; the latter was originally defined from a solution of the linearized self-consistent potential equation. Using an exact solution of the self-consistent potential equation, the distance at which the potential vanishes differs from the Debye-Hückel radius by a factor of √2 . The preceding (Secs. II-VI) simple logarithmic exact solutions of the self-consistent potential equations involve no arbitrary constants, and thus are special or singular integrals not the general integral. The general solution of the self-consistent potential equation is obtained in the plane parallel case (Sec. VII), and it involves two arbitrary constants that can be reduced to one via a translation (Sec. VIII). The plots of dimensionless potential (Figure 1), electric field (Figure 2), charge density (Figure 3), and total charge between ζ and infinity (Figure 4), versus distance normalized to Debye-Hückel radius ζ ≡ z/a, show that (Sec. IX) there is a continuum of solutions, ranging from a charge distribution concentrated inside the Debye-Hückel radius to one spread-out beyond it. The latter case leads to the limiting case of logarithmic potential, and stronger electric field; the former case, of very concentrated charge distribution, leads to a fratricide effect and weaker electric field.

On the Debye–Hückel effect of electric screening

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

Campos, L. M. B. C.; Lau, F. J. P.

2014-07-15

The paper considers non-linear self-consistent electric potential equation (Sec. I), due to a cloud made of a single species of electric charges, satisfying a Boltzmann distribution law (Sec. II). Exact solutions are obtained in a simple logarithmic form, in three cases: (Sec. III) spherical radial symmetry; (Sec. IV) plane parallel symmetry; (Sec. V) a special case of azimuthal-cylindrical symmetry. All these solutions, and their transformations (Sec. VI), involve the Debye-Hückel radius; the latter was originally defined from a solution of the linearized self-consistent potential equation. Using an exact solution of the self-consistent potential equation, the distance at which the potentialmore » vanishes differs from the Debye-Hückel radius by a factor of √(2). The preceding (Secs. II–VI) simple logarithmic exact solutions of the self-consistent potential equations involve no arbitrary constants, and thus are special or singular integrals not the general integral. The general solution of the self-consistent potential equation is obtained in the plane parallel case (Sec. VII), and it involves two arbitrary constants that can be reduced to one via a translation (Sec. VIII). The plots of dimensionless potential (Figure 1), electric field (Figure 2), charge density (Figure 3), and total charge between ζ and infinity (Figure 4), versus distance normalized to Debye-Hückel radius ζ ≡ z/a, show that (Sec. IX) there is a continuum of solutions, ranging from a charge distribution concentrated inside the Debye-Hückel radius to one spread-out beyond it. The latter case leads to the limiting case of logarithmic potential, and stronger electric field; the former case, of very concentrated charge distribution, leads to a fratricide effect and weaker electric field.« less

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.

Gluten-containing grains skew gluten assessment in oats due to sample grind non-homogeneity.

PubMed

Fritz, Ronald D; Chen, Yumin; Contreras, Veronica

2017-02-01

Oats are easily contaminated with gluten-rich kernels of wheat, rye and barley. These contaminants are like gluten 'pills', shown here to skew gluten analysis results. Using R-Biopharm R5 ELISA, we quantified gluten in gluten-free oatmeal servings from an in-market survey. For samples with a 5-20ppm reading on a first test, replicate analyses provided results ranging <5ppm to >160ppm. This suggests sample grinding may inadequately disperse gluten to allow a single accurate gluten assessment. To ascertain this, and characterize the distribution of 0.25-g gluten test results for kernel contaminated oats, twelve 50g samples of pure oats, each spiked with a wheat kernel, showed that 0.25g test results followed log-normal-like distributions. With this, we estimate probabilities of mis-assessment for a 'single measure/sample' relative to the <20ppm regulatory threshold, and derive an equation relating the probability of mis-assessment to sample average gluten content. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

Fuchsia : A tool for reducing differential equations for Feynman master integrals to epsilon form

NASA Astrophysics Data System (ADS)

Gituliar, Oleksandr; Magerya, Vitaly

2017-10-01

We present Fuchsia - an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients ∂x J(x , ɛ) = A(x , ɛ) J(x , ɛ) finds a basis transformation T(x , ɛ) , i.e., J(x , ɛ) = T(x , ɛ) J‧(x , ɛ) , such that the system turns into the epsilon form : ∂xJ‧(x , ɛ) = ɛ S(x) J‧(x , ɛ) , where S(x) is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator ɛ. That makes the construction of the transformation T(x , ɛ) crucial for obtaining solutions of the initial system. In principle, Fuchsia can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals. Program Files doi:http://dx.doi.org/10.17632/zj6zn9vfkh.1 Licensing provisions: MIT Programming language:Python 2.7 Nature of problem: Feynman master integrals may be calculated from solutions of a linear system of differential equations with rational coefficients. Such a system can be easily solved as an ɛ-series when its epsilon form is known. Hence, a tool which is able to find the epsilon form transformations can be used to evaluate Feynman master integrals. Solution method: The solution method is based on the Lee algorithm (Lee, 2015) which consists of three main steps: fuchsification, normalization, and factorization. During the fuchsification step a given system of differential equations is transformed into the Fuchsian form with the help of the Moser method (Moser, 1959). Next, during the normalization step the system is transformed to the form where eigenvalues of all residues are proportional to the dimensional regulator ɛ. Finally, the system is factorized to the epsilon form by finding an unknown transformation which satisfies a system of linear equations. Additional comments including Restrictions and Unusual features: Systems of single-variable differential equations are considered. A system needs to be reducible to Fuchsian form and eigenvalues of its residues must be of the form n + m ɛ, where n is integer. Performance depends upon the input matrix, its size, number of singular points and their degrees. It takes around an hour to reduce an example 74 × 74 matrix with 20 singular points on a PC with a 1.7 GHz Intel Core i5 CPU. An additional slowdown is to be expected for matrices with complex and/or irrational singular point locations, as these are particularly difficult for symbolic algebra software to handle.

The four fixed points of scale invariant single field cosmological models

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

Xue, BingKan, E-mail: bxue@princeton.edu

2012-10-01

We introduce a new set of flow parameters to describe the time dependence of the equation of state and the speed of sound in single field cosmological models. A scale invariant power spectrum is produced if these flow parameters satisfy specific dynamical equations. We analyze the flow of these parameters and find four types of fixed points that encompass all known single field models. Moreover, near each fixed point we uncover new models where the scale invariance of the power spectrum relies on having simultaneously time varying speed of sound and equation of state. We describe several distinctive new modelsmore » and discuss constraints from strong coupling and superluminality.« less

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

Harstad, E. N.; Harlow, Francis Harvey,; Schreyer, H. L.

Our goal is to develop constitutive relations for the behavior of a solid polymer during high-strain-rate deformations. In contrast to the classic thermodynamic techniques for deriving stress-strain response in static (equilibrium) circumstances, we employ a statistical-mechanics approach, in which we evolve a probability distribution function (PDF) for the velocity fluctuations of the repeating units of the chain. We use a Langevin description for the dynamics of a single repeating unit and a Lioville equation to describe the variations of the PDF. Moments of the PDF give the conservation equations for a single polymer chain embedded in other similar chains. Tomore » extract single-chain analytical constitutive relations these equations have been solved for representative loading paths. By this process we discover that a measure of nonuniform chain link displacement serves this purpose very well. We then derive an evolution equation for the descriptor function, with the result being a history-dependent constitutive relation.« less

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

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Taylor, Arthur C., III

1994-01-01

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

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.

Center manifolds, normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions

NASA Astrophysics Data System (ADS)

Holmes, Philip J.

1981-06-01

We study the instabilities known to aeronautical engineers as flutter and divergence. Mathematically, these states correspond to bifurcations to limit cycles and multiple equilibrium points in a differential equation. Making use of the center manifold and normal form theorems, we concentrate on the situation in which flutter and divergence become coupled, and show that there are essentially two ways in which this is likely to occur. In the first case the system can be reduced to an essential model which takes the form of a single degree of freedom nonlinear oscillator. This system, which may be analyzed by conventional phase-plane techniques, captures all the qualitative features of the full system. We discuss the reduction and show how the nonlinear terms may be simplified and put into normal form. Invariant manifold theory and the normal form theorem play a major role in this work and this paper serves as an introduction to their application in mechanics. Repeating the approach in the second case, we show that the essential model is now three dimensional and that far more complex behavior is possible, including nonperiodic and ‘chaotic’ motions. Throughout, we take a two degree of freedom system as an example, but the general methods are applicable to multi- and even infinite degree of freedom problems.

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

ERIC Educational Resources Information Center

Becker, William E.; Toutkoushian, Robert K.

1995-01-01

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

Complex antioxidants in a randomized single-blinded study of memory in seniors.

PubMed

Summers, William K; Martin, Roy L; Liu, Yimeng; Peña, Bernice; Marsh, Gary M

2018-04-01

Oxidative injury to the brain and aging are theoretical co-causes of Alzheimer's Disease (AD). Amyloid plaques and tangles are then secondary phenomenon. The preclinical state would then be 'normal' elderly. A potent complex antioxidant (antiOx) was tested against a popular one-a-day multivitamin (mV) in a randomized single blind design in 'normal' senior subjects over 6 months. Memory testing was done at baseline, 1, 3, and 6 months. The generalized estimating equation (GEE) approach was used to compare the change score of NLT 100 and 20 WR between two groups over time. Analysis of the antiOx group (30 subjects) demonstrated significant improvement in declarative memory (change score for NLT 100 at month 6 = 6.36 p < 0.0001) and working memory (change score for 20 WR at month 6 = 3.23, p < 0.0001). A change-score analysis over 6 months suggests possible neurogenesis in the antiOx group. The mV group (33 subjects) had a change score of the NLT 100 and 20WR on the sixth month of 2.20 and 0.32 (p = 0.07, 0.35). A complex antioxidant blend, sold as an over-the-counter (OTC) supplement, can improve memory in elder subjects. Antioxidants may be beneficial in AD and other neurodegerative diseases.

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.

Solving nonlinear equilibrium equations of deformable systems by method of embedded polygons

NASA Astrophysics Data System (ADS)

Razdolsky, A. G.

2017-09-01

Solving of nonlinear algebraic equations is an obligatory stage of studying the equilibrium paths of nonlinear deformable systems. The iterative method for solving a system of nonlinear algebraic equations stated in an explicit or implicit form is developed in the present work. The method consists of constructing a sequence of polygons in Euclidean space that converge into a single point that displays the solution of the system. Polygon vertices are determined on the assumption that individual equations of the system are independent from each other and each of them is a function of only one variable. Initial positions of vertices for each subsequent polygon are specified at the midpoints of certain straight segments determined at the previous iteration. The present algorithm is applied for analytical investigation of the behavior of biaxially compressed nonlinear-elastic beam-column with an open thin-walled cross-section. Numerical examples are made for the I-beam-column on the assumption that its material follows a bilinear stress-strain diagram. A computer program based on the shooting method is developed for solving the problem. The method is reduced to numerical integration of a system of differential equations and to the solution of a system of nonlinear algebraic equations between the boundary values of displacements at the ends of the beam-column. A stress distribution at the beam-column cross-sections is determined by subdividing the cross-section area into many small cells. The equilibrium path for the twisting angle and the lateral displacements tend to the stationary point when the load is increased. Configuration of the path curves reveals that the ultimate load is reached shortly once the maximal normal stresses at the beam-column fall outside the limit of the elastic region. The beam-column has a unique equilibrium state for each value of the load, that is, there are no equilibrium states once the maximum load is reached.

Evolution of the shock front and turbulence structures in the shock/turbulence interaction

NASA Technical Reports Server (NTRS)

Kevlahan, N.; Mahesh, K.; Lee, S.

1992-01-01

The interaction of a weak shock front with isotropic turbulence has been investigated using Direct Numerical Simulation (DNS). Two problems were considered: the ability of the field equation (the equation for a propagating surface) to model the shock; and a quantitative study of the evolution of turbulence structure using the database generated by Lee et al. Field equation model predictions for front shape have been compared with DNS results; good agreement is found for shock wave interaction with 2D turbulence and for a single steady vorticity wave. In the interaction of 3D isotropic turbulence with a normal shock, strong alignment of vorticity with the intermediate eigenvector of the rate of strain tensor (S(sup *)(sub ij) = S(sub ij) - (1/3)(delta(sub ij))(S(sub kk))) is seen to develop upstream of the shock and to be further amplified on passage through the shock. Vorticity tends to align at 90 deg to the largest eigenvector, but there is no preferred alignment with the smallest eigenvector. Upstream of the shock, the alignments continue to develop even after the velocity derivative skewness saturates. There is a significant tendency, which increases with time throughout the computational domain, for velocity to align with vorticity. The alignment between velocity and vorticity is strongest in eddy regions and weakest in convergence regions.

Off-equilibrium infrared structure of self-interacting scalar fields: Universal scaling, vortex-antivortex superfluid dynamics, and Bose-Einstein condensation

NASA Astrophysics Data System (ADS)

Deng, Jian; Schlichting, Soeren; Venugopalan, Raju; Wang, Qun

2018-05-01

We map the infrared dynamics of a relativistic single-component (N =1 ) interacting scalar field theory to that of nonrelativistic complex scalar fields. The Gross-Pitaevskii (GP) equation, describing the real-time dynamics of single-component ultracold Bose gases, is obtained at first nontrivial order in an expansion proportional to the powers of λ ϕ2/m2 where λ , ϕ , and m are the coupling constant, the scalar field, and the particle mass respectively. Our analytical studies are corroborated by numerical simulations of the spatial and momentum structure of overoccupied scalar fields in (2+1)-dimensions. Universal scaling of infrared modes, vortex-antivortex superfluid dynamics, and the off-equilibrium formation of a Bose-Einstein condensate are observed. Our results for the universal scaling exponents are in agreement with those extracted in the numerical simulations of the GP equation. As in these simulations, we observe coarsening phase kinetics in the Bose superfluid with strongly anomalous scaling exponents relative to that of vertex resummed kinetic theory. Our relativistic field theory framework further allows one to study more closely the coupling between superfluid and normal fluid modes, specifically the turbulent momentum and spatial structure of the coupling between a quasiparticle cascade to the infrared and an energy cascade to the ultraviolet. We outline possible applications of the formalism to the dynamics of vortex-antivortex formation and to the off-equilibrium dynamics of the strongly interacting matter formed in heavy-ion collisions.

Successfully Transitioning to Linear Equations

ERIC Educational Resources Information Center

Colton, Connie; Smith, Wendy M.

2014-01-01

The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…

Single and Double ITCZ in Aqua-Planet Models with Globally Uniform Sea Surface Temperature and Solar Insolation: An Interpretation

NASA Technical Reports Server (NTRS)

Chao, Winston C.; Chen, Baode; Einaudi, Franco (Technical Monitor)

2001-01-01

It has been known for more than a decade that an aqua-planet model with globally uniform sea surface temperature and solar insolation angle can generate ITCZ (intertropical convergence zone). Previous studies have shown that the ITCZ under such model settings can be changed between a single ITCZ over the equator and a double ITCZ straddling the equator through one of several measures. These measures include switching to a different cumulus parameterization scheme, changes within the cumulus parameterization scheme, and changes in other aspects of the model design such as horizontal resolution. In this paper an interpretation for these findings is offered. The latitudinal location of the ITCZ is the latitude where the balance of two types of attraction on the ITCZ, both due to earth's rotation, exists. The first type is equator-ward and is directly related to the earth's rotation and thus not sensitive to model design changes. The second type is poleward and is related to the convective circulation and thus is sensitive to model design changes. Due to the shape of the attractors, the balance of the two types of attractions is reached either at the equator or more than 10 degrees away from the equator. The former case results in a single ITCZ over the equator and the latter case a double ITCZ straddling the equator.

Loop equations and bootstrap methods in the lattice

DOE PAGES

Anderson, Peter D.; Kruczenski, Martin

2017-06-17

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

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.

Predicting the cover-up of dead branches using a simple single regressor equation

Treesearch

Christopher M. Oswalt; Wayne K. Clatterbuck; E.C. Burkhardt

2007-01-01

Information on the effects of branch diameter on branch occlusion is necessary for building models capable of forecasting the effect of management decisions on tree or log grade. We investigated the relationship between branch size and subsequent branch occlusion through diameter growth with special attention toward the development of a simple single regressor equation...

An interacting boundary layer model for cascades

NASA Technical Reports Server (NTRS)

Davis, R. T.; Rothmayer, A. P.

1983-01-01

A laminar, incompressible interacting boundary layer model is developed for two-dimensional cascades. In the limit of large cascade spacing these equations reduce to the interacting boundary layer equations for a single body immersed in an infinite stream. A fully implicit numerical method is used to solve the governing equations, and is found to be at least as efficient as the same technique applied to the single body problem. Solutions are then presented for a cascade of finite flat plates and a cascade of finite sine-waves, with cusped leading and trailing edges.

Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures

NASA Astrophysics Data System (ADS)

Pötz, Walter

2017-11-01

A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

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.

A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth

PubMed Central

Macklin, Paul

2011-01-01

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth. PMID:21331304

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.

Diffuse interface immersed boundary method for multi-fluid flows with arbitrarily moving rigid bodies

NASA Astrophysics Data System (ADS)

Patel, Jitendra Kumar; Natarajan, Ganesh

2018-05-01

We present an interpolation-free diffuse interface immersed boundary method for multiphase flows with moving bodies. A single fluid formalism using the volume-of-fluid approach is adopted to handle multiple immiscible fluids which are distinguished using the volume fractions, while the rigid bodies are tracked using an analogous volume-of-solid approach that solves for the solid fractions. The solution to the fluid flow equations are carried out using a finite volume-immersed boundary method, with the latter based on a diffuse interface philosophy. In the present work, we assume that the solids are filled with a "virtual" fluid with density and viscosity equal to the largest among all fluids in the domain. The solids are assumed to be rigid and their motion is solved using Newton's second law of motion. The immersed boundary methodology constructs a modified momentum equation that reduces to the Navier-Stokes equations in the fully fluid region and recovers the no-slip boundary condition inside the solids. An implicit incremental fractional-step methodology in conjunction with a novel hybrid staggered/non-staggered approach is employed, wherein a single equation for normal momentum at the cell faces is solved everywhere in the domain, independent of the number of spatial dimensions. The scalars are all solved for at the cell centres, with the transport equations for solid and fluid volume fractions solved using a high-resolution scheme. The pressure is determined everywhere in the domain (including inside the solids) using a variable coefficient Poisson equation. The solution to momentum, pressure, solid and fluid volume fraction equations everywhere in the domain circumvents the issue of pressure and velocity interpolation, which is a source of spurious oscillations in sharp interface immersed boundary methods. A well-balanced algorithm with consistent mass/momentum transport ensures robust simulations of high density ratio flows with strong body forces. The proposed diffuse interface immersed boundary method is shown to be discretely mass-preserving while being temporally second-order accurate and exhibits nominal second-order accuracy in space. We examine the efficacy of the proposed approach through extensive numerical experiments involving one or more fluids and solids, that include two-particle sedimentation in homogeneous and stratified environment. The results from the numerical simulations show that the proposed methodology results in reduced spurious force oscillations in case of moving bodies while accurately resolving complex flow phenomena in multiphase flows with moving solids. These studies demonstrate that the proposed diffuse interface immersed boundary method, which could be related to a class of penalisation approaches, is a robust and promising alternative to computationally expensive conformal moving mesh algorithms as well as the class of sharp interface immersed boundary methods for multibody problems in multi-phase flows.

The pharmacokinetics of peginterferon lambda-1a following single dose administration to subjects with impaired renal function.

PubMed

Hruska, Matthew W; Adamczyk, Robert; Colston, Elizabeth; Hesney, Michael; Stonier, Michele; Myler, Heather; Bertz, Richard

2015-09-01

This open label study was conducted to assess the effect of renal impairment (RI) on the pharmacokinetics (PK) of peginterferon lambda-1a (Lambda). Subjects (age 18-75 years, BMI 18-35 kg m(-2) ) were enrolled into one of five renal function groups: normal (n = 12), mild RI (n = 8), moderate RI (n = 8), severe RI (n = 7), end-stage renal disease (ESRD, n = 8) based on estimated glomerular filtration rate (eGFR) calculated using the Modification of Diet in Renal Disease (MDRD) equation. Subjects received a single dose of Lambda (180 µg) subcutaneously on day 1 followed by PK serum sample collections through day 29. Safety, tolerability and immunogenicity data were collected through day 43. PK parameters were estimated and summarized by group. Geometric mean ratios (GMR) and 90% confidence intervals (CIs) were calculated between normal and RI groups. With decreasing eGFR, Lambda exposure (Cmax , AUC) increased while apparent clearance (CL/F) and apparent volume of distribution (V/F) decreased. Relative to subjects with normal renal function (geometric mean AUC = 99.5 ng ml(-1) h), Lambda exposure estimates (AUC) were slightly increased in the mild RI group (geometric mean [90% CI]: 1.20 [0.82, 1.77]) and greater in the moderate (1.95 [1.35, 2.83]), severe RI (1.95 [1.30, 2.93]) and ESRD (1.88 [1.30, 2.73]) groups. Lambda was generally well tolerated. The results demonstrated that RI reduces the clearance of Lambda and suggests that dose modifications may not be required in patients with mild RI but may be required in patients with moderate to severe RI or ESRD. © 2015 The British Pharmacological Society.

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

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

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

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

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…

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

DOE PAGES

Moral, Pierre Del; Jasra, Ajay; Law, Kody J. H.; ...

2017-08-24

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic partial differential equations (PDEs). The examples involve the inversion of observations of themore » solution of (i) a 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional Poisson equation to infer the external forcing.« less

Universal binding energy relations in metallic adhesion

NASA Technical Reports Server (NTRS)

Ferrante, J.; Smith, J. R.; Rose, J. J.

1984-01-01

Rose, Smith, and Ferrante have discovered scaling relations which map the adhesive binding energy calculated by Ferrante and Smith onto a single universal binding energy curve. These binding energies are calculated for all combinations of Al(111), Zn(0001), Mg(0001), and Na(110) in contact. The scaling involves normalizing the energy by the maximum binding energy and normalizing distances by a suitable combination of Thomas-Fermi screening lengths. Rose et al. have also found that the calculated cohesive energies of K, Ba, Cu, Mo, and Sm scale by similar simple relations, suggesting the universal relation may be more general than for the simple free electron metals for which it was derived. In addition, the scaling length was defined more generally in order to relate it to measurable physical properties. Further this universality can be extended to chemisorption. A simple and yet quite accurate prediction of a zero temperature equation of state (volume as a function of pressure for metals and alloys) is presented. Thermal expansion coefficients and melting temperatures are predicted by simple, analytic expressions, and results compare favorably with experiment for a broad range of metals.

Radial pressure profiles in a cold‐flow gas‐solid vortex reactor

PubMed Central

Pantzali, Maria N.; Kovacevic, Jelena Z.; Marin, Guy B.; Shtern, Vladimir N.

2015-01-01

A unique normalized radial pressure profile characterizes the bed of a gas‐solid vortex reactor over a range of particle densities and sizes, solid capacities, and gas flow rates: 950–1240 kg/m3, 1–2 mm, 2 kg to maximum solids capacity, and 0.4–0.8 Nm3/s (corresponding to gas injection velocities of 55–110 m/s), respectively. The combined momentum conservation equations of both gas and solid phases predict this pressure profile when accounting for the corresponding measured particle velocities. The pressure profiles for a given type of particles and a given solids loading but for different gas injection velocities merge into a single curve when normalizing the pressures with the pressure value downstream of the bed. The normalized—with respect to the overall pressure drop—pressure profiles for different gas injection velocities in particle‐free flow merge in a unique profile. © 2015 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 61: 4114–4125, 2015 PMID:27667827

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.

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

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

PubMed Central

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

2015-01-01

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

Mean Expected Error in Prediction of Total Body Water: A True Accuracy Comparison between Bioimpedance Spectroscopy and Single Frequency Regression Equations

PubMed Central

Abtahi, Shirin; Abtahi, Farhad; Ellegård, Lars; Johannsson, Gudmundur; Bosaeus, Ingvar

2015-01-01

For several decades electrical bioimpedance (EBI) has been used to assess body fluid distribution and body composition. Despite the development of several different approaches for assessing total body water (TBW), it remains uncertain whether bioimpedance spectroscopic (BIS) approaches are more accurate than single frequency regression equations. The main objective of this study was to answer this question by calculating the expected accuracy of a single measurement for different EBI methods. The results of this study showed that all methods produced similarly high correlation and concordance coefficients, indicating good accuracy as a method. Even the limits of agreement produced from the Bland-Altman analysis indicated that the performance of single frequency, Sun's prediction equations, at population level was close to the performance of both BIS methods; however, when comparing the Mean Absolute Percentage Error value between the single frequency prediction equations and the BIS methods, a significant difference was obtained, indicating slightly better accuracy for the BIS methods. Despite the higher accuracy of BIS methods over 50 kHz prediction equations at both population and individual level, the magnitude of the improvement was small. Such slight improvement in accuracy of BIS methods is suggested insufficient to warrant their clinical use where the most accurate predictions of TBW are required, for example, when assessing over-fluidic status on dialysis. To reach expected errors below 4-5%, novel and individualized approaches must be developed to improve the accuracy of bioimpedance-based methods for the advent of innovative personalized health monitoring applications. PMID:26137489

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.

Empirical Equation Based Chirality (n, m) Assignment of Semiconducting Single Wall Carbon Nanotubes from Resonant Raman Scattering Data

PubMed Central

Arefin, Md Shamsul

2012-01-01

This work presents a technique for the chirality (n, m) assignment of semiconducting single wall carbon nanotubes by solving a set of empirical equations of the tight binding model parameters. The empirical equations of the nearest neighbor hopping parameters, relating the term (2n− m) with the first and second optical transition energies of the semiconducting single wall carbon nanotubes, are also proposed. They provide almost the same level of accuracy for lower and higher diameter nanotubes. An algorithm is presented to determine the chiral index (n, m) of any unknown semiconducting tube by solving these empirical equations using values of radial breathing mode frequency and the first or second optical transition energy from resonant Raman spectroscopy. In this paper, the chirality of 55 semiconducting nanotubes is assigned using the first and second optical transition energies. Unlike the existing methods of chirality assignment, this technique does not require graphical comparison or pattern recognition between existing experimental and theoretical Kataura plot. PMID:28348319

Assessing flow paths in a karst aquifer based on multiple dye tracing tests using stochastic simulation and the MODFLOW-CFP code

NASA Astrophysics Data System (ADS)

Assari, Amin; Mohammadi, Zargham

2017-09-01

Karst systems show high spatial variability of hydraulic parameters over small distances and this makes their modeling a difficult task with several uncertainties. Interconnections of fractures have a major role on the transport of groundwater, but many of the stochastic methods in use do not have the capability to reproduce these complex structures. A methodology is presented for the quantification of tortuosity using the single normal equation simulation (SNESIM) algorithm and a groundwater flow model. A training image was produced based on the statistical parameters of fractures and then used in the simulation process. The SNESIM algorithm was used to generate 75 realizations of the four classes of fractures in a karst aquifer in Iran. The results from six dye tracing tests were used to assign hydraulic conductivity values to each class of fractures. In the next step, the MODFLOW-CFP and MODPATH codes were consecutively implemented to compute the groundwater flow paths. The 9,000 flow paths obtained from the MODPATH code were further analyzed to calculate the tortuosity factor. Finally, the hydraulic conductivity values calculated from the dye tracing experiments were refined using the actual flow paths of groundwater. The key outcomes of this research are: (1) a methodology for the quantification of tortuosity; (2) hydraulic conductivities, that are incorrectly estimated (biased low) with empirical equations that assume Darcian (laminar) flow with parallel rather than tortuous streamlines; and (3) an understanding of the scale-dependence and non-normal distributions of tortuosity.

Modulation transfer function of partial gating detector by liquid crystal auto-controlling light intensity

NASA Astrophysics Data System (ADS)

Yang, Xusan; Tang, Yuanhe; Liu, Kai; Liu, Hanchen; Gao, Haiyang; Li, Qing; Zhang, Ruixia; Ye, Na; Liang, Yuan; Zhao, Gaoxiang

2008-12-01

Based on the electro-optical properties of liquid crystal, we have designed a novel partial gating detector. Liquid crystal can be taken to change its own transmission according to the light intensity outside. Every single pixel of the image is real-time modulated by liquid crystal, thus the strong light is weakened and low light goes through the detector normally .The purpose of partial-gating strong light (>105lx) can be achieved by this detector. The modulation transfer function (MTF) equations of the main optical sub-systems are calculated in this paper, they are liquid crystal panels, linear fiber panel and CCD array detector. According to the relevant size, the MTF value of this system is fitted out. The result is MTF= 0.518 at Nyquist frequency.

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.

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.

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.

a Thtee-Dimensional Variational Assimilation Scheme for Satellite Aod

NASA Astrophysics Data System (ADS)

Liang, Y.; Zang, Z.; You, W.

2018-04-01

A three-dimensional variational data assimilation scheme is designed for satellite AOD based on the IMPROVE (Interagency Monitoring of Protected Visual Environments) equation. The observation operator that simulates AOD from the control variables is established by the IMPROVE equation. All of the 16 control variables in the assimilation scheme are the mass concentrations of aerosol species from the Model for Simulation Aerosol Interactions and Chemistry scheme, so as to take advantage of this scheme in providing comprehensive analyses of species concentrations and size distributions as well as be calculating efficiently. The assimilation scheme can save computational resources as the IMPROVE equation is a quadratic equation. A single-point observation experiment shows that the information from the single-point AOD is effectively spread horizontally and vertically.

Single evolution equation in a light-matter pairing system

NASA Astrophysics Data System (ADS)

Bugaychuk, S.; Tobisch, E.

2018-03-01

The coupled system including wave mixing and nonlinear dynamics of a nonlocal optical medium is usually studied (1) numerically, with the medium being regarded as a black box, or (2) experimentally, making use of some empirical assumptions. In this paper we deduce for the first time a single evolution equation describing the dynamics of the pairing system as a holistic complex. For a non-degenerate set of parameters, we obtain the nonlinear Schrödinger equation with coefficients being written out explicitly. Analytical solutions of this equation can be experimentally realized in any photorefractive medium, e.g. in photorefractive, liquid or photonic crystals. For instance, a soliton-like solution can be used in dynamical holography for designing an artificial grating with maximal amplification of an image.

Transformation of nonlinear discrete-time system into the extended observer form

NASA Astrophysics Data System (ADS)

Kaparin, V.; Kotta, Ü.

2018-04-01

The paper addresses the problem of transforming discrete-time single-input single-output nonlinear state equations into the extended observer form, which, besides the input and output, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of both the extended coordinate and output transformations, solving the problem, are formulated in terms of differential one-forms, associated with the input-output equation, corresponding to the state equations. An algorithm for transformation of state equations into the extended observer form is proposed and illustrated by an example. Moreover, the considered approach is compared with the method of dynamic observer error linearisation, which likewise is intended to enlarge the class of systems transformable into an observer form.

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.

Accurate analytic solution of chemical master equations for gene regulation networks in a single cell

NASA Astrophysics Data System (ADS)

Huang, Guan-Rong; Saakian, David B.; Hu, Chin-Kun

2018-01-01

Studying gene regulation networks in a single cell is an important, interesting, and hot research topic of molecular biology. Such process can be described by chemical master equations (CMEs). We propose a Hamilton-Jacobi equation method with finite-size corrections to solve such CMEs accurately at the intermediate region of switching, where switching rate is comparable to fast protein production rate. We applied this approach to a model of self-regulating proteins [H. Ge et al., Phys. Rev. Lett. 114, 078101 (2015), 10.1103/PhysRevLett.114.078101] and found that as a parameter related to inducer concentration increases the probability of protein production changes from unimodal to bimodal, then to unimodal, consistent with phenotype switching observed in a single cell.

Procedure for normalization of cDNA libraries

DOEpatents

Bonaldo, Maria DeFatima; Soares, Marcelo Bento

1997-01-01

This invention provides a method to normalize a cDNA library constructed in a vector capable of being converted to single-stranded circles and capable of producing complementary nucleic acid molecules to the single-stranded circles comprising: (a) converting the cDNA library in single-stranded circles; (b) generating complementary nucleic acid molecules to the single-stranded circles; (c) hybridizing the single-stranded circles converted in step (a) with complementary nucleic acid molecules of step (b) to produce partial duplexes to an appropriate Cot; (e) separating the unhybridized single-stranded circles from the hybridized single-stranded circles, thereby generating a normalized cDNA library.

Performance of an inverted pendulum model directly applied to normal human gait.

PubMed

Buczek, Frank L; Cooney, Kevin M; Walker, Matthew R; Rainbow, Michael J; Concha, M Cecilia; Sanders, James O

2006-03-01

In clinical gait analysis, we strive to understand contributions to body support and propulsion as this forms a basis for treatment selection, yet the relative importance of gravitational forces and joint powers can be controversial even for normal gait. We hypothesized that an inverted pendulum model, propelled only by gravity, would be inadequate to predict velocities and ground reaction forces during gait. Unlike previous ballistic and passive dynamic walking studies, we directly compared model predictions to gait data for 24 normal children. We defined an inverted pendulum from the average center-of-pressure to the instantaneous center-of-mass, and derived equations of motion during single support that allowed a telescoping action. Forward and inverse dynamics predicted pendulum velocities and ground reaction forces, and these were statistically and graphically compared to actual gait data for identical strides. Results of forward dynamics replicated those in the literature, with reasonable predictions for velocities and anterior ground reaction forces, but poor predictions for vertical ground reaction forces. Deviations from actual values were explained by joint powers calculated for these subjects. With a telescoping action during inverse dynamics, predicted vertical forces improved dramatically and gained a dual-peak pattern previously missing in the literature, yet expected for normal gait. These improvements vanished when telescoping terms were set to zero. Because this telescoping action is difficult to explain without muscle activity, we believe these results support the need for both gravitational forces and joint powers in normal gait. Our approach also begins to quantify the relative contributions of each.

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

Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Ivanov, S. K.; Kamchatnov, A. M.; Congy, T.; Pavloff, N.

2017-12-01

We provide a classification of the possible flows of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single polarization mode (also denoted as "magnetic excitation") obeying a system of equations equivalent to the Landau-Lifshitz equation for an easy-plane ferromagnet. We present the full set of one-phase periodic solutions. The corresponding Whitham modulation equations are obtained together with formulas connecting their solutions with the Riemann invariants of the modulation equations. The problem is not genuinely nonlinear, and this results in a non-single-valued mapping of the solutions of the Whitham equations with physical wave patterns as well as the appearance of interesting elements—contact dispersive shock waves—that are absent in more standard, genuinely nonlinear situations. Our analytic results are confirmed by numerical simulations.

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.

Preliminary Planar Formation: Flight Dynamics Near Sun-Earth L2 Point

NASA Technical Reports Server (NTRS)

Segerman, Alan M.; Zedd, Michael F.

2003-01-01

NASA's Goddard Space Flight Center is planning a series of missions in the vicinity of the Sun-Earth L2 libration point. Some of these projects will involve a distributed space system of telescope spacecraft acting together as a single telescope for high-resolution. The individual telescopes will be configured in a plane, surrounding a hub, where the telescope plane can be aimed toward various astronomical targets of interest. In preparation for these missions, it is necessary to develop an improved understanding of the dynamical behavior of objects in a planar configuration near L2. The classical circular restricted three body problem is taken as the basis for the analysis. At first order, the motion of such a telescope relative to the hub is described by a system of linear second order differential equations. These equations are identical to the circular restricted problem's linear equations describing the hub motion about L2. Therefore, the fundamental frequencies, both parallel to and normal to the ecliptic plane, are the same for the relative telescope motion as for the hub motion. To maintain the telescope plane for the duration necessary for the planned observations, a halo-type orbit of the telescopes about the hub is investigated. By using a halo orbit, the individual telescopes remain in approximately the same plane over the observation duration. For such an orbit, the fundamental periods parallel to and normal to the ecliptic plane are forced to be the same by careful selection of the initial conditions in order to adjust the higher order forces. The relative amplitudes of the resulting oscillations are associated with the orientation of the telescope plane relative to the ecliptic. As in the circular restricted problem, initial conditions for the linearized equations must be selected so as not to excite the convergent or divergent linear modes. In a higher order analysis, the telescope relative motion equations include the effects of the position of the hub relative to L2. In this paper, the differential equations are developed through second order in the distance of the hub from the libration point. A modified Lindstedt-Poincad perturbation method is employed to construct the solution of these differential equations through that same order of magnitude. In the course of the solution process, relationships are determined between the initial conditions of the telescopes, selected in order to avoid resonance excitation. As the differential equations include the hub position, it is necessary to simultaneously develop the solution for the hub. As has been done in past analyses of the circular restricted problem, the hub position is written in a power series formulation in terms of its distance from L2. Then, in order to be included in the telescope equations, the hub solution is cast in terms of the nonlinear frequency of the relative telescope motion. In the course of the analysis, it is determined that the hub should also maintain a halo orbit - about L2. Additionally, relationships are formed between the initial conditions of the telescopes and the hub. These relationships may be used to associate sets of initial conditions with particular orientations of the telescope plane. The accuracy of the analytical solution is verified through various simulations and comparison to numerical integration of the differential equations. The results of the simulations are presented, along with a graphical representation of the relationships between the initial conditions of the telescopes and hub.

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.

Multiple imputation by chained equations for systematically and sporadically missing multilevel data.

PubMed

Resche-Rigon, Matthieu; White, Ian R

2018-06-01

In multilevel settings such as individual participant data meta-analysis, a variable is 'systematically missing' if it is wholly missing in some clusters and 'sporadically missing' if it is partly missing in some clusters. Previously proposed methods to impute incomplete multilevel data handle either systematically or sporadically missing data, but frequently both patterns are observed. We describe a new multiple imputation by chained equations (MICE) algorithm for multilevel data with arbitrary patterns of systematically and sporadically missing variables. The algorithm is described for multilevel normal data but can easily be extended for other variable types. We first propose two methods for imputing a single incomplete variable: an extension of an existing method and a new two-stage method which conveniently allows for heteroscedastic data. We then discuss the difficulties of imputing missing values in several variables in multilevel data using MICE, and show that even the simplest joint multilevel model implies conditional models which involve cluster means and heteroscedasticity. However, a simulation study finds that the proposed methods can be successfully combined in a multilevel MICE procedure, even when cluster means are not included in the imputation models.

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.

Reference range of fetal nasal bone length between 18 and 24 weeks of pregnancy in an unselected Brazilian population: experience from a single service.

PubMed

Araujo Júnior, Edward; Martins, Wellington P; Pires, Claudio Rodrigues; Moron, Antonio Fernandes; Zanforlin Filho, Sebastião Marques

2014-08-01

To determine reference range of fetal nasal bone length (NBL) during the second trimester of pregnancy in a Brazilian population. This was a retrospective cross-sectional study with 2681 normal singleton pregnancies between 18 and 24 weeks of gestation. The NBL was obtained in the mid-sagittal plane of the fetal face profile using the following landmarks: nasal bone, overlying skin and the tip of the nose. The NBL was measured by placing the calipers in the out-to-out position. To assess the correlation between NBL and gestational age (GA), polynomial equations were calculated, with adjustments by coefficient of determination (R(2)). The mean of NBL ranged from 5.72 ± 0.87 mm at 18-18 + 6 weeks to 7.45 ± 1.23 mm at 24-24+6 weeks of pregnancy. We observed a good correlation between NBL and GA, best represented by a linear equation: NBL = 0.080+0.276*GA (R(2 )= 0.16). We established a reference range of fetal NBL in the second trimester of pregnancy in a Brazilian population.

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

Spectroscopic determination of leaf biochemistry using band-depth analysis of absorption features and stepwise multiple linear regression

USGS Publications Warehouse

Kokaly, R.F.; Clark, R.N.

1999-01-01

We develop a new method for estimating the biochemistry of plant material using spectroscopy. Normalized band depths calculated from the continuum-removed reflectance spectra of dried and ground leaves were used to estimate their concentrations of nitrogen, lignin, and cellulose. Stepwise multiple linear regression was used to select wavelengths in the broad absorption features centered at 1.73 ??m, 2.10 ??m, and 2.30 ??m that were highly correlated with the chemistry of samples from eastern U.S. forests. Band depths of absorption features at these wavelengths were found to also be highly correlated with the chemistry of four other sites. A subset of data from the eastern U.S. forest sites was used to derive linear equations that were applied to the remaining data to successfully estimate their nitrogen, lignin, and cellulose concentrations. Correlations were highest for nitrogen (R2 from 0.75 to 0.94). The consistent results indicate the possibility of establishing a single equation capable of estimating the chemical concentrations in a wide variety of species from the reflectance spectra of dried leaves. The extension of this method to remote sensing was investigated. The effects of leaf water content, sensor signal-to-noise and bandpass, atmospheric effects, and background soil exposure were examined. Leaf water was found to be the greatest challenge to extending this empirical method to the analysis of fresh whole leaves and complete vegetation canopies. The influence of leaf water on reflectance spectra must be removed to within 10%. Other effects were reduced by continuum removal and normalization of band depths. If the effects of leaf water can be compensated for, it might be possible to extend this method to remote sensing data acquired by imaging spectrometers to give estimates of nitrogen, lignin, and cellulose concentrations over large areas for use in ecosystem studies.We develop a new method for estimating the biochemistry of plant material using spectroscopy. Normalized band depths calculated from the continuum-removed reflectance spectra of dried and ground leaves were used to estimate their concentrations of nitrogen, lignin, and cellulose. Stepwise multiple linear regression was used to select wavelengths in the broad absorption features centered at 1.73 ??m, 2.10 ??m, and 2.301 ??m that were highly correlated with the chemistry of samples from eastern U.S. forests. Band depths of absorption features at these wavelengths were found to also be highly correlated with the chemistry of four other sites. A subset of data from the eastern U.S. forest sites was used to derive linear equations that were applied to the remaining data to successfully estimate their nitrogen, lignin, and cellulose concentrations. Correlations were highest for nitrogen (R2 from 0.75 to 0.94). The consistent results indicate the possibility of establishing a single equation capable of estimating the chemical concentrations in a wide variety of species from the reflectance spectra of dried leaves. The extension of this method to remote sensing was investigated. The effects of leaf water content, sensor signal-to-noise and bandpass, atmospheric effects, and background soil exposure were examined. Leaf water was found to be the greatest challenge to extending this empirical method to the analysis of fresh whole leaves and complete vegetation canopies. The influence of leaf water on reflectance spectra must be removed to within 10%. Other effects were reduced by continuum removal and normalization of band depths. If the effects of leaf water can be compensated for, it might be possible to extend this method to remote sensing data acquired by imaging spectrometers to give estimates of nitrogen, lignin, and cellulose concentrations over large areas for use in ecosystem studies.

Nonlinear Drift-Kinetic Equation in the Presence of a Circularly Polarized Wave

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E. N.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

Equations of the single particle motion and nonlinear kinetic equation for plasma in the presence of a circularly polarized wave of arbitrary frequency in the drift approximation are presented. The nonstationarity and inhomogeneity of the plasma-wave system are taken into account.

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.

An Evaluation of the Single-Group Growth Model as an Alternative to Common-Item Equating. Research Report. ETS RR-16-01

ERIC Educational Resources Information Center

Wei, Youhua; Morgan, Rick

2016-01-01

As an alternative to common-item equating when common items do not function as expected, the single-group growth model (SGGM) scaling uses common examinees or repeaters to link test scores on different forms. The SGGM scaling assumes that, for repeaters taking adjacent administrations, the conditional distribution of scale scores in later…

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.

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.

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.

Scaling from single molecule to macroscopic adhesion at polymer/metal interfaces.

PubMed

Utzig, Thomas; Raman, Sangeetha; Valtiner, Markus

2015-03-10

Understanding the evolution of macroscopic adhesion based on fundamental molecular interactions is crucial to designing strong and smart polymer/metal interfaces that play an important role in many industrial and biomedical applications. Here we show how macroscopic adhesion can be predicted on the basis of single molecular interactions. In particular, we carry out dynamic single molecule-force spectroscopy (SM-AFM) in the framework of Bell-Evans' theory to gain information about the energy barrier between the bound and unbound states of an amine/gold junction. Furthermore, we use Jarzynski's equality to obtain the equilibrium ground-state energy difference of the amine/gold bond from these nonequilibrium force measurements. In addition, we perform surface forces apparatus (SFA) experiments to measure macroscopic adhesion forces at contacts where approximately 10(7) amine/gold bonds are formed simultaneously. The SFA approach provides an amine/gold interaction energy (normalized by the number of interacting molecules) of (36 ± 1)k(B)T, which is in excellent agreement with the interaction free energy of (35 ± 3)k(B)T calculated using Jarzynski's equality and single-molecule AFM experiments. Our results validate Jarzynski's equality for the field of polymer/metal interactions by measuring both sides of the equation. Furthermore, the comparison of SFA and AFM shows how macroscopic interaction energies can be predicted on the basis of single molecular interactions, providing a new strategy to potentially predict adhesive properties of novel glues or coatings as well as bio- and wet adhesion.

A single-scattering correction for the seismo-acoustic parabolic equation.

PubMed

Collins, Michael D

2012-04-01

An efficient single-scattering correction that does not require iterations is derived and tested for the seismo-acoustic parabolic equation. The approach is applicable to problems involving gradual range dependence in a waveguide with fluid and solid layers, including the key case of a sloping fluid-solid interface. The single-scattering correction is asymptotically equivalent to a special case of a single-scattering correction for problems that only have solid layers [Küsel et al., J. Acoust. Soc. Am. 121, 808-813 (2007)]. The single-scattering correction has a simple interpretation (conservation of interface conditions in an average sense) that facilitated its generalization to problems involving fluid layers. Promising results are obtained for problems in which the ocean bottom interface has a small slope.

Modeling Blazar Spectra by Solving an Electron Transport Equation

NASA Astrophysics Data System (ADS)

Lewis, Tiffany; Finke, Justin; Becker, Peter A.

2018-01-01

Blazars are luminous active galaxies across the entire electromagnetic spectrum, but the spectral formation mechanisms, especially the particle acceleration, in these sources are not well understood. We develop a new theoretical model for simulating blazar spectra using a self-consistent electron number distribution. Specifically, we solve the particle transport equation considering shock acceleration, adiabatic expansion, stochastic acceleration due to MHD waves, Bohm diffusive particle escape, synchrotron radiation, and Compton radiation, where we implement the full Compton cross-section for seed photons from the accretion disk, the dust torus, and 26 individual broad lines. We used a modified Runge-Kutta method to solve the 2nd order equation, including development of a new mathematical method for normalizing stiff steady-state ordinary differential equations. We show that our self-consistent, transport-based blazar model can qualitatively fit the IR through Fermi g-ray data for 3C 279, with a single-zone, leptonic configuration. We use the solution for the electron distribution to calculate multi-wavelength SED spectra for 3C 279. We calculate the particle and magnetic field energy densities, which suggest that the emitting region is not always in equipartition (a common assumption), but sometimes matter dominated. The stratified broad line region (based on ratios in quasar reverberation mapping, and thus adding no free parameters) improves our estimate of the location of the emitting region, increasing it by ~5x. Our model provides a novel view into the physics at play in blazar jets, especially the relative strength of the shock and stochastic acceleration, where our model is well suited to distinguish between these processes, and we find that the latter tends to dominate.

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.

Homeostatic plasticity for single node delay-coupled reservoir computing.

PubMed

Toutounji, Hazem; Schumacher, Johannes; Pipa, Gordon

2015-06-01

Supplementing a differential equation with delays results in an infinite-dimensional dynamical system. This property provides the basis for a reservoir computing architecture, where the recurrent neural network is replaced by a single nonlinear node, delay-coupled to itself. Instead of the spatial topology of a network, subunits in the delay-coupled reservoir are multiplexed in time along one delay span of the system. The computational power of the reservoir is contingent on this temporal multiplexing. Here, we learn optimal temporal multiplexing by means of a biologically inspired homeostatic plasticity mechanism. Plasticity acts locally and changes the distances between the subunits along the delay, depending on how responsive these subunits are to the input. After analytically deriving the learning mechanism, we illustrate its role in improving the reservoir's computational power. To this end, we investigate, first, the increase of the reservoir's memory capacity. Second, we predict a NARMA-10 time series, showing that plasticity reduces the normalized root-mean-square error by more than 20%. Third, we discuss plasticity's influence on the reservoir's input-information capacity, the coupling strength between subunits, and the distribution of the readout coefficients.

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.

Procedure for normalization of cDNA libraries

DOEpatents

Bonaldo, M.D.; Soares, M.B.

1997-12-30

This invention provides a method to normalize a cDNA library constructed in a vector capable of being converted to single-stranded circles and capable of producing complementary nucleic acid molecules to the single-stranded circles comprising: (a) converting the cDNA library in single-stranded circles; (b) generating complementary nucleic acid molecules to the single-stranded circles; (c) hybridizing the single-stranded circles converted in step (a) with complementary nucleic acid molecules of step (b) to produce partial duplexes to an appropriate Cot; (e) separating the unhybridized single-stranded circles from the hybridized single-stranded circles, thereby generating a normalized cDNA library. 1 fig.

Solving Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Krogh, F. T.

1987-01-01

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

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

ERIC Educational Resources Information Center

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

2010-01-01

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

Periodic and rational solutions of the reduced Maxwell-Bloch equations

NASA Astrophysics Data System (ADS)

Wei, Jiao; Wang, Xin; Geng, Xianguo

2018-06-01

We investigate the reduced Maxwell-Bloch (RMB) equations which describe the propagation of short optical pulses in dielectric materials with resonant non-degenerate transitions. The general Nth-order periodic solutions are provided by means of the Darboux transformation. The Nth-order degenerate periodic and Nth-order rational solutions containing several free parameters with compact determinant representations are derived from two different limiting cases of the obtained general periodic solutions, respectively. Explicit expressions of these solutions from first to second order are presented. Typical nonlinear wave patterns for the four components of the RMB equations such as single-peak, double-peak-double-dip, double-peak and single-dip structures in the second-order rational solutions are shown. This kind of the rational solutions correspond to rogue waves in the reduced Maxwell-Bloch equations.

Equations of motion of slung-load systems, including multilift systems

NASA Technical Reports Server (NTRS)

Cicolani, Luigi S.; Kanning, Gerd

1992-01-01

General simulation equations are derived for the rigid body motion of slung-load systems. This work is motivated by an interest in trajectory control for slung loads carried by two or more helicopters. An approximation of these systems consists of several rigid bodies connected by straight-line cables or links. The suspension can be assumed elastic or inelastic. Equations for the general system are obtained from the Newton-Euler rigid-body equations with the introduction of generalized velocity coordinates. Three forms are obtained: two generalize previous case-specific results for single-helicopter systems with elastic and inelastic suspensions, respectively; and the third is a new formulation for inelastic suspensions. The latter is derived from the elastic suspension equations by choosing the generalized coordinates so that motion induced by cable stretching is separated from motion with invariant cable lengths, and by then nulling the stretching coordinates to get a relation for the suspension forces. The result is computationally more efficient than the conventional formulation, is readily integrated with the elastic suspension formulation, and is easily applied to the complex dual-lift and multilift systems. Results are given for two-helicopter systems; three configurations are included and these can be integrated in a single simulation. Equations are also given for some single-helicopter systems, for comparison with the previous literature, and for a multilift system. Equations for degenerate-body approximations (point masses, rigid rods) are also formulated and results are given for dual-lift and multilift systems. Finally, linearlized equations of motion are given for general slung-load systems are presented along with results for the two-helicopter system with a spreader bar.

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2001-01-01

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

Single-cell copy number variation detection

PubMed Central

2011-01-01

Detection of chromosomal aberrations from a single cell by array comparative genomic hybridization (single-cell array CGH), instead of from a population of cells, is an emerging technique. However, such detection is challenging because of the genome artifacts and the DNA amplification process inherent to the single cell approach. Current normalization algorithms result in inaccurate aberration detection for single-cell data. We propose a normalization method based on channel, genome composition and recurrent genome artifact corrections. We demonstrate that the proposed channel clone normalization significantly improves the copy number variation detection in both simulated and real single-cell array CGH data. PMID:21854607

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

PubMed

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

2016-01-15

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

Reduction operators of Burgers equation.

PubMed

Pocheketa, Oleksandr A; Popovych, Roman O

2013-02-01

The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.

Reduction operators of Burgers equation

PubMed Central

Pocheketa, Oleksandr A.; Popovych, Roman O.

2013-01-01

The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special “no-go” case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf–Cole transformation to a parameterized family of Lie reductions of the linear heat equation. PMID:23576819

Spike solutions in Gierer#x2013;Meinhardt model with a time dependent anomaly exponent

NASA Astrophysics Data System (ADS)

Nec, Yana

2018-01-01

Experimental evidence of complex dispersion regimes in natural systems, where the growth of the mean square displacement in time cannot be characterised by a single power, has been accruing for the past two decades. In such processes the exponent γ(t) in ⟨r2⟩ ∼ tγ(t) at times might be approximated by a piecewise constant function, or it can be a continuous function. Variable order differential equations are an emerging mathematical tool with a strong potential to model these systems. However, variable order differential equations are not tractable by the classic differential equations theory. This contribution illustrates how a classic method can be adapted to gain insight into a system of this type. Herein a variable order Gierer-Meinhardt model is posed, a generic reaction- diffusion system of a chemical origin. With a fixed order this system possesses a solution in the form of a constellation of arbitrarily situated localised pulses, when the components' diffusivity ratio is asymptotically small. The pattern was shown to exist subject to multiple step-like transitions between normal diffusion and sub-diffusion, as well as between distinct sub-diffusive regimes. The analytical approximation obtained permits qualitative analysis of the impact thereof. Numerical solution for typical cross-over scenarios revealed such features as earlier equilibration and non-monotonic excursions before attainment of equilibrium. The method is general and allows for an approximate numerical solution with any reasonably behaved γ(t).

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

The Distribution of Fixation Durations during Reading: Effects of Stimulus Quality

ERIC Educational Resources Information Center

White, Sarah J.; Staub, Adrian

2012-01-01

Participants' eye movements were recorded as they read single sentences presented normally, presented entirely in faint text, or presented normally except for a single faint word. Fixations were longer when the entire sentence was faint than when the sentence was presented normally. In addition, fixations were much longer on a single faint word…

Cost comparison of re-usable and single-use fibrescopes in a large English teaching hospital.

PubMed

McCahon, R A; Whynes, D K

2015-06-01

A number of studies in the U.S.A. and mainland Europe have described the costs of fibreoptic tracheal intubation. However, no such data from the UK appear available. We performed a cost assessment of fibreoptic intubation, using re-usable (various devices from Olympus, Acutronic and Karl Storz) and single-use (Ambu aScope) fibrescopes, at the Queens Medical Centre, Nottingham, U.K., between 1 January 2009 and 31 March 2014. The total annual cost of fibreoptic intubation with re-usable fibrescopes was £46,385. Based on 141 fibreoptic intubations per year, this equated to £329 per use, an average dominated by repair/maintenance costs (43%) and capital depreciation costs (42%). In comparison, the total annual cost of using single-use fibrescopes for the same work would have been around £200 per use. The analysis enabled us to develop a generic model, wherein we were able to describe the relationship between total cost of use vs number of uses for a fibrescope. An 'isopleth' was identified for this relationship: a line that joined all the points where the cost of re-usable vs single-use fibrescopes was equal. It appears cheaper to use single-use fibrescopes at up to 200 fibreoptic intubations per year (a range commensurate with normal practice) even when the repair rate for re-usable fibrescopes is low. Any centre, knowing its fibrescope use and repair rate, can plot its data similarly to help ascertain which of the re-usable or single-use fibrescope represents better value. © 2015 The Association of Anaesthetists of Great Britain and Ireland.

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Astrophysics Data System (ADS)

Papell, S. Stephen; Nyland, Ted W.; Saiyed, Naseem H.

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomas devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1 - X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Technical Reports Server (NTRS)

Papell, S. S.; Nyland, Ted W.; Saiyed, Naseem H.

1992-01-01

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomson devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1-X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Technical Reports Server (NTRS)

Papell, S. Stephen; Nyland, Ted W.; Saiyed, Naseem H.

1992-01-01

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomas devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1 - X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

NASA Astrophysics Data System (ADS)

Papell, S. S.; Nyland, Ted W.; Saiyed, Naseem H.

1992-07-01

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomson devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1-X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

PubMed

Wapenaar, Kees

2017-06-01

A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.

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.

The free-electron laser - Maxwell's equations driven by single-particle currents

NASA Technical Reports Server (NTRS)

Colson, W. B.; Ride, S. K.

1980-01-01

It is shown that if single particle currents are coupled to Maxwell's equations, the resulting set of self-consistent nonlinear equations describes the evolution of the electron beam and the amplitude and phase of the free-electron-laser field. The formulation is based on the slowly varying amplitude and phase approximation, and the distinction between microscopic and macroscopic scales, which distinguishes the microscopic bunching from the macroscopic pulse propagation. The capabilities of this new theoretical approach become apparent when its predictions for the ultrashort pulse free-electron laser are compared to experimental data; the optical pulse evolution, determined simply and accurately, agrees well with observations.

Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.

PubMed

Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C

2011-06-01

The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.

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

PubMed

Chatterjee, Abhijit; Vlachos, Dionisios G

2007-07-21

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

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

Equations of motion of slung load systems with results for dual lift

NASA Technical Reports Server (NTRS)

Cicolani, Luigi S.; Kanning, Gerd

1990-01-01

General simulation equations are derived for the rigid body motion of slung load systems. These systems are viewed as consisting of several rigid bodies connected by straight-line cables or links. The suspension can be assumed to be elastic or inelastic, both cases being of interest in simulation and control studies. Equations for the general system are obtained via D'Alembert's principle and the introduction of generalized velocity coordinates. Three forms are obtained. Two of these generalize previous case-specific results for single helicopter systems with elastic or inelastic suspensions. The third is a new formulation for inelastic suspensions. It is derived from the elastic suspension equations by choosing the generalized coordinates so as to separate motion due to cable stretching from motion with invariant cable lengths. The result is computationally more efficient than the conventional formulation, and is readily integrated with the elastic suspension formulation and readily applied to the complex dual lift and multilift systems. Equations are derived for dual lift systems. Three proposed suspension arrangements can be integrated in a single equation set. The equations are given in terms of the natural vectors and matrices of three-dimensional rigid body mechanics and are tractable for both analysis and programming.

Nebo: An efficient, parallel, and portable domain-specific language for numerically solving partial differential equations

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

Earl, Christopher; Might, Matthew; Bagusetty, Abhishek

This study presents Nebo, a declarative domain-specific language embedded in C++ for discretizing partial differential equations for transport phenomena on multiple architectures. Application programmers use Nebo to write code that appears sequential but can be run in parallel, without editing the code. Currently Nebo supports single-thread execution, multi-thread execution, and many-core (GPU-based) execution. With single-thread execution, Nebo performs on par with code written by domain experts. With multi-thread execution, Nebo can linearly scale (with roughly 90% efficiency) up to 12 cores, compared to its single-thread execution. Moreover, Nebo’s many-core execution can be over 140x faster than its single-thread execution.

Nebo: An efficient, parallel, and portable domain-specific language for numerically solving partial differential equations

DOE PAGES

Earl, Christopher; Might, Matthew; Bagusetty, Abhishek; ...

2016-01-26

This study presents Nebo, a declarative domain-specific language embedded in C++ for discretizing partial differential equations for transport phenomena on multiple architectures. Application programmers use Nebo to write code that appears sequential but can be run in parallel, without editing the code. Currently Nebo supports single-thread execution, multi-thread execution, and many-core (GPU-based) execution. With single-thread execution, Nebo performs on par with code written by domain experts. With multi-thread execution, Nebo can linearly scale (with roughly 90% efficiency) up to 12 cores, compared to its single-thread execution. Moreover, Nebo’s many-core execution can be over 140x faster than its single-thread execution.

Anisotropic constitutive modeling for nickel base single crystal superalloys using a crystallographic approach

NASA Technical Reports Server (NTRS)

Stouffer, D. C.; Sheh, M. Y.

1988-01-01

A micromechanical model based on crystallographic slip theory was formulated for nickel-base single crystal superalloys. The current equations include both drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments have been conducted to evaluate the effect of back stress in single crystals. The results showed that (1) the back stress is orientation dependent; and (2) the back stress state variable in the inelastic flow equation is necessary for predicting anelastic behavior of the material. The model also demonstrated improved fatigue predictive capability. Model predictions and experimental data are presented for single crystal superalloy Rene N4 at 982 C.

Biomass equations for shrub species of Tamualipan thornscrub of North-Eastern Mexico

Treesearch

J. Navar; E. Mendez; A. Najera; J. Graciano; V. Dale; B. Parresol

2004-01-01

Nine additive allometric equations for computing above-ground, standing biomass were developed for the plant community and for each of 18 single species typical of the Tamaulipan thornscrub of north-eastern Mexico. Equations developed using additive procedures in seemingly unrelated linear regression provided statistical efficiency in total biomass estimates at the...

Applications of the Peng-Robinson Equation of State Using Mathematica

ERIC Educational Resources Information Center

Binous, Housam

2008-01-01

A single equation of state (EOS) such as the Peng-Robinson EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state including adiabatic flash calculation, determination of the solubility of methanol in natural gas, and the calculation of high-pressure chemical equilibrium. The problems…

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

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.

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.

Method for construction of normalized cDNA libraries

DOEpatents

Soares, Marcelo B.; Efstratiadis, Argiris

1998-01-01

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form comprising: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3' noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to appropriate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library. This invention also provides normalized cDNA libraries generated by the above-described method and uses of the generated libraries.

Method for construction of normalized cDNA libraries

DOEpatents

Soares, M.B.; Efstratiadis, A.

1998-11-03

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form comprising: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3` noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to appropriate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library. This invention also provides normalized cDNA libraries generated by the above-described method and uses of the generated libraries. 19 figs.

Theoretical basis, experimental design, and computerized simulation of synergism and antagonism in drug combination studies.

PubMed

Chou, Ting-Chao

2006-09-01

The median-effect equation derived from the mass-action law principle at equilibrium-steady state via mathematical induction and deduction for different reaction sequences and mechanisms and different types of inhibition has been shown to be the unified theory for the Michaelis-Menten equation, Hill equation, Henderson-Hasselbalch equation, and Scatchard equation. It is shown that dose and effect are interchangeable via defined parameters. This general equation for the single drug effect has been extended to the multiple drug effect equation for n drugs. These equations provide the theoretical basis for the combination index (CI)-isobologram equation that allows quantitative determination of drug interactions, where CI < 1, = 1, and > 1 indicate synergism, additive effect, and antagonism, respectively. Based on these algorithms, computer software has been developed to allow automated simulation of synergism and antagonism at all dose or effect levels. It displays the dose-effect curve, median-effect plot, combination index plot, isobologram, dose-reduction index plot, and polygonogram for in vitro or in vivo studies. This theoretical development, experimental design, and computerized data analysis have facilitated dose-effect analysis for single drug evaluation or carcinogen and radiation risk assessment, as well as for drug or other entity combinations in a vast field of disciplines of biomedical sciences. In this review, selected examples of applications are given, and step-by-step examples of experimental designs and real data analysis are also illustrated. The merging of the mass-action law principle with mathematical induction-deduction has been proven to be a unique and effective scientific method for general theory development. The median-effect principle and its mass-action law based computer software are gaining increased applications in biomedical sciences, from how to effectively evaluate a single compound or entity to how to beneficially use multiple drugs or modalities in combination therapies.

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.

Normalized cDNA libraries

DOEpatents

Soares, Marcelo B.; Efstratiadis, Argiris

1997-01-01

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form comprising: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3' noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to moderate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library.

Normalized cDNA libraries

DOEpatents

Soares, M.B.; Efstratiadis, A.

1997-06-10

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form comprising: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3{prime} noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to moderate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library. 4 figs.

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.

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

NASA Astrophysics Data System (ADS)

Binosi, Daniele; Papavassiliou, Joannis

2018-03-01

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

Probing static disorder in Arrhenius kinetics by single-molecule force spectroscopy.

PubMed

Kuo, Tzu-Ling; Garcia-Manyes, Sergi; Li, Jingyuan; Barel, Itay; Lu, Hui; Berne, Bruce J; Urbakh, Michael; Klafter, Joseph; Fernández, Julio M

2010-06-22

The widely used Arrhenius equation describes the kinetics of simple two-state reactions, with the implicit assumption of a single transition state with a well-defined activation energy barrier DeltaE, as the rate-limiting step. However, it has become increasingly clear that the saddle point of the free-energy surface in most reactions is populated by ensembles of conformations, leading to nonexponential kinetics. Here we present a theory that generalizes the Arrhenius equation to include static disorder of conformational degrees of freedom as a function of an external perturbation to fully account for a diverse set of transition states. The effect of a perturbation on static disorder is best examined at the single-molecule level. Here we use force-clamp spectroscopy to study the nonexponential kinetics of single ubiquitin proteins unfolding under force. We find that the measured variance in DeltaE shows both force-dependent and independent components, where the force-dependent component scales with F(2), in excellent agreement with our theory. Our study illustrates a novel adaptation of the classical Arrhenius equation that accounts for the microscopic origins of nonexponential kinetics, which are essential in understanding the rapidly growing body of single-molecule data.

A panning DLT procedure for three-dimensional videography.

PubMed

Yu, B; Koh, T J; Hay, J G

1993-06-01

The direct linear transformation (DLT) method [Abdel-Aziz and Karara, APS Symposium on Photogrammetry. American Society of Photogrammetry, Falls Church, VA (1971)] is widely used in biomechanics to obtain three-dimensional space coordinates from film and video records. This method has some major shortcomings when used to analyze events which take place over large areas. To overcome these shortcomings, a three-dimensional data collection method based on the DLT method, and making use of panning cameras, was developed. Several small single control volumes were combined to construct a large total control volume. For each single control volume, a regression equation (calibration equation) is developed to express each of the 11 DLT parameters as a function of camera orientation, so that the DLT parameters can then be estimated from arbitrary camera orientations. Once the DLT parameters are known for at least two cameras, and the associated two-dimensional film or video coordinates of the event are obtained, the desired three-dimensional space coordinates can be computed. In a laboratory test, five single control volumes (in a total control volume of 24.40 x 2.44 x 2.44 m3) were used to test the effect of the position of the single control volume on the accuracy of the computed three dimensional space coordinates. Linear and quadratic calibration equations were used to test the effect of the order of the equation on the accuracy of the computed three dimensional space coordinates. For four of the five single control volumes tested, the mean resultant errors associated with the use of the linear calibration equation were significantly larger than those associated with the use of the quadratic calibration equation. The position of the single control volume had no significant effect on the mean resultant errors in computed three dimensional coordinates when the quadratic calibration equation was used. Under the same data collection conditions, the mean resultant errors in the computed three dimensional coordinates associated with the panning and stationary DLT methods were 17 and 22 mm, respectively. The major advantages of the panning DLT method lie in the large image sizes obtained and in the ease with which the data can be collected. The method also has potential for use in a wide variety of contexts. The major shortcoming of the method is the large amount of digitizing necessary to calibrate the total control volume. Adaptations of the method to reduce the amount of digitizing required are being explored.

Estimating equations for glomerular filtration rate in the era of creatinine standardization: a systematic review.

PubMed

Earley, Amy; Miskulin, Dana; Lamb, Edmund J; Levey, Andrew S; Uhlig, Katrin

2012-06-05

Clinical laboratories are increasingly reporting estimated glomerular filtration rate (GFR) by using serum creatinine assays traceable to a standard reference material. To review the performance of GFR estimating equations to inform the selection of a single equation by laboratories and the interpretation of estimated GFR by clinicians. A systematic search of MEDLINE, without language restriction, between 1999 and 21 October 2011. Cross-sectional studies in adults that compared the performance of 2 or more creatinine-based GFR estimating equations with a reference GFR measurement. Eligible equations were derived or reexpressed and validated by using creatinine measurements traceable to the standard reference material. Reviewers extracted data on study population characteristics, measured GFR, creatinine assay, and equation performance. Eligible studies compared the MDRD (Modification of Diet in Renal Disease) Study and CKD-EPI (Chronic Kidney Disease Epidemiology Collaboration) equations or modifications thereof. In 12 studies in North America, Europe, and Australia, the CKD-EPI equation performed better at higher GFRs (approximately >60 mL/min per 1.73 m(2)) and the MDRD Study equation performed better at lower GFRs. In 5 of 8 studies in Asia and Africa, the equations were modified to improve their performance by adding a coefficient derived in the local population or removing a coefficient. Methods of GFR measurement and study populations were heterogeneous. Neither the CKD-EPI nor the MDRD Study equation is optimal for all populations and GFR ranges. Using a single equation for reporting requires a tradeoff to optimize performance at either higher or lower GFR ranges. A general practice and public health perspective favors the CKD-EPI equation. Kidney Disease: Improving Global Outcomes.

Imaging electrical conductivity, permeability, and/or permittivity contrasts using the Born Scattering Inversion (BSI)

NASA Astrophysics Data System (ADS)

Darrh, A.; Downs, C. M.; Poppeliers, C.

2017-12-01

Born Scattering Inversion (BSI) of electromagnetic (EM) data is a geophysical imaging methodology for mapping weak conductivity, permeability, and/or permittivity contrasts in the subsurface. The high computational cost of full waveform inversion is reduced by adopting the First Born Approximation for scattered EM fields. This linearizes the inverse problem in terms of Born scattering amplitudes for a set of effective EM body sources within a 3D imaging volume. Estimation of scatterer amplitudes is subsequently achieved by solving the normal equations. Our present BSI numerical experiments entail Fourier transforming real-valued synthetic EM data to the frequency-domain, and minimizing the L2 residual between complex-valued observed and predicted data. We are testing the ability of BSI to resolve simple scattering models. For our initial experiments, synthetic data are acquired by three-component (3C) electric field receivers distributed on a plane above a single point electric dipole within a homogeneous and isotropic wholespace. To suppress artifacts, candidate Born scatterer locations are confined to a volume beneath the receiver array. Also, we explore two different numerical linear algebra algorithms for solving the normal equations: Damped Least Squares (DLS), and Non-Negative Least Squares (NNLS). Results from NNLS accurately recover the source location only for a large dense 3C receiver array, but fail when the array is decimated, or is restricted to horizontal component data. Using all receiver stations and all components per station, NNLS results are relatively insensitive to a sub-sampled frequency spectrum, suggesting that coarse frequency-domain sampling may be adequate for good target resolution. Results from DLS are insensitive to diminishing array density, but contain spatially oscillatory structure. DLS-generated images are consistently centered at the known point source location, despite an abundance of surrounding structure.

Macroscopic response in active nonlinear photonic crystals.

PubMed

Alagappan, Gandhi; John, Sajeev; Li, Er Ping

2013-09-15

We derive macroscopic equations of motion for the slowly varying electric field amplitude in three-dimensional active nonlinear optical nanostructures. We show that the microscopic Maxwell equations and polarization dynamics can be simplified to a macroscopic one-dimensional problem in the direction of group velocity. For a three-level active material, we derive the steady-state equations for normal mode frequency, threshold pumping, nonlinear Bloch mode amplitude, and lasing in photonic crystals. Our analytical results accurately recapture the results of exact numerical methods.

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.

Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential

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

Iacob, Felix, E-mail: felix@physics.uvt.ro; Lute, Marina, E-mail: marina.lute@upt.ro

2015-12-15

We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.

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

Nonlinear Drift-Kinetic Equation in the Presence of a Circularly Polarized Wave

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E. N.; Six, N. Frank (Technical Monitor)

2002-01-01

Equations of the single particle motion and nonlinear kinetic equation for plasma in the presence of a circularly polarized wave of arbitrary frequency in the drift approximation are presented. The nonstationarity and inhomogeneity of the plasma-wave system are taken into account. The time dependent part of the ponderomotive force is discussed.

Applications of the Peng-Robinson Equation of State Using MATLAB[R

ERIC Educational Resources Information Center

Nasri, Zakia; Binous, Housam

2009-01-01

A single equation of state (EOS) such as the Peng-Robinson (PR) EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state, including estimation of pure component properties and computation of the vapor-liquid equilibrium (VLE) diagram for binary mixtures. We perform high-pressure…

Elastic light single-scattering spectroscopy for detection of dysplastic tissues

NASA Astrophysics Data System (ADS)

Canpolat, Murat; Denkçeken, Tuba; Akman, Ayşe.; Alpsoy, Erkan; Tuncer, Recai; Akyüz, Mahmut; Baykara, Mehmet; Yücel, Selçuk; Başsorgun, Ibrahim; ćiftçioǧlu, M. Akif; Gökhan, Güzide Ayşe.; Gürer, ElifInanç; Peştereli, Elif; Karaveli, Šeyda

2013-11-01

Elastic light single-scattering spectroscopy (ELSSS) system has been developed and tested in diagnosis of cancerous tissues of different organs. ELSSS system consists of a miniature visible light spectrometer, a single fiber optical probe, a halogen tungsten light source and a laptop. Measurements were performed on excised brain, skin, cervix and prostate tumor specimens and surrounding normal tissues. Single fiber optical probe with a core diameter of 100 μm was used to deliver white light to and from tissue. Single optical fiber probe mostly detects singly scattered light from tissue rather than diffused light. Therefore, measured spectra are sensitive to size of scatters in tissue such as cells, nuclei, mitochondria and other organelles of cells. Usually, nuclei of tumor cells are larger than nuclei of normal cells. Therefore, spectrum of singly scattered light of tumor tissue is different than normal tissue. The spectral slopes were shown to be positive for normal brain, skin and prostate and cervix tissues and negative for the tumors of the same tissues. Signs of the spectral slopes were used as a discrimination parameter to differentiate tumor from normal tissues for the three organ tissues. Sensitivity and specificity of the system in differentiation between tumors from normal tissues were 93% and %100 for brain, 87% and 85% for skin, 93.7% and 46.1% for cervix and 98% and 100% for prostate.

STEADY STATE FLAMMABLE GAS RELEASE RATE CALCULATION AND LOWER FLAMMABILITY LEVEL EVALUATION FOR HANFORD TANK WASTE

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

HU TA

2009-10-26

Assess the steady-state flammability level at normal and off-normal ventilation conditions. The hydrogen generation rate was calculated for 177 tanks using the rate equation model. Flammability calculations based on hydrogen, ammonia, and methane were performed for 177 tanks for various scenarios.

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…

Real time quantitative phase microscopy based on single-shot transport of intensity equation (ssTIE) method

NASA Astrophysics Data System (ADS)

Yu, Wei; Tian, Xiaolin; He, Xiaoliang; Song, Xiaojun; Xue, Liang; Liu, Cheng; Wang, Shouyu

2016-08-01

Microscopy based on transport of intensity equation provides quantitative phase distributions which opens another perspective for cellular observations. However, it requires multi-focal image capturing while mechanical and electrical scanning limits its real time capacity in sample detections. Here, in order to break through this restriction, real time quantitative phase microscopy based on single-shot transport of the intensity equation method is proposed. A programmed phase mask is designed to realize simultaneous multi-focal image recording without any scanning; thus, phase distributions can be quantitatively retrieved in real time. It is believed the proposed method can be potentially applied in various biological and medical applications, especially for live cell imaging.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

The application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems is discussed. The methods consist of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line-, or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to that of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

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…

A sharp interface model for void growth in irradiated materials

NASA Astrophysics Data System (ADS)

Hochrainer, Thomas; El-Azab, Anter

2015-03-01

A thermodynamic formalism for the interaction of point defects with free surfaces in single-component solids has been developed and applied to the problem of void growth by absorption of point defects in irradiated metals. This formalism consists of two parts, a detailed description of the dynamics of defects within the non-equilibrium thermodynamic frame, and the application of the second law of thermodynamics to provide closure relations for all kinetic equations. Enforcing the principle of non-negative entropy production showed that the description of the problem of void evolution under irradiation must include a relationship between the normal fluxes of defects into the void surface and the driving thermodynamic forces for the void surface motion; these thermodynamic forces are identified for both vacancies and interstitials and the relationships between these forces and the normal point defect fluxes are established using the concepts of transition state theory. The latter theory implies that the defect accommodation into the surface is a thermally activated process. Numerical examples are given to illustrate void growth dynamics in this new formalism and to investigate the effect of the surface energy barriers on void growth. Consequences for phase field models of void growth are discussed.

Experimental investigation of turbulent flow through a circular-to-rectangular transition duct. Ph.D. Thesis - Washington Univ.

NASA Technical Reports Server (NTRS)

Davis, David O.

1991-01-01

Steady, incompressible, turbulent, swirl-free flow through a circular-to-rectangular transition duck was studied experimentally. The cross-sectional area remains the same at the exit as at the inlet, but varies through the transition section to a maximum value approximately 15 percent above the inlet value. The cross-sectional geometry everywhere along the duct is defined by the equation of a superellipse. Mean and turbulence data were accumulated utilizing pressure and hot-wire instrumentation at five stations along the test section. Data are presented for operating bulk Reynolds numbers of 88,000 and 390,000. Measured quantities include total and static pressure, the three components of the mean velocity vector, and the six components of the Reynolds stress tensor. In addition to the transition duct measurements, a hot-wire technique which relies on the sequential use of single rotatable normal and slant-wire probes was proposed. The technique is applicable for measurement of the total mean velocity vector and the complete Reynolds stress tensor when the primary flow is arbitrarily skewed relative to a plane which lies normal to the probe axis of rotation.

Streamwise Vorticity Generation in Laminar and Turbulent Jets

NASA Technical Reports Server (NTRS)

Demuren, Aodeji O.; Wilson, Robert V.

1999-01-01

Complex streamwise vorticity fields are observed in the evolution of non-circular jets. Generation mechanisms are investigated via Reynolds-averaged (RANS), large-eddy (LES) and direct numerical (DNS) simulations of laminar and turbulent rectangular jets. Complex vortex interactions are found in DNS of laminar jets, but axis-switching is observed only when a single instability mode is present in the incoming mixing layer. With several modes present, the structures are not coherent and no axis-switching occurs, RANS computations also produce no axis-switching. On the other hand, LES of high Reynolds number turbulent jets produce axis-switching even for cases with several instability modes in the mixing layer. Analysis of the source terms of the mean streamwise vorticity equation through post-processing of the instantaneous results shows that, complex interactions of gradients of the normal and shear Reynolds stresses are responsible for the generation of streamwise vorticity which leads to axis-switching. RANS computations confirm these results. k - epsilon turbulence model computations fail to reproduce the phenomenon, whereas algebraic Reynolds stress model (ASM) computations, in which the secondary normal and shear stresses are computed explicitly, succeeded in reproducing the phenomenon accurately.

The effect of viscoelasticity on the stability of a pulmonary airway liquid layer

NASA Astrophysics Data System (ADS)

Halpern, David; Fujioka, Hideki; Grotberg, James B.

2010-01-01

The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer, which may cause the lung's airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid, which is modeled using the Oldroyd-B constitutive equation or as a Jeffreys fluid. To examine the role of mucus alone, a single layer of a viscoelastic fluid is considered. A system of nonlinear evolution equations is derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate g for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Closure occurs if the minimum core radius, Rmin(t), reaches zero within one breath. Solutions of the nonlinear evolution equations reveal that Rmin normally decreases to zero faster with increasing relaxation time parameter, the Weissenberg number We. For small values of the dimensionless film thickness parameter ɛ, the closure time, tc, increases slightly with We, while for moderate values of ɛ, ranging from 14% to 18% of the tube radius, tc decreases rapidly with We provided the solvent viscosity is sufficiently small. Viscoelasticity was found to have little effect for ɛ >0.18, indicating the strong influence of surface tension. The film thickness parameter ɛ and the Weissenberg number We also have a significant effect on the maximum shear stress on tube wall, max(τw), and thus, potentially, an impact on cell damage. Max(τw) increases with ɛ for fixed We, and it decreases with increasing We for small We provided the solvent viscosity parameter is sufficiently small. For large ɛ ≈0.2, there is no significant difference between the Newtonian flow case and the large We cases.

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

Double-exponential decay of orientational correlations in semiflexible polyelectrolytes.

PubMed

Bačová, P; Košovan, P; Uhlík, F; Kuldová, J; Limpouchová, Z; Procházka, K

2012-06-01

In this paper we revisited the problem of persistence length of polyelectrolytes. We performed a series of Molecular Dynamics simulations using the Debye-Hückel approximation for electrostatics to test several equations which go beyond the classical description of Odijk, Skolnick and Fixman (OSF). The data confirm earlier observations that in the limit of large contour separations the decay of orientational correlations can be described by a single-exponential function and the decay length can be described by the OSF relation. However, at short countour separations the behaviour is more complex. Recent equations which introduce more complicated expressions and an additional length scale could describe the results very well on both the short and the long length scale. The equation of Manghi and Netz when used without adjustable parameters could capture the qualitative trend but deviated in a quantitative comparison. Better quantitative agreement within the estimated error could be obtained using three equations with one adjustable parameter: 1) the equation of Manghi and Netz; 2) the equation proposed by us in this paper; 3) the equation proposed by Cannavacciuolo and Pedersen. Two characteristic length scales can be identified in the data: the intrinsic or bare persistence length and the electrostatic persistence length. All three equations use a single parameter to describe a smooth crossover from the short-range behaviour dominated by the intrinsic stiffness of the chain to the long-range OSF-like behaviour.

Method for construction of normalized cDNA libraries

DOEpatents

Soares, Marcelo B.; Efstratiadis, Argiris

1996-01-01

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form comprising: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3' noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to moderate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library.

Method for construction of normalized cDNA libraries

DOEpatents

Soares, M.B.; Efstratiadis, A.

1996-01-09

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form. The method comprises: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3` noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to moderate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library. 4 figs.

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.

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.

Divergent series and memory of the initial condition in the long-time solution of some anomalous diffusion problems.

PubMed

Yuste, S Bravo; Borrego, R; Abad, E

2010-02-01

We consider various anomalous d -dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry. The motion of particles is described by a fractional diffusion equation. Their mean-square displacement is given by r(2) proportional, variant t(gamma)(00 , the emergence of such series in the long-time domain is a specific feature of subdiffusion problems. We present a method to regularize such series, and, in some cases, validate the procedure by using alternative techniques (Laplace transform method and numerical simulations). In the normal diffusion case, we find that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single (the main) decay mode in the long-time regime. In remarkable contrast, long-time memory of the initial condition is present in the subdiffusive case as the spatial part Psi1(r) describing the long-time decay of the solution to the steady state is determined by a weighted superposition of all spatial modes characteristic of the normal diffusion problem, the weight being dependent on the initial condition. Interestingly, Psi1(r) turns out to be independent of the anomalous diffusion exponent gamma .

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size.

PubMed

Schwalger, Tilo; Deger, Moritz; Gerstner, Wulfram

2017-04-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

Effect of Morphologic Features of Neurons on the Extracellular Electric Potential: A Simulation Study Using Cable Theory and Electro-Quasi-Static Equations.

PubMed

Bestel, R; Appali, R; van Rienen, U; Thielemann, C

2017-11-01

Microelectrode arrays serve as an indispensable tool in electro-physiological research to study the electrical activity of neural cells, enabling measurements of single cell as well as network communication analysis. Recent experimental studies have reported that the neuronal geometry has an influence on electrical signaling and extracellular recordings. However, the corresponding mechanisms are not yet fully understood and require further investigation. Allowing systematic parameter studies, computational modeling provides the opportunity to examine the underlying effects that influence extracellular potentials. In this letter, we present an in silico single cell model to analyze the effect of geometrical variability on the extracellular electric potentials. We describe finite element models of a single neuron with varying geometric complexity in three-dimensional space. The electric potential generation of the neuron is modeled using Hodgkin-Huxley equations. The signal propagation is described with electro-quasi-static equations, and results are compared with corresponding cable equation descriptions. Our results show that both the geometric dimensions and the distribution of ion channels of a neuron are critical factors that significantly influence both the amplitude and shape of extracellular potentials.

Predictive equations for the estimation of body size in seals and sea lions (Carnivora: Pinnipedia)

PubMed Central

Churchill, Morgan; Clementz, Mark T; Kohno, Naoki

2014-01-01

Body size plays an important role in pinniped ecology and life history. However, body size data is often absent for historical, archaeological, and fossil specimens. To estimate the body size of pinnipeds (seals, sea lions, and walruses) for today and the past, we used 14 commonly preserved cranial measurements to develop sets of single variable and multivariate predictive equations for pinniped body mass and total length. Principal components analysis (PCA) was used to test whether separate family specific regressions were more appropriate than single predictive equations for Pinnipedia. The influence of phylogeny was tested with phylogenetic independent contrasts (PIC). The accuracy of these regressions was then assessed using a combination of coefficient of determination, percent prediction error, and standard error of estimation. Three different methods of multivariate analysis were examined: bidirectional stepwise model selection using Akaike information criteria; all-subsets model selection using Bayesian information criteria (BIC); and partial least squares regression. The PCA showed clear discrimination between Otariidae (fur seals and sea lions) and Phocidae (earless seals) for the 14 measurements, indicating the need for family-specific regression equations. The PIC analysis found that phylogeny had a minor influence on relationship between morphological variables and body size. The regressions for total length were more accurate than those for body mass, and equations specific to Otariidae were more accurate than those for Phocidae. Of the three multivariate methods, the all-subsets approach required the fewest number of variables to estimate body size accurately. We then used the single variable predictive equations and the all-subsets approach to estimate the body size of two recently extinct pinniped taxa, the Caribbean monk seal (Monachus tropicalis) and the Japanese sea lion (Zalophus japonicus). Body size estimates using single variable regressions generally under or over-estimated body size; however, the all-subset regression produced body size estimates that were close to historically recorded body length for these two species. This indicates that the all-subset regression equations developed in this study can estimate body size accurately. PMID:24916814

Flood-frequency prediction methods for unregulated streams of Tennessee, 2000

USGS Publications Warehouse

Law, George S.; Tasker, Gary D.

2003-01-01

Up-to-date flood-frequency prediction methods for unregulated, ungaged rivers and streams of Tennessee have been developed. Prediction methods include the regional-regression method and the newer region-of-influence method. The prediction methods were developed using stream-gage records from unregulated streams draining basins having from 1 percent to about 30 percent total impervious area. These methods, however, should not be used in heavily developed or storm-sewered basins with impervious areas greater than 10 percent. The methods can be used to estimate 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence-interval floods of most unregulated rural streams in Tennessee. A computer application was developed that automates the calculation of flood frequency for unregulated, ungaged rivers and streams of Tennessee. Regional-regression equations were derived by using both single-variable and multivariable regional-regression analysis. Contributing drainage area is the explanatory variable used in the single-variable equations. Contributing drainage area, main-channel slope, and a climate factor are the explanatory variables used in the multivariable equations. Deleted-residual standard error for the single-variable equations ranged from 32 to 65 percent. Deleted-residual standard error for the multivariable equations ranged from 31 to 63 percent. These equations are included in the computer application to allow easy comparison of results produced by the different methods. The region-of-influence method calculates multivariable regression equations for each ungaged site and recurrence interval using basin characteristics from 60 similar sites selected from the study area. Explanatory variables that may be used in regression equations computed by the region-of-influence method include contributing drainage area, main-channel slope, a climate factor, and a physiographic-region factor. Deleted-residual standard error for the region-of-influence method tended to be only slightly smaller than those for the regional-regression method and ranged from 27 to 62 percent.

A single-molecule force spectroscopy study of the interactions between lectins and carbohydrates on cancer and normal cells

NASA Astrophysics Data System (ADS)

Zhao, Weidong; Cai, Mingjun; Xu, Haijiao; Jiang, Junguang; Wang, Hongda

2013-03-01

The interaction forces between carbohydrates and lectins were investigated by single-molecule force spectroscopy on both cancer and normal cells. The binding kinetics was also studied, which shows that the carbohydrate-lectin complex on cancer cells is less stable than that on normal cells.The interaction forces between carbohydrates and lectins were investigated by single-molecule force spectroscopy on both cancer and normal cells. The binding kinetics was also studied, which shows that the carbohydrate-lectin complex on cancer cells is less stable than that on normal cells. Electronic supplementary information (ESI) available: Experimental details. See DOI: 10.1039/c3nr00553d

Analysis of Flow Behavior of an Nb-Ti Microalloyed Steel During Hot Deformation

NASA Astrophysics Data System (ADS)

Mohebbi, Mohammad Sadegh; Parsa, Mohammad Habibi; Rezayat, Mohammad; Orovčík, L'ubomír

2018-03-01

The hot flow behavior of an Nb-Ti microalloyed steel is investigated through hot compression test at various strain rates and temperatures. By the combination of dynamic recovery (DRV) and dynamic recrystallization (DRX) models, a phenomenological constitutive model is developed to derive the flow stress. The predefined activation energy of Q = 270 kJ/mol and the exponent of n = 5 are successfully set to derive critical stress at the onset of DRX and saturation stress of DRV as functions of the Zener-Hollomon parameter by the classical hyperbolic sine equation. The remaining parameters of the constitutive model are determined by fitting them to the experiments. Through substitution of a normalized strain in the DRV model and considering the interconnections between dependent parameters, a new model is developed. It is shown that, despite its fewer parameters, this model is in good agreement with the experiments. Accurate analyses of flow data along with microstructural analyses indicate that the dissolution of NbC precipitates and its consequent solid solution strengthening and retardation of DRX are responsible for the distinguished behaviors in the two temperature ranges between T < 1100 °C and T ≥ 1100 °C. Nevertheless, it is shown that a single constitutive equation can still be employed for the present steel in the whole tested temperature ranges.

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

Analysis of bonded joints. [shear stress and stress-strain diagrams

NASA Technical Reports Server (NTRS)

Srinivas, S.

1975-01-01

A refined elastic analysis of bonded joints which accounts for transverse shear deformation and transverse normal stress was developed to obtain the stresses and displacements in the adherends and in the bond. The displacements were expanded in terms of polynomials in the thicknesswise coordinate; the coefficients of these polynomials were functions of the axial coordinate. The stress distribution was obtained in terms of these coefficients by using strain-displacement and stress-strain relations. The governing differential equations were obtained by integrating the equations of equilibrium, and were solved. The boundary conditions (interface or support) were satisfied to complete the analysis. Single-lap, flush, and double-lap joints were analyzed, along with the effects of adhesive properties, plate thicknesses, material properties, and plate taper on maximum peel and shear stresses in the bond. The results obtained by using the thin-beam analysis available in the literature were compared with the results obtained by using the refined analysis. In general, thin-beam analysis yielded reasonably accurate results, but in certain cases the errors were high. Numerical investigations showed that the maximum peel and shear stresses in the bond can be reduced by (1) using a combination of flexible and stiff bonds, (2) using stiffer lap plates, and (3) tapering the plates.

Development of a human eye model incorporated with intraocular scattering for visual performance assessment

NASA Astrophysics Data System (ADS)

Chen, Yi-Chun; Jiang, Chong-Jhih; Yang, Tsung-Hsun; Sun, Ching-Cherng

2012-07-01

A biometry-based human eye model was developed by using the empirical anatomic and optical data of ocular parameters. The gradient refractive index of the crystalline lens was modeled by concentric conicoid isoindical surfaces and was adaptive to accommodation and age. The chromatic dispersion of ocular media was described by Cauchy equations. The intraocular scattering model was composed of volumetric Mie scattering in the cornea and the crystalline lens, and a diffusive-surface model at the retina fundus. The retina was regarded as a Lambertian surface and was assigned its corresponding reflectance at each wavelength. The optical performance of the eye model was evaluated in CodeV and ASAP and presented by the modulation transfer functions at single and multiple wavelengths. The chromatic optical powers obtained from this model resembled that of the average physiological eyes. The scattering property was assessed by means of glare veiling luminance and compared with the CIE general disability glare equation. By replacing the transparent lens with a cataractous lens, the disability glare curve of cataracts was generated to compare with the normal disability glare curve. This model has high potential for investigating visual performance in ordinary lighting and display conditions and under the influence of glare sources.

Silicon Nitride Equation of State

NASA Astrophysics Data System (ADS)

Swaminathan, Pazhayannur; Brown, Robert

2015-06-01

This report presents the development a global, multi-phase equation of state (EOS) for the ceramic silicon nitride (Si3N4) . Structural forms include amorphous silicon nitride normally used as a thin film and three crystalline polymorphs. Crystalline phases include hexagonal α-Si3N4, hexagonalβ-Si3N4, and the cubic spinel c-Si3N4. Decomposition at about 1900 °C results in a liquid silicon phase and gas phase products such as molecular nitrogen, atomic nitrogen, and atomic silicon. The silicon nitride EOS was developed using EOSPro which is a new and extended version of the PANDA II code. Both codes are valuable tools and have been used successfully for a variety of material classes. Both PANDA II and EOSPro can generate a tabular EOS that can be used in conjunction with hydrocodes. The paper describes the development efforts for the component solid phases and presents results obtained using the EOSPro phase transition model to investigate the solid-solid phase transitions in relation to the available shock data. Furthermore, the EOSPro mixture model is used to develop a model for the decomposition products and then combined with the single component solid models to study the global phase diagram. Sponsored by the NASA Goddard Space Flight Center Living With a Star program office.

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

Spectral enstrophy budget in a shear-less flow with turbulent/non-turbulent interface

NASA Astrophysics Data System (ADS)

Cimarelli, Andrea; Cocconi, Giacomo; Frohnapfel, Bettina; De Angelis, Elisabetta

2015-12-01

A numerical analysis of the interaction between decaying shear free turbulence and quiescent fluid is performed by means of global statistical budgets of enstrophy, both, at the single-point and two point levels. The single-point enstrophy budget allows us to recognize three physically relevant layers: a bulk turbulent region, an inhomogeneous turbulent layer, and an interfacial layer. Within these layers, enstrophy is produced, transferred, and finally destroyed while leading to a propagation of the turbulent front. These processes do not only depend on the position in the flow field but are also strongly scale dependent. In order to tackle this multi-dimensional behaviour of enstrophy in the space of scales and in physical space, we analyse the spectral enstrophy budget equation. The picture consists of an inviscid spatial cascade of enstrophy from large to small scales parallel to the interface moving towards the interface. At the interface, this phenomenon breaks, leaving place to an anisotropic cascade where large scale structures exhibit only a cascade process normal to the interface thus reducing their thickness while retaining their lengths parallel to the interface. The observed behaviour could be relevant for both the theoretical and the modelling approaches to flow with interacting turbulent/nonturbulent regions. The scale properties of the turbulent propagation mechanisms highlight that the inviscid turbulent transport is a large-scale phenomenon. On the contrary, the viscous diffusion, commonly associated with small scale mechanisms, highlights a much richer physics involving small lengths, normal to the interface, but at the same time large scales, parallel to the interface.

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.

Equivalent-Groups versus Single-Group Equating Designs for the Accelerated CAT-ASVAB (Computerized Adaptive Test-Armed Services Vocational Aptitude Battery) Project.

DTIC Science & Technology

1987-01-01

DESIGNS FOR THE ACCELERATED CAT -ASVAB * PROJECT Peter H. Stoloff DTIC’- , " SELECTE -NOV 2 3 987 A Division of Hudson Institute CENTER FOR NAVAL ANALYSES...65153M C0031 SI TITLE (Include Security Classification) Equivalent-Groups Versus Single-Group Equating Designs For The Accelerated CAT -ASVAB Project...GROUP ACAP (Accelerated CAT -ASVAB Program), Aptitude tests, ASVAB (Armed 05 10 Services Vocational Aptitude Battery), CAT (Computerized Adaptive Test

Design of energy-storage reactors for single-winding constant-frequency dc-to-dc converters operating in the discontinuous-reactor-current mode

NASA Technical Reports Server (NTRS)

Chen, D. Y.; Owen, H. A., Jr.; Wilson, T. G.

1980-01-01

This paper presents an algorithm and equations for designing the energy-storage reactor for dc-to-dc converters which are constrained to operate in the discontinuous-reactor-current mode. This design procedure applied to the three widely used single-winding configurations: the voltage step-up, the current step-up, and the voltage-or-current step-up converters. A numerical design example is given to illustrate the use of the design algorithm and design equations.

Response of an oscillatory differential delay equation to a single stimulus.

PubMed

Mackey, Michael C; Tyran-Kamińska, Marta; Walther, Hans-Otto

2017-04-01

Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are able to completely characterize the perturbed response to a pulse of positive amplitude and duration with onset at different points in the limit cycle. We determine the perturbed minima and maxima and period of the limit cycle and show how the pulse modifies these from the unperturbed case.

The effect of air flow, panel curvature, and internal pressurization on field-incidence transmission loss. [acoustic propagation through aircraft fuselage

NASA Technical Reports Server (NTRS)

Koval, L. R.

1975-01-01

In the context of sound transmission through aircraft fuselage panels, equations for the field-incidence transmission loss (TL) of a single-walled panel are derived that include the effects of external air flow, panel curvature, and internal fuselage pressurization. These effects are incorporated into the classical equations for the TL of single panels, and the resulting double integral for field-incidence TL is numerically evaluated for a specific set of parameters.

Research in millimeter wave techniques

NASA Technical Reports Server (NTRS)

Mcmillan, R. W.

1977-01-01

The following is investigated; (1) the design of a 183 GHz single ended fundamental mixer to serve as a back up mixer to the subharmonic mixer for airborne applications, (2) attainment of 6 db single sideband conversion loss with the 6 GHz subharmonic mixer model, together with initial tests to determine the feasibility of pumping the mixer at w sub s/4, (3) additional ground based radiometric measurements, and (4) derivation of equations for power transmission of wire grid interferometers, and initial tests to verify these equations.

Absolute Hugoniot measurements from a spherically convergent shock using x-ray radiography

NASA Astrophysics Data System (ADS)

Swift, Damian C.; Kritcher, Andrea L.; Hawreliak, James A.; Lazicki, Amy; MacPhee, Andrew; Bachmann, Benjamin; Döppner, Tilo; Nilsen, Joseph; Collins, Gilbert W.; Glenzer, Siegfried; Rothman, Stephen D.; Kraus, Dominik; Falcone, Roger W.

2018-05-01

The canonical high pressure equation of state measurement is to induce a shock wave in the sample material and measure two mechanical properties of the shocked material or shock wave. For accurate measurements, the experiment is normally designed to generate a planar shock which is as steady as possible in space and time, and a single state is measured. A converging shock strengthens as it propagates, so a range of shock pressures is induced in a single experiment. However, equation of state measurements must then account for spatial and temporal gradients. We have used x-ray radiography of spherically converging shocks to determine states along the shock Hugoniot. The radius-time history of the shock, and thus its speed, was measured by radiographing the position of the shock front as a function of time using an x-ray streak camera. The density profile of the shock was then inferred from the x-ray transmission at each instant of time. Simultaneous measurement of the density at the shock front and the shock speed determines an absolute mechanical Hugoniot state. The density profile was reconstructed using the known, unshocked density which strongly constrains the density jump at the shock front. The radiographic configuration and streak camera behavior were treated in detail to reduce systematic errors. Measurements were performed on the Omega and National Ignition Facility lasers, using a hohlraum to induce a spatially uniform drive over the outside of a solid, spherical sample and a laser-heated thermal plasma as an x-ray source for radiography. Absolute shock Hugoniot measurements were demonstrated for carbon-containing samples of different composition and initial density, up to temperatures at which K-shell ionization reduced the opacity behind the shock. Here we present the experimental method using measurements of polystyrene as an example.

Efficient and simpler method to construct normalized cDNA libraries with improved representations of full-length cDNAs

DOEpatents

Soares, Marcelo Bento; Bonaldo, Maria de Fatima

1998-01-01

This invention provides a method to normalize a cDNA library comprising: (a) constructing a directionally cloned library containing cDNA inserts wherein the insert is capable of being amplified by polymerase chain reaction; (b) converting a double-stranded cDNA library into single-stranded DNA circles; (c) generating single-stranded nucleic acid molecules complementary to the single-stranded DNA circles converted in step (b) by polymerase chain reaction with appropriate primers; (d) hybridizing the single-stranded DNA circles converted in step (b) with the complementary single-stranded nucleic acid molecules generated in step (c) to produce partial duplexes to an appropriate Cot; and (e) separating the unhybridized single-stranded DNA circles from the hybridized DNA circles, thereby generating a normalized cDNA library. This invention also provides a method to normalize a cDNA library wherein the generating of single-stranded nucleic acid molecules complementary to the single-stranded DNA circles converted in step (b) is by excising cDNA inserts from the double-stranded cDNA library; purifying the cDNA inserts from cloning vectors; and digesting the cDNA inserts with an exonuclease. This invention further provides a method to construct a subtractive cDNA library following the steps described above. This invention further provides normalized and/or subtractive cDNA libraries generated by the above methods.

Efficient and simpler method to construct normalized cDNA libraries with improved representations of full-length cDNAs

DOEpatents

Soares, M.B.; Fatima Bonaldo, M. de

1998-12-08

This invention provides a method to normalize a cDNA library comprising: (a) constructing a directionally cloned library containing cDNA inserts wherein the insert is capable of being amplified by polymerase chain reaction; (b) converting a double-stranded cDNA library into single-stranded DNA circles; (c) generating single-stranded nucleic acid molecules complementary to the single-stranded DNA circles converted in step (b) by polymerase chain reaction with appropriate primers; (d) hybridizing the single-stranded DNA circles converted in step (b) with the complementary single-stranded nucleic acid molecules generated in step (c) to produce partial duplexes to an appropriate Cot; and (e) separating the unhybridized single-stranded DNA circles from the hybridized DNA circles, thereby generating a normalized cDNA library. This invention also provides a method to normalize a cDNA library wherein the generating of single-stranded nucleic acid molecules complementary to the single-stranded DNA circles converted in step (b) is by excising cDNA inserts from the double-stranded cDNA library; purifying the cDNA inserts from cloning vectors; and digesting the cDNA inserts with an exonuclease. This invention further provides a method to construct a subtractive cDNA library following the steps described above. This invention further provides normalized and/or subtractive cDNA libraries generated by the above methods. 25 figs.

The Rangeland Hydrology and Erosion Model

NASA Astrophysics Data System (ADS)

Nearing, M. A.

2016-12-01

The Rangeland Hydrology and Erosion Model (RHEM) is a process-based model that was designed to address rangelands conditions. RHEM is designed for government agencies, land managers and conservationists who need sound, science-based technology to model, assess, and predict runoff and erosion rates on rangelands and to assist in evaluating rangeland conservation practices effects. RHEM is an event-based model that estimates runoff, erosion, and sediment delivery rates and volumes at the spatial scale of the hillslope and the temporal scale of as single rainfall event. It represents erosion processes under normal and fire-impacted rangeland conditions. Moreover, it adopts a new splash erosion and thin sheet-flow transport equation developed from rangeland data, and it links the model hydrologic and erosion parameters with rangeland plant community by providing a new system of parameter estimation equations based on 204 plots at 49 rangeland sites distributed across 15 western U.S. states. A dynamic partial differential sediment continuity equation is used to model the total detachment rate of concentrated flow and rain splash and sheet flow. RHEM is also designed to be used as a calculator, or "engine", within other watershed scale models. From the research perspective RHEM acts as a vehicle for incorporating new scientific findings from rangeland infiltration, runoff, and erosion studies. Current applications of the model include: 1) a web site for general use (conservation planning, research, etc.), 2) National Resource Inventory reports to Congress, 3) as a computational engine within watershed scale models (e.g., KINEROS, HEC), 4) Ecological Site & State and Transition Descriptions, 5) proposed in 2015 to become part of the NRCS Desktop applications for field offices.

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.

Quantum model of a hysteresis in a single-domain magnetically soft ferromagnetic

NASA Astrophysics Data System (ADS)

Ignatiev, V. K.; Lebedev, N. G.; Orlov, A. A.

2018-01-01

A quantum model of a single-domain magnetically soft ferromagnetic is proposed. The α-Fe crystal in a state of the saturation magnetization and a variable magnetic field is considered as a sample. The method of an effective Hamiltonian, including the operators of the Zeeman energy, the spin-orbit interaction and the interaction with the crystal field, is used in the model. An expansion of trial single-electron wave function in a series in small parameter of the spin-orbit interaction is suggested to account for the magnetic anisotropy. Within the framework of the Heisenberg representation, the nonlinear equations of motion for the magnetization and the orbital moment of single domain are obtained. Parameters of the modelling Hamiltonian are found from a comparison with experimental data on the magnetic anisotropy of iron. A phenomenological term of the magnetic friction is introduced into equation of the magnetization motion. Nonlinear equations are solved numerically by the Runge-Kutta method. A dependence of the single domain magnetization on magnetic field intensity has a characteristic form of a hysteresis loop which parameters are quantitatively coordinated with experimental data of researches of magnetic properties of nanoparticles of iron and iron oxide. The method is extended for modelling the magnetization dynamics of multi-domain ferromagnetic in the approximation of a strong crystal field.

The origin of the moon and the single-impact hypothesis. I

NASA Technical Reports Server (NTRS)

Benz, W.; Slattery, W. L.; Cameron, A. G. W.

1986-01-01

One of the newer ideas regarding the origin of the moon is concerned with a single-impact hypothesis. It is pointed out that this theory has the advantage of overcoming most of the difficulties with the classical theories. The angular momentum of the earth-moon system can easily be obtained by varying the initial conditions of the impact. A series of three-dimensional numerical simulations of the collision between the earth and an object of about 1/10 its mass is presented. Different impact velocities, impact parameters, and initial internal energies are considered. Attention is given to assumptions, the equation of state, numerical techniques utilizing the momentum equation and the energy conservation equation, tests, and initial conditions and units.

Analytical solutions for avalanche-breakdown voltages of single-diffused Gaussian junctions

NASA Astrophysics Data System (ADS)

Shenai, K.; Lin, H. C.

1983-03-01

Closed-form solutions of the potential difference between the two edges of the depletion layer of a single diffused Gaussian p-n junction are obtained by integrating Poisson's equation and equating the magnitudes of the positive and negative charges in the depletion layer. By using the closed form solution of the static Poisson's equation and Fulop's average ionization coefficient, the ionization integral in the depletion layer is computed, which yields the correct values of avalanche breakdown voltage, depletion layer thickness at breakdown, and the peak electric field as a function of junction depth. Newton's method is used for rapid convergence. A flowchart to perform the calculations with a programmable hand-held calculator, such as the TI-59, is shown.

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.

Stresses in adhesively bonded joints: A closed form solution. [plate theory

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.; Aydinoglu, M. N.

1980-01-01

The plane strain of adhesively bonded structures which consist of two different orthotropic adherents is considered. Assuming that the thicknesses of the adherends are constant and are small in relation to the lateral dimensions of the bonded region, the adherends are treated as plates. The transverse shear effects in the adherends and the in-plane normal strain in the adhesive are taken into account. The problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form. A single lap joint and a stiffened plate under various loading conditions are considered as examples. To verify the basic trend of the solutions obtained from the plate theory a sample problem is solved by using the finite element method and by treating the adherends and the adhesive as elastic continua. The plate theory not only predicts the correct trend for the adhesive stresses but also gives rather surprisingly accurate results.

Galapagos Islands taken by the STS-109 crew

NASA Image and Video Library

2002-03-10

STS109-718-102 (1-12 March 2002) --- The astronauts on board the Space Shuttle Columbia took this 70mm picture featuring the Galapagos Islands. For orientation purposes, north is towards the bottom of the view. Most of the largest island in the Galapagos group, Isla Isabela, stretches across the middle of the frame. The circular feature on this island at bottom is Volcano Wolf (1707 meters in altitude). Volcano Darwin (1280 meters in sea level) is the next volcano above and to the left, partly ringed with cloud. The single island top right is Isla Fernandina, the top of another volcano (1547 meters). Recent lava flows appear as darker surfaces and the older surfaces appear green, as a result of unusual rains and vegetational greening in this normally arid part of the world. The Equator passes exactly through Volcano Wolf, roughly left to right.

LQS_INVERSION v. 1.0

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

Weiss, Chester J

FORTRAN90 codes for inversion of electrostatic geophysical data in terms of three subsurface parameters in a single-well, oilfield environment: the linear charge density of the steel well casing (L), the point charge associated with an induced fracture filled with a conductive contrast agent (Q) and the location of said fracture (s). Theory is described in detail in Weiss et al. (Geophysics, 2016). Inversion strategy is to loop over candidate fracture locations, and at each one minimize the squared Cartesian norm of the data misfit to arrive at L and Q. Solution method is to construct the 2x2 linear system ofmore » normal equations and compute L and Q algebraically. Practical Application: Oilfield environments where observed electrostatic geophysical data can reasonably be assumed by a simple L-Q-s model. This may include hydrofracking operations, as postulated in Weiss et al. (2016), but no field validation examples have so far been provided.« less

Vectorial laws of refraction and reflection using the cross product and dot product.

PubMed

Tkaczyk, Eric R

2012-03-01

We demonstrate that published vectorial laws of reflection and refraction of light based solely on the cross product do not, in general, uniquely determine the direction of the reflected and refracted waves without additional information. This is because the cross product does not have a unique inverse operation, which is explained in this Letter in linear algebra terms. However, a vector is in fact uniquely determined if both the cross product (vector product) and dot product (scalar product) with a known vector are specified, which can be written as a single equation with a left-invertible matrix. It is thus possible to amend the vectorial laws of reflection and refraction to incorporate both the cross and dot products for a complete specification with unique solution. This enables highly efficient, unambiguous computation of reflected and refracted wave vectors from the incident wave and surface normal. © 2012 Optical Society of America

Regularizing the r-mode Problem for Nonbarotropic Relativistic Stars

NASA Technical Reports Server (NTRS)

Lockitch, Keith H.; Andersson, Nils; Watts, Anna L.

2004-01-01

We present results for r-modes of relativistic nonbarotropic stars. We show that the main differential equation, which is formally singular at lowest order in the slow-rotation expansion, can be regularized if one considers the initial value problem rather than the normal mode problem. However, a more physically motivated way to regularize the problem is to include higher order terms. This allows us to develop a practical approach for solving the problem and we provide results that support earlier conclusions obtained for uniform density stars. In particular, we show that there will exist a single r-mode for each permissible combination of 1 and m. We discuss these results and provide some caveats regarding their usefulness for estimates of gravitational-radiation reaction timescales. The close connection between the seemingly singular relativistic r-mode problem and issues arising because of the presence of co-rotation points in differentially rotating stars is also clarified.

Estimation of Geodetic and Geodynamical Parameters with VieVS

NASA Technical Reports Server (NTRS)

Spicakova, Hana; Bohm, Johannes; Bohm, Sigrid; Nilsson, tobias; Pany, Andrea; Plank, Lucia; Teke, Kamil; Schuh, Harald

2010-01-01

Since 2008 the VLBI group at the Institute of Geodesy and Geophysics at TU Vienna has focused on the development of a new VLBI data analysis software called VieVS (Vienna VLBI Software). One part of the program, currently under development, is a unit for parameter estimation in so-called global solutions, where the connection of the single sessions is done by stacking at the normal equation level. We can determine time independent geodynamical parameters such as Love and Shida numbers of the solid Earth tides. Apart from the estimation of the constant nominal values of Love and Shida numbers for the second degree of the tidal potential, it is possible to determine frequency dependent values in the diurnal band together with the resonance frequency of Free Core Nutation. In this paper we show first results obtained from the 24-hour IVS R1 and R4 sessions.

Nonlinear instability of half-solitons on star graphs

NASA Astrophysics Data System (ADS)

Kairzhan, Adilbek; Pelinovsky, Dmitry E.

2018-06-01

We consider a half-soliton stationary state of the nonlinear Schrödinger equation with the power nonlinearity on a star graph consisting of N edges and a single vertex. For the subcritical power nonlinearity, the half-soliton state is a degenerate critical point of the action functional under the mass constraint such that the second variation is nonnegative. By using normal forms, we prove that the degenerate critical point is a saddle point, for which the small perturbations to the half-soliton state grow slowly in time resulting in the nonlinear instability of the half-soliton state. The result holds for any N ≥ 3 and arbitrary subcritical power nonlinearity. It gives a precise dynamical characterization of the previous result of Adami et al. (2012) [2], where the half-soliton state was shown to be a saddle point of the action functional under the mass constraint for N = 3 and for cubic nonlinearity.

Taylor dispersion in two-dimensional bacterial turbulence

NASA Astrophysics Data System (ADS)

Huang, Yongxiang; Ou, Wenyu; Chen, Ming; Lu, Zhiming; Jiang, Nan; Liu, Yulu; Qiu, Xiang; Zhou, Quan

2017-05-01

In this work, single particle dispersion was analyzed for a bacterial turbulence by retrieving the virtual Lagrangian trajectory via numerical integration of the Lagrangian equation. High-order displacement functions were calculated for cases with and without mean velocity effect. The two-regime power-law behavior for short and long time evolutions was identified experimentally, which was separated by the Lagrangian integral time. For the case with the mean velocity effect, the experimental Hurst numbers were determined to be 0.94 and 0.97 for short and long time evolutions, respectively. For the case without the mean velocity effect, the values were 0.88 and 0.58. Moreover, very weak intermittency correction was detected. All measured Hurst numbers were above 1/2, the value of the normal diffusion, which verifies the super-diffusion behavior of living fluid. This behavior increases the efficiency of bacteria to obtain food.

Extension of the Viscous Collision Limiting Direct Simulation Monte Carlo Technique to Multiple Species

NASA Technical Reports Server (NTRS)

Liechty, Derek S.; Burt, Jonathan M.

2016-01-01

There are many flows fields that span a wide range of length scales where regions of both rarefied and continuum flow exist and neither direct simulation Monte Carlo (DSMC) nor computational fluid dynamics (CFD) provide the appropriate solution everywhere. Recently, a new viscous collision limited (VCL) DSMC technique was proposed to incorporate effects of physical diffusion into collision limiter calculations to make the low Knudsen number regime normally limited to CFD more tractable for an all-particle technique. This original work had been derived for a single species gas. The current work extends the VCL-DSMC technique to gases with multiple species. Similar derivations were performed to equate numerical and physical transport coefficients. However, a more rigorous treatment of determining the mixture viscosity is applied. In the original work, consideration was given to internal energy non-equilibrium, and this is also extended in the current work to chemical non-equilibrium.

Prediction of flyover jet noise spectra from static tests

NASA Astrophysics Data System (ADS)

Michel, U.; Michalke, A.

A scaling law for predicting the overall flyover noise of a single stream shock-free circular jet from static experiments is outlined. It is valid for isothermal and hot jets. It assumes that the jet flow and turbulence field are axially stretched in flight. Effects of the boundary layer within the nozzle and along the engine nacelle are neglected. The scaling laws for the power spectral density and spectra with constant relative bandwidth can be derived. In order to compare static and inflight directivities, the far field point relative to the source position must be denoted by the emission angle and the wave normal distance. From the solution of the convective Lighthill equation in a coordinate system fixed to the jet nozzle (wind tunnel case), the power spectral density of sound pressure at a given frequency is found. Predictions for Aerotrain compare well with measured values.

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

NASA Technical Reports Server (NTRS)

Soh, Woo Y.

1992-01-01

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

The Scaling Group of the 1-D Invisicid Euler Equations

NASA Astrophysics Data System (ADS)

Schmidt, Emma; Ramsey, Scott; Boyd, Zachary; Baty, Roy

2017-11-01

The one dimensional (1-D) compressible Euler equations in non-ideal media support scale invariant solutions under a variety of initial conditions. Famous scale invariant solutions include the Noh, Sedov, Guderley, and collapsing cavity hydrodynamic test problems. We unify many classical scale invariant solutions under a single scaling group analysis. The scaling symmetry group generator provides a framework for determining all scale invariant solutions emitted by the 1-D Euler equations for arbitrary geometry, initial conditions, and equation of state. We approach the Euler equations from a geometric standpoint, and conduct scaling analyses for a broad class of materials.

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.

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.

On the commutator of C^{\\infty}} -symmetries and the reduction of Euler-Lagrange equations

NASA Astrophysics Data System (ADS)

Ruiz, A.; Muriel, C.; Olver, P. J.

2018-04-01

A novel procedure to reduce by four the order of Euler-Lagrange equations associated to nth order variational problems involving single variable integrals is presented. In preparation, a new formula for the commutator of two \

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.

Coordinating Procedural and Conceptual Knowledge to Make Sense of Word Equations: Understanding the Complexity of a "Simple" Completion Task at the Learner's Resolution

ERIC Educational Resources Information Center

Taber, Keith S.; Bricheno, Pat

2009-01-01

The present paper discusses the conceptual demands of an apparently straightforward task set to secondary-level students--completing chemical word equations with a single omitted term. Chemical equations are of considerable importance in chemistry, and school students are expected to learn to be able to write and interpret them. However, it is…

Numerical simulation of the processes in the normal incidence tube for high acoustic pressure levels

NASA Astrophysics Data System (ADS)

Fedotov, E. S.; Khramtsov, I. V.; Kustov, O. Yu.

2016-10-01

Numerical simulation of the acoustic processes in an impedance tube at high levels of acoustic pressure is a way to solve a problem of noise suppressing by liners. These studies used liner specimen that is one cylindrical Helmholtz resonator. The evaluation of the real and imaginary parts of the liner acoustic impedance and sound absorption coefficient was performed for sound pressure levels of 130, 140 and 150 dB. The numerical simulation used experimental data having been obtained on the impedance tube with normal incidence waves. At the first stage of the numerical simulation it was used the linearized Navier-Stokes equations, which describe well the imaginary part of the liner impedance whatever the sound pressure level. These equations were solved by finite element method in COMSOL Multiphysics program in axisymmetric formulation. At the second stage, the complete Navier-Stokes equations were solved by direct numerical simulation in ANSYS CFX in axisymmetric formulation. As the result, the acceptable agreement between numerical simulation and experiment was obtained.

Elastic parabolic equation and normal mode solutions for seismo-acoustic propagation in underwater environments with ice covers.

PubMed

Collis, Jon M; Frank, Scott D; Metzler, Adam M; Preston, Kimberly S

2016-05-01

Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.

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.

Analytical and Numerical Results for an Adhesively Bonded Joint Subjected to Pure Bending

NASA Technical Reports Server (NTRS)

Smeltzer, Stanley S., III; Lundgren, Eric

2006-01-01

A one-dimensional, semi-analytical methodology that was previously developed for evaluating adhesively bonded joints composed of anisotropic adherends and adhesives that exhibit inelastic material behavior is further verified in the present paper. A summary of the first-order differential equations and applied joint loading used to determine the adhesive response from the methodology are also presented. The method was previously verified against a variety of single-lap joint configurations from the literature that subjected the joints to cases of axial tension and pure bending. Using the same joint configuration and applied bending load presented in a study by Yang, the finite element analysis software ABAQUS was used to further verify the semi-analytical method. Linear static ABAQUS results are presented for two models, one with a coarse and one with a fine element meshing, that were used to verify convergence of the finite element analyses. Close agreement between the finite element results and the semi-analytical methodology were determined for both the shear and normal stress responses of the adhesive bondline. Thus, the semi-analytical methodology was successfully verified using the ABAQUS finite element software and a single-lap joint configuration subjected to pure bending.

Modeling the Role of Dislocation Substructure During Class M and Exponential Creep. Revised

NASA Technical Reports Server (NTRS)

Raj, S. V.; Iskovitz, Ilana Seiden; Freed, A. D.

1995-01-01

The different substructures that form in the power-law and exponential creep regimes for single phase crystalline materials under various conditions of stress, temperature and strain are reviewed. The microstructure is correlated both qualitatively and quantitatively with power-law and exponential creep as well as with steady state and non-steady state deformation behavior. These observations suggest that creep is influenced by a complex interaction between several elements of the microstructure, such as dislocations, cells and subgrains. The stability of the creep substructure is examined in both of these creep regimes during stress and temperature change experiments. These observations are rationalized on the basis of a phenomenological model, where normal primary creep is interpreted as a series of constant structure exponential creep rate-stress relationships. The implications of this viewpoint on the magnitude of the stress exponent and steady state behavior are discussed. A theory is developed to predict the macroscopic creep behavior of a single phase material using quantitative microstructural data. In this technique the thermally activated deformation mechanisms proposed by dislocation physics are interlinked with a previously developed multiphase, three-dimensional. dislocation substructure creep model. This procedure leads to several coupled differential equations interrelating macroscopic creep plasticity with microstructural evolution.

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.

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.

A coupled cluster theory with iterative inclusion of triple excitations and associated equation of motion formulation for excitation energy and ionization potential

NASA Astrophysics Data System (ADS)

Maitra, Rahul; Akinaga, Yoshinobu; Nakajima, Takahito

2017-08-01

A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference.

Nonlinear Analysis of Bonded Composite Single-LAP Joints

NASA Technical Reports Server (NTRS)

Oterkus, E.; Barut, A.; Madenci, E.; Smeltzer, S. S.; Ambur, D. R.

2004-01-01

This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite single-lap joints with tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesive and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karman s nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layer between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress-strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, their in-plane and bending stiffness matrices are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. Comparisons are made with corresponding results obtained from finite-element analysis. The results confirm the validity of the solution method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesive, of a single-lap joint

Dependence of Impedance of Embedded Single Cells on Cellular Behaviour.

PubMed

Cho, Sungbo; Castellarnau, Marc; Samitier, Josep; Thielecke, Hagen

2008-02-21

Non-invasive single cell analyses are increasingly required for the medicaldiagnostics of test substances or the development of drugs and therapies on the single celllevel. For the non-invasive characterisation of cells, impedance spectroscopy whichprovides the frequency dependent electrical properties has been used. Recently,microfludic systems have been investigated to manipulate the single cells and tocharacterise the electrical properties of embedded cells. In this article, the impedance ofpartially embedded single cells dependent on the cellular behaviour was investigated byusing the microcapillary. An analytical equation was derived to relate the impedance ofembedded cells with respect to the morphological and physiological change ofextracellular interface. The capillary system with impedance measurement showed afeasibility to monitor the impedance change of embedded single cells caused bymorphological and physiological change of cell during the addition of DMSO. By fittingthe derived equation to the measured impedance of cell embedded at different negativepressure levels, it was able to extrapolate the equivalent gap and gap conductivity betweenthe cell and capillary wall representing the cellular behaviour.

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.

A crystallographic model for the tensile and fatigue response for Rene N4 at 982 C

NASA Technical Reports Server (NTRS)

Sheh, M. Y.; Stouffer, D. C.

1990-01-01

An anisotropic constitutive model based on crystallographic slip theory was formulated for nickel-base single-crystal superalloys. The current equations include both drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments have been conducted to evaluate the existence of back stress in single crystals. The results showed that the back stress effect of reverse inelastic flow on the unloading stress is orientation-dependent, and a back stress state variable in the inelastic flow equation is necessary for predicting inelastic behavior. Model correlations and predictions of experimental data are presented for the single crystal superalloy Rene N4 at 982 C.

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.

Linear stability analysis of the Vlasov-Poisson equations in high density plasmas in the presence of crossed fields and density gradients

NASA Technical Reports Server (NTRS)

Kaup, D. J.; Hansen, P. J.; Choudhury, S. Roy; Thomas, Gary E.

1986-01-01

The equations for the single-particle orbits in a nonneutral high density plasma in the presence of inhomogeneous crossed fields are obtained. Using these orbits, the linearized Vlasov equation is solved as an expansion in the orbital radii in the presence of inhomogeneities and density gradients. A model distribution function is introduced whose cold-fluid limit is exactly the same as that used in many previous studies of the cold-fluid equations. This model function is used to reduce the linearized Vlasov-Poisson equations to a second-order ordinary differential equation for the linearized electrostatic potential whose eigenvalue is the perturbation frequency.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

PubMed Central

Gerstner, Wulfram

2017-01-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. PMID:28422957

Pooling across cells to normalize single-cell RNA sequencing data with many zero counts.

PubMed

Lun, Aaron T L; Bach, Karsten; Marioni, John C

2016-04-27

Normalization of single-cell RNA sequencing data is necessary to eliminate cell-specific biases prior to downstream analyses. However, this is not straightforward for noisy single-cell data where many counts are zero. We present a novel approach where expression values are summed across pools of cells, and the summed values are used for normalization. Pool-based size factors are then deconvolved to yield cell-based factors. Our deconvolution approach outperforms existing methods for accurate normalization of cell-specific biases in simulated data. Similar behavior is observed in real data, where deconvolution improves the relevance of results of downstream analyses.

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

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.

Body composition in athletes and sports nutrition: an examination of the bioimpedance analysis technique.

PubMed

Moon, J R

2013-01-01

The purpose of the current review was to evaluate how body composition can be utilised in athletes, paying particular attention to the bioelectrical impedance analysis (BIA) technique. Various body composition methods are discussed, as well as the unique characteristics of athletes that can lead to large errors when predicting fat mass (FM) and fat-free mass (FFM). Basic principles of BIA are discussed, and past uses of the BIA technique in athletes are explored. Single-prediction validation studies and studies tracking changes in FM and FFM are discussed with applications for athletes. Although extensive research in the area of BIA and athletes has been conducted, there remains a large gap in the literature pertaining to a single generalised athlete equation developed using a multiple-compartment model that includes total body water (TBW). Until a generalised athlete-specific BIA equation developed from a multiple-compartment is published, it is recommended that generalised equations such as those published by Lukaski and Bolonchuk and Lohman be used in athletes. However, BIA equations developed for specific athletes may also produce acceptable values and are still acceptable for use until more research is conducted. The use of a valid BIA equation/device should produce values similar to those of hydrostatic weighing and dual-energy X-ray absorptiometry. However, researchers and practitioners need to understand the individual variability associated with BIA estimations for both single assessments and repeated measurements. Although the BIA method shows promise for estimating body composition in athletes, future research should focus on the development of general athlete-specific equations using a TBW-based three- or four-compartment model.

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…

Computational tools for fitting the Hill equation to dose-response curves.

PubMed

Gadagkar, Sudhindra R; Call, Gerald B

2015-01-01

Many biological response curves commonly assume a sigmoidal shape that can be approximated well by means of the 4-parameter nonlinear logistic equation, also called the Hill equation. However, estimation of the Hill equation parameters requires access to commercial software or the ability to write computer code. Here we present two user-friendly and freely available computer programs to fit the Hill equation - a Solver-based Microsoft Excel template and a stand-alone GUI-based "point and click" program, called HEPB. Both computer programs use the iterative method to estimate two of the Hill equation parameters (EC50 and the Hill slope), while constraining the values of the other two parameters (the minimum and maximum asymptotes of the response variable) to fit the Hill equation to the data. In addition, HEPB draws the prediction band at a user-defined confidence level, and determines the EC50 value for each of the limits of this band to give boundary values that help objectively delineate sensitive, normal and resistant responses to the drug being tested. Both programs were tested by analyzing twelve datasets that varied widely in data values, sample size and slope, and were found to yield estimates of the Hill equation parameters that were essentially identical to those provided by commercial software such as GraphPad Prism and nls, the statistical package in the programming language R. The Excel template provides a means to estimate the parameters of the Hill equation and plot the regression line in a familiar Microsoft Office environment. HEPB, in addition to providing the above results, also computes the prediction band for the data at a user-defined level of confidence, and determines objective cut-off values to distinguish among response types (sensitive, normal and resistant). Both programs are found to yield estimated values that are essentially the same as those from standard software such as GraphPad Prism and the R-based nls. Furthermore, HEPB also has the option to simulate 500 response values based on the range of values of the dose variable in the original data and the fit of the Hill equation to that data. Copyright © 2014. Published by Elsevier Inc.

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.

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.

VLBI-SLR Combination Solution Using GEODYN

NASA Technical Reports Server (NTRS)

MacMillan, Dan; Pavlis, Despina; Lemoine, Frank; Chinn, Douglas; Rowlands, David

2010-01-01

We would like to generate a multi-technique solution combining all of the geodetic techniques (VLBI, SLR, GPS, and DORIS) using the same software and using the same a priori models. Here we use GEODYN software and consider only the VLBI-SLR combination. Here we report initial results of our work on the combination. We first performed solutions with GEODYN using only VLBI data and found that VLBI EOP solution results produced with GEODYN agree with results using CALC/SOLVE at the 1-sigma level. We then combined the VLBI normal equations in GEODYN with weekly SLR normal equations for the period 2007-2008. Agreement of estimated Earth orientation parameters with IERS C04 were not significantly different for the VLBI-only, SLR-only, and VLBI+SLR solutions

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

An Ab Initio and Kinetic Monte Carlo Simulation Study of Lithium Ion Diffusion on Graphene

PubMed Central

Zhong, Kehua; Yang, Yanmin; Xu, Guigui; Zhang, Jian-Min; Huang, Zhigao

2017-01-01

The Li+ diffusion coefficients in Li+-adsorbed graphene systems were determined by combining first-principle calculations based on density functional theory with Kinetic Monte Carlo simulations. The calculated results indicate that the interactions between Li ions have a very important influence on lithium diffusion. Based on energy barriers directly obtained from first-principle calculations for single-Li+ and two-Li+ adsorbed systems, a new equation predicting energy barriers with more than two Li ions was deduced. Furthermore, it is found that the temperature dependence of Li+ diffusion coefficients fits well to the Arrhenius equation, rather than meeting the equation from electrochemical impedance spectroscopy applied to estimate experimental diffusion coefficients. Moreover, the calculated results also reveal that Li+ concentration dependence of diffusion coefficients roughly fits to the equation from electrochemical impedance spectroscopy in a low concentration region; however, it seriously deviates from the equation in a high concentration region. So, the equation from electrochemical impedance spectroscopy technique could not be simply used to estimate the Li+ diffusion coefficient for all Li+-adsorbed graphene systems with various Li+ concentrations. Our work suggests that interactions between Li ions, and among Li ion and host atoms will influence the Li+ diffusion, which determines that the Li+ intercalation dependence of Li+ diffusion coefficient should be changed and complex. PMID:28773122

Assessment of the Effects of Entrainment and Wind Shear on Nuclear Cloud Rise Modeling

NASA Astrophysics Data System (ADS)

Zalewski, Daniel; Jodoin, Vincent

2001-04-01

Accurate modeling of nuclear cloud rise is critical in hazard prediction following a nuclear detonation. This thesis recommends improvements to the model currently used by DOD. It considers a single-term versus a three-term entrainment equation, the value of the entrainment and eddy viscous drag parameters, as well as the effect of wind shear in the cloud rise following a nuclear detonation. It examines departures from the 1979 version of the Department of Defense Land Fallout Interpretive Code (DELFIC) with the current code used in the Hazard Prediction and Assessment Capability (HPAC) code version 3.2. The recommendation for a single-term entrainment equation, with constant value parameters, without wind shear corrections, and without cloud oscillations is based on both a statistical analysis using 67 U.S. nuclear atmospheric test shots and the physical representation of the modeling. The statistical analysis optimized the parameter values of interest for four cases: the three-term entrainment equation with wind shear and without wind shear as well as the single-term entrainment equation with and without wind shear. The thesis then examines the effect of cloud oscillations as a significant departure in the code. Modifications to user input atmospheric tables are identified as a potential problem in the calculation of stabilized cloud dimensions in HPAC.

Single and Double ITCZ in Aqua-Planet Models with Globally and Temporally Uniform Sea Surface Temperature and Solar Insolation: An Interpretation

NASA Technical Reports Server (NTRS)

Chao, Winston C.; Chen, Baode; Lau, William K. M. (Technical Monitor)

2002-01-01

Previous studies (Chao 2000, Chao and Chen 2001, Kirtman and Schneider 2000, Sumi 1992) have shown that, by means of one of several model design changes, the structure of the ITCZ in an aqua-planet model with globally uniform SST and solar angle (U-SST-SA) can change between a single ITCZ at the equator and a double ITCZ straddling the equator. These model design changes include switching to a different cumulus parameterization scheme (e.g., from relaxed Arakawa Schubert scheme (RAS) to moist convective adjustment scheme (MCA)), changes within the cumulus parameterization scheme, and changes in other aspects of the model, such as horizontal resolution. Sometimes only one component of the double ITCZ shows up; but still this is an ITCZ away from the equator, quite distinct from a single ITCZ over the equator. Since these model results were obtained by different investigators using different models which have yielded reasonable general circulation, they are considered as reliable. Chao and Chen (2001; hereafter CC01) have made an initial attempt to interpret these findings based on the concept of rotational ITCZ attractors that they introduced. The purpose of this paper is to offer a more complete interpretation.

A numerical approach for assessing effects of shear on equivalent permeability and nonlinear flow characteristics of 2-D fracture networks

NASA Astrophysics Data System (ADS)

Liu, Richeng; Li, Bo; Jiang, Yujing; Yu, Liyuan

2018-01-01

Hydro-mechanical properties of rock fractures are core issues for many geoscience and geo-engineering practices. Previous experimental and numerical studies have revealed that shear processes could greatly enhance the permeability of single rock fractures, yet the shear effects on hydraulic properties of fractured rock masses have received little attention. In most previous fracture network models, single fractures are typically presumed to be formed by parallel plates and flow is presumed to obey the cubic law. However, related studies have suggested that the parallel plate model cannot realistically represent the surface characters of natural rock fractures, and the relationship between flow rate and pressure drop will no longer be linear at sufficiently large Reynolds numbers. In the present study, a numerical approach was established to assess the effects of shear on the hydraulic properties of 2-D discrete fracture networks (DFNs) in both linear and nonlinear regimes. DFNs considering fracture surface roughness and variation of aperture in space were generated using an originally developed code DFNGEN. Numerical simulations by solving Navier-Stokes equations were performed to simulate the fluid flow through these DFNs. A fracture that cuts through each model was sheared and by varying the shear and normal displacements, effects of shear on equivalent permeability and nonlinear flow characteristics of DFNs were estimated. The results show that the critical condition of quantifying the transition from a linear flow regime to a nonlinear flow regime is: 10-4 〈 J < 10-3, where J is the hydraulic gradient. When the fluid flow is in a linear regime (i.e., J < 10-4), the relative deviation of equivalent permeability induced by shear, δ2, is linearly correlated with J with small variations, while for fluid flow in the nonlinear regime (J 〉 10-3), δ2 is nonlinearly correlated with J. A shear process would reduce the equivalent permeability significantly in the orientation perpendicular to the sheared fracture as much as 53.86% when J = 1, shear displacement Ds = 7 mm, and normal displacement Dn = 1 mm. By fitting the calculated results, the mathematical expression for δ2 is established to help choose proper governing equations when solving fluid flow problems in fracture networks.

Application of reaction-diffusion models to cell patterning in Xenopus retina. Initiation of patterns and their biological stability.

PubMed

Shoaf, S A; Conway, K; Hunt, R K

1984-08-07

We have examined the behavior of two reaction-diffusion models, originally proposed by Gierer & Meinhardt (1972) and by Kauffman, Shymko & Trabert (1978), for biological pattern formation. Calculations are presented for pattern formation on a disc (approximating the geometry of a number of embryonic anlagen including the frog eye rudiment), emphasizing the sensitivity of patterns to changes in initial conditions and to perturbations in the geometry of the morphogen-producing space. Analysis of the linearized equations from the models enabled us to select appropriate parameters and disc size for pattern growth. A computer-implemented finite element method was used to solve the non-linear model equations reiteratively. For the Gierer-Meinhardt model, initial activation (varying in size over two orders of magnitude) of one point on the disc's edge was sufficient to generate the primary gradient. Various parts of the disc were removed (remaining only as diffusible space) from the morphogen-producing cycle to investigate the effects of cells dropping out of the cycle due to cell death or malfunction (single point removed) or differentiation (center removed), as occur in the Xenopus eye rudiment. The resulting patterns had the same general shape and amplitude as normal gradients. Nor did a two-fold increase in disc size affect the pattern-generating ability of the model. Disc fragments bearing their primary gradient patterns were fused (with gradients in opposite directions, but each parallel to the fusion line). The resulting patterns generated by the model showed many similarities to results of "compound eye" experiments in Xenopus. Similar patterns were obtained with the model of Kauffman's group (1978), but we found less stability of the pattern subject to simulations of central differentiation. However, removal of a single point from the morphogen cycle (cell death) did not result in any change. The sensitivity of the Kauffman et al. model to shape perturbations is not surprising since the model was originally designed to use shape and increasing size during growth to generate a sequence of transient patterns. However, the Gierer-Meinhardt model is remarkably stable even when subjected to a wide range of perturbations in the diffusible space, thus allowing it to cope with normal biological variability, and offering an exciting range of possibilities for reaction-diffusion models as mechanisms underlying the spatial patterns of tissue structures.

Do over 200 million healthy altitude residents really suffer from chronic Acid-base disorders?

PubMed

Zubieta-Calleja, Gustavo; Zubieta-Castillo, Gustavo; Zubieta-Calleja, Luis; Ardaya-Zubieta, Gustavo; Paulev, Poul-Erik

2011-01-01

As the oxygen tension of inspired air falls with increasing altitude in normal subjects, hyperventilation ensues. This acute respiratory alkalosis, induces increased renal excretion of bicarbonate, returning the pH back to normal, giving rise to compensated respiratory alkalosis or chronic hypocapnia. It seems a contradiction that so many normal people at high altitude should permanently live as chronic acid-base patients. Blood gas analyses of 1,865 subjects at 3,510 m, reported a P(a)CO(2) (arterial carbon dioxide tension ± SEM) = 29.4 ± 0.16 mmHg and pH = 7.40 ± 0.005. Base excess, calculated with the Van Slyke sea level equation, is -5 mM (milliMolar or mmol/l) as an average, suggesting chronic hypocapnia. THID, a new term replacing "Base Excess" is determined by titration to a pH of 7.40 at a P(a)CO(2) of 5.33 kPa (40 mmHg) at sea level, oxygen saturated and at 37°C blood temperature. Since our new modified Van Slyke equations operate with normal values for P(a)CO(2) at the actual altitude, a calculation of THID will always result in normal values-that is, zero.

Establishment of Local Trip Generation Rates or Equations for Mixed-Use Developments in Kansas

DOT National Transportation Integrated Search

2012-10-01

Currently, the trip generation rates and equations contained in the Institute of Transportation Engineers (ITE) : Trip Generation Manual, 8th Edition are based on the information collected at single-use, free-standing sites and cannot : be directly a...

A phase space approach to wave propagation with dispersion.

PubMed

Ben-Benjamin, Jonathan S; Cohen, Leon; Loughlin, Patrick J

2015-08-01

A phase space approximation method for linear dispersive wave propagation with arbitrary initial conditions is developed. The results expand on a previous approximation in terms of the Wigner distribution of a single mode. In contrast to this previously considered single-mode case, the approximation presented here is for the full wave and is obtained by a different approach. This solution requires one to obtain (i) the initial modal functions from the given initial wave, and (ii) the initial cross-Wigner distribution between different modal functions. The full wave is the sum of modal functions. The approximation is obtained for general linear wave equations by transforming the equations to phase space, and then solving in the new domain. It is shown that each modal function of the wave satisfies a Schrödinger-type equation where the equivalent "Hamiltonian" operator is the dispersion relation corresponding to the mode and where the wavenumber is replaced by the wavenumber operator. Application to the beam equation is considered to illustrate the approach.

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.

Bi-Hamiltonian Structure in 2-d Field Theory

NASA Astrophysics Data System (ADS)

Ferapontov, E. V.; Galvão, C. A. P.; Mokhov, O. I.; Nutku, Y.

We exhibit the bi-Hamiltonian structure of the equations of associativity (Witten-Dijkgraaf-Verlinde-Verlinde-Dubrovin equations) in 2-d topological field theory, which reduce to a single equation of Monge-Ampère type $ fttt}=f{xxt;;;;;2 - fxxx}f{xtt ,$ in the case of three primary fields. The first Hamiltonian structure of this equation is based on its representation as a 3-component system of hydrodynamic type and the second Hamiltonian structure follows from its formulation in terms of a variational principle with a degenerate Lagrangian.

On the various forms of the energy equation for a dilute, monatomic mixture of nonreacting gases

NASA Technical Reports Server (NTRS)

Kennedy, Christopher A.

1994-01-01

In the case of gas mixtures, the governing equations become rather formidable and a complete listing of the equations in their various forms and methods to evaluate the transport coefficients is difficult to find. This paper seeks to compile common, as well as less well known, results in a single document. Various relationships between equations describing conservation of energy for a dilute, monatomic, nonreacting gas in local equilibrium are provided. The gas is treated as nonrelativistic, not subject to magnetic or electric fields, or radiative effects.

Nonlocal symmetry and explicit solutions from the CRE method of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Zhao, Zhonglong; Han, Bo

2018-04-01

In this paper, we analyze the integrability of the Boussinesq equation by using the truncated Painlevé expansion and the CRE method. Based on the truncated Painlevé expansion, the nonlocal symmetry and Bäcklund transformation of this equation are obtained. A prolonged system is introduced to localize the nonlocal symmetry to the local Lie point symmetry. It is proved that the Boussinesq equation is CRE solvable. The two-solitary-wave fusion solutions, single soliton solutions and soliton-cnoidal wave solutions are presented by means of the Bäcklund transformations.

Design of Circular, Square, Single, and Multi-layer Induction Coils for Electromagnetic Priming Using Inductance Estimates

NASA Astrophysics Data System (ADS)

Fritzsch, Robert; Kennedy, Mark W.; Aune, Ragnhild E.

2018-02-01

Special induction coils used for electro magnetic priming of ceramic foam filters in liquid metal filtration have been designed using a combination of analytical and finite element modeling. Relatively simple empirical equations published by Wheeler in 1928 and 1982 have been used during the design process. The equations were found to accurately predict the z-component of the magnetic flux densities of both single- and multi-layer coils as verified both experimentally and by using COMSOL® 5.1 multiphysics simulations.

Fifth-order complex Korteweg-de Vries-type equations

NASA Astrophysics Data System (ADS)

Khanal, Netra; Wu, Jiahong; Yuan, Juan-Ming

2012-05-01

This paper studies spatially periodic complex-valued solutions of the fifth-order Korteweg-de Vries (KdV)-type equations. The aim is at several fundamental issues including the existence, uniqueness and finite-time blowup problems. Special attention is paid to the Kawahara equation, a fifth-order KdV-type equation. When a Burgers dissipation is attached to the Kawahara equation, we establish the existence and uniqueness of the Fourier series solution with the Fourier modes decaying algebraically in terms of the wave numbers. We also examine a special series solution to the Kawahara equation and prove the convergence and global regularity of such solutions associated with a single mode initial data. In addition, finite-time blowup results are discussed for the special series solution of the Kawahara equation.

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

NASA Astrophysics Data System (ADS)

Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo

2009-10-01

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

A 3% Measurement of the Beam Normal Single Spin Asymmetry in Forward Angle Elastic Electron-Proton Scattering using the Qweak Setup

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

Waidyawansa, Dinayadura Buddhini

2013-08-01

The beam normal single spin asymmetry generated in the scattering of transversely polarized electrons from unpolarized nucleons is an observable of the imaginary part of the two-photon exchange process. Moreover, it is a potential source of false asymmetry in parity violating electron scattering experiments. The Q{sub weak} experiment uses parity violating electron scattering to make a direct measurement of the weak charge of the proton. The targeted 4% measurement of the weak charge of the proton probes for parity violating new physics beyond the Standard Model. The beam normal single spin asymmetry at Q{sub weak} kinematics is at least threemore » orders of magnitude larger than 5 ppb precision of the parity violating asymmetry. To better understand this parity conserving background, the Q{sub weak} Collaboration has performed elastic scattering measurements with fully transversely polarized electron beam on the proton and aluminum. This dissertation presents the analysis of the 3% measurement (1.3% statistical and 2.6% systematic) of beam normal single spin asymmetry in electronproton scattering at a Q2 of 0.025 (GeV/c)2. It is the most precise existing measurement of beam normal single spin asymmetry available at the time. A measurement of this precision helps to improve the theoretical models on beam normal single spin asymmetry and thereby our understanding of the doubly virtual Compton scattering process.« less

Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations

NASA Astrophysics Data System (ADS)

Novruzov, Emil

2017-11-01

This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, ut -uxxt +[ f (u) ] x -[ f (u) ] xxx +[ g (u) + f″/(u) 2 ux2 ] x = 0 that includes the Camassa-Holm equation as well as the hyperelastic-rod wave equation (f (u) = ku2 / 2 and g (u) = (3 - k) u2 / 2) as special cases. We establish some a local-in-space blow-up criterion (i.e., a criterion involving only the properties of the data u0 in a neighborhood of a single point) simplifying and precising earlier blow-up criteria for this equation.

Nonlinear Diophantine equation 11 x +13 y = z 2

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

Generalized Freud's equation and level densities with polynomial potential

NASA Astrophysics Data System (ADS)

Boobna, Akshat; Ghosh, Saugata

2013-08-01

We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.

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).

Investigations Regarding Anesthesia during Hypovolemic Conditions.

DTIC Science & Technology

1982-09-25

i / b ,- 18 For each level of hemoglobin, the equation was "normalized" to a pH of 7.400 for a BE of zero and a PCO of 40.0 torr, Orr et al. (171...the shifted BE values. Curve nomogram. Using the equations resulting from the above curve- fitting procedure, we calculated the relationship between pH...model for a given BE (i.e., pH = m i log PCO 2 + bi). Solve the following set of equations for pHind and log dX - 0 d(PHind) where X = (pHl - pHind) 2

Impact of dose size in single fraction spatially fractionated (grid) radiotherapy for melanoma

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

Zhang, Hualin, E-mail: hualin.zhang@northwestern.edu, E-mail: hualinzhang@yahoo.com; Zhong, Hualiang; Barth, Rolf F.

2014-02-15

Purpose: To evaluate the impact of dose size in single fraction, spatially fractionated (grid) radiotherapy for selectively killing infiltrated melanoma cancer cells of different tumor sizes, using different radiobiological models. Methods: A Monte Carlo technique was employed to calculate the 3D dose distribution of a commercially available megavoltage grid collimator in a 6 MV beam. The linear-quadratic (LQ) and modified linear quadratic (MLQ) models were used separately to evaluate the therapeutic outcome of a series of single fraction regimens that employed grid therapy to treat both acute and late responding melanomas of varying sizes. The dose prescription point was atmore » the center of the tumor volume. Dose sizes ranging from 1 to 30 Gy at 100% dose line were modeled. Tumors were either touching the skin surface or having their centers at a depth of 3 cm. The equivalent uniform dose (EUD) to the melanoma cells and the therapeutic ratio (TR) were defined by comparing grid therapy with the traditional open debulking field. The clinical outcomes from recent reports were used to verify the authors’ model. Results: Dose profiles at different depths and 3D dose distributions in a series of 3D melanomas treated with grid therapy were obtained. The EUDs and TRs for all sizes of 3D tumors involved at different doses were derived through the LQ and MLQ models, and a practical equation was derived. The EUD was only one fifth of the prescribed dose. The TR was dependent on the prescribed dose and on the LQ parameters of both the interspersed cancer and normal tissue cells. The results from the LQ model were consistent with those of the MLQ model. At 20 Gy, the EUD and TR by the LQ model were 2.8% higher and 1% lower than by the MLQ, while at 10 Gy, the EUD and TR as defined by the LQ model were only 1.4% higher and 0.8% lower, respectively. The dose volume histograms of grid therapy for a 10 cm tumor showed different dosimetric characteristics from those of conventional radiotherapy. A significant portion of the tumor volume received a very large dose in grid therapy, which ensures significant tumor cell killing in these regions. Conversely, some areas received a relatively small dose, thereby sparing interspersed normal cells and increasing radiation tolerance. The radiobiology modeling results indicated that grid therapy could be useful for treating acutely responding melanomas infiltrating radiosensitive normal tissues. The theoretical model predictions were supported by the clinical outcomes. Conclusions: Grid therapy functions by selectively killing infiltrating tumor cells and concomitantly sparing interspersed normal cells. The TR depends on the radiosensitivity of the cell population, dose, tumor size, and location. Because the volumes of very high dose regions are small, the LQ model can be used safely to predict the clinical outcomes of grid therapy. When treating melanomas with a dose of 15 Gy or higher, single fraction grid therapy is clearly advantageous for sparing interspersed normal cells. The existence of a threshold fraction dose, which was found in the authors’ theoretical simulations, was confirmed by clinical observations.« less

A model for hematopoietic death in man from irradiation of bone marrow during radioimmunotherapy.

PubMed

Scott, B R; Dillehay, L E

1990-11-01

There are numerous institutions worldwide performing clinical trials of radioimmunotherapy (RIT) for cancer. For RIT, an exponentially decaying radionuclide is attached by using a chelating agent to a specific monoclonal or polyclonal tumour antibody (e.g. antiferritin IgG). The major limitation to RIT is toxicity to normal tissue in organs other than the one containing the tumour (e.g. bone marrow). The focus of this manuscript is on modelling the risk (or probability) of hematopoietic death in man for exponentially decaying patterns of high-energy beta irradiation (e.g. 90Y) of bone marrow by radioimmunoglobulin injected into the blood. The analytical solutions presented are only applicable to protocols for which significant uptake of radioactivity by the bone marrow does not occur, and only for high energy beta emitters. However, the generic equation used to obtain the analytical solutions is applicable to any continuous pattern of high energy beta irradiation. A model called the "normalized dose model" was used to generate calculated values for the LD50 as a function of the effective half-time for the radioimmunoglobulin in the blood. A less complicated empirical model was used to describe the calculated values. This model is presumed to be valid for effective half-times in blood of up to about 20 days. For longer effective half-times, the LD50 can be estimated using the normalized-dose model presented. In this manuscript, we also provide a modified Weibull model that allows estimation of the risk of hematopoietic death for single or multiple injections (in one cycle) of radioimmunoglobulin, for patients with normal susceptibility to irradiation and for patients with heightened susceptibility. With the modified Weibull model, the risk of hematopoietic death depends on the level of medical treatment provided to mitigate radiation injuries.

Interlaminar Stresses by Refined Beam Theories and the Sinc Method Based on Interpolation of Highest Derivative

NASA Technical Reports Server (NTRS)

Slemp, Wesley C. H.; Kapania, Rakesh K.; Tessler, Alexander

2010-01-01

Computation of interlaminar stresses from the higher-order shear and normal deformable beam theory and the refined zigzag theory was performed using the Sinc method based on Interpolation of Highest Derivative. The Sinc method based on Interpolation of Highest Derivative was proposed as an efficient method for determining through-the-thickness variations of interlaminar stresses from one- and two-dimensional analysis by integration of the equilibrium equations of three-dimensional elasticity. However, the use of traditional equivalent single layer theories often results in inaccuracies near the boundaries and when the lamina have extremely large differences in material properties. Interlaminar stresses in symmetric cross-ply laminated beams were obtained by solving the higher-order shear and normal deformable beam theory and the refined zigzag theory with the Sinc method based on Interpolation of Highest Derivative. Interlaminar stresses and bending stresses from the present approach were compared with a detailed finite element solution obtained by ABAQUS/Standard. The results illustrate the ease with which the Sinc method based on Interpolation of Highest Derivative can be used to obtain the through-the-thickness distributions of interlaminar stresses from the beam theories. Moreover, the results indicate that the refined zigzag theory is a substantial improvement over the Timoshenko beam theory due to the piecewise continuous displacement field which more accurately represents interlaminar discontinuities in the strain field. The higher-order shear and normal deformable beam theory more accurately captures the interlaminar stresses at the ends of the beam because it allows transverse normal strain. However, the continuous nature of the displacement field requires a large number of monomial terms before the interlaminar stresses are computed as accurately as the refined zigzag theory.

The simulation of shock- and impact-driven flows with Mie-Gruneisen equations of state

NASA Astrophysics Data System (ADS)

Ward, Geoffrey M.

An investigation of shock- and impact-driven flows with Mie-Gruneisen equation of state derived from a linear shock-particle speed Hugoniot relationship is presented. Cartesian mesh methods using structured adaptive refinement are applied to simulate several flows of interest in an Eulerian frame of reference. The flows central to the investigation include planar Richtmyer-Meshkov instability, the impact of a sphere with a plate, and an impact-driven Mach stem. First, for multicomponent shock-driven flows, a dimensionally unsplit, spatially high-order, hybrid, center-difference, limiter methodology is developed. Effective switching between center-difference and upwinding schemes is achieved by a set of robust tolerance and Lax-entropy-based criteria [49]. Oscillations that result from such a mixed stencil scheme are minimized by requiring that the upwinding method approaches the center-difference method in smooth regions. The solver is then applied to investigate planar Richtmyer-Meshkov instability in the context of an equation of state comparison. Comparisons of simulations with materials modeled by isotropic stress Mie-Gruneisen equations of state derived from a linear shock-particle speed Hugoniot relationship [36,52] to those of perfect gases are made with the intention of exposing the role of the equation of state. First, results for single- and triple-mode planar Richtmyer-Meshkov instability between mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Gruneisen equations of state are presented for the case of a reflected shock. The single-mode case is explored for incident shock Mach numbers of 1.5 and 2.5. Additionally, examined is single-mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. Vorticity distribution and corrugation centerline shortly after shock interaction is also examined. The formation of incipient weak shock waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected. Next, the ghost fluid method [83] is explored for application to impact-driven flows with Mie-Gruneisen equations of state in a vacuum. Free surfaces are defined utilizing a level-set approach. The level-set is reinitialized to the signed distance function periodically by solution to a Hamilton-Jacobi differential equation in artificial time. Flux reconstruction along each Cartesian direction of the domain is performed by subdividing in a way that allows for robust treatment of grid-scale sized voids. Ghost cells in voided regions near the material-vacuum interface are determined from surface-normal Riemann problem solution. The method is then applied to several impact problems of interest. First, a one-dimensional impact problem is examined in Mie-Gruneisen aluminum with simple point erosion used to model separation by spallation under high tension. A similar three-dimensional axisymmetric simulation of two rods impacting is then performed without a model for spallation. Further results for three-dimensional axisymmetric simulation of a sphere hitting a plate are then presented. Finally, a brief investigation of the assumptions utilized in modeling solids as isotropic fluids is undertaken. An Eulerian solver approach to handling elastic and elastic-plastic solids is utilized for comparison to the simple fluid model assumption. First, in one dimension an impact problem is examined for elastic, elastic-plastic, and fluid equations of state for aluminum. The results demonstrate that in one dimension the fluid models the plastic shock structure of the flow well. Further investigation is made using a three-dimensional axisymmetric simulation of an impact problem involving a copper cylinder surrounded by aluminum. An aluminum slab impact drives a faster shock in the outer aluminum region yielding a Mach reflection in the copper. The results demonstrate similar plastic shock structures. Several differences are also notable that include a lack of roll-up instability at the material interface and slip-line emanating from the Mach stem's triple point. (Abstract shortened by UMI.)

Establishment of Local Trip Generation Rates or Equations for Mixed-Use Developments in Kansas : Technical Summary

DOT National Transportation Integrated Search

2012-10-01

Currently, the trip generation rates and equations contained in the Institute of Transportation Engineers (ITE) Trip Generation Manual, 8th Edition are based on the information collected at single-use, free-standing sites and cannot be directly appli...

Internal null controllability of a linear Schrödinger-KdV system on a bounded interval

NASA Astrophysics Data System (ADS)

Araruna, Fágner D.; Cerpa, Eduardo; Mercado, Alberto; Santos, Maurício C.

2016-01-01

The control of a linear dispersive system coupling a Schrödinger and a linear Korteweg-de Vries equation is studied in this paper. The system can be viewed as three coupled real-valued equations by taking real and imaginary parts in the Schrödinger equation. The internal null controllability is proven by using either one complex-valued control on the Schrödinger equation or two real-valued controls, one on each equation. Notice that the single Schrödinger equation is not known to be controllable with a real-valued control. The standard duality method is used to reduce the controllability property to an observability inequality, which is obtained by means of a Carleman estimates approach.

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

PubMed

Levy, Tal J; Rabani, Eran

2013-04-28

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

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

PubMed

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

2014-05-01

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