Theory and Circuit Model for Lossy Coaxial Transmission Line

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

Genoni, T. C.; Anderson, C. N.; Clark, R. E.

2017-04-01

The theory of signal propagation in lossy coaxial transmission lines is revisited and new approximate analytic formulas for the line impedance and attenuation are derived. The accuracy of these formulas from DC to 100 GHz is demonstrated by comparison to numerical solutions of the exact field equations. Based on this analysis, a new circuit model is described which accurately reproduces the line response over the entire frequency range. Circuit model calculations are in excellent agreement with the numerical and analytic results, and with finite-difference-time-domain simulations which resolve the skindepths of the conducting walls.

Theoretical study on phase-locking of a radial array CO2 laser

NASA Astrophysics Data System (ADS)

Xu, Yonggen

2014-11-01

The phase-locking of the radial array CO2 laser (RAL) is introduced based on the injection-locking principle. The characteristic parameters of laser beams used in the phase-locking are described, and the coupling coefficient c00 between the injected mode and the eigenmode of RAL is calculated. The laser modes from RAL are the low-order Hermite Gaussian modes due to the diffraction loss. The analytical formula for the output beam through an ABCD optical system is derived according Collins formula. The numerical examples are given to illustrate our analytical results.

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

Calculation method for steady-state pollutant concentration in mixing zones considering variable lateral diffusion coefficient.

PubMed

Wu, Wen; Wu, Zhouhu; Song, Zhiwen

2017-07-01

Prediction of the pollutant mixing zone (PMZ) near the discharge outfall in Huangshaxi shows large error when using the methods based on the constant lateral diffusion assumption. The discrepancy is due to the lack of consideration of the diffusion coefficient variation. The variable lateral diffusion coefficient is proposed to be a function of the longitudinal distance from the outfall. Analytical solution of the two-dimensional advection-diffusion equation of a pollutant is derived and discussed. Formulas to characterize the geometry of the PMZ are derived based on this solution, and a standard curve describing the boundary of the PMZ is obtained by proper choices of the normalization scales. The change of PMZ topology due to the variable diffusion coefficient is then discussed using these formulas. The criterion of assuming the lateral diffusion coefficient to be constant without large error in PMZ geometry is found. It is also demonstrated how to use these analytical formulas in the inverse problems including estimating the lateral diffusion coefficient in rivers by convenient measurements, and determining the maximum allowable discharge load based on the limitations of the geometrical scales of the PMZ. Finally, applications of the obtained formulas to onsite PMZ measurements in Huangshaxi present excellent agreement.

Effect of train carbody's parameters on vertical bending stiffness performance

NASA Astrophysics Data System (ADS)

Yang, Guangwu; Wang, Changke; Xiang, Futeng; Xiao, Shoune

2016-10-01

Finite element analysis(FEA) and modal test are main methods to give the first-order vertical bending vibration frequency of train carbody at present, but they are inefficiency and waste plenty of time. Based on Timoshenko beam theory, the bending deformation, moment of inertia and shear deformation are considered. Carbody is divided into some parts with the same length, and it's stiffness is calculated with series principle, it's cross section area, moment of inertia and shear shape coefficient is equivalent by segment length, and the fimal corrected first-order vertical bending vibration frequency analytical formula is deduced. There are 6 simple carbodies and 1 real carbody as examples to test the formula, all analysis frequencies are very close to their FEA frequencies, and especially for the real carbody, the error between analysis and experiment frequency is 0.75%. Based on the analytic formula, sensitivity analysis of the real carbody's design parameters is done, and some main parameters are found. The series principle of carbody stiffness is introduced into Timoshenko beam theory to deduce a formula, which can estimate the first-order vertical bending vibration frequency of carbody quickly without traditional FEA method and provide a reference to design engineers.

Dispersive analysis of the pion transition form factor.

PubMed

Hoferichter, M; Kubis, B; Leupold, S; Niecknig, F; Schneider, S P

We analyze the pion transition form factor using dispersion theory. We calculate the singly-virtual form factor in the time-like region based on data for the [Formula: see text] cross section, generalizing previous studies on [Formula: see text] decays and [Formula: see text] scattering, and verify our result by comparing to [Formula: see text] data. We perform the analytic continuation to the space-like region, predicting the poorly-constrained space-like transition form factor below [Formula: see text], and extract the slope of the form factor at vanishing momentum transfer [Formula: see text]. We derive the dispersive formalism necessary for the extension of these results to the doubly-virtual case, as required for the pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

Design optimization of an axial-field eddy-current magnetic coupling based on magneto-thermal analytical model

NASA Astrophysics Data System (ADS)

Fontchastagner, Julien; Lubin, Thierry; Mezani, Smaïl; Takorabet, Noureddine

2018-03-01

This paper presents a design optimization of an axial-flux eddy-current magnetic coupling. The design procedure is based on a torque formula derived from a 3D analytical model and a population algorithm method. The main objective of this paper is to determine the best design in terms of magnets volume in order to transmit a torque between two movers, while ensuring a low slip speed and a good efficiency. The torque formula is very accurate and computationally efficient, and is valid for any slip speed values. Nevertheless, in order to solve more realistic problems, and then, take into account the thermal effects on the torque value, a thermal model based on convection heat transfer coefficients is also established and used in the design optimization procedure. Results show the effectiveness of the proposed methodology.

Nuclear isospin effect on α-decay half-lives

NASA Astrophysics Data System (ADS)

Akrawy, Dashty T.; Hassanabadi, H.; Hosseini, S. S.; Santhosh, K. P.

2018-07-01

The α-decay half-lives for the even-even, even-odd, odd-even and odd-odd of 356 nuclei in the range 52 ≤Zp ≤ 118 have been studied within the analytical formula of Royer and also within the modified analytical formula of Royer. We calculated the new coefficient of the Royer by fitting 356 isotopes. Also, we considered the Denisov and Khudenko formula and obtained the new coefficient for the modified Denisov and Khudenko formula. We calculated the standard deviation and the average deviation. Analytical results are compared with the experimental data. The results are in better agreement with the experimental data when the effect of the isospin considered for the parent nuclei.

Simple Analytic Formula for the Period of the Nonlinear Pendulum via the Struve Function: Connection to Acoustical Impedance Matching

ERIC Educational Resources Information Center

Douvropoulos, Theodosios G.

2012-01-01

An approximate formula for the period of pendulum motion beyond the small amplitude regime is obtained based on physical arguments. Two different schemes of different accuracy are developed: in the first less accurate scheme, emphasis is given on the non-quadratic form of the potential in connection to isochronism, and a specific form of a generic…

SU-E-P-45: An Analytical Formula for Deriving Mechanical Iso-Center of Rotational Gantry Treatment Unit Rotational Gantry Treatment Unit

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

Ding, X; Bues, M

2015-06-15

Purpose: To present an analytical formula for deriving mechanical isocenter (MIC) of a rotational gantry treatment unit. The input data to the formula is obtained by a custom-made device. The formula has been implemented and used in an operational proton therapy facility since 2005. Methods: The custom made device consisted of 3 mutually perpendicular dial indicators and 5 clinometers, to obtain displacement data and gantry angle data simultaneously. During measurement, a steel sphere was affixed to the patient couch, and the device was attached to the snout rotating with the gantry. The displacement data and angle data were obtained simultaneouslymore » at angular increments of less than 1 degree. The analytical formula took the displacement and angle as input and derived the positions of dial indicator tips (DIT) position in room-fixed coordinate system. The formula derivation presupposes trigonometry and 3-dimentional coordinate transformations. Due to the symmetry properties of the defining equations, the DIT position can be solved for analytically without using mathematical approximations. We define the mean of all points in the DIT trajectory as the MIC. The formula was implemented in computer code, which has been employed during acceptance test, commissioning, as well as routine QA practice in an operational proton facility since 2005. Results: It took one minute for the custom-made device to acquire the measurement data for a full gantry rotation. The DIT trajectory and MIS are instantaneously available after the measurement. The MIC Result agrees well with vendor’s Result, which came from a different measurement setup, as well as different data analysis algorithm. Conclusion: An analytical formula for deriving mechanical isocenter was developed and validated. The formula is considered to be absolutely accurate mathematically. Be analyzing measured data of radial displacements as function of gantry angle, the formula calculates the MI position in room coordinate.« less

The analysis of predictability of recent alpha decay formulae and the alpha partial half-lives of some exotic nuclei

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

Dasgupta-Schubert, N.; Reyes, M. A.; Tamez, V. A.

2009-04-20

Alpha decay is one of the two main decay modes of the heaviest nuclei, (SHE), and constitutes one of the dominant decay modes of highly neutron deficient medium mass nuclei ('exotics'). Thus identifying and characterizing the alpha decay chains form a crucial part of the identification of SHE. We report the extension of the previously developed method for the detailed and systematic investigation of the reliability of the three main extant analytical formulae of alpha decay half-lives: the generalized liquid drop model based formula of Royer et al. (FR), the Sobiczewski modified semi-empirical Viola-Seaborg formula (VSS) and the recent phenomenologicalmore » formula of Sobiczewski and Parkhomenko (SP)« less

Development of "one-pot" method for multi-class compounds in porcine formula feed by multi-function impurity adsorption cleaning followed ultra-performance liquid chromatography-tandem mass spectrometry detection.

PubMed

Wang, Peilong; Wang, Xiao; Zhang, Wei; Su, Xiaoou

2014-02-01

A novel and efficient determination method for multi-class compounds including β-agonists, sedatives, nitro-imidazoles and aflatoxins in porcine formula feed based on a fast "one-pot" extraction/multifunction impurity adsorption (MFIA) clean-up procedure has been developed. 23 target analytes belonging to four different class compounds could be determined simultaneously in a single run. Conditions for "one-pot" extraction were studied in detail. Under the optimized conditions, the multi-class compounds in porcine formula feed samples were extracted and purified with methanol contained ammonia and absorbents by one step. The compounds in extracts were purified by using multi types of absorbent based on MFIA in one pot. The multi-walled carbon nanotubes were employed to improved clean-up efficiency. Shield BEH C18 column was used to separate 23 target analytes, followed by tandem mass spectrometry (MS/MS) detection using an electro-spray ionization source in positive mode. Recovery studies were done at three fortification levels. Overall average recoveries of target compounds in porcine formula feed at each levels were >51.6% based on matrix fortified calibration with coefficients of variation from 2.7% to 13.2% (n=6). The limit of determination (LOD) of these compounds in porcine formula feed sample matrix was <5.0 μg/kg. This method was successfully applied in screening and confirmation of target drugs in >30 porcine formula feed samples. It was demonstrated that the integration of the MFIA protocol with the MS/MS instrument could serve as a valuable strategy for rapid screening and reliable confirmatory analysis of multi-class compounds in real samples. Copyright © 2013 Elsevier B.V. All rights reserved.

An analytic formula for H-infinity norm sensitivity with applications to control system design

NASA Technical Reports Server (NTRS)

Giesy, Daniel P.; Lim, Kyong B.

1992-01-01

An analytic formula for the sensitivity of singular value peak variation with respect to parameter variation is derived. As a corollary, the derivative of the H-infinity norm of a stable transfer function with respect to a parameter is presented. It depends on some of the first two derivatives of the transfer function with respect to frequency and the parameter. For cases when the transfer function has a linear system realization whose matrices depend on the parameter, analytic formulas for these first two derivatives are derived, and an efficient algorithm for calculating them is discussed. Examples are given which provide numerical verification of the H-infinity norm sensitivity formula and which demonstrate its utility in designing control systems satisfying H-infinity norm constraints. In the appendix, derivative formulas for singular values are paraphrased.

Magnetic fields for transporting charged beams

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

Parzen, G.

1976-01-01

The transport of charged particle beams requires magnetic fields that must be shaped correctly and very accurately. During the last 20 years or so, many studies have been made, both analytically and through the use of computer programs, of various magnetic shapes that have proved to be useful. Many of the results for magnetic field shapes can be applied equally well to electric field shapes. A report is given which gathers together the results that have more general significance and would be useful in designing a configuration to produce a desired magnetic field shape. The field shapes studied include themore » fields in dipoles, quadrupoles, sextupoles, octupoles, septum magnets, combined-function magnets, and electrostatic septums. Where possible, empirical formulas are proposed, based on computer and analytical studies and on magnetic field measurements. These empirical formulas are often easier to use than analytical formulas and often include effects that are difficult to compute analytically. In addition, results given in the form of tables and graphs serve as illustrative examples. The field shapes studied include uniform fields produced by window-frame magnets, C-magnets, H-magnets, and cosine magnets; linear fields produced by various types of quadrupoles; quadratic and cubic fields produced by sextupoles and octupoles; combinations of uniform and linear fields; and septum fields with sharp boundaries.« less

Thermal Cyclotron Absorption Coefficients. II. Opacities in the Stokes Formalism

NASA Astrophysics Data System (ADS)

Vaeth, H. M.; Chanmugam, G.

1995-05-01

We extend the discussion of the calculation of the cyclotron opacities α± of the ordinary and extraordinary mode (Chanmugam et al.) to the opacities κ, q, υ in the Stokes formalism. We derive formulae with which a can be calculated from κ, q, υ. We are hence able to compare our calculations of the opacities, which are based on the single-particle method, with results obtained with the dielectric tensor method of Tam or. Excellent agreement is achieved. We present extensive tables of the opacities in the Stokes formalism for frequencies up to 25ωc, where ωc is the cyclotron frequency, and temperatures kT = 5, 10,20, 30,40, and 50 keV. Furthermore, we derive approximate formulae with which κ, q, υ can be calculated from α± and hence use the Robinson & Melrose analytic formulae for α± in order to calculate the opacities in the Stokes formalism. We compare these opacities to accurate numerical opacities and find that the analytic formulae can reproduce the qualitative behavior of the opacities in the regions where the harmonic structure is unimportant.

Analytical research on impacting load of aircraft crashing upon moveable concrete target

NASA Astrophysics Data System (ADS)

Zhu, Tong; Ou, Zhuocheng; Duan, Zhuoping; Huang, Fenglei

2018-03-01

The impact load of an aircraft impact upon moveable concrete target was analyzed in this paper by both theoretical and numerical methods. The aircraft was simplified as a one dimensional pole and stress-wave theory was used to deduce the new formula. Furthermore, aiming to compare with previous experimental data, a numerical calculation based on the new formula had been carried out which showed good agreement with the experimental data. The approach, a new formula with particular numerical method, can predict not only the impact load but also the deviation between moveable and static concrete target.

A time-domain Kirchhoff formula for the convective acoustic wave equation

NASA Astrophysics Data System (ADS)

Ghorbaniasl, Ghader; Siozos-Rousoulis, Leonidas; Lacor, Chris

2016-03-01

Kirchhoff's integral method allows propagated sound to be predicted, based on the pressure and its derivatives in time and space obtained on a data surface located in the linear flow region. Kirchhoff's formula for noise prediction from high-speed rotors and propellers suffers from the limitation of the observer located in uniform flow, thus requiring an extension to arbitrarily moving media. This paper presents a Kirchhoff formulation for moving surfaces in a uniform moving medium of arbitrary configuration. First, the convective wave equation is derived in a moving frame, based on the generalized functions theory. The Kirchhoff formula is then obtained for moving surfaces in the time domain. The formula has a similar form to the Kirchhoff formulation for moving surfaces of Farassat and Myers, with the presence of additional terms owing to the moving medium effect. The equation explicitly accounts for the influence of mean flow and angle of attack on the radiated noise. The formula is verified by analytical cases of a monopole source located in a moving medium.

Experimental Validation of Lightning-Induced Electromagnetic (Indirect) Coupling to Short Monopole Antennas

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

Crull, E W; Brown Jr., C G; Perkins, M P

2008-07-30

For short monopoles in this low-power case, it has been shown that a simple circuit model is capable of accurate predictions for the shape and magnitude of the antenna response to lightning-generated electric field coupling effects, provided that the elements of the circuit model have accurate values. Numerical EM simulation can be used to provide more accurate values for the circuit elements than the simple analytical formulas, since the analytical formulas are used outside of their region of validity. However, even with the approximate analytical formulas the simple circuit model produces reasonable results, which would improve if more accurate analyticalmore » models were used. This report discusses the coupling analysis approaches taken to understand the interaction between a time-varying EM field and a short monopole antenna, within the context of lightning safety for nuclear weapons at DOE facilities. It describes the validation of a simple circuit model using laboratory study in order to understand the indirect coupling of energy into a part, and the resulting voltage. Results show that in this low-power case, the circuit model predicts peak voltages within approximately 32% using circuit component values obtained from analytical formulas and about 13% using circuit component values obtained from numerical EM simulation. We note that the analytical formulas are used outside of their region of validity. First, the antenna is insulated and not a bare wire and there are perhaps fringing field effects near the termination of the outer conductor that the formula does not take into account. Also, the effective height formula is for a monopole directly over a ground plane, while in the time-domain measurement setup the monopole is elevated above the ground plane by about 1.5-inch (refer to Figure 5).« less

Radiative processes in the intracluster plasma

NASA Astrophysics Data System (ADS)

Itoh, N.; Sakamoto, T.; Kusano, S.; Kawana, Y.; Nozawa, S.

2002-02-01

We present useful analytic fitting formulae for the study of the radiative processes which take place in the hot intracluster plasma (the plasma which exists in the clusters of galaxies). The first is for the frequency-integrated emissivity of the relativistic thermal bremsstrahlung. The Gaunt factor for the relativistic thermal bremsstrahlung as a function of the ionic charge Zj, the electron temperature Te, and the photon frequency omega has been recently calculated by us and its analytic fitting formula has been presented. In this paper we will integrate this Gaunt factor over the photon frequency omega and express the results by accurate analytic fitting formulae. These results will be useful when one wishes to evaluate the total amount of energy emitted by the hot intracluster plasma as well as other hot plasmas that exist in supernova remnants. The present results for the frequency-integrated emissivity of the thermal bremsstrahlung generally have accuracy of the order of 0.1%, thus making the present results the most accurate to date that calculate the thermal bremsstrahlung due to electron-ion scattering. The present accurate results will be especially useful for the analysis of the precision data taken by the Chandra X-Ray Observatory and XMM-Newton. The second analytic fitting formula that we will present in this paper is for the thermal Sunyaev-Zeldovich effect for clusters of galaxies. The thermal Sunyaev-Zeldovich effect for clusters of galaxies has been recently calculated with high precision by the present authors as well as by other groups. We have, in particular, presented an analytic fitting formula for this effect. In this paper we will present an analytic fitting formula which has still higher accuracy. The present fitting formula will be particularly suited for the forthcoming measurements of the kinematical Sunyaev-Zeldovich effect such as the BOLOCAM project that will be carried out in the crossover frequency region where the thermal Sunyaev-Zeldovich signal changes from negative to positive sign.

Viscous damping and spring force in periodic perforated planar microstructures when the Reynolds’ equation cannot be applied

PubMed Central

Homentcovschi, Dorel; Miles, Ronald N.

2010-01-01

A model of squeeze-film behavior is developed based on Stokes’ equations for viscous, compressible isothermal flows. The flow domain is an axisymmetrical, unit cell approximation of a planar, periodic, perforated microstructure. The model is developed for cases when the lubrication approximation cannot be applied. The complex force generated by vibrations of the diaphragm driving the flow has two components: the damping force and the spring force. While for large frequencies the spring force dominates, at low (acoustical) frequencies the damping force is the most important part. The analytical approach developed here yields an explicit formula for both forces. In addition, using a finite element software package, the damping force is also obtained numerically. A comparison is made between the analytic result, numerical solution, and some experimental data found in the literature, which validates the analytic formula and provides compelling arguments about its value in designing microelectomechanical devices. PMID:20329828

Method development and validation for total haloxyfop analysis in infant formulas and related ingredient matrices using liquid chromatography-tandem mass spectrometry.

PubMed

Koesukwiwat, Urairat; Vaclavik, Lukas; Mastovska, Katerina

2018-05-08

According to the European Commission directive 2006/141/EC, haloxyfop residue levels should not exceed 0.003 mg/kg in ready-to-feed infant formula, and the residue definition includes sum of haloxyfop, its esters, salts, and conjugates expressed as haloxyfop. A simple method for total haloxyfop analysis in infant formula and related ingredient matrices was developed and validated using liquid chromatography-tandem mass spectrometry (LC-MS/MS). The sample preparation consisted of an alkaline hydrolysis with methanolic sodium hydroxide to release haloxyfop (parent acid) from its bound forms prior to the extraction with acetonitrile. A mixture of magnesium sulfate (MgSO 4 ) and sodium chloride (NaCl) (4:1, w/w) was added to the extract to induce phase separation and force the analyte into the upper acetonitrile-methanol layer and then a 1-mL aliquot was subsequently cleaned up by dispersive solid phase extraction with 150 mg of MgSO 4 and 50 mg of octadecyl (C 18 ) sorbent. The analytical procedure was developed and carefully optimized to enable low-level, total haloxyfop analysis in a variety of challenging matrices, including infant formulas and their important high-carbohydrate, high-protein, high-fat, and emulsifier ingredients. The final method was validated in two different laboratories by fortifying samples with haloxyfop and haloxyfop-methyl, which was used as a model compound simulating bound forms of the analyte. Mean recoveries of haloxyfop across all fortification levels and evaluated matrices ranged between 92.2 and 114% with repeatability, within-lab reproducibility, and reproducibility RSDs ≤ 14%. Based on the validation results, this method was capable to convert the haloxyfop ester into the parent acid in a wide range of sample types and to reliably identify and quantify total haloxyfop at the target 0.003 mg/kg level in infant formulas (both powdered and ready-to-feed liquid forms). Graphical abstract LC-MS/MS-based workflow for the determination of the total haloxyfop in infant formula and related ingredients.

Phenomenological model to fit complex permittivity data of water from radio to optical frequencies.

PubMed

Shubitidze, Fridon; Osterberg, Ulf

2007-04-01

A general factorized form of the dielectric function together with a fractional model-based parameter estimation method is used to provide an accurate analytical formula for the complex refractive index in water for the frequency range 10(8)-10(16)Hz . The analytical formula is derived using a combination of a microscopic frequency-dependent rational function for adjusting zeros and poles of the dielectric dispersion together with the macroscopic statistical Fermi-Dirac distribution to provide a description of both the real and imaginary parts of the complex permittivity for water. The Fermi-Dirac distribution allows us to model the dramatic reduction in the imaginary part of the permittivity in the visible window of the water spectrum.

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

Chhiber, R; Usmanov, AV; Matthaeus, WH

Simple estimates of the number of Coulomb collisions experienced by the interplanetary plasma to the point of observation, i.e., the “collisional age”, can be usefully employed in the study of non-thermal features of the solar wind. Usually these estimates are based on local plasma properties at the point of observation. Here we improve the method of estimation of the collisional age by employing solutions obtained from global three-dimensional magnetohydrodynamics simulations. This enables evaluation of the complete analytical expression for the collisional age without using approximations. The improved estimation of the collisional timescale is compared with turbulence and expansion timescales tomore » assess the relative importance of collisions. The collisional age computed using the approximate formula employed in previous work is compared with the improved simulation-based calculations to examine the validity of the simplified formula. We also develop an analytical expression for the evaluation of the collisional age and we find good agreement between the numerical and analytical results. Finally, we briefly discuss the implications for an improved estimation of collisionality along spacecraft trajectories, including Solar Probe Plus.« less

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

Hirano, Teruyuki; Suto, Yasushi; Taruya, Atsushi

We obtain analytical expressions for the velocity anomaly due to the Rossiter-McLaughlin (RM) effect, for the case when the anomalous radial velocity is obtained by cross-correlation with a stellar template spectrum. In the limit of vanishing width of the stellar absorption lines, our result reduces to the formula derived by Ohta et al., which is based on the first moment of distorted stellar lines. Our new formula contains a term dependent on the stellar line width, which becomes important when rotational line broadening is appreciable. We generate mock transit spectra for four existing exoplanetary systems (HD 17156, TrES-2, TrES-4, andmore » HD 209458) following the procedure of Winn et al., and find that the new formula is in better agreement with the velocity anomaly extracted from the mock data. Thus, our result provides a more reliable analytical description of the velocity anomaly due to the RM effect, and explains the previously observed dependence of the velocity anomaly on the stellar rotation velocity.« less

An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells

DOE PAGES

Diot, Steven; François, Marianne M.

2015-10-22

In this study, we are interested in an interface reconstruction method for 3D arbitrary convex cells that could be used in multi-material flow simulations for instance. We assume that the interface is represented by a plane whose normal vector is known and we focus on the volume-matching step that consists in finding the plane constant so that it splits the cell according to a given volume fraction. We follow the same approach as in the recent authors' publication for 2D arbitrary convex cells in planar and axisymmetrical geometries, namely we derive an analytical formula for the volume of the specificmore » prismatoids obtained when decomposing the cell using the planes that are parallel to the interface and passing through all the cell nodes. This formula is used to bracket the interface plane constant such that the volume-matching problem is rewritten in a single prismatoid in which the same formula is used to find the final solution. Finally, the proposed method is tested against an important number of reproducible configurations and shown to be at least five times faster.« less

Stochastic-analytic approach to the calculation of multiply scattered lidar returns

NASA Astrophysics Data System (ADS)

Gillespie, D. T.

1985-08-01

The problem of calculating the nth-order backscattered power of a laser firing short pulses at time zero into an homogeneous cloud with specified scattering and absorption parameters, is discussed. In the problem, backscattered power is measured at any time less than zero by a small receiver colocated with the laser and fitted with a forward looking conical baffle. Theoretical calculations are made on the premise that the laser pulse is composed of propagating photons which are scattered and absorbed by the cloud particles in a probabilistic manner. The effect of polarization was not taken into account in the calculations. An exact formula is derived for backscattered power, based on direct physical arguments together with a rigorous analysis of random variables. It is shown that, for values of n less than or equal to 2, the obtained formula is a well-behaved (3n-4) dimensionless integral. The computational feasibility of the integral formula is demonstrated for a model cloud of isotropically scattering particles. An analytical formula is obtained for a value of n = 2, and a Monte Carlo program was used to obtain numerical results for values of n = 3, . . ., 6.

A Modified Formula of the First-order Approximation for Assessing the Contribution of Climate Change to Runoff Based on the Budyko Hypothesis

NASA Astrophysics Data System (ADS)

Liu, W.; Ning, T.; Han, X.

2015-12-01

The climate elasticity based on the Budyko curves has been widely used to evaluate the hydrological responses to climate change. The Mezentsev-Choudhury-Yang formula is one of the representative analytical equations for Budyko curves. Previous researches mostly used the variation of runoff (R) caused by the changes of annual precipitation (P) and potential evapotranspiration (ET0) as the hydrological response to climate change and evaluated it by a first-order approximation in a form of total differential, the major components of which include the partial derivatives of R to P and ET0, as well as climate elasticity on this basis. Based on analytic derivation and the characteristics of Budyko curves, this study proposed a modified formula of the first-order approximation to reduce the errors from the approximation. In the calculation of partial derivatives and climate elasticity, the values of P and ET0 were taken to the sum of their base values and half increments, respectively. The calculation was applied in 33 catchments of the Hai River basin in China and the results showed that the mean absolute value of relative error of approximated runoff change decreased from 8.4% to 0.4% and the maximum value, from 23.4% to 1.3%. Given the variation values of P, ET0 and the controlling parameter (n), the modified formula can exactly quantify the contributions of climate fluctuation and underlying surface change to runoff. Taking the Murray-Darling basin in Australia as an example of the contribution calculated by the modified formula, the reductions of mean annual runoff caused by changes of P, ET0 and n from 1895-1996 to 1997-2006 were 2.6, 0.6 and 2.9 mm, respectively, and the sum of them was 6.1 mm, which was completely consistent with the observed runoff. The modified formula of the first-order approximation proposed in this study can be not only used to assess the contributions of climate change to the runoff, but also widely used to analyze the effects of similar issues based on a certain functional relationship in hydrological and climate changes.

Glycation products in infant formulas: chemical, analytical and physiological aspects.

PubMed

Pischetsrieder, Monika; Henle, Thomas

2012-04-01

Infant formulas are milk-based products, which are adapted to the composition of human milk. To ensure microbiological safety and long shelf life, infant formulas usually undergo rigid heat treatment. As a consequence of the special composition and the heat regimen, infant formulas are more prone to thermally induced degradation reactions than regular milk products. Degradation reactions observed during milk processing comprise lactosylation yielding the Amadori product lactulosyllysine, the formation of advanced glycation end products (AGEs), and protein-free sugar degradation products, as well as protein or lipid oxidation. Several methods have been developed to estimate the heat impact applied during the manufacturing of infant formulas, including indirect methods such as fluorescence analysis as well as the analysis of defined reaction products. Most studies confirm a higher degree of damage in infant formulas compared to regular milk products. Differences between various types of infant formulas, such as liquid, powdered or hypoallergenic formulas depend on the analyzed markers and brands. A considerable portion of protein degradation products in infant formulas can be avoided when process parameters and the quality of the ingredients are carefully controlled. The nutritional consequences of thermal degradation products in infant formulas are largely unknown.

A New Newton-Like Iterative Method for Roots of Analytic Functions

ERIC Educational Resources Information Center

Otolorin, Olayiwola

2005-01-01

A new Newton-like iterative formula for the solution of non-linear equations is proposed. To derive the formula, the convergence criteria of the one-parameter iteration formula, and also the quasilinearization in the derivation of Newton's formula are reviewed. The result is a new formula which eliminates the limitations of other methods. There is…

VOFTools - A software package of calculation tools for volume of fluid methods using general convex grids

NASA Astrophysics Data System (ADS)

López, J.; Hernández, J.; Gómez, P.; Faura, F.

2018-02-01

The VOFTools library includes efficient analytical and geometrical routines for (1) area/volume computation, (2) truncation operations that typically arise in VOF (volume of fluid) methods, (3) area/volume conservation enforcement (VCE) in PLIC (piecewise linear interface calculation) reconstruction and(4) computation of the distance from a given point to the reconstructed interface. The computation of a polyhedron volume uses an efficient formula based on a quadrilateral decomposition and a 2D projection of each polyhedron face. The analytical VCE method is based on coupling an interpolation procedure to bracket the solution with an improved final calculation step based on the above volume computation formula. Although the library was originally created to help develop highly accurate advection and reconstruction schemes in the context of VOF methods, it may have more general applications. To assess the performance of the supplied routines, different tests, which are provided in FORTRAN and C, were implemented for several 2D and 3D geometries.

Approximation of epidemic models by diffusion processes and their statistical inference.

PubMed

Guy, Romain; Larédo, Catherine; Vergu, Elisabeta

2015-02-01

Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.

Analytical skin friction and heat transfer formula for compressible internal flows

NASA Technical Reports Server (NTRS)

Dechant, Lawrence J.; Tattar, Marc J.

1994-01-01

An analytic, closed-form friction formula for turbulent, internal, compressible, fully developed flow was derived by extending the incompressible law-of-the-wall relation to compressible cases. The model is capable of analyzing heat transfer as a function of constant surface temperatures and surface roughness as well as analyzing adiabatic conditions. The formula reduces to Prandtl's law of friction for adiabatic, smooth, axisymmetric flow. In addition, the formula reduces to the Colebrook equation for incompressible, adiabatic, axisymmetric flow with various roughnesses. Comparisons with available experiments show that the model averages roughly 12.5 percent error for adiabatic flow and 18.5 percent error for flow involving heat transfer.

Hollow Gaussian Schell-model beam and its propagation

NASA Astrophysics Data System (ADS)

Wang, Li-Gang; Wang, Li-Qin

2008-03-01

In this paper, we present a new model, hollow Gaussian Schell-model beams (HGSMBs), to describe the practical dark hollow beams. An analytical propagation formula for HGSMBs passing through a paraxial first-order optical system is derived based on the theory of coherence. Based on the derived formula, an application example showing the influence of spatial coherence on the propagation of beams is illustrated. It is found that the beam propagating properties of HGSMBs will be greatly affected by their spatial coherence. Our model provides a very convenient way for analyzing the propagation properties of partially coherent dark hollow beams.

A simple calculation method for determination of equivalent square field.

PubMed

Shafiei, Seyed Ali; Hasanzadeh, Hadi; Shafiei, Seyed Ahmad

2012-04-01

Determination of the equivalent square fields for rectangular and shielded fields is of great importance in radiotherapy centers and treatment planning software. This is accomplished using standard tables and empirical formulas. The goal of this paper is to present a formula based on analysis of scatter reduction due to inverse square law to obtain equivalent field. Tables are published by different agencies such as ICRU (International Commission on Radiation Units and measurements), which are based on experimental data; but there exist mathematical formulas that yield the equivalent square field of an irregular rectangular field which are used extensively in computation techniques for dose determination. These processes lead to some complicated and time-consuming formulas for which the current study was designed. In this work, considering the portion of scattered radiation in absorbed dose at a point of measurement, a numerical formula was obtained based on which a simple formula was developed to calculate equivalent square field. Using polar coordinate and inverse square law will lead to a simple formula for calculation of equivalent field. The presented method is an analytical approach based on which one can estimate the equivalent square field of a rectangular field and may be used for a shielded field or an off-axis point. Besides, one can calculate equivalent field of rectangular field with the concept of decreased scatter radiation with inverse square law with a good approximation. This method may be useful in computing Percentage Depth Dose and Tissue-Phantom Ratio which are extensively used in treatment planning.

Point spread functions and deconvolution of ultrasonic images.

PubMed

Dalitz, Christoph; Pohle-Fröhlich, Regina; Michalk, Thorsten

2015-03-01

This article investigates the restoration of ultrasonic pulse-echo C-scan images by means of deconvolution with a point spread function (PSF). The deconvolution concept from linear system theory (LST) is linked to the wave equation formulation of the imaging process, and an analytic formula for the PSF of planar transducers is derived. For this analytic expression, different numerical and analytic approximation schemes for evaluating the PSF are presented. By comparing simulated images with measured C-scan images, we demonstrate that the assumptions of LST in combination with our formula for the PSF are a good model for the pulse-echo imaging process. To reconstruct the object from a C-scan image, we compare different deconvolution schemes: the Wiener filter, the ForWaRD algorithm, and the Richardson-Lucy algorithm. The best results are obtained with the Richardson-Lucy algorithm with total variation regularization. For distances greater or equal twice the near field distance, our experiments show that the numerically computed PSF can be replaced with a simple closed analytic term based on a far field approximation.

A time-domain Kirchhoff formula for the convective acoustic wave equation

PubMed Central

Ghorbaniasl, Ghader; Siozos-Rousoulis, Leonidas; Lacor, Chris

2016-01-01

Kirchhoff’s integral method allows propagated sound to be predicted, based on the pressure and its derivatives in time and space obtained on a data surface located in the linear flow region. Kirchhoff’s formula for noise prediction from high-speed rotors and propellers suffers from the limitation of the observer located in uniform flow, thus requiring an extension to arbitrarily moving media. This paper presents a Kirchhoff formulation for moving surfaces in a uniform moving medium of arbitrary configuration. First, the convective wave equation is derived in a moving frame, based on the generalized functions theory. The Kirchhoff formula is then obtained for moving surfaces in the time domain. The formula has a similar form to the Kirchhoff formulation for moving surfaces of Farassat and Myers, with the presence of additional terms owing to the moving medium effect. The equation explicitly accounts for the influence of mean flow and angle of attack on the radiated noise. The formula is verified by analytical cases of a monopole source located in a moving medium. PMID:27118912

General monogamy of Tsallis q -entropy entanglement in multiqubit systems

NASA Astrophysics Data System (ADS)

Luo, Yu; Tian, Tian; Shao, Lian-He; Li, Yongming

2016-06-01

In this paper, we study the monogamy inequality of Tsallis q -entropy entanglement. We first provide an analytic formula of Tsallis q -entropy entanglement in two-qubit systems for 5/-√{13 } 2 ≤q ≤5/+√{13 } 2 . The analytic formula of Tsallis q -entropy entanglement in 2 ⊗d system is also obtained and we show that Tsallis q -entropy entanglement satisfies a set of hierarchical monogamy equalities. Furthermore, we prove the squared Tsallis q -entropy entanglement follows a general inequality in the qubit systems. Based on the monogamy relations, a set of multipartite entanglement indicators is constructed, which can detect all genuine multiqubit entangled states even in the case of N -tangle vanishes. Moreover, we study some examples in multipartite higher-dimensional system for the monogamy inequalities.

Analytical studies on holographic superconductor in the probe limit

NASA Astrophysics Data System (ADS)

Peng, Yan; Liu, Guohua

2017-09-01

We investigate the holographic superconductor model constructed in the (2+1)-dimensional AdS soliton background in the probe limit. With analytical methods, we obtain the formula of critical phase transition points with respect to the scalar mass. We also generalize this formula to higher-dimensional space-time. We mention that these formulas are precise compared to numerical results. In addition, we find a correspondence between the value of the charged scalar field at the tip and the scalar operator at infinity around the phase transition points.

Theory of the control of structures by low authority controllers

NASA Technical Reports Server (NTRS)

Aubrun, J. N.

1978-01-01

The novel idea presented is based on the observation that if a structure is controlled by distributed systems of sensors and actuators with limited authority, i.e., if the controller is allowed to modify only moderately the natural modes and frequencies of the structure, then it should be possible to apply root perturbation techniques to predict analytically the behavior of the total system. Attention is given to the root perturbation formula first derived by Jacobi for infinitesimal perturbations which neglect the induced eigenvector perturbation, a more general form of Jacobi's formula, first-order structural equations and modal state vectors, state-space equations for damper-augmented structures, and modal damping prediction formulas.

Simplified Formulae System for Resonant Inverse Compton Scattering of a Fast Electron in an Intense Magnetic Field

NASA Technical Reports Server (NTRS)

You, J. H.; Chen, W. P.; Zhang, S. N.; Chen, L.; Liu, D.; Chou, C. K.

2003-01-01

We present simple analytical formulae for the emission spectrum and total power of a special kind of resonant inverse Compton scattering (RICS) of a relativistic electron in an intense magnetic field. In contrast with the available formulae system, we obtain a markedly simplified one based on the semiclassical quantum theory, which is more understandable for people who are unfamiliar with quantum electrodynamics. We show that the RICS process, under an appropriate 'accommodation condition' derived in this paper, is predominantly much more efficient than the coexistent ordinary inverse Compton scattering, and produces highly beamed high-frequency radiation with moderately good monochromaticity. Our formulae are simple to use - thus offering a lucid physical intuition for the theory - and may find wide applications in hard X-ray and gamma-ray astrophysics.

Transport of a decay chain in homogenous porous media: analytical solutions.

PubMed

Bauer, P; Attinger, S; Kinzelbach, W

2001-06-01

With the aid of integral transforms, analytical solutions for the transport of a decay chain in homogenous porous media are derived. Unidirectional steady-state flow and radial steady-state flow in single and multiple porosity media are considered. At least in Laplace domain, all solutions can be written in closed analytical formulae. Partly, the solutions can also be inverted analytically. If not, analytical calculation of the steady-state concentration distributions, evaluation of temporal moments and numerical inversion are still possible. Formulae for several simple boundary conditions are given and visualized in this paper. The derived novel solutions are widely applicable and are very useful for the validation of numerical transport codes.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result.

PubMed

Wu, Yang; Kelly, Damien P

2014-12-12

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

A simple calculation method for determination of equivalent square field

PubMed Central

Shafiei, Seyed Ali; Hasanzadeh, Hadi; Shafiei, Seyed Ahmad

2012-01-01

Determination of the equivalent square fields for rectangular and shielded fields is of great importance in radiotherapy centers and treatment planning software. This is accomplished using standard tables and empirical formulas. The goal of this paper is to present a formula based on analysis of scatter reduction due to inverse square law to obtain equivalent field. Tables are published by different agencies such as ICRU (International Commission on Radiation Units and measurements), which are based on experimental data; but there exist mathematical formulas that yield the equivalent square field of an irregular rectangular field which are used extensively in computation techniques for dose determination. These processes lead to some complicated and time-consuming formulas for which the current study was designed. In this work, considering the portion of scattered radiation in absorbed dose at a point of measurement, a numerical formula was obtained based on which a simple formula was developed to calculate equivalent square field. Using polar coordinate and inverse square law will lead to a simple formula for calculation of equivalent field. The presented method is an analytical approach based on which one can estimate the equivalent square field of a rectangular field and may be used for a shielded field or an off-axis point. Besides, one can calculate equivalent field of rectangular field with the concept of decreased scatter radiation with inverse square law with a good approximation. This method may be useful in computing Percentage Depth Dose and Tissue-Phantom Ratio which are extensively used in treatment planning. PMID:22557801

Anomaly formulas for the complex-valued analytic torsion on compact bordisms

PubMed Central

Maldonado Molina, Osmar

2013-01-01

We extend the complex-valued analytic torsion, introduced by Burghelea and Haller on closed manifolds, to compact Riemannian bordisms. We do so by considering a flat complex vector bundle over a compact Riemannian manifold, endowed with a fiberwise nondegenerate symmetric bilinear form. The Riemmanian metric and the bilinear form are used to define non-selfadjoint Laplacians acting on vector-valued smooth forms under absolute and relative boundary conditions. In order to define the complex-valued analytic torsion in this situation, we study spectral properties of these generalized Laplacians. Then, as main results, we obtain so-called anomaly formulas for this torsion. Our reasoning takes into account that the coefficients in the heat trace asymptotic expansion associated to the boundary value problem under consideration, are locally computable. The anomaly formulas for the complex-valued Ray–Singer torsion are derived first by using the corresponding ones for the Ray–Singer metric, obtained by Brüning and Ma on manifolds with boundary, and then an argument of analytic continuation. In odd dimensions, our anomaly formulas are in accord with the corresponding results of Su, without requiring the variations of the Riemannian metric and bilinear structures to be supported in the interior of the manifold. PMID:27087744

High-Contrast Gratings based Spoof Surface Plasmons

NASA Astrophysics Data System (ADS)

Li, Zhuo; Liu, Liangliang; Xu, Bingzheng; Ning, Pingping; Chen, Chen; Xu, Jia; Chen, Xinlei; Gu, Changqing; Qing, Quan

2016-02-01

In this work, we explore the existence of spoof surface plasmons (SSPs) supported by deep-subwavelength high-contrast gratings (HCGs) on a perfect electric conductor plane. The dispersion relation of the HCGs-based SSPs is derived analyt- ically by combining multimode network theory with rigorous mode matching method, which has nearly the same form with and can be degenerated into that of the SSPs arising from deep-subwavelength metallic gratings (MGs). Numerical simula- tions validate the analytical dispersion relation and an effective medium approximation is also presented to obtain the same analytical dispersion formula. This work sets up a unified theoretical framework for SSPs and opens up new vistas in surface plasmon optics.

On the superposition principle in interference experiments.

PubMed

Sinha, Aninda; H Vijay, Aravind; Sinha, Urbasi

2015-05-14

The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrödinger equation.

Leading non-Gaussian corrections for diffusion orientation distribution function.

PubMed

Jensen, Jens H; Helpern, Joseph A; Tabesh, Ali

2014-02-01

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed from the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves on the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. 2013 John Wiley & Sons, Ltd.

Leading Non-Gaussian Corrections for Diffusion Orientation Distribution Function

PubMed Central

Jensen, Jens H.; Helpern, Joseph A.; Tabesh, Ali

2014-01-01

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed out of the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves upon the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. PMID:24738143

An analytic formula for the supercluster mass function

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

Lim, Seunghwan; Lee, Jounghun, E-mail: slim@astro.umass.edu, E-mail: jounghun@astro.snu.ac.kr

2014-03-01

We present an analytic formula for the supercluster mass function, which is constructed by modifying the extended Zel'dovich model for the halo mass function. The formula has two characteristic parameters whose best-fit values are determined by fitting to the numerical results from N-body simulations for the standard ΛCDM cosmology. The parameters are found to be independent of redshifts and robust against variation of the key cosmological parameters. Under the assumption that the same formula for the supercluster mass function is valid for non-standard cosmological models, we show that the relative abundance of the rich superclusters should be a powerful indicatormore » of any deviation of the real universe from the prediction of the standard ΛCDM model.« less

An alternative model for a partially coherent elliptical dark hollow beam

NASA Astrophysics Data System (ADS)

Li, Xu; Wang, Fei; Cai, Yangjian

2011-04-01

An alternative theoretical model named partially coherent hollow elliptical Gaussian beam (HEGB) is proposed to describe a partially coherent beam with an elliptical dark hollow profile. Explicit expression for the propagation factors of a partially coherent HEGB is derived. Based on the generalized Collins formula, analytical formulae for the cross-spectral density and mean-squared beam width of a partially coherent HEGB, propagating through a paraxial ABCD optical system, are derived. Propagation properties of a partially coherent HEGB in free space are studied as a numerical example.

Corrected Four-Sphere Head Model for EEG Signals.

PubMed

Næss, Solveig; Chintaluri, Chaitanya; Ness, Torbjørn V; Dale, Anders M; Einevoll, Gaute T; Wójcik, Daniel K

2017-01-01

The EEG signal is generated by electrical brain cell activity, often described in terms of current dipoles. By applying EEG forward models we can compute the contribution from such dipoles to the electrical potential recorded by EEG electrodes. Forward models are key both for generating understanding and intuition about the neural origin of EEG signals as well as inverse modeling, i.e., the estimation of the underlying dipole sources from recorded EEG signals. Different models of varying complexity and biological detail are used in the field. One such analytical model is the four-sphere model which assumes a four-layered spherical head where the layers represent brain tissue, cerebrospinal fluid (CSF), skull, and scalp, respectively. While conceptually clear, the mathematical expression for the electric potentials in the four-sphere model is cumbersome, and we observed that the formulas presented in the literature contain errors. Here, we derive and present the correct analytical formulas with a detailed derivation. A useful application of the analytical four-sphere model is that it can serve as ground truth to test the accuracy of numerical schemes such as the Finite Element Method (FEM). We performed FEM simulations of the four-sphere head model and showed that they were consistent with the corrected analytical formulas. For future reference we provide scripts for computing EEG potentials with the four-sphere model, both by means of the correct analytical formulas and numerical FEM simulations.

Corrected Four-Sphere Head Model for EEG Signals

PubMed Central

Næss, Solveig; Chintaluri, Chaitanya; Ness, Torbjørn V.; Dale, Anders M.; Einevoll, Gaute T.; Wójcik, Daniel K.

2017-01-01

The EEG signal is generated by electrical brain cell activity, often described in terms of current dipoles. By applying EEG forward models we can compute the contribution from such dipoles to the electrical potential recorded by EEG electrodes. Forward models are key both for generating understanding and intuition about the neural origin of EEG signals as well as inverse modeling, i.e., the estimation of the underlying dipole sources from recorded EEG signals. Different models of varying complexity and biological detail are used in the field. One such analytical model is the four-sphere model which assumes a four-layered spherical head where the layers represent brain tissue, cerebrospinal fluid (CSF), skull, and scalp, respectively. While conceptually clear, the mathematical expression for the electric potentials in the four-sphere model is cumbersome, and we observed that the formulas presented in the literature contain errors. Here, we derive and present the correct analytical formulas with a detailed derivation. A useful application of the analytical four-sphere model is that it can serve as ground truth to test the accuracy of numerical schemes such as the Finite Element Method (FEM). We performed FEM simulations of the four-sphere head model and showed that they were consistent with the corrected analytical formulas. For future reference we provide scripts for computing EEG potentials with the four-sphere model, both by means of the correct analytical formulas and numerical FEM simulations. PMID:29093671

An extended Zel'dovich model for the halo mass function

NASA Astrophysics Data System (ADS)

Lim, Seunghwan; Lee, Jounghun

2013-01-01

A new way to construct a fitting formula for the halo mass function is presented. Our formula is expressed as a solution to the modified Jedamzik matrix equation that automatically satisfies the normalization constraint. The characteristic parameters expressed in terms of the linear shear eigenvalues are empirically determined by fitting the analytic formula to the numerical results from the high-resolution N-body simulation and found to be independent of scale, redshift and background cosmology. Our fitting formula with the best-fit parameters is shown to work excellently in the wide mass-range at various redshifts: The ratio of the analytic formula to the N-body results departs from unity by up to 10% and 5% over 1011 <= M/(h-1Msolar) <= 5 × 1015 at z = 0,0.5 and 1 for the FoF-halo and SO-halo cases, respectively.

Simplified analysis about horizontal displacement of deep soil under tunnel excavation

NASA Astrophysics Data System (ADS)

Tian, Xiaoyan; Gu, Shuancheng; Huang, Rongbin

2017-11-01

Most of the domestic scholars focus on the study about the law of the soil settlement caused by subway tunnel excavation, however, studies on the law of horizontal displacement are lacking. And it is difficult to obtain the horizontal displacement data of any depth in the project. At present, there are many formulas for calculating the settlement of soil layers. In terms of integral solutions of Mindlin classic elastic theory, stochastic medium theory, source-sink theory, the Peck empirical formula is relatively simple, and also has a strong applicability at home. Considering the incompressibility of rock and soil mass, based on the principle of plane strain, the calculation formula of the horizontal displacement of the soil along the cross section of the tunnel was derived by using the Peck settlement formula. The applicability of the formula is verified by comparing with the existing engineering cases, a simple and rapid analytical method for predicting the horizontal displacement is presented.

Analytical formulas for short bunch wakes in a flat dechirper

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

Bane, Karl; Stupakov, Gennady; Zagorodnov, Igor

2016-08-04

We develop analytical models of the longitudinal and transverse wakes, on and off axis for a flat, corrugated beam pipe with realistic parameters, and then compare them with numerical calculations, and generally find good agreement. These analytical “first order” formulas approximate the droop at the origin of the longitudinal wake and of the slope of the transverse wakes; they represent an improvement in accuracy over earlier, “zeroth order” formulas. In example calculations for the RadiaBeam/LCLS dechirper using typical parameters, we find a 16% droop in the energy chirp at the bunch tail compared to simpler calculations. As a result, withmore » the beam moved to 200 μm from one jaw in one dechirper section, one can achieve a 3 MV transverse kick differential over a 30 μm length.« less

Observability during planetary approach navigation

NASA Technical Reports Server (NTRS)

Bishop, Robert H.; Burkhart, P. Daniel; Thurman, Sam W.

1993-01-01

The objective of the research is to develop an analytic technique to predict the relative navigation capability of different Earth-based radio navigation measurements. In particular, the problem is to determine the relative ability of geocentric range and Doppler measurements to detect the effects of the target planet gravitational attraction on the spacecraft during the planetary approach and near-encounter mission phases. A complete solution to the two-dimensional problem has been developed. Relatively simple analytic formulas are obtained for range and Doppler measurements which describe the observability content of the measurement data along the approach trajectories. An observability measure is defined which is based on the observability matrix for nonlinear systems. The results show good agreement between the analytic observability analysis and the computational batch processing method.

Recent α decay half-lives and analytic expression predictions including superheavy nuclei

NASA Astrophysics Data System (ADS)

Royer, G.; Zhang, H. F.

2008-03-01

New recent experimental α decay half-lives have been compared with the results obtained from previously proposed formulas depending only on the mass and charge numbers of the α emitter and the Qα value. For the heaviest nuclei they are also compared with calculations using the Density-Dependent M3Y (DDM3Y) effective interaction and the Viola-Seaborg-Sobiczewski (VSS) formulas. The correct agreement allows us to make predictions for the α decay half-lives of other still unknown superheavy nuclei from these analytic formulas using the extrapolated Qα of G. Audi, A. H. Wapstra, and C. Thibault [Nucl. Phys. A729, 337 (2003)].

Manipulation of radial-variant polarization for creating tunable bifocusing spots.

PubMed

Gu, Bing; Pan, Yang; Wu, Jia-Lu; Cui, Yiping

2014-02-01

We propose and generate a new radial-variant vector field (RV-VF) with a distribution of states of polarization described by the square of the radius and exploit its focusing property. Theoretically, we present the analytical expressions for the three-dimensional electric field of the vector field focused by a thin lens under the nonparaxial and paraxial approximations based on the vectorial Rayleigh-Sommerfeld formulas. Numerical simulations indicate that this focused field exhibits bifocusing spots along the optical axis. The underlying mechanism for generating the bifocusing property is analyzed in detail. We give the analytical formula for the interval between two foci. Experimentally, we generate the RV-VFs with alterable topological charge and demonstrate that the interval between two foci is controllable by tuning the radial topological charge. This particular focal field has specific applications for biparticle trapping, manipulating, alignment, transportation, and accelerating along the optical axis.

A direct method for nonlinear ill-posed problems

NASA Astrophysics Data System (ADS)

Lakhal, A.

2018-02-01

We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.

A numerical test of the topographic bias

NASA Astrophysics Data System (ADS)

Sjöberg, L. E.; Joud, M. S. S.

2018-02-01

In 1962 A. Bjerhammar introduced the method of analytical continuation in physical geodesy, implying that surface gravity anomalies are downward continued into the topographic masses down to an internal sphere (the Bjerhammar sphere). The method also includes analytical upward continuation of the potential to the surface of the Earth to obtain the quasigeoid. One can show that also the common remove-compute-restore technique for geoid determination includes an analytical continuation as long as the complete density distribution of the topography is not known. The analytical continuation implies that the downward continued gravity anomaly and/or potential are/is in error by the so-called topographic bias, which was postulated by a simple formula of L E Sjöberg in 2007. Here we will numerically test the postulated formula by comparing it with the bias obtained by analytical downward continuation of the external potential of a homogeneous ellipsoid to an inner sphere. The result shows that the postulated formula holds: At the equator of the ellipsoid, where the external potential is downward continued 21 km, the computed and postulated topographic biases agree to less than a millimetre (when the potential is scaled to the unit of metre).

The thermoelectric properties of strongly correlated systems

NASA Astrophysics Data System (ADS)

Cai, Jianwei

Strongly correlated systems are among the most interesting and complicated systems in physics. Large Seebeck coefficients are found in some of these systems, which highlight the possibility for thermoelectric applications. In this thesis, we study the thermoelectric properties of these strongly correlated systems with various methods. We derived analytic formulas for the resistivity and Seebeck coefficient of the periodic Anderson model based on the dynamic mean field theory. These formulas were possible as the self energy of the single impurity Anderson model could be given by an analytic ansatz derived from experiments and numerical calculations instead of complicated numerical calculations. The results show good agreement with the experimental data of rare-earth compound in a restricted temperature range. These formulas help to understand the properties of periodic Anderson model. Based on the study of rare-earth compounds, we proposed a design for the thermoelectric meta-material. This manmade material is made of quantum dots linked by conducting linkers. The quantum dots act as the rare-earth atoms with heavier mass. We set up a model similar to the periodic Anderson model for this new material. The new model was studied with the perturbation theory for energy bands. The dynamic mean field theory with numerical renormalization group as the impurity solver was used to study the transport properties. With these studies, we confirmed the improved thermoelectric properties of the designed material.

Spiral trajectory design: a flexible numerical algorithm and base analytical equations.

PubMed

Pipe, James G; Zwart, Nicholas R

2014-01-01

Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories. Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results. Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement. A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories. Copyright © 2013 Wiley Periodicals, Inc.

General Analytical Schemes for the Characterization of Pectin-Based Edible Gelled Systems

PubMed Central

Haghighi, Maryam; Rezaei, Karamatollah

2012-01-01

Pectin-based gelled systems have gained increasing attention for the design of newly developed food products. For this reason, the characterization of such formulas is a necessity in order to present scientific data and to introduce an appropriate finished product to the industry. Various analytical techniques are available for the evaluation of the systems formulated on the basis of pectin and the designed gel. In this paper, general analytical approaches for the characterization of pectin-based gelled systems were categorized into several subsections including physicochemical analysis, visual observation, textural/rheological measurement, microstructural image characterization, and psychorheological evaluation. Three-dimensional trials to assess correlations among microstructure, texture, and taste were also discussed. Practical examples of advanced objective techniques including experimental setups for small and large deformation rheological measurements and microstructural image analysis were presented in more details. PMID:22645484

The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry.

PubMed

Yang, Yi; Tang, Xiangyang

2012-12-01

The x-ray differential phase contrast imaging implemented with the Talbot interferometry has recently been reported to be capable of providing tomographic images corresponding to attenuation-contrast, phase-contrast, and dark-field contrast, simultaneously, from a single set of projection data. The authors believe that, along with small-angle x-ray scattering, the second-order phase derivative Φ(") (s)(x) plays a role in the generation of dark-field contrast. In this paper, the authors derive the analytic formulae to characterize the contribution made by the second-order phase derivative to the dark-field contrast (namely, second-order differential phase contrast) and validate them via computer simulation study. By proposing a practical retrieval method, the authors investigate the potential of second-order differential phase contrast imaging for extensive applications. The theoretical derivation starts at assuming that the refractive index decrement of an object can be decomposed into δ = δ(s) + δ(f), where δ(f) corresponds to the object's fine structures and manifests itself in the dark-field contrast via small-angle scattering. Based on the paraxial Fresnel-Kirchhoff theory, the analytic formulae to characterize the contribution made by δ(s), which corresponds to the object's smooth structures, to the dark-field contrast are derived. Through computer simulation with specially designed numerical phantoms, an x-ray differential phase contrast imaging system implemented with the Talbot interferometry is utilized to evaluate and validate the derived formulae. The same imaging system is also utilized to evaluate and verify the capability of the proposed method to retrieve the second-order differential phase contrast for imaging, as well as its robustness over the dimension of detector cell and the number of steps in grating shifting. Both analytic formulae and computer simulations show that, in addition to small-angle scattering, the contrast generated by the second-order derivative is magnified substantially by the ratio of detector cell dimension over grating period, which plays a significant role in dark-field imaging implemented with the Talbot interferometry. The analytic formulae derived in this work to characterize the second-order differential phase contrast in the dark-field imaging implemented with the Talbot interferometry are of significance, which may initiate more activities in the research and development of x-ray differential phase contrast imaging for extensive preclinical and eventually clinical applications.

Analytical description of generation of the residual current density in the plasma produced by a few-cycle laser pulse

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

Silaev, A. A., E-mail: silaev@appl.sci-nnov.ru; Vvedenskii, N. V., E-mail: vved@appl.sci-nnov.ru; University of Nizhny Novgorod, Nizhny Novgorod 603950

2015-05-15

When a gas is ionized by a few-cycle laser pulse, some residual current density (RCD) of free electrons remains in the produced plasma after the passage of the laser pulse. This quasi-dc RCD is an initial impetus to plasma polarization and excitation of the plasma oscillations which can radiate terahertz (THz) waves. In this work, the analytical model for calculation of RCD excited by a few-cycle laser pulse is developed for the first time. The dependences of the RCD on the carrier-envelope phase (CEP), wavelength, duration, and intensity of the laser pulse are derived. It is shown that maximum RCDmore » corresponding to optimal CEP increases with the laser pulse wavelength, which indicates the prospects of using mid-infrared few-cycle laser pulses in the schemes of generation of high-power THz pulses. Analytical formulas for optimal pulse intensity and maximum efficiency of excitation of the RCD are obtained. Basing on numerical solution of the 3D time-dependent Schrödinger equation for hydrogen atoms, RCD dependence on CEP is calculated in a wide range of wavelengths. High accuracy of analytical formulas is demonstrated at the laser pulse parameters which correspond to the tunneling regime of ionization.« less

Comprehensive representation of the Lennard-Jones equation of state based on molecular dynamics simulation data

NASA Astrophysics Data System (ADS)

Pieprzyk, S.; Brańka, A. C.; Maćkowiak, Sz.; Heyes, D. M.

2018-03-01

The equation of state (EoS) of the Lennard-Jones fluid is calculated using a new set of molecular dynamics data which extends to higher temperature than in previous studies. The modified Benedict-Webb-Rubin (MBWR) equation, which goes up to ca. T ˜ 6, is reparametrized with new simulation data. A new analytic form for the EoS, which breaks the fluid range into two regions with different analytic forms and goes up to ca. T ≃ 35, is also proposed. The accuracy of the new formulas is at least as good as the MBWR fit and goes to much higher temperature allowing it to now encompass the Amagat line. The fitted formula extends into the high temperature range where the system can be well represented by inverse power potential scaling, which means that our specification of the equation of state covers the entire (ρ, T) plane. Accurate analytic fit formulas for the Boyle, Amagat, and inversion curves are presented. Parametrizations of the extrema loci of the isochoric, CV, and isobaric, CP, heat capacities are given. As found by others, a line maxima of CP terminates in the critical point region, and a line of minima of CP terminates on the freezing line. The line of maxima of CV terminates close to or at the critical point, and a line of minima of CV terminates to the right of the critical point. No evidence for a divergence in CV in the critical region is found.

A climate-based malaria model with the use of bed nets.

PubMed

Wang, Xiunan; Zhao, Xiao-Qiang

2018-07-01

Insecticide-treated bed nets (ITNs) are among the most important and effective intervention measures against malaria. In order to investigate the impact of bed net use on disease control, we formulate a periodic vector-bias malaria model incorporating the juvenile stage of mosquitoes and the use of ITNs. We derive the vector reproduction ratio [Formula: see text] and the basic reproduction ratio [Formula: see text]. We show that the global dynamics of the model is completely determined by these two reproduction ratios. More precisely, the mosquito-free periodic solution is globally attractive if [Formula: see text]; the unique disease-free periodic solution is globally attractive if [Formula: see text] and [Formula: see text]; and the model admits a unique positive periodic solution and it is globally attractive if [Formula: see text] and [Formula: see text]. Numerically, we study the malaria transmission case in Port Harcourt, Nigeria. Our findings show that the use of ITNs has a positive effect on reducing [Formula: see text], and that malaria may be eliminated from this area if over 75% of the human population were to use ITNs. The simulation about the long term behavior of solutions has good agreement with the obtained analytic result. Moreover, we find that the ignorance of the vector-bias effect may result in underestimation of the basic reproduction ratio [Formula: see text]. Another notable result is that the infection risk would be underestimated if the basic reproduction ratio [Formula: see text] of the time-averaged autonomous system were used.

Recent {alpha} decay half-lives and analytic expression predictions including superheavy nuclei

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

Royer, G.; Zhang, H. F.

New recent experimental {alpha} decay half-lives have been compared with the results obtained from previously proposed formulas depending only on the mass and charge numbers of the {alpha} emitter and the Q{sub {alpha}} value. For the heaviest nuclei they are also compared with calculations using the Density-Dependent M3Y (DDM3Y) effective interaction and the Viola-Seaborg-Sobiczewski (VSS) formulas. The correct agreement allows us to make predictions for the {alpha} decay half-lives of other still unknown superheavy nuclei from these analytic formulas using the extrapolated Q{sub {alpha}} of G. Audi, A. H. Wapstra, and C. Thibault [Nucl. Phys. A729, 337 (2003)].

Improved multidimensional semiclassical tunneling theory.

PubMed

Wagner, Albert F

2013-12-12

We show that the analytic multidimensional semiclassical tunneling formula of Miller et al. [Miller, W. H.; Hernandez, R.; Handy, N. C.; Jayatilaka, D.; Willets, A. Chem. Phys. Lett. 1990, 172, 62] is qualitatively incorrect for deep tunneling at energies well below the top of the barrier. The origin of this deficiency is that the formula uses an effective barrier weakly related to the true energetics but correctly adjusted to reproduce the harmonic description and anharmonic corrections of the reaction path at the saddle point as determined by second order vibrational perturbation theory. We present an analytic improved semiclassical formula that correctly includes energetic information and allows a qualitatively correct representation of deep tunneling. This is done by constructing a three segment composite Eckart potential that is continuous everywhere in both value and derivative. This composite potential has an analytic barrier penetration integral from which the semiclassical action can be derived and then used to define the semiclassical tunneling probability. The middle segment of the composite potential by itself is superior to the original formula of Miller et al. because it incorporates the asymmetry of the reaction barrier produced by the known reaction exoergicity. Comparison of the semiclassical and exact quantum tunneling probability for the pure Eckart potential suggests a simple threshold multiplicative factor to the improved formula to account for quantum effects very near threshold not represented by semiclassical theory. The deep tunneling limitations of the original formula are echoed in semiclassical high-energy descriptions of bound vibrational states perpendicular to the reaction path at the saddle point. However, typically ab initio energetic information is not available to correct it. The Supporting Information contains a Fortran code, test input, and test output that implements the improved semiclassical tunneling formula.

Agent-based model for the h-index - exact solution

NASA Astrophysics Data System (ADS)

Żogała-Siudem, Barbara; Siudem, Grzegorz; Cena, Anna; Gagolewski, Marek

2016-01-01

Hirsch's h-index is perhaps the most popular citation-based measure of scientific excellence. In 2013, Ionescu and Chopard proposed an agent-based model describing a process for generating publications and citations in an abstract scientific community [G. Ionescu, B. Chopard, Eur. Phys. J. B 86, 426 (2013)]. Within such a framework, one may simulate a scientist's activity, and - by extension - investigate the whole community of researchers. Even though the Ionescu and Chopard model predicts the h-index quite well, the authors provided a solution based solely on simulations. In this paper, we complete their results with exact, analytic formulas. What is more, by considering a simplified version of the Ionescu-Chopard model, we obtained a compact, easy to compute formula for the h-index. The derived approximate and exact solutions are investigated on a simulated and real-world data sets.

Soft x-ray continuum radiation transmitted through metallic filters: an analytical approach to fast electron temperature measurements.

PubMed

Delgado-Aparicio, L; Tritz, K; Kramer, T; Stutman, D; Finkenthal, M; Hill, K; Bitter, M

2010-10-01

A new set of analytic formulas describes the transmission of soft x-ray continuum radiation through a metallic foil for its application to fast electron temperature measurements in fusion plasmas. This novel approach shows good agreement with numerical calculations over a wide range of plasma temperatures in contrast with the solutions obtained when using a transmission approximated by a single-Heaviside function [S. von Goeler et al., Rev. Sci. Instrum. 70, 599 (1999)]. The new analytic formulas can improve the interpretation of the experimental results and thus contribute in obtaining fast temperature measurements in between intermittent Thomson scattering data.

Constraints on the [Formula: see text] form factor from analyticity and unitarity.

PubMed

Ananthanarayan, B; Caprini, I; Kubis, B

Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic [Formula: see text] form factor and certain experimental data, we investigate this form factor using analyticity and unitarity in a framework known as the method of unitarity bounds. We use a QCD correlator computed on the spacelike axis by operator product expansion and perturbative QCD as input, and exploit unitarity and the positivity of its spectral function, including the two-pion contribution that can be reliably calculated using high-precision data on the pion form factor. From this information, we derive upper and lower bounds on the modulus of the [Formula: see text] form factor in the elastic region. The results provide a significant check on those obtained with standard dispersion relations, confirming the existence of a disagreement with experimental data in the region around [Formula: see text].

Random matrix theory of singular values of rectangular complex matrices I: Exact formula of one-body distribution function in fixed-trace ensemble

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

Adachi, Satoshi; Toda, Mikito; Kubotani, Hiroto

The fixed-trace ensemble of random complex matrices is the fundamental model that excellently describes the entanglement in the quantum states realized in a coupled system by its strongly chaotic dynamical evolution [see H. Kubotani, S. Adachi, M. Toda, Phys. Rev. Lett. 100 (2008) 240501]. The fixed-trace ensemble fully takes into account the conservation of probability for quantum states. The present paper derives for the first time the exact analytical formula of the one-body distribution function of singular values of random complex matrices in the fixed-trace ensemble. The distribution function of singular values (i.e. Schmidt eigenvalues) of a quantum state ismore » so important since it describes characteristics of the entanglement in the state. The derivation of the exact analytical formula utilizes two recent achievements in mathematics, which appeared in 1990s. The first is the Kaneko theory that extends the famous Selberg integral by inserting a hypergeometric type weight factor into the integrand to obtain an analytical formula for the extended integral. The second is the Petkovsek-Wilf-Zeilberger theory that calculates definite hypergeometric sums in a closed form.« less

Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential

PubMed Central

Wang, Ying; Zhou, Yu; Zhou, Shuyu

2016-01-01

We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study. PMID:27922129

Satellite Orbit Under Influence of a Drag - Analytical Approach

NASA Astrophysics Data System (ADS)

Martinović, M. M.; Šegan, S. D.

2017-12-01

The report studies some changes in orbital elements of the artificial satellites of Earth under influence of atmospheric drag. In order to develop possibilities of applying the results in many future cases, an analytical interpretation of the orbital element perturbations is given via useful, but very long expressions. The development is based on the TD88 air density model, recently upgraded with some additional terms. Some expressions and formulae were developed by the computer algebra system Mathematica and tested in some hypothetical cases. The results have good agreement with iterative (numerical) approach.

Fractional Fourier transform of truncated elliptical Gaussian beams.

PubMed

Du, Xinyue; Zhao, Daomu

2006-12-20

Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical expression for an elliptical Gaussian beam (EGB) truncated by an elliptical aperture and passing through a fractional Fourier transform system is derived by use of vector integration. The approximate analytical results provide more convenience for studying the propagation and transformation of truncated EGBs than the usual way by using the integral formula directly, and the efficiency of numerical calculation is significantly improved.

Determination of Chloride in Infant Formula and Adult/Pediatric Nutritional Formula by Potentiometric Titration: Single-Laboratory Validation, First Action 2015.07.

PubMed

Bolong, Wu; Fengxia, Zhang; Xiaoning, Ma; Fengjuan, Zhou; Brunelle, Sharon L

2016-01-01

A potentiometric method for determination of chloride was validated against AOAC Standard Method Performance Requirement (SMPR(®)) 2014.015. Ten AOAC Stakeholder Panel on Infant Formula and Adult Nutritionals (SPIFAN) matrixes, including National Institute of Standards and Technology (NIST) Standard Reference Material (SRM) 1849a, were tested in duplicate on 6 independent days. The repeatability (RSDr) ranged from 0.43 to 1.34%, and the intermediate reproducibility (RSDiR) ranged from 0.80 to 3.04%. All results for NIST SRM 1849a were within the range of the certified concentration (701 ± 17 mg/100 g). Recovery was demonstrated with two overspike levels, 50 and 100%, in the 10 SPIFAN matrixes. Samples were tested in duplicate on 3 different days, and all results were within the SMPR requirement of 95 to 105%. The LOQs of the method for powdered products and ready-to-feed or reconstituted products were 20 mg/100 g and 2.2 mg/100 mL, respectively. A wide analytical range from the LOQ to 99.5% chlorine content can be reached with an appropriate dilution factor, but in practice, the upper analytical value observed in routine matrix testing was approximately 1080 mg/100 g in skim milk powder. This is a rapid, simple, and reliable chlorine-testing method applicable to infant formula, adult nutritionals, and ingredients used in these dairy-based products, such as skim milk powder, desalted whey powder, whey protein powder, and whole milk powder.

Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs.

PubMed

Yoon, Nara; Vander Velde, Robert; Marusyk, Andriy; Scott, Jacob G

2018-05-07

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, [Formula: see text] and [Formula: see text], each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for [Formula: see text] and [Formula: see text], we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., [Formula: see text]-long for DrugA and [Formula: see text]-long for DrugB with [Formula: see text] and [Formula: see text]). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, [Formula: see text], and the effect of each drug. We determine a critical ratio, which we term [Formula: see text], at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, [Formula: see text] changes monotonically to [Formula: see text] and then, during the second stage, remains at [Formula: see text] thereafter. Beyond our analytic results, we explored an individual-based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.

Cooperative Coevolution with Formula-Based Variable Grouping for Large-Scale Global Optimization.

PubMed

Wang, Yuping; Liu, Haiyan; Wei, Fei; Zong, Tingting; Li, Xiaodong

2017-08-09

For a large-scale global optimization (LSGO) problem, divide-and-conquer is usually considered an effective strategy to decompose the problem into smaller subproblems, each of which can then be solved individually. Among these decomposition methods, variable grouping is shown to be promising in recent years. Existing variable grouping methods usually assume the problem to be black-box (i.e., assuming that an analytical model of the objective function is unknown), and they attempt to learn appropriate variable grouping that would allow for a better decomposition of the problem. In such cases, these variable grouping methods do not make a direct use of the formula of the objective function. However, it can be argued that many real-world problems are white-box problems, that is, the formulas of objective functions are often known a priori. These formulas of the objective functions provide rich information which can then be used to design an effective variable group method. In this article, a formula-based grouping strategy (FBG) for white-box problems is first proposed. It groups variables directly via the formula of an objective function which usually consists of a finite number of operations (i.e., four arithmetic operations "[Formula: see text]", "[Formula: see text]", "[Formula: see text]", "[Formula: see text]" and composite operations of basic elementary functions). In FBG, the operations are classified into two classes: one resulting in nonseparable variables, and the other resulting in separable variables. In FBG, variables can be automatically grouped into a suitable number of non-interacting subcomponents, with variables in each subcomponent being interdependent. FBG can easily be applied to any white-box problem and can be integrated into a cooperative coevolution framework. Based on FBG, a novel cooperative coevolution algorithm with formula-based variable grouping (so-called CCF) is proposed in this article for decomposing a large-scale white-box problem into several smaller subproblems and optimizing them respectively. To further enhance the efficiency of CCF, a new local search scheme is designed to improve the solution quality. To verify the efficiency of CCF, experiments are conducted on the standard LSGO benchmark suites of CEC'2008, CEC'2010, CEC'2013, and a real-world problem. Our results suggest that the performance of CCF is very competitive when compared with those of the state-of-the-art LSGO algorithms.

Ratio-based estimators for a change point in persistence.

PubMed

Halunga, Andreea G; Osborn, Denise R

2012-11-01

We study estimation of the date of change in persistence, from [Formula: see text] to [Formula: see text] or vice versa. Contrary to statements in the original papers, our analytical results establish that the ratio-based break point estimators of Kim [Kim, J.Y., 2000. Detection of change in persistence of a linear time series. Journal of Econometrics 95, 97-116], Kim et al. [Kim, J.Y., Belaire-Franch, J., Badillo Amador, R., 2002. Corringendum to "Detection of change in persistence of a linear time series". Journal of Econometrics 109, 389-392] and Busetti and Taylor [Busetti, F., Taylor, A.M.R., 2004. Tests of stationarity against a change in persistence. Journal of Econometrics 123, 33-66] are inconsistent when a mean (or other deterministic component) is estimated for the process. In such cases, the estimators converge to random variables with upper bound given by the true break date when persistence changes from [Formula: see text] to [Formula: see text]. A Monte Carlo study confirms the large sample downward bias and also finds substantial biases in moderate sized samples, partly due to properties at the end points of the search interval.

Corridor of existence of thermodynamically consistent solution of the Ornstein-Zernike equation.

PubMed

Vorob'ev, V S; Martynov, G A

2007-07-14

We obtain the exact equation for a correction to the Ornstein-Zernike (OZ) equation based on the assumption of the uniqueness of thermodynamical functions. We show that this equation is reduced to a differential equation with one arbitrary parameter for the hard sphere model. The compressibility factor within narrow limits of this parameter variation can either coincide with one of the formulas obtained on the basis of analytical solutions of the OZ equation or assume all intermediate values lying in a corridor between these solutions. In particular, we find the value of this parameter when the thermodynamically consistent compressibility factor corresponds to the Carnahan-Stirling formula.

Periodic Orbits and Semiclassical Form Factor in Barrier Billiards

NASA Astrophysics Data System (ADS)

Giraud, O.

2005-11-01

Using heuristic arguments based on the trace formulas, we analytically calculate the semiclassical two-point correlation form factor for a family of rectangular billiards with a barrier of height irrational with respect to the side of the billiard and located at any rational position p/q from the side. To do this, we first obtain the asymptotic density of lengths for each family of periodic orbits by a Siegel-Veech formula. The result obtained for these pseudo-integrable, non-Veech billiards is different but not far from the value of 1/2 expected for semi-Poisson statistics and from values of obtained previously in the case of Veech billiards.

Quantitative estimation of minimum offset for multichannel surface-wave survey with actively exciting source

USGS Publications Warehouse

Xu, Y.; Xia, J.; Miller, R.D.

2006-01-01

Multichannel analysis of surface waves is a developing method widely used in shallow subsurface investigations. The field procedures and related parameters are very important for successful applications. Among these parameters, the source-receiver offset range is seldom discussed in theory and normally determined by empirical or semi-quantitative methods in current practice. This paper discusses the problem from a theoretical perspective. A formula for quantitatively evaluating a layered homogenous elastic model was developed. The analytical results based on simple models and experimental data demonstrate that the formula is correct for surface wave surveys for near-surface applications. ?? 2005 Elsevier B.V. All rights reserved.

Enhancement of linear/nonlinear optical responses of molecular vibrations using metal nanoantennas

NASA Astrophysics Data System (ADS)

Morichika, Ikki; Kusa, Fumiya; Takegami, Akinobu; Ashihara, Satoshi

2017-04-01

Plasmonic enhancements of optical near-fields with metal nanostructures offer extensive potential for amplifying lightmatter interactions. We analytically formulate the enhancement of linear and nonlinear optical responses of molecular vibrations through resonant nanoantennas, based on a coupled-dipole model. We apply the formulae to evaluation of signal enhancement factors in the antenna-enhanced vibrational spectroscopy.

Spatial correlations and exact solution of the problem of the boson peak profile in amorphous media

NASA Astrophysics Data System (ADS)

Kirillov, Sviatoslav A.; A. Voyiatzis, George; Kolomiyets, Tatiana M.; H. Anastasiadis, Spiros

1999-11-01

Based on a model correlation function which covers spatial correlations from Gaussian to exponential, we have arrived at an exact analytic solution of the problem of the Boson peak profile in amorphous media. Probe fits made for polyisoprene and triacetin prove the working ability of the formulae obtained.

Mathematical developments regarding the general theory of the Earth magnetism

NASA Technical Reports Server (NTRS)

Schmidt, A.

1983-01-01

A literature survey on the Earth's magnetic field, citing the works of Gauss, Erman-Petersen, Quintus Icilius and Neumayer is presented. The general formulas for the representation of the potential and components of the Earth's magnetic force are presented. An analytical representation of magnetic condition of the Earth based on observations is also made.

An analytic formula for heating due to ozone absorption

NASA Technical Reports Server (NTRS)

Lindzen, R. S.; Will, D. I.

1972-01-01

An attempt was made to devise a simple expression or formula to describe radiative heating in the atmosphere by ozone absorption. Such absorption occurs in the Hartley, Huggins, and Chappuis bands and is only slightly temperature and pressure dependent.

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

Bassi, Gabriele; Blednykh, Alexei; Smalyuk, Victor

A novel algorithm for self-consistent simulations of long-range wakefield effects has been developed and applied to the study of both longitudinal and transverse coupled-bunch instabilities at NSLS-II. The algorithm is implemented in the new parallel tracking code space (self-consistent parallel algorithm for collective effects) discussed in the paper. The code is applicable for accurate beam dynamics simulations in cases where both bunch-to-bunch and intrabunch motions need to be taken into account, such as chromatic head-tail effects on the coupled-bunch instability of a beam with a nonuniform filling pattern, or multibunch and single-bunch effects of a passive higher-harmonic cavity. The numericalmore » simulations have been compared with analytical studies. For a beam with an arbitrary filling pattern, intensity-dependent complex frequency shifts have been derived starting from a system of coupled Vlasov equations. The analytical formulas and numerical simulations confirm that the analysis is reduced to the formulation of an eigenvalue problem based on the known formulas of the complex frequency shifts for the uniform filling pattern case.« less

Analytical mass formula and nuclear surface properties in the ETF approximation. Part I: symmetric nuclei

NASA Astrophysics Data System (ADS)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

2016-08-01

The problem of determination of nuclear surface energy is addressed within the framework of the extended Thomas Fermi (ETF) approximation using Skyrme functionals. We propose an analytical model for the density profiles with variationally determined diffuseness parameters. In this first paper, we consider the case of symmetric nuclei. In this situation, the ETF functional can be exactly integrated, leading to an analytical formula expressing the surface energy as a function of the couplings of the energy functional. The importance of non-local terms is stressed and it is shown that they cannot be deduced simply from the local part of the functional, as it was suggested in previous works.

Analytic H I-to-H2 Photodissociation Transition Profiles

NASA Astrophysics Data System (ADS)

Bialy, Shmuel; Sternberg, Amiel

2016-05-01

We present a simple analytic procedure for generating atomic (H I) to molecular ({{{H}}}2) density profiles for optically thick hydrogen gas clouds illuminated by far-ultraviolet radiation fields. Our procedure is based on the analytic theory for the structure of one-dimensional H I/{{{H}}}2 photon-dominated regions, presented by Sternberg et al. Depth-dependent atomic and molecular density fractions may be computed for arbitrary gas density, far-ultraviolet field intensity, and the metallicity-dependent H2 formation rate coefficient, and dust absorption cross section in the Lyman-Werner photodissociation band. We use our procedure to generate a set of {{H}} {{I}}{-}{to}{-}{{{H}}}2 transition profiles for a wide range of conditions, from the weak- to strong-field limits, and from super-solar down to low metallicities. We show that if presented as functions of dust optical depth, the {{H}} {{I}} and {{{H}}}2 density profiles depend primarily on the Sternberg “α G parameter” (dimensionless) that determines the dust optical depth associated with the total photodissociated {{H}} {{I}} column. We derive a universal analytic formula for the {{H}} {{I}}{-}{to}{-}{{{H}}}2 transition points as a function of just α G. Our formula will be useful for interpreting emission-line observations of H I/{{{H}}}2 interfaces, for estimating star formation thresholds, and for sub-grid components in hydrodynamics simulations.

Analysis of the Precision of Variable Flip Angle T1 Mapping with Emphasis on the Noise Propagated from RF Transmit Field Maps.

PubMed

Lee, Yoojin; Callaghan, Martina F; Nagy, Zoltan

2017-01-01

In magnetic resonance imaging, precise measurements of longitudinal relaxation time ( T 1 ) is crucial to acquire useful information that is applicable to numerous clinical and neuroscience applications. In this work, we investigated the precision of T 1 relaxation time as measured using the variable flip angle method with emphasis on the noise propagated from radiofrequency transmit field ([Formula: see text]) measurements. The analytical solution for T 1 precision was derived by standard error propagation methods incorporating the noise from the three input sources: two spoiled gradient echo (SPGR) images and a [Formula: see text] map. Repeated in vivo experiments were performed to estimate the total variance in T 1 maps and we compared these experimentally obtained values with the theoretical predictions to validate the established theoretical framework. Both the analytical and experimental results showed that variance in the [Formula: see text] map propagated comparable noise levels into the T 1 maps as either of the two SPGR images. Improving precision of the [Formula: see text] measurements significantly reduced the variance in the estimated T 1 map. The variance estimated from the repeatedly measured in vivo T 1 maps agreed well with the theoretically-calculated variance in T 1 estimates, thus validating the analytical framework for realistic in vivo experiments. We concluded that for T 1 mapping experiments, the error propagated from the [Formula: see text] map must be considered. Optimizing the SPGR signals while neglecting to improve the precision of the [Formula: see text] map may result in grossly overestimating the precision of the estimated T 1 values.

Contamination of dried blood spots - an underestimated risk in newborn screening.

PubMed

Winter, Theresa; Lange, Anja; Hannemann, Anke; Nauck, Matthias; Müller, Cornelia

2018-01-26

Newborn screening (NBS) is an established screening procedure in many countries worldwide, aiming at the early detection of inborn errors of metabolism. For decades, dried blood spots have been the standard specimen for NBS. The procedure of blood collection is well described and standardized and includes many critical pre-analytical steps. We examined the impact of contamination of some anticipated common substances on NBS results obtained from dry spot samples. This possible pre-analytical source of uncertainty has been poorly examined in the past. Capillary blood was obtained from 15 adult volunteers and applied to 10 screening filter papers per volunteer. Nine filter papers were contaminated without visible trace. The contaminants were baby diaper rash cream, baby wet wipes, disinfectant, liquid infant formula, liquid infant formula hypoallergenic (HA), ultrasonic gel, breast milk, feces, and urine. The differences between control and contaminated samples were evaluated for 45 NBS quantities. We estimated if the contaminations might lead to false-positive NBS results. Eight of nine investigated contaminants significantly altered NBS analyte concentrations and potentially caused false-positive screening outcomes. A contamination with feces was most influential, affecting 24 of 45 tested analytes followed by liquid infant formula (HA) and urine, affecting 19 and 13 of 45 analytes, respectively. A contamination of filter paper samples can have a substantial effect on the NBS results. Our results underline the importance of good pre-analytical training to make the staff aware of the threat and ensure reliable screening results.

Propagation of a general-type beam through a truncated fractional Fourier transform optical system.

PubMed

Zhao, Chengliang; Cai, Yangjian

2010-03-01

Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.

Variances and uncertainties of the sample laboratory-to-laboratory variance (S(L)2) and standard deviation (S(L)) associated with an interlaboratory study.

PubMed

McClure, Foster D; Lee, Jung K

2012-01-01

The validation process for an analytical method usually employs an interlaboratory study conducted as a balanced completely randomized model involving a specified number of randomly chosen laboratories, each analyzing a specified number of randomly allocated replicates. For such studies, formulas to obtain approximate unbiased estimates of the variance and uncertainty of the sample laboratory-to-laboratory (lab-to-lab) STD (S(L)) have been developed primarily to account for the uncertainty of S(L) when there is a need to develop an uncertainty budget that includes the uncertainty of S(L). For the sake of completeness on this topic, formulas to estimate the variance and uncertainty of the sample lab-to-lab variance (S(L)2) were also developed. In some cases, it was necessary to derive the formulas based on an approximate distribution for S(L)2.

Leading multi-soft limits from scattering equations

NASA Astrophysics Data System (ADS)

Zlotnikov, Michael

2017-10-01

A Cachazo-He-Yuan (CHY) type formula is derived for the leading gluon, bi-adjoint scalar ϕ 3, Yang-Mills-scalar and non-linear sigma model m-soft factors S m in arbitrary dimension. The general formula is used to evaluate explicit examples for up to three soft legs analytically and up to four soft legs numerically via comparison with amplitude ratios under soft kinematics. A structural pattern for gluon m-soft factor is inferred and a simpler formula for its calculation is conjectured. In four dimensions, a Cachazo-Svrček-Witten (CSW) recursive procedure producing the leading m-soft gluon factor in spinor helicity formalism is developed as an alternative, and Britto-Cachazo-Feng-Witten (BCFW) recursion is used to obtain the leading four-soft gluon factor for all analytically distinct helicity configurations.

Bulk diffusion in a kinetically constrained lattice gas

NASA Astrophysics Data System (ADS)

Arita, Chikashi; Krapivsky, P. L.; Mallick, Kirone

2018-03-01

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green-Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient cannot be computed except when a lattice gas additionally satisfies the gradient condition. We develop a procedure to systematically obtain analytical approximations for the diffusion coefficient for non-gradient lattice gases with known equilibrium. The method relies on a variational formula found by Varadhan and Spohn which is a version of the Green-Kubo formula particularly suitable for diffusive lattice gases. Restricting the variational formula to finite-dimensional sub-spaces allows one to perform the minimization and gives upper bounds for the diffusion coefficient. We apply this approach to a kinetically constrained non-gradient lattice gas in two dimensions, viz. to the Kob-Andersen model on the square lattice.

KAM Tori for 1D Nonlinear Wave Equationswith Periodic Boundary Conditions

NASA Astrophysics Data System (ADS)

Chierchia, Luigi; You, Jiangong

In this paper, one-dimensional (1D) nonlinear wave equations with periodic boundary conditions are considered; V is a periodic smooth or analytic function and the nonlinearity f is an analytic function vanishing together with its derivative at u≡0. It is proved that for ``most'' potentials V(x), the above equation admits small-amplitude periodic or quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system. The proof is based on an infinite dimensional KAM theorem which allows for multiple normal frequencies.

New Methods for the Analysis of Fat-Soluble Vitamins in Infant Formula and Adult Nutritionals.

PubMed

Gilliland, Don

2016-01-01

The AOAC Stakeholder Panel on Infant Formula and Adult Nutritionals (SPIFAN) defined fat-soluble vitamins (FSVs) to include vitamins A, D, E, and K. The levels of FSVs have been closely scrutinized because of a number of factors, including nutrition value especially in foods used to provide sole-source nutrition and the potential for health risks associated with content both below and above recommended levels. Stricter scrutiny and emphasis on nutrient-level compliance with regulatory requirements placed an increased demand on analytical methods that were fit-for-purpose, provided accurate and precise results. Over time, compendial methods have been developed and published by organizations such as AOAC INTERNATIONAL, the European Committee for Standardization, the International Dairy Federation, and the International Organization for Standardization, among others. In general, these methods have shown adequate precision for regulatory compliance based on example food matrixes for which they were designed. However, method evaluation for infant formulas and adult nutritional products was limited to very few matrixes within these categories. As such, method applicability gaps were noted and correlated with more complicated or diverse product matrixes. AOAC undertook the task of modernizing test methods for the determination of nutrients in infant formulas and in adult nutritional products formulated specifically for both healthy adults and those requiring specific nutritional intake. Composition of products in this category continued to evolve, which in turn presented increasing and new challenges to analytical methodology. A summary of a new generation of candidate compendial methods for determination of FSVs in these matrixes, identified by SPIFAN, is presented here.

Characteristic analysis on UAV-MIMO channel based on normalized correlation matrix.

PubMed

Gao, Xi jun; Chen, Zi li; Hu, Yong Jiang

2014-01-01

Based on the three-dimensional GBSBCM (geometrically based double bounce cylinder model) channel model of MIMO for unmanned aerial vehicle (UAV), the simple form of UAV space-time-frequency channel correlation function which includes the LOS, SPE, and DIF components is presented. By the methods of channel matrix decomposition and coefficient normalization, the analytic formula of UAV-MIMO normalized correlation matrix is deduced. This formula can be used directly to analyze the condition number of UAV-MIMO channel matrix, the channel capacity, and other characteristic parameters. The simulation results show that this channel correlation matrix can be applied to describe the changes of UAV-MIMO channel characteristics under different parameter settings comprehensively. This analysis method provides a theoretical basis for improving the transmission performance of UAV-MIMO channel. The development of MIMO technology shows practical application value in the field of UAV communication.

Characteristic Analysis on UAV-MIMO Channel Based on Normalized Correlation Matrix

PubMed Central

Xi jun, Gao; Zi li, Chen; Yong Jiang, Hu

2014-01-01

Based on the three-dimensional GBSBCM (geometrically based double bounce cylinder model) channel model of MIMO for unmanned aerial vehicle (UAV), the simple form of UAV space-time-frequency channel correlation function which includes the LOS, SPE, and DIF components is presented. By the methods of channel matrix decomposition and coefficient normalization, the analytic formula of UAV-MIMO normalized correlation matrix is deduced. This formula can be used directly to analyze the condition number of UAV-MIMO channel matrix, the channel capacity, and other characteristic parameters. The simulation results show that this channel correlation matrix can be applied to describe the changes of UAV-MIMO channel characteristics under different parameter settings comprehensively. This analysis method provides a theoretical basis for improving the transmission performance of UAV-MIMO channel. The development of MIMO technology shows practical application value in the field of UAV communication. PMID:24977185

Correlation singularities in a partially coherent electromagnetic beam with initially radial polarization.

PubMed

Zhang, Yongtao; Cui, Yan; Wang, Fei; Cai, Yangjian

2015-05-04

We have investigated the correlation singularities, coherence vortices of two-point correlation function in a partially coherent vector beam with initially radial polarization, i.e., partially coherent radially polarized (PCRP) beam. It is found that these singularities generally occur during free space propagation. Analytical formulae for characterizing the dynamics of the correlation singularities on propagation are derived. The influence of the spatial coherence length of the beam on the evolution properties of the correlation singularities and the conditions for creation and annihilation of the correlation singularities during propagation have been studied in detail based on the derived formulae. Some interesting results are illustrated. These correlation singularities have implication for interference experiments with a PCRP beam.

Determination of furfural and hydroxymethylfurfural from baby formula using headspace solid phase microextraction based on nanostructured polypyrrole fiber coupled with ion mobility spectrometry.

PubMed

Kamalabadi, Mahdie; Ghaemi, Elham; Mohammadi, Abdorreza; Alizadeh, Naader

2015-08-15

Furfural (Fu) and hydroxymethylfurfural (HMFu) are extracted using a dodecylbenzenesulfonate-doped polypyrrole coating as a fiber for headspace solid phase microextraction (HS-SPME) method in baby formula samples and detected using ion mobility spectrometry (IMS). Sample pH, salt effect, extraction time and temperature were investigated and optimized as effective parameters in HS-SPME. The calibration curves were linear in the range of 20-300 ng g(-1) (R(2)>0.99). Limits of detection for Fu and HMFu were 6 ng g(-1) and 5 ng g(-1), respectively. The RSD% of Fu and HMFu for five analyses was 4.4 and 4.9, respectively. The proposed method was successfully applied to determine of Fu and HMFu in the different baby formula samples with satisfactory result. The results were in agreement with those obtained using HPLC analysis. The HS-SPME-IMS is precise, selective and sensitive analytical method for determination of Fu and HMFu in baby formula samples, without any derivatization process. Copyright © 2015 Elsevier Ltd. All rights reserved.

Aberration measurement technique based on an analytical linear model of a through-focus aerial image.

PubMed

Yan, Guanyong; Wang, Xiangzhao; Li, Sikun; Yang, Jishuo; Xu, Dongbo; Erdmann, Andreas

2014-03-10

We propose an in situ aberration measurement technique based on an analytical linear model of through-focus aerial images. The aberrations are retrieved from aerial images of six isolated space patterns, which have the same width but different orientations. The imaging formulas of the space patterns are investigated and simplified, and then an analytical linear relationship between the aerial image intensity distributions and the Zernike coefficients is established. The linear relationship is composed of linear fitting matrices and rotation matrices, which can be calculated numerically in advance and utilized to retrieve Zernike coefficients. Numerical simulations using the lithography simulators PROLITH and Dr.LiTHO demonstrate that the proposed method can measure wavefront aberrations up to Z(37). Experiments on a real lithography tool confirm that our method can monitor lens aberration offset with an accuracy of 0.7 nm.

Cylindrical angular spectrum using Fourier coefficients of point light source and its application to fast hologram calculation.

PubMed

Oh, Seungtaik; Jeong, Il Kwon

2015-11-16

We will introduce a new simple analytic formula of the Fourier coefficient of the 3D field distribution of a point light source to generate a cylindrical angular spectrum which captures the object wave in 360° in the 3D Fourier space. Conceptually, the cylindrical angular spectrum can be understood as a cylindrical version of the omnidirectional spectral approach of Sando et al. Our Fourier coefficient formula is based on an intuitive observation that a point light radiates uniformly in all directions. Our formula is defined over all frequency vectors lying on the entire sphere in the 3D Fourier space and is more natural and computationally more efficient for all around recording of the object wave than that of the previous omnidirectional spectral method. A generalized frequency-based occlusion culling method for an arbitrary complex object is also proposed to enhance the 3D quality of a hologram. As a practical application of the cylindrical angular spectrum, an interactive hologram example is presented together with implementation details.

Water equivalent thickness values of materials used in beams of protons, helium, carbon and iron ions.

PubMed

Zhang, Rui; Taddei, Phillip J; Fitzek, Markus M; Newhauser, Wayne D

2010-05-07

Heavy charged particle beam radiotherapy for cancer is of increasing interest because it delivers a highly conformal radiation dose to the target volume. Accurate knowledge of the range of a heavy charged particle beam after it penetrates a patient's body or other materials in the beam line is very important and is usually stated in terms of the water equivalent thickness (WET). However, methods of calculating WET for heavy charged particle beams are lacking. Our objective was to test several simple analytical formulas previously developed for proton beams for their ability to calculate WET values for materials exposed to beams of protons, helium, carbon and iron ions. Experimentally measured heavy charged particle beam ranges and WET values from an iterative numerical method were compared with the WET values calculated by the analytical formulas. In most cases, the deviations were within 1 mm. We conclude that the analytical formulas originally developed for proton beams can also be used to calculate WET values for helium, carbon and iron ion beams with good accuracy.

Water equivalent thickness values of materials used in beams of protons, helium, carbon and iron ions

PubMed Central

Zhang, Rui; Taddei, Phillip J; Fitzek, Markus M; Newhauser, Wayne D

2010-01-01

Heavy charged particle beam radiotherapy for cancer is of increasing interest because it delivers a highly conformal radiation dose to the target volume. Accurate knowledge of the range of a heavy charged particle beam after it penetrates a patient’s body or other materials in the beam line is very important and is usually stated in terms of the water equivalent thickness (WET). However, methods of calculating WET for heavy charged particle beams are lacking. Our objective was to test several simple analytical formulas previously developed for proton beams for their ability to calculate WET values for materials exposed to beams of protons, helium, carbon and iron ions. Experimentally measured heavy charged particle beam ranges and WET values from an iterative numerical method were compared with the WET values calculated by the analytical formulas. Inmost cases, the deviations were within 1 mm. We conclude that the analytical formulas originally developed for proton beams can also be used to calculate WET values for helium, carbon and iron ion beams with good accuracy. PMID:20371908

MODELS OF KILONOVA/MACRONOVA EMISSION FROM BLACK HOLE–NEUTRON STAR MERGERS

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

Kawaguchi, Kyohei; Shibata, Masaru; Kyutoku, Koutarou

2016-07-01

Black hole–neutron star (BH–NS) mergers are among the most promising gravitational-wave sources for ground-based detectors, and gravitational waves from BH–NS mergers are expected to be detected in the next few years. The simultaneous detection of electromagnetic counterparts with gravitational waves would provide rich information about merger events. Among the possible electromagnetic counterparts from BH–NS mergers is the so-called kilonova/macronova, emission powered by the decay of radioactive r-process nuclei, which is one of the best targets for follow-up observations. We derive fitting formulas for the mass and the velocity of ejecta from a generic BH–NS merger based on recently performed numerical-relativitymore » simulations. We combine these fitting formulas with a new semi-analytic model for a BH–NS kilonova/macronova lightcurve, which reproduces the results of radiation-transfer simulations. Specifically, the semi-analytic model reproduces the results of each band magnitude obtained by the previous radiation-transfer simulations within ∼1 mag. By using this semi-analytic model we found that, at 400 Mpc, the kilonova/macronova is as bright as 22–24 mag for cases with a small chirp mass and a high black hole spin, and >28 mag for a large chirp mass and a low black hole spin. We also apply our model to GRB 130603B as an illustration, and show that a BH–NS merger with a rapidly spinning black hole and a large neutron star radius is favored.« less

Molecular formula composition of β-caryophyllene ozonolysis SOA formed in humid and dry conditions

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

Kundu, Shuvashish; Fisseha, Rebeka; Putman, Annie L.

Here, we studied the molecular formula composition of six β-caryophyllene SOA samples using ultrahigh resolution Fourier transform ion cyclotron resonance mass spectrometry under various reaction conditions. The SOA samples were generated in dry or low relative humidity (RH) chamber conditions with or without cyclohexane. All of the studied SOA mass spectra have three distinct clusters of hundreds of negative ions referred to as Group I (100 < m/z < 400), Group II (400 < m/z < 700) and Group III (700 < m/z < 1 000) compounds. C 14-16H 22-28O 2-11, C 28-29H 42-48O 6-16 and C 42-43H 68-70O 14-16more » were observed as highly abundant organic compounds in the compound class of Group I, II and III, respectively. The relative intensities of most analytes were higher in humid conditions compared to those in dry conditions, indicating the importance of water-dependent reactions and the catalytic role of water both in the presence and absence of cyclohexane. In addition, molecular formulas with higher average carbon numbers were observed in humid SOA than in dry SOA in the absence of cyclohexane, suggesting a decrease of cleavage reactions in humid condition. This study characterizes β-caryophyllene ozonolysis SOA based on ultrahigh mass resolution and demonstrates the significance of humidity in terms of the molecular distributions and relative abundances of the analytes. We also discuss the possible mechanism for the formation of Group I-III compounds based on the current understanding of SOA formation in the atmosphere.« less

Molecular formula composition of β-caryophyllene ozonolysis SOA formed in humid and dry conditions

DOE PAGES

Kundu, Shuvashish; Fisseha, Rebeka; Putman, Annie L.; ...

2016-12-22

Here, we studied the molecular formula composition of six β-caryophyllene SOA samples using ultrahigh resolution Fourier transform ion cyclotron resonance mass spectrometry under various reaction conditions. The SOA samples were generated in dry or low relative humidity (RH) chamber conditions with or without cyclohexane. All of the studied SOA mass spectra have three distinct clusters of hundreds of negative ions referred to as Group I (100 < m/z < 400), Group II (400 < m/z < 700) and Group III (700 < m/z < 1 000) compounds. C 14-16H 22-28O 2-11, C 28-29H 42-48O 6-16 and C 42-43H 68-70O 14-16more » were observed as highly abundant organic compounds in the compound class of Group I, II and III, respectively. The relative intensities of most analytes were higher in humid conditions compared to those in dry conditions, indicating the importance of water-dependent reactions and the catalytic role of water both in the presence and absence of cyclohexane. In addition, molecular formulas with higher average carbon numbers were observed in humid SOA than in dry SOA in the absence of cyclohexane, suggesting a decrease of cleavage reactions in humid condition. This study characterizes β-caryophyllene ozonolysis SOA based on ultrahigh mass resolution and demonstrates the significance of humidity in terms of the molecular distributions and relative abundances of the analytes. We also discuss the possible mechanism for the formation of Group I-III compounds based on the current understanding of SOA formation in the atmosphere.« less

Accuracy of analytic energy level formulas applied to hadronic spectroscopy of heavy mesons

NASA Technical Reports Server (NTRS)

Badavi, Forooz F.; Norbury, John W.; Wilson, John W.; Townsend, Lawrence W.

1988-01-01

Linear and harmonic potential models are used in the nonrelativistic Schroedinger equation to obtain article mass spectra for mesons as bound states of quarks. The main emphasis is on the linear potential where exact solutions of the S-state eigenvalues and eigenfunctions and the asymptotic solution for the higher order partial wave are obtained. A study of the accuracy of two analytical energy level formulas as applied to heavy mesons is also included. Cornwall's formula is found to be particularly accurate and useful as a predictor of heavy quarkonium states. Exact solution for all partial waves of eigenvalues and eigenfunctions for a harmonic potential is also obtained and compared with the calculated discrete spectra of the linear potential. Detailed derivations of the eigenvalues and eigenfunctions of the linear and harmonic potentials are presented in appendixes.

Accurate mass measurements and their appropriate use for reliable analyte identification.

PubMed

Godfrey, A Ruth; Brenton, A Gareth

2012-09-01

Accurate mass instrumentation is becoming increasingly available to non-expert users. This data can be mis-used, particularly for analyte identification. Current best practice in assigning potential elemental formula for reliable analyte identification has been described with modern informatic approaches to analyte elucidation, including chemometric characterisation, data processing and searching using facilities such as the Chemical Abstracts Service (CAS) Registry and Chemspider.

Correlation of the Glomerular Filtration Rate Measured With the Use of DTPA-Tc99m in Live Kidney Donors With Equations Based on Creatinine and Cystatin C.

PubMed

Garcia-Covarrubias, L; Barragan, J; Castro, I; Hernandez, K; Reding, A; Hinojosa, H; Prieto, P; Garcia, A; Alejandra, C; Ortuño, D; Carmona, M; Fernández, D; Diliz, H

2018-03-01

Renal donation leads to a risk of developing chronic kidney disease, with an incidence of 0.47%. To evaluate for its presence, formulas based on serum creatinine are used, but up to 80% of these formulas underestimate the glomerular filtration rate (GFR) in donors. The aim of this work was to confirm the highest correlation of the GFR as measured with the use of DTPA-Tc99m with the GFR as estimated by means of the formula based on serum cystatin C (CKD-EPI creatinine-cystatin C) in healthy kidney donors. In this observational, analytic, cross-sectional study, the GFR of kidney donors was determined ≥1 year after donation by means of DTPA gammagram and estimation with the use of conventional formulations and with cystatin C. Of 112 donors, 38 (34%) were included, 20 (60%) were female, with an overall average age of 40 years, 36.5 months after donation, and body mass index of 25.5 kg/m 2 . Correlation with the GFR as measured by means of DTPA gammagram was better with the use of CKD-EPI cystatin C (0.402; P = .020) and CKD-EPI creatinine-cystatin (0.549; P < .001) than the conventional formulas. Linear correlation with serum cystatin C was 0.825 (P < .001; 95% confidence interval, -105.3 to -63.2) for the CKD-EPI cystatin C formula, 0.77 (P < .001; -89.9 to -48.1) for the CKD-EPI creatinine-cystatin formula, and 0.525 (P = .002; -91.1 to -23.2) for DTPA-Tc99m scintigraphy. There is a strong correlation between estimate the GFR by equations based on cystatin C and the measurement of the GFR by DTPA-Tc99m gammagram. Copyright © 2017 Elsevier Inc. All rights reserved.

Spatiotemporal behaviour of isodiffracting hollow Gaussian pulsed beams

NASA Astrophysics Data System (ADS)

Xu, Yanbing; Lü, Baida

2007-05-01

A model of isodiffracting hollow Gaussian pulsed beams (HGPBs) is presented. Based on the Fourier transform method, an analytical formula for the HGPBs propagating in free space is derived, which enables us to study the spatiotemporal behaviour of the ultrashort pulsed beams. Some interesting phenomena of ultrashort pulsed beams, such as the symmetrical temporal profiles, the dark rings, etc, are discussed in detail and illustrated numerically.

Two-point resistance of the Möbius ladder

NASA Astrophysics Data System (ADS)

Chair, Noureddine; Dannoun, Elham Mohammed Ali

2015-03-01

Exact formulas for the two-point resistance and the Kirchhoff index of the Möbius ladder are given based on the recently developed analytical approach by Chair (2012 Ann. Phys. 327 2899). The expression for the two-point resistance is written in terms of the two-point resistance of N/2-cycle graph and the Bejaia and the Pisa numbers recently introduced by the first author.

Analytic Modeling of Insurgencies

DTIC Science & Technology

2014-08-01

Counterinsurgency, Situational Awareness, Civilians, Lanchester 1. Introduction Combat modeling is one of the oldest areas of operations research, dating...Army. The ground-breaking work of Lanchester in 1916 [1] marks the beginning of formal models of conflicts, where mathematical formulas and, later...Warfare model [3], which is a Lanchester - based mathematical model (see more details about this model later on), and McCormick’s Magic Diamond model [4

Complex dark-field contrast and its retrieval in x-ray phase contrast imaging implemented with Talbot interferometry.

PubMed

Yang, Yi; Tang, Xiangyang

2014-10-01

Under the existing theoretical framework of x-ray phase contrast imaging methods implemented with Talbot interferometry, the dark-field contrast refers to the reduction in interference fringe visibility due to small-angle x-ray scattering of the subpixel microstructures of an object to be imaged. This study investigates how an object's subpixel microstructures can also affect the phase of the intensity oscillations. Instead of assuming that the object's subpixel microstructures distribute in space randomly, the authors' theoretical derivation starts by assuming that an object's attenuation projection and phase shift vary at a characteristic size that is not smaller than the period of analyzer grating G₂ and a characteristic length dc. Based on the paraxial Fresnel-Kirchhoff theory, the analytic formulae to characterize the zeroth- and first-order Fourier coefficients of the x-ray irradiance recorded at each detector cell are derived. Then the concept of complex dark-field contrast is introduced to quantify the influence of the object's microstructures on both the interference fringe visibility and the phase of intensity oscillations. A method based on the phase-attenuation duality that holds for soft tissues and high x-ray energies is proposed to retrieve the imaginary part of the complex dark-field contrast for imaging. Through computer simulation study with a specially designed numerical phantom, they evaluate and validate the derived analytic formulae and the proposed retrieval method. Both theoretical analysis and computer simulation study show that the effect of an object's subpixel microstructures on x-ray phase contrast imaging method implemented with Talbot interferometry can be fully characterized by a complex dark-field contrast. The imaginary part of complex dark-field contrast quantifies the influence of the object's subpixel microstructures on the phase of intensity oscillations. Furthermore, at relatively high energies, for soft tissues it can be retrieved for imaging with a method based on the phase-attenuation duality. The analytic formulae derived in this work to characterize the complex dark-field contrast in x-ray phase contrast imaging method implemented with Talbot interferometry are of significance, which may initiate more activities in the research and development of x-ray differential phase contrast imaging for extensive biomedical applications.

Modeling direct interband tunneling. II. Lower-dimensional structures

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

Pan, Andrew, E-mail: pandrew@ucla.edu; Chui, Chi On; California NanoSystems Institute, University of California, Los Angeles, Los Angeles, California 90095

We investigate the applicability of the two-band Hamiltonian and the widely used Kane analytical formula to interband tunneling along unconfined directions in nanostructures. Through comparisons with k·p and tight-binding calculations and quantum transport simulations, we find that the primary correction is the change in effective band gap. For both constant fields and realistic tunnel field-effect transistors, dimensionally consistent band gap scaling of the Kane formula allows analytical and numerical device simulations to approximate non-equilibrium Green's function current characteristics without arbitrary fitting. This allows efficient first-order calibration of semiclassical models for interband tunneling in nanodevices.

Multidimensional Extension of the Generalized Chowla-Selberg Formula

NASA Astrophysics Data System (ADS)

Elizalde, E.

After recalling the precise existence conditions of the zeta function of a pseudodifferential operator, and the concept of reflection formula, an exponentially convergent expression for the analytic continuation of a multidimensional inhomogeneous Epstein-type zeta function of the general form with A the p×p$ matrix of a quadratic form, a p vector and q a constant, is obtained. It is valid on the whole complex s-plane, is exponentially convergent and provides the residua at the poles explicitly. It reduces to the famous formula of Chowla and Selberg in the particular case p=2, , q=0. Some variations of the formula and physical applications are considered.

A new approach to aid the characterisation and identification of metabolites of a model drug; partial isotope enrichment combined with novel formula elucidation software.

PubMed

Hobby, Kirsten; Gallagher, Richard T; Caldwell, Patrick; Wilson, Ian D

2009-01-01

This work describes the identification of 'isotopically enriched' metabolites of 4-cyanoaniline using the unique features of the software package 'Spectral Simplicity'. The software is capable of creating the theoretical mass spectra for partially isotope-enriched compounds, and subsequently performing an elemental composition analysis to give the elemental formula for the 'isotopically enriched' metabolite. A novel mass spectral correlation method, called 'FuzzyFit', was employed. 'FuzzyFit' utilises the expected experimental distribution of errors in both mass accuracy and isotope pattern and enables discrimination between statistically probable and improbable candidate formulae. The software correctly determined the molecular formulae of ten previously described metabolites of 4-cyanoaniline confirming the technique of partial isotope enrichment can produce results analogous to standard methodologies. Six previously unknown species were also identified, based on the presence of the unique 'designer' isotope ratio. Three of the unknowns were tentatively identified as N-acetylglutamine, O-methyl-N acetylglucuronide and a putative fatty acid conjugate. The discovery of a significant number of unknown species of a model drug with a comprehensive history of investigation highlights the potential for enhancement to the analytical process by the use of 'designer' isotope ratio compounds. The 'FuzzyFit' methodology significantly aided the elucidation of candidate formulae, by provision of a vastly simplified candidate formula data set. Copyright (c) 2008 John Wiley & Sons, Ltd.

Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems.

PubMed

Guérin, T; Dean, D S

2015-12-01

We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.

Systematic study of α-decay half-lives using Royer and related formula

NASA Astrophysics Data System (ADS)

Akrawy, Dashty T.; Hassanabadi, H.; Hosseini, S. S.; Santhosh, K. P.

2018-03-01

The alpha decay half-lives of 356 isotopes were studied using the Royer and related Formula and are compared with experimental data. The study shows that the predicted half-lives match well with experimental data over a wide range for each (Z , N) parity of the parent nuclei. We have calculated the standard deviation of log10 ⁡Tα (s), for each formula and our study indicate that, for alpha decay studies, generally, analytical ℓ-dependent formula proposed by Royer, with σRB = 0.4373, is the best model followed by the formula proposed by Denisov and Khudenko (DK), σDK = 0.4743 for all 356 nuclei. We hope the present study is a clear indicator of the predictive power of Royer and related formula.

Brownian aggregation rate of colloid particles with several active sites

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

Nekrasov, Vyacheslav M.; Yurkin, Maxim A.; Chernyshev, Andrei V., E-mail: chern@ns.kinetics.nsc.ru

2014-08-14

We theoretically analyze the aggregation kinetics of colloid particles with several active sites. Such particles (so-called “patchy particles”) are well known as chemically anisotropic reactants, but the corresponding rate constant of their aggregation has not yet been established in a convenient analytical form. Using kinematic approximation for the diffusion problem, we derived an analytical formula for the diffusion-controlled reaction rate constant between two colloid particles (or clusters) with several small active sites under the following assumptions: the relative translational motion is Brownian diffusion, and the isotropic stochastic reorientation of each particle is Markovian and arbitrarily correlated. This formula was shownmore » to produce accurate results in comparison with more sophisticated approaches. Also, to account for the case of a low number of active sites per particle we used Monte Carlo stochastic algorithm based on Gillespie method. Simulations showed that such discrete model is required when this number is less than 10. Finally, we applied the developed approach to the simulation of immunoagglutination, assuming that the formed clusters have fractal structure.« less

Self-consistent Simulations and Analysis of the Coupled-Bunch Instability for Arbitrary Multi-Bunch Configurations

DOE PAGES

Bassi, Gabriele; Blednykh, Alexei; Smalyuk, Victor

2016-02-24

A novel algorithm for self-consistent simulations of long-range wakefield effects has been developed and applied to the study of both longitudinal and transverse coupled-bunch instabilities at NSLS-II. The algorithm is implemented in the new parallel tracking code space (self-consistent parallel algorithm for collective effects) discussed in the paper. The code is applicable for accurate beam dynamics simulations in cases where both bunch-to-bunch and intrabunch motions need to be taken into account, such as chromatic head-tail effects on the coupled-bunch instability of a beam with a nonuniform filling pattern, or multibunch and single-bunch effects of a passive higher-harmonic cavity. The numericalmore » simulations have been compared with analytical studies. For a beam with an arbitrary filling pattern, intensity-dependent complex frequency shifts have been derived starting from a system of coupled Vlasov equations. The analytical formulas and numerical simulations confirm that the analysis is reduced to the formulation of an eigenvalue problem based on the known formulas of the complex frequency shifts for the uniform filling pattern case.« less

Polarizing beam-splitter rotation in Martin-Puplett interferometers for spectroscopic measurements at millimeter wavelengths

NASA Astrophysics Data System (ADS)

D'Alessandro, Giuseppe; de Bernardis, Paolo; di Tano, Silvio; Masi, Silvia; Mele, Lorenzo

2017-09-01

The spectroscopic measurement of the Cosmic Microwave Background at mm and sub-mm wavelengths received significant attention recently, aimed at measuring tiny spectral distortions of the Cosmic Microwave Background (CMB) relevant for cosmology. Several experiments, including OLIMPO (Masi et al. 2003), PRISM (André et al., 2014), MILLIMETRON (Smirnov and Baryshev, 2012), PIXIE (Kogut and Fixsen, 2011) are based on a Martin-Puplett Fourier-transform spectrometer. Its differential capabilities are the key to success in these difficult measurements. The polarizing beam splitter is the optical core of a Martin-Puplett interferometer. In this paper we analyze, analytically and experimentally, the systematic effects induced by a beam splitter orientation different from the canonical 45 ° . These effects are potenitally important for the delicate measurements of CMB spectral distortions. We find an analytical formula describing the effect, and verify experimentally, in the range 150-600 GHz, that our formula correctly describes the results (with a C.L. of 88 %). We also demonstrate that the rotation of the beam splitter does not induce distortions in the measured spectra.

Method validation for simultaneous determination of chromium, molybdenum and selenium in infant formulas by ICP-OES and ICP-MS.

PubMed

Khan, Naeem; Jeong, In Seon; Hwang, In Min; Kim, Jae Sung; Choi, Sung Hwa; Nho, Eun Yeong; Choi, Ji Yeon; Kwak, Byung-Man; Ahn, Jang-Hyuk; Yoon, Taehyung; Kim, Kyong Su

2013-12-15

This study aimed to validate the analytical method for simultaneous determination of chromium (Cr), molybdenum (Mo), and selenium (Se) in infant formulas available in South Korea. Various digestion methods of dry-ashing, wet-digestion and microwave were evaluated for samples preparation and both inductively coupled plasma optical emission spectrometry (ICP-OES) and inductively coupled plasma mass spectrometry (ICP-MS) were compared for analysis. The analytical techniques were validated by detection limits, precision, accuracy and recovery experiments. Results showed that wet-digestion and microwave methods were giving satisfactory results for sample preparation, while ICP-MS was found more sensitive and effective technique than ICP-OES. The recovery (%) of Se, Mo and Cr by ICP-OES were 40.9, 109.4 and 0, compared to 99.1, 98.7 and 98.4, respectively by ICP-MS. The contents of Cr, Mo and Se in infant formulas by ICP-MS were found in good nutritional values in accordance to nutrient standards for infant formulas CODEX values. Copyright © 2013 Elsevier Ltd. All rights reserved.

Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium

PubMed Central

Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying

2015-01-01

A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066

Semiclassical Dynamicswith Exponentially Small Error Estimates

NASA Astrophysics Data System (ADS)

Hagedorn, George A.; Joye, Alain

We construct approximate solutions to the time-dependent Schrödingerequation for small values of ħ. If V satisfies appropriate analyticity and growth hypotheses and , these solutions agree with exact solutions up to errors whose norms are bounded by for some C and γ>0. Under more restrictive hypotheses, we prove that for sufficiently small T', implies the norms of the errors are bounded by for some C', γ'>0, and σ > 0.

A Semiempirical Formula for Single-Electron-Capture Cross Sections of Multiply Charged Ions Colliding with H, H2 and He

NASA Astrophysics Data System (ADS)

Nakai, Yohta; Shirai, Toshizo; Tabata, Tatsuo; Ito, Rinsuke

1989-01-01

A universal analytic formula is given for the total cross sections of single-electron capture by multiply-charged ions colliding with H, H2 or He. Values of constants in the formula have been determined by least-squares fit to experimental data collected from the literature. The formula is applicable to ions of almost all atomic species with charge q greater than 4 (for the H and H2 targets) or 5 (for the He target) in the energy region from about 1 to 107 eV amu-1. The root-mean-square deviation of the data from the formula is 29%. The formula shows that the cross sections are proportional to q1.07 at low energies and to q2.86 at high energies. Other trends of the cross sections that can be derived from the formula are also discussed.

Coherent and partially coherent dark hollow beams with rectangular symmetry and paraxial propagation properties

NASA Astrophysics Data System (ADS)

Cai, Yangjian; Zhang, Lei

2006-07-01

A theoretical model is proposed to describe coherent dark hollow beams (DHBs) with rectangular symmetry. The electric field of a coherent rectangular DHB is expressed as a superposition of a series of the electric field of a finite series of fundamental Gaussian beams. Analytical propagation formulas for a coherent rectangular DHB passing through paraxial optical systems are derived in a tensor form. Furthermore, for the more general case, we propose a theoretical model to describe a partially coherent rectangular DHB. Analytical propagation formulas for a partially coherent rectangular DHB passing through paraxial optical systems are derived. The beam propagation factor (M2 factor) for both coherent and partially coherent rectangular DHBs are studied. Numerical examples are given by using the derived formulas. Our models and method provide an effective way to describe and treat the propagation of coherent and partially coherent rectangular DHBs.

Cross-section and rate formulas for electron-impact ionization, excitation, deexcitation, and total depopulation of excited atoms

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

Vriens, L.; Smeets, A.H.M.

1980-09-01

For electron-induced ionization, excitation, and de-excitation, mainly from excited atomic states, a detailed analysis is presented of the dependence of the cross sections and rate coefficients on electron energy and temperature, and on atomic parameters. A wide energy range is covered, including sudden as well as adiabatic collisions. By combining the available experimental and theoretical information, a set of simple analytical formulas is constructed for the cross sections and rate coefficients of the processes mentioned, for the total depopulation, and for three-body recombination. The formulas account for large deviations from classical and semiclassical scaling, as found for excitation. They agreemore » with experimental data and with the theories in their respective ranges of validity, but have a wider range of validity than the separate theories. The simple analytical form further facilitates the application in plasma modeling.« less

Barycentric parameterizations for isotropic BRDFs.

PubMed

Stark, Michael M; Arvo, James; Smits, Brian

2005-01-01

A bidirectional reflectance distribution function (BRDF) is often expressed as a function of four real variables: two spherical coordinates in each of the the "incoming" and "outgoing" directions. However, many BRDFs reduce to functions of fewer variables. For example, isotropic reflection can be represented by a function of three variables. Some BRDF models can be reduced further. In this paper, we introduce new sets of coordinates which we use to reduce the dimensionality of several well-known analytic BRDFs as well as empirically measured BRDF data. The proposed coordinate systems are barycentric with respect to a triangular support with a direct physical interpretation. One coordinate set is based on the BRDF model proposed by Lafortune. Another set, based on a model of Ward, is associated with the "halfway" vector common in analytical BRDF formulas. Through these coordinate sets we establish lower bounds on the approximation error inherent in the models on which they are based. We present a third set of coordinates, not based on any analytical model, that performs well in approximating measured data. Finally, our proposed variables suggest novel ways of constructing and visualizing BRDFs.

Simultaneous Determination of 10 Ultratrace Elements in Infant Formula, Adult Nutritionals, and Milk Products by ICP/MS After Pressure Digestion: Single-Laboratory Validation.

PubMed

Dubascoux, Stephane; Nicolas, Marine; Rime, Celine Fragniere; Payot, Janique Richoz; Poitevin, Eric

2015-01-01

A single-laboratory validation (SLV) is presented for the simultaneous determination of 10 ultratrace elements (UTEs) including aluminum (Al), arsenic (As), cadmium (Cd), cobalt (Co), chromium (Cr), mercury (Hg), molybdenum (Mo), lead (Pb), selenium (Se), and tin (Sn) in infant formulas, adult nutritionals, and milk based products by inductively coupled plasma (ICP)/MS after acidic pressure digestion. This robust and routine multielemental method is based on several official methods with modifications of sample preparation using either microwave digestion or high pressure ashing and of analytical conditions using ICP/MS with collision cell technology. This SLV fulfills AOAC method performance criteria in terms of linearity, specificity, sensitivity, precision, and accuracy and fully answers most international regulation limits for trace contaminants and/or recommended nutrient levels established for 10 UTEs in targeted matrixes.

Comparison of maximum runup through analytical and numerical approaches for different fault parameters estimates

NASA Astrophysics Data System (ADS)

Kanoglu, U.; Wronna, M.; Baptista, M. A.; Miranda, J. M. A.

2017-12-01

The one-dimensional analytical runup theory in combination with near shore synthetic waveforms is a promising tool for tsunami rapid early warning systems. Its application in realistic cases with complex bathymetry and initial wave condition from inverse modelling have shown that maximum runup values can be estimated reasonably well. In this study we generate a simplistic bathymetry domains which resemble realistic near-shore features. We investigate the accuracy of the analytical runup formulae to the variation of fault source parameters and near-shore bathymetric features. To do this we systematically vary the fault plane parameters to compute the initial tsunami wave condition. Subsequently, we use the initial conditions to run the numerical tsunami model using coupled system of four nested grids and compare the results to the analytical estimates. Variation of the dip angle of the fault plane showed that analytical estimates have less than 10% difference for angles 5-45 degrees in a simple bathymetric domain. These results shows that the use of analytical formulae for fast run up estimates constitutes a very promising approach in a simple bathymetric domain and might be implemented in Hazard Mapping and Early Warning.

Push Force Analysis of Anchor Block of the Oil and Gas Pipeline in a Single-Slope Tunnel Based on the Energy Balance Method

PubMed Central

Yan, Yifei; Zhang, Lisong; Yan, Xiangzhen

2016-01-01

In this paper, a single-slope tunnel pipeline was analysed considering the effects of vertical earth pressure, horizontal soil pressure, inner pressure, thermal expansion force and pipeline—soil friction. The concept of stagnation point for the pipeline was proposed. Considering the deformation compatibility condition of the pipeline elbow, the push force of anchor blocks of a single-slope tunnel pipeline was derived based on an energy method. Then, the theoretical formula for this force is thus generated. Using the analytical equation, the push force of the anchor block of an X80 large-diameter pipeline from the West—East Gas Transmission Project was determined. Meanwhile, to verify the results of the analytical method, and the finite element method, four categories of finite element codes were introduced to calculate the push force, including CAESARII, ANSYS, AutoPIPE and ALGOR. The results show that the analytical results agree well with the numerical results, and the maximum relative error is only 4.1%. Therefore, the results obtained with the analytical method can satisfy engineering requirements. PMID:26963097

Arbitrarily accurate twin composite π -pulse sequences

NASA Astrophysics Data System (ADS)

Torosov, Boyan T.; Vitanov, Nikolay V.

2018-04-01

We present three classes of symmetric broadband composite pulse sequences. The composite phases are given by analytic formulas (rational fractions of π ) valid for any number of constituent pulses. The transition probability is expressed by simple analytic formulas and the order of pulse area error compensation grows linearly with the number of pulses. Therefore, any desired compensation order can be produced by an appropriate composite sequence; in this sense, they are arbitrarily accurate. These composite pulses perform equally well as or better than previously published ones. Moreover, the current sequences are more flexible as they allow total pulse areas of arbitrary integer multiples of π .

Analytical pricing formulas for hybrid variance swaps with regime-switching

NASA Astrophysics Data System (ADS)

Roslan, Teh Raihana Nazirah; Cao, Jiling; Zhang, Wenjun

2017-11-01

The problem of pricing discretely-sampled variance swaps under stochastic volatility, stochastic interest rate and regime-switching is being considered in this paper. An extension of the Heston stochastic volatility model structure is done by adding the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. In addition, the parameters of the model are permitted to have transitions following a Markov chain process which is continuous and discoverable. This hybrid model can be used to illustrate certain macroeconomic conditions, for example the changing phases of business stages. The outcome of our regime-switching hybrid model is presented in terms of analytical pricing formulas for variance swaps.

Multi-class method for determination of veterinary drug residues and other contaminants in infant formula by ultra performance liquid chromatography-tandem mass spectrometry.

PubMed

Zhan, Jia; Zhong, Ying-ying; Yu, Xue-jun; Peng, Jin-feng; Chen, Shubing; Yin, Ju-yi; Zhang, Jia-Jie; Zhu, Yan

2013-06-01

A rapid, simple and generic analytical method which was able to simultaneously determine 220 undesirable chemical residues in infant formula had been developed. The method comprised of extraction with acetonitrile, clean-up by low temperature and water precipitation, and analysis by ultra performance liquid chromatography coupled with electrospray ionization tandem mass spectrometry (UPLC-ESI-MS-MS) using multiple reaction monitoring (MRM) mode. Most fat materials in acetonitrile extract were eliminated by low temperature clean-up. The water precipitation, providing a necessary and supplementary cleanup, could avoid losses of hydrophobic analytes (avermectins, ionophores). Average recoveries for spiked infant formula were in the range from 57% to 147% with associated RSD values between 1% and 28%. For over 80% of the analytes, the recoveries were between 70% and 120% with RSD values in the range of 1-15%. The limits of quantification (LOQs) were from 0.01 to 5 μg/kg, which were usually sufficient to verify the compliance of products with legal tolerances. Application of this method in routine monitoring programs would imply a drastic reduction of both effort and time. Copyright © 2012 Elsevier Ltd. All rights reserved.

Frechet derivatives for shallow water ocean acoustic inverse problems

NASA Astrophysics Data System (ADS)

Odom, Robert I.

2003-04-01

For any inverse problem, finding a model fitting the data is only half the problem. Most inverse problems of interest in ocean acoustics yield nonunique model solutions, and involve inevitable trade-offs between model and data resolution and variance. Problems of uniqueness and resolution and variance trade-offs can be addressed by examining the Frechet derivatives of the model-data functional with respect to the model variables. Tarantola [Inverse Problem Theory (Elsevier, Amsterdam, 1987), p. 613] published analytical formulas for the basic derivatives, e.g., derivatives of pressure with respect to elastic moduli and density. Other derivatives of interest, such as the derivative of transmission loss with respect to attenuation, can be easily constructed using the chain rule. For a range independent medium the analytical formulas involve only the Green's function and the vertical derivative of the Green's function for the medium. A crucial advantage of the analytical formulas for the Frechet derivatives over numerical differencing is that they can be computed with a single pass of any program which supplies the Green's function. Various derivatives of interest in shallow water ocean acoustics are presented and illustrated by an application to the sensitivity of measured pressure to shallow water sediment properties. [Work supported by ONR.

Predicting playing frequencies for clarinets: A comparison between numerical simulations and simplified analytical formulas.

PubMed

Coyle, Whitney L; Guillemain, Philippe; Kergomard, Jean; Dalmont, Jean-Pierre

2015-11-01

When designing a wind instrument such as a clarinet, it can be useful to be able to predict the playing frequencies. This paper presents an analytical method to deduce these playing frequencies using the input impedance curve. Specifically there are two control parameters that have a significant influence on the playing frequency, the blowing pressure and reed opening. Four effects are known to alter the playing frequency and are examined separately: the flow rate due to the reed motion, the reed dynamics, the inharmonicity of the resonator, and the temperature gradient within the clarinet. The resulting playing frequencies for the first register of a particular professional level clarinet are found using the analytical formulas presented in this paper. The analytical predictions are then compared to numerically simulated results to validate the prediction accuracy. The main conclusion is that in general the playing frequency decreases above the oscillation threshold because of inharmonicity, then increases above the beating reed regime threshold because of the decrease of the flow rate effect.

Sensitivity analysis of non-cohesive sediment transport formulae

NASA Astrophysics Data System (ADS)

Pinto, Lígia; Fortunato, André B.; Freire, Paula

2006-10-01

Sand transport models are often based on semi-empirical equilibrium transport formulae that relate sediment fluxes to physical properties such as velocity, depth and characteristic sediment grain sizes. In engineering applications, errors in these physical properties affect the accuracy of the sediment fluxes. The present analysis quantifies error propagation from the input physical properties to the sediment fluxes, determines which ones control the final errors, and provides insight into the relative strengths, weaknesses and limitations of four total load formulae (Ackers and White, Engelund and Hansen, van Rijn, and Karim and Kennedy) and one bed load formulation (van Rijn). The various sources of uncertainty are first investigated individually, in order to pinpoint the key physical properties that control the errors. Since the strong non-linearity of most sand transport formulae precludes analytical approaches, a Monte Carlo method is validated and used in the analysis. Results show that the accuracy in total sediment transport evaluations is mainly determined by errors in the current velocity and in the sediment median grain size. For the bed load transport using the van Rijn formula, errors in the current velocity alone control the final accuracy. In a final set of tests, all physical properties are allowed to vary simultaneously in order to analyze the combined effect of errors. The combined effect of errors in all the physical properties is then compared to an estimate of the errors due to the intrinsic limitations of the formulae. Results show that errors in the physical properties can be dominant for typical uncertainties associated with these properties, particularly for small depths. A comparison between the various formulae reveals that the van Rijn formula is more sensitive to basic physical properties. Hence, it should only be used when physical properties are known with precision.

Non-steady peristaltic propulsion with exponential variable viscosity: a study of transport through the digestive system.

PubMed

Tripathi, Dharmendra; Pandey, S K; Siddiqui, Abdul; Bég, O Anwar

2014-01-01

A theoretical study is presented for transient peristaltic flow of an incompressible fluid with variable viscosity in a finite length cylindrical tube as a simulation of transport in physiological vessels and biomimetic peristaltic pumps. The current axisymmetric analysis is qualitatively similar to two-dimensional analysis but exhibits quantitative variations. The current analysis is motivated towards further elucidating the physiological migration of gastric suspensions (food bolus) in the human digestive system. It also applies to variable viscosity industrial fluid (waste) peristaltic pumping systems. First, an axisymmetric model is analysed in the limit of large wavelength ([Formula: see text]) and low Reynolds number ([Formula: see text]) for axial velocity, radial velocity, pressure, hydromechanical efficiency and stream function in terms of radial vibration of the wall ([Formula: see text]), amplitude of the wave ([Formula: see text]), averaged flow rate ([Formula: see text]) and variable viscosity ([Formula: see text]). Subsequently, the peristaltic flow of a fluid with an exponential viscosity model is examined, which is based on the analytical solutions for pressure, wall shear stress, hydromechanical efficiency and streamline patterns in the finite length tube. The results are found to correlate well with earlier studies using a constant viscosity formulation. This study reveals some important features in the flow characteristics including the observation that pressure as well as both number and size of lower trapped bolus increases. Furthermore, the study indicates that hydromechanical efficiency reduces with increasing magnitude of viscosity parameter.

Exact recovery of sparse multiple measurement vectors by [Formula: see text]-minimization.

PubMed

Wang, Changlong; Peng, Jigen

2018-01-01

The joint sparse recovery problem is a generalization of the single measurement vector problem widely studied in compressed sensing. It aims to recover a set of jointly sparse vectors, i.e., those that have nonzero entries concentrated at a common location. Meanwhile [Formula: see text]-minimization subject to matrixes is widely used in a large number of algorithms designed for this problem, i.e., [Formula: see text]-minimization [Formula: see text] Therefore the main contribution in this paper is two theoretical results about this technique. The first one is proving that in every multiple system of linear equations there exists a constant [Formula: see text] such that the original unique sparse solution also can be recovered from a minimization in [Formula: see text] quasi-norm subject to matrixes whenever [Formula: see text]. The other one is showing an analytic expression of such [Formula: see text]. Finally, we display the results of one example to confirm the validity of our conclusions, and we use some numerical experiments to show that we increase the efficiency of these algorithms designed for [Formula: see text]-minimization by using our results.

A Cameron-Storvick Theorem for Analytic Feynman Integrals on Product Abstract Wiener Space and Applications

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

Choi, Jae Gil, E-mail: jgchoi@dankook.ac.kr; Chang, Seung Jun, E-mail: sejchang@dankook.ac.kr

In this paper we derive a Cameron-Storvick theorem for the analytic Feynman integral of functionals on product abstract Wiener space B{sup 2}. We then apply our result to obtain an evaluation formula for the analytic Feynman integral of unbounded functionals on B{sup 2}. We also present meaningful examples involving functionals which arise naturally in quantum mechanics.

Analytical solutions of travel time to a pumping well with variable evapotranspiration.

PubMed

Chen, Tian-Fei; Wang, Xu-Sheng; Wan, Li; Li, Hailong

2014-01-01

Analytical solutions of groundwater travel time to a pumping well in an unconfined aquifer have been developed in previous studies, however, the change in evapotranspiration was not considered. Here, we develop a mathematical model of unconfined flow toward a discharge well with redistribution of groundwater evapotranspiration for travel time analysis. Dependency of groundwater evapotranspiration on the depth to water table is described using a linear formula with an extinction depth. Analytical solutions of groundwater level and travel time are obtained. For a typical hypothetical example, these solutions perfectly agree with the numerical simulation results based on MODFLOW and MODPATH. As indicated in a dimensionless framework, a lumped parameter which is proportional to the pumping rate controls the distributions of groundwater evapotranspiration rate and the travel time along the radial direction. © 2013, National Ground Water Association.

Path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models

NASA Astrophysics Data System (ADS)

Lemmens, D.; Wouters, M.; Tempere, J.; Foulon, S.

2008-07-01

We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.

Connection between encounter volume and diffusivity in geophysical flows

NASA Astrophysics Data System (ADS)

Rypina, Irina I.; Smith, Stefan G. Llewellyn; Pratt, Larry J.

2018-04-01

Trajectory encounter volume - the volume of fluid that passes close to a reference fluid parcel over some time interval - has been recently introduced as a measure of mixing potential of a flow. Diffusivity is the most commonly used characteristic of turbulent diffusion. We derive the analytical relationship between the encounter volume and diffusivity under the assumption of an isotropic random walk, i.e., diffusive motion, in one and two dimensions. We apply the derived formulas to produce maps of encounter volume and the corresponding diffusivity in the Gulf Stream region of the North Atlantic based on satellite altimetry, and discuss the mixing properties of Gulf Stream rings. Advantages offered by the derived formula for estimating diffusivity from oceanographic data are discussed, as well as applications to other disciplines.

Fraction number of trapped atoms and velocity distribution function in sub-recoil laser cooling scheme

NASA Astrophysics Data System (ADS)

Alekseev, V. A.; Krylova, D. D.

1996-02-01

The analytical investigation of Bloch equations is used to describe the main features of the 1D velocity selective coherent population trapping cooling scheme. For the initial stage of cooling the fraction of cooled atoms is derived in the case of a Gaussian initial velocity distribution. At very long times of interaction the fraction of cooled atoms and the velocity distribution function are described by simple analytical formulae and do not depend on the initial distribution. These results are in good agreement with those of Bardou, Bouchaud, Emile, Aspect and Cohen-Tannoudji based on statistical analysis in terms of Levy flights and with Monte-Carlo simulations of the process.

Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

PubMed

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-08-01

Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

Approximate Formula for the Vertical Asymptote of Projectile Motion in Midair

ERIC Educational Resources Information Center

Chudinov, Peter Sergey

2010-01-01

The classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. An analytical approach is used for the investigation. An approximate formula is obtained for one of the characteristics of the motion--the vertical…

Design sensitivity analysis of nonlinear structural response

NASA Technical Reports Server (NTRS)

Cardoso, J. B.; Arora, J. S.

1987-01-01

A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use.

Computation of HORRAT values.

PubMed

McClure, Foster D; Lee, Jung-Keun

2003-01-01

The formula for the Horwitz ratio (HORRAT) as presented in the Study Director's Manual of AOAC INTERNATIONAL is applicable only when the concentration is in the unit/unit form (e.g., microg/microg, g/g, etc.). When the analyte concentration is a trace or mass fraction amount (e.g., microg/g), the formula generates incorrect HORRAT values. Alternative calculation procedures are presented to circumvent such problems.

Characterization of the gas sensors based on polymer-coated resonant microcantilevers for the detection of volatile organic compounds.

PubMed

Dong, Ying; Gao, Wei; Zhou, Qin; Zheng, Yi; You, Zheng

2010-06-25

The gas sensors based on polymer-coated resonant microcantilevers for volatile organic compounds (VOCs) detection are investigated. A method to characterize the gas sensors through sensor calibration is proposed. The expressions for the estimation of the characteristic parameters are derived. The effect of the polymer coating location on the sensor's sensitivity is investigated and the formula to calculate the polymer-analyte partition coefficient without knowing the polymer coating features is presented for the first time. Three polymers: polyethyleneoxide (PEO), polyethylenevinylacetate (PEVA) and polyvinylalcohol (PVA) are used to perform the experiments. Six organic solvents: toluene, benzene, ethanol, acetone, hexane and octane are used as analytes. The response time, reversibility, hydrophilicity, sensitivity and selectivity of the polymer layers are discussed. According to the results, highly sensitive sensors for each of the analytes are proposed. Based on the characterization method, a convenient and flexible way to the construction of electric nose system by the polymer-coated resonant microcantilevers can be achieved. Copyright 2010 Elsevier B.V. All rights reserved.

Local box-counting dimensions of discrete quantum eigenvalue spectra: Analytical connection to quantum spectral statistics

NASA Astrophysics Data System (ADS)

Sakhr, Jamal; Nieminen, John M.

2018-03-01

Two decades ago, Wang and Ong, [Phys. Rev. A 55, 1522 (1997)], 10.1103/PhysRevA.55.1522 hypothesized that the local box-counting dimension of a discrete quantum spectrum should depend exclusively on the nearest-neighbor spacing distribution (NNSD) of the spectrum. In this Rapid Communication, we validate their hypothesis by deriving an explicit formula for the local box-counting dimension of a countably-infinite discrete quantum spectrum. This formula expresses the local box-counting dimension of a spectrum in terms of single and double integrals of the NNSD of the spectrum. As applications, we derive an analytical formula for Poisson spectra and closed-form approximations to the local box-counting dimension for spectra having Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE), and Gaussian symplectic ensemble (GSE) spacing statistics. In the Poisson and GOE cases, we compare our theoretical formulas with the published numerical data of Wang and Ong and observe excellent agreement between their data and our theory. We also study numerically the local box-counting dimensions of the Riemann zeta function zeros and the alternate levels of GOE spectra, which are often used as numerical models of spectra possessing GUE and GSE spacing statistics, respectively. In each case, the corresponding theoretical formula is found to accurately describe the numerically computed local box-counting dimension.

Lyapunov dimension formula for the global attractor of the Lorenz system

NASA Astrophysics Data System (ADS)

Leonov, G. A.; Kuznetsov, N. V.; Korzhemanova, N. A.; Kusakin, D. V.

2016-12-01

The exact Lyapunov dimension formula for the Lorenz system for a positive measure set of parameters, including classical values, was analytically obtained first by G.A. Leonov in 2002. Leonov used the construction technique of special Lyapunov-type functions, which was developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters, of the system, such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values including all parameters, which satisfy the classical physical limitations.

Analytical expressions for the closure probability of a stiff wormlike chain for finite capture radius.

PubMed

Guérin, T

2017-08-01

Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability η(r_{c}) that the distance between the chain extremities is smaller than some capture radius r_{c}. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.

Analytic halo approach to the bispectrum of galaxies in redshift space

NASA Astrophysics Data System (ADS)

Yamamoto, Kazuhiro; Nan, Yue; Hikage, Chiaki

2017-02-01

We present an analytic formula for the galaxy bispectrum in redshift space on the basis of the halo approach description with the halo occupation distribution of central galaxies and satellite galaxies. This work is an extension of a previous work on the galaxy power spectrum, which illuminated the significant contribution of satellite galaxies to the higher multipole spectrum through the nonlinear redshift space distortions of their random motions. Behaviors of the multipoles of the bispectrum are compared with results of numerical simulations assuming a halo occupation distribution of the low-redshift (LOWZ) sample of the Sloan Digital Sky Survey (SDSS) III baryon oscillation spectroscopic survey (BOSS) survey. Also presented are analytic approximate formulas for the multipoles of the bispectrum, which is useful to understanding their characteristic properties. We demonstrate that the Fingers of God effect is quite important for the higher multipoles of the bispectrum in redshift space, depending on the halo occupation distribution parameters.

Quantitative photoacoustic imaging in the acoustic regime using SPIM

NASA Astrophysics Data System (ADS)

Beigl, Alexander; Elbau, Peter; Sadiq, Kamran; Scherzer, Otmar

2018-05-01

While in standard photoacoustic imaging the propagation of sound waves is modeled by the standard wave equation, our approach is based on a generalized wave equation with variable sound speed and material density, respectively. In this paper we present an approach for photoacoustic imaging, which in addition to the recovery of the absorption density parameter, the imaging parameter of standard photoacoustics, also allows us to reconstruct the spatially varying sound speed and density, respectively, of the medium. We provide analytical reconstruction formulas for all three parameters based in a linearized model based on single plane illumination microscopy (SPIM) techniques.

Correction coefficient for see-through labyrinth seal

NASA Astrophysics Data System (ADS)

Hasnedl, Dan; Epikaridis, Premysl; Slama, Vaclav

In a steam turbine design, the flow-part design and blade shapes are influenced by the design mass-flow through each turbine stage. If it would be possible to predict this mass-flow more precisely, it will result in optimized design and therefore an efficiency benefit. This article is concerned with improving the prediction of losses caused by the seal leakage. In the common simulation of the thermodynamic cycle of a steam turbine, analytical formulas are used in order to simulate the seal leakage. Therefore, this article describes an improvement of analytical formulas used in a turbine heat balance calculation. The results are verified by numerical simulations and experimental data from the steam test rig.

Wavefront aberrations: analytical method to convert Zernike coefficients from a pupil to a scaled arbitrarily decentered one

NASA Astrophysics Data System (ADS)

Comastri, S. A.; Perez, Liliana I.; Pérez, Gervasio D.; Bastida, K.; Martin, G.

2008-04-01

The wavefront aberration of any image forming system and, in particular, of a human eye, is often expanded in Zernike modes each mode being weighed by a coefficient that depends both on the image forming components of the system and on the contour, size and centering of the pupil. In the present article, expanding up to 7th order the wavefront aberration, an analytical method to compute a new set of Zernike coefficients corresponding to a pupil in terms of an original set evaluated via ray tracing for a dilated and transversally arbitrarily displaced pupil is developed. A transformation matrix of dimension 36×36 is attained multiplying the scaling-horizontal traslation matrix previously derived by appropriate rotation matrices. Multiplying the original coefficients by this transformation matrix, analytical formulas for each new coefficient are attained and supplied and, for the information concerning the wavefront aberration to be available, these formulas must be employed in cases in which the new pupil is contained in the original one. The use of these analytical formulas is exemplified applying them to study the effect of pupil contraction and/or decentering in 3 situations: calculation of corneal aberrations of a keratoconic subject for the natural photopic pupil size and various decenterings; coma compensation by means of pupil shift in a fictitious system solely having primary aberrations and evaluation of the amount of astigmatism and coma of a hypothetical system originally having spherical aberration alone.

Topological and statistical properties of nonlinear force-free fields

NASA Astrophysics Data System (ADS)

Mangalam, A.; Prasad, A.

2018-01-01

We use our semi-analytic solution of the nonlinear force-free field equation to construct three-dimensional magnetic fields that are applicable to the solar corona and study their statistical properties for estimating the degree of braiding exhibited by these fields. We present a new formula for calculating the winding number and compare it with the formula for the crossing number. The comparison is shown for a toy model of two helices and for realistic cases of nonlinear force-free fields; conceptually the formulae are nearly the same but the resulting distributions calculated for a given topology can be different. We also calculate linkages, which are useful topological quantities that are independent measures of the contribution of magnetic braiding to the total free energy and relative helicity of the field. Finally, we derive new analytical bounds for the free energy and relative helicity for the field configurations in terms of the linking number. These bounds will be of utility in estimating the braided energy available for nano-flares or for eruptions.

The analysis of non-linear dynamic behavior (including snap-through) of postbuckled plates by simple analytical solution

NASA Technical Reports Server (NTRS)

Ng, C. F.

1988-01-01

Static postbuckling and nonlinear dynamic analysis of plates are usually accomplished by multimode analyses, although the methods are complicated and do not give straightforward understanding of the nonlinear behavior. Assuming single-mode transverse displacement, a simple formula is derived for the transverse load displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the static postbuckling displacement and nonlinear dynamic responses of postbuckled plates under sinusoidal or random excitation. Regions with softening and hardening spring behavior are identified. Also, the highly nonlinear motion of snap-through and its effects on the overall dynamic response can be easily interpreted using the single-mode formula. Theoretical results are compared with experimental results obtained using a buckled aluminum panel, using discrete frequency and broadband point excitation. Some important effects of the snap-through motion on the dynamic response of the postbuckled plates are found.

Mechanical oscillatory behavior of a C60 fullerene tunneling through open carbon nanocones

NASA Astrophysics Data System (ADS)

Sadeghi, F.; Ansari, R.

2017-07-01

This paper deals with the mechanical oscillatory behavior of a C60 fullerene inside open carbon nanocones (CNCs). The fullerene molecule is assumed to enter the nanocone through its small end or wide end. Following our previously published study, semi-analytical expressions for the evaluation of vdW interactions are presented which facilitate obtaining a formula for oscillation frequency. The equation of motion is numerically solved to attain the time histories of separation distance and velocity of the fullerene molecule. Based on the conservation of the mechanical energy law, a new semi-analytical formula is also derived to accurately evaluate the oscillation frequency of the system. With respect to the present formulation, a detailed parametric study is conducted to gain an insight into the effects of both geometrical parameters (small-end radius, wide-end radius and vertex angle of nanocone) and initial conditions (initial separation distance and initial velocity) on the oscillatory behavior of C60 fullerene-open CNC oscillators. For given geometrical parameters and initial conditions, it is shown that higher oscillation frequencies can be achieved when the fullerene molecule enters the open nanocone through its small end.

On the efficiency and reversibility of active ligand transport induced by alternating rectangular electric pulses.

PubMed Central

Chen, Y; Tsong, T Y

1994-01-01

The stationary-state kinetic properties of a simplified two-state electro-conformational coupling model (ECC) in the presence of alternating rectangular electric potential pulses are derived analytically. Analytic expressions for the transport flux, the rate of electric energy dissipation, and the efficiency of the transducing system are obtained as a function of the amplitude and frequency of the oscillation. These formulas clarify some fundamental concept of the ECC model and are directly applicable to the interpretation and design of experiments. Based on these formulas, the reversibility and the degree of coupling of the system can be studied quantitatively. It is found that the oscillation-induced free energy transduction is reversible and tight-coupled only when the amplitude of the oscillating electric field is infinitely large. In general, the coupling is not tight when the amplitude of the electric field is finite. Furthermore, depending on the kinetic parameters of the model, there may exist a "critical" electric field amplitude, below which free energy transduction is not reversible. That is, energy may be transduced from the electric to the chemical, but not from the chemical to the electric. PMID:8075348

Constrained minimization problems for the reproduction number in meta-population models.

PubMed

Poghotanyan, Gayane; Feng, Zhilan; Glasser, John W; Hill, Andrew N

2018-02-14

The basic reproduction number ([Formula: see text]) can be considerably higher in an SIR model with heterogeneous mixing compared to that from a corresponding model with homogeneous mixing. For example, in the case of measles, mumps and rubella in San Diego, CA, Glasser et al. (Lancet Infect Dis 16(5):599-605, 2016. https://doi.org/10.1016/S1473-3099(16)00004-9 ), reported an increase of 70% in [Formula: see text] when heterogeneity was accounted for. Meta-population models with simple heterogeneous mixing functions, e.g., proportionate mixing, have been employed to identify optimal vaccination strategies using an approach based on the gradient of the effective reproduction number ([Formula: see text]), which consists of partial derivatives of [Formula: see text] with respect to the proportions immune [Formula: see text] in sub-groups i (Feng et al. in J Theor Biol 386:177-187, 2015.  https://doi.org/10.1016/j.jtbi.2015.09.006 ; Math Biosci 287:93-104, 2017.  https://doi.org/10.1016/j.mbs.2016.09.013 ). These papers consider cases in which an optimal vaccination strategy exists. However, in general, the optimal solution identified using the gradient may not be feasible for some parameter values (i.e., vaccination coverages outside the unit interval). In this paper, we derive the analytic conditions under which the optimal solution is feasible. Explicit expressions for the optimal solutions in the case of [Formula: see text] sub-populations are obtained, and the bounds for optimal solutions are derived for [Formula: see text] sub-populations. This is done for general mixing functions and examples of proportionate and preferential mixing are presented. Of special significance is the result that for general mixing schemes, both [Formula: see text] and [Formula: see text] are bounded below and above by their corresponding expressions when mixing is proportionate and isolated, respectively.

Qualitative evaluation of maternal milk and commercial infant formulas via LIBS.

PubMed

Abdel-Salam, Z; Al Sharnoubi, J; Harith, M A

2013-10-15

This study focuses on the use of laser-induced breakdown spectroscopy (LIBS) for the evaluation of the nutrients in maternal milk and some commercially available infant formulas. The results of such evaluation are vital for adequate and healthy feeding for babies during lactation period. Laser-induced breakdown spectroscopy offers special advantages in comparison to the other conventional analytical techniques. Specifically, LIBS is a straightforward technique that can be used in situ to provide qualitative analytical information in few minutes for the samples under investigation without preparation processes. The samples studied in the current work were maternal milk samples collected during the first 3 months of lactation (not colostrum milk) and samples from six different types of commercially available infant formulas. The samples' elemental composition has been compared with respect to the relative abundance of the elements of nutrition importance, namely Mg, Ca, Na, and Fe using their spectral emission lines in the relevant LIBS spectra. In addition, CN and C2 molecular emission bands in the same spectra have been studied as indicators of proteins content in the samples. The obtained analytical results demonstrate the higher elemental contents of the maternal milk compared with the commercial formulas samples. Similar results have been obtained as for the proteins content. It has been also shown that calcium and proteins have similar relative concentration trends in the studied samples. This work demonstrates the feasibility of adopting LIBS as a fast, safe, less costly technique evaluating qualitatively the nutrients content of both maternal and commercial milk samples. Copyright © 2013 Elsevier B.V. All rights reserved.

Light distribution in diffractive multifocal optics and its optimization.

PubMed

Portney, Valdemar

2011-11-01

To expand a geometrical model of diffraction efficiency and its interpretation to the multifocal optic and to introduce formulas for analysis of far and near light distribution and their application to multifocal intraocular lenses (IOLs) and to diffraction efficiency optimization. Medical device consulting firm, Newport Coast, California, USA. Experimental study. Application of a geometrical model to the kinoform (single focus diffractive optical element) was expanded to a multifocal optic to produce analytical definitions of light split between far and near images and light loss to other diffraction orders. The geometrical model gave a simple interpretation of light split in a diffractive multifocal IOL. An analytical definition of light split between far, near, and light loss was introduced as curve fitting formulas. Several examples of application to common multifocal diffractive IOLs were developed; for example, to light-split change with wavelength. The analytical definition of diffraction efficiency may assist in optimization of multifocal diffractive optics that minimize light loss. Formulas for analysis of light split between different foci of multifocal diffractive IOLs are useful in interpreting diffraction efficiency dependence on physical characteristics, such as blaze heights of the diffractive grooves and wavelength of light, as well as for optimizing multifocal diffractive optics. Disclosure is found in the footnotes. Copyright © 2011 ASCRS and ESCRS. Published by Elsevier Inc. All rights reserved.

Global stability for epidemic models on multiplex networks.

PubMed

Huang, Yu-Jhe; Juang, Jonq; Liang, Yu-Hao; Wang, Hsin-Yu

2018-05-01

In this work, we consider an epidemic model in a two-layer network in which the dynamics of susceptible-infected-susceptible process in the physical layer coexists with that of a cyclic process of unaware-aware-unaware in the virtual layer. For such multiplex network, we shall define the basic reproduction number [Formula: see text] in the virtual layer, which is similar to the basic reproduction number [Formula: see text] defined in the physical layer. We show analytically that if [Formula: see text] and [Formula: see text], then the disease and information free equilibrium is globally stable and if [Formula: see text] and [Formula: see text], then the disease free and information saturated equilibrium is globally stable for all initial conditions except at the origin. In the case of [Formula: see text], whether the disease dies out or not depends on the competition between how well the information is transmitted in the virtual layer and how contagious the disease is in the physical layer. In particular, it is numerically demonstrated that if the difference in [Formula: see text] and [Formula: see text] is greater than the product of [Formula: see text], the deviation of [Formula: see text] from 1 and the relative infection rate for an aware susceptible individual, then the disease dies out. Otherwise, the disease breaks out.

On the possibility of analytical approximation of line forms during random disorders of the resonance frequencies in molecular vibration-rotation spectra for satellite sounding

NASA Technical Reports Server (NTRS)

Fomin, V. V.

1979-01-01

The generalization spectral line contour concept and formulas for a two component mixture, as well as consequences of the general formula are discussed. The calculation procedure, initial information, calculation results and comparison of calculations with available experimental data, for radiation absorption in three CO2 bands are presented.

Generation of standard gas mixtures of halogenated, aliphatic, and aromatic compounds and prediction of the individual output rates based on molecular formula and boiling point.

PubMed

Thorenz, Ute R; Kundel, Michael; Müller, Lars; Hoffmann, Thorsten

2012-11-01

In this work, we describe a simple diffusion capillary device for the generation of various organic test gases. Using a set of basic equations the output rate of the test gas devices can easily be predicted only based on the molecular formula and the boiling point of the compounds of interest. Since these parameters are easily accessible for a large number of potential analytes, even for those compounds which are typically not listed in physico-chemical handbooks or internet databases, the adjustment of the test gas source to the concentration range required for the individual analytical application is straightforward. The agreement of the predicted and measured values is shown to be valid for different groups of chemicals, such as halocarbons, alkanes, alkenes, and aromatic compounds and for different dimensions of the diffusion capillaries. The limits of the predictability of the output rates are explored and observed to result in an underprediction of the output rates when very thin capillaries are used. It is demonstrated that pressure variations are responsible for the observed deviation of the output rates. To overcome the influence of pressure variations and at the same time to establish a suitable test gas source for highly volatile compounds, also the usability of permeation sources is explored, for example for the generation of molecular bromine test gases.

Internal gravity, self-energy, and disruption of comets and asteroids

NASA Astrophysics Data System (ADS)

Dobrovolskis, Anthony R.; Korycansky, D. G.

2018-03-01

The internal gravity and self-gravitational energy of a comet, asteroid, or small moon have applications to their geophysics, including their formation, evolution, cratering, and disruption, the stresses and strains inside such objects, sample return, eventual asteroid mining, and planetary defense strategies for potentially hazardous objects. This paper describes the relation of an object's self-energy to its collisional disruption energy, and shows how to determine an object's self-energy from its internal gravitational potential. Any solid object can be approximated to any desired accuracy by a polyhedron of sufficient complexity. An analytic formula is known for the gravitational potential of any homogeneous polyhedron, but it is widely believed that this formula applies only on the surface or outside of the object. Here we show instead that this formula applies equally well inside the object. We have used these formulae to develop a numerical code which evaluates the self-energy of any homogeneous polyhedron, along with the gravitational potential and attraction both inside and outside of the object, as well as the slope of its surface. Then we use our code to find the internal, external, and surface gravitational fields of the Platonic solids, asteroid (216) Kleopatra, and comet 67P/Churyumov-Gerasimenko, as well as their surface slopes and their self-gravitational energies. We also present simple spherical, ellipsoidal, cuboidal, and duplex models of Kleopatra and comet 67P, and show how to generalize our methods to inhomogeneous objects and magnetic fields. At present, only the self-energies of spheres, ellipsoids, and cuboids (boxes) are known analytically (or semi-analytically). The Supplementary Material contours the central potential and self-energy of homogeneous ellipsoids and cuboids of all aspect ratios, and also analytically the self-gravitational energy of a "duplex" consisting of two coupled spheres. The duplex is a good model for "contact binary" comets and asteroids; in fact, most comets seem to be bilobate, and might be described better as "dirty snowmen" than as "dirty snowballs".

Analytical expressions for the log-amplitude correlation function of a plane wave through anisotropic atmospheric refractive turbulence.

PubMed

Gudimetla, V S Rao; Holmes, Richard B; Smith, Carey; Needham, Gregory

2012-05-01

The effect of anisotropic Kolmogorov turbulence on the log-amplitude correlation function for plane-wave fields is investigated using analysis, numerical integration, and simulation. A new analytical expression for the log-amplitude correlation function is derived for anisotropic Kolmogorov turbulence. The analytic results, based on the Rytov approximation, agree well with a more general wave-optics simulation based on the Fresnel approximation as well as with numerical evaluations, for low and moderate strengths of turbulence. The new expression reduces correctly to previously published analytic expressions for isotropic turbulence. The final results indicate that, as asymmetry becomes greater, the Rytov variance deviates from that given by the standard formula. This deviation becomes greater with stronger turbulence, up to moderate turbulence strengths. The anisotropic effects on the log-amplitude correlation function are dominant when the separation of the points is within the Fresnel length. In the direction of stronger turbulence, there is an enhanced dip in the correlation function at a separation close to the Fresnel length. The dip is diminished in the weak-turbulence axis, suggesting that energy redistribution via focusing and defocusing is dominated by the strong-turbulence axis. The new analytical expression is useful when anisotropy is observed in relevant experiments. © 2012 Optical Society of America

Fractionation in normal tissues: the (α/β)eff concept can account for dose heterogeneity and volume effects.

PubMed

Hoffmann, Aswin L; Nahum, Alan E

2013-10-07

The simple Linear-Quadratic (LQ)-based Withers iso-effect formula (WIF) is widely used in external-beam radiotherapy to derive a new tumour dose prescription such that there is normal-tissue (NT) iso-effect when changing the fraction size and/or number. However, as conventionally applied, the WIF is invalid unless the normal-tissue response is solely determined by the tumour dose. We propose a generalized WIF (gWIF) which retains the tumour prescription dose, but replaces the intrinsic fractionation sensitivity measure (α/β) by a new concept, the normal-tissue effective fractionation sensitivity, [Formula: see text], which takes into account both the dose heterogeneity in, and the volume effect of, the late-responding normal-tissue in question. Closed-form analytical expressions for [Formula: see text] ensuring exact normal-tissue iso-effect are derived for: (i) uniform dose, and (ii) arbitrary dose distributions with volume-effect parameter n = 1 from the normal-tissue dose-volume histogram. For arbitrary dose distributions and arbitrary n, a numerical solution for [Formula: see text] exhibits a weak dependence on the number of fractions. As n is increased, [Formula: see text] increases from its intrinsic value at n = 0 (100% serial normal-tissue) to values close to or even exceeding the tumour (α/β) at n = 1 (100% parallel normal-tissue), with the highest values of [Formula: see text] corresponding to the most conformal dose distributions. Applications of this new concept to inverse planning and to highly conformal modalities are discussed, as is the effect of possible deviations from LQ behaviour at large fraction sizes.

Electrolyte diodes with weak acids and bases. I. Theory and an approximate analytical solution.

PubMed

Iván, Kristóf; Simon, Péter L; Wittmann, Mária; Noszticzius, Zoltán

2005-10-22

Until now acid-base diodes and transistors applied strong mineral acids and bases exclusively. In this work properties of electrolyte diodes with weak electrolytes are studied and compared with those of diodes with strong ones to show the advantages of weak acids and bases in these applications. The theoretical model is a one dimensional piece of gel containing fixed ionizable groups and connecting reservoirs of an acid and a base. The electric current flowing through the gel is measured as a function of the applied voltage. The steady-state current-voltage characteristic (CVC) of such a gel looks like that of a diode under these conditions. Results of our theoretical, numerical, and experimental investigations are reported in two parts. In this first, theoretical part governing equations necessary to calculate the steady-state CVC of a reverse-biased electrolyte diode are presented together with an approximate analytical solution of this reaction-diffusion-ionic migration problem. The applied approximations are quasielectroneutrality and quasiequilibrium. It is shown that the gel can be divided into an alkaline and an acidic zone separated by a middle weakly acidic region. As a further approximation it is assumed that the ionization of the fixed acidic groups is complete in the alkaline zone and that it is completely suppressed in the acidic one. The general solution given here describes the CVC and the potential and ionic concentration profiles of diodes applying either strong or weak electrolytes. It is proven that previous formulas valid for a strong acid-strong base diode can be regarded as a special case of the more general formulas presented here.

High Z neoclassical transport: Application and limitation of analytical formulae for modelling JET experimental parameters

NASA Astrophysics Data System (ADS)

Breton, S.; Casson, F. J.; Bourdelle, C.; Angioni, C.; Belli, E.; Camenen, Y.; Citrin, J.; Garbet, X.; Sarazin, Y.; Sertoli, M.; JET Contributors

2018-01-01

Heavy impurities, such as tungsten (W), can exhibit strongly poloidally asymmetric density profiles in rotating or radio frequency heated plasmas. In the metallic environment of JET, the poloidal asymmetry of tungsten enhances its neoclassical transport up to an order of magnitude, so that neoclassical convection dominates over turbulent transport in the core. Accounting for asymmetries in neoclassical transport is hence necessary in the integrated modeling framework. The neoclassical drift kinetic code, NEO [E. Belli and J. Candy, Plasma Phys. Controlled Fusion P50, 095010 (2008)], includes the impact of poloidal asymmetries on W transport. However, the computational cost required to run NEO slows down significantly integrated modeling. A previous analytical formulation to describe heavy impurity neoclassical transport in the presence of poloidal asymmetries in specific collisional regimes [C. Angioni and P. Helander, Plasma Phys. Controlled Fusion 56, 124001 (2014)] is compared in this work to numerical results from NEO. Within the domain of validity of the formula, the factor for reducing the temperature screening due to poloidal asymmetries had to be empirically adjusted. After adjustment, the modified formula can reproduce NEO results outside of its definition domain, with some limitations: When main ions are in the banana regime, the formula reproduces NEO results whatever the collisionality regime of impurities, provided that the poloidal asymmetry is not too large. However, for very strong poloidal asymmetries, agreement requires impurities in the Pfirsch-Schlüter regime. Within the JETTO integrated transport code, the analytical formula combined with the poloidally symmetric neoclassical code NCLASS [W. A. Houlberg et al., Phys. Plasmas 4, 3230 (1997)] predicts the same tungsten profile as NEO in certain cases, while saving a factor of one thousand in computer time, which can be useful in scoping studies. The parametric dependencies of the temperature screening reduction due to poloidal asymmetries would need to be better characterised for this faster model to be extended to a more general applicability.

Analysis of Mathematical Modelling on Potentiometric Biosensors

PubMed Central

Mehala, N.; Rajendran, L.

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

Analysis of mathematical modelling on potentiometric biosensors.

PubMed

Mehala, N; Rajendran, L

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

Determination of the aerosol size distribution by analytic inversion of the extinction spectrum in the complex anomalous diffraction approximation.

PubMed

Franssens, G; De Maziére, M; Fonteyn, D

2000-08-20

A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz's model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.

A Simple Method for Deriving the Confidence Regions for the Penalized Cox’s Model via the Minimand Perturbation†

PubMed Central

Lin, Chen-Yen; Halabi, Susan

2017-01-01

We propose a minimand perturbation method to derive the confidence regions for the regularized estimators for the Cox’s proportional hazards model. Although the regularized estimation procedure produces a more stable point estimate, it remains challenging to provide an interval estimator or an analytic variance estimator for the associated point estimate. Based on the sandwich formula, the current variance estimator provides a simple approximation, but its finite sample performance is not entirely satisfactory. Besides, the sandwich formula can only provide variance estimates for the non-zero coefficients. In this article, we present a generic description for the perturbation method and then introduce a computation algorithm using the adaptive least absolute shrinkage and selection operator (LASSO) penalty. Through simulation studies, we demonstrate that our method can better approximate the limiting distribution of the adaptive LASSO estimator and produces more accurate inference compared with the sandwich formula. The simulation results also indicate the possibility of extending the applications to the adaptive elastic-net penalty. We further demonstrate our method using data from a phase III clinical trial in prostate cancer. PMID:29326496

A Simple Method for Deriving the Confidence Regions for the Penalized Cox's Model via the Minimand Perturbation.

PubMed

Lin, Chen-Yen; Halabi, Susan

2017-01-01

We propose a minimand perturbation method to derive the confidence regions for the regularized estimators for the Cox's proportional hazards model. Although the regularized estimation procedure produces a more stable point estimate, it remains challenging to provide an interval estimator or an analytic variance estimator for the associated point estimate. Based on the sandwich formula, the current variance estimator provides a simple approximation, but its finite sample performance is not entirely satisfactory. Besides, the sandwich formula can only provide variance estimates for the non-zero coefficients. In this article, we present a generic description for the perturbation method and then introduce a computation algorithm using the adaptive least absolute shrinkage and selection operator (LASSO) penalty. Through simulation studies, we demonstrate that our method can better approximate the limiting distribution of the adaptive LASSO estimator and produces more accurate inference compared with the sandwich formula. The simulation results also indicate the possibility of extending the applications to the adaptive elastic-net penalty. We further demonstrate our method using data from a phase III clinical trial in prostate cancer.

New Patterns of the Two-Dimensional Rogue Waves: (2+1)-Dimensional Maccari System

NASA Astrophysics Data System (ADS)

Wang, Gai-Hua; Wang, Li-Hong; Rao, Ji-Guang; He, Jing-Song

2017-06-01

The ocean rogue wave is one kind of puzzled destructive phenomenon that has not been understood thoroughly so far. The two-dimensional nature of this wave has inspired the vast endeavors on the recognizing new patterns of the rogue waves based on the dynamical equations with two-spatial variables and one-temporal variable, which is a very crucial step to prevent this disaster event at the earliest stage. Along this issue, we present twelve new patterns of the two-dimensional rogue waves, which are reduced from a rational and explicit formula of the solutions for a (2+1)-dimensional Maccari system. The extreme points (lines) of the first-order lumps (rogue waves) are discussed according to their analytical formulas. For the lower-order rogue waves, we show clearly in formula that parameter b 2 plays a significant role to control these patterns. Supported by the National Natural Science Foundation of China under Grant No. 11671219, the K. C. Wong Magna Fund in Ningbo University, Gai-Hua Wang is also supported by the Scientific Research Foundation of Graduate School of Ningbo University

A two-phase Poisson process model and its application to analysis of cancer mortality among A-bomb survivors.

PubMed

Ohtaki, Megu; Tonda, Tetsuji; Aihara, Kazuyuki

2015-10-01

We consider a two-phase Poisson process model where only early successive transitions are assumed to be sensitive to exposure. In the case where intensity transitions are low, we derive analytically an approximate formula for the distribution of time to event for the excess hazard ratio (EHR) due to a single point exposure. The formula for EHR is a polynomial in exposure dose. Since the formula for EHR contains no unknown parameters except for the number of total stages, number of exposure-sensitive stages, and a coefficient of exposure effect, it is applicable easily under a variety of situations where there exists a possible latency time from a single point exposure to occurrence of event. Based on the multistage hypothesis of cancer, we formulate a radiation carcinogenesis model in which only some early consecutive stages of the process are sensitive to exposure, whereas later stages are not affected. An illustrative analysis using the proposed model is given for cancer mortality among A-bomb survivors. Copyright © 2015 Elsevier Inc. All rights reserved.

[Multi-mathematical modelings for compatibility optimization of Jiangzhi granules].

PubMed

Yang, Ming; Zhang, Li; Ge, Yingli; Lu, Yanliu; Ji, Guang

2011-12-01

To investigate into the method of "multi activity index evaluation and combination optimized of mult-component" for Chinese herbal formulas. According to the scheme of uniform experimental design, efficacy experiment, multi index evaluation, least absolute shrinkage, selection operator (LASSO) modeling, evolutionary optimization algorithm, validation experiment, we optimized the combination of Jiangzhi granules based on the activity indexes of blood serum ALT, ALT, AST, TG, TC, HDL, LDL and TG level of liver tissues, ratio of liver tissue to body. Analytic hierarchy process (AHP) combining with criteria importance through intercriteria correlation (CRITIC) for multi activity index evaluation was more reasonable and objective, it reflected the information of activity index's order and objective sample data. LASSO algorithm modeling could accurately reflect the relationship between different combination of Jiangzhi granule and the activity comprehensive indexes. The optimized combination of Jiangzhi granule showed better values of the activity comprehensive indexed than the original formula after the validation experiment. AHP combining with CRITIC can be used for multi activity index evaluation and LASSO algorithm, it is suitable for combination optimized of Chinese herbal formulas.

Stream Lifetimes Against Planetary Encounters

NASA Technical Reports Server (NTRS)

Valsecchi, G. B.; Lega, E.; Froeschle, Cl.

2011-01-01

We study, both analytically and numerically, the perturbation induced by an encounter with a planet on a meteoroid stream. Our analytical tool is the extension of pik s theory of close encounters, that we apply to streams described by geocentric variables. The resulting formulae are used to compute the rate at which a stream is dispersed by planetary encounters into the sporadic background. We have verified the accuracy of the analytical model using a numerical test.

Propagation properties of hollow sinh-Gaussian beams through fractional Fourier transform optical systems

NASA Astrophysics Data System (ADS)

Tang, Bin; Jiang, ShengBao; Jiang, Chun; Zhu, Haibin

2014-07-01

A hollow sinh-Gaussian beam (HsG) is an appropriate model to describe the dark-hollow beam. Based on Collins integral formula and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of a HsG beam passing through fractional Fourier transform (FRFT) optical systems with and without apertures have been studied in detail by some typical numerical examples. The results obtained using the approximate analytical formula are in good agreement with those obtained using numerical integral calculation. Further, the studies indicate that the normalized intensity distribution of the HsG beam in FRFT plane is closely related with not only the fractional order but also the beam order and the truncation parameter. The FRFT optical systems provide a convenient way for laser beam shaping.

Turbulent equipartition pinch of toroidal momentum in spherical torus

NASA Astrophysics Data System (ADS)

Hahm, T. S.; Lee, J.; Wang, W. X.; Diamond, P. H.; Choi, G. J.; Na, D. H.; Na, Y. S.; Chung, K. J.; Hwang, Y. S.

2014-12-01

We present a new analytic expression for turbulent equipartition (TEP) pinch of toroidal angular momentum originating from magnetic field inhomogeneity of spherical torus (ST) plasmas. Starting from a conservative modern nonlinear gyrokinetic equation (Hahm et al 1988 Phys. Fluids 31 2670), we derive an expression for pinch to momentum diffusivity ratio without using a usual tokamak approximation of B ∝ 1/R which has been previously employed for TEP momentum pinch derivation in tokamaks (Hahm et al 2007 Phys. Plasmas 14 072302). Our new formula is evaluated for model equilibria of National Spherical Torus eXperiment (NSTX) (Ono et al 2001 Nucl. Fusion 41 1435) and Versatile Experiment Spherical Torus (VEST) (Chung et al 2013 Plasma Sci. Technol. 15 244) plasmas. Our result predicts stronger inward pinch for both cases, as compared to the prediction based on the tokamak formula.

A study of coherence of soft gluons in hadron jets

NASA Astrophysics Data System (ADS)

Akrawy, M. Z.; Alexander, G.; Allison, J.; Allport, P. P.; Anderson, K. J.; Armitage, J. C.; Arnison, G. T. J.; Ashton, P.; Azuelos, G.; Baines, J. T. M.; Ball, A. H.; Banks, J.; Barker, G. J.; Barlow, R. J.; Batley, J. R.; Becker, J.; Behnke, T.; Bell, K. W.; Bella, G.; Bethke, S.; Biebel, O.; Binder, U.; Bloodworth, I. J.; Bock, P.; Breuker, H.; Brown, R. M.; Brun, R.; Buijs, A.; Burckhart, H. J.; Capiluppi, P.; Carnegie, R. K.; Carter, A. A.; Carter, J. R.; Chang, C. Y.; Charlton, D. G.; Chrin, J. T. M.; Clarke, P. E. L.; Cohen, I.; Collins, W. J.; Conboy, J. E.; Couch, M.; Coupland, M.; Cuffiani, M.; Dado, S.; Dallavalle, G. M.; Debu, P.; Deninno, M. M.; Dieckmann, A.; Dittmar, M.; Dixit, M. S.; Duchovni, E.; Duerdoth, I. P.; Dumas, D. J. P.; El Mamouni, H.; Elcombe, P. A.; Estabrooks, P. G.; Etzion, E.; Fabbri, F.; Farthouat, P.; Fischer, H. M.; Fong, D. G.; French, M. T.; Fukunaga, C.; Gaidot, A.; Ganel, O.; Gary, J. W.; Gascon, J.; Geddes, N. I.; Gee, C. N. P.; Geich-Gimbel, C.; Gensler, S. W.; Gentit, F. X.; Giacomelli, G.; Gibson, V.; Gibson, W. R.; Gillies, J. D.; Goldberg, J.; Goodrick, M. J.; Gorn, W.; Granite, D.; Gross, E.; Grunhaus, J.; Hagedorn, H.; Hagemann, J.; Hansroul, M.; Hargrove, C. K.; Harrus, I.; Hart, J.; Hattersley, P. M.; Hauschild, M.; Hawkes, C. M.; Heflin, E.; Hemingway, R. J.; Heuer, R. D.; Hill, J. C.; Hillier, S. J.; Ho, C.; Hobbs, J. D.; Hobson, P. R.; Hochman, D.; Holl, B.; Homer, R. J.; Hou, S. R.; Howarth, C. P.; Hughes-Jones, R. E.; Humbert, R.; Igo-Kemenes, P.; Ihssen, H.; Imrie, D. C.; Jawahery, A.; Jeffreys, P. W.; Jeremie, H.; Jimack, M.; Jobes, M.; Jones, R. W. L.; Jovanovic, P.; Karlen, D.; Kawagoe, K.; Kawamoto, T.; Kellogg, R. G.; Kennedy, B. W.; Kleinwort, C.; Klem, D. E.; Knop, G.; Kobayashi, T.; Kokott, T. P.; Köpke, L.; Kowalewski, R.; Kreutzmann, H.; Kroll, J.; Kuwano, M.; Kyberd, P.; Lafferty, G. D.; Lamarche, F.; Larson, W. J.; Layter, J. G.; Le Du, P.; Leblanc, P.; Lee, A. M.; Lehto, M. H.; Lellouch, D.; Lennert, P.; Lessard, L.; Levinson, L.; Lloyd, S. L.; Loebinger, F. K.; Lorah, J. M.; Lorazo, B.; Losty, M. J.; Ludwig, J.; Ma, J.; Macbeth, A. A.; Mannelli, M.; Marcellini, S.; Maringer, G.; Martin, A. J.; Martin, J. P.; Mashimo, T.; Mättig, P.; Maur, U.; McMahon, T. J.; McNutt, J. R.; McPherson, A. C.; Meijers, F.; Menszner, D.; Merritt, F. S.; Mes, H.; Michelini, A.; Middleton, R. P.; Mikenberg, G.; Miller, D. J.; Milstene, C.; Minowa, M.; Mohr, W.; Montanari, A.; Mori, T.; Moss, M. W.; Murphy, P. G.; Murray, W. J.; Nellen, B.; Nguyen, H. H.; Nozaki, M.; O'Dowd, A. J. P.; O'Neale, S. W.; O'Neill, B. P.; Oakham, F. G.; Odorici, F.; Ogg, M.; Oh, H.; Oreglia, M. J.; Orito, S.; Pansart, J. P.; Patrick, G. N.; Pawley, S. J.; Pfister, P.; Pilcher, J. E.; Pinfold, J. L.; Plane, D. E.; Poli, B.; Pouladdej, A.; Pritchard, T. W.; Quast, G.; Raab, J.; Redmond, M. W.; Rees, D. L.; Regimbald, M.; Riles, K.; Roach, C. M.; Robins, S. A.; Rollnik, A.; Roney, J. M.; Rossberg, S.; Rossi, A. M.; Routenburg, P.; Runge, K.; Runolfsson, O.; Sanghera, S.; Sansum, R. A.; Sasaki, M.; Saunders, B. J.; Schaile, A. D.; Schaile, O.; Schappert, W.; Scharff-Hansen, P.; Schreiber, S.; Schwarz, J.; Shapira, A.; Shen, B. C.; Sherwood, P.; Simon, A.; Singh, P.; Siroli, G. P.; Skuia, A.; Smith, A. M.; Smith, T. J.; Snow, G. A.; Springer, R. W.; Sproston, M.; Stephens, K.; Stier, H. E.; Ströhmer, R.; Strom, D.; Takeda, H.; Takeshita, T.; Tsukamoto, T.; Turner, M. F.; Tysarczyk-Niemeyer, G.; Van den plas, D.; VanDalen, G. J.; Vasseur, G.; Virtue, C. J.; von der Schmitt, H.; von Krogh, J.; Wagner, A.; Wahl, C.; Ward, C. P.; Ward, D. R.; Waterhouse, J.; Watkins, P. M.; Watson, A. T.; Watson, N. K.; Weber, M.; Weisz, S.; Wells, P. S.; Wermes, N.; Weymann, M.; Wilson, G. W.; Wilson, J. A.; Wingerter, I.; Winterer, V.-H.; Wood, N. C.; Wotton, S.; Wuensch, B.; Wyatt, T. R.; Yaari, R.; Yang, Y.; Yekutieli, G.; Yoshida, T.; Zeuner, W.; Zorn, G. T.; OPAL Collaboration

1990-09-01

We study the inclusive momentum distribution of charged particles in multihadronic events produced in e +e - annihilations at ECM∼ M(Z 0). We find agreement with the analytical formulae for gluon production that include the phenomena of soft gluon interference. Using data from CM energies between 14 and 91 GeV, we study the dependence of the inclusive momentum distribution on the centre of momentum energy. We find that the analytical formulae describe the data over the entire energy range. Both the momentum distribution at a fixed energy and the change with energy are described by QCD shower Monte Carlo's which include either coherent gluon branchings or string fragmentation. Simple incoherent models with independent fragmentation fail to reproduce the energy dependence and momentum spectra.

An analytic formula for the relativistic incoherent Thomson backscattering spectrum for a drifting bi-Maxwellian plasma

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

Naito, O.

2015-08-15

An analytic formula has been derived for the relativistic incoherent Thomson backscattering spectrum for a drifting anisotropic plasma when the scattering vector is parallel to the drifting direction. The shape of the scattering spectrum is insensitive to the electron temperature perpendicular to the scattering vector, but its amplitude may be modulated. As a result, while the measured temperature correctly represents the electron distribution parallel to the scattering vector, the electron density may be underestimated when the perpendicular temperature is higher than the parallel temperature. Since the scattering spectrum in shorter wavelengths is greatly enhanced by the existence of drift, themore » diagnostics might be used to measure local electron current density in fusion plasmas.« less

An analytical computation of magnetic field generated from a cylinder ferromagnet

NASA Astrophysics Data System (ADS)

Taniguchi, Tomohiro

2018-04-01

An analytical formulation to compute a magnetic field generated from an uniformly magnetized cylinder ferromagnet is developed. Exact solutions of the magnetic field generated from the magnetization pointing in an arbitrary direction are derived, which are applicable both inside and outside the ferromagnet. The validities of the present formulas are confirmed by comparing them with demagnetization coefficients estimated in earlier works. The results will be useful for designing practical applications, such as high-density magnetic recording and microwave generators, where nanostructured ferromagnets are coupled to each other through the dipole interactions and show cooperative phenomena such as synchronization. As an example, the magnetic field generated from a spin torque oscillator for magnetic recording based on microwave assisted magnetization reversal is studied.

Spectra for the reemission of attosecond and shorter electromagnetic pulses by multielectron atoms

NASA Astrophysics Data System (ADS)

Makarov, D. N.; Matveev, V. I.

2017-08-01

Based on the analytical solution of the Schrödinger equation, we have considered the reemission of attosecond and shorter electromagnetic pulses by multielectron atoms in the sudden perturbation approximation. We have developed a technique of calculating the spectra for the reemission of attosecond and shorter electromagnetic pulses by neutral multielectron atoms with nuclear charges from 1 to 92. The results are presented in the form of analytical formulas dependent on several coefficients and screening parameters tabulated for all of the atoms whose electron densities are described by the well-known Dirac-Hartree-Fock-Slater model. As examples we have calculated the spectra for the reemission by lithium, carbon, calcium, and iron atoms for two types of incident pulse: Gaussian and "sombrero."

TTVFaster: First order eccentricity transit timing variations (TTVs)

NASA Astrophysics Data System (ADS)

Agol, Eric; Deck, Katherine

2016-04-01

TTVFaster implements analytic formulae for transit time variations (TTVs) that are accurate to first order in the planet-star mass ratios and in the orbital eccentricities; the implementations are available in several languages, including IDL, Julia, Python and C. These formulae compare well with more computationally expensive N-body integrations in the low-eccentricity, low mass-ratio regime when applied to simulated and to actual multi-transiting Kepler planet systems.

On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.

2003-05-01

A formula expressing the Laguerre coefficients of a general-order derivative of an infinitely differentiable function in terms of its original coefficients is proved, and a formula expressing explicitly the derivatives of Laguerre polynomials of any degree and for any order as a linear combination of suitable Laguerre polynomials is deduced. A formula for the Laguerre coefficients of the moments of one single Laguerre polynomial of certain degree is given. Formulae for the Laguerre coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Laguerre coefficients are also obtained. A simple approach in order to build and solve recursively for the connection coefficients between Jacobi-Laguerre and Hermite-Laguerre polynomials is described. An explicit formula for these coefficients between Jacobi and Laguerre polynomials is given, of which the ultra-spherical polynomials of the first and second kinds and Legendre polynomials are important special cases. An analytical formula for the connection coefficients between Hermite and Laguerre polynomials is also obtained.

On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.

2004-01-01

Formulae expressing explicitly the Jacobi coefficients of a general-order derivative (integral) of an infinitely differentiable function in terms of its original expansion coefficients, and formulae for the derivatives (integrals) of Jacobi polynomials in terms of Jacobi polynomials themselves are stated. A formula for the Jacobi coefficients of the moments of one single Jacobi polynomial of certain degree is proved. Another formula for the Jacobi coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its original expanded coefficients is also given. A simple approach in order to construct and solve recursively for the connection coefficients between Jacobi-Jacobi polynomials is described. Explicit formulae for these coefficients between ultraspherical and Jacobi polynomials are deduced, of which the Chebyshev polynomials of the first and second kinds and Legendre polynomials are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Jacobi and Hermite-Jacobi are developed.

Cost-effectiveness of partially-hydrolyzed formula for prevention of atopic dermatitis in Australia.

PubMed

Su, John; Prescott, Susan; Sinn, John; Tang, Mimi; Smith, Peter; Heine, Ralf G; Spieldenner, Jörg; Iskedjian, Michael

2012-01-01

To perform an economic evaluation of a specific brand of partially hydrolyzed infant formula (PHF-W) in the prevention of atopic dermatitis (AD) among Australian infants. A cost-effectiveness analysis was undertaken from the perspectives of the Department of Health and Aging (DHA), of the family of the affected subject and of society as a whole in Australia, based on a decision-analytic model following a hypothetical representative cohort of Australian newborns who are not exclusively breastfed and who have a familial history of allergic disease (i.e., are deemed 'at risk'). Costs, consequences, and incremental cost-effectiveness ratios (ICER) were calculated for PHF-W vs standard cow's milk based infant formula (SF), and, in a secondary analysis, vs extensively hydrolyzed infant formula (EHF-Whey), when the latter was used for the prevention of AD. From a representative starting cohort of 87,724 'at risk' newborns in Australia in 2009, the expected ICERs for PHF-W vs SF were AU$496 from the perspective of the DHA and savings of AUD1739 and AU$1243 from the family and societal perspectives, respectively. When compared to EHF-Whey, PHF-W was associated with savings for the cohort of AU$5,183,474 and AU$6,736,513 from the DHA and societal perspectives. The generalizability and transferability of results to other settings, populations, or brands of infant formula should be made with caution. Whenever possible, a conservative approach directing bias against PHF-W rather than its comparators was applied in the base case analysis. Assumptions were verified in one-way and probabilistic sensitivity analyses, which confirmed the robustness of the model. PHF-W appears to be cost-effective when compared to SF from the DHA perspective, dominant over SF from the other perspectives, and dominant over EHF-Whey from all perspectives, in the prevention of AD in 'at risk' infants not exclusively breastfed, in Australia.

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

NASA Astrophysics Data System (ADS)

Izacard, Olivier

2016-08-01

In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula, and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. The latter demystifies the Maxwell's demon by statistically describing non-isolated systems.

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

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

Izacard, Olivier, E-mail: izacard@llnl.gov

In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basismore » sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula, and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. The latter demystifies the Maxwell's demon by statistically describing non-isolated systems.« less

Bootstrap Current for the Edge Pedestal Plasma in a Diverted Tokamak Geometry

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

Koh, S.; Chang, C. S.; Ku, S.

The edge bootstrap current plays a critical role in the equilibrium and stability of the steep edge pedestal plasma. The pedestal plasma has an unconventional and difficult neoclassical property, as compared with the core plasma. It has a narrow passing particle region in velocity space that can be easily modified or destroyed by Coulomb collisions. At the same time, the edge pedestal plasma has steep pressure and electrostatic potential gradients whose scale-lengths are comparable with the ion banana width, and includes a magnetic separatrix surface, across which the topological properties of the magnetic field and particle orbits change abruptly. Amore » driftkinetic particle code XGC0, equipped with a mass-momentum-energy conserving collision operator, is used to study the edge bootstrap current in a realistic diverted magnetic field geometry with a self-consistent radial electric field. When the edge electrons are in the weakly collisional banana regime, surprisingly, the present kinetic simulation confirms that the existing analytic expressions [represented by O. Sauter et al. , Phys. Plasmas 6 , 2834 (1999)] are still valid in this unconventional region, except in a thin radial layer in contact with the magnetic separatrix. The agreement arises from the dominance of the electron contribution to the bootstrap current compared with ion contribution and from a reasonable separation of the trapped-passing dynamics without a strong collisional mixing. However, when the pedestal electrons are in plateau-collisional regime, there is significant deviation of numerical results from the existing analytic formulas, mainly due to large effective collisionality of the passing and the boundary layer trapped particles in edge region. In a conventional aspect ratio tokamak, the edge bootstrap current from kinetic simulation can be significantly less than that from the Sauter formula if the electron collisionality is high. On the other hand, when the aspect ratio is close to unity, the collisional edge bootstrap current can be significantly greater than that from the Sauter formula. Rapid toroidal rotation of the magnetic field lines at the high field side of a tight aspect-ratio tokamak is believed to be the cause of the different behavior. A new analytic fitting formula, as a simple modification to the Sauter formula, is obtained to bring the analytic expression to a better agreement with the edge kinetic simulation results« less

Bootstrap current for the edge pedestal plasma in a diverted tokamak geometry

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

Koh, S.; Choe, W.; Chang, C. S.

The edge bootstrap current plays a critical role in the equilibrium and stability of the steep edge pedestal plasma. The pedestal plasma has an unconventional and difficult neoclassical property, as compared with the core plasma. It has a narrow passing particle region in velocity space that can be easily modified or destroyed by Coulomb collisions. At the same time, the edge pedestal plasma has steep pressure and electrostatic potential gradients whose scale-lengths are comparable with the ion banana width, and includes a magnetic separatrix surface, across which the topological properties of the magnetic field and particle orbits change abruptly. Amore » drift-kinetic particle code XGC0, equipped with a mass-momentum-energy conserving collision operator, is used to study the edge bootstrap current in a realistic diverted magnetic field geometry with a self-consistent radial electric field. When the edge electrons are in the weakly collisional banana regime, surprisingly, the present kinetic simulation confirms that the existing analytic expressions [represented by O. Sauter et al., Phys. Plasmas 6, 2834 (1999)] are still valid in this unconventional region, except in a thin radial layer in contact with the magnetic separatrix. The agreement arises from the dominance of the electron contribution to the bootstrap current compared with ion contribution and from a reasonable separation of the trapped-passing dynamics without a strong collisional mixing. However, when the pedestal electrons are in plateau-collisional regime, there is significant deviation of numerical results from the existing analytic formulas, mainly due to large effective collisionality of the passing and the boundary layer trapped particles in edge region. In a conventional aspect ratio tokamak, the edge bootstrap current from kinetic simulation can be significantly less than that from the Sauter formula if the electron collisionality is high. On the other hand, when the aspect ratio is close to unity, the collisional edge bootstrap current can be significantly greater than that from the Sauter formula. Rapid toroidal rotation of the magnetic field lines at the high field side of a tight aspect-ratio tokamak is believed to be the cause of the different behavior. A new analytic fitting formula, as a simple modification to the Sauter formula, is obtained to bring the analytic expression to a better agreement with the edge kinetic simulation results.« less

Feynman Path Integral Approach to Electron Diffraction for One and Two Slits: Analytical Results

ERIC Educational Resources Information Center

Beau, Mathieu

2012-01-01

In this paper we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulae, various approximations of the electron distribution are shown which facilitate the interpretation of the results.…

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

Morante, S., E-mail: morante@roma2.infn.it; Rossi, G.C., E-mail: rossig@roma2.infn.it; Centro Fermi-Museo Storico della Fisica e Centro Studi e Ricerche E. Fermi, Compendio del Viminale, Piazza del Viminale 1, I-00184 Rome

We give a novel and simple proof of the DFT expression for the interatomic force field that drives the motion of atoms in classical Molecular Dynamics, based on the observation that the ground state electronic energy, seen as a functional of the external potential, is the Legendre transform of the Hohenberg–Kohn functional, which in turn is a functional of the electronic density. We show in this way that the so-called Hellmann–Feynman analytical formula, currently used in numerical simulations, actually provides the exact expression of the interatomic force.

Effect of polarization on the evolution of electromagnetic hollow Gaussian Schell-model beam

NASA Astrophysics Data System (ADS)

Long, Xuewen; Lu, Keqing; Zhang, Yuhong; Guo, Jianbang; Li, Kehao

2011-02-01

Based on the theory of coherence, an analytical propagation formula for partially polarized and partially coherent hollow Gaussian Schell-model beams (HGSMBs) passing through a paraxial optical system is derived. Furthermore, we show that the degree of polarization of source may affect the evolution of HGSMBs and a tunable dark region may exist. For two special cases of fully coherent and partially coherent δxx = δyy, normalized intensity distributions are independent of the polarization of source.

Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.; Ahmed, H. M.

2004-08-01

A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed.

The mean and variance of phylogenetic diversity under rarefaction

PubMed Central

Matsen, Frederick A.

2013-01-01

Summary Phylogenetic diversity (PD) depends on sampling depth, which complicates the comparison of PD between samples of different depth. One approach to dealing with differing sample depth for a given diversity statistic is to rarefy, which means to take a random subset of a given size of the original sample. Exact analytical formulae for the mean and variance of species richness under rarefaction have existed for some time but no such solution exists for PD.We have derived exact formulae for the mean and variance of PD under rarefaction. We confirm that these formulae are correct by comparing exact solution mean and variance to that calculated by repeated random (Monte Carlo) subsampling of a dataset of stem counts of woody shrubs of Toohey Forest, Queensland, Australia. We also demonstrate the application of the method using two examples: identifying hotspots of mammalian diversity in Australasian ecoregions, and characterising the human vaginal microbiome.There is a very high degree of correspondence between the analytical and random subsampling methods for calculating mean and variance of PD under rarefaction, although the Monte Carlo method requires a large number of random draws to converge on the exact solution for the variance.Rarefaction of mammalian PD of ecoregions in Australasia to a common standard of 25 species reveals very different rank orderings of ecoregions, indicating quite different hotspots of diversity than those obtained for unrarefied PD. The application of these methods to the vaginal microbiome shows that a classical score used to quantify bacterial vaginosis is correlated with the shape of the rarefaction curve.The analytical formulae for the mean and variance of PD under rarefaction are both exact and more efficient than repeated subsampling. Rarefaction of PD allows for many applications where comparisons of samples of different depth is required. PMID:23833701

The mean and variance of phylogenetic diversity under rarefaction.

PubMed

Nipperess, David A; Matsen, Frederick A

2013-06-01

Phylogenetic diversity (PD) depends on sampling depth, which complicates the comparison of PD between samples of different depth. One approach to dealing with differing sample depth for a given diversity statistic is to rarefy, which means to take a random subset of a given size of the original sample. Exact analytical formulae for the mean and variance of species richness under rarefaction have existed for some time but no such solution exists for PD.We have derived exact formulae for the mean and variance of PD under rarefaction. We confirm that these formulae are correct by comparing exact solution mean and variance to that calculated by repeated random (Monte Carlo) subsampling of a dataset of stem counts of woody shrubs of Toohey Forest, Queensland, Australia. We also demonstrate the application of the method using two examples: identifying hotspots of mammalian diversity in Australasian ecoregions, and characterising the human vaginal microbiome.There is a very high degree of correspondence between the analytical and random subsampling methods for calculating mean and variance of PD under rarefaction, although the Monte Carlo method requires a large number of random draws to converge on the exact solution for the variance.Rarefaction of mammalian PD of ecoregions in Australasia to a common standard of 25 species reveals very different rank orderings of ecoregions, indicating quite different hotspots of diversity than those obtained for unrarefied PD. The application of these methods to the vaginal microbiome shows that a classical score used to quantify bacterial vaginosis is correlated with the shape of the rarefaction curve.The analytical formulae for the mean and variance of PD under rarefaction are both exact and more efficient than repeated subsampling. Rarefaction of PD allows for many applications where comparisons of samples of different depth is required.

Positive-Negative Birefringence in Multiferroic Layered Metasurfaces.

PubMed

Khomeriki, R; Chotorlishvili, L; Tralle, I; Berakdar, J

2016-11-09

We uncover and identify the regime for a magnetically and ferroelectrically controllable negative refraction of a light-traversing multiferroic, oxide-based metastructure consisting of alternating nanoscopic ferroelectric (SrTiO 3 ) and ferromagnetic (Y 3 Fe 2 (FeO 4 ) 3 , YIG) layers. We perform analytical and numerical simulations based on discretized, coupled equations for the self-consistent Maxwell/ferroelectric/ferromagnetic dynamics and obtain a biquadratic relation for the refractive index. Various scenarios of ordinary and negative refraction in different frequency ranges are analyzed and quantified by simple analytical formula that are confirmed by full-fledge numerical simulations. Electromagnetic waves injected at the edges of the sample are propagated exactly numerically. We discovered that, for particular GHz frequencies, waves with different polarizations are characterized by different signs of the refractive index, giving rise to novel types of phenomena such as a positive-negative birefringence effect and magnetically controlled light trapping and accelerations.

Highly accurate analytic formulae for projectile motion subjected to quadratic drag

NASA Astrophysics Data System (ADS)

Turkyilmazoglu, Mustafa

2016-05-01

The classical phenomenon of motion of a projectile fired (thrown) into the horizon through resistive air charging a quadratic drag onto the object is revisited in this paper. No exact solution is known that describes the full physical event under such an exerted resistance force. Finding elegant analytical approximations for the most interesting engineering features of dynamical behavior of the projectile is the principal target. Within this purpose, some analytical explicit expressions are derived that accurately predict the maximum height, its arrival time as well as the flight range of the projectile at the highest ascent. The most significant property of the proposed formulas is that they are not restricted to the initial speed and firing angle of the object, nor to the drag coefficient of the medium. In combination with the available approximations in the literature, it is possible to gain information about the flight and complete the picture of a trajectory with high precision, without having to numerically simulate the full governing equations of motion.

Into the theory of the partial-filling affinity capillary electrophoresis and the determination of apparent stability constants of analyte-ligand complexes.

PubMed

Ansorge, Martin; Dubský, Pavel; Ušelová, Kateřina

2018-03-01

The partial-filling affinity capillary electrophoresis (pf-ACE) works with a ligand present in a background electrolyte that forms a weak complex with an analyte. In contrast to a more popular mobility-shift affinity capillary electrophoresis, only a short plug of the ligand is introduced into a capillary in the pf-ACE. Both methods can serve for determining apparent stability constants of the formed complexes but this task is hindered in the pf-ACE by the fact that the analyte spends only a part of its migration time in a contact with the ligand. In 1998, Amini and Westerlund published a linearization strategy that allows for extracting an effective mobility of an analyte in the presence of a neutral ligand out of the pf-ACE data. The main purpose of this paper is to show that the original formula is only approximate. We derive a new formula and demonstrate its applicability by means of computer simulations. We further inspect several strategies of data processing in the pf-ACE regarding a risk of an error propagation. This establishes a good practice of determining apparent stability constants of analyte-ligand complexes by means of the pf-ACE. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

One-dimensional model of interacting-step fluctuations on vicinal surfaces: Analytical formulas and kinetic Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Patrone, Paul N.; Einstein, T. L.; Margetis, Dionisios

2010-12-01

We study analytically and numerically a one-dimensional model of interacting line defects (steps) fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for approximately solving systems of coupled nonlinear stochastic differential equations (SDEs) governing fluctuations in surface motion. In our analytical approach, the starting point is the Burton-Cabrera-Frank (BCF) model by which step motion is driven by diffusion of adsorbed atoms on terraces and atom attachment-detachment at steps. The step energy accounts for entropic and nearest-neighbor elastic-dipole interactions. By including Gaussian white noise to the equations of motion for terrace widths, we formulate large systems of SDEs under different choices of diffusion coefficients for the noise. We simplify this description via (i) perturbation theory and linearization of the step interactions and, alternatively, (ii) a mean-field (MF) approximation whereby widths of adjacent terraces are replaced by a self-consistent field but nonlinearities in step interactions are retained. We derive simplified formulas for the time-dependent terrace-width distribution (TWD) and its steady-state limit. Our MF analytical predictions for the TWD compare favorably with kinetic Monte Carlo simulations under the addition of a suitably conservative white noise in the BCF equations.

A Functional Analytic Approach To Computer-Interactive Mathematics

PubMed Central

2005-01-01

Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on particular formula-to-formula and formula-to-graph relations as these formulas pertain to reflections and vertical and horizontal shifts. In training A-B, standard formulas served as samples and factored formulas served as comparisons. In training B-C, factored formulas served as samples and graphs served as comparisons. Subsequently, the program assessed for mutually entailed B-A and C-B relations as well as combinatorially entailed C-A and A-C relations. After all participants demonstrated mutual entailment and combinatorial entailment, we employed a test of novel relations to assess 40 different and complex variations of the original training formulas and their respective graphs. Six of 10 participants who completed training demonstrated perfect or near-perfect performance in identifying novel formula-to-graph relations. Three of the 4 participants who made more than three incorrect responses during the assessment of novel relations showed some commonality among their error patterns. Derived transfer of stimulus control using mathematical relations is discussed. PMID:15898471

A functional analytic approach to computer-interactive mathematics.

PubMed

Ninness, Chris; Rumph, Robin; McCuller, Glen; Harrison, Carol; Ford, Angela M; Ninness, Sharon K

2005-01-01

Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on particular formula-to-formula and formula-to-graph relations as these formulas pertain to reflections and vertical and horizontal shifts. In training A-B, standard formulas served as samples and factored formulas served as comparisons. In training B-C, factored formulas served as samples and graphs served as comparisons. Subsequently, the program assessed for mutually entailed B-A and C-B relations as well as combinatorially entailed C-A and A-C relations. After all participants demonstrated mutual entailment and combinatorial entailment, we employed a test of novel relations to assess 40 different and complex variations of the original training formulas and their respective graphs. Six of 10 participants who completed training demonstrated perfect or near-perfect performance in identifying novel formula-to-graph relations. Three of the 4 participants who made more than three incorrect responses during the assessment of novel relations showed some commonality among their error patterns. Derived transfer of stimulus control using mathematical relations is discussed.

A short history of the development of the Turc-Mezentsev water balance formula

NASA Astrophysics Data System (ADS)

Andréassian, Vazken; Lebecherel, Laure

2013-04-01

In the 1950s, a formula linking long term average evaporation to long-term average precipitation and potential evaporation was quasi-simultaneously proposed in France and in the Soviet Union. However, because Turc and Mezentsev published in French and Russian respectively, their work has received limited attention, and the formula they proposed is often given different names. • Work of Lucien Turc in France (1954) Lucien Turc, a French soil scientist, worked at the Versailles soil science laboratory of the French National Agronomical Research Institute. For agronomic purposes, he was interested in developing a formula to estimate actual evapotranspiration from precipitation and temperature data. Since lysimeter data were so scarce at that time, he had the idea to derive such a formula from catchment water balance. With the help of the hydrologist Maurice Pardé, he assembled a set of data on 254 catchments from all over the world. He derived long-term average actual evapotranspiration (E) from estimates of long-term average precipitation (P) and long-term average discharge (Q). Then, Turc looked for a mathematical function linking two non-dimensional terms: the aridity index (the ratio of precipitation P and potential evapotranspiration E0) and the evapotranspiration rate (the ratio of E and E0). He proposed the following formulation: E/P=1/[1+(P/E0)**n]**(1/n) in which n is an exponent to estimate. Turc graphically looked for the most convenient value for n, and concluded that the best fit was "with n=3, or may be n=2" (Turc, 1954, p.563). • Work of Varfolomeï Mezentsev in the Soviet Union (1955) Mezentsev (1955) worked at the University of Omsk in Siberia. He started his analysis from a formula proposed by Bagrov (1953): dE/dP=1-(E/E0)**n (Eq.1) This formula presents the interesting property to integrate into the Schreiber (1904) water balance formula for n=1:and into the Ol'Dekop (1911) water balance formula for n=2. But it had no analytical solution for other values of n. Mezentsev (1955) complexified Bagrov's formula by rewriting it as follows: dE/dP=[1-(E/E0)**n]**(1+1/n) (Eq.2) which keeps the same interpretation as Eq. 1. Eq. 2 can be integrated analytically and yields Eq. 3: E/P=1/[1+(P/E0)**n]**(1/n) (Eq.3) which is identical to the general formulation proposed by Turc. Based on a set of 35 catchments of the Siberian plateau, Mezentsev suggested using the value of 2.3 for parameter n, which is close to the value advised by Turc. References Bagrov, N. A., 1953. O srednem mnogoletnem ispraeniiz c paverknosti sushi (on the average long-term evaporation from the land surface), Meteorologia i Gidrologia, 10, 20-25. Mezentsev, V., 1955. More on the computation of total evaporation (Yechio raz o rastchetie srednevo summarnovo ispareniia). Meteorologia i Gidrologia, 5: 24-26. Turc, L., 1954. Le bilan d'eau des sols: relation entre les précipitations, l'évaporation et l'écoulement. Annales Agronomiques, Série A(5): 491-595.

Sample sizes needed for specified margins of relative error in the estimates of the repeatability and reproducibility standard deviations.

PubMed

McClure, Foster D; Lee, Jung K

2005-01-01

Sample size formulas are developed to estimate the repeatability and reproducibility standard deviations (Sr and S(R)) such that the actual error in (Sr and S(R)) relative to their respective true values, sigmar and sigmaR, are at predefined levels. The statistical consequences associated with AOAC INTERNATIONAL required sample size to validate an analytical method are discussed. In addition, formulas to estimate the uncertainties of (Sr and S(R)) were derived and are provided as supporting documentation. Formula for the Number of Replicates Required for a Specified Margin of Relative Error in the Estimate of the Repeatability Standard Deviation.

Tunnel ionization of atoms and molecules: How accurate are the weak-field asymptotic formulas?

NASA Astrophysics Data System (ADS)

Labeye, Marie; Risoud, François; Maquet, Alfred; Caillat, Jérémie; Taïeb, Richard

2018-05-01

Weak-field asymptotic formulas for the tunnel ionization rate of atoms and molecules in strong laser fields are often used for the analysis of strong field recollision experiments. We investigate their accuracy and domain of validity for different model systems by confronting them to exact numerical results, obtained by solving the time dependent Schrödinger equation. We find that corrections that take the dc-Stark shift into account are a simple and efficient way to improve the formula. Furthermore, analyzing the different approximations used, we show that error compensation plays a crucial role in the fair agreement between exact and analytical results.

Electrical and thermoelectric transport properties of two-dimensional fermionic systems with k-cubic spin-orbit coupling.

PubMed

Mawrie, Alestin; Verma, Sonu; Ghosh, Tarun Kanti

2017-10-25

We investigate the effect of k-cubic spin-orbit interaction on the electrical and thermoelectric transport properties of two-dimensional fermionic systems. We obtain exact analytical expressions of the inverse relaxation time (IRT) and the Drude conductivity for long-range Coulomb and short-range delta scattering potentials. The IRT reveals that the scattering is completely suppressed along the three directions [Formula: see text] with [Formula: see text]. We also obtain analytical results of the thermopower and thermal conductivity at low temperature. The thermoelectric transport coefficients obey the Wiedemann-Franz law, even in the presence of k-cubic Rashba spin-orbit interaction (RSOI) at low temperature. In the presence of a quantizing magnetic field, the signature of the RSOI is revealed through the appearance of the beating pattern in the Shubnikov-de Haas (SdH) oscillations of thermopower and thermal conductivity in the low magnetic field regime. The empirical formulae for the SdH oscillation frequencies accurately describe the locations of the beating nodes. The beating pattern in magnetothermoelectric measurement can be used to extract the spin-orbit coupling constant.

Assessment of infant formula quality and composition using Vis-NIR, MIR and Raman process analytical technologies.

PubMed

Wang, Xiao; Esquerre, Carlos; Downey, Gerard; Henihan, Lisa; O'Callaghan, Donal; O'Donnell, Colm

2018-06-01

In this study, visible and near-infrared (Vis-NIR), mid-infrared (MIR) and Raman process analytical technologies were investigated for assessment of infant formula quality and compositional parameters namely preheat temperature, storage temperature, storage time, fluorescence of advanced Maillard products and soluble tryptophan (FAST) index, soluble protein, fat and surface free fat (SFF) content. PLS-DA models developed using spectral data with appropriate data pre-treatment and significant variables selected using Martens' uncertainty test had good accuracy for the discrimination of preheat temperature (92.3-100%) and storage temperature (91.7-100%). The best PLS regression models developed yielded values for the ratio of prediction error to deviation (RPD) of 3.6-6.1, 2.1-2.7, 1.7-2.9, 1.6-2.6 and 2.5-3.0 for storage time, FAST index, soluble protein, fat and SFF content prediction respectively. Vis-NIR, MIR and Raman were demonstrated to be potential PAT tools for process control and quality assurance applications in infant formula and dairy ingredient manufacture. Copyright © 2018 Elsevier B.V. All rights reserved.

Asymptotics of bivariate generating functions with algebraic singularities

NASA Astrophysics Data System (ADS)

Greenwood, Torin

Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.

Size separation of analytes using monomeric surfactants

DOEpatents

Yeung, Edward S.; Wei, Wei

2005-04-12

A sieving medium for use in the separation of analytes in a sample containing at least one such analyte comprises a monomeric non-ionic surfactant of the of the general formula, B-A, wherein A is a hydrophilic moiety and B is a hydrophobic moiety, present in a solvent at a concentration forming a self-assembled micelle configuration under selected conditions and having an aggregation number providing an equivalent weight capable of effecting the size separation of the sample solution so as to resolve a target analyte(s) in a solution containing the same, the size separation taking place in a chromatography or electrophoresis separation system.

An analytical model for transient deformation of viscoelastically coated beams: Applications to static-mode microcantilever chemical sensors

NASA Astrophysics Data System (ADS)

Heinrich, S. M.; Wenzel, M. J.; Josse, F.; Dufour, I.

2009-06-01

The problem governing the transient deformation of an elastic cantilever beam with viscoelastic coating, subjected to a time-dependent coating eigenstrain, is mathematically formulated. An analytical solution for an exponential eigenstrain history, exact within the context of beam theory, is obtained in terms of the coating and base layer thicknesses, the elastic modulus of the base material, the initial coating modulus, the coating relaxation percentage (0%-100%), and the time constants of the coating's relaxation process and its eigenstrain history. Approximate formulas, valid for thin coatings, are derived as special cases to provide insight into system behavior. Main results include (1) the time histories of the beam curvature and the coating stresses, (2) a criterion governing the response type (monotonic or "overshoot" response), and (3) simple expressions for the overshoot ratio, defined as the peak response scaled by the steady-state response, and the time at which the peak response occurs. Applications to polymer-coated microcantilever-based chemical sensors operating in the static mode are discussed.

Chicken-based formula is better tolerated than extensively hydrolyzed casein formula for the management of cow milk protein allergy in infants.

PubMed

Jirapinyo, Pipop; Densupsoontorn, Narumon; Kangwanpornsiri, Channagan; Wongarn, Renu

2012-01-01

The effective treatment of cow milk allergy in infants consists of elimination of cow milk protein and the introduction of formulas based on an extensively hydrolyzed protein formula or an amino acid-based formula. However, about 10% of these infants are still allergic to an extensively hydrolyzed protein formula and an amino acid-based formula is very expensive. We conducted a study to verify whether the new chicken-based formula will be better tolerated than an extensively hydrolyzed protein formula for the treatment of cow milk allergy in infants. One hundred infants, diagnosed with cow milk allergy by double-blind, placebo-controlled food challenge tests, were enrolled in a double-blind, randomized, cross-over study to compare a response to an extensively hydrolyzed protein formula and the chicken-based formula. Subjects were randomly given one of the two formulas for 2 weeks. There was a 2-week washout period of taking an amino acid-based formula before being switched to the other formula for another 2 weeks. If the subjects showed allergic symptoms during the 2 weeks of test formula, they would be announced as intolerance or allergic to that formula. Sixty seven of 80 confirmed subjects agreed to enroll their infants. Fifty-eight subjects completed the study. Twenty and 33 infants were tolerant whereas and 38 and 25 infants were intolerant to an extensively hydrolyzed protein formula and the chicken-based formula, respectively. The chicken-based formula showed significantly better tolerance than an extensively hydrolyzed protein formula in the management of cow milk allergy in infants.

Explicit formulas for effective piezoelectric coefficients of ferroelectric 0-3 composites based on effective medium theory

NASA Astrophysics Data System (ADS)

Wong, C. K.; Poon, Y. M.; Shin, F. G.

2003-01-01

Explicit formulas were derived for the effective piezoelectric stress coefficients of a 0-3 composite of ferroelectric spherical particles in a ferroelectric matrix which were then combined to give the more commonly used strain coefficients. Assuming that the elastic stiffness of the inclusion phase is sufficiently larger than that of the matrix phase, the previously derived explicit expressions for the case of a low volume concentration of inclusion particles [C. K. Wong, Y. M. Poon, and F. G. Shin, Ferroelectrics 264, 39 (2001); J. Appl. Phys. 90, 4690 (2001)] were "transformed" analytically by an effective medium theory (EMT) with appropriate approximations, to suit the case of a more concentrated suspension. Predictions of the EMT expressions were compared with the experimental values of composites of lead zirconate titanate ceramic particles dispersed in polyvinylidene fluoride and polyvinylidene fluoride-trifluoroethylene copolymer, reported by Furukawa [IEEE Trans. Electr. Insul. 24, 375 (1989)] and by Ng et al. [IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1308 (2000)] respectively. Fairly good agreement was obtained. Comparisons with other predictions, including the predictions given by numerically solving the EMT scheme, were also made. It was found that the analytic and numeric EMT schemes agreed with each other very well for an inclusion of volume fraction not exceeding 60%.

Discovering anomalous events from urban informatics data

NASA Astrophysics Data System (ADS)

Jayarajah, Kasthuri; Subbaraju, Vigneshwaran; Weerakoon, Dulanga; Misra, Archan; Tam, La Thanh; Athaide, Noel

2017-05-01

Singapore's "smart city" agenda is driving the government to provide public access to a broader variety of urban informatics sources, such as images from traffic cameras and information about buses servicing different bus stops. Such informatics data serves as probes of evolving conditions at different spatiotemporal scales. This paper explores how such multi-modal informatics data can be used to establish the normal operating conditions at different city locations, and then apply appropriate outlier-based analysis techniques to identify anomalous events at these selected locations. We will introduce the overall architecture of sociophysical analytics, where such infrastructural data sources can be combined with social media analytics to not only detect such anomalous events, but also localize and explain them. Using the annual Formula-1 race as our candidate event, we demonstrate a key difference between the discriminative capabilities of different sensing modes: while social media streams provide discriminative signals during or prior to the occurrence of such an event, urban informatics data can often reveal patterns that have higher persistence, including before and after the event. In particular, we shall demonstrate how combining data from (i) publicly available Tweets, (ii) crowd levels aboard buses, and (iii) traffic cameras can help identify the Formula-1 driven anomalies, across different spatiotemporal boundaries.

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

Izacard, Olivier

In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basismore » sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula, and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. In conclusion, the latter demystifies the Maxwell's demon by statistically describing non-isolated systems.« less

Probing-models for interdigitated electrode systems with ferroelectric thin films

NASA Astrophysics Data System (ADS)

Nguyen, Cuong H.; Nigon, Robin; Raeder, Trygve M.; Hanke, Ulrik; Halvorsen, Einar; Muralt, Paul

2018-05-01

In this paper, a new method to characterize ferroelectric thin films with interdigitated electrodes is presented. To obtain accurate properties, all parasitic contributions should be subtracted from the measurement results and accurate models for the ferroelectric film are required. Hence, we introduce a phenomenological model for the parasitic capacitance. Moreover, two common analytical models based on conformal transformations are compared and used to calculate the capacitance and the electric field. With a thin film approximation, new simplified electric field and capacitance formulas are derived. By using these formulas, more consistent CV, PV and stress-field loops for samples with different geometries are obtained. In addition, an inhomogeneous distribution of the permittivity due to the non-uniform electric field is modelled by finite element simulation in an iterative way. We observed that this inhomogeneous distribution can be treated as a homogeneous one with an effective value of the permittivity.

α decay and cluster radioactivity of nuclei of interest to the synthesis of Z =119 , 120 isotopes

NASA Astrophysics Data System (ADS)

Poenaru, D. N.; Gherghescu, R. A.

2018-04-01

Super-heavy nuclei of interest for the forthcoming synthesis of the isotopes with Z =119 , 120 are investigated. One of the very interesting latest experiments was performed at the velocity filter SHIP (GSI Darmstadt) trying to produce 299120 in a fusion reaction 248Cm(54Cr,3 n )299120 . We report calculations of α -decay half-lives using four models: AKRA (Akrawy), ASAF (analytical superasymmetric fission), UNIV (universal formula), and semFIS (semi-empirical formula based on fission theory). The released energy, Q , is calculated using the theoretical model of atomic masses, WS4. For Sr,9492 cluster radioactivity of 120,302300 we predict a branching ratio relative to α decay of -0.10 and 0.49, respectively, meaning that it is worth trying to detect such kinds of decay modes in competition with α decay.

Generalized non-Local Resistance Expression and its Application in F/N/F Spintronic Structure with Graphene Channel

NASA Astrophysics Data System (ADS)

Wei, Huazhou; Fu, Shiwei

We report our work on the spin transport properties in the F/N/F(ferromagnets/normal metal/ferromagnets) spintronic structure from a new theoretical perspective. A significant problem in the field is to explain the inferior measured order of magnitude for spin lifetime. Based on the known non-local resistance formula and the mechanism analysis of spin-flipping within the interfaces between F and N, we analytically derive a broadly applicable new non-local resistance expression and a generalized Hanle curve formula. After employing them in the F/N/F structure under different limits, especially in the case of graphene channel, we find that the fitting from experimental data would yield a longer spin lifetime, which approaches its theoretical predicted value in graphene. The authors acknowledge the financial support by China University of Petroleum-Beijing and the Key Laboratory of Optical Detection Technology for Oil and Gas in this institution.

A semi-analytical description of protein folding that incorporates detailed geometrical information

PubMed Central

Suzuki, Yoko; Noel, Jeffrey K.; Onuchic, José N.

2011-01-01

Much has been done to study the interplay between geometric and energetic effects on the protein folding energy landscape. Numerical techniques such as molecular dynamics simulations are able to maintain a precise geometrical representation of the protein. Analytical approaches, however, often focus on the energetic aspects of folding, including geometrical information only in an average way. Here, we investigate a semi-analytical expression of folding that explicitly includes geometrical effects. We consider a Hamiltonian corresponding to a Gaussian filament with structure-based interactions. The model captures local features of protein folding often averaged over by mean-field theories, for example, loop contact formation and excluded volume. We explore the thermodynamics and folding mechanisms of beta-hairpin and alpha-helical structures as functions of temperature and Q, the fraction of native contacts formed. Excluded volume is shown to be an important component of a protein Hamiltonian, since it both dominates the cooperativity of the folding transition and alters folding mechanisms. Understanding geometrical effects in analytical formulae will help illuminate the consequences of the approximations required for the study of larger proteins. PMID:21721664

New aspects in single-body meteor physics

NASA Astrophysics Data System (ADS)

Pecina, P.; Ceplecha, Z.

1983-03-01

An exact analytical solution of the atmospheric meteoroid single-body problem is presented expressing the distance along the trajectory as a function of time, which yields a least-square fit of the observed trajectory, and analytical expressions for the velocity at the point of maximum deceleration are derived. These results are used to determine the ablation coefficient from observations. These methods are applied to 17 Prairie Network fireballs observed below the maximum deceleration point and to the Innisfree fireball, and the results are found to be superior to the ones obtained with the usual interpolation formula. A model of luminous efficiencies for small velocities and for masses up to several hundred grams based on data on Innisfree and on artificial rocketry meteors is proposed and applied to separate the shape-density coefficient from the meteoroid mass.

Antiferromagnetic nano-oscillator in external magnetic fields

NASA Astrophysics Data System (ADS)

Checiński, Jakub; Frankowski, Marek; Stobiecki, Tomasz

2017-11-01

We describe the dynamics of an antiferromagnetic nano-oscillator in an external magnetic field of any given time distribution. The oscillator is powered by a spin current originating from spin-orbit effects in a neighboring heavy metal layer and is capable of emitting a THz signal in the presence of an additional easy-plane anisotropy. We derive an analytical formula describing the interaction between such a system and an external field, which can affect the output signal character. Interactions with magnetic pulses of different shapes, with a sinusoidal magnetic field and with a sequence of rapidly changing magnetic fields are discussed. We also perform numerical simulations based on the Landau-Lifshitz-Gilbert equation with spin-transfer torque effects to verify the obtained results and find a very good quantitative agreement between analytical and numerical predictions.

Value of the distant future: Model-independent results

NASA Astrophysics Data System (ADS)

Katz, Yuri A.

2017-01-01

This paper shows that the model-independent account of correlations in an interest rate process or a log-consumption growth process leads to declining long-term tails of discount curves. Under the assumption of an exponentially decaying memory in fluctuations of risk-free real interest rates, I derive the analytical expression for an apt value of the long run discount factor and provide a detailed comparison of the obtained result with the outcome of the benchmark risk-free interest rate models. Utilizing the standard consumption-based model with an isoelastic power utility of the representative economic agent, I derive the non-Markovian generalization of the Ramsey discounting formula. Obtained analytical results allowing simple calibration, may augment the rigorous cost-benefit and regulatory impact analysis of long-term environmental and infrastructure projects.

The neuron net method for processing the clear pixels and method of the analytical formulas for processing the cloudy pixels of POLDER instrument images

NASA Astrophysics Data System (ADS)

Melnikova, I.; Mukai, S.; Vasilyev, A.

Data of remote measurements of reflected radiance with the POLDER instrument on board of ADEOS satellite are used for retrieval of the optical thickness, single scattering albedo and phase function parameter of cloudy and clear atmosphere. The method of perceptron neural network that from input values of multiangle radiance and Solar incident angle allows to obtain surface albedo, the optical thickness, single scattering albedo and phase function parameter in case of clear sky. Two last parameters are determined as optical average for atmospheric column. The calculation of solar radiance with using the MODTRAN-3 code with taking into account multiple scattering is accomplished for neural network learning. All mentioned parameters were randomly varied on the base of statistical models of possible measured parameters variation. Results of processing one frame of remote observation that consists from 150,000 pixels are presented. The methodology elaborated allows operative determining optical characteristics as cloudy as clear atmosphere. Further interpretation of these results gives the possibility to extract the information about total contents of atmospheric aerosols and absorbing gases in the atmosphere and create models of the real cloudiness An analytical method of interpretation that based on asymptotic formulas of multiple scattering theory is applied to remote observations of reflected radiance in case of cloudy pixel. Details of the methodology and error analysis were published and discussed earlier. Here we present results of data processing of pixel size 6x6 km In many studies the optical thickness is evaluated earlier in the assumption of the conservative scattering. But in case of true absorption in clouds the large errors in parameter obtained are possible. The simultaneous retrieval of two parameters at every wavelength independently is the advantage comparing with earlier studies. The analytical methodology is based on the transfer theory asymptotic formula inversion for optically thick stratus clouds. The model of horizontally infinite layer is considered. The slight horizontal heterogeneity is approximately taken into account. Formulas containing only the measured values of two-direction radiance and functions of solar and view angles were derived earlier. The 6 azimuth harmonics of reflection function are taken into account. The simple approximation of the cloud top boarder heterogeneity is used. The clouds, projecting upper the cloud top plane causes the increase of diffuse radiation in the incident flux. It is essential for calculation of radiative characteristics, which depends on lighting conditions. Escape and reflection functions describe this dependence for reflected radiance and local albedo of semi-infinite medium - for irradiance. Thus the functions depending on solar incident angle is to replace by their modifications. Firstly optical thickness of every pixel is obtained with simple formula assuming conservative scattering for all available view directions. Deviations between obtained values may be taken as a measure of the cloud top deviation from the plane. The special parameter is obtained, which takes into account the shadowing effect. Then single scattering albedo and optical thickness (with the true absorption assuming) are obtained for pairs of view directions with equal optical thickness. After that the averaging of values obtained and relative error evaluation is accomplished for all viewing directions of every pixel. The procedure is repeated for all wavelengths and pixels independently.

Alpha decay calculations with a new formula

NASA Astrophysics Data System (ADS)

Akrawy, D. T.; Poenaru, D. N.

2017-10-01

A new semi-empirical formula for calculations of α decay half-lives is presented. It was derived from the Royer relationship by introducing new parameters which are fixed by fit to a set of experimental data. We are using three sets: set A with 130 e-e (even-even), 119 e-o (even-odd), 109 o-e, and 96 o-o, set B with 188 e-e, 147 e-o, 131 o-e and 114 o-o, and set C with 136 e-e, 84 e-o, 76 o-e and 48 o-o alpha emitters. A comparison of results obtained with the new formula (newF) and the following well known relationships: semiempirical relationship based on fission theory (semFIS), analytical superasymmetric fission (ASAF) model and universal formula (UNIV) made in terms of rms standard deviation. We also introduced a weighted mean value of this quantity, allowing us to compare the global properties of a given model. For set B the order of the four models is the following: semFIS, UNIV, newF and ASAF. Nevertheless for even-even alpha emitters, UNIV gives the second best result after semFIS, and for odd-even parents the second is newF. Despite its simplicity in comparison with semFIS, newF, presented in this article, behaves quite well, competing with the other well known relationships.

Irradiance tailoring by fractional Fourier transform of a radial Gaussian beam array

NASA Astrophysics Data System (ADS)

Zhou, Pu; Wang, Xiaolin; Ma, Yanxing; Ma, Haotong; Liu, Zejin

2011-03-01

The fractional Fourier transform (FRFT) is applied to a radial Gaussian beam array. Analytical formula is derived for the irradiance distribution of coherent and incoherent radial Gaussian beam array in FRFT domain using Collins integral formula. It is revealed that the irradiance pattern can be tailored to be controllable dark-hollow, flat-topped and Gaussian beam pattern by changing of the fractional order of FRFT and the coherent state of the laser array.

Irradiance tailoring by fractional Fourier transform of a radial Gaussian beam array

NASA Astrophysics Data System (ADS)

Zhou, Pu; Wang, Xiaolin; Ma, Yanxing; Ma, Haotong; Liu, Zejin

2010-07-01

The fractional Fourier transform (FRFT) is applied to a radial Gaussian beam array. Analytical formula is derived for the irradiance distribution of coherent and incoherent radial Gaussian beam array in FRFT domain using Collins integral formula. It is revealed that the irradiance pattern can be tailored to be controllable dark-hollow, flat-topped and Gaussian beam pattern by changing of the fractional order of FRFT and the coherent state of the laser array.

Modernization of AOAC Nutrient Methods by Stakeholder Panel on Infant Formula and Adult Nutritionals.

PubMed

Sullivan, Darryl

2016-01-01

Infant formula is one of the most highly regulated products in the world. To comply with global regulations and to ensure the products are manufactured within product specifications, accurate analytical testing is required. Most of the AOAC INTERNATIONAL legacy test methods for infant formula were developed and validated in the 1980s and 1990s. Although these methods performed very well for many years, infant formulas have been updated, and today's products contain many new and novel ingredients. There were a number of cases in which the legacy AOAC methods began to result in problems with the analysis of modern infant formulas, and the use of these methods caused some disputes with regulatory agencies. In 2010, AOAC reached an agreement with the International Formula Council, which has changed its name to the Infant Nutrition Council of America, regarding a project to modernize these AOAC infant-formula test methods. This agreement led to the development of Standard Method Performance Requirements (SMPRs(®)) for 28 nutrients. After SMPR approval, methods were collected, evaluated, validated, and approved through the AOAC Official Methods(SM) process. Forty-seven methods have been approved as AOAC First Action Methods, and eight have been approved as Final Action.

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

Hirano, Teruyuki; Winn, Joshua N.; Albrecht, Simon

We present an improved formula for the anomalous radial velocity of the star during planetary transits due to the Rossiter-McLaughlin (RM) effect. The improvement comes from a more realistic description of the stellar absorption line profiles, taking into account stellar rotation, macroturbulence, thermal broadening, pressure broadening, and instrumental broadening. Although the formula is derived for the case in which radial velocities are measured by cross-correlation, we show through numerical simulations that the formula accurately describes the cases where the radial velocities are measured with the iodine absorption-cell technique. The formula relies on prior knowledge of the parameters describing macroturbulence, instrumentalmore » broadening, and other broadening mechanisms, but even 30% errors in those parameters do not significantly change the results in typical circumstances. We show that the new analytic formula agrees with previous ones that had been computed on a case-by-case basis via numerical simulations. Finally, as one application of the new formula, we reassess the impact of the differential rotation on the RM velocity anomaly. We show that differential rotation of a rapidly rotating star may have a significant impact on future RM observations.« less

On a boundary-localized Higgs boson in 5D theories.

PubMed

Barceló, Roberto; Mitra, Subhadip; Moreau, Grégory

In the context of a simple five-dimensional (5D) model with bulk matter coupled to a brane-localized Higgs boson, we point out a non-commutativity in the 4D calculation of the mass spectrum for excited fermion towers: the obtained expression depends on the choice in ordering the limits, [Formula: see text] (infinite Kaluza-Klein tower) and [Formula: see text] ([Formula: see text] being the parameter introduced for regularizing the Higgs Dirac peak). This introduces the question of which one is the correct order; we then show that the two possible orders of regularization (called I and II) are experimentally equivalent, as both can typically reproduce the measured observables, but that the one with less degrees of freedom (I) could be uniquely excluded by future experimental constraints. This conclusion is based on the exact matching between the 4D and 5D analytical calculations of the mass spectrum - via regularizations of type I and II. Beyond a deeper insight into the Higgs peak regularizations, this matching brings another confirmation of the validity of the 5D mixed formalism. All the conclusions, deduced from regularizing the Higgs peak through a brane shift or a smoothed square profile, are expected to remain similar in realistic models with a warped extra-dimension. The complementary result of the study is that the non-commutativity disappears, both in the 4D and the 5D calculations, in the presence of higher order derivative operators. For clarity, the 4D and 5D analytical calculations, matching with each other, are presented in the first part of the paper, while the second part is devoted to the interpretation of the results.

Mixed-order phase transition in a colloidal crystal.

PubMed

Alert, Ricard; Tierno, Pietro; Casademunt, Jaume

2017-12-05

Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and nonequilibrium systems, but their experimental observation has remained elusive. Here, we analytically predict and experimentally realize a mixed-order equilibrium phase transition. Specifically, a discontinuous solid-solid transition in a 2D crystal of paramagnetic colloidal particles is induced by a magnetic field [Formula: see text] At the transition field [Formula: see text], the energy landscape of the system becomes completely flat, which causes diverging fluctuations and correlation length [Formula: see text] Mean-field critical exponents are predicted, since the upper critical dimension of the transition is [Formula: see text] Our colloidal system provides an experimental test bed to probe the unconventional properties of mixed-order phase transitions.

The generalized liquid drop model alpha-decay formula: Predictability analysis and superheavy element alpha half-lives

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

Dasgupta-Schubert, N.; Reyes, M.A.

2007-11-15

The predictive accuracy of the generalized liquid drop model (GLDM) formula for alpha-decay half-lives has been investigated in a detailed manner and a variant of the formula with improved coefficients is proposed. The method employs the experimental alpha half-lives of the well-known alpha standards to obtain the coefficients of the analytical formula using the experimental Q{sub {alpha}} values (the DSR-E formula), as well as the finite range droplet model (FRDM) derived Q{sub {alpha}} values (the FRDM-FRDM formula). The predictive accuracy of these formulae was checked against the experimental alpha half-lives of an independent set of nuclei (TEST) that span approximatelymore » the same Z, A region as the standards and possess reliable alpha spectroscopic data, and were found to yield good results for the DSR-E formula but not for the FRDM-FRDM formula. The two formulae were used to obtain the alpha half-lives of superheavy elements (SHE) and heavy nuclides where the relative accuracy was found to be markedly improved for the FRDM-FRDM formula, which corroborates the appropriateness of the FRDM masses and the GLDM prescription for high Z, A nuclides. Further improvement resulted, especially for the FRDM-FRDM formula, after a simple linear optimization over the calculated and experimental half-lives of TEST was used to re-calculate the half-lives of the SHE and heavy nuclides. The advantage of this optimization was that it required no re-calculation of the coefficients of the basic DSR-E or FRDM-FRDM formulae. The half-lives for 324 medium-mass to superheavy alpha decaying nuclides, calculated using these formulae and the comparison with experimental half-lives, are presented.« less

Two types of phase diagrams for two-species Bose-Einstein condensates and the combined effect of the parameters

NASA Astrophysics Data System (ADS)

Li, Z. B.; Liu, Y. M.; Yao, D. X.; Bao, C. G.

2017-07-01

Under the Thomas-Fermi approximation, an approach is proposed to solve the coupled Gross-Pitaevskii equations (CGP) for the two-species Bose-Einstein condensate analytically. The essence of this approach is to find out the building blocks to build the solution. By introducing the weighted strengths, relatively simpler analytical solutions have been obtained. A number of formulae have been deduced to relate the parameters when the system is experimentally tuned at various status. These formulae demonstrate the combined effect of the parameters, and are useful for the evaluation of their magnitudes. The whole parameter space is divided into zones, where each supports a specific phase. All the boundaries separating these zones have analytical expressions. Based on the division, the phase diagrams against any set of parameters can be plotted. In addition, by introducing a model for the asymmetric states, the total energies of the lowest symmetric and asymmetric states have been compared. Thereby, in which case the former will be replaced by the latter has been evaluated. The CGP can be written in a matrix form. For repulsive inter-species interaction V AB , when the parameters vary and cross over the singular point of the matrix, a specific state transition will happen and the total energy of the lowest symmetric state will increase remarkably. This provides an excellent opportunity for the lowest asymmetric state to emerge as the ground state. For attractive V AB , when the parameters tend to a singular point, the system will tend to collapse. The effects caused by the singular points have been particularly studied.

A structured population model with diffusion in structure space.

PubMed

Pugliese, Andrea; Milner, Fabio

2018-05-09

A structured population model is described and analyzed, in which individual dynamics is stochastic. The model consists of a PDE of advection-diffusion type in the structure variable. The population may represent, for example, the density of infected individuals structured by pathogen density x, [Formula: see text]. The individuals with density [Formula: see text] are not infected, but rather susceptible or recovered. Their dynamics is described by an ODE with a source term that is the exact flux from the diffusion and advection as [Formula: see text]. Infection/reinfection is then modeled moving a fraction of these individuals into the infected class by distributing them in the structure variable through a probability density function. Existence of a global-in-time solution is proven, as well as a classical bifurcation result about equilibrium solutions: a net reproduction number [Formula: see text] is defined that separates the case of only the trivial equilibrium existing when [Formula: see text] from the existence of another-nontrivial-equilibrium when [Formula: see text]. Numerical simulation results are provided to show the stabilization towards the positive equilibrium when [Formula: see text] and towards the trivial one when [Formula: see text], result that is not proven analytically. Simulations are also provided to show the Allee effect that helps boost population sizes at low densities.

Correcting for diffusion in carbon-14 dating of ground water

USGS Publications Warehouse

Sanford, W.E.

1997-01-01

It has generally been recognized that molecular diffusion can be a significant process affecting the transport of carbon-14 in the subsurface when occurring either from a permeable aquifer into a confining layer or from a fracture into a rock matrix. An analytical solution that is valid for steady-state radionuclide transport through fractured rock is shown to be applicable to many multilayered aquifer systems. By plotting the ratio of the rate of diffusion to the rate of decay of carbon-14 over the length scales representative of several common hydrogeologic settings, it is demonstrated that diffusion of carbon-14 should often be not only a significant process, but a dominant one relative to decay. An age-correction formula is developed and applied to the Bangkok Basin of Thailand, where a mean carbon-14-based age of 21,000 years was adjusted to 11,000 years to account for diffusion. This formula and its graphical representation should prove useful for many studies, for they can be used first to estimate the potential role of diffusion and then to make a simple first-order age correction if necessary.It has generally been recognized that molecular diffusion can be a significant process affecting the transport of carbon-14 in the subsurface when occurring either from a permeable aquifer into a confining layer or from a fracture into a rock matrix. An analytical solution that is valid for steady-state radionuclide transport through fractured rock is shown to be applicable to many multilayered aquifer systems. By plotting the ratio of the rate of diffusion to the rate of decay of carbon-14 over the length scales representative of several common hydrogeologic settings, it is demonstrated that diffusion of carbon-14 should often be not only a significant process, but a dominant one relative to decay. An age-correction formula is developed and applied to the Bangkok Basin of Thailand, where a mean carbon-14-based age of 21,000 years was adjusted to 11,000 years to account for diffusion. This formula and its graphical representation should prove useful for many studies, for they can be used first to estimate the potential role of diffusion and then to make a simple first-order age correction if necessary.

Higher-order jump conditions for conservation laws

NASA Astrophysics Data System (ADS)

Oksuzoglu, Hakan

2018-04-01

The hyperbolic conservation laws admit discontinuous solutions where the solution variables can have finite jumps in space and time. The jump conditions for conservation laws are expressed in terms of the speed of the discontinuity and the state variables on both sides. An example from the Gas Dynamics is the Rankine-Hugoniot conditions for the shock speed. Here, we provide an expression for the acceleration of the discontinuity in terms of the state variables and their spatial derivatives on both sides. We derive a jump condition for the shock acceleration. Using this general expression, we show how to obtain explicit shock acceleration formulas for nonlinear hyperbolic conservation laws. We start with the Burgers' equation and check the derived formula with an analytical solution. We next derive formulas for the Shallow Water Equations and the Euler Equations of Gas Dynamics. We will verify our formulas for the Euler Equations using an exact solution for the spherically symmetric blast wave problem. In addition, we discuss the potential use of these formulas for the implementation of shock fitting methods.

An Approximate Solution to the Equation of Motion for Large-Angle Oscillations of the Simple Pendulum with Initial Velocity

ERIC Educational Resources Information Center

Johannessen, Kim

2010-01-01

An analytic approximation of the solution to the differential equation describing the oscillations of a simple pendulum at large angles and with initial velocity is discussed. In the derivation, a sinusoidal approximation has been applied, and an analytic formula for the large-angle period of the simple pendulum is obtained, which also includes…

Magnetically-driven medical robots: An analytical magnetic model for endoscopic capsules design

NASA Astrophysics Data System (ADS)

Li, Jing; Barjuei, Erfan Shojaei; Ciuti, Gastone; Hao, Yang; Zhang, Peisen; Menciassi, Arianna; Huang, Qiang; Dario, Paolo

2018-04-01

Magnetic-based approaches are highly promising to provide innovative solutions for the design of medical devices for diagnostic and therapeutic procedures, such as in the endoluminal districts. Due to the intrinsic magnetic properties (no current needed) and the high strength-to-size ratio compared with electromagnetic solutions, permanent magnets are usually embedded in medical devices. In this paper, a set of analytical formulas have been derived to model the magnetic forces and torques which are exerted by an arbitrary external magnetic field on a permanent magnetic source embedded in a medical robot. In particular, the authors modelled cylindrical permanent magnets as general solution often used and embedded in magnetically-driven medical devices. The analytical model can be applied to axially and diametrically magnetized, solid and annular cylindrical permanent magnets in the absence of the severe calculation complexity. Using a cylindrical permanent magnet as a selected solution, the model has been applied to a robotic endoscopic capsule as a pilot study in the design of magnetically-driven robots.

Simple Analytical Forms of the Perpendicular Diffusion Coefficient for Two-component Turbulence. III. Damping Model of Dynamical Turbulence

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

Gammon, M.; Shalchi, A., E-mail: andreasm4@yahoo.com

2017-10-01

In several astrophysical applications one needs analytical forms of cosmic-ray diffusion parameters. Some examples are studies of diffusive shock acceleration and solar modulation. In the current article we explore perpendicular diffusion based on the unified nonlinear transport theory. While we focused on magnetostatic turbulence in Paper I, we included the effect of dynamical turbulence in Paper II of the series. In the latter paper we assumed that the temporal correlation time does not depend on the wavenumber. More realistic models have been proposed in the past, such as the so-called damping model of dynamical turbulence. In the present paper wemore » derive analytical forms for the perpendicular diffusion coefficient of energetic particles in two-component turbulence for this type of time-dependent turbulence. We present new formulas for the perpendicular diffusion coefficient and we derive a condition for which the magnetostatic result is recovered.« less

Cyclic plasticity models and application in fatigue analysis

NASA Technical Reports Server (NTRS)

Kalev, I.

1981-01-01

An analytical procedure for prediction of the cyclic plasticity effects on both the structural fatigue life to crack initiation and the rate of crack growth is presented. The crack initiation criterion is based on the Coffin-Manson formulae extended for multiaxial stress state and for inclusion of the mean stress effect. This criterion is also applied for the accumulated damage ahead of the existing crack tip which is assumed to be related to the crack growth rate. Three cyclic plasticity models, based on the concept of combination of several yield surfaces, are employed for computing the crack growth rate of a crack plane stress panel under several cyclic loading conditions.

Monogamy relation of multi-qubit systems for squared Tsallis-q entanglement

NASA Astrophysics Data System (ADS)

Yuan, Guang-Ming; Song, Wei; Yang, Ming; Li, Da-Chuang; Zhao, Jun-Long; Cao, Zhuo-Liang

2016-06-01

Tsallis-q entanglement is a bipartite entanglement measure which is the generalization of entanglement of formation for q tending to 1. We first expand the range of q for the analytic formula of Tsallis-q entanglement. For , we prove the monogamy relation in terms of the squared Tsallis-q entanglement for an arbitrary multi-qubit systems. It is shown that the multipartite entanglement indicator based on squared Tsallis-q entanglement still works well even when the indicator based on the squared concurrence loses its efficacy. We also show that the μ-th power of Tsallis-q entanglement satisfies the monogamy or polygamy inequalities for any three-qubit state.

Monogamy relation of multi-qubit systems for squared Tsallis-q entanglement.

PubMed

Yuan, Guang-Ming; Song, Wei; Yang, Ming; Li, Da-Chuang; Zhao, Jun-Long; Cao, Zhuo-Liang

2016-06-27

Tsallis-q entanglement is a bipartite entanglement measure which is the generalization of entanglement of formation for q tending to 1. We first expand the range of q for the analytic formula of Tsallis-q entanglement. For , we prove the monogamy relation in terms of the squared Tsallis-q entanglement for an arbitrary multi-qubit systems. It is shown that the multipartite entanglement indicator based on squared Tsallis-q entanglement still works well even when the indicator based on the squared concurrence loses its efficacy. We also show that the μ-th power of Tsallis-q entanglement satisfies the monogamy or polygamy inequalities for any three-qubit state.

Nonparaxial and paraxial focusing of azimuthal-variant vector beams.

PubMed

Gu, Bing; Cui, Yiping

2012-07-30

Based on the vectorial Rayleigh-Sommerfeld formulas under the weak nonparaxial approximation, we investigate the propagation behavior of a lowest-order Laguerre-Gaussian beam with azimuthal-variant states of polarization. We present the analytical expressions for the radial, azimuthal, and longitudinal components of the electric field with an arbitrary integer topological charge m focused by a nonaperturing thin lens. We illustrate the three-dimensional optical intensities, energy flux distributions, beam waists, and focal shifts of the focused azimuthal-variant vector beams under the nonparaxial and paraxial approximations.

Properties of two-mode squeezed number states

NASA Technical Reports Server (NTRS)

Chizhov, Alexei V.; Murzakhmetov, B. K.

1994-01-01

Photon statistics and phase properties of two-mode squeezed number states are studied. It is shown that photon number distribution and Pegg-Barnett phase distribution for such states have similar (N + 1)-peak structure for nonzero value of the difference in the number of photons between modes. Exact analytical formulas for phase distributions based on different phase approaches are derived. The Pegg-Barnett phase distribution and the phase quasiprobability distribution associated with the Wigner function are close to each other, while the phase quasiprobability distribution associated with the Q function carries less phase information.

On spatial mutation-selection models

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

Kondratiev, Yuri, E-mail: kondrat@math.uni-bielefeld.de; Kutoviy, Oleksandr, E-mail: kutoviy@math.uni-bielefeld.de, E-mail: kutovyi@mit.edu; Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

2013-11-15

We discuss the selection procedure in the framework of mutation models. We study the regulation for stochastically developing systems based on a transformation of the initial Markov process which includes a cost functional. The transformation of initial Markov process by cost functional has an analytic realization in terms of a Kimura-Maruyama type equation for the time evolution of states or in terms of the corresponding Feynman-Kac formula on the path space. The state evolution of the system including the limiting behavior is studied for two types of mutation-selection models.

Computer modeling of lung cancer diagnosis-to-treatment process

PubMed Central

Ju, Feng; Lee, Hyo Kyung; Osarogiagbon, Raymond U.; Yu, Xinhua; Faris, Nick

2015-01-01

We introduce an example of a rigorous, quantitative method for quality improvement in lung cancer care-delivery. Computer process modeling methods are introduced for lung cancer diagnosis, staging and treatment selection process. Two types of process modeling techniques, discrete event simulation (DES) and analytical models, are briefly reviewed. Recent developments in DES are outlined and the necessary data and procedures to develop a DES model for lung cancer diagnosis, leading up to surgical treatment process are summarized. The analytical models include both Markov chain model and closed formulas. The Markov chain models with its application in healthcare are introduced and the approach to derive a lung cancer diagnosis process model is presented. Similarly, the procedure to derive closed formulas evaluating the diagnosis process performance is outlined. Finally, the pros and cons of these methods are discussed. PMID:26380181

Effect(s) of Language Tasks on Severity of Disfluencies in Preschool Children with Stuttering.

PubMed

Zamani, Peyman; Ravanbakhsh, Majid; Weisi, Farzad; Rashedi, Vahid; Naderi, Sara; Hosseinzadeh, Ayub; Rezaei, Mohammad

2017-04-01

Speech disfluency in children can be increased or decreased depending on the type of linguistic task presented to them. In this study, the effect of sentence imitation and sentence modeling on severity of speech disfluencies in preschool children with stuttering is investigated. In this cross-sectional descriptive analytical study, 58 children with stuttering (29 with mild stuttering and 29 with moderate stuttering) and 58 typical children aged between 4 and 6 years old participated. The severity of speech disfluencies was assessed by SSI-3 and TOCS before and after offering each task. In boys with mild stuttering, The mean stuttering severity scores in two tasks of sentence imitation and sentence modeling were [Formula: see text] and [Formula: see text] respectively ([Formula: see text]). But, in boys with moderate stuttering the stuttering severity in the both tasks were [Formula: see text] and [Formula: see text] respectively ([Formula: see text]). In girls with mild stuttering, the stuttering severity in two tasks of sentence imitation and sentence modeling were [Formula: see text] and [Formula: see text] respectively ([Formula: see text]). But, in girls with moderate stuttering the mean stuttering severity in the both tasks were [Formula: see text] and [Formula: see text] respectively ([Formula: see text]). In both gender of typical children, the score of speech disfluencies had no significant difference between two tasks ([Formula: see text]). In preschool children with mild stuttering and peer non-stutters, performing the tasks of sentence imitation and sentence modeling could not increase the severity of stuttering. But, in preschool children with moderate stuttering, doing the task of sentence modeling increased the stuttering severity score.

Propagation of various dark hollow beams through an apertured paraxial ABCD optical system

NASA Astrophysics Data System (ADS)

Cai, Yangjian; Ge, Di

2006-08-01

Propagation of a dark hollow beam (DHB) of circular, elliptical or rectangular symmetry through an apertured paraxial ABCD optical system is investigated. Approximate analytical formulas for various DHBs propagating through an apertured paraxial optical system are derived by expanding the hard-aperture function into a finite sum of complex Gaussian functions in terms of a tensor method. Some numerical results are given. Our formulas provide a convenient way for studying the propagation of various DHBs through an apertured paraxial optical system.

On the dependence of charge density on surface curvature of an isolated conductor

NASA Astrophysics Data System (ADS)

Bhattacharya, Kolahal

2016-03-01

A study of the relation between the electrostatic charge density at a point on a conducting surface and the curvature of the surface (at that point) is presented. Two major papers in the scientific literature on this topic are reviewed and the apparent discrepancy between them is resolved. Hence, a step is taken towards obtaining a general analytic formula for relating the charge density with surface curvature of conductors. The merit of this formula and its limitations are discussed.

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

DOE PAGES

Izacard, Olivier

2016-08-02

In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basismore » sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula, and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. In conclusion, the latter demystifies the Maxwell's demon by statistically describing non-isolated systems.« less

Temporal Evolution of the Gamma-ray Burst Afterglow Spectrum for an Observer: GeV-TeV Synchrotron Self-Compton Light Curve

NASA Astrophysics Data System (ADS)

Fukushima, Takuma; To, Sho; Asano, Katsuaki; Fujita, Yutaka

2017-08-01

We numerically simulate the gamma-ray burst (GRB) afterglow emission with a one-zone time-dependent code. The temporal evolutions of the decelerating shocked shell and energy distributions of electrons and photons are consistently calculated. The photon spectrum and light curves for an observer are obtained taking into account the relativistic propagation of the shocked shell and the curvature of the emission surface. We find that the onset time of the afterglow is significantly earlier than the previous analytical estimate. The analytical formulae of the shock propagation and light curve for the radiative case are also different from our results. Our results show that even if the emission mechanism is switching from synchrotron to synchrotron self-Compton, the gamma-ray light curves can be a smooth power law, which agrees with the observed light curve and the late detection of a 32 GeV photon in GRB 130427A. The uncertainty of the model parameters obtained with the analytical formula is discussed, especially in connection with the closure relation between spectral index and decay index.

Non-Gaussian limit fluctuations in active swimmer suspensions

NASA Astrophysics Data System (ADS)

Kurihara, Takashi; Aridome, Msato; Ayade, Heev; Zaid, Irwin; Mizuno, Daisuke

2017-03-01

We investigate the hydrodynamic fluctuations in suspensions of swimming microorganisms (Chlamydomonas) by observing the probe particles dispersed in the media. Short-term fluctuations of probe particles were superdiffusive and displayed heavily tailed non-Gaussian distributions. The analytical theory that explains the observed distribution was derived by summing the power-law-decaying hydrodynamic interactions from spatially distributed field sources (here, swimming microorganisms). The summing procedure, which we refer to as the physical limit operation, is applicable to a variety of physical fluctuations to which the classical central limiting theory does not apply. Extending the analytical formula to compare to experiments in active swimmer suspensions, we show that the non-Gaussian shape of the observed distribution obeys the analytic theory concomitantly with independently determined parameters such as the strength of force generations and the concentration of Chlamydomonas. Time evolution of the distributions collapsed to a single master curve, except for their extreme tails, for which our theory presents a qualitative explanation. Investigations thereof and the complete agreement with theoretical predictions revealed broad applicability of the formula to dispersions of active sources of fluctuations.

The singular values of the imbedding operators of some classes of analytic functions of several variables

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

Parfenov, O.G.

1994-12-25

We discuss three results. The first exhibits the order of decrease of the s-values as a function of the CR-dimension of a compact set on which we approximate the class of analytic functions being studied. The second is an asymptotic formula for the case when the domain of analyticity and the compact set are Reinhart domains. The third is the computation of the s-values of a special operator that is of interest for approximation theory on one-dimensional manifolds.

Theory comparison and numerical benchmarking on neoclassical toroidal viscosity torque

NASA Astrophysics Data System (ADS)

Wang, Zhirui; Park, Jong-Kyu; Liu, Yueqiang; Logan, Nikolas; Kim, Kimin; Menard, Jonathan E.

2014-04-01

Systematic comparison and numerical benchmarking have been successfully carried out among three different approaches of neoclassical toroidal viscosity (NTV) theory and the corresponding codes: IPEC-PENT is developed based on the combined NTV theory but without geometric simplifications [Park et al., Phys. Rev. Lett. 102, 065002 (2009)]; MARS-Q includes smoothly connected NTV formula [Shaing et al., Nucl. Fusion 50, 025022 (2010)] based on Shaing's analytic formulation in various collisionality regimes; MARS-K, originally computing the drift kinetic energy, is upgraded to compute the NTV torque based on the equivalence between drift kinetic energy and NTV torque [J.-K. Park, Phys. Plasma 18, 110702 (2011)]. The derivation and numerical results both indicate that the imaginary part of drift kinetic energy computed by MARS-K is equivalent to the NTV torque in IPEC-PENT. In the benchmark of precession resonance between MARS-Q and MARS-K/IPEC-PENT, the agreement and correlation between the connected NTV formula and the combined NTV theory in different collisionality regimes are shown for the first time. Additionally, both IPEC-PENT and MARS-K indicate the importance of the bounce harmonic resonance which can greatly enhance the NTV torque when E ×B drift frequency reaches the bounce resonance condition.

Theoretical prediction of pullout strengths for dental and orthopaedic screws with conical profile and buttress threads.

PubMed

Shih, Kao-Shang; Hou, Sheng-Mou; Lin, Shang-Chih

2017-12-01

The pullout strength of a screw is an indicator of how secure bone fragments are being held in place. Such bone-purchasing ability is sensitive to bone quality, thread design, and the pilot hole, and is often evaluated by experimental and numerical methods. Historically, there are some mathematical formulae to simulate the screw withdrawal from the synthetic bone. There are great variations in screw specifications. However, extensive investigation of the correlation between experimental and analytical results has not been reported in literature. Referring to the literature formulae, this study aims to evaluate the differences in the calculated pullout strengths. The pullout tests of the surgical screws are measured and the sawbone is used as the testing block. The absolute errors and correlation coefficients of the experimental and analytical results are calculated as the comparison baselines of the formulae. The absolute error of the dental, traumatic, and spinal groups are 21.7%, 95.5%, and 37.0%, respectively. For the screws with a conical profile and/or tiny threads, the calculated and measured results are not well correlated. The formulae are not accurate indicators of the pullout strengths of the screws where the design parameters are slightly varied. However, the experimental and numerical results are highly correlated for the cylindrical screws. The pullout strength of a conical screw is higher than that of its counterpart, but all formulae consistently predict the opposite results. In general, the bony purchase of the buttress threads is securer than that of the symmetric thread. An absolute error of up to 51.4% indicates the theoretical results cannot predict the actual value of the pullout strength. Only thread diameter, pitch, and depth are considered in the investigated formulae. The thread profile and shape should be formulated to modify the slippage mechanism at the bone-screw interfaces and simulate the strength change in the squeezed bones, especially for the conical screw. Copyright © 2017. Published by Elsevier B.V.

SU-E-J-65: Evaluation of a Radiation-Induced Cell Proliferation Probability Formula Using Monte Carlo Simulation

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

Watanabe, Y; Dahlman, E

2014-06-01

Purpose: To evaluate the analytic formula of the cell death probability after single fraction dose. Methods: Cancer cells endlessly divide, but radiation causes the cancer cells to die. Not all cells die right away after irradiation. Instead, they continue dividing for next few cell cycles before they stop dividing and die. At the end of every cell cycle, the cell decides if it undertakes the mitotic process with a certain probability, Pdiv, which is altered by the radiation. Previously, by using a simple analytic model of radiobiology experiments, we obtained a formula of Pdeath (= 1 − Pdiv). A questionmore » is if the proposed probability can reproduce the well-known survival data of the LQ model. In this study, we evaluated the formula by doing a Monte Carlo simulation of the cell proliferation process. Starting with Ns seed cells, the cell proliferation process was simulated for N generations or until all cells die. We counted the number of living cells at the end. Assuming that the cell colony survived when more than Nc cells were still alive, the surviving fraction S was estimated. We compared the S vs. dose, or S-D curve, with the LQ model. Results: The results indicated that our formula does not reproduce the experimentally observed S-D curve without selecting appropriate α and α/β. With parameter optimization, there was a fair agreement between the MC result and the LQ curve of dose lower than 20Gy. However, the survival fraction of MC decreased much faster in comparison to the LQ data for doses higher than 20 Gy. Conclusion: This study showed that the previously derived probability of cell death per cell cycle is not sufficiently accurate to replicate common radiobiological experiments. The formula must be modified by considering its cell cycle dependence and some other unknown effects.« less

Method for the quantification of current use and persistent pesticides in cow milk, human milk and baby formula using gas chromatography tandem mass spectrometry.

PubMed

Chen, Xianyu; Panuwet, Parinya; Hunter, Ronald E; Riederer, Anne M; Bernoudy, Geneva C; Barr, Dana Boyd; Ryan, P Barry

2014-11-01

The aim of this study was to develop an analytical method for the quantification of organochlorine (OC), organophosphate (OP), carbamate, and pyrethroid insecticide residues in cow milk, human milk, and baby formula. A total of 25 compounds were included in this method. Sample extraction procedures combined liquid-liquid extraction, freezing-lipid filtration, dispersive primary-secondary amine cleanup, and solid-phase extraction together for effective extraction and elimination of matrix interferences. Target compounds were analyzed using gas chromatography with electron impact ionization-tandem mass spectrometry (GC-EI-MS/MS) in the multiple reaction monitoring (MRM) mode. Average extraction recoveries obtained from cow milk samples fortified at two different concentrations (10 ng/mL and 25 ng/mL), ranged from 34% to 102%, with recoveries for the majority of target compounds falling between 60% and 80%. Similar ranges were found for formula fortified at 25 ng/mL. The estimated limits of detection for most target analytes were in the low pg/mL level (range 3-1600 pg/mL). The accuracies and precisions were within the range of 80-120% and less than 15%, respectively. This method was tested for its viability by analyzing 10 human milk samples collected from anonymous donors, 10 cow milk samples and 10 baby formula samples purchased from local grocery stores in the United States. Hexachlorobenzene, p,p-dicofol, o,p-DDE, p,p-DDE, and chlorpyrifos were found in all samples analyzed. We found detectable levels of permethrin, cyfluthrin, and fenvalerate in some of the cow milk samples but not in human milk or baby formula samples. Some of the pesticides, such as azinphos-methyl, heptachlor epoxide, and the pesticide synergist piperonyl butoxide, were detected in some of the cow milk and human milk samples but not in baby formula samples. Copyright © 2014. Published by Elsevier B.V.

Comparative analysis of electric field influence on the quantum wells with different boundary conditions.: I. Energy spectrum, quantum information entropy and polarization.

PubMed

Olendski, Oleg

2015-04-01

Analytical solutions of the Schrödinger equation for the one-dimensional quantum well with all possible permutations of the Dirichlet and Neumann boundary conditions (BCs) in perpendicular to the interfaces uniform electric field [Formula: see text] are used for the comparative investigation of their interaction and its influence on the properties of the system. Limiting cases of the weak and strong voltages allow an easy mathematical treatment and its clear physical explanation; in particular, for the small [Formula: see text], the perturbation theory derives for all geometries a linear dependence of the polarization on the field with the BC-dependent proportionality coefficient being positive (negative) for the ground (excited) states. Simple two-level approximation elementary explains the negative polarizations as a result of the field-induced destructive interference of the unperturbed modes and shows that in this case the admixture of only the neighboring states plays a dominant role. Different magnitudes of the polarization for different BCs in this regime are explained physically and confirmed numerically. Hellmann-Feynman theorem reveals a fundamental relation between the polarization and the speed of the energy change with the field. It is proved that zero-voltage position entropies [Formula: see text] are BC independent and for all states but the ground Neumann level (which has [Formula: see text]) are equal to [Formula: see text] while the momentum entropies [Formula: see text] depend on the edge requirements and the level. Varying electric field changes position and momentum entropies in the opposite directions such that the entropic uncertainty relation is satisfied. Other physical quantities such as the BC-dependent zero-energy and zero-polarization fields are also studied both numerically and analytically. Applications to different branches of physics, such as ocean fluid dynamics and atmospheric and metallic waveguide electrodynamics, are discussed.

Exact analytical formulae for linearly distributed vortex and source sheets in uence computation in 2D vortex methods

NASA Astrophysics Data System (ADS)

Kuzmina, K. S.; Marchevsky, I. K.; Ryatina, E. P.

2017-11-01

We consider the methodology of numerical schemes development for two-dimensional vortex method. We describe two different approaches to deriving integral equation for unknown vortex sheet intensity. We simulate the velocity of the surface line of an airfoil as the influence of attached vortex and source sheets. We consider a polygonal approximation of the airfoil and assume intensity distributions of free and attached vortex sheets and attached source sheet to be approximated with piecewise constant or piecewise linear (continuous or discontinuous) functions. We describe several specific numerical schemes that provide different accuracy and have a different computational cost. The study shows that a Galerkin-type approach to solving boundary integral equation requires computing several integrals and double integrals over the panels. We obtain exact analytical formulae for all the necessary integrals, which makes it possible to raise significantly the accuracy of vortex sheet intensity computation and improve the quality of velocity and vorticity field representation, especially in proximity to the surface line of the airfoil. All the formulae are written down in the invariant form and depend only on the geometric relationship between the positions of the beginnings and ends of the panels.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

NASA Astrophysics Data System (ADS)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations

NASA Astrophysics Data System (ADS)

Doha, E. H.

2002-02-01

An analytical formula expressing the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is stated in a more compact form and proved in a simpler way than the formula suggested by Phillips and Karageorghis (27 (1990) 823). A new formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is given. The tensor product of ultraspherical polynomials is used to approximate a function of more than one variable. Formulae expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are described.

Re-understanding the law-of-the-wall for wall-bounded turbulence based on in-depth investigation of DNS data

NASA Astrophysics Data System (ADS)

Cao, Bochao; Xu, Hongyi

2018-05-01

Based on direct numerical simulation (DNS) data of the straight ducts, namely square and rectangular annular ducts, detailed analyses were conducted for the mean streamwise velocity, relevant velocity scales, and turbulence statistics. It is concluded that turbulent boundary layers (TBL) should be broadly classified into three types (Type-A, -B, and -C) in terms of their distribution patterns of the time-averaged local wall-shear stress (τ _w ) or the mean local frictional velocity (u_τ ) . With reference to the Type-A TBL analysis by von Karman in developing the law-of-the-wall using the time-averaged local frictional velocity (u_τ ) as scale, the current study extended the approach to the Type-B TBL and obtained the analytical expressions for streamwise velocity in the inner-layer using ensemble-averaged frictional velocity (\\bar{{u}}_τ ) as scale. These analytical formulae were formed by introducing the general damping and enhancing functions. Further, the research applied a near-wall DNS-guided integration to the governing equations of Type-B TBL and quantitatively proved the correctness and accuracy of the inner-layer analytical expressions for this type.

Analytical scheme calculations of angular momentum coupling and recoupling coefficients

NASA Astrophysics Data System (ADS)

Deveikis, A.; Kuznecovas, A.

2007-03-01

We investigate the Scheme programming language opportunities to analytically calculate the Clebsch-Gordan coefficients, Wigner 6j and 9j symbols, and general recoupling coefficients that are used in the quantum theory of angular momentum. The considered coefficients are calculated by a direct evaluation of the sum formulas. The calculation results for large values of quantum angular momenta were compared with analogous calculations with FORTRAN and Java programming languages.

Optimized formulas for the gravitational field of a tesseroid

NASA Astrophysics Data System (ADS)

Grombein, Thomas; Seitz, Kurt; Heck, Bernhard

2013-07-01

Various tasks in geodesy, geophysics, and related geosciences require precise information on the impact of mass distributions on gravity field-related quantities, such as the gravitational potential and its partial derivatives. Using forward modeling based on Newton's integral, mass distributions are generally decomposed into regular elementary bodies. In classical approaches, prisms or point mass approximations are mostly utilized. Considering the effect of the sphericity of the Earth, alternative mass modeling methods based on tesseroid bodies (spherical prisms) should be taken into account, particularly in regional and global applications. Expressions for the gravitational field of a point mass are relatively simple when formulated in Cartesian coordinates. In the case of integrating over a tesseroid volume bounded by geocentric spherical coordinates, it will be shown that it is also beneficial to represent the integral kernel in terms of Cartesian coordinates. This considerably simplifies the determination of the tesseroid's potential derivatives in comparison with previously published methodologies that make use of integral kernels expressed in spherical coordinates. Based on this idea, optimized formulas for the gravitational potential of a homogeneous tesseroid and its derivatives up to second-order are elaborated in this paper. These new formulas do not suffer from the polar singularity of the spherical coordinate system and can, therefore, be evaluated for any position on the globe. Since integrals over tesseroid volumes cannot be solved analytically, the numerical evaluation is achieved by means of expanding the integral kernel in a Taylor series with fourth-order error in the spatial coordinates of the integration point. As the structure of the Cartesian integral kernel is substantially simplified, Taylor coefficients can be represented in a compact and computationally attractive form. Thus, the use of the optimized tesseroid formulas particularly benefits from a significant decrease in computation time by about 45 % compared to previously used algorithms. In order to show the computational efficiency and to validate the mathematical derivations, the new tesseroid formulas are applied to two realistic numerical experiments and are compared to previously published tesseroid methods and the conventional prism approach.

Custom-oriented wavefront sensor for human eye properties measurements

NASA Astrophysics Data System (ADS)

Galetskiy, Sergey; Letfullin, Renat; Dubinin, Alex; Cherezova, Tatyana; Belyakov, Alexey; Kudryashov, Alexis

2005-12-01

The problem of correct measurement of human eye aberrations is very important with the rising widespread of a surgical procedure for reducing refractive error in the eye, so called, LASIK (laser-assisted in situ keratomileusis). In this paper we show capabilities to measure aberrations by means of the aberrometer built in our lab together with Active Optics Ltd. We discuss the calibration of the aberrometer and show invalidity to use for the ophthalmic calibration purposes the analytical equation based on thin lens formula. We show that proper analytical equation suitable for calibration should have dependence on the square of the distance increment and we illustrate this both by experiment and by Zemax Ray tracing modeling. Also the error caused by inhomogeneous intensity distribution of the beam imaged onto the aberrometer's Shack-Hartmann sensor is discussed.

Optical characterization of nonimaging dish concentrator for the application of dense-array concentrator photovoltaic system.

PubMed

Tan, Ming-Hui; Chong, Kok-Keong; Wong, Chee-Woon

2014-01-20

Optimization of the design of a nonimaging dish concentrator (NIDC) for a dense-array concentrator photovoltaic system is presented. A new algorithm has been developed to determine configuration of facet mirrors in a NIDC. Analytical formulas were derived to analyze the optical performance of a NIDC and then compared with a simulated result obtained from a numerical method. Comprehensive analysis of optical performance via analytical method has been carried out based on facet dimension and focal distance of the concentrator with a total reflective area of 120 m2. The result shows that a facet dimension of 49.8 cm, focal distance of 8 m, and solar concentration ratio of 411.8 suns is the most optimized design for the lowest cost-per-output power, which is US$1.93 per watt.

A new frequency domain analytical solution of a cascade of diffusive channels for flood routing

NASA Astrophysics Data System (ADS)

Cimorelli, Luigi; Cozzolino, Luca; Della Morte, Renata; Pianese, Domenico; Singh, Vijay P.

2015-04-01

Simplified flood propagation models are often employed in practical applications for hydraulic and hydrologic analyses. In this paper, we present a new numerical method for the solution of the Linear Parabolic Approximation (LPA) of the De Saint Venant equations (DSVEs), accounting for the space variation of model parameters and the imposition of appropriate downstream boundary conditions. The new model is based on the analytical solution of a cascade of linear diffusive channels in the Laplace Transform domain. The time domain solutions are obtained using a Fourier series approximation of the Laplace Inversion formula. The new Inverse Laplace Transform Diffusive Flood Routing model (ILTDFR) can be used as a building block for the construction of real-time flood forecasting models or in optimization models, because it is unconditionally stable and allows fast and fairly precise computation.

Water flow in fractured rock masses: numerical modeling for tunnel inflow assessment

NASA Astrophysics Data System (ADS)

Gattinoni, P.; Scesi, L.; Terrana, S.

2009-04-01

Water circulation in rocks represents a very important element to solve many problems linked with civil, environmental and mining engineering. In particular, the interaction of tunnelling with groundwater has become a very relevant problem not only due to the need to safeguard water resources from impoverishment and from the pollution risk, but also to guarantee the safety of workers and to assure the efficiency of the tunnel drainage systems. The evaluation of the hydrogeological risk linked to the underground excavation is very complex, either for the large number of variables involved or for the lack of data available during the planning stage. The study is aimed to quantify the influence of some geo-structural parameters (i.e. discontinuities dip and dip direction) on the tunnel drainage process, comparing the traditional analytical method to the modeling approach, with specific reference to the case of anisotropic rock masses. To forecast the tunnel inflows, a few Authors suggest analytic formulations (Goodman et al., 1965; Knutsson et al., 1996; Ribacchi et al., 2002; Park et al., 2008; Perrochet et al., 2007; Cesano et al., 2003; Hwang et al., 2007), valid for infinite, homogeneous and isotropic aquifer, in which the permeability value is given as a modulus of equivalent hydraulic conductivity Keq. On the contrary, in discontinuous rock masses the water flow is strongly controlled by joints orientation, by their hydraulic characteristics and by rocks fracturing conditions. The analytic equations found in the technical literature could be very useful, but often they don't reflect the real phenomena of the tunnel inflow in rock masses. Actually, these equations are based on the hypothesis of homogeneous aquifer, and then they don't give good agreement for an heterogeneous fractured medium. In this latter case, the numerical modelling could provide the best results, but only with a detailed conceptual model of the water circulation, high costs and long simulation times. Therefore, the integration of analytic method and numerical modeling is very important to adapt the analytic formula to the specific hydrogeological structure. The study was carried out through a parametrical modeling, so that groundwater flow was simulated with the DEM Model UDEC 2D, considering different geometrical (tunnel depth and radius) and hydrogeological settings (piezometrical). The influence of geo-structural setting (as dip and dip direction of discontinuities, with reference to their permeability) on tunnel drainage process was quantified. The simulations are aimed to create a sufficient data set of tunnel inflows, in different geological-structural setting, enabling a quantitative comparison between numerical and the well-known analytic formulas (i.e. Goodman and El Tani equations). Results of this comparison point out the following aspects: - the geological-structural setting critical for hydrogeological risk in tunnel corresponds to joints having low dip (close to 0°) that favour the drainage processes and the increasing of the tunnel inflow; - the rock mass anisotropy strongly influences both the tunnel inflow and the water table drawdown; - the reliability of analytic formulas for the tunnel inflow assessment in discontinuous rock masses depends on the geostractural setting; actually the analytic formulas overestimate the tunnel inflow and this overestimation is bigger for geostructural setting having discontinuities with higher dips. Finally, using the results of parametrical modeling, the previous cited analytic formulas were corrected to point out an empirical equation that gives the tunnel inflow as a function of the different geological-structural setting, with particular regard to: - the horizontal component of discontinuities, - the hydraulic conductivity anisotropy ratio, - the orientation of the hydraulic conductivity tensor. The obtained empirical equation allows a first evaluation of the tunnel inflow, in which joint characteristics are taken into account, very useful to identify the areas where in-depth studies are required. References Cesano D., Bagtzoglou A.C., Olofsson B. (2003). Quantifying fractured rock hydraulic heterogeneity and groundwater inflow prediction in underground excavations: the heterogeneity index. Tunneling and Underground Space Technology, 18, pp. 19-34. El Tani M. (2003). Circular tunnel in a semi-infinite aquifer. Tunnelling and Groundwater Space Technology, 18, pp. 49-55. Goodman R.E., Moye D.G., Van Schalkwyk A., Javandel I. (1965). Ground water inflow during tunnel driving. Eng. Geol., 2, pp. 39-56. Hwang J-H., Lu C-C. (2007). A semi-analytical method for analyzing the tunnel water inflow. Tunneling and Underground Space Technology, 22, pp. 39-46. Itasca (2001). UDEC, User's guide. Itasca Consultino Group Inc., Minneapolis, Minnesota. Knutsson G., Olofsson B., Cesano D. (1996). Prognosis of groundwater inflows and drawdown due to the construction of rock tunnels in heterogeneous media. Res. Proj. Rep. Kungl Tekniska, Stokholm. Park K-H., Owatsiriwong A., Lee G-G. (2008). Analytical solution for steady-state groundwater inflow into a drained circular tunnel in a semi-infinite aquifer: a revisit. Tunnelling and Underground Space Technology, 23, pp. 206-209. Perrochet P., Dematteis A. (2007). Modelling Transient Discharge into a Tunnel Drilled in Heterogeneous Formation. Ground Water, 45(6), pp. 786-790.

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses.

PubMed

Chen, Yong; Yan, Zhenya; Mihalache, Dumitru; Malomed, Boris A

2017-04-28

Since the parity-time-([Formula: see text]-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with [Formula: see text]-symmetric potentials have been investigated. However, previous studies of [Formula: see text]-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized [Formula: see text]-symmetric Scarf-II potentials. The broken linear [Formula: see text] symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than [Formula: see text]-symmetric ones, but feature similar properties. Our results may suggest new experiments for [Formula: see text]-symmetric nonlinear waves in nonlinear nonuniform optical media.

Analytical characterization and structure elucidation of metabolites from Aspergillus ochraceus MP2 fungi.

PubMed

Meenupriya, J; Thangaraj, M

2011-10-01

To isolate and characterize the bioactive secondary metabolites from Aspergillus ochraceus (A. ochraceus) MP2 fungi. The anti bacterial activity of marine sponge derived fungi A. ochraceus MP2 was thoroughly investigated against antagonistic human pathogens. The optimum inhibitory concentration of the fungi in the elite solvent was also determined. The promising extracts that showed good antimicrobial activity were subjected to further analytical separation to get individual distinct metabolites and the eluants were further identified by GC MS instrumental analysis. The molecular characterization of the elite fungal strains were done by isolating their genomic DNA and amplify the internal transcribed spacer (ITS) region of 5.8s rRNA using specific ITS primer. The novelty of the strain was proved by homology search tools and elite sequences was submitted to GENBANK. Three bioactive compounds were characterized to reveal their identity, chemical formula and structure. The first elutant was identified asα- Campholene aldehyde with chemical formula C10 H16 O and molecular weight 152 Da. The second elutant was identified as Lucenin-2 and chemical formula C27 H30 O16 and molecular weight 610 Da. The third elutant was identified as 6-Ethyloct- 3-yl- 2- ethylhexyl ester with Chemical formula C26 H42 O4 with molecular weight 418 Da. The isolated compounds showed significant antimicrobial activity against potential human pathogens. Microbial secondary metabolites represent a large source of compounds endowed with ingenious structures and potent biological activities.

Digital mammographic tumor classification using transfer learning from deep convolutional neural networks.

PubMed

Huynh, Benjamin Q; Li, Hui; Giger, Maryellen L

2016-07-01

Convolutional neural networks (CNNs) show potential for computer-aided diagnosis (CADx) by learning features directly from the image data instead of using analytically extracted features. However, CNNs are difficult to train from scratch for medical images due to small sample sizes and variations in tumor presentations. Instead, transfer learning can be used to extract tumor information from medical images via CNNs originally pretrained for nonmedical tasks, alleviating the need for large datasets. Our database includes 219 breast lesions (607 full-field digital mammographic images). We compared support vector machine classifiers based on the CNN-extracted image features and our prior computer-extracted tumor features in the task of distinguishing between benign and malignant breast lesions. Five-fold cross validation (by lesion) was conducted with the area under the receiver operating characteristic (ROC) curve as the performance metric. Results show that classifiers based on CNN-extracted features (with transfer learning) perform comparably to those using analytically extracted features [area under the ROC curve [Formula: see text

Determination of Five Chemical Markers in DF Formula, the Herbal Composition of Ephedra intermedia, Rheum palmatum, and Lithospermum erythrorhizon, Using High-performance Liquid Chromatography-ultraviolet Detection.

PubMed

Jeong, Birang; Roh, Jong Seong; Yoon, Michung; Yoon, Yoosik; Shin, Soon Shik; Cho, Hyun Joo; Kwon, Yong Soo; Yang, Heejung

2018-01-01

DF formula is a herbal preparation comprised three medicinal herbs, namely, Ephedra intermedia , Rheum palmatum , and Lithospermum erythrorhizon , which is being used for the treatment of obesity and liver fibrosis in Korean local clinics. Since the abovementioned three herbs exist with different proportions in DF formula and their chemical markers have different physiochemical properties; it is quite challenging to develop an analytical methodology for the determination of these chemical markers. For the analysis of the three herbs, five chemicals, (+)-pseudoephedrine (1) and (-)-ephedrine (2) for E. intermedia , aloe-emodin (3), and chrysophanol (4) for R. palmatum , and shikonin (5) for L. erythrorhizon , were selected for method validation of DF formula, and the analytical conditions were optimized and validated using high-performance liquid chromatography coupled with an ultraviolet detector (HPLC-UV). The specificities for the five compounds 1-5 were determined by their UV absorption spectra (1-4: 215 nm and 5: 520 nm). Their calibration curves showed good linear regressions with high correlation coefficient values ( R 2 > 0.9997). The limits of detection of these five markers were in the range 0.4-2.1 ng/mL, with the exception of 5 (12.7 ng/mL). The intraday variability for all the chemical markers was less than a Relative standard deviation (RSD) of 3%, except for 5 (RSD = 12.6%). In the case of interday analysis, 1 (1.0%), 2 (3.1%), and 4 (3.7%) showed much lower variabilities (RSD < 5%) than 3 (7.6%) and 5 (8.2%). Moreover, the five chemical markers showed good recoveries with good accuracies in the range of 90%-110%. The developed HPLC-UV method for the determination of the five chemical markers of the components of DF formula was validated. DF formula, the herbal composition of Ephedra intermedia , Rheum palmatum and Lithospermum erythrorhizon Five chemical markers in DF formula were (+)-pseudoephedrine (1) and (-)-ephedrine (2) for E. intermedia , aloe-emodin (3) and chrysopanol (4) for R. palmatum , and shikonin (5) for L. erythrorhizon , with quite different physico-chemical propertiesFive chemical markers in DF formula were determined by HPLC-UV Abbreviations used: EP: (-)-ephedrine; PSEP: (+)-pseudoephedrine; HPLC: High-performance liquid chromatography; UV: Ultraviolet; LOD: Limit of detection; LOQ: Limit of quantification; RSD: Relative standard deviation.

Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci

NASA Astrophysics Data System (ADS)

Kirk, Toby L.

2018-03-01

This paper presents new analytical formulae for flow in a channel with one or both walls patterned with a longitudinal array of ridges and arbitrarily protruding menisci. Derived from a matched asymptotic expansion, they extend results by Crowdy (J. Fluid Mech., vol. 791, 2016, R7) for shear flow, and thus make no restriction on the protrusion into or out of the liquid. The slip length formula is compared against full numerical solutions and, despite the assumption of small ridge period in its derivation, is found to have a very large range of validity; relative errors are small even for periods large enough for the protruding menisci to degrade the flow and touch the opposing wall.

Time delay of critical images in the vicinity of cusp point of gravitational-lens systems

NASA Astrophysics Data System (ADS)

Alexandrov, A.; Zhdanov, V.

2016-12-01

We consider approximate analytical formulas for time-delays of critical images of a point source in the neighborhood of a cusp-caustic. We discuss zero, first and second approximations in powers of a parameter that defines the proximity of the source to the cusp. These formulas link the time delay with characteristics of the lens potential. The formula of zero approximation was obtained by Congdon, Keeton & Nordgren (MNRAS, 2008). In case of a general lens potential we derived first order correction thereto. If the potential is symmetric with respect to the cusp axis, then this correction is identically equal to zero. For this case, we obtained second order correction. The relations found are illustrated by a simple model example.

Unified semiclassical approach to electronic transport from diffusive to ballistic regimes

NASA Astrophysics Data System (ADS)

Geng, Hao; Deng, Wei-Yin; Ren, Yue-Jiao; Sheng, Li; Xing, Ding-Yu

2016-09-01

We show that by integrating out the electric field and incorporating proper boundary conditions, a Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General analytical formulas of the conductance in D = 1,2,3 dimensions are obtained, which recover the Boltzmann-Drude formula and Landauer-Büttiker formula in the diffusive and ballistic limits, respectively. This intuitive and efficient approach can be applied to investigate the interplay of system size and impurity scattering in various charge and spin transport phenomena, when the quantum interference effect is not important. Project supported by the National Basic Research Program of China (Grant Nos. 2015CB921202 and 2014CB921103) and the National Natural Science Foundation of China (Grant No. 11225420).

Approximate analytical description of the elastic strain field due to an inclusion in a continuous medium with cubic anisotropy

NASA Astrophysics Data System (ADS)

Nenashev, A. V.; Koshkarev, A. A.; Dvurechenskii, A. V.

2018-03-01

We suggest an approach to the analytical calculation of the strain distribution due to an inclusion in elastically anisotropic media for the case of cubic anisotropy. The idea consists in the approximate reduction of the anisotropic problem to a (simpler) isotropic problem. This gives, for typical semiconductors, an improvement in accuracy by an order of magnitude, compared to the isotropic approximation. Our method allows using, in the case of elastically anisotropic media, analytical solutions obtained for isotropic media only, such as analytical formulas for the strain due to polyhedral inclusions. The present work substantially extends the applicability of analytical results, making them more suitable for describing real systems, such as epitaxial quantum dots.

Analysis of Thermal Track Buckling in the Lateral Plane

DOT National Transportation Integrated Search

1976-09-01

The post-buckling equilibrium states are determined analytically. To obtain a consistent formulation of the problem, use is made of the principle of virtual displacements and the variational calculus for variable matching points. The obtained formula...

TEMPERATURE COEFFICIENTS OF HETEROGENEOUS U-238-U-235 FUELED REACTORS

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

Astley, E.R.; Mansius, C.A.

1958-05-14

An analytical method of determining the effective reactivity coefficient from fundamental cross sections using the four factor formula is presented. Values of the coefficient obtained by this method compare well with experiment. (A.C.)

A simple analytical formula to compute clear sky total and photosynthetically available solar irradiance at the ocean surface

NASA Technical Reports Server (NTRS)

Frouin, Robert; Lingner, David W.; Gautier, Catherine; Baker, Karen S.; Smith, Ray C.

1989-01-01

A simple but accurate analytical formula was developed for computing the total and the photosynthetically available solar irradiances at the ocean surface under clear skies, which takes into account the processes of scattering by molecules and aerosols within the atmosphere and of absorption by the water vapor, ozone, and aerosols. These processes are parameterized as a function of solar zenith angle, aerosol type, atmospheric visibility, and vertically integrated water-vapor and ozone amounts. Comparisons of the calculated and measured total and photosynthetically available solar irradiances for several experiments in tropical and mid-latitude ocean regions show 39 and 14 Wm/sq m rms errors (6.5 and 4.7 percent of the average measured values) on an hourly time scale, respectively. The proposed forumula is unique in its ability to predict surface solar irradiance in the photosynthetically active spectral interval.

Fresnel coefficients and Fabry-Perot formula for spatially dispersive metallic layers

NASA Astrophysics Data System (ADS)

Pitelet, Armel; Mallet, Émilien; Centeno, Emmanuel; Moreau, Antoine

2017-07-01

The repulsion between free electrons inside a metal makes its optical response spatially dispersive, so that it is not described by Drude's model but by a hydrodynamic model. We give here fully analytic results for a metallic slab in this framework, thanks to a two-mode cavity formalism leading to a Fabry-Perot formula, and show that a simplification can be made that preserves the accuracy of the results while allowing much simpler analytic expressions. For metallic layers thicker than 2.7 nm modified Fresnel coefficients can actually be used to accurately predict the response of any multilayer with spatially dispersive metals (for reflection, transmission, or the guided modes). Finally, this explains why adding a small dielectric layer [Y. Luo et al., Phys. Rev. Lett. 111, 093901 (2013), 10.1103/PhysRevLett.111.093901] allows one to reproduce the effects of nonlocality in many cases, and especially for multilayers.

Extended Glauber Model of Antiproton-Nucleus Annihilation for All Energies and Mass Numbers

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

Lee, Teck-Ghee; Wong, Cheuk-Yin

2014-01-01

Previous analytical formulas in the Glauber model for high-energy nucleus-nucleus collisions developed by Wong are utilized and extended to study Antiproton-nucleus annihilations for both high and low energies, after taking into account the effects of Coulomb and nuclear interactions, and the change of the antiproton momentum inside a nucleus. The extended analytical formulas capture the main features of the experimental antiproton-nucleus annihilation cross sections for all energies and mass numbers. At high antiproton energies, they exhibit the granular property for the lightest nuclei and the black-disk limit for the heavy nuclei. At low antiproton energies, they display the effect ofmore » the antiproton momentum increase due to the nuclear interaction for the light nuclei, and the effect of the magnification due to the attractive Coulomb interaction for the heavy nuclei.« less

Determination of Labeled Fatty Acids Content in Milk Products, Infant Formula and Adult/Pediatric Nutritional Formula by Capillary Gas Chromatography: First Action 2012.13.

PubMed

2015-06-24

The method described below is intended for the quantification of all fatty acids, including commercially important groups of fatty acids used for labeling reasons (i.e., TFA, SFA, MUFA, PUFA, omega-3, omega-6, omega-9) and/or individual fatty acids (i.e., LA, ALA, ARA, EPA, DHA) in milk products, infant formula and adult/pediatric nutritional formula. These products often contain milk fat and/or vegetable oils, and are supplemented or not supplemented with oils rich in long chain polyunsaturated fatty acids (LC-PUFA). The determination is performed by direct transesterification of ready-to-feed liquid concentrate or powder products, without prior fat extraction. The single laboratory validation (SLV) data was submitted to the Stakeholder Panel on Infant Formula and Adult Nutritionals (SPIFAN) Expert Review Panel (ERP) for review at the AOAC INTERNATIONAL annual meeting held September 30 to October 3, 2012 in Las Vegas, Nevada. The ERP determined that the data reviewed met the Standard Method Performance Requirements (SMPR 2012.11) set by SPIFAN and was approved as an AOAC Official First Action. The analytical range for SPIFAN samples was between 0.001-7.94 g/100 g reconstituted product, or ready-to-feed liquid. The quantitation limit was estimated as 0.001 g/100 g, while repeatability and intermediate precision were both less than 1.8 % RSD above 0.05 g/100 g, and <3.5% RSD at 0.00 5g/100 g, respectively. Recovery values based on spiking experiments at two different levels of linoleic and linolenic acids ranged from 100.0% to 102.9% for 3 different SPIFAN products. All the parameters evaluated during the SLV were well within the values defined in SMPR 2012.011 (September 2012).

Lorentz force electrical impedance tomography using magnetic field measurements.

PubMed

Zengin, Reyhan; Gençer, Nevzat Güneri

2016-08-21

In this study, magnetic field measurement technique is investigated to image the electrical conductivity properties of biological tissues using Lorentz forces. This technique is based on electrical current induction using ultrasound together with an applied static magnetic field. The magnetic field intensity generated due to induced currents is measured using two coil configurations, namely, a rectangular loop coil and a novel xy coil pair. A time-varying voltage is picked-up and recorded while the acoustic wave propagates along its path. The forward problem of this imaging modality is defined as calculation of the pick-up voltages due to a given acoustic excitation and known body properties. Firstly, the feasibility of the proposed technique is investigated analytically. The basic field equations governing the behaviour of time-varying electromagnetic fields are presented. Secondly, the general formulation of the partial differential equations for the scalar and magnetic vector potentials are derived. To investigate the feasibility of this technique, numerical studies are conducted using a finite element method based software. To sense the pick-up voltages a novel coil configuration (xy coil pairs) is proposed. Two-dimensional numerical geometry with a 16-element linear phased array (LPA) ultrasonic transducer (1 MHz) and a conductive body (breast fat) with five tumorous tissues is modeled. The static magnetic field is assumed to be 4 Tesla. To understand the performance of the imaging system, the sensitivity matrix is analyzed. The sensitivity matrix is obtained for two different locations of LPA transducer with eleven steering angles from [Formula: see text] to [Formula: see text] at intervals of [Formula: see text]. The characteristics of the imaging system are shown with the singular value decomposition (SVD) of the sensitivity matrix. The images are reconstructed with the truncated SVD algorithm. The signal-to-noise ratio in measurements is assumed 80 dB. Simulation studies based on the sensitivity matrix analysis reveal that perturbations with [Formula: see text] mm size can be detected up to a 3.5 cm depth.

Effect of Infant Formula on Streptococcus Mutans Biofilm Formation.

PubMed

Hinds, Laura M; Moser, Elizabeth A S; Eckert, George; Gregory, Richard L

This study investigated the effect that infant formula had on biofilm growth of Streptococcus mutans. Specifically, it compared biofilm growth in media containing lactose-based and sucrose-based formulas. It also analyzed biofilm formation with formulas of varying iron content. Biofilm growth was tested with the specific infant formula components sucrose, lactose, and ferric chloride. The study was designed to determine if these types of infant formulas and components affected S. mutans biofilm formation differently. A 24-hour culture of S. mutans was treated with various concentrations of infant formula diluted in bacteriological media. To test for biofilm formation, S. mutans was cultured with and without the infant formula and formula components. The biofilms were washed, fixed, and stained with crystal violet. The absorbance was measured to evaluate biofilm growth and total absorbance. Sucrose-based formulas provided significant increases in biofilm growth when compared to lactose-based formulas at two dilutions (1:5, 1:20). Similac Sensitive RS (sucrose-based) at most dilutions provided the most significant increase in biofilm growth when compared to the control. Sucrose tested as an individual component provided more of a significant increase on biofilm growth than lactose or iron when compared to the control. A low iron formula provided a significant increase in biofilm growth at one dilution (1:5) when compared to formula containing a normal iron content. There was no significant difference in biofilm growth when comparing high iron formula to normal iron formula or low iron formula. There was no significant difference when comparing Similac PM 60/40 (low iron formula) to Similac PM 60/40 with additional ferric chloride. The results of this study demonstrated that sucrose-based formula provided more of a significant increase in biofilm growth compared to lactose-based formula. Sucrose alone provided a significant increase of biofilm growth at more dilutions when compared to the control than lactose and iron. The amount of iron in formula had a significant effect on biofilm formation only when comparing low iron formula to normal iron formula at the highest concentration (1:5). There was no significant difference in biofilm growth when iron was added to the low iron formula. The information obtained expands current knowledge regarding the influence of infant formula on the primary dentition and reinforces the importance of oral hygiene habits once the first tooth erupts.

A Requirements-Driven Optimization Method for Acoustic Liners Using Analytic Derivatives

NASA Technical Reports Server (NTRS)

Berton, Jeffrey J.; Lopes, Leonard V.

2017-01-01

More than ever, there is flexibility and freedom in acoustic liner design. Subject to practical considerations, liner design variables may be manipulated to achieve a target attenuation spectrum. But characteristics of the ideal attenuation spectrum can be difficult to know. Many multidisciplinary system effects govern how engine noise sources contribute to community noise. Given a hardwall fan noise source to be suppressed, and using an analytical certification noise model to compute a community noise measure of merit, the optimal attenuation spectrum can be derived using multidisciplinary systems analysis methods. In a previous paper on this subject, a method deriving the ideal target attenuation spectrum that minimizes noise perceived by observers on the ground was described. A simple code-wrapping approach was used to evaluate a community noise objective function for an external optimizer. Gradients were evaluated using a finite difference formula. The subject of this paper is an application of analytic derivatives that supply precise gradients to an optimization process. Analytic derivatives improve the efficiency and accuracy of gradient-based optimization methods and allow consideration of more design variables. In addition, the benefit of variable impedance liners is explored using a multi-objective optimization.

Analytical and numerical solutions for heat transfer and effective thermal conductivity of cracked media

NASA Astrophysics Data System (ADS)

Tran, A. B.; Vu, M. N.; Nguyen, S. T.; Dong, T. Q.; Le-Nguyen, K.

2018-02-01

This paper presents analytical solutions to heat transfer problems around a crack and derive an adaptive model for effective thermal conductivity of cracked materials based on singular integral equation approach. Potential solution of heat diffusion through two-dimensional cracked media, where crack filled by air behaves as insulator to heat flow, is obtained in a singular integral equation form. It is demonstrated that the temperature field can be described as a function of temperature and rate of heat flow on the boundary and the temperature jump across the cracks. Numerical resolution of this boundary integral equation allows determining heat conduction and effective thermal conductivity of cracked media. Moreover, writing this boundary integral equation for an infinite medium embedding a single crack under a far-field condition allows deriving the closed-form solution of temperature discontinuity on the crack and particularly the closed-form solution of temperature field around the crack. These formulas are then used to establish analytical effective medium estimates. Finally, the comparison between the developed numerical and analytical solutions allows developing an adaptive model for effective thermal conductivity of cracked media. This model takes into account both the interaction between cracks and the percolation threshold.

Analytical Problems and Suggestions in the Analysis of Behavioral Economic Demand Curves.

PubMed

Yu, Jihnhee; Liu, Liu; Collins, R Lorraine; Vincent, Paula C; Epstein, Leonard H

2014-01-01

Behavioral economic demand curves (Hursh, Raslear, Shurtleff, Bauman, & Simmons, 1988) are innovative approaches to characterize the relationships between consumption of a substance and its price. In this article, we investigate common analytical issues in the use of behavioral economic demand curves, which can cause inconsistent interpretations of demand curves, and then we provide methodological suggestions to address those analytical issues. We first demonstrate that log transformation with different added values for handling zeros changes model parameter estimates dramatically. Second, demand curves are often analyzed using an overparameterized model that results in an inefficient use of the available data and a lack of assessment of the variability among individuals. To address these issues, we apply a nonlinear mixed effects model based on multivariate error structures that has not been used previously to analyze behavioral economic demand curves in the literature. We also propose analytical formulas for the relevant standard errors of derived values such as P max, O max, and elasticity. The proposed model stabilizes the derived values regardless of using different added increments and provides substantially smaller standard errors. We illustrate the data analysis procedure using data from a relative reinforcement efficacy study of simulated marijuana purchasing.

Empirical and semi-analytical models for predicting peak outflows caused by embankment dam failures

NASA Astrophysics Data System (ADS)

Wang, Bo; Chen, Yunliang; Wu, Chao; Peng, Yong; Song, Jiajun; Liu, Wenjun; Liu, Xin

2018-07-01

Prediction of peak discharge of floods has attracted great attention for researchers and engineers. In present study, nine typical nonlinear mathematical models are established based on database of 40 historical dam failures. The first eight models that were developed with a series of regression analyses are purely empirical, while the last one is a semi-analytical approach that was derived from an analytical solution of dam-break floods in a trapezoidal channel. Water depth above breach invert (Hw), volume of water stored above breach invert (Vw), embankment length (El), and average embankment width (Ew) are used as independent variables to develop empirical formulas of estimating the peak outflow from breached embankment dams. It is indicated from the multiple regression analysis that a function using the former two variables (i.e., Hw and Vw) produce considerably more accurate results than that using latter two variables (i.e., El and Ew). It is shown that the semi-analytical approach works best in terms of both prediction accuracy and uncertainty, and the established empirical models produce considerably reasonable results except the model only using El. Moreover, present models have been compared with other models available in literature for estimating peak discharge.

Challenges in defining an optimal approach to formula-based allocations of public health funds in the United States.

PubMed

Buehler, James W; Holtgrave, David R

2007-03-29

Controversy and debate can arise whenever public health agencies determine how program funds should be allocated among constituent jurisdictions. Two common strategies for making such allocations are expert review of competitive applications and the use of funding formulas. Despite widespread use of funding formulas by public health agencies in the United States, formula allocation strategies in public health have been subject to relatively little formal scrutiny, with the notable exception of the attention focused on formula funding of HIV care programs. To inform debates and deliberations in the selection of a formula-based approach, we summarize key challenges to formula-based funding, based on prior reviews of federal programs in the United States. The primary challenge lies in identifying data sources and formula calculation methods that both reflect and serve program objectives, with or without adjustments for variations in the cost of delivering services, the availability of local resources, capacity, or performance. Simplicity and transparency are major advantages of formula-based allocations, but these advantages can be offset if formula-based allocations are perceived to under- or over-fund some jurisdictions, which may result from how guaranteed minimum funding levels are set or from "hold-harmless" provisions intended to blunt the effects of changes in formula design or random variations in source data. While fairness is considered an advantage of formula-based allocations, the design of a formula may implicitly reflect unquestioned values concerning equity versus equivalence in setting funding policies. Whether or how past or projected trends are taken into account can also have substantial impacts on allocations. Insufficient attention has been focused on how the approach to designing funding formulas in public health should differ for treatment or service versus prevention programs. Further evaluations of formula-based versus competitive allocation methods are needed to promote the optimal use of public health funds. In the meantime, those who use formula-based strategies to allocate funds should be familiar with the nuances of this approach.

The simultaneous integration of many trajectories using nilpotent normal forms

NASA Technical Reports Server (NTRS)

Grayson, Matthew A.; Grossman, Robert

1990-01-01

Taylor's formula shows how to approximate a certain class of functions by polynomials. The approximations are arbitrarily good in some neighborhood whenever the function is analytic and they are easy to compute. The main goal is to give an efficient algorithm to approximate a neighborhood of the configuration space of a dynamical system by a nilpotent, explicitly integrable dynamical system. The major areas covered include: an approximating map; the generalized Baker-Campbell-Hausdorff formula; the Picard-Taylor method; the main theorem; simultaneous integration of trajectories; and examples.

Monogamy relation of multi-qubit systems for squared Tsallis-q entanglement

PubMed Central

Yuan, Guang-Ming; Song, Wei; Yang, Ming; Li, Da-Chuang; Zhao, Jun-Long; Cao, Zhuo-Liang

2016-01-01

Tsallis-q entanglement is a bipartite entanglement measure which is the generalization of entanglement of formation for q tending to 1. We first expand the range of q for the analytic formula of Tsallis-q entanglement. For , we prove the monogamy relation in terms of the squared Tsallis-q entanglement for an arbitrary multi-qubit systems. It is shown that the multipartite entanglement indicator based on squared Tsallis-q entanglement still works well even when the indicator based on the squared concurrence loses its efficacy. We also show that the μ-th power of Tsallis-q entanglement satisfies the monogamy or polygamy inequalities for any three-qubit state. PMID:27346605

78 FR 28729 - Airworthiness Directives; The Boeing Company Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2013-05-16

... Boeing Company Model 757-200 and -200PF series airplanes. That AD currently requires modifying the... specifies a maximum compliance time limit that overrides the optional threshold formula results. This AD was... analytical loads that [[Page 28730

Refracted arrival waves in a zone of silence from a finite thickness mixing layer.

PubMed

Suzuki, Takao; Lele, Sanjiva K

2002-02-01

Refracted arrival waves which propagate in the zone of silence of a finite thickness mixing layer are analyzed using geometrical acoustics in two dimensions. Here, two simplifying assumptions are made: (i) the mean flow field is transversely sheared, and (ii) the mean velocity and temperature profiles approach the free-stream conditions exponentially. Under these assumptions, ray trajectories are analytically solved, and a formula for acoustic pressure amplitude in the far field is derived in the high-frequency limit. This formula is compared with the existing theory based on a vortex sheet corresponding to the low-frequency limit. The analysis covers the dependence on the Mach number as well as on the temperature ratio. The results show that both limits have some qualitative similarities, but the amplitude in the zone of silence at high frequencies is proportional to omega(-1/2), while that at low frequencies is proportional to omega(-3/2), omega being the angular frequency of the source.

Cramer-Rao bound analysis of wideband source localization and DOA estimation

NASA Astrophysics Data System (ADS)

Yip, Lean; Chen, Joe C.; Hudson, Ralph E.; Yao, Kung

2002-12-01

In this paper, we derive the Cramér-Rao Bound (CRB) for wideband source localization and DOA estimation. The resulting CRB formula can be decomposed into two terms: one that depends on the signal characteristic and one that depends on the array geometry. For a uniformly spaced circular array (UCA), a concise analytical form of the CRB can be given by using some algebraic approximation. We further define a DOA beamwidth based on the resulting CRB formula. The DOA beamwidth can be used to design the sampling angular spacing for the Maximum-likelihood (ML) algorithm. For a randomly distributed array, we use an elliptical model to determine the largest and smallest effective beamwidth. The effective beamwidth and the CRB analysis of source localization allow us to design an efficient algorithm for the ML estimator. Finally, our simulation results of the Approximated Maximum Likelihood (AML) algorithm are demonstrated to match well to the CRB analysis at high SNR.

Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background.

PubMed

Minin, Serge; Kamalabadi, Farzad

2009-12-20

We derive analytical equations for uncertainties in parameters extracted by nonlinear least-squares fitting of a Gaussian emission function with an unknown continuum background component in the presence of additive white Gaussian noise. The derivation is based on the inversion of the full curvature matrix (equivalent to Fisher information matrix) of the least-squares error, chi(2), in a four-variable fitting parameter space. The derived uncertainty formulas (equivalent to Cramer-Rao error bounds) are found to be in good agreement with the numerically computed uncertainties from a large ensemble of simulated measurements. The derived formulas can be used for estimating minimum achievable errors for a given signal-to-noise ratio and for investigating some aspects of measurement setup trade-offs and optimization. While the intended application is Fabry-Perot spectroscopy for wind and temperature measurements in the upper atmosphere, the derivation is generic and applicable to other spectroscopy problems with a Gaussian line shape.

The forced sound transmission of finite single leaf walls using a variational technique.

PubMed

Brunskog, Jonas

2012-09-01

The single wall is the simplest element of concern in building acoustics, but there still remain some open questions regarding the sound insulation of this simple case. The two main reasons for this are the effects on the excitation and sound radiation of the wall when it has a finite size, and the fact that the wave field in the wall is consisting of two types of waves, namely forced waves due to the exciting acoustic field, and free bending waves due to reflections in the boundary. The aim of the present paper is to derive simple analytical formulas for the forced part of the airborne sound insulation of a single homogeneous wall of finite size, using a variational technique based on the integral-differential equation of the fluid loaded wall. The so derived formulas are valid in the entire audible frequency range. The results are compared with full numerical calculations, measurements and alternative theory, with reasonable agreement.

A standard library for modeling satellite orbits on a microcomputer

NASA Astrophysics Data System (ADS)

Beutel, Kenneth L.

1988-03-01

Introductory students of astrodynamics and the space environment are required to have a fundamental understanding of the kinematic behavior of satellite orbits. This thesis develops a standard library that contains the basic formulas for modeling earth orbiting satellites. This library is used as a basis for implementing a satellite motion simulator that can be used to demonstrate orbital phenomena in the classroom. Surveyed are the equations of orbital elements, coordinate systems and analytic formulas, which are made into a standard method for modeling earth orbiting satellites. The standard library is written in the C programming language and is designed to be highly portable between a variety of computer environments. The simulation draws heavily on the standards established by the library to produce a graphics-based orbit simulation program written for the Apple Macintosh computer. The simulation demonstrates the utility of the standard library functions but, because of its extensive use of the Macintosh user interface, is not portable to other operating systems.

Modeling the within-host dynamics of cholera: bacterial-viral interaction.

PubMed

Wang, Xueying; Wang, Jin

2017-08-01

Novel deterministic and stochastic models are proposed in this paper for the within-host dynamics of cholera, with a focus on the bacterial-viral interaction. The deterministic model is a system of differential equations describing the interaction among the two types of vibrios and the viruses. The stochastic model is a system of Markov jump processes that is derived based on the dynamics of the deterministic model. The multitype branching process approximation is applied to estimate the extinction probability of bacteria and viruses within a human host during the early stage of the bacterial-viral infection. Accordingly, a closed-form expression is derived for the disease extinction probability, and analytic estimates are validated with numerical simulations. The local and global dynamics of the bacterial-viral interaction are analysed using the deterministic model, and the result indicates that there is a sharp disease threshold characterized by the basic reproduction number [Formula: see text]: if [Formula: see text], vibrios ingested from the environment into human body will not cause cholera infection; if [Formula: see text], vibrios will grow with increased toxicity and persist within the host, leading to human cholera. In contrast, the stochastic model indicates, more realistically, that there is always a positive probability of disease extinction within the human host.

Coalescence computations for large samples drawn from populations of time-varying sizes

PubMed Central

Polanski, Andrzej; Szczesna, Agnieszka; Garbulowski, Mateusz; Kimmel, Marek

2017-01-01

We present new results concerning probability distributions of times in the coalescence tree and expected allele frequencies for coalescent with large sample size. The obtained results are based on computational methodologies, which involve combining coalescence time scale changes with techniques of integral transformations and using analytical formulae for infinite products. We show applications of the proposed methodologies for computing probability distributions of times in the coalescence tree and their limits, for evaluation of accuracy of approximate expressions for times in the coalescence tree and expected allele frequencies, and for analysis of large human mitochondrial DNA dataset. PMID:28170404

Magnus expansion method for two-level atom interacting with few-cycle pulse

NASA Astrophysics Data System (ADS)

Begzjav, T.; Ben-Benjamin, J. S.; Eleuch, H.; Nessler, R.; Rostovtsev, Y.; Shchedrin, G.

2018-06-01

Using the Magnus expansion to the fourth order, we obtain analytic expressions for the atomic state of a two-level system driven by a laser pulse of arbitrary shape with small pulse area. We also determine the limitation of our obtained formulas due to limited range of convergence of the Magnus series. We compare our method to the recently developed method of Rostovtsev et al. (PRA 2009, 79, 063833) for several detunings. Our analysis shows that our technique based on the Magnus expansion can be used as a complementary method to the one in PRA 2009.

Applications of δ-function perturbation to the pricing of derivative securities

NASA Astrophysics Data System (ADS)

Decamps, Marc; De Schepper, Ann; Goovaerts, Marc

2004-11-01

In the recent econophysics literature, the use of functional integrals is widespread for the calculation of option prices. In this paper, we extend this approach in several directions by means of δ-function perturbations. First, we show that results about infinitely repulsive δ-function are applicable to the pricing of barrier options. We also introduce functional integrals over skew paths that give rise to a new European option formula when combined with δ-function potential. We propose accurate closed-form approximations based on the theory of comonotonic risks in case the functional integrals are not analytically computable.

Atmospheric guidance law for planar skip trajectories

NASA Technical Reports Server (NTRS)

Mease, K. D.; Mccreary, F. A.

1985-01-01

The applicability of an approximate, closed-form, analytical solution to the equations of motion, as a basis for a deterministic guidance law for controlling the in-plane motion during a skip trajectory, is investigated. The derivation of the solution by the method of matched asymptotic expansions is discussed. Specific issues that arise in the application of the solution to skip trajectories are addressed. Based on the solution, an explicit formula for the approximate energy loss due to an atmospheric pass is derived. A guidance strategy is proposed that illustrates the use of the approximate solution. A numerical example shows encouraging performance.

Effect of turbulent atmosphere on the on-axis average intensity of Pearcey-Gaussian beam

NASA Astrophysics Data System (ADS)

F, Boufalah; L, Dalil-Essakali; H, Nebdi; A, Belafhal

2016-06-01

The propagation characteristics of the Pearcey-Gaussian (PG) beam in turbulent atmosphere are investigated in this paper. The Pearcey beam is a new kind of paraxial beam, based on the Pearcey function of catastrophe theory, which describes diffraction about a cusp caustic. By using the extended Huygens-Fresnel integral formula in the paraxial approximation and the Rytov theory, an analytical expression of axial intensity for the considered beam family is derived. Some numerical results for PG beam propagating in atmospheric turbulence are given by studying the influences of some factors, including incident beam parameters and turbulence strengths.

Direct estimation and correction of bias from temporally variable non-stationary noise in a channelized Hotelling model observer.

PubMed

Fetterly, Kenneth A; Favazza, Christopher P

2016-08-07

Channelized Hotelling model observer (CHO) methods were developed to assess performance of an x-ray angiography system. The analytical methods included correction for known bias error due to finite sampling. Detectability indices ([Formula: see text]) corresponding to disk-shaped objects with diameters in the range 0.5-4 mm were calculated. Application of the CHO for variable detector target dose (DTD) in the range 6-240 nGy frame(-1) resulted in [Formula: see text] estimates which were as much as 2.9×  greater than expected of a quantum limited system. Over-estimation of [Formula: see text] was presumed to be a result of bias error due to temporally variable non-stationary noise. Statistical theory which allows for independent contributions of 'signal' from a test object (o) and temporally variable non-stationary noise (ns) was developed. The theory demonstrates that the biased [Formula: see text] is the sum of the detectability indices associated with the test object [Formula: see text] and non-stationary noise ([Formula: see text]). Given the nature of the imaging system and the experimental methods, [Formula: see text] cannot be directly determined independent of [Formula: see text]. However, methods to estimate [Formula: see text] independent of [Formula: see text] were developed. In accordance with the theory, [Formula: see text] was subtracted from experimental estimates of [Formula: see text], providing an unbiased estimate of [Formula: see text]. Estimates of [Formula: see text] exhibited trends consistent with expectations of an angiography system that is quantum limited for high DTD and compromised by detector electronic readout noise for low DTD conditions. Results suggest that these methods provide [Formula: see text] estimates which are accurate and precise for [Formula: see text]. Further, results demonstrated that the source of bias was detector electronic readout noise. In summary, this work presents theory and methods to test for the presence of bias in Hotelling model observers due to temporally variable non-stationary noise and correct this bias when the temporally variable non-stationary noise is independent and additive with respect to the test object signal.

Degenerate limit thermodynamics beyond leading order for models of dense matter

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

Constantinou, Constantinos, E-mail: c.constantinou@fz-juelich.de; Muccioli, Brian, E-mail: bm956810@ohio.edu; Prakash, Madappa, E-mail: prakash@ohio.edu

2015-12-15

Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of non-relativistic and relativistic models of hot and dense matter currently used in nuclear physics and astrophysics (supernovae, proto-neutron stars and neutron star mergers) as well as in condensed matter physics. We consider the general case of arbitrary dimensionality of momentum space and an arbitrary degree of relativity (for relativistic models). For non-relativistic zero-range interactions, knowledge of the Landau effective mass suffices to compute next-to-leading order effects,more » but for finite-range interactions, momentum derivatives of the Landau effective mass function up to second order are required. Results from our analytical formulas are compared with the exact results for zero- and finite-range potential and relativistic mean-field theoretical models. In all cases, inclusion of next-to-leading order temperature effects substantially extends the ranges of partial degeneracy for which the analytical treatment remains valid. Effects of many-body correlations that deserve further investigation are highlighted.« less

Adding a solar-radiance function to the Hošek-Wilkie skylight model.

PubMed

Hošek, Lukáš; Wilkie, Alexander

2013-01-01

One prerequisite for realistic renderings of outdoor scenes is the proper capturing of the sky's appearance. Currently, an explicit simulation of light scattering in the atmosphere isn't computationally feasible, and won't be in the foreseeable future. Captured luminance patterns have proven their usefulness in practice but can't meet all user needs. To fill this capability gap, computer graphics technology has employed analytical models of sky-dome luminance patterns for more than two decades. For technical reasons, such models deal with only the sky dome's appearance, though, and exclude the solar disc. The widely used model proposed by Arcot Preetham and colleagues employed a separately derived analytical formula for adding a solar emitter of suitable radiant intensity. Although this yields reasonable results, the formula is derived in a manner that doesn't exactly match the conditions in their sky-dome model. But the more sophisticated a skylight model is and the more subtly it can represent different conditions, the more the solar radiance should exactly match the skylight's conditions. Toward that end, researchers propose a solar-radiance function that exactly matches a recently published high-quality analytical skylight model.

A Generalized Michaelis-Menten Equation in Protein Synthesis: Effects of Mis-Charged Cognate tRNA and Mis-Reading of Codon.

PubMed

Dutta, Annwesha; Chowdhury, Debashish

2017-05-01

The sequence of amino acid monomers in the primary structure of a protein is decided by the corresponding sequence of codons (triplets of nucleic acid monomers) on the template messenger RNA (mRNA). The polymerization of a protein, by incorporation of the successive amino acid monomers, is carried out by a molecular machine called ribosome. We develop a stochastic kinetic model that captures the possibilities of mis-reading of mRNA codon and prior mis-charging of a tRNA. By a combination of analytical and numerical methods, we obtain the distribution of the times taken for incorporation of the successive amino acids in the growing protein in this mathematical model. The corresponding exact analytical expression for the average rate of elongation of a nascent protein is a 'biologically motivated' generalization of the Michaelis-Menten formula for the average rate of enzymatic reactions. This generalized Michaelis-Menten-like formula (and the exact analytical expressions for a few other quantities) that we report here display the interplay of four different branched pathways corresponding to selection of four different types of tRNA.

Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions

NASA Astrophysics Data System (ADS)

Eccles, Chris; Roy, Sanil; Gray, Thomas H.; Zaccone, Alessio

2017-11-01

Accounting for viscous damping within Fokker-Planck equations led to various improvements in the understanding and analysis of nuclear fission of heavy nuclei. Analytical expressions for the fission time are typically provided by Kramers' theory, which improves on the Bohr-Wheeler estimate by including the time scale related to many-particle dissipative processes along the deformation coordinate. However, Kramers' formula breaks down for sufficiently high excitation energies where Kramers' assumption of a large barrier no longer holds. Focusing on the overdamped regime for energies T >1 MeV, Kramers' theory should be replaced by a new analytical theory derived from the Ornstein-Uhlenbeck first-passage time method that is proposed here. The theory is applied to fission time data from fusion-fission experiments on 16O+208Pb→224Th . The proposed model provides an internally consistent one-parameter fitting of fission data with a constant nuclear friction as the fitting parameter, whereas Kramers' fitting requires a value of friction which falls out of the allowed range. The theory provides also an analytical formula that in future work can be easily implemented in numerical codes such as cascade or joanne4.

The role of settling velocity formulation in the determination of gully pot trapping efficiency: comparison between analytical and experimental data.

PubMed

Ciccarello, Annalisa; Bolognesi, Andrea; Maglionico, Marco; Artina, Sandro

2012-01-01

Roadside gully pots are the connecting points between surface runoff and the underground drainage network; therefore they can be considered as the most superficial component of urban drainage systems. Gully pots are supposed to trap particulate matter washed off the catchment surface, but also to collect and convey stormwater into the network. The continuous accumulation of particulate matter results in a progressive loss of the gully pot hydraulic conveyance, thereby increasing the probability of urban flooding during rainstorm events. This study has therefore the objective to determine which variables influence the gully pot capability of retaining solids (efficiency), both experimentally and analytically. Several laboratory tests have been performed on a simple plastic gully pot, with different inflow rates and using both mono and hetero-disperse particle samples. Particular attention has been given to the influence exerted by the way particle settling velocity is expressed: efficiency has been analytically determined by means of multiple settling velocity formulas proposed by various authors and eventually compared to experimental data. Results deriving from the adoption of each single settling velocity formula have been extensively analysed, showing fairly different outcomes.

Temporal Evolution of the Gamma-ray Burst Afterglow Spectrum for an Observer: GeV–TeV Synchrotron Self-Compton Light Curve

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

Fukushima, Takuma; Fujita, Yutaka; To, Sho

We numerically simulate the gamma-ray burst (GRB) afterglow emission with a one-zone time-dependent code. The temporal evolutions of the decelerating shocked shell and energy distributions of electrons and photons are consistently calculated. The photon spectrum and light curves for an observer are obtained taking into account the relativistic propagation of the shocked shell and the curvature of the emission surface. We find that the onset time of the afterglow is significantly earlier than the previous analytical estimate. The analytical formulae of the shock propagation and light curve for the radiative case are also different from our results. Our results showmore » that even if the emission mechanism is switching from synchrotron to synchrotron self-Compton, the gamma-ray light curves can be a smooth power law, which agrees with the observed light curve and the late detection of a 32 GeV photon in GRB 130427A. The uncertainty of the model parameters obtained with the analytical formula is discussed, especially in connection with the closure relation between spectral index and decay index.« less

Screening of 23 β-lactams in foodstuffs by LC-MS/MS using an alkaline QuEChERS-like extraction.

PubMed

Bessaire, Thomas; Mujahid, Claudia; Beck, Andrea; Tarres, Adrienne; Savoy, Marie-Claude; Woo, Pei-Mun; Mottier, Pascal; Desmarchelier, Aurélien

2018-04-01

A fast and robust high performance LC-MS/MS screening method was developed for the analysis of β-lactam antibiotics in foods of animal origin: eggs, raw milk, processed dairy ingredients, infant formula, and meat- and fish-based products including baby foods. QuEChERS extraction with some adaptations enabled 23 drugs to be simultaneously monitored. Screening target concentrations were set at levels adequate to ensure compliance with current European, Chinese, US and Canadian regulations. The method was fully validated according to the European Community Reference Laboratories Residues Guidelines using 93 food samples of different composition. False-negative and false-positive rates were below 5% for all analytes. The method is adequate for use in high-routine laboratories. A 1-year study was additionally conducted to assess the stability of the 23 analytes in the working standard solution.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks.

PubMed

Smerlak, Matteo; Stoll, Brady; Gupta, Agam; Magdanz, James S

2015-01-01

The financial crisis illustrated the need for a functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult to model analytically, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. We obtain a closed-form formula for the "critical degree" (the number of creditors per bank below which an individual shock can propagate throughout the network), and relate failures distributions to network topologies, in particular scalefree ones. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology.

COMBINATION OF DENSITY AND ENERGY MODULATION IN MICROBUNCHING ANALYSIS

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

Tsai, Cheng Ying; Li, Rui

2016-05-01

Microbunching instability (MBI) has been one of the most challenging issues in the transport of high-brightness electron beams for modern recirculating or energy recovery linac machines. Recently we have developed and implemented a Vlasov solver [1] to calculate the microbunching gain for an arbitrary beamline lattice, based on the extension of existing theoretical formulation [2-4] for the microbunching amplification from an initial density perturbation to the final density modulation. For more thorough analyses, in addition to the case of (initial) density to (final) density amplification, we extend in this paper the previous formulation to more general cases, including energy tomore » density, density to energy and energy to energy amplifications for a recirculation machine. Such semi-analytical formulae are then incorporated into our Vlasov solver, and qualitative agreement is obtained when the semi-analytical Vlasov results are compared with particle tracking simulation using ELEGANT [5].« less

Robustness and fragility in coupled oscillator networks under targeted attacks.

PubMed

Yuan, Tianyu; Aihara, Kazuyuki; Tanaka, Gouhei

2017-01-01

The dynamical tolerance of coupled oscillator networks against local failures is studied. As the fraction of failed oscillator nodes gradually increases, the mean oscillation amplitude in the entire network decreases and then suddenly vanishes at a critical fraction as a phase transition. This critical fraction, widely used as a measure of the network robustness, was analytically derived for random failures but not for targeted attacks so far. Here we derive the general formula for the critical fraction, which can be applied to both random failures and targeted attacks. We consider the effects of targeting oscillator nodes based on their degrees. First we deal with coupled identical oscillators with homogeneous edge weights. Then our theory is applied to networks with heterogeneous edge weights and to those with nonidentical oscillators. The analytical results are validated by numerical experiments. Our results reveal the key factors governing the robustness and fragility of oscillator networks.

Theoretical optimum of implant positional index design.

PubMed

Semper, W; Kraft, S; Krüger, T; Nelson, K

2009-08-01

Rotational freedom of the implant-abutment connection influences its screw joint stability; for optimization, influential factors need to be evaluated based on a previously developed closed formula. The underlying hypothesis is that the manufacturing tolerances, geometric pattern, and dimensions of the index do not influence positional stability. We used the dimensions of 5 commonly used implant systems with a clearance of 20 microm to calculate the extent of rotational freedom; a 3D simulation (SolidWorks) validated the analytical findings. Polygonal positional indices showed the highest degrees of rotational freedom. The polygonal profile displayed higher positional stability than the polygons, but less positional accuracy than the cam-groove connection. Features of a maximal rotation-safe positional index were determined. The analytical calculation of rotational freedom of implant positional indices is possible. Rotational freedom is dependent on the geometric design of the index and may be decreased by incorporating specific aspects into the positional index design.

Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks

PubMed Central

Smerlak, Matteo; Stoll, Brady; Gupta, Agam; Magdanz, James S.

2015-01-01

The financial crisis illustrated the need for a functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult to model analytically, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. We obtain a closed-form formula for the “critical degree” (the number of creditors per bank below which an individual shock can propagate throughout the network), and relate failures distributions to network topologies, in particular scalefree ones. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology. PMID:26207631

An accurate analytic description of neutrino oscillations in matter

NASA Astrophysics Data System (ADS)

Akhmedov, E. Kh.; Niro, Viviana

2008-12-01

A simple closed-form analytic expression for the probability of two-flavour neutrino oscillations in a matter with an arbitrary density profile is derived. Our formula is based on a perturbative expansion and allows an easy calculation of higher order corrections. The expansion parameter is small when the density changes relatively slowly along the neutrino path and/or neutrino energy is not very close to the Mikheyev-Smirnov-Wolfenstein (MSW) resonance energy. Our approximation is not equivalent to the adiabatic approximation and actually goes beyond it. We demonstrate the validity of our results using a few model density profiles, including the PREM density profile of the Earth. It is shown that by combining the results obtained from the expansions valid below and above the MSW resonance one can obtain a very good description of neutrino oscillations in matter in the entire energy range, including the resonance region.

Simple Expressions for the Design of Linear Tapers in Overmoded Corrugated Waveguides

DOE PAGES

Schaub, S. C.; Shapiro, M. A.; Temkin, R. J.

2015-08-16

In this paper, simple analytical formulae are presented for the design of linear tapers with very low mode conversion loss in overmoded corrugated waveguides. For tapers from waveguide radius a2 to a1, with a11a 2/λ. Here, λ is the wavelength of radiation. The fractional loss of the HE 11 mode in an optimized taper is 0.0293(a 2-a 1) 4/amore » $$2\\atop{1}$$1a$$2\\atop{2}$$. These formulae are accurate when a2≲2a 1. Slightly more complex formulae, accurate for a 2≤4a 1, are also presented in this paper. The loss in an overmoded corrugated linear taper is less than 1 % when a 2≤2.12a 1 and less than 0.1 % when a 2≤1.53a 1. The present analytic results have been benchmarked against a rigorous mode matching code and have been found to be very accurate. The results for linear tapers are compared with the analogous expressions for parabolic tapers. Finally, parabolic tapers may provide lower loss, but linear tapers with moderate values of a 2/a 1 may be attractive because of their simplicity of fabrication.« less

Urinary D-lactate excretion in infants receiving Lactobacillus johnsonii with formula.

PubMed

Haschke-Becher, Elisabeth; Brunser, Oscar; Cruchet, Sylvia; Gotteland, Martin; Haschke, Ferdinand; Bachmann, Claude

2008-01-01

Supplementation with certain probiotics can improve gut microbial flora and immune function but should not have adverse effects. This study aimed to assess the risk of D-lactate accumulation and subsequent metabolic acidosis in infants fed on formula containing Lactobacillus johnsonii (La1). In the framework of a double-blind, randomized controlled trial enrolling 71 infants aged 4-5 months, morning urine samples were collected before and 4 weeks after being fed formulas with or without La1 (1 x 10(8)/g powder) or being breastfed. Urinary D- and L-lactate concentrations were assayed by enzymatic, fluorimetric methods and excretion was normalized per mol creatinine. At baseline, no significant differences in urinary D-/L-lactate excretion among the formula-fed and breastfed groups were found. After 4 weeks, D-lactate excretion did not differ between the two formula groups, but was higher in both formula groups than in breastfed infants. In all infants receiving La1, urinary D-lactate concentrations remained within the concentration ranges of age-matched healthy infants which had been determined in an earlier study using the same analytical method. Urinary L-lactate also did not vary over time or among groups. Supplementation of La1 to formula did not affect urinary lactate excretion and there is no evidence of an increased risk of lactic acidosis. Copyright 2008 S. Karger AG, Basel.

An empirical, graphical, and analytical study of the relationship between vegetation indices. [derived from LANDSAT data

NASA Technical Reports Server (NTRS)

Lautenschlager, L.; Perry, C. R., Jr. (Principal Investigator)

1981-01-01

The development of formulae for the reduction of multispectral scanner measurements to a single value (vegetation index) for predicting and assessing vegetative characteristics is addressed. The origin, motivation, and derivation of some four dozen vegetation indices are summarized. Empirical, graphical, and analytical techniques are used to investigate the relationships among the various indices. It is concluded that many vegetative indices are very similar, some being simple algebraic transforms of others.

[In vitro availability of minerals in infant foods with different protein source].

PubMed

Pérez-Llamas, F; Larqué, E; Marín, J F; Zamora, S

2001-01-01

As the result of the digestion process, it is produced at gastrointestinal level interactions between proteins-minerals and minerals-minerals that might modify the bioavailability of the nutrients initially designed for an adequate nutrition in infant formulas. The aim of the present study is to compare the in vitro availability of some minerals and trace elements (calcium, phosphorus, magnesium, iron and zinc) in infant formulas of initiation elaborated with different protein sources: formulas based on cow milk protein (whey-casein) versus vegetal protein (soy-based infant formulas). Also, for evaluating the effects of the different mineral supplementation in the availability of minerals, it was used infant formulas from two different manufacturers. Milk-protein based infant formulas showed for both manufacturers higher dialysis percentage (%) of phosphorus and zinc than the soy-protein based formulas. The availability of iron in the soy formula of the manufacturer A lowered significantly (P < 0.05) respect to the whey-casein based formula (9.6 +/- 2.3 versus 4.6 +/- 0.8), but not respect to the whey-casein formula of manufacturer B (9.6 +/- 1.1 versus 9.0 +/- 0.7), which might be due to the lowest proportion of phytic acid in this last commercial formula. Dialysability of all the minerals analysed from soy-protein based formulas showed significant differences depending on the manufacturer. The purification processes of the soy protein have a high repercussion in the mineral availability of soy-based infant formulas. It could be more interesting to use soy proteins more purified, with low level of phytic acid, in the elaboration of soy infants formulas, than the supplementation them with high amounts of minerals.

Bondi or not Bondi: the impact of resolution on accretion and drag force modelling for supermassive black holes

NASA Astrophysics Data System (ADS)

Beckmann, R. S.; Slyz, A.; Devriendt, J.

2018-07-01

Whilst in galaxy-size simulations, supermassive black holes (SMBHs) are entirely handled by sub-grid algorithms, computational power now allows the accretion radius of such objects to be resolved in smaller scale simulations. In this paper, we investigate the impact of resolution on two commonly used SMBH sub-grid algorithms; the Bondi-Hoyle-Lyttleton (BHL) formula for accretion on to a point mass, and the related estimate of the drag force exerted on to a point mass by a gaseous medium. We find that when the accretion region around the black hole scales with resolution, and the BHL formula is evaluated using local mass-averaged quantities, the accretion algorithm smoothly transitions from the analytic BHL formula (at low resolution) to a supply-limited accretion scheme (at high resolution). However, when a similar procedure is employed to estimate the drag force, it can lead to significant errors in its magnitude, and/or apply this force in the wrong direction in highly resolved simulations. At high Mach numbers and for small accretors, we also find evidence of the advective-acoustic instability operating in the adiabatic case, and of an instability developing around the wake's stagnation point in the quasi-isothermal case. Moreover, at very high resolution, and Mach numbers above M_∞ ≥ 3, the flow behind the accretion bow shock becomes entirely dominated by these instabilities. As a result, accretion rates on to the black hole drop by about an order of magnitude in the adiabatic case, compared to the analytic BHL formula.

Bondi or not Bondi: the impact of resolution on accretion and drag force modelling for Supermassive Black Holes

NASA Astrophysics Data System (ADS)

Beckmann, R. S.; Slyz, A.; Devriendt, J.

2018-04-01

Whilst in galaxy-size simulations, supermassive black holes (SMBH) are entirely handled by sub-grid algorithms, computational power now allows the accretion radius of such objects to be resolved in smaller scale simulations. In this paper, we investigate the impact of resolution on two commonly used SMBH sub-grid algorithms; the Bondi-Hoyle-Lyttleton (BHL) formula for accretion onto a point mass, and the related estimate of the drag force exerted onto a point mass by a gaseous medium. We find that when the accretion region around the black hole scales with resolution, and the BHL formula is evaluated using local mass-averaged quantities, the accretion algorithm smoothly transitions from the analytic BHL formula (at low resolution) to a supply limited accretion (SLA) scheme (at high resolution). However, when a similar procedure is employed to estimate the drag force it can lead to significant errors in its magnitude, and/or apply this force in the wrong direction in highly resolved simulations. At high Mach numbers and for small accretors, we also find evidence of the advective-acoustic instability operating in the adiabatic case, and of an instability developing around the wake's stagnation point in the quasi-isothermal case. Moreover, at very high resolution, and Mach numbers above M_∞ ≥ 3, the flow behind the accretion bow shock becomes entirely dominated by these instabilities. As a result, accretion rates onto the black hole drop by about an order of magnitude in the adiabatic case, compared to the analytic BHL formula.

Induction of cytochrome P450 1A by cow milk-based formula: a comparative study between human milk and formula

PubMed Central

Xu, Haibo; Rajesan, Ratheishan; Harper, Patricia; Kim, Richard B; Lonnerdal, Bo; Yang, Mingdong; Uematsu, Satoko; Hutson, Janine; Watson-MacDonell, Jo; Ito, Shinya

2005-01-01

During the treatment of neonatal apnea, formula-fed infants, compared to breastfed infants, show nearly three-fold increase in clearance of caffeine, a substrate of cytochrome P450 1A (CYP1A) and in part CYP3A4. However, human milk is known to contain higher concentrations of environmental pollutants than infant formula, which are potent CYP1A inducers. To gain insight into the mechanism underlying this apparent contradiction, we characterized CYP1A and CYP3A4 induction by human milk and cow milk-based infant formula. The mRNA and protein expression of CYP1A1/1A2 were significantly induced by cow milk-based formula, but not by human milk, in HepG2 cells. Luciferase reporter assay demonstrated that cow milk-based formula but not human milk activated aryl hydrocarbon receptor (AhR) significantly. The cotreatment of 3,4-dimethoxyflavone, an AhR antagonist, abolished the formula-induced CYP1A expression. In addition, AhR activation by dibenzo[a,h]anthracene, a potent AhR agonist, was significantly suppressed by infant formula and even more by human milk. In contrast, CYP3A4 mRNA expression was only mildly induced by formula and human milk. Consistently, neither formula nor human milk substantially activated pregnane X receptor (PXR). Effects of whey and soy protein-based formulas on the AhR–CYP1A and the PXR–CYP3A4 pathways were similar to those of cow milk-based formula. In conclusion, infant formula, but not human milk, enhances in vitro CYP1A expression via an AhR-mediated pathway, providing a potential mechanistic basis for the increased caffeine elimination in formula-fed infants. PMID:15997229

Induction of cytochrome P450 1A by cow milk-based formula: a comparative study between human milk and formula.

PubMed

Xu, Haibo; Rajesan, Ratheishan; Harper, Patricia; Kim, Richard B; Lonnerdal, Bo; Yang, Mingdong; Uematsu, Satoko; Hutson, Janine; Watson-MacDonell, Jo; Ito, Shinya

2005-09-01

During the treatment of neonatal apnea, formula-fed infants, compared to breastfed infants, show nearly three-fold increase in clearance of caffeine, a substrate of cytochrome P450 1A (CYP1A) and in part CYP3A4. However, human milk is known to contain higher concentrations of environmental pollutants than infant formula, which are potent CYP1A inducers. To gain insight into the mechanism underlying this apparent contradiction, we characterized CYP1A and CYP3A4 induction by human milk and cow milk-based infant formula. The mRNA and protein expression of CYP1A1/1A2 were significantly induced by cow milk-based formula, but not by human milk, in HepG2 cells. Luciferase reporter assay demonstrated that cow milk-based formula but not human milk activated aryl hydrocarbon receptor (AhR) significantly. The cotreatment of 3,4-dimethoxyflavone, an AhR antagonist, abolished the formula-induced CYP1A expression. In addition, AhR activation by dibenzo[a,h]anthracene, a potent AhR agonist, was significantly suppressed by infant formula and even more by human milk. In contrast, CYP3A4 mRNA expression was only mildly induced by formula and human milk. Consistently, neither formula nor human milk substantially activated pregnane X receptor (PXR). Effects of whey and soy protein-based formulas on the AhR-CYP1A and the PXR-CYP3A4 pathways were similar to those of cow milk-based formula. In conclusion, infant formula, but not human milk, enhances in vitro CYP1A expression via an AhR-mediated pathway, providing a potential mechanistic basis for the increased caffeine elimination in formula-fed infants.

Mass Distribution and Gravitational Potential of the Milky Way

NASA Astrophysics Data System (ADS)

Ninković, Slobodan

2017-04-01

Models of mass distribution in the Milky Way are discussed where those yielding the potential analytically are preferred. It is noted that there are three main contributors to the Milky Way potential: bulge, disc and dark halo. In the case of the disc the Miyamoto-Nagai formula, as simple enough, has shown as a very good solution, but it has not been able to satisfy all requirements. Therefore, improvements, such as adding new terms or combining several Miyamoto-Nagai terms, have been attempted. Unlike the disc, in studying the bulge and dark halo the flattening is usually neglected, which offers the possibility of obtaining an exact solution of the Poisson equation. It is emphasized that the Hernquist formula, used very often for the bulge potential, is a special case of another formula and the properties of that formula are analysed. In the case of the dark halo, the slopes of its cumulative mass for the inner and outer parts are explained through a new formalism presented here for the first time.

A Malaria Transmission Model with Temperature-Dependent Incubation Period.

PubMed

Wang, Xiunan; Zhao, Xiao-Qiang

2017-05-01

Malaria is an infectious disease caused by Plasmodium parasites and is transmitted among humans by female Anopheles mosquitoes. Climate factors have significant impact on both mosquito life cycle and parasite development. To consider the temperature sensitivity of the extrinsic incubation period (EIP) of malaria parasites, we formulate a delay differential equations model with a periodic time delay. We derive the basic reproduction ratio [Formula: see text] and establish a threshold type result on the global dynamics in terms of [Formula: see text], that is, the unique disease-free periodic solution is globally asymptotically stable if [Formula: see text]; and the model system admits a unique positive periodic solution which is globally asymptotically stable if [Formula: see text]. Numerically, we parameterize the model with data from Maputo Province, Mozambique, and simulate the long-term behavior of solutions. The simulation result is consistent with the obtained analytic result. In addition, we find that using the time-averaged EIP may underestimate the basic reproduction ratio.

Theory comparison and numerical benchmarking on neoclassical toroidal viscosity torque

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

Wang, Zhirui; Park, Jong-Kyu; Logan, Nikolas

Systematic comparison and numerical benchmarking have been successfully carried out among three different approaches of neoclassical toroidal viscosity (NTV) theory and the corresponding codes: IPEC-PENT is developed based on the combined NTV theory but without geometric simplifications [Park et al., Phys. Rev. Lett. 102, 065002 (2009)]; MARS-Q includes smoothly connected NTV formula [Shaing et al., Nucl. Fusion 50, 025022 (2010)] based on Shaing's analytic formulation in various collisionality regimes; MARS-K, originally computing the drift kinetic energy, is upgraded to compute the NTV torque based on the equivalence between drift kinetic energy and NTV torque [J.-K. Park, Phys. Plasma 18, 110702more » (2011)]. The derivation and numerical results both indicate that the imaginary part of drift kinetic energy computed by MARS-K is equivalent to the NTV torque in IPEC-PENT. In the benchmark of precession resonance between MARS-Q and MARS-K/IPEC-PENT, the agreement and correlation between the connected NTV formula and the combined NTV theory in different collisionality regimes are shown for the first time. Additionally, both IPEC-PENT and MARS-K indicate the importance of the bounce harmonic resonance which can greatly enhance the NTV torque when E×B drift frequency reaches the bounce resonance condition.« less

New Proofs of Some q-Summation and q-Transformation Formulas

PubMed Central

Liu, Xian-Fang; Bi, Ya-Qing; Luo, Qiu-Ming

2014-01-01

We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of q-series based on our expectation formula. Although these formulas in themselves are not the probability results, the proofs given are based on probabilistic concepts. PMID:24895675

Recent trends in analytical procedures in forensic toxicology.

PubMed

Van Bocxlaer, Jan F

2005-12-01

Forensic toxicology is a very demanding discipline,heavily dependent on good analytical techniques. That is why new trends appear continuously. In the past years. LC-MS has revolutionized target compound analysis and has become the trend, also in toxicology. In LC-MS screening analysis, things are less straightforward and several approaches exist. One promising approach based on accurate LC-MSTOF mass measurements and elemental formula based library searches is discussed. This way of screening has already proven its applicability but at the same time it became obvious that a single accurate mass measurement lacks some specificity when using large compound libraries. CE too is a reemerging approach. The increasingly polar and ionic molecules encountered make it a worthwhile addition to e.g. LC, as illustrated for the analysis of GHB. A third recent trend is the use of MALDI mass spectrometry for small molecules. It is promising for its ease-of-use and high throughput. Unfortunately, re-ports of disappointment but also accomplishment, e.g. the quantitative analysis of LSD as discussed here, alternate, and it remains to be seen whether MALDI really will establish itself. Indeed, not all new trends will prove themselves but the mere fact that many appear in the world of analytical toxicology nowadays is, in itself, encouraging for the future of (forensic) toxicology.

Novel design configurations for permanent magnet wind generators

NASA Astrophysics Data System (ADS)

Chen, Yicheng

2004-12-01

The aim of this research is to search for optimal designs of permanent magnet (PM) wind generators of different topologies. The dissertation deals with the development of analytical design equations and formulas for PM wind generators of different topologies, including equivalent magnetic circuit model for magnets, calculation of leakage flux, influence of d-q axis armature reaction, flux waveform analysis, as well as performance verification. 3-D and simplified 2-D finite element analysis is used to enhance the design precision, by which analytical formulas are modified. A new and improved formula is proposed for lamination loss calculations, based on a large experimental data set provided by steel manufacturers. The temperature stability of NdFeB magnets is analyzed and some proposals for eliminating irreversible demagnetization are presented. Two existing experimental machines are used to validate the design equations. The genetic algorithms are used to investigate the multi-objective design optimization of PM wind generators for a high efficiency and light-weight design. The reasoning behind the selection of the objective functions, design variables and constraints are given as guidance for the PM wind generator optimum design. The implementation of the genetic algorithm is also given. A comparison of PM wind generators of different topologies is presented. Conclusions are drawn for topology selections of PM wind generators. The group of soft magnetic composites (SMC) has recently been expanded by the introduction of new materials with significantly improved frequency properties. This has made SMC a viable alternative to steel laminations for a range of new applications, especially axial-flux wind generators. The isotropic nature of the SMC combined with the unique shaping possibilities opens up new design solutions for axial-flux wind generators. Through careful design, an axial-flux PM wind generator with SMC core is built and tested, demonstrating the advantages of better performance, reduced size and weight, fewer parts and lower cost.

An Analytic Solution to the Computation of Power and Sample Size for Genetic Association Studies under a Pleiotropic Mode of Inheritance.

PubMed

Gordon, Derek; Londono, Douglas; Patel, Payal; Kim, Wonkuk; Finch, Stephen J; Heiman, Gary A

2016-01-01

Our motivation here is to calculate the power of 3 statistical tests used when there are genetic traits that operate under a pleiotropic mode of inheritance and when qualitative phenotypes are defined by use of thresholds for the multiple quantitative phenotypes. Specifically, we formulate a multivariate function that provides the probability that an individual has a vector of specific quantitative trait values conditional on having a risk locus genotype, and we apply thresholds to define qualitative phenotypes (affected, unaffected) and compute penetrances and conditional genotype frequencies based on the multivariate function. We extend the analytic power and minimum-sample-size-necessary (MSSN) formulas for 2 categorical data-based tests (genotype, linear trend test [LTT]) of genetic association to the pleiotropic model. We further compare the MSSN of the genotype test and the LTT with that of a multivariate ANOVA (Pillai). We approximate the MSSN for statistics by linear models using a factorial design and ANOVA. With ANOVA decomposition, we determine which factors most significantly change the power/MSSN for all statistics. Finally, we determine which test statistics have the smallest MSSN. In this work, MSSN calculations are for 2 traits (bivariate distributions) only (for illustrative purposes). We note that the calculations may be extended to address any number of traits. Our key findings are that the genotype test usually has lower MSSN requirements than the LTT. More inclusive thresholds (top/bottom 25% vs. top/bottom 10%) have higher sample size requirements. The Pillai test has a much larger MSSN than both the genotype test and the LTT, as a result of sample selection. With these formulas, researchers can specify how many subjects they must collect to localize genes for pleiotropic phenotypes. © 2017 S. Karger AG, Basel.

A fast indirect method to compute functions of genomic relationships concerning genotyped and ungenotyped individuals, for diversity management.

PubMed

Colleau, Jean-Jacques; Palhière, Isabelle; Rodríguez-Ramilo, Silvia T; Legarra, Andres

2017-12-01

Pedigree-based management of genetic diversity in populations, e.g., using optimal contributions, involves computation of the [Formula: see text] type yielding elements (relationships) or functions (usually averages) of relationship matrices. For pedigree-based relationships [Formula: see text], a very efficient method exists. When all the individuals of interest are genotyped, genomic management can be addressed using the genomic relationship matrix [Formula: see text]; however, to date, the computational problem of efficiently computing [Formula: see text] has not been well studied. When some individuals of interest are not genotyped, genomic management should consider the relationship matrix [Formula: see text] that combines genotyped and ungenotyped individuals; however, direct computation of [Formula: see text] is computationally very demanding, because construction of a possibly huge matrix is required. Our work presents efficient ways of computing [Formula: see text] and [Formula: see text], with applications on real data from dairy sheep and dairy goat breeding schemes. For genomic relationships, an efficient indirect computation with quadratic instead of cubic cost is [Formula: see text], where Z is a matrix relating animals to genotypes. For the relationship matrix [Formula: see text], we propose an indirect method based on the difference between vectors [Formula: see text], which involves computation of [Formula: see text] and of products such as [Formula: see text] and [Formula: see text], where [Formula: see text] is a working vector derived from [Formula: see text]. The latter computation is the most demanding but can be done using sparse Cholesky decompositions of matrix [Formula: see text], which allows handling very large genomic and pedigree data files. Studies based on simulations reported in the literature show that the trends of average relationships in [Formula: see text] and [Formula: see text] differ as genomic selection proceeds. When selection is based on genomic relationships but management is based on pedigree data, the true genetic diversity is overestimated. However, our tests on real data from sheep and goat obtained before genomic selection started do not show this. We present efficient methods to compute elements and statistics of the genomic relationships [Formula: see text] and of matrix [Formula: see text] that combines ungenotyped and genotyped individuals. These methods should be useful to monitor and handle genomic diversity.

The neutron-gamma Feynman variance to mean approach: Gamma detection and total neutron-gamma detection (theory and practice)

NASA Astrophysics Data System (ADS)

Chernikova, Dina; Axell, Kåre; Avdic, Senada; Pázsit, Imre; Nordlund, Anders; Allard, Stefan

2015-05-01

Two versions of the neutron-gamma variance to mean (Feynman-alpha method or Feynman-Y function) formula for either gamma detection only or total neutron-gamma detection, respectively, are derived and compared in this paper. The new formulas have particular importance for detectors of either gamma photons or detectors sensitive to both neutron and gamma radiation. If applied to a plastic or liquid scintillation detector, the total neutron-gamma detection Feynman-Y expression corresponds to a situation where no discrimination is made between neutrons and gamma particles. The gamma variance to mean formulas are useful when a detector of only gamma radiation is used or when working with a combined neutron-gamma detector at high count rates. The theoretical derivation is based on the Chapman-Kolmogorov equation with the inclusion of general reactions and corresponding intensities for neutrons and gammas, but with the inclusion of prompt reactions only. A one energy group approximation is considered. The comparison of the two different theories is made by using reaction intensities obtained in MCNPX simulations with a simplified geometry for two scintillation detectors and a 252Cf-source. In addition, the variance to mean ratios, neutron, gamma and total neutron-gamma are evaluated experimentally for a weak 252Cf neutron-gamma source, a 137Cs random gamma source and a 22Na correlated gamma source. Due to the focus being on the possibility of using neutron-gamma variance to mean theories for both reactor and safeguards applications, we limited the present study to the general analytical expressions for Feynman-alpha formulas.

Determination of Five Chemical Markers in DF Formula, the Herbal Composition of Ephedra intermedia, Rheum palmatum, and Lithospermum erythrorhizon, Using High-performance Liquid Chromatography-ultraviolet Detection

PubMed Central

Jeong, Birang; Roh, Jong Seong; Yoon, Michung; Yoon, Yoosik; Shin, Soon Shik; Cho, Hyun Joo; Kwon, Yong Soo; Yang, Heejung

2018-01-01

Background: DF formula is a herbal preparation comprised three medicinal herbs, namely, Ephedra intermedia, Rheum palmatum, and Lithospermum erythrorhizon, which is being used for the treatment of obesity and liver fibrosis in Korean local clinics. Objective: Since the abovementioned three herbs exist with different proportions in DF formula and their chemical markers have different physiochemical properties; it is quite challenging to develop an analytical methodology for the determination of these chemical markers. Materials and Methods: For the analysis of the three herbs, five chemicals, (+)-pseudoephedrine (1) and (−)-ephedrine (2) for E. intermedia, aloe-emodin (3), and chrysophanol (4) for R. palmatum, and shikonin (5) for L. erythrorhizon, were selected for method validation of DF formula, and the analytical conditions were optimized and validated using high-performance liquid chromatography coupled with an ultraviolet detector (HPLC-UV). Results: The specificities for the five compounds 1–5 were determined by their UV absorption spectra (1–4: 215 nm and 5: 520 nm). Their calibration curves showed good linear regressions with high correlation coefficient values (R2 > 0.9997). The limits of detection of these five markers were in the range 0.4–2.1 ng/mL, with the exception of 5 (12.7 ng/mL). The intraday variability for all the chemical markers was less than a Relative standard deviation (RSD) of 3%, except for 5 (RSD = 12.6%). In the case of interday analysis, 1 (1.0%), 2 (3.1%), and 4 (3.7%) showed much lower variabilities (RSD < 5%) than 3 (7.6%) and 5 (8.2%). Moreover, the five chemical markers showed good recoveries with good accuracies in the range of 90%–110%. Conclusions: The developed HPLC-UV method for the determination of the five chemical markers of the components of DF formula was validated. SUMMARY DF formula, the herbal composition of Ephedra intermedia, Rheum palmatum and Lithospermum erythrorhizonFive chemical markers in DF formula were (+)-pseudoephedrine (1) and (-)-ephedrine (2) for E. intermedia, aloe-emodin (3) and chrysopanol (4) for R. palmatum, and shikonin (5) for L. erythrorhizon, with quite different physico-chemical propertiesFive chemical markers in DF formula were determined by HPLC-UV Abbreviations used: EP: (−)-ephedrine; PSEP: (+)-pseudoephedrine; HPLC: High-performance liquid chromatography; UV: Ultraviolet; LOD: Limit of detection; LOQ: Limit of quantification; RSD: Relative standard deviation. PMID:29720825

Chemicals identified in human biological media: a data base. Third annual report, October 1981

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

Cone, M.V.; Baldauf, M.F.; Martin, F.M.

1981-12-01

Part 2 contains the data base in tabular format. There are two sections, the first with records on nondrug substances, and the second with records on drugs. Chemicals in each section are arranged alphabetically by CAS preferred name, CAS registry number, formula, atomic weight, melting point, boiling point, and vapor pressure. Tissues are listed alphabetically with exposure route, analytical method, number of cases, range, and mean - when available in the source document. A variety of information may also be included that is pertinent to the range and mean as well as experimental design, demography, health effects, pathology, morphology, andmore » toxicity. Review articles are included in the data base; however, no data have been extracted from such documents because the original research articles are included.« less

Optimization with artificial neural network systems - A mapping principle and a comparison to gradient based methods

NASA Technical Reports Server (NTRS)

Leong, Harrison Monfook

1988-01-01

General formulae for mapping optimization problems into systems of ordinary differential equations associated with artificial neural networks are presented. A comparison is made to optimization using gradient-search methods. The performance measure is the settling time from an initial state to a target state. A simple analytical example illustrates a situation where dynamical systems representing artificial neural network methods would settle faster than those representing gradient-search. Settling time was investigated for a more complicated optimization problem using computer simulations. The problem was a simplified version of a problem in medical imaging: determining loci of cerebral activity from electromagnetic measurements at the scalp. The simulations showed that gradient based systems typically settled 50 to 100 times faster than systems based on current neural network optimization methods.

Infant exposure of perfluorinated compounds: levels in breast milk and commercial baby food.

PubMed

Llorca, Marta; Farré, Marinella; Picó, Yolanda; Teijón, Marisa Lopez; Alvarez, Juan G; Barceló, Damià

2010-08-01

In this study, an analytical method to determine six perfluorinated compounds (PFCs) based on alkaline digestion and solid phase extraction (SPE) followed by liquid chromatography-quadrupole-linear ion trap mass spectrometry (LC-QqLIT-MS) was validated for the analysis of human breast milk, milk infant formulas and cereals baby food. The average recoveries of the different matrices were in general higher than 70% with a relative standard deviation (RSD) lower than 21% and method limits of detection (MLOD) ranging from 1.2 to 362 ng/L for the different compounds and matrices. The method was applied to investigate the occurrence of PFCs in 20 samples of human breast milk, and 5 samples of infant formulas and cereal baby food (3 brands of commercial milk infant formulas and 2 brands of cereals baby food). Breast milk samples were collected in 2008 from donors living in Barcelona city (Spain) on the 40 days postpartum. Perfluorooctanesulfonate (PFOS) and perfluoro-7-methyloctanoic acid (i,p-PFNA) were predominant being present in the 95% of breast milk samples. Perfluorooctanoic acid (PFOA) was quantified in 8 of the 20 breast milk samples at concentrations in the range of 21-907 ng/L. Commercial formulas and food were purchased also in 2009 from a retail store. The six PFCs were detected in all brands of milk infant formulas and cereals baby food analyzed, being perfluorodecanoic acid (PFDA), PFOS, PFOA and i,p-PFNA the compounds detected in higher concentrations (up to 1289 ng/kg). PFCs presence can be associated to possible migration from packaging and containers during production processes. Finally, based on estimated body weight and newborn intake, PFOS and PFOA daily intakes and risk indexes (RI) were estimated for the firsts 6 month of life. We found that ingestion rates of PFOS and PFOA, with exception of one breast milk sample did not exceed the tolerable daily intake (TDI) recommended by the EFSA. However, more research is needed in order to assess possible risk associated to PFCs contamination during early stages of life. Copyright 2010 Elsevier Ltd. All rights reserved.

Methodological issues regarding power of classical test theory (CTT) and item response theory (IRT)-based approaches for the comparison of patient-reported outcomes in two groups of patients - a simulation study

PubMed Central

2010-01-01

Background Patients-Reported Outcomes (PRO) are increasingly used in clinical and epidemiological research. Two main types of analytical strategies can be found for these data: classical test theory (CTT) based on the observed scores and models coming from Item Response Theory (IRT). However, whether IRT or CTT would be the most appropriate method to analyse PRO data remains unknown. The statistical properties of CTT and IRT, regarding power and corresponding effect sizes, were compared. Methods Two-group cross-sectional studies were simulated for the comparison of PRO data using IRT or CTT-based analysis. For IRT, different scenarios were investigated according to whether items or person parameters were assumed to be known, to a certain extent for item parameters, from good to poor precision, or unknown and therefore had to be estimated. The powers obtained with IRT or CTT were compared and parameters having the strongest impact on them were identified. Results When person parameters were assumed to be unknown and items parameters to be either known or not, the power achieved using IRT or CTT were similar and always lower than the expected power using the well-known sample size formula for normally distributed endpoints. The number of items had a substantial impact on power for both methods. Conclusion Without any missing data, IRT and CTT seem to provide comparable power. The classical sample size formula for CTT seems to be adequate under some conditions but is not appropriate for IRT. In IRT, it seems important to take account of the number of items to obtain an accurate formula. PMID:20338031

Nationwide Multicenter Reference Interval Study for 28 Common Biochemical Analytes in China.

PubMed

Xia, Liangyu; Chen, Ming; Liu, Min; Tao, Zhihua; Li, Shijun; Wang, Liang; Cheng, Xinqi; Qin, Xuzhen; Han, Jianhua; Li, Pengchang; Hou, Li'an; Yu, Songlin; Ichihara, Kiyoshi; Qiu, Ling

2016-03-01

A nationwide multicenter study was conducted in the China to explore sources of variation of reference values and establish reference intervals for 28 common biochemical analytes, as a part of the International Federation of Clinical Chemistry and Laboratory Medicine, Committee on Reference Intervals and Decision Limits (IFCC/C-RIDL) global study on reference values. A total of 3148 apparently healthy volunteers were recruited in 6 cities covering a wide area in China. Blood samples were tested in 2 central laboratories using Beckman Coulter AU5800 chemistry analyzers. Certified reference materials and value-assigned serum panel were used for standardization of test results. Multiple regression analysis was performed to explore sources of variation. Need for partition of reference intervals was evaluated based on 3-level nested ANOVA. After secondary exclusion using the latent abnormal values exclusion method, reference intervals were derived by a parametric method using the modified Box-Cox formula. Test results of 20 analytes were made traceable to reference measurement procedures. By the ANOVA, significant sex-related and age-related differences were observed in 12 and 12 analytes, respectively. A small regional difference was observed in the results for albumin, glucose, and sodium. Multiple regression analysis revealed BMI-related changes in results of 9 analytes for man and 6 for woman. Reference intervals of 28 analytes were computed with 17 analytes partitioned by sex and/or age. In conclusion, reference intervals of 28 common chemistry analytes applicable to Chinese Han population were established by use of the latest methodology. Reference intervals of 20 analytes traceable to reference measurement procedures can be used as common reference intervals, whereas others can be used as the assay system-specific reference intervals in China.

Nationwide Multicenter Reference Interval Study for 28 Common Biochemical Analytes in China

PubMed Central

Xia, Liangyu; Chen, Ming; Liu, Min; Tao, Zhihua; Li, Shijun; Wang, Liang; Cheng, Xinqi; Qin, Xuzhen; Han, Jianhua; Li, Pengchang; Hou, Li’an; Yu, Songlin; Ichihara, Kiyoshi; Qiu, Ling

2016-01-01

Abstract A nationwide multicenter study was conducted in the China to explore sources of variation of reference values and establish reference intervals for 28 common biochemical analytes, as a part of the International Federation of Clinical Chemistry and Laboratory Medicine, Committee on Reference Intervals and Decision Limits (IFCC/C-RIDL) global study on reference values. A total of 3148 apparently healthy volunteers were recruited in 6 cities covering a wide area in China. Blood samples were tested in 2 central laboratories using Beckman Coulter AU5800 chemistry analyzers. Certified reference materials and value-assigned serum panel were used for standardization of test results. Multiple regression analysis was performed to explore sources of variation. Need for partition of reference intervals was evaluated based on 3-level nested ANOVA. After secondary exclusion using the latent abnormal values exclusion method, reference intervals were derived by a parametric method using the modified Box–Cox formula. Test results of 20 analytes were made traceable to reference measurement procedures. By the ANOVA, significant sex-related and age-related differences were observed in 12 and 12 analytes, respectively. A small regional difference was observed in the results for albumin, glucose, and sodium. Multiple regression analysis revealed BMI-related changes in results of 9 analytes for man and 6 for woman. Reference intervals of 28 analytes were computed with 17 analytes partitioned by sex and/or age. In conclusion, reference intervals of 28 common chemistry analytes applicable to Chinese Han population were established by use of the latest methodology. Reference intervals of 20 analytes traceable to reference measurement procedures can be used as common reference intervals, whereas others can be used as the assay system-specific reference intervals in China. PMID:26945390

Fractional Talbot field and of finite gratings: compact analytical formulation.

PubMed

Arrizón, V; Rojo-Velázquez, G

2001-06-01

We present a compact analytical formulation for the fractional Talbot effect at the paraxial domain of a finite grating. Our results show that laterally shifted distorted images of the grating basic cell form the Fresnel field at a fractional Talbot plane of the grating. Our formulas give the positions of those images and show that they are given by the convolution of the nondistorted cells (modulated by a quadratic phase factor) with the Fourier transform of the finite-grating pupil.

From medical tradition to traditional medicine: A Tibetan formula in the European framework.

PubMed

Schwabl, Herbert; Vennos, Cécile

2015-06-05

The increasing prevalence of complex multi-factorial chronic diseases and multimorbidity reveals the need for an enlargement of the therapeutic options. Potent multicompound herbal formulations from traditional medicine systems such as Tibetan Medicine might meet the requirements. With its practice over the centuries Tibetan Medicine is one of the important medical heritages of the world. In the 20th century Tibetan formulas came to Switzerland, where the formula Gabur-25 was then registered as medicine in 1977 (Padma 28, Swissmedic No 35872). The new European directive 2004/24/EC opened the avenue for traditional herbal medicinal products and registrations followed in Austria (HERB-00037) and the UK (39568/0001). The aim of this review was to analyse not only the critical points and hazards but also chances that occur in the endeavour of bringing a ethnopharmacological based preparation to the market within a modern Western medical and regulatory framework and to discuss the necessary transformation steps from a traditional herbal formula towards a modern pharmaceutical product with the example of the Tibetan formula Gabur-25. The historic transformation process from the 19th to the 21st century is analysed, using the registration documents and other material from the library of Padma AG, Hinwil, Switzerland. The transformation of a traditional formula into a modern traditional herbal medicinal product according to the present EU regulations is a multi faceted process. The modern indication represents only a small part of the possible traditional indications. Quality and product labelling has to be adopted to modern standards. The formula, once registered, is a fixed combination of herbal and mineral ingredients. Contrary to this the concept of Asian medical tradition allows a certain flexibility in the composition of an herbal formula. The ingredients are constantly adapted to local conditions, availability of raw material and therapeutic situation. The example shows that in principle complex herbal formulas from Asian medicine can meet the requirements of the European regime of traditional herbal medicinal products. A structured process of transformation from a traditional herbal formula to a modern medicinal product has to include selection of a suitable formula, development of an analytic concept and selection of a suitable indication with regard to the empirical set of possible indications. To extend the range of high quality medicinal products from other medical traditions within the European context the European legislators have to re-evaluate the imposed restrictions given in directive 2004/24/EC. Without amendment of the prerequisite of 15 years documented use in the EU and the limitation of indications for traditional herbal medicinal products, European citizens will be excluded from access to high quality medical traditions with their accumulated empirical knowledge. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Lattice QCD and the timelike pion form factor.

PubMed

Meyer, Harvey B

2011-08-12

We present a formula that allows one to calculate the pion form factor in the timelike region 2m(π) ≤ √(s) ≤ 4m(π) in lattice QCD. The form factor quantifies the contribution of two-pion states to the vacuum polarization. It must be known very accurately in order to reduce the theoretical uncertainty on the anomalous magnetic moment of the muon. At the same time, the formula constitutes a rare example where, in a restricted kinematic regime, the spectral function of a conserved current can be determined from Euclidean observables without an explicit analytic continuation.

Minimum-Cost Aircraft Descent Trajectories with a Constrained Altitude Profile

NASA Technical Reports Server (NTRS)

Wu, Minghong G.; Sadovsky, Alexander V.

2015-01-01

An analytical formula for solving the speed profile that accrues minimum cost during an aircraft descent with a constrained altitude profile is derived. The optimal speed profile first reaches a certain speed, called the minimum-cost speed, as quickly as possible using an appropriate extreme value of thrust. The speed profile then stays on the minimum-cost speed as long as possible, before switching to an extreme value of thrust for the rest of the descent. The formula is applied to an actual arrival route and its sensitivity to winds and airlines' business objectives is analyzed.

Spatial derivatives of flow quantities behind curved shocks of all strengths

NASA Technical Reports Server (NTRS)

Darden, C. M.

1984-01-01

Explicit formulas in terms of shock curvature are developed for spatial derivatives of flow quantities behind a curved shock for two-dimensional inviscid steady flow. Factors which yield the equations indeterminate as the shock strength approaches 0 have been cancelled analytically so that formulas are valid for shocks of any strength. An application for the method is shown in the solution of shock coalescence when nonaxisymmetric effects are felt through derivatives in the circumferential direction. The solution of this problem requires flow derivatives behind the shock in both the axial and radial direction.

Sound velocity in five-component air mixtures of various densities

NASA Astrophysics Data System (ADS)

Bogdanova, N. V.; Rydalevskaya, M. A.

2018-05-01

The local equilibrium flows of five-component air mixtures are considered. Gas dynamic equations are derived from the kinetic equations for aggregate values of collision invariants. It is shown that the traditional formula for sound velocity is true in air mixtures considered with the chemical reactions and the internal degrees of freedom. This formula connects the square of sound velocity with pressure and density. However, the adiabatic coefficient is not constant under existing conditions. The analytical expression for this coefficient is obtained. The examples of its calculation in air mixtures of various densities are presented.

Analytical theory of coherent synchrotron radiation wakefield of short bunches shielded by conducting parallel plates

NASA Astrophysics Data System (ADS)

Stupakov, Gennady; Zhou, Demin

2016-04-01

We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. All our formulas are benchmarked against numerical simulations with the CSRZ computer code.

Analytical effective tensor for flow-through composites

DOEpatents

Sviercoski, Rosangela De Fatima [Los Alamos, NM

2012-06-19

A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective tensor K.sup.a suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.

Analytical theory of coherent synchrotron radiation wakefield of short bunches shielded by conducting parallel plates

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

Stupakov, Gennady; Zhou, Demin

2016-04-21

We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. All our formulas are benchmarked against numerical simulations with the CSRZ computer code.

Determination of Free and Total Choline and Carnitine in Infant Formula and Adult/Pediatric Nutritional Formula by Liquid Chromatography/Tandem Mass Spectrometry (LC/MS/MS): Single-Laboratory Validation, First Action 2015.10.

PubMed

Ellingson, David J; Shippar, Jeffrey J; Gilmore, Justin M

2016-01-01

Analytical methods for the analysis of both L-carnitine and choline are needed for reliable and accurate determination in infant formula and adult/pediatric nutritional formula. These compounds are different in how they are utilized by the human body, but are structurally similar. L-carnitine and choline are quaternary ammonium compounds, enabling both to be retained under acidic conditions with strong cation exchange (SCX) chromatography. This method analyzes both compounds simultaneously as either the free forms or as a total amount that includes bound sources such as phosphatidylcholine or acetylcarnitine. The free analysis consists of water extraction and analysis by LC/MS/MS, while the total analysis consists of extraction by acid assisted microwave hydrolysis and analysis by LC/MS/MS. Calibration standards used for calculations are extracted with all samples in the batch. A single laboratory validation (SLV) was performed following the guidelines of the AOAC Stakeholder Panel on Infant Formula and Adult Nutritionals (SPIFAN) utilizing the kit of materials provided. The results achieved meet the requirements of SMPR 2012.010 and 2012.013 for L-carnitine and total choline, respectively.

Correlation between cystatin C-based formulas, Schwartz formula and urinary creatinine clearance for glomerular filtration rate estimation in children with kidney disease.

PubMed

Safaei-Asl, Afshin; Enshaei, Mercede; Heydarzadeh, Abtin; Maleknejad, Shohreh

2016-01-01

Assessment of glomerular filtration rate (GFR) is an important tool for monitoring renal function. Regarding to limitations in available methods, we intended to calculate GFR by cystatin C (Cys C) based formulas and determine correlation rate of them with current methods. We studied 72 children (38 boys and 34 girls) with renal disorders. The 24 hour urinary creatinine (Cr) clearance was the gold standard method. GFR was measured with Schwartz formula and Cys C-based formulas (Grubb, Hoek, Larsson and Simple). Then correlation rates of these formulas were determined. Using Pearson correlation coefficient, a significant positive correlation between all formulas and the standard method was seen (R(2) for Schwartz, Hoek, Larsson, Grubb and Simple formula was 0.639, 0.722, 0.705, 0.712, 0.722, respectively) (P<0.001). Cys C-based formulas could predict the variance of standard method results with high power. These formulas had correlation with Schwarz formula by R(2) 0.62-0.65 (intermediate correlation). Using linear regression and constant (y-intercept), it revealed that Larsson, Hoek and Grubb formulas can estimate GFR amounts with no statistical difference compared with standard method; but Schwartz and Simple formulas overestimate GFR. This study shows that Cys C-based formulas have strong relationship with 24 hour urinary Cr clearance. Hence, they can determine GFR in children with kidney injury, easier and with enough accuracy. It helps the physician to diagnosis of renal disease in early stages and improves the prognosis.

Reference Intervals of Hematology and Clinical Chemistry Analytes for 1-Year-Old Korean Children

PubMed Central

Lee, Hye Ryun; Roh, Eun Youn; Chang, Ju Young

2016-01-01

Background Reference intervals need to be established according to age. We established reference intervals of hematology and chemistry from community-based healthy 1-yr-old children and analyzed their iron status according to the feeding methods during the first six months after birth. Methods A total of 887 children who received a medical check-up between 2010 and 2014 at Boramae Hospital (Seoul, Korea) were enrolled. A total of 534 children (247 boys and 287 girls) were enrolled as reference individuals after the exclusion of data obtained from children with suspected iron deficiency. Hematology and clinical chemistry analytes were measured, and the reference value of each analyte was estimated by using parametric (mean±2 SD) or nonparametric methods (2.5-97.5th percentile). Iron, total iron-binding capacity, and ferritin were measured, and transferrin saturation was calculated. Results As there were no differences in the mean values between boys and girls, we established the reference intervals for 1-yr-old children regardless of sex. The analysis of serum iron status according to feeding methods during the first six months revealed higher iron, ferritin, and transferrin saturation levels in children exclusively or mainly fed formula than in children exclusively or mainly fed breast milk. Conclusions We established reference intervals of hematology and clinical chemistry analytes from community-based healthy children at one year of age. These reference intervals will be useful for interpreting results of medical check-ups at one year of age. PMID:27374715

Reference Intervals of Hematology and Clinical Chemistry Analytes for 1-Year-Old Korean Children.

PubMed

Lee, Hye Ryun; Shin, Sue; Yoon, Jong Hyun; Roh, Eun Youn; Chang, Ju Young

2016-09-01

Reference intervals need to be established according to age. We established reference intervals of hematology and chemistry from community-based healthy 1-yr-old children and analyzed their iron status according to the feeding methods during the first six months after birth. A total of 887 children who received a medical check-up between 2010 and 2014 at Boramae Hospital (Seoul, Korea) were enrolled. A total of 534 children (247 boys and 287 girls) were enrolled as reference individuals after the exclusion of data obtained from children with suspected iron deficiency. Hematology and clinical chemistry analytes were measured, and the reference value of each analyte was estimated by using parametric (mean±2 SD) or nonparametric methods (2.5-97.5th percentile). Iron, total iron-binding capacity, and ferritin were measured, and transferrin saturation was calculated. As there were no differences in the mean values between boys and girls, we established the reference intervals for 1-yr-old children regardless of sex. The analysis of serum iron status according to feeding methods during the first six months revealed higher iron, ferritin, and transferrin saturation levels in children exclusively or mainly fed formula than in children exclusively or mainly fed breast milk. We established reference intervals of hematology and clinical chemistry analytes from community-based healthy children at one year of age. These reference intervals will be useful for interpreting results of medical check-ups at one year of age.

Analytical dose evaluation of neutron and secondary gamma-ray skyshine from nuclear facilities

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

Hayashi, K.; Nakamura, T.

1985-11-01

The skyshine dose distributions of neutron and secondary gamma rays were calculated systematically using the Monte Carlo method for distances up to 2 km from the source. The energy of source neutrons ranged from thermal to 400 MeV; their emission angle from 0 to 90 deg from the ver tical was treated with a distribution of the direction cosine containing five equal intervals. Calculated dose distributions D(r) were fitted to the formula; D(r) = Q exp (-r/lambda)/r. The value of Q and lambda are slowly varied functions of energy. This formula was applied to the benchmark problems of neutron skyshinemore » from fission, fusion, and accelerator facilities, and good agreement was achieved. This formula will be quite useful for shielding designs of various nuclear facilities.« less

Cloud effects on ultraviolet photoclimatology

NASA Technical Reports Server (NTRS)

Green, A. E. S.; Spinhirne, J. D.

1978-01-01

The purpose of this study is to quantify for the needs of photobiology the influence of clouds upon the ultraviolet spectral irradiance reaching the ground. Towards this end, analytic formulas are developed which approximately characterize the influence of clouds upon total solar radiation. These may be used in conjunction with a solar pyranometer to assign an effective visual optical depth for the cloud cover. A formula is also developed which characterizes the influence of the optical depth of clouds upon the UV spectral irradiance in the 280-340 nm region. Thus total solar energy observations to assign cloud optical properties can be used to calculate the UV spectral irradiance at the ground in the presence of these clouds. As incidental by-products of this effort, convenient formulas are found for the direct and diffuse components of total solar energy.

Throughput and delay analysis of IEEE 802.15.6-based CSMA/CA protocol.

PubMed

Ullah, Sana; Chen, Min; Kwak, Kyung Sup

2012-12-01

The IEEE 802.15.6 is a new communication standard on Wireless Body Area Network (WBAN) that focuses on a variety of medical, Consumer Electronics (CE) and entertainment applications. In this paper, the throughput and delay performance of the IEEE 802.15.6 is presented. Numerical formulas are derived to determine the maximum throughput and minimum delay limits of the IEEE 802.15.6 for an ideal channel with no transmission errors. These limits are derived for different frequency bands and data rates. Our analysis is validated by extensive simulations using a custom C+ + simulator. Based on analytical and simulation results, useful conclusions are derived for network provisioning and packet size optimization for different applications.

Delving Deeper: Transforming Shapes Physically and Analytically

ERIC Educational Resources Information Center

Rathouz, Margaret; Novak, Christopher; Clifford, John

2013-01-01

Constructing formulas "from scratch" for calculating geometric measurements of shapes--for example, the area of a triangle--involves reasoning deductively and drawing connections between different methods (Usnick, Lamphere, and Bright 1992). Visual and manipulative models also play a role in helping students understand the underlying…

Unified semiclassical theory for the two-state system: an analytical solution for general nonadiabatic tunneling.

PubMed

Zhu, Chaoyuan; Lin, Sheng Hsien

2006-07-28

Unified semiclasical solution for general nonadiabatic tunneling between two adiabatic potential energy surfaces is established by employing unified semiclassical solution for pure nonadiabatic transition [C. Zhu, J. Chem. Phys. 105, 4159 (1996)] with the certain symmetry transformation. This symmetry comes from a detailed analysis of the reduced scattering matrix for Landau-Zener type of crossing as a special case of nonadiabatic transition and nonadiabatic tunneling. Traditional classification of crossing and noncrossing types of nonadiabatic transition can be quantitatively defined by the rotation angle of adiabatic-to-diabatic transformation, and this rotational angle enters the analytical solution for general nonadiabatic tunneling. The certain two-state exponential potential models are employed for numerical tests, and the calculations from the present general nonadiabatic tunneling formula are demonstrated in very good agreement with the results from exact quantum mechanical calculations. The present general nonadiabatic tunneling formula can be incorporated with various mixed quantum-classical methods for modeling electronically nonadiabatic processes in photochemistry.

An invariance property of generalized Pearson random walks in bounded geometries

NASA Astrophysics Data System (ADS)

Mazzolo, Alain

2009-03-01

Invariance properties of random walks in bounded domains are a topic of growing interest since they contribute to improving our understanding of diffusion in confined geometries. Recently, limited to Pearson random walks with exponentially distributed straight paths, it has been shown that under isotropic uniform incidence, the average length of the trajectories through the domain is independent of the random walk characteristic and depends only on the ratio of the volume's domain over its surface. In this paper, thanks to arguments of integral geometry, we generalize this property to any isotropic bounded stochastic process and we give the conditions of its validity for isotropic unbounded stochastic processes. The analytical form for the traveled distance from the boundary to the first scattering event that ensures the validity of the Cauchy formula is also derived. The generalization of the Cauchy formula is an analytical constraint that thus concerns a very wide range of stochastic processes, from the original Pearson random walk to a Rayleigh distribution of the displacements, covering many situations of physical importance.

Pricing foreign equity option under stochastic volatility tempered stable Lévy processes

NASA Astrophysics Data System (ADS)

Gong, Xiaoli; Zhuang, Xintian

2017-10-01

Considering that financial assets returns exhibit leptokurtosis, asymmetry properties as well as clustering and heteroskedasticity effect, this paper substitutes the logarithm normal jumps in Heston stochastic volatility model by the classical tempered stable (CTS) distribution and normal tempered stable (NTS) distribution to construct stochastic volatility tempered stable Lévy processes (TSSV) model. The TSSV model framework permits infinite activity jump behaviors of return dynamics and time varying volatility consistently observed in financial markets through subordinating tempered stable process to stochastic volatility process, capturing leptokurtosis, fat tailedness and asymmetry features of returns. By employing the analytical characteristic function and fast Fourier transform (FFT) technique, the formula for probability density function (PDF) of TSSV returns is derived, making the analytical formula for foreign equity option (FEO) pricing available. High frequency financial returns data are employed to verify the effectiveness of proposed models in reflecting the stylized facts of financial markets. Numerical analysis is performed to investigate the relationship between the corresponding parameters and the implied volatility of foreign equity option.

COMPARISON OF CHILDREN'S FOLLOW-ON INSTANT POWDERED COW'S MILK FORMULA, BUFFALO MILK FORMULA AND CHICKEN-BASED FORMULA ON ENAMEL MICROHARDNESS OF BOVINE TEETH IN VITRO.

PubMed

Vongsavan, Kadkao; Rirattanapong, Praphasri; Surarit, Rudee

2016-03-01

Dental caries are a major public health problem worldwide. The aim of this study was to compare the effects of children's follow-on instant powdered cow's milk formula, buffalo milk formula and a chicken-based formula on microhardness of bovine enamel with artificial caries-like lesions. Forty bovine teeth were each placed in acrylic blocks and the enamel surfaces were polished to create flat 5 x 5 millimeter surfaces. The teeth surfaces were then demineralized using 0.1M lactic acid (pH 4.5) to achieve an enamel microhardness of 35-65 Vickers Hardness Numbers (VHN). All specimens were then randomly allocated into one of 4 groups (n=10/group). For remineralization, each group was soaked in a different kind of milk formula for 2 hours at 37°C except group 1 which was a negative control (artificial saliva) group. Group 2 was soaked in Murrah™ buffalo milk formula (a positive control ), group 3 in S-26-Promil-Gold™ (cow's milk formula) and group 4 in a chicken-based formula (Siriraj Hospital, Mahidol University). The microhardness of the specimens was then measured again. Data were analyzed using a one-way ANOVA and paired t-test with a 95% confidence interval. After exposure to the formula, the mean VHN for each study group was significantly higher (paired t-test, p < 0.05) except for group 1 (p = 0.345). The mean VHN for the the Murrah™ buffalo milk formula, the chicken-based formula and the S-26-Promil-Gold™ formula group were not significantly different from each other (one-way ANOVA, p > 0.05). In conclusion, S-26-Promil-Gold™ follow-on cow milk formula, Murrah™ buffalo milk formula and the chicken-based formula all increased bovine enamel microhardness after soaking for 2 hours.

29 CFR 547.1 - Essential requirements for qualifications.

Code of Federal Regulations, 2014 CFR

2014-07-01

... in accordance with a definite formula specified in the plan, which formula may be based on one or... formula or method of calculation specified in the plan, which formula or method of calculation is based on...

Bone mineralization and vitamin D/calcium daily intake of infants fed breast-milk, milk-based formula or soy-based formula

USDA-ARS?s Scientific Manuscript database

A cross-sectional analysis of bone mineralization during the first year of life of infants (N=107) exclusively fed breast-milk (BF), milk-based formula (MF), or soy-based formula (SF) for at least the first 4 months of life was conducted. Participants were part of the longitudinal Beginnings study. ...

Phonon dispersion on Ag (100) surface: A modified analytic embedded atom method study

NASA Astrophysics Data System (ADS)

Xiao-Jun, Zhang; Chang-Le, Chen

2016-01-01

Within the harmonic approximation, the analytic expression of the dynamical matrix is derived based on the modified analytic embedded atom method (MAEAM) and the dynamics theory of surface lattice. The surface phonon dispersions along three major symmetry directions , and X¯M¯ are calculated for the clean Ag (100) surface by using our derived formulas. We then discuss the polarization and localization of surface modes at points X¯ and M¯ by plotting the squared polarization vectors as a function of the layer index. The phonon frequencies of the surface modes calculated by MAEAM are compared with the available experimental and other theoretical data. It is found that the present results are generally in agreement with the referenced experimental or theoretical results, with a maximum deviation of 10.4%. The agreement shows that the modified analytic embedded atom method is a reasonable many-body potential model to quickly describe the surface lattice vibration. It also lays a significant foundation for studying the surface lattice vibration in other metals. Project supported by the National Natural Science Foundation of China (Grant Nos. 61471301 and 61078057), the Scientific Research Program Funded by Shaanxi Provincial Education Department, China (Grant No. 14JK1301), and the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20126102110045).

Alkaloids Profiling of Fumaria capreolata by Analytical Platforms Based on the Hyphenation of Gas Chromatography and Liquid Chromatography with Quadrupole-Time-of-Flight Mass Spectrometry.

PubMed

Contreras, María Del Mar; Bribi, Noureddine; Gómez-Caravaca, Ana María; Gálvez, Julio; Segura-Carretero, Antonio

2017-01-01

Two analytical platforms, gas chromatography (GC) coupled to quadrupole-time-of-flight (QTOF) mass spectrometry (MS) and reversed-phase ultrahigh performance liquid chromatography (UHPLC) coupled to diode array (DAD) and QTOF detection, were applied in order to study the alkaloid profile of Fumaria capreolata . The use of these mass analyzers enabled tentatively identifying the alkaloids by matching their accurate mass signals and suggested molecular formulae with those previously reported in libraries and databases. Moreover, the proposed structures were corroborated by studying their fragmentation pattern obtained by both platforms. In this way, 8 and 26 isoquinoline alkaloids were characterized using GC-QTOF-MS and RP-UHPLC-DAD-QTOF-MS, respectively, and they belonged to the following subclasses: protoberberine, protopine, aporphine, benzophenanthridine, spirobenzylisoquinoline, morphinandienone, and benzylisoquinoline. Moreover, the latter analytical method was selected to determine at 280 nm the concentration of protopine (9.6 ± 0.7 mg/g), a potential active compound of the extract. In conclusion, although GC-MS has been commonly used for the analysis of this type of phytochemicals, RP-UHPLC-DAD-QTOF-MS provided essential complementary information. This analytical method can be applied for the quality control of phytopharmaceuticals containing Fumaria extracts currently found in the market.

Alkaloids Profiling of Fumaria capreolata by Analytical Platforms Based on the Hyphenation of Gas Chromatography and Liquid Chromatography with Quadrupole-Time-of-Flight Mass Spectrometry

PubMed Central

Bribi, Noureddine; Gómez-Caravaca, Ana María

2017-01-01

Two analytical platforms, gas chromatography (GC) coupled to quadrupole-time-of-flight (QTOF) mass spectrometry (MS) and reversed-phase ultrahigh performance liquid chromatography (UHPLC) coupled to diode array (DAD) and QTOF detection, were applied in order to study the alkaloid profile of Fumaria capreolata. The use of these mass analyzers enabled tentatively identifying the alkaloids by matching their accurate mass signals and suggested molecular formulae with those previously reported in libraries and databases. Moreover, the proposed structures were corroborated by studying their fragmentation pattern obtained by both platforms. In this way, 8 and 26 isoquinoline alkaloids were characterized using GC-QTOF-MS and RP-UHPLC-DAD-QTOF-MS, respectively, and they belonged to the following subclasses: protoberberine, protopine, aporphine, benzophenanthridine, spirobenzylisoquinoline, morphinandienone, and benzylisoquinoline. Moreover, the latter analytical method was selected to determine at 280 nm the concentration of protopine (9.6 ± 0.7 mg/g), a potential active compound of the extract. In conclusion, although GC-MS has been commonly used for the analysis of this type of phytochemicals, RP-UHPLC-DAD-QTOF-MS provided essential complementary information. This analytical method can be applied for the quality control of phytopharmaceuticals containing Fumaria extracts currently found in the market. PMID:29348751

Investigation of plasmonic resonances in the two-dimensional electron gas of an InGaAs/InP high electron mobility transistor

NASA Astrophysics Data System (ADS)

Cleary, Justin W.; Peale, Robert E.; Saxena, Himanshu; Buchwald, Walter R.

2011-05-01

The observation of THz regime transmission resonances in an InGaAs/InP high electron mobility transistor (HEMT) can be attributed to excitation of plasmons in its two-dimensional electron gas (2DEG). Properties of grating-based, gate-voltage tunable resonances are shown to be adequately modeled using commercial finite element method (FEM) software when the HEMT layer structure, gate geometry and sheet charge concentration are taken into account. The FEM results are shown to produce results consistent with standard analytical theories in the 10-100 cm-1 wavenumber range. An original analytic formula presented here describes how the plasmonic resonance may change in the presence of a virtual gate, or region of relatively high free charge carriers that lies in the HEMT between the physical grating gate and the 2DEG. The virtual gate and corresponding analytic formulation are able to account for the red-shifting experimentally observed in plasmonic resonances. The calculation methods demonstrated here have the potential to greatly aid in the design of future detection devices that require specifically tuned plasmonic modes in the 2DEG of a HEMT, as well as giving new insights to aid in the development of more complete analytic theories.

High-performance liquid chromatography coupled with tandem mass spectrometry technology in the analysis of Chinese Medicine Formulas: A bibliometric analysis (1997-2015).

PubMed

He, Xi-Ran; Li, Chun-Guang; Zhu, Xiao-Shu; Li, Yuan-Qing; Jarouche, Mariam; Bensoussan, Alan; Li, Ping-Ping

2017-01-01

There is a recognized challenge in analyzing traditional Chinese medicine formulas because of their complex chemical compositions. The application of modern analytical techniques such as high-performance liquid chromatography coupled with a tandem mass spectrometry has improved the characterization of various compounds from traditional Chinese medicine formulas significantly. This study aims to conduct a bibliometric analysis to recognize the overall trend of high-performance liquid chromatography coupled with tandem mass spectrometry approaches in the analysis of traditional Chinese medicine formulas, its significance and possible underlying interactions between individual herbs in these formulas. Electronic databases were searched systematically, and the identified studies were collected and analyzed using Microsoft Access 2010, Graph Pad 5.0 software and Ucinet software package. 338 publications between 1997 and 2015 were identified, and analyzed in terms of annual growth and accumulated publications, top journals, forms of traditional Chinese medicine preparations and highly studied formulas and single herbs, as well as social network analysis of single herbs. There is a significant increase trend in using high-performance liquid chromatography coupled with tandem mass spectrometry related techniques in analysis of commonly used forms of traditional Chinese medicine formulas in the last 3 years. Stringent quality control is of great significance for the modernization and globalization of traditional Chinese medicine, and this bibliometric analysis provided the first and comprehensive summary within this field. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

"Non-cold" dark matter at small scales: a general approach

NASA Astrophysics Data System (ADS)

Murgia, R.; Merle, A.; Viel, M.; Totzauer, M.; Schneider, A.

2017-11-01

Structure formation at small cosmological scales provides an important frontier for dark matter (DM) research. Scenarios with small DM particle masses, large momenta or hidden interactions tend to suppress the gravitational clustering at small scales. The details of this suppression depend on the DM particle nature, allowing for a direct link between DM models and astrophysical observations. However, most of the astrophysical constraints obtained so far refer to a very specific shape of the power suppression, corresponding to thermal warm dark matter (WDM), i.e., candidates with a Fermi-Dirac or Bose-Einstein momentum distribution. In this work we introduce a new analytical fitting formula for the power spectrum, which is simple yet flexible enough to reproduce the clustering signal of large classes of non-thermal DM models, which are not at all adequately described by the oversimplified notion of WDM . We show that the formula is able to fully cover the parameter space of sterile neutrinos (whether resonantly produced or from particle decay), mixed cold and warm models, fuzzy dark matter, as well as other models suggested by effective theory of structure formation (ETHOS). Based on this fitting formula, we perform a large suite of N-body simulations and we extract important nonlinear statistics, such as the matter power spectrum and the halo mass function. Finally, we present first preliminary astrophysical constraints, based on linear theory, from both the number of Milky Way satellites and the Lyman-α forest. This paper is a first step towards a general and comprehensive modeling of small-scale departures from the standard cold DM model.

Who gets how much: funding formulas in federal public health programs.

PubMed

Buehler, James W; Holtgrave, David R

2007-01-01

Federal public health programs use a mix of formula-based and competitive methods to allocate funds among states and other constituent jurisdictions. Characteristics of formula-based allocations used by a convenience sample of four programs, three from the Centers for Disease Control and Prevention and one from the Health Resources and Services Administration, are described to illustrate formula-based allocation methods in public health. Data sources in these public health formulas include population counts and funding proportions based on historical precedent. None include factors that adjust allocations based on variations in the availability of local resources or the cost of delivering services. Formula-funded activities are supplemented by programs that target specific prevention needs or encourage development of innovative methods to address emerging problems, using set-aside funds. A public health finance research agenda should address ways to improve the fit between funding allocation formulas and program objectives.

Two Prophecy Formulas for Assessing the Reliability of Item Response Theory-Based Ability Estimates

ERIC Educational Resources Information Center

Raju, Nambury S.; Oshima, T.C.

2005-01-01

Two new prophecy formulas for estimating item response theory (IRT)-based reliability of a shortened or lengthened test are proposed. Some of the relationships between the two formulas, one of which is identical to the well-known Spearman-Brown prophecy formula, are examined and illustrated. The major assumptions underlying these formulas are…

Analytical determination of the heat transfer coefficient for gas, liquid and liquid metal flows in the tube based on stochastic equations and equivalence of measures for continuum

NASA Astrophysics Data System (ADS)

Dmitrenko, Artur V.

2017-11-01

The stochastic equations of continuum are used for determining the heat transfer coefficients. As a result, the formulas for Nusselt (Nu) number dependent on the turbulence intensity and scale instead of only on the Reynolds (Peclet) number are proposed for the classic flows of a nonisothermal fluid in a round smooth tube. It is shown that the new expressions for the classical heat transfer coefficient Nu, which depend only on the Reynolds number, should be obtained from these new general formulas if to use the well-known experimental data for the initial turbulence. It is found that the limitations of classical empirical and semiempirical formulas for heat transfer coefficients and their deviation from the experimental data depend on different parameters of initial fluctuations in the flow for different experiments in a wide range of Reynolds or Peclet numbers. Based on these new dependences, it is possible to explain that the differences between the experimental results for the fixed Reynolds or Peclet numbers are caused by the difference in values of flow fluctuations for each experiment instead of only due to the systematic error in the experiment processing. Accordingly, the obtained general dependences of Nu for a smooth round tube can serve as the basis for clarifying the experimental results and empirical formulas used for continuum flows in various power devices. Obtained results show that both for isothermal and for nonisothermal flows, the reason for the process of transition from a deterministic state into a turbulent one is determined by the physical law of equivalence of measures between them. Also the theory of stochastic equations and the law of equivalence of measures could determine mechanics which is basis in different phenomena of self-organization and chaos theory.

Inclusion of Topological Measurements into Analytic Estimates of Effective Permeability in Fractured Media

NASA Astrophysics Data System (ADS)

Sævik, P. N.; Nixon, C. W.

2017-11-01

We demonstrate how topology-based measures of connectivity can be used to improve analytical estimates of effective permeability in 2-D fracture networks, which is one of the key parameters necessary for fluid flow simulations at the reservoir scale. Existing methods in this field usually compute fracture connectivity using the average fracture length. This approach is valid for ideally shaped, randomly distributed fractures, but is not immediately applicable to natural fracture networks. In particular, natural networks tend to be more connected than randomly positioned fractures of comparable lengths, since natural fractures often terminate in each other. The proposed topological connectivity measure is based on the number of intersections and fracture terminations per sampling area, which for statistically stationary networks can be obtained directly from limited outcrop exposures. To evaluate the method, numerical permeability upscaling was performed on a large number of synthetic and natural fracture networks, with varying topology and geometry. The proposed method was seen to provide much more reliable permeability estimates than the length-based approach, across a wide range of fracture patterns. We summarize our results in a single, explicit formula for the effective permeability.

Comparison of PSF maxima and minima of multiple annuli coded aperture (MACA) and complementary multiple annuli coded aperture (CMACA) systems

NASA Astrophysics Data System (ADS)

Ratnam, Challa; Lakshmana Rao, Vadlamudi; Lachaa Goud, Sivagouni

2006-10-01

In the present paper, and a series of papers to follow, the Fourier analytical properties of multiple annuli coded aperture (MACA) and complementary multiple annuli coded aperture (CMACA) systems are investigated. First, the transmission function for MACA and CMACA is derived using Fourier methods and, based on the Fresnel-Kirchoff diffraction theory, the formulae for the point spread function are formulated. The PSF maxima and minima are calculated for both the MACA and CMACA systems. The dependence of these properties on the number of zones is studied and reported in this paper.

Cosmic muon flux measurements at the Kimballton Underground Research Facility

NASA Astrophysics Data System (ADS)

Kalousis, L. N.; Guarnaccia, E.; Link, J. M.; Mariani, C.; Pelkey, R.

2014-08-01

In this article, the results from a series of muon flux measurements conducted at the Kimballton Underground Research Facility (KURF), Virginia, United States, are presented. The detector employed for these investigations, is made of plastic scintillator bars readout by wavelength shifting fibers and multianode photomultiplier tubes. Data was taken at several locations inside KURF, spanning rock overburden values from ~ 200 to 1450 m.w.e. From the extracted muon rates an empirical formula was devised, that estimates the muon flux inside the mine as a function of the overburden. The results are in good agreement with muon flux calculations based on analytical models and MUSIC.

Entanglement of two blocks of spins in the critical Ising model

NASA Astrophysics Data System (ADS)

Facchi, P.; Florio, G.; Invernizzi, C.; Pascazio, S.

2008-11-01

We compute the entropy of entanglement of two blocks of L spins at a distance d in the ground state of an Ising chain in an external transverse magnetic field. We numerically study the von Neumann entropy for different values of the transverse field. At the critical point we obtain analytical results for blocks of size L=1 and 2. In the general case, the critical entropy is shown to be additive when d→∞ . Finally, based on simple arguments, we derive an expression for the entropy at the critical point as a function of both L and d . This formula is in excellent agreement with numerical results.

Propagation of partially coherent vector anomalous vortex beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Zhang, Xu; Wang, Haiyan; Tang, Lei

2018-01-01

A theoretical model is proposed to describe a partially coherent vector anomalous vortex(AV) beam. Based on the extended Huygens-Fresnel principle, analytical propagation formula for the proposed beams in turbulent atmosphere is derived. The spectral properties of the partially coherent vector AV beam are explored by using the unified theory of coherence and polarization in detail. It is interesting to find that the turbulence of atmosphere and the source parameter of the partially coherent vector AV beam( order, topological charge, coherence length, beam waist size etc) have significantly impacted the propagation properties of the partially coherent vector AV beam in turbulent atmosphere.

Solenoid Fringe Field Effects for the Neutrino Factory Linac - MAD-X Investigation

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

M. Aslaninejad,C. Bontoiu,J. Pasternak,J. Pozimski,Alex Bogacz

2010-05-01

International Design Study for the Neutrino Factory (IDS-NF) assumes the first stage of muon acceleration (up to 900 MeV) to be implemented with a solenoid based Linac. The Linac consists of three styles of cryo-modules, containing focusing solenoids and varying number of SRF cavities for acceleration. Fringe fields of the solenoids and the focusing effects in the SRF cavities have significant impact on the transverse beam dynamics. Using an analytical formula, the effects of fringe fields are studied in MAD-X. The resulting betatron functions are compared with the results of beam dynamics simulations using OptiM code.

Infant dietary exposure to dioxins and dioxin-like compounds in Greece.

PubMed

Costopoulou, Danae; Vassiliadou, Irene; Leondiadis, Leondios

2013-09-01

The dietary exposure of infants to polychlorinated dibenzo dioxins and furans (PCDD/Fs) and dioxin like polychlorinated biphenyls (dl-PCBs) is an issue of great social impact. We investigated for the first time the dietary intake of these compounds in infants living in Greece. We included in our study two age groups: 0-6 months, when infants are fed exclusively by human milk and/or formula milk, and 6 to 12 months, when solid food is introduced to nutrition. We took into consideration analytical results for PCDD/Fs and dl-PCBs concentrations in the most popular infant formulae in the Greek market, previous data for mother milk concentrations of PCDD/Fs and dl-PCBs from Greece, and finally analytical data for fat-containing food products from the Greek market. In the first study group, it was found than in infants exclusively fed by breast milk, the calculated sum of PCDD/Fs and dioxin-like PCBs (60.3-80.4 TEQ pg/kg body weight) was significantly higher than that of infants that consume a combination of human milk and formula (31.2-41.6 TEQ pg/kg body weight). In the second study group, separate daily intake estimations were performed for babies receiving human milk (estimated total daily intake 19.76-24.95 TEQ pg/kg body weight) and formula milk (estimated total daily intake 1.60-2.24 TEQ pg/kg body weight). The risks of this exposure should not be overestimated because nursing is restricted to a limited period of human life and besides, the potential consumption of higher levels of dioxin-like compounds is fully compensated by the significant benefits of breast-feeding. Copyright © 2013 Elsevier Ltd. All rights reserved.

Loading-unloading response of circular GLARE fiber-metal laminates under lateral indentation

NASA Astrophysics Data System (ADS)

Tsamasphyros, George J.; Bikakis, George S.

2015-01-01

GLARE is a Fiber-Metal laminated material used in aerospace structures which are frequently subjected to various impact damages. Hence, the response of GLARE plates subjected to lateral indentation is very important. In this paper, analytical expressions are derived and a non-linear finite element modeling procedure is proposed in order to predict the static load-indentation curves of circular GLARE plates during loading and unloading by a hemispherical indentor. We have recently published analytical formulas and a finite element procedure for the static indentation of circular GLARE plates which are now used during the loading stage. Here, considering that aluminum layers are in a state of membrane yield and employing energy balance during unloading, the unloading path is determined. Using this unloading path, an algebraic equation is derived for calculating the permanent dent depth of the GLARE plate after the indentor's withdrawal. Furthermore, our finite element procedure is modified in order to simulate the unloading stage as well. The derived formulas and the proposed finite element modeling procedure are applied successfully to GLARE 2-2/1-0.3 and to GLARE 3-3/2-0.4 circular plates. The analytical results are compared with corresponding FEM results and a good agreement is found. The analytically calculated permanent dent depth is within 6 % for the GLARE 2 plate, and within 7 % for the GLARE 3 plate, of the corresponding numerically calculated result. No other solution of this problem is known to the authors.

Plasma Properties in the Plume of a Hall Thruster Cluster

DTIC Science & Technology

2003-06-04

The Hall thruster cluster is an attractive propulsion approach for spacecraft requiring very high-power electric propulsion systems. This article...probes in the plume of a low-power, four-engine Hall thruster cluster. Simple analytical formulas are introduced that allow these quantities to be

Virtual photon impact factors with exact gluon kinematics

NASA Astrophysics Data System (ADS)

Bialas, A.; Navelet, H.; Peschanski, R.

2001-06-01

An explicit analytic formula for the transverse and longitudinal impact factors ST, L( N, γ) of the photon using kT factorization with exact gluon kinematics is given. Applications to the QCD dipole model and the extraction of the unintegrated gluon structure function from data are proposed.

Cost-effectiveness model for a specific mixture of prebiotics in The Netherlands.

PubMed

Lenoir-Wijnkoop, I; van Aalderen, W M C; Boehm, G; Klaassen, D; Sprikkelman, A B; Nuijten, M J C

2012-02-01

The objective of this study was to assess the cost-effectiveness of the use of prebiotics for the primary prevention of atopic dermatitis in The Netherlands. A model was constructed using decision analytical techniques. The model was developed to estimate the health economic impact of prebiotic preventive disease management of atopic dermatitis. Data sources used include published literature, clinical trials and official price/tariff lists and national population statistics. The comparator was no supplementation with prebiotics. The primary perspective for conducting the economic evaluation was based on the situation in The Netherlands in 2009. The results show that the use of prebiotics infant formula (IMMUNOFORTIS(®)) leads to an additional cost of € 51 and an increase in Quality Adjusted Life Years (QALY) of 0.108, when compared with no prebiotics. Consequently, the use of infant formula with a specific mixture of prebiotics results in an incremental cost-effectiveness ratio (ICER) of € 472. The sensitivity analyses show that the ICER remains in all analyses far below the threshold of € 20,000/QALY. This study shows that the favourable health benefit of the use of a specific mixture of prebiotics results in positive short- and long-term health economic benefits. In addition, this study demonstrates that the use of infant formula with a specific mixture of prebiotics is a highly cost-effective way of preventing atopic dermatitis in The Netherlands.

Training-free compressed sensing for wireless neural recording using analysis model and group weighted [Formula: see text]-minimization.

PubMed

Sun, Biao; Zhao, Wenfeng; Zhu, Xinshan

2017-06-01

Data compression is crucial for resource-constrained wireless neural recording applications with limited data bandwidth, and compressed sensing (CS) theory has successfully demonstrated its potential in neural recording applications. In this paper, an analytical, training-free CS recovery method, termed group weighted analysis [Formula: see text]-minimization (GWALM), is proposed for wireless neural recording. The GWALM method consists of three parts: (1) the analysis model is adopted to enforce sparsity of the neural signals, therefore overcoming the drawbacks of conventional synthesis models and enhancing the recovery performance. (2) A multi-fractional-order difference matrix is constructed as the analysis operator, thus avoiding the dictionary learning procedure and reducing the need for previously acquired data and computational complexities. (3) By exploiting the statistical properties of the analysis coefficients, a group weighting approach is developed to enhance the performance of analysis [Formula: see text]-minimization. Experimental results on synthetic and real datasets reveal that the proposed approach outperforms state-of-the-art CS-based methods in terms of both spike recovery quality and classification accuracy. Energy and area efficiency of the GWALM make it an ideal candidate for resource-constrained, large scale wireless neural recording applications. The training-free feature of the GWALM further improves its robustness to spike shape variation, thus making it more practical for long term wireless neural recording.

Simultaneous determination of water-soluble vitamins in SRM 1849 Infant/Adult Nutritional Formula powder by liquid chromatography-isotope dilution mass spectrometry.

PubMed

Goldschmidt, Robert J; Wolf, Wayne R

2010-05-01

Assessing dietary intake of vitamins from all sources, including foods, dietary supplements, and fortified foods, would be aided considerably by having analytical methodologies that are capable of simultaneous determination of several vitamins. Vitamins naturally present in foods may occur in different chemical forms, with levels ranging over several orders of magnitude. Vitamins in dietary supplements and fortified foods, however, are typically added in a single chemical form, and matrix issues are usually not as complex. These sources should thus be relatively amenable to approaches that aim for simultaneous determination of multiple vitamins. Our recent work has focused on development of liquid chromatography (LC)-UV/fluorescence and LC-tandem mass spectrometry methods for the simultaneous determination of water-soluble vitamins (thiamine, niacin, pyridoxine, pantothenic acid, folic acid, biotin, and riboflavin) in dietary supplement tablets and fortified foods, such as formula powders and breakfast cereals. As part of the validation of our methods and collaboration in characterization of a new NIST SRM 1849 Infant/Adult Nutritional Formula powder, we report data on SRM 1849 using isotope dilution mass spectrometric methods. Use of available NIST Standard Reference Materials(R) as test matrices in our method development and validation gives a benchmark for future application of these methods. We compare three chromatographic approaches and provide data on stability of vitamin standard solutions for LC-based multiple vitamin determinations.

Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

NASA Astrophysics Data System (ADS)

Šprlák, Michal; Novák, Pavel

2017-02-01

New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.

Analytical Investigation of the Decrease in the Size of the Habitable Zone Due to a Limited CO2 Outgassing Rate

NASA Astrophysics Data System (ADS)

Abbot, Dorian S.

2016-08-01

The habitable zone concept is important because it focuses the scientific search for extraterrestrial life and aids the planning of future telescopes. Recent work has shown that planets near the outer edge of the habitable zone might not actually be able to stay warm and habitable if CO2 outgassing rates are not large enough to maintain high CO2 partial pressures against removal by silicate weathering. In this paper, I use simple equations for the climate and CO2 budget of a planet in the habitable zone that can capture the qualitative behavior of the system. With these equations I derive an analytical formula for an effective outer edge of the habitable zone, including limitations imposed by the CO2 outgassing rate. I then show that climate cycles between a snowball state and a warm climate are only possible beyond this limit if the weathering rate in the snowball climate is smaller than the CO2 outgassing rate (otherwise stable snowball states result). I derive an analytical solution for the climate cycles including a formula for their period in this limit. This work allows us to explore the qualitative effects of weathering processes on the effective outer edge of the habitable zone, which is important because weathering parameterizations are uncertain.

Analytical Investigation of the Decrease in the Size of the Habitable Zone due to Limited CO2 Outgassing Rate

NASA Astrophysics Data System (ADS)

Abbot, D. S.

2016-12-01

The habitable zone concept is important because it focuses the scientific search for extraterrestrial life and aids the planning of future telescopes. Recent work has shown that planets near the outer edge of the habitable zone might not actually be able to stay warm and habitable if CO2 outgassing rates are not large enough to maintain high CO2 partial pressures against removal by silicate weathering. I use simple equations for the climate and CO2 budget of a planet in the habitable zone that can capture the qualitative behavior of the system. With these equations I derive an analytical formula for an effective outer edge of the habitable zone, including limitations imposed by the CO2 outgassing rate. I then show that climate cycles between a Snowball state and a warm climate are only possible beyond this limit if the weathering rate in the Snowball climate is smaller than the CO2 outgassing rate (otherwise stable Snowball states result). I derive an analytical solution for the climate cycles including a formula for their period in this limit. This work allows us to explore the qualitative effects of weathering processes on the effective outer edge of the habitable zone, which is important because weathering parameterizations are uncertain.

24 CFR 905.10 - Capital Fund formula (CFF).

Code of Federal Regulations, 2010 CFR

2010-04-01

... Grant formula system or the Comprehensive Improvement Assistance Program (CIAP) formula system will be... formula share had the FFY 1999 formula system been applied to these CFF eligible units. The FFY 1999 formula system is based upon the FFY 1999 Comprehensive Grant formula system for PHAs with 250 or more...

A Simple Automated Method for the Determination of Nitrate and Nitrite in Infant Formula and Milk Powder Using Sequential Injection Analysis

PubMed Central

Pistón, Mariela; Mollo, Alicia; Knochen, Moisés

2011-01-01

A fast and efficient automated method using a sequential injection analysis (SIA) system, based on the Griess, reaction was developed for the determination of nitrate and nitrite in infant formulas and milk powder. The system enables to mix a measured amount of sample (previously constituted in the liquid form and deproteinized) with the chromogenic reagent to produce a colored substance whose absorbance was recorded. For nitrate determination, an on-line prereduction step was added by passing the sample through a Cd minicolumn. The system was controlled from a PC by means of a user-friendly program. Figures of merit include linearity (r2 > 0.999 for both analytes), limits of detection (0.32 mg kg−1 NO3-N, and 0.05 mg kg−1 NO2-N), and precision (sr%) 0.8–3.0. Results were statistically in good agreement with those obtained with the reference ISO-IDF method. The sampling frequency was 30 hour−1 (nitrate) and 80 hour−1 (nitrite) when performed separately. PMID:21960750

Vitamin D concentrations in fortified foods and dietary supplements intended for infants: Implications for vitamin D intake.

PubMed

Verkaik-Kloosterman, Janneke; Seves, S Marije; Ocké, Marga C

2017-04-15

Due to potential overages to cover losses during shelf life, the actual vitamin D concentration of fortified foods and dietary supplements may deviate from the label. In this pilot study the vitamin D concentrations of fortified foods (n=29; follow-on formula, baby porridge, curd cheese dessert) and dietary supplements (n=15), both specifically intended for infants, were analytically determined. Compared to the declared values, the vitamin D content ranged from 50% to 153% for fortified foods and from 8% to 177% for supplements. In general, both instant follow-on formula and oil-based supplements had a measured vitamin D content similar to or higher than the labelled value. Ready-to-eat baby porridge was the only category in which all measured vitamin D concentrations were below the declared value (74-81%). The use of label information for fortified foods and dietary supplements may result in invalid estimations of vitamin D intake distributions of infants; both under- and overestimation may occur. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Counterfeit Adderall Containing Aceclofenac from Internet Pharmacies.

PubMed

Gaudiano, Maria Cristina; Borioni, Anna; Antoniella, Eleonora; Valvo, Luisa

2016-07-01

A nontargeted approach based on liquid chromatography equipped with a quadrupole time-of-flight mass detector (LC-MS Q-TOF) joined to nuclear magnetic resonance (NMR) analysis allowed rapid identification and quantification of the anti-inflammatory drug aceclofenac in illegal Adderall tablets. The largest chromatographic peak had m/z = 354.030 and m/z = 376.012 matching, respectively, the ionic structures (M + H) + and (M + Na) + of a molecule M. The accurate mass data generated the molecular formula C 16 H 13 Cl 2 NO 4 . A screening of the pharmaceutical active substances having that molecular formula together with the MS/MS fragmentation pattern suggested aceclofenac. Aceclofenac structure was unambiguously confirmed by 1 H and 13 C NMR experiments. The aceclofenac content was 90 mg/tablet (RSD 2%) as detected by quantitative NMR. Information on the identity and content of illegal drugs is required for legal purposes; it supports in evaluating the effective impact on users safety, and it is useful for control laboratories using a targeted approach in their analytical activities. © 2016 American Academy of Forensic Sciences.

Feynman formulas for semigroups generated by an iterated Laplace operator

NASA Astrophysics Data System (ADS)

Buzinov, M. S.

2017-04-01

In the present paper, we find representations of a one-parameter semigroup generated by a finite sum of iterated Laplace operators and an additive perturbation (the potential). Such semigroups and the evolution equations corresponding to them find applications in the field of physics, chemistry, biology, and pattern recognition. The representations mentioned above are obtained in the form of Feynman formulas, i.e., in the form of a limit of multiple integrals as the multiplicity tends to infinity. The term "Feynman formula" was proposed by Smolyanov. Smolyanov's approach uses Chernoff's theorems. A simple form of representations thus obtained enables one to use them for numerical modeling the dynamics of the evolution system as a method for the approximation of solutions of equations. The problems considered in this note can be treated using the approach suggested by Remizov (see also the monograph of Smolyanov and Shavgulidze on path integrals). The representations (of semigroups) obtained in this way are more complicated than those given by the Feynman formulas; however, it is possible to bypass some analytical difficulties.

Finite word length effects on digital filter implementation.

NASA Technical Reports Server (NTRS)

Bowman, J. D.; Clark, F. H.

1972-01-01

This paper is a discussion of two known techniques to analyze finite word length effects on digital filters. These techniques are extended to several additional programming forms and the results verified experimentally. A correlation of the analytical weighting functions for the two methods is made through the Mason Gain Formula.

Testing Understanding and Understanding Testing.

ERIC Educational Resources Information Center

Pedersen, Jean; Ross, Peter

1985-01-01

Provides examples in which graphs are used in the statements of problems or in their solutions as a means of testing understanding of mathematical concepts. Examples (appropriate for a beginning course in calculus and analytic geometry) include slopes of lines and curves, quadratic formula, properties of the definite integral, and others. (JN)

Universality in volume-law entanglement of scrambled pure quantum states.

PubMed

Nakagawa, Yuya O; Watanabe, Masataka; Fujita, Hiroyuki; Sugiura, Sho

2018-04-24

A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. The thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases, however, quantum correlations break the correspondence and mandate a correction to this simple volume law. The elucidation of the size dependence of the entanglement entropy is thus essentially important in linking quantum physics with thermodynamics. Here we derive an analytic formula of the entanglement entropy for a class of pure states called cTPQ states representing equilibrium. We numerically find that our formula applies universally to any sufficiently scrambled pure state representing thermal equilibrium, i.e., energy eigenstates of non-integrable models and states after quantum quenches. Our formula is exploited as diagnostics for chaotic systems; it can distinguish integrable models from non-integrable models and many-body localization phases from chaotic phases.

Current matrix element in HAL QCD's wavefunction-equivalent potential method

NASA Astrophysics Data System (ADS)

Watanabe, Kai; Ishii, Noriyoshi

2018-04-01

We give a formula to calculate a matrix element of a conserved current in the effective quantum mechanics defined by the wavefunction-equivalent potentials proposed by the HAL QCD collaboration. As a first step, a non-relativistic field theory with two-channel coupling is considered as the original theory, with which a wavefunction-equivalent HAL QCD potential is obtained in a closed analytic form. The external field method is used to derive the formula by demanding that the result should agree with the original theory. With this formula, the matrix element is obtained by sandwiching the effective current operator between the left and right eigenfunctions of the effective Hamiltonian associated with the HAL QCD potential. In addition to the naive one-body current, the effective current operator contains an additional two-body term emerging from the degrees of freedom which has been integrated out.

Acoustic sounding of wind velocity profiles in a stratified moving atmosphere.

PubMed

Ostashev, V E; Georges, T M; Clifford, S F; Goedecke, G H

2001-06-01

The paper deals with analytical and numerical studies of the effects of atmospheric stratification on acoustic remote sensing of wind velocity profiles by sodars. Both bistatic and monostatic schemes are considered. Formulas for the Doppler shift of an acoustic echo signal scattered by atmospheric turbulence advected with the mean wind in a stratified moving atmosphere are derived. Numerical studies of these formulas show that errors in retrieving wind velocity can be of the order of 1 m/s if atmospheric stratification is ignored. Formulas for the height at which wind velocity is retrieved are also derived. Approaches are proposed which allow one to take into account the effects of atmospheric stratification when restoring the wind velocity profile from measured values of the Doppler shift and the time interval of acoustic impulse propagation from a sodar to the scattering volume and back to the ground.

Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function

NASA Technical Reports Server (NTRS)

King, H. F.; Komornicki, A.

1986-01-01

Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.

Estimating the Gibbs energy of hydration from molecular dynamics trajectories obtained by integral equations of the theory of liquids in the RISM approximation

NASA Astrophysics Data System (ADS)

Tikhonov, D. A.; Sobolev, E. V.

2011-04-01

A method of integral equations of the theory of liquids in the reference interaction site model (RISM) approximation is used to estimate the Gibbs energy averaged over equilibrium trajectories computed by molecular mechanics. Peptide oxytocin is selected as the object of interest. The Gibbs energy is calculated using all chemical potential formulas introduced in the RISM approach for the excess chemical potential of solvation and is compared with estimates by the generalized Born model. Some formulas are shown to give the wrong sign of Gibbs energy changes when peptide passes from the gas phase into water environment; the other formulas give overestimated Gibbs energy changes with the right sign. Note that allowance for the repulsive correction in the approximate analytical expressions for the Gibbs energy derived by thermodynamic perturbation theory is not a remedy.

Bending elasticity of macromolecules: analytic predictions from the wormlike chain model.

PubMed

Polley, Anirban; Samuel, Joseph; Sinha, Supurna

2013-01-01

We present a study of the bend angle distribution of semiflexible polymers of short and intermediate lengths within the wormlike chain model. This enables us to calculate the elastic response of a stiff molecule to a bending moment. Our results go beyond the Hookean regime and explore the nonlinear elastic behavior of a single molecule. We present analytical formulas for the bend angle distribution and for the moment-angle relation. Our analytical study is compared against numerical Monte Carlo simulations. The functional forms derived here can be applied to fluorescence microscopic studies on actin and DNA. Our results are relevant to recent studies of "kinks" and cyclization in short and intermediate length DNA strands.

Analytical theory of coherent synchrotron radiation wakefield of short bunches shielded by conducting parallel plates

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

Stupakov, Gennady; Zhou, Demin

2016-04-21

We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. Furthermore, all our formulas are benchmarked against numerical simulations with the CSRZ computermore » code.« less

Body surface assessment with 3D laser-based anthropometry: reliability, validation, and improvement of empirical surface formulae.

PubMed

Kuehnapfel, Andreas; Ahnert, Peter; Loeffler, Markus; Scholz, Markus

2017-02-01

Body surface area is a physiological quantity relevant for many medical applications. In clinical practice, it is determined by empirical formulae. 3D laser-based anthropometry provides an easy and effective way to measure body surface area but is not ubiquitously available. We used data from laser-based anthropometry from a population-based study to assess validity of published and commonly used empirical formulae. We performed a large population-based study on adults collecting classical anthropometric measurements and 3D body surface assessments (N = 1435). We determined reliability of the 3D body surface assessment and validity of 18 different empirical formulae proposed in the literature. The performance of these formulae is studied in subsets of sex and BMI. Finally, improvements of parameter settings of formulae and adjustments for sex and BMI were considered. 3D body surface measurements show excellent intra- and inter-rater reliability of 0.998 (overall concordance correlation coefficient, OCCC was used as measure of agreement). Empirical formulae of Fujimoto and Watanabe, Shuter and Aslani and Sendroy and Cecchini performed best with excellent concordance with OCCC > 0.949 even in subgroups of sex and BMI. Re-parametrization of formulae and adjustment for sex and BMI slightly improved results. In adults, 3D laser-based body surface assessment is a reliable alternative to estimation by empirical formulae. However, there are empirical formulae showing excellent results even in subgroups of sex and BMI with only little room for improvement.

External validation of change formulae in neuropsychology with neuroimaging biomarkers: a methodological recommendation and preliminary clinical data.

PubMed

Duff, Kevin; Suhrie, Kayla R; Dalley, Bonnie C A; Anderson, Jeffrey S; Hoffman, John M

2018-06-08

Within neuropsychology, a number of mathematical formulae (e.g. reliable change index, standardized regression based) have been used to determine if change across time has reliably occurred. When these formulae have been compared, they often produce different results, but 'different' results do not necessarily indicate which formulae are 'best.' The current study sought to further our understanding of change formulae by comparing them to clinically relevant external criteria (amyloid deposition and hippocampal volume). In a sample of 25 older adults with varying levels of cognitive intactness, participants were tested twice across one week with a brief cognitive battery. Seven different change scores were calculated for each participant. An amyloid PET scan (to get a composite of amyloid deposition) and an MRI (to get hippocampal volume) were also obtained. Deviation-based change formulae (e.g. simple discrepancy score, reliable change index with or without correction for practice effects) were all identical in their relationship to the two neuroimaging biomarkers, and all were non-significant. Conversely, regression-based change formulae (e.g. simple and complex indices) showed stronger relationships to amyloid deposition and hippocampal volume. These results highlight the need for external validation of the various change formulae used by neuropsychologists in clinical settings and research projects. The findings also preliminarily suggest that regression-based change formulae may be more relevant than deviation-based change formulae in this context.

Measurement of third-order nonlinear susceptibility tensor in InP using extended Z-scan technique with elliptical polarization

NASA Astrophysics Data System (ADS)

Oishi, Masaki; Shinozaki, Tomohisa; Hara, Hikaru; Yamamoto, Kazunuki; Matsusue, Toshio; Bando, Hiroyuki

2018-05-01

The elliptical polarization dependence of the two-photon absorption coefficient β in InP has been measured by the extended Z-scan technique for thick materials in the wavelength range from 1640 to 1800 nm. The analytical formula of the Z-scan technique has been extended with consideration of multiple reflections. The Z-scan results have been fitted very well by the formula and β has been evaluated accurately. The three independent elements of the third-order nonlinear susceptibility tensor in InP have also been determined accurately from the elliptical polarization dependence of β.

Capacity of a quantum memory channel correlated by matrix product states

NASA Astrophysics Data System (ADS)

Mulherkar, Jaideep; Sunitha, V.

2018-04-01

We study the capacity of a quantum channel where channel acts like controlled phase gate with the control being provided by a one-dimensional quantum spin chain environment. Due to the correlations in the spin chain, we get a quantum channel with memory. We derive formulas for the quantum capacity of this channel when the spin state is a matrix product state. Particularly, we derive exact formulas for the capacity of the quantum memory channel when the environment state is the ground state of the AKLT model and the Majumdar-Ghosh model. We find that the behavior of the capacity for the range of the parameters is analytic.

Broadband impedance calculations and single bunch instabilities estimations of of the HLS-II storage ring

NASA Astrophysics Data System (ADS)

Zhang, Qing-Kun; Wang, Lin; Li, Wei-Min; Gao, Wei-Wei

2015-12-01

The upgrade project of the Hefei Light Source storage ring is under way. In this paper, the broadband impedances of resistive wall and coated ceramic vacuum chamber are calculated using the analytic formula, and the wake fields and impedances of other designed vacuum chambers are simulated by CST code, and then a broadband impedance model is obtained. Using the theoretical formula, longitudinal and transverse single bunch instabilities are discussed. With the carefully-designed vacuum chamber, we find that the thresholds of the beam instabilities are higher than the beam current goal. Supported by Natural Science Foundation of China (11175182, 11175180)

An invariant asymptotic formula for solutions of second-order linear ODE's

NASA Technical Reports Server (NTRS)

Gingold, H.

1988-01-01

An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).

Squeezing and its graphical representations in the anharmonic oscillator model

NASA Astrophysics Data System (ADS)

Tanaś, R.; Miranowicz, A.; Kielich, S.

1991-04-01

The problem of squeezing and its graphical representations in the anharmonic oscillator model is considered. Explicit formulas for squeezing, principal squeezing, and the quasiprobability distribution (QPD) function are given and illustrated graphically. Approximate analytical formulas for the variances, extremal variances, and QPD are obtained for the case of small nonlinearities and large numbers of photons. The possibility of almost perfect squeezing in the model is demonstrated and its graphical representations in the form of variance lemniscates and QPD contours are plotted. For large numbers of photons the crescent shape of the QPD contours is hardly visible and quite regular ellipses are obtained.

Dynamic characteristics of oxygen consumption.

PubMed

Ye, Lin; Argha, Ahmadreza; Yu, Hairong; Celler, Branko G; Nguyen, Hung T; Su, Steven

2018-04-23

Previous studies have indicated that oxygen uptake ([Formula: see text]) is one of the most accurate indices for assessing the cardiorespiratory response to exercise. In most existing studies, the response of [Formula: see text] is often roughly modelled as a first-order system due to the inadequate stimulation and low signal to noise ratio. To overcome this difficulty, this paper proposes a novel nonparametric kernel-based method for the dynamic modelling of [Formula: see text] response to provide a more robust estimation. Twenty healthy non-athlete participants conducted treadmill exercises with monotonous stimulation (e.g., single step function as input). During the exercise, [Formula: see text] was measured and recorded by a popular portable gas analyser ([Formula: see text], COSMED). Based on the recorded data, a kernel-based estimation method was proposed to perform the nonparametric modelling of [Formula: see text]. For the proposed method, a properly selected kernel can represent the prior modelling information to reduce the dependence of comprehensive stimulations. Furthermore, due to the special elastic net formed by [Formula: see text] norm and kernelised [Formula: see text] norm, the estimations are smooth and concise. Additionally, the finite impulse response based nonparametric model which estimated by the proposed method can optimally select the order and fit better in terms of goodness-of-fit comparing to classical methods. Several kernels were introduced for the kernel-based [Formula: see text] modelling method. The results clearly indicated that the stable spline (SS) kernel has the best performance for [Formula: see text] modelling. Particularly, based on the experimental data from 20 participants, the estimated response from the proposed method with SS kernel was significantly better than the results from the benchmark method [i.e., prediction error method (PEM)] ([Formula: see text] vs [Formula: see text]). The proposed nonparametric modelling method is an effective method for the estimation of the impulse response of VO 2 -Speed system. Furthermore, the identified average nonparametric model method can dynamically predict [Formula: see text] response with acceptable accuracy during treadmill exercise.

Viscous decay of nonlinear oscillations of a spherical bubble at large Reynolds number

NASA Astrophysics Data System (ADS)

Smith, W. R.; Wang, Q. X.

2017-08-01

The long-time viscous decay of large-amplitude bubble oscillations is considered in an incompressible Newtonian fluid, based on the Rayleigh-Plesset equation. At large Reynolds numbers, this is a multi-scaled problem with a short time scale associated with inertial oscillation and a long time scale associated with viscous damping. A multi-scaled perturbation method is thus employed to solve the problem. The leading-order analytical solution of the bubble radius history is obtained to the Rayleigh-Plesset equation in a closed form including both viscous and surface tension effects. Some important formulae are derived including the following: the average energy loss rate of the bubble system during each cycle of oscillation, an explicit formula for the dependence of the oscillation frequency on the energy, and an implicit formula for the amplitude envelope of the bubble radius as a function of the energy. Our theory shows that the energy of the bubble system and the frequency of oscillation do not change on the inertial time scale at leading order, the energy loss rate on the long viscous time scale being inversely proportional to the Reynolds number. These asymptotic predictions remain valid during each cycle of oscillation whether or not compressibility effects are significant. A systematic parametric analysis is carried out using the above formula for the energy of the bubble system, frequency of oscillation, and minimum/maximum bubble radii in terms of the Reynolds number, the dimensionless initial pressure of the bubble gases, and the Weber number. Our results show that the frequency and the decay rate have substantial variations over the lifetime of a decaying oscillation. The results also reveal that large-amplitude bubble oscillations are very sensitive to small changes in the initial conditions through large changes in the phase shift.

Radiation-driven winds of hot stars. VI - Analytical solutions for wind models including the finite cone angle effect

NASA Technical Reports Server (NTRS)

Kudritzki, R. P.; Pauldrach, A.; Puls, J.; Abbott, D. C.

1989-01-01

Analytical solutions for radiation-driven winds of hot stars including the important finite cone angle effect (see Pauldrach et al., 1986; Friend and Abbott, 1986) are derived which approximate the detailed numerical solutions of the exact wind equation of motion very well. They allow a detailed discussion of the finite cone angle effect and provide for given line force parameters k, alpha, delta definite formulas for mass-loss rate M and terminal velocity v-alpha as function of stellar parameters.

Distance numbers and Wiener indices of IPR fullerenes with formula C10(n-2) (n ≥ 8) in analytical forms

NASA Astrophysics Data System (ADS)

Ghosh, Tapanendu; Mondal, Sukanya; Mondal, Swapnadeep; Mandal, Bholanath

2018-06-01

The IPR fullerenes C10(n-2) with n ≥ 8 have been considered for obtaining their distance numbers and hence the Wiener indices in analytical forms for both even and odd n. The distance numbers along with their patterns have been found to give the number of 13C NMR signals with their respective intensity ratios. Logarithms of Wiener indices have been found to correlate well with the band (HOMO-LUMO) gaps and resonance energies of the respective fullerenes.

A Stochastic Super-Exponential Growth Model for Population Dynamics

NASA Astrophysics Data System (ADS)

Avila, P.; Rekker, A.

2010-11-01

A super-exponential growth model with environmental noise has been studied analytically. Super-exponential growth rate is a property of dynamical systems exhibiting endogenous nonlinear positive feedback, i.e., of self-reinforcing systems. Environmental noise acts on the growth rate multiplicatively and is assumed to be Gaussian white noise in the Stratonovich interpretation. An analysis of the stochastic super-exponential growth model with derivations of exact analytical formulae for the conditional probability density and the mean value of the population abundance are presented. Interpretations and various applications of the results are discussed.

One-dimensional magnetohydrodynamics of a cylindrical liner imploded by an azimuthal magnetic field and compressing an axial field

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

Hamann, F., E-mail: franck.hamann@cea.fr; Combis, P.; Videau, L.

The one-dimensional magnetohydrodynamics of a plasma cylindrical liner is addressed in the case of a two components magnetic field. The azimuthal component is responsible for the implosion of the liner and the axial field is compressed inside the liner. A complete set of analytical profiles for the magnetic field components, the density, and the local velocity are proposed at the scale of the liner thickness. Numerical simulations are also presented to test the validity of the analytical formulas.

Shedding light on food fraud: spectrophotometric and spectroscopic methods as a tool against economically motivated adulteration of food

NASA Astrophysics Data System (ADS)

Petronijević, R. B.; Velebit, B.; Baltić, T.

2017-09-01

Intentional modification of food or substitution of food ingredients with the aim of gaining profit is food fraud or economically motivated adulteration (EMA). EMA appeared in the food supply chain, and following the global expansion of the food market, has become a world-scale problem for the global economy. Food frauds have involved oils, milk and meat products, infant formula, honey, juices, spices, etc. New legislation was enacted in the last decade in order to fight EMA. Effective analytical methods for food fraud detection are few and still in development. The majority of the methods in common use today for EMA detection are time consuming and inappropriate for use on the production line or out of the laboratory. The next step in the evolution of analytical techniques to combat food fraud is development of fast, accurate methods applicable using portable or handheld devices. Spectrophotometric and spectroscopic methods combined with chemometric analysis, and perhaps in combination with other rapid physico-chemical techniques, could be the answer. This review discusses some analytical techniques based on spectrophotometry and spectroscopy, which are used to reveal food fraud and EMA.

From bead to rod: Comparison of theories by measuring translational drag coefficients of micron-sized magnetic bead-chains in Stokes flow

PubMed Central

Lu, Chen; Zhao, Xiaodan; Kawamura, Ryo

2017-01-01

Frictional drag force on an object in Stokes flow follows a linear relationship with the velocity of translation and a translational drag coefficient. This drag coefficient is related to the size, shape, and orientation of the object. For rod-like objects, analytical solutions of the drag coefficients have been proposed based on three rough approximations of the rod geometry, namely the bead model, ellipsoid model, and cylinder model. These theories all agree that translational drag coefficients of rod-like objects are functions of the rod length and aspect ratio, but differ among one another on the correction factor terms in the equations. By tracking the displacement of the particles through stationary fluids of calibrated viscosity in magnetic tweezers setup, we experimentally measured the drag coefficients of micron-sized beads and their bead-chain formations with chain length of 2 to 27. We verified our methodology with analytical solutions of dimers of two touching beads, and compared our measured drag coefficient values of rod-like objects with theoretical calculations. Our comparison reveals several analytical solutions that used more appropriate approximation and derived formulae that agree with our measurement better. PMID:29145447

A study of density effects in plasmas using analytical approximations for the self-consistent potential

NASA Astrophysics Data System (ADS)

Poirier, M.

2015-06-01

Density effects in ionized matter require particular attention since they modify energies, wavefunctions and transition rates with respect to the isolated-ion situation. The approach chosen in this paper is based on the ion-sphere model involving a Thomas-Fermi-like description for free electrons, the bound electrons being described by a full quantum mechanical formalism. This permits to deal with plasmas out of thermal local equilibrium, assuming only a Maxwell distribution for free electrons. For H-like ions, such a theory provides simple and rather accurate analytical approximations for the potential created by free electrons. Emphasis is put on the plasma potential rather than on the electron density, since the energies and wavefunctions depend directly on this potential. Beyond the uniform electron gas model, temperature effects may be analyzed. In the case of H-like ions, this formalism provides analytical perturbative expressions for the energies, wavefunctions and transition rates. Explicit expressions are given in the case of maximum orbital quantum number, and compare satisfactorily with results from a direct integration of the radial Schrödinger equation. Some formulas for lower orbital quantum numbers are also proposed.

Reference Materials: Critical Importance to the Infant Formula Industry.

PubMed

Wargo, Wayne F

2017-09-01

Infant formula is one of the most regulated foods in the world. It has advanced in complexity over the years as a result of numerous research innovations. To ensure product safety and quality, analytical technologies have also had to advance to keep pace. Given the rigorous performance demands expected of these methods and the ever-growing array of complex matrixes, there is the potential for gaps to exist in current Official MethodsSM and other recognized international methods for infant formula and adult nutritionals. Food safety concerns, particularly for infants, drive the need for extensive testing by manufacturers and regulators. The net effect is the potential for an increase in time- and resource-consuming regulatory disputes. In an effort to mitigate such costly activities, AOAC INTERNATIONAL, under the direction of the Infant Formula Council of America-a trade association of manufacturers and marketers of formulated nutritional products-agreed to establish voluntary consensus Standard Method Performance Requirements, and, ultimately, to identify and publish globally recognized, fit-for-purpose standard methods. To accomplish this task, nutritional reference materials (RMs), representing all major commercially available nutritional formulations, were (and continue to be) a critical necessity. In this paper, various types of RMs will be defined, followed by review and discussion of their importance to the infant formula industry.

Intervening on risk factors for coronary heart disease: an application of the parametric g-formula.

PubMed

Taubman, Sarah L; Robins, James M; Mittleman, Murray A; Hernán, Miguel A

2009-12-01

Estimating the population risk of disease under hypothetical interventions--such as the population risk of coronary heart disease (CHD) were everyone to quit smoking and start exercising or to start exercising if diagnosed with diabetes--may not be possible using standard analytic techniques. The parametric g-formula, which appropriately adjusts for time-varying confounders affected by prior exposures, is especially well suited to estimating effects when the intervention involves multiple factors (joint interventions) or when the intervention involves decisions that depend on the value of evolving time-dependent factors (dynamic interventions). We describe the parametric g-formula, and use it to estimate the effect of various hypothetical lifestyle interventions on the risk of CHD using data from the Nurses' Health Study. Over the period 1982-2002, the 20-year risk of CHD in this cohort was 3.50%. Under a joint intervention of no smoking, increased exercise, improved diet, moderate alcohol consumption and reduced body mass index, the estimated risk was 1.89% (95% confidence interval: 1.46-2.41). We discuss whether the assumptions required for the validity of the parametric g-formula hold in the Nurses' Health Study data. This work represents the first large-scale application of the parametric g-formula in an epidemiologic cohort study.

Universal fitting formulae for baryon oscillation surveys

NASA Astrophysics Data System (ADS)

Blake, Chris; Parkinson, David; Bassett, Bruce; Glazebrook, Karl; Kunz, Martin; Nichol, Robert C.

2006-01-01

The next generation of galaxy surveys will attempt to measure the baryon oscillations in the clustering power spectrum with high accuracy. These oscillations encode a preferred scale which may be used as a standard ruler to constrain cosmological parameters and dark energy models. In this paper we present simple analytical fitting formulae for the accuracy with which the preferred scale may be determined in the tangential and radial directions by future spectroscopic and photometric galaxy redshift surveys. We express these accuracies as a function of survey parameters such as the central redshift, volume, galaxy number density and (where applicable) photometric redshift error. These fitting formulae should greatly increase the efficiency of optimizing future surveys, which requires analysis of a potentially vast number of survey configurations and cosmological models. The formulae are calibrated using a grid of Monte Carlo simulations, which are analysed by dividing out the overall shape of the power spectrum before fitting a simple decaying sinusoid to the oscillations. The fitting formulae reproduce the simulation results with a fractional scatter of 7 per cent (10 per cent) in the tangential (radial) directions over a wide range of input parameters. We also indicate how sparse-sampling strategies may enhance the effective survey area if the sampling scale is much smaller than the projected baryon oscillation scale.

The use of reference change values in clinical laboratories.

PubMed

Bugdayci, Guler; Oguzman, Hamdi; Arattan, Havva Yasemin; Sasmaz, Guler

2015-01-01

The use of Reference Change Values (RCV) has been advocated as very useful for monitoring individuals. Most of these are performed for monitoring individuals in acute situations and for following up the improvement or deterioration of chronic diseases. In our study, we aimed at evaluating the RCV calculation for 24 clinical chemistry analytes widely used in clinical laboratories and the utilization of this data. Twenty-four serum samples were analyzed with Abbott kits (Abbott Laboratories, Abbott Park, IL, USA), manufactured for use with the Architect c8000 (Abbott Laboratories, Abbott Park, IL, USA) auto-analyzer. We calculated RCV using the following formula: RCV = Z x 2 1/2x (CVA2 + CVw2)1/2. Four reference change values (RCV) were calculated for each analyte using four statistical probabilities (0.95, and 0.99, unidirectional and bidirectional). Moreover, by providing an interval after identifying upper and lower limits with the Reference Change Factor (RCF), serially measured tests were calculated by using two formulas: exp (Z x 2 1/2 x (CV(A)2 + CVw2)½/100) for RCF(UP) and (1/RCF(UP)) for RCF(DOWN). RCVs of these analytes were calculated as 14.63% for glucose, 29.88% for urea, 17.75% for ALP, 53.39% for CK, 46.98% for CK-MB, 21.00% amylase, 8.00% for total protein, 8.70% for albumin, 51.08% for total bilirubin, 86.34% for direct bilirubin, 6.40% for calcium, 15.03% for creatinine, 21.47% for urate, 14.19% for total cholesterol, 46.62% for triglyceride, 20.51% for HDL-cholesterol, 29.59% for AST, 46.31% for ALT, 31.54% for GGT, 20.92% for LDH, 19.75% for inorganic phosphate, 3.05% for sodium, 11.75% for potassium, 4.44% for chloride (RCV, p < 0.05, unidirectionally). We suggest using RCV as well as using population-based reference intervals in clinical laboratories. RCV could be available as a tool for making clinical decision, especially when monitoring individuals.

Improvement of Glucose Metabolism in Patients with Impaired Glucose Tolerance or Diabetes by Long-Term Administration of a Palatinose-Based Liquid Formula as a Part of Breakfast

PubMed Central

Sakuma, Masae; Arai, Hidekazu; Mizuno, Akira; Fukaya, Makiko; Matsuura, Motoi; Sasaki, Hajime; Yamanaka-Okumura, Hisami; Yamamoto, Hironori; Taketani, Yutaka; Doi, Toshio; Takeda, Eiji

2009-01-01

A palatinose-based liquid formula (palatinose-formula), suppresses postprandial plasma glucose and insulin levels in healthy men. The objective of this study was to investigate the effects of long-term palatinose-formula ingestion on glucose metabolism in patients with impaired glucose tolerance (IGT) or type 2 diabetes. Two patients with IGT and 7 patients with type 2 diabetes participated in the palatinose-formula and dextrin-based liquid formula (dextrin-formula) loading test and long-term palatinose-formula administration study. After a 3-month control period, palatinose-formula (1046 kJ) was ingested daily by patients as a part of breakfast for 5 months. In the loading test, palatinose-formula suppressed postprandial plasma glucose and insulin levels and areas under the curve compared with those after dextrin-formula ingestion. In the long-term study, glycated hemoglobin levels (after 3 months and 5 months of treatment) and serum 8-hydroxydeoxyguanosine levels (after 5 months of treatment) were markedly decreased comparing with those at baseline. Intake of 1046 kJ palatinose-formula as a part of breakfast over a long-term period may be effective for improvement of glucose metabolism in patients with IGT or type 2 diabetes. PMID:19794923

Descendants of the first stars: the distinct chemical signature of second generation stars

NASA Astrophysics Data System (ADS)

Hartwig, Tilman; Yoshida, Naoki; Magg, Mattis; Frebel, Anna; Glover, Simon C. O.; Gómez, Facundo A.; Griffen, Brendan; Ishigaki, Miho N.; Ji, Alexander P.; Klessen, Ralf S.; O'Shea, Brian W.; Tominaga, Nozomu

2018-05-01

Extremely metal-poor (EMP) stars in the Milky Way (MW) allow us to infer the properties of their progenitors by comparing their chemical composition to the metal yields of the first supernovae. This method is most powerful when applied to mono-enriched stars, i.e. stars that formed from gas that was enriched by only one previous supernova. We present a novel diagnostic to identify this subclass of EMP stars. We model the first generations of star formation semi-analytically, based on dark matter halo merger trees that yield MW-like halos at the present day. Radiative and chemical feedback are included self-consistently and we trace all elements up to zinc. Mono-enriched stars account for only ˜1% of second generation stars in our fiducial model and we provide an analytical formula for this probability. We also present a novel analytical diagnostic to identify mono-enriched stars, based on the metal yields of the first supernovae. This new diagnostic allows us to derive our main results independently from the specific assumptions made regarding Pop III star formation, and we apply it to a set of observed EMP stars to demonstrate its strengths and limitations. Our results may provide selection criteria for current and future surveys and therefore contribute to a deeper understanding of EMP stars and their progenitors.

Simple Physics-Based Analytical Formulas for the Potentials of Mean Force of the Interaction of Amino Acid Side Chains in Water. VII. Charged-Hydrophobic/Polar and Polar-Hydrophobic/Polar Side Chains.

PubMed

Makowski, Mariusz; Liwo, Adam; Scheraga, Harold A

2017-01-19

The physics-based potentials of side-chain-side-chain interactions corresponding to pairs composed of charged and polar, polar and polar, charged and hydrophobic, and hydrophobic and hydrophobic side chains have been determined. A total of 144 four-dimensional potentials of mean force (PMFs) of all possible pairs of molecules modeling these pairs were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation, and the analytical expressions were then fitted to the PMFs. Depending on the type of interacting sites, the analytical approximation to the PMF is a sum of terms corresponding to van der Waals interactions and cavity-creation involving the nonpolar sections of the side chains and van der Waals, cavity-creation, and electrostatic (charge-dipole or dipole-dipole) interaction energies and polarization energies involving the charged or polar sections of the side chains. The model used in this work reproduces all features of the interacting pairs. The UNited RESidue force field with the new side-chain-side-chain interaction potentials was preliminarily tested with the N-terminal part of the B-domain of staphylococcal protein A (PDBL 1BDD ; a three-α-helix bundle) and UPF0291 protein YnzC from Bacillus subtilis (PDB: 2HEP ; an α-helical hairpin).

Towards physics responsible for large-scale Lyman-α forest bias parameters

DOE PAGES

Agnieszka M. Cieplak; Slosar, Anze

2016-03-08

Using a series of carefully constructed numerical experiments based on hydrodynamic cosmological SPH simulations, we attempt to build an intuition for the relevant physics behind the large scale density (b δ) and velocity gradient (b η) biases of the Lyman-α forest. Starting with the fluctuating Gunn-Peterson approximation applied to the smoothed total density field in real-space, and progressing through redshift-space with no thermal broadening, redshift-space with thermal broadening and hydrodynamically simulated baryon fields, we investigate how approximations found in the literature fare. We find that Seljak's 2012 analytical formulae for these bias parameters work surprisingly well in the limit ofmore » no thermal broadening and linear redshift-space distortions. We also show that his b η formula is exact in the limit of no thermal broadening. Since introduction of thermal broadening significantly affects its value, we speculate that a combination of large-scale measurements of b η and the small scale flux PDF might be a sensitive probe of the thermal state of the IGM. Lastly, we find that large-scale biases derived from the smoothed total matter field are within 10–20% to those based on hydrodynamical quantities, in line with other measurements in the literature.« less

Fully Bayesian inference for structural MRI: application to segmentation and statistical analysis of T2-hypointensities.

PubMed

Schmidt, Paul; Schmid, Volker J; Gaser, Christian; Buck, Dorothea; Bührlen, Susanne; Förschler, Annette; Mühlau, Mark

2013-01-01

Aiming at iron-related T2-hypointensity, which is related to normal aging and neurodegenerative processes, we here present two practicable approaches, based on Bayesian inference, for preprocessing and statistical analysis of a complex set of structural MRI data. In particular, Markov Chain Monte Carlo methods were used to simulate posterior distributions. First, we rendered a segmentation algorithm that uses outlier detection based on model checking techniques within a Bayesian mixture model. Second, we rendered an analytical tool comprising a Bayesian regression model with smoothness priors (in the form of Gaussian Markov random fields) mitigating the necessity to smooth data prior to statistical analysis. For validation, we used simulated data and MRI data of 27 healthy controls (age: [Formula: see text]; range, [Formula: see text]). We first observed robust segmentation of both simulated T2-hypointensities and gray-matter regions known to be T2-hypointense. Second, simulated data and images of segmented T2-hypointensity were analyzed. We found not only robust identification of simulated effects but also a biologically plausible age-related increase of T2-hypointensity primarily within the dentate nucleus but also within the globus pallidus, substantia nigra, and red nucleus. Our results indicate that fully Bayesian inference can successfully be applied for preprocessing and statistical analysis of structural MRI data.

Dual-Laboratory Validation of a Method for the Determination of Fructans in Infant Formula and Adult Nutritionals: First Action 2016.14.

PubMed

Brunt, Kommer; Sanders, Peter; Spichtig, Véronique; Ernste-Nota, Veronica; Sawicka, Paulina; Iwanoff, Kimberley; Van Soest, Jeroen; Lin, Paul Kong Thoo; Austin, Sean

2017-05-01

Until recently, only two AOAC Official MethodsSM have been available for the analysis of fructans: Method 997.08 and Method 999.03. Both are based on the analysis of the fructan component monosaccharides (glucose and fructose) after hydrolysis. The two methods have some limitations due to the strategies used for removing background interferences (such as from sucrose, α-glucooligosaccharides, and free sugars). The method described in this paper has been developed to overcome those limitations. The method is largely based on Method 999.03 and uses combined enzymatic and SPE steps to remove the interfering components without impacting the final analytical result. The method has been validated in two laboratories on infant formula and adult nutritionals. Recoveries were in the range of 86-119%, with most being in the range of 91-104%. RSDr values were in the range of 0.7-2.6%, with one exception when the fructan concentration was close to the LOQ, resulting in an RSDr of 8.9%. The performance is generally within the requirements outlined in the AOAC Standard Method Performance Requirements (SMPR® 2014.002), which specifies recoveries in the range of 90-110% and RSDr values below 6%.

Towards physics responsible for large-scale Lyman-α forest bias parameters

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

Agnieszka M. Cieplak; Slosar, Anze

Using a series of carefully constructed numerical experiments based on hydrodynamic cosmological SPH simulations, we attempt to build an intuition for the relevant physics behind the large scale density (b δ) and velocity gradient (b η) biases of the Lyman-α forest. Starting with the fluctuating Gunn-Peterson approximation applied to the smoothed total density field in real-space, and progressing through redshift-space with no thermal broadening, redshift-space with thermal broadening and hydrodynamically simulated baryon fields, we investigate how approximations found in the literature fare. We find that Seljak's 2012 analytical formulae for these bias parameters work surprisingly well in the limit ofmore » no thermal broadening and linear redshift-space distortions. We also show that his b η formula is exact in the limit of no thermal broadening. Since introduction of thermal broadening significantly affects its value, we speculate that a combination of large-scale measurements of b η and the small scale flux PDF might be a sensitive probe of the thermal state of the IGM. Lastly, we find that large-scale biases derived from the smoothed total matter field are within 10–20% to those based on hydrodynamical quantities, in line with other measurements in the literature.« less

Bayesian Inference of Natural Rankings in Incomplete Competition Networks

PubMed Central

Park, Juyong; Yook, Soon-Hyung

2014-01-01

Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest – essential in determining reward and penalty – is frequently an ambiguous task due to the incomplete (partially filled) nature of competition networks. Here we introduce the “Natural Ranking,” an unambiguous ranking method applicable to a round robin tournament, and formulate an analytical model based on the Bayesian formula for inferring the expected mean and error of the natural ranking of nodes from an incomplete network. We investigate its potential and uses in resolving important issues of ranking by applying it to real-world competition networks. PMID:25163528

Robust LOD scores for variance component-based linkage analysis.

PubMed

Blangero, J; Williams, J T; Almasy, L

2000-01-01

The variance component method is now widely used for linkage analysis of quantitative traits. Although this approach offers many advantages, the importance of the underlying assumption of multivariate normality of the trait distribution within pedigrees has not been studied extensively. Simulation studies have shown that traits with leptokurtic distributions yield linkage test statistics that exhibit excessive Type I error when analyzed naively. We derive analytical formulae relating the deviation from the expected asymptotic distribution of the lod score to the kurtosis and total heritability of the quantitative trait. A simple correction constant yields a robust lod score for any deviation from normality and for any pedigree structure, and effectively eliminates the problem of inflated Type I error due to misspecification of the underlying probability model in variance component-based linkage analysis.

Compact cross-dispersion device based on a prism and a plane transmission grating

NASA Astrophysics Data System (ADS)

Yang, Qinghua; Wang, Weiqiang

2018-05-01

This paper presents a cross-dispersion prism-grating device using a plane transmission grating attached directly to a prism, which is different from traditional cross-dispersion grating-prism systems that are based on the reflection grating. Unlike conventional direct-vision grism or constant-dispersion grism in which both the prism and grating have the same dispersion direction, for this device the dispersion directions of the prism and grating are different. The analytical expressions for the cross-dispersion of this device are derived in detail and the formulas of the footprint of the dispersed spectra are given. The numerical results and ray-tracing simulations by ZEMAX are shown. The device provides a compact, small-sized and broadband cross-dispersion device used for the medium resolution spectrometer.

Bayesian Inference of Natural Rankings in Incomplete Competition Networks

NASA Astrophysics Data System (ADS)

Park, Juyong; Yook, Soon-Hyung

2014-08-01

Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest - essential in determining reward and penalty - is frequently an ambiguous task due to the incomplete (partially filled) nature of competition networks. Here we introduce the ``Natural Ranking,'' an unambiguous ranking method applicable to a round robin tournament, and formulate an analytical model based on the Bayesian formula for inferring the expected mean and error of the natural ranking of nodes from an incomplete network. We investigate its potential and uses in resolving important issues of ranking by applying it to real-world competition networks.

Soy-Based Therapeutic Baby Formulas: Testable Hypotheses Regarding the Pros and Cons.

PubMed

Westmark, Cara J

2016-01-01

Soy-based infant formulas have been consumed in the United States since 1909, and currently constitute a significant portion of the infant formula market. There are efforts underway to generate genetically modified soybeans that produce therapeutic agents of interest with the intent to deliver those agents in a soy-based infant formula platform. The threefold purpose of this review article is to first discuss the pros and cons of soy-based infant formulas, then present testable hypotheses to discern the suitability of a soy platform for drug delivery in babies, and finally start a discussion to inform public policy on this important area of infant nutrition.

Analytical response function for planar Ge detectors

NASA Astrophysics Data System (ADS)

García-Alvarez, Juan A.; Maidana, Nora L.; Vanin, Vito R.; Fernández-Varea, José M.

2016-04-01

We model the response function (RF) of planar HPGe x-ray spectrometers for photon energies between around 10 keV and 100 keV. The RF is based on the proposal of Seltzer [1981. Nucl. Instrum. Methods 188, 133-151] and takes into account the full-energy absorption in the Ge active volume, the escape of Ge Kα and Kβ x-rays and the escape of photons after one Compton interaction. The relativistic impulse approximation is employed instead of the Klein-Nishina formula to describe incoherent photon scattering in the Ge crystal. We also incorporate a simple model for the continuous component of the spectrum produced by the escape of photo-electrons from the active volume. In our calculations we include external interaction contributions to the RF: (i) the incoherent scattering effects caused by the detector's Be window and (ii) the spectrum produced by photo-electrons emitted in the Ge dead layer that reach the active volume. The analytical RF model is compared with pulse-height spectra simulated using the PENELOPE Monte Carlo code.

Hollow vortex Gaussian beams

NASA Astrophysics Data System (ADS)

Zhou, GuoQuan; Cai, YangJian; Dai, ChaoQing

2013-05-01

A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular momentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respectively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter γ, and transfer matrix elements A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in optical micromanipulation.

Two dimensional model for coherent synchrotron radiation

NASA Astrophysics Data System (ADS)

Huang, Chengkun; Kwan, Thomas J. T.; Carlsten, Bruce E.

2013-01-01

Understanding coherent synchrotron radiation (CSR) effects in a bunch compressor requires an accurate model accounting for the realistic beam shape and parameters. We extend the well-known 1D CSR analytic model into two dimensions and develop a simple numerical model based on the Liénard-Wiechert formula for the CSR field of a coasting beam. This CSR numerical model includes the 2D spatial dependence of the field in the bending plane and is accurate for arbitrary beam energy. It also removes the singularity in the space charge field calculation present in a 1D model. Good agreement is obtained with 1D CSR analytic result for free electron laser (FEL) related beam parameters but it can also give a more accurate result for low-energy/large spot size beams and off-axis/transient fields. This 2D CSR model can be used for understanding the limitation of various 1D models and for benchmarking fully electromagnetic multidimensional particle-in-cell simulations for self-consistent CSR modeling.

Partially ionized hydrogen plasma in strong magnetic fields.

PubMed

Potekhin, A Y; Chabrier, G; Shibanov, Y A

1999-08-01

We study the thermodynamic properties of a partially ionized hydrogen plasma in strong magnetic fields, B approximately 10(12)-10(13) G, typical of neutron stars. The properties of the plasma depend significantly on the quantum-mechanical sizes and binding energies of the atoms, which are strongly modified by thermal motion across the field. We use new fitting formulas for the atomic binding energies and sizes, based on accurate numerical calculations and valid for any state of motion of the atom. In particular, we take into account decentered atomic states, neglected in previous studies of thermodynamics of magnetized plasmas. We also employ analytic fits for the thermodynamic functions of nonideal fully ionized electron-ion Coulomb plasmas. This enables us to construct an analytic model of the free energy. An ionization equilibrium equation is derived, taking into account the strong magnetic field effects and the nonideality effects. This equation is solved by an iteration technique. Ionization degrees, occupancies, and the equation of state are calculated.

Nonlinearity in bacterial population dynamics: Proposal for experiments for the observation of abrupt transitions in patches

PubMed Central

Kenkre, V. M.; Kumar, Niraj

2008-01-01

An explicit proposal for experiments leading to abrupt transitions in spatially extended bacterial populations in a Petri dish is presented on the basis of an exact formula obtained through an analytic theory. The theory provides accurately the transition expressions despite the fact that the actual solutions, which involve strong nonlinearity, are inaccessible to it. The analytic expressions are verified through numerical solutions of the relevant nonlinear equation. The experimental setup suggested uses opaque masks in a Petri dish bathed in ultraviolet radiation [Lin A-L, et al. (2004) Biophys J 87:75–80 and Perry N (2005) J R Soc Interface 2:379–387], but is based on the interplay of two distances the bacteria must traverse, one of them favorable and the other adverse. As a result of this interplay feature, the experiments proposed introduce highly enhanced reliability in interpretation of observations and in the potential for extraction of system parameters. PMID:19033185

26 CFR 1.411(a)(13)-1 - Statutory hybrid plans.

Code of Federal Regulations, 2014 CFR

2014-04-01

... another benefit amount) and at least one of those formulas is a statutory hybrid benefit formula, the... certain statutory hybrid plans that determine benefits under a lump sum-based benefit formula. Paragraph... current balance or current value under a lump sum-based benefit formula. Pursuant to section 411(a)(13)(A...

26 CFR 1.411(a)(13)-1 - Statutory hybrid plans.

Code of Federal Regulations, 2013 CFR

2013-04-01

... another benefit amount) and at least one of those formulas is a statutory hybrid benefit formula, the... certain statutory hybrid plans that determine benefits under a lump sum-based benefit formula. Paragraph... current balance or current value under a lump sum-based benefit formula. Pursuant to section 411(a)(13)(A...

26 CFR 1.411(a)(13)-1 - Statutory hybrid plans.

Code of Federal Regulations, 2012 CFR

2012-04-01

... another benefit amount) and at least one of those formulas is a statutory hybrid benefit formula, the... certain statutory hybrid plans that determine benefits under a lump sum-based benefit formula. Paragraph... current balance or current value under a lump sum-based benefit formula. Pursuant to section 411(a)(13)(A...

26 CFR 1.411(a)(13)-1 - Statutory hybrid plans.

Code of Federal Regulations, 2011 CFR

2011-04-01

... another benefit amount) and at least one of those formulas is a statutory hybrid benefit formula, the... certain statutory hybrid plans that determine benefits under a lump sum-based benefit formula. Paragraph... current balance or current value under a lump sum-based benefit formula. Pursuant to section 411(a)(13)(A...

Infant formula promotes bone growth in neonatal piglets by enhancing osteoblastogenesis through bone morphogenic protein signaling

USDA-ARS?s Scientific Manuscript database

Relatively few studies have examined the effects of formula feeding relative to breast-feeding on bone in the neonate. Using peripheral quantitative CT scan and histomorphometric analysis, we demonstrated that neonatal piglets fed with soy-based formula (SF) and cow milk-based formula (MF) for 21 or...

Breast development in the first 2 years of life: an association with soy-based infant formulas.

PubMed

Zung, Amnon; Glaser, Tamar; Kerem, Zohar; Zadik, Zvi

2008-02-01

To evaluate the estrogenic effect of soy-based formulas in female infants. These formulas contain significant amounts of phytoestrogens, compounds with structural similarity to estradiol. A cross-sectional study consisting of 694 female infants ages 3 to 24 months that consecutively attended 10 general pediatric clinics, none of them having been referred for breast development. The presence of breast buds served as a marker for the endocrine effect of soy-derived phytoestrogens. Of the participants, 92 had consumed soy formulas for more than 3 months. Breast tissue was more prevalent in the second year of life in infants fed soy-based formula vs those that were breast-fed and those fed dairy-based formula (22.0% vs 10.3%; P = 0.02) with an odds ratio of 2.45 (95% confidence interval 1.11-5.39). No differences in breast bud prevalence were observed during the first year of life. Unlike infants on dairy-based formulas and breast-feeding, infants fed a soy-based formula did not demonstrate a decline in the prevalence of breast during the second year of life. We suggest that phytoestrogens impose a preserving effect on breast tissue that is evolved in early infancy, leading eventually to a slower waning of infantile breast tissue.

Growth and Clinical Variables in Nitrogen-Restricted Piglets Fed an Adjusted Essential Amino Acid Mix: Effects of Partially Intact Protein-Based Diets.

PubMed

Worsøe, Päivi S; Sangild, Per T; van Goudoever, Johannes B; Koletzko, Berthold; van der Beek, Eline M; Abrahamse-Berkeveld, Marieke; Burrin, Douglas G; van de Heijning, Bert J M; Thymann, Thomas

2018-06-13

Current recommendations for protein levels in infant formula are intended to ensure that growth matches or exceeds growth of breastfed infants, but may provide a surplus of amino acids (AAs). Recent infant studies with AA-based formulas support specific adjustment of the essential amino acid (EAA) composition allowing for potential lowering of total protein levels. With the use of a combination of intact protein and free EAAs, we designed a formula that meets these adjusted EAA requirements for infants. Our objective was to test whether this adjusted formula is safe and supports growth in a protein-restricted piglet model, and whether it shows better growth than an isonitrogenous formula based on free AAs. Term piglets (Landrace × Yorkshire × Duroc, n = 72) were fed 1 of 4 isoenergetic formulas containing 70% intact protein and 30% of an EAA mixture or a complete AA-based control for 20 d: standard formula (ST-100), ST-100 with 25% reduction in proteinaceous nitrogen (ST-75), ST-75 with an adjusted EAA composition (O-75), or a diet as O-75, given as a complete AA-based diet (O-75AA). After an initial adaptation period, ST-75 and O-75 pigs showed similar growth rates, both lower than ST-100 pigs (∼25 compared with 31 g · kg-1 · d-1, respectively). The O-75AA pigs showed further reduced growth rate (15 g · kg-1 · d-1) and fat proportion (both P < 0.05, relative to O-75). Formula based partly on intact protein is superior to AA-based formula in this experimental setting. The 25% lower, but EAA-adjusted, partially intact protein-based formula resulted in similar weight gain with a concomitant increased AA catabolism, compared with the standard 25% lower standard formula in artificially reared, protein-restricted piglets. Further studies should investigate if and how the specific EAA adjustments that allow for lowering of total protein levels will affect growth and body composition development in formula-fed infants.

Ultrathin nanoporous membranes for insulator-based dielectrophoresis.

PubMed

Mukaibo, Hitomi; Wang, Tonghui; Perez-Gonzalez, Victor H; Getpreecharsawas, Jirachai; Wurzer, Jack; Lapizco-Encinas, Blanca H; McGrath, James L

2018-06-08

Insulator-based dielectrophoresis (iDEP) is a simple, scalable mechanism that can be used for directly manipulating particle trajectories in pore-based filtration and separation processes. However, iDEP manipulation of nanoparticles presents unique challenges as the dielectrophoretic force [Formula: see text] exerted on the nanoparticles can easily be overshadowed by opposing kinetic forces. In this study, a molecularly thin, SiN-based nanoporous membrane (NPN) is explored as a breakthrough technology that enhances [Formula: see text] By numerically assessing the gradient of the electric field square [Formula: see text]-a common measure for [Formula: see text] magnitude-it was found that the unique geometrical features of NPN (pore tapering, sharp pore corner and ultrathin thickness) act in favor of intensifying the overall [Formula: see text] A comparative study indicated that [Formula: see text] generated in NPN are four orders of magnitude larger than track-etched polycarbonate membranes with comparable pore size. The stronger [Formula: see text] suggests that iDEP can be conducted under lower voltage bias with NPN: reducing joule heating concerns and enabling solutions to have higher ionic strength. Enabling higher ionic strength solutions may also extend the opportunities of iDEP applications under physiologically relevant conditions. This study also highlights the effects of [Formula: see text] induced by the ion accumulation along charged surfaces (electric-double layer (EDL)). EDL-based [Formula: see text] exists along the entire charged surface, including locations where geometry-based iDEP is negligible. The high surface-to-volume ratio of NPN offers a unique platform for exploiting such EDL-based DEP systems. The EDL-based [Formula: see text] was also found to offset the geometry-based [Formula: see text] but this effect was easily circumvented by reducing the EDL thickness (e.g. increasing the ionic strength from 0.1 to 100 mM). The results from this study imply the potential application of iDEP as a direct, in-operando antifouling mechanism for ultrafiltration technology, and also as an active tuning mechanism to control the cut-off size limit for continuous selectivity of nanomembrane-based separations.

Rice protein-based infant formula: current status and future development.

PubMed

Koo, W W K; Lasekan, J B

2007-02-01

Rice is the world's leading staple cereal food and is the major source of protein for many parts of the world. Rice is among the first solid foods fed to infants in many cultures, in part because of its hypoallergenicity from lack of gluten. Nutritional quality of rice protein compares favorably with other cereal proteins including wheat, oat and barley. It is rich in methionine and cystine, although as is the case for other cereals, it is an incomplete protein source for human infants with lysine and threonine being the primary limiting amino acids. Fortification of rice proteins with these two limiting amino acids improves its protein quality. Rice protein-based infant formulas (RPF) were initially based on high protein rice flours, but more recently are based on rice protein concentrates, isolates or hydrolysates, fortified with lysine and threonine. Hypoallergenicity efficacy, particularly for hydrolyzed rice protein-based formulas, has been reported, and limited data indicated that rice protein based infant formula may provide potentially adequate alternative if standard milk- or soy protein-based formulas are not tolerated. Unlike the rice-protein based infant formula, rice beverage formulas made from rice flour are nutritionally inadequate for infants. Reports have indicated stunted growth in infants/children fed rice beverage formulas. Future development for the RPF include those based on genetically improved rice with high lysine and threonine content, supplementation with appropriate mineral and fat blend, and long-term clinical studies in infants to confirm its efficacy and safety.

Comparison of postoperative vault height predictability using white-to-white or sulcus diameter-based sizing for the visian implantable collamer lens.

PubMed

Reinstein, Dan Z; Lovisolo, Carlo F; Archer, Timothy J; Gobbe, Marine

2013-01-01

To compare vault height predictability of Implantable Collamer Lens (ICL; Staar Surgical) sizing using a sulcus diameter-based formula or the manufacturer-recommended white-to-white-based method. In 50 myopic eyes, ICL size was calculated using both a formula including sulcus diameter and the traditional formula based on white-to-white diameter. Sulcus diameter was measured using Artemis 2 very high-frequency (VHF) digital ultrasound (ArcScan Inc). Implantation was based on the sulcus diameter derived size. Actual postoperative vault height achieved was measured by VHF digital ultrasound scanning. Circle segment trigonometry was used to calculate the vault height that would have resulted had lens sizing been based on the white-to-white formula. The same lens size would have been used in 60% of eyes, a smaller lens would have been used in 34% of eyes and a larger lens in 6% of eyes had lens sizing been based on the white-to-white formula. Mean vault for eyes with lenses sized using the sulcus diameter formula was 0.37±0.16 mm (range: 0.08 to 0.92 mm), with 2% <0.09 mm, the recognized low-vault height for risk of cataract. Circle segment trigonometry predicted that the vault height would have been 0.24±0.28 mm (range: -0.31 to 0.92 mm), with 26% <0.09 mm had lens sizing been based on the white-to-white formula. Significantly better predictability of postoperative vault height was achieved by including sulcus diameter into the ICL sizing formula compared with using the traditional white-to-white-based formula. Copyright 2013, SLACK Incorporated.

Analytical formulae for computing the critical current of an Nb3Sn strand under bending

NASA Astrophysics Data System (ADS)

Ciazynski, D.; Torre, A.

2010-12-01

Works on bending strain in Nb3Sn wires were initiated in support of the 'react-and-wind' technique used to manufacture superconducting coils. More recently, the bending strains of Nb3Sn strands in cable-in-conduit conductors (CICC) under high Lorentz forces have been thought to be partly responsible for the degradation of the conductor performance in terms of critical current and n index, particularly for the international thermonuclear experimental reactor (ITER) conductors. This has led to a new wave of experiments and modelling on this subject. The computation of the current transport capability in an Nb3Sn wire under uniform bending used to be carried out through the so-called Ekin's models, and more recently through numerical simulations with electric networks. The flaws of Ekin's models are that they consider only two extreme cases or limits, namely the so-called long twist pitch (LTP) or short twist pitch (STP) cases, and that these models only allow computation of a value for the critical current without reference to the n index of the superconducting filaments (i.e. this index is implicitly assumed to be infinite). Although the numerical models allow a fine description of the wire under operation and can take into account the filament's n index, they need a refined meshing to be accurate enough and their results may be sensitive to boundary conditions (i.e. current injection in the wire), also general intrinsic parameters cannot be easily identified. In this paper, we propose clearly to go further than Ekin's models by developing, from a homogeneous model and Maxwell's equations, an analytical model to establish the general equation governing the evolution of the electric field inside an Nb3Sn strand under uniform bending (with possible longitudinal strain). Within the usual strand fabrication limits, this equation allows the definition of one single parameter to discriminate the STP and LTP cases. It is also shown that whereas Ekin's LTP model corresponds well to a limiting solution of the problem when the transverse resistivity tends toward zero (or the twist pitch tends towards infinity), Ekin's STP model must be modified (improved) when the filament's n index is finite. Since the general equation cannot be solved analytically, we start from the LTP model and develop a first order correction to be applied when the transverse resistivity, the twist pitch and the filament's n index are finite. Using a simple but realistic law for depicting the strain dependence of the critical current density in the Nb3Sn filaments, we can fully compute the corrected expression and give the result under a general analytical formula for a strand submitted to both bending and compressive/tensile strains. The results are then compared in two different cases with those obtained with the numerical code CARMEN (based on an electrical network) developed at CEA. Last, a semi-empirical formula has been developed to evolve continuously from the LTP limit to the improved STP limit when the transverse resistivity evolves from zero to infinity. The results given by this formula are again compared with the numerical simulations in two different cases. Last, comparisons with experimental results are discussed.

A penalized quantitative structure-property relationship study on melting point of energetic carbocyclic nitroaromatic compounds using adaptive bridge penalty.

PubMed

Al-Fakih, A M; Algamal, Z Y; Lee, M H; Aziz, M

2018-05-01

A penalized quantitative structure-property relationship (QSPR) model with adaptive bridge penalty for predicting the melting points of 92 energetic carbocyclic nitroaromatic compounds is proposed. To ensure the consistency of the descriptor selection of the proposed penalized adaptive bridge (PBridge), we proposed a ridge estimator ([Formula: see text]) as an initial weight in the adaptive bridge penalty. The Bayesian information criterion was applied to ensure the accurate selection of the tuning parameter ([Formula: see text]). The PBridge based model was internally and externally validated based on [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], the Y-randomization test, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and the applicability domain. The validation results indicate that the model is robust and not due to chance correlation. The descriptor selection and prediction performance of PBridge for the training dataset outperforms the other methods used. PBridge shows the highest [Formula: see text] of 0.959, [Formula: see text] of 0.953, [Formula: see text] of 0.949 and [Formula: see text] of 0.959, and the lowest [Formula: see text] and [Formula: see text]. For the test dataset, PBridge shows a higher [Formula: see text] of 0.945 and [Formula: see text] of 0.948, and a lower [Formula: see text] and [Formula: see text], indicating its better prediction performance. The results clearly reveal that the proposed PBridge is useful for constructing reliable and robust QSPRs for predicting melting points prior to synthesizing new organic compounds.

Path Loss Prediction Formula in Urban Area for the Fourth-Generation Mobile Communication Systems

NASA Astrophysics Data System (ADS)

Kitao, Koshiro; Ichitsubo, Shinichi

A site-general type prediction formula is created based on the measurement results in an urban area in Japan assuming that the prediction frequency range required for Fourth-Generation (4G) Mobile Communication Systems is from 3 to 6GHz, the distance range is 0.1 to 3km, and the base station (BS) height range is from 10 to 100m. Based on the measurement results, the path loss (dB) is found to be proportional to the logarithm of the distance (m), the logarithm of the BS height (m), and the logarithm of the frequency (GHz). Furthermore, we examine the extension of existing formulae such as the Okumura-Hata, Walfisch-Ikegami, and Sakagami formulae for 4G systems and propose a prediction formula based on the Extended Sakagami formula.

Flavor, relative palatability and components of cow's milk hydrolysed formulas and amino acid-based formula.

PubMed

Miraglia Del Giudice, Michele; D'Auria, Enza; Peroni, Diego; Palazzo, Samuele; Radaelli, Giovanni; Comberiati, Pasquale; Galdo, Francesca; Maiello, Nunzia; Riva, Enrica

2015-06-03

Both extensively hydrolysed formulas (eHF) and amino acid-based formula (AAFs) have been demonstrated effective for the treatment of CMA. However, in clinical practice, parents complain that hydrolysates are rejected by children due to their bad taste. Flavor of hydrolysed formulas has been poorly investigated although it affects the acceptance of milk over all the other attributes. The aim of the present study was to understand the factors underlying the unpleasant flavor of hydrolysed 25 formulas and amino acid-based formula. One hundred and fifty trained panelists performed a randomized-double-blind test with different milks. The smell, texture, taste and aftertaste of each formula were evaluated on a scale ranging from -2 (worst) to 2 (best). Formulas showed significant difference, as compared to cow's milk, in smell, texture, taste and aftertaste. Overall, whey eHFs were judged of better palatability than casein eHF and the AAFs (p < 0.05). Whey eHF showed significant differences among them for sensory attributes, especially for taste and aftertaste. These results suggest that a broad range of flavor exists among the hydrolysed formulas. Further studies, adequately designed to investigate the relationship between milks' flavor and nutrient profile of hydrolysed formulas are warranted.

Population Density and Moment-based Approaches to Modeling Domain Calcium-mediated Inactivation of L-type Calcium Channels.

PubMed

Wang, Xiao; Hardcastle, Kiah; Weinberg, Seth H; Smith, Gregory D

2016-03-01

We present a population density and moment-based description of the stochastic dynamics of domain [Formula: see text]-mediated inactivation of L-type [Formula: see text] channels. Our approach accounts for the effect of heterogeneity of local [Formula: see text] signals on whole cell [Formula: see text] currents; however, in contrast with prior work, e.g., Sherman et al. (Biophys J 58(4):985-995, 1990), we do not assume that [Formula: see text] domain formation and collapse are fast compared to channel gating. We demonstrate the population density and moment-based modeling approaches using a 12-state Markov chain model of an L-type [Formula: see text] channel introduced by Greenstein and Winslow (Biophys J 83(6):2918-2945, 2002). Simulated whole cell voltage clamp responses yield an inactivation function for the whole cell [Formula: see text] current that agrees with the traditional approach when domain dynamics are fast. We analyze the voltage-dependence of [Formula: see text] inactivation that may occur via slow heterogeneous domain [[Formula: see text

Systematic study on the competition between α-decay and spontaneous fission of superheavy nuclei

NASA Astrophysics Data System (ADS)

Zhang, Y. L.; Wang, Y. Z.

2017-10-01

The competition between α-decay and spontaneous fission (SF) of Z = 112 isotopes are studied. The α-decay half-lives are estimated by the generalized liquid-drop model (GLDM) and several sets of analytic formulas. These formulas include the Royer formula, Viola-Seaborg semiempirical (VSS) formula and universal decay law (UDL). For the SF, its half-lives are calculated by using the Xu, Ren, Karpov and Santhosh formulas. It is shown that the predicted α-decay half-lives by different approaches are more or less identical. However, the SF half-lives are highly sensitive to models. To test the accuracies of different SF formulas, the half-lives of 56 even-even heavy nuclei are calculated by these formulas. By comparing with the experimental data, it is found that the Xu formula is the most accurate one to reproduce the experimental SF half-lives. This allows us to make a systematic prediction on the competition between α-decay and SF of even-even superheavy nuclei (SHN) with Z = 104- 120 by using the Xu formula and the above mentioned models on α-decay. The calculations suggest that 258,260104, 268-276110, 270-280112, 272-286114, 274-294116, 284-302118 and 292-308120 have smaller α-decay half-lives than those of SF. Thus these nuclei can be synthesized and identified via α-decay in the laboratory. In addition, it is observed that N = 162, 178, 184 and 196 may be the submagic or magic numbers. Finally, an extensive study on the possible α-decay chains for Z = 120 isotopes is performed. It is predicted that six sequential α-decay chains can be observed from 292-296120, four α-decay chains from 298120, three α-decay chains from 300,302120, two α-decay chains from 304,306120, and only one α-decay chain from 308120. These nuclei are the most likely candidates to be synthesized experimentally via α-decay in the near future.

Biases and Standard Errors of Standardized Regression Coefficients

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Chan, Wai

2011-01-01

The paper obtains consistent standard errors (SE) and biases of order O(1/n) for the sample standardized regression coefficients with both random and given predictors. Analytical results indicate that the formulas for SEs given in popular text books are consistent only when the population value of the regression coefficient is zero. The sample…

Actuation of Piezoelectric Layered Beams With and Coupling.

PubMed

Nguyen, Cuong H; Hanke, Ulrik; Halvorsen, Einar

2018-05-01

In this paper, we derive and compare the linear static bending of piezoelectric actuators with transversal ( ) and longitudinal ( ) coupling. The transducers are, respectively, structures utilizing top and bottom electrodes (TBEs) and interdigitated electrodes (IDEs). While the theory is well developed for the TBE beam, governing equations for the bending of the piezoelectric beams with IDEs are far less developed. We improve on this by deriving the governing equation for the IDE beam with an arbitrary number of layers and with coupling consistently included. In addition, we introduce a phenomenological quadratic form for the nonuniform field that lets us derive a deflection formula with nontrivial effects of the field accounted for. The theory is applied to derive deflection formulas for both cantilever and clamped-clamped beams. All analytic results are validated with numerical simulations. From the analytic models, two different figures of merit (FOMs) are derived. We show that these FOMs are the same for cantilevers and doubly clamped beams. The analysis indicates the optimal transducer length for clamped-clamped beams and gives a criterion that can be used to determine which design concept ( or ) gives the largest deflection.

Application of the backward extrapolation method to pulsed neutron sources

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

Talamo, Alberto; Gohar, Yousry

We report particle detectors operated in pulse mode are subjected to the dead-time effect. When the average of the detector counts is constant over time, correcting for the dead-time effect is simple and can be accomplished by analytical formulas. However, when the average of the detector counts changes over time it is more difficult to take into account the dead-time effect. When a subcritical nuclear assembly is driven by a pulsed neutron source, simple analytical formulas cannot be applied to the measured detector counts to correct for the dead-time effect because of the sharp change of the detector counts overmore » time. This work addresses this issue by using the backward extrapolation method. The latter can be applied not only to a continuous (e.g. californium) external neutron source but also to a pulsed external neutron source (e.g. by a particle accelerator) driving a subcritical nuclear assembly. Finally, the backward extrapolation method allows to obtain from the measured detector counts both the dead-time value and the real detector counts.« less

GEOS satellite tracking corrections for refraction in the ionosphere

NASA Technical Reports Server (NTRS)

Berbert, J. H.; Parker, H. C.

1970-01-01

The analytic formulations at different elevation angles and at a frequency of 2-GHz for the ionospheric refraction corrections used on the GEOS satellite tracking data are compared. The formulas and ray trace results for elevations greater than 10 deg, where most satellite tracking is done, differ in elevation, range, and range rate by less than 0.4 millidegrees (1.4 arc-seconds), 12 meters, and 12 cm/sec, respectively. In comparison to most operational requirements, this is insignificant. However, for the GEOS Observation Systems Intercomparison Investigation, these differences are equivalent in size to observed differences in system biases for some of the best electronic geodetic tracking systems and are probably contributing to the observed biases. The ray trace results and most of the more detailed analytic correction formulas show that the ionospheric refraction correction for range rate on an overhead pass is a maximum for elevation angles between 15 deg and 30 deg and falls off rapidly for both higher and lower elevation angles, contrary to the effect of the troposphere and to some reports in the literature.

Application of the backward extrapolation method to pulsed neutron sources

DOE PAGES

Talamo, Alberto; Gohar, Yousry

2017-09-23

We report particle detectors operated in pulse mode are subjected to the dead-time effect. When the average of the detector counts is constant over time, correcting for the dead-time effect is simple and can be accomplished by analytical formulas. However, when the average of the detector counts changes over time it is more difficult to take into account the dead-time effect. When a subcritical nuclear assembly is driven by a pulsed neutron source, simple analytical formulas cannot be applied to the measured detector counts to correct for the dead-time effect because of the sharp change of the detector counts overmore » time. This work addresses this issue by using the backward extrapolation method. The latter can be applied not only to a continuous (e.g. californium) external neutron source but also to a pulsed external neutron source (e.g. by a particle accelerator) driving a subcritical nuclear assembly. Finally, the backward extrapolation method allows to obtain from the measured detector counts both the dead-time value and the real detector counts.« less

Valuing options in shot noise market

NASA Astrophysics Data System (ADS)

Laskin, Nick

2018-07-01

A new exactly solvable option pricing model has been introduced and elaborated. It is assumed that a stock price follows a Geometric shot noise process. An arbitrage-free integro-differential option pricing equation has been obtained and solved. The new Greeks have been analytically calculated. It has been shown that in diffusion approximation the developed option pricing model incorporates the well-known Black-Scholes equation and its solution. The stochastic dynamic origin of the Black-Scholes volatility has been uncovered. To model the observed market stock price patterns consisting of high frequency small magnitude and low frequency large magnitude jumps, the superposition of two Geometric shot noises has been implemented. A new generalized option pricing equation has been obtained and its exact solution was found. Merton's jump-diffusion formula for option price was recovered in diffusion approximation. Despite the non-Gaussian nature of probability distributions involved, the new option pricing model has the same degree of analytical tractability as the Black-Scholes model and the Merton jump-diffusion model. This attractive feature allows one to derive exact formulas to value options and option related instruments in the market with jump-like price patterns.

Formula feeding alters hepatic gene expression signature, iron and cholesterol homeostasis in the neonatal pig

USDA-ARS?s Scientific Manuscript database

Although the American Academy of Pediatrics recommends breast feeding for at least the first 6 months of life, formula feeding remains more popular in the US. In the current study, neonatal piglets were breast-fed or were fed commercially available milk-based formula (MF) or soy-based formula (SF) ...

Soy-Based Therapeutic Baby Formulas: Testable Hypotheses Regarding the Pros and Cons

PubMed Central

Westmark, Cara J.

2017-01-01

Soy-based infant formulas have been consumed in the United States since 1909, and currently constitute a significant portion of the infant formula market. There are efforts underway to generate genetically modified soybeans that produce therapeutic agents of interest with the intent to deliver those agents in a soy-based infant formula platform. The threefold purpose of this review article is to first discuss the pros and cons of soy-based infant formulas, then present testable hypotheses to discern the suitability of a soy platform for drug delivery in babies, and finally start a discussion to inform public policy on this important area of infant nutrition. PMID:28149839

Analytical modeling of demagnetizing effect in magnetoelectric ferrite/PZT/ferrite trilayers taking into account a mechanical coupling

NASA Astrophysics Data System (ADS)

Loyau, V.; Aubert, A.; LoBue, M.; Mazaleyrat, F.

2017-03-01

In this paper, we investigate the demagnetizing effect in ferrite/PZT/ferrite magnetoelectric (ME) trilayer composites consisting of commercial PZT discs bonded by epoxy layers to Ni-Co-Zn ferrite discs made by a reactive Spark Plasma Sintering (SPS) technique. ME voltage coefficients (transversal mode) were measured on ferrite/PZT/ferrite trilayer ME samples with different thicknesses or phase volume ratio in order to highlight the influence of the magnetic field penetration governed by these geometrical parameters. Experimental ME coefficients and voltages were compared to analytical calculations using a quasi-static model. Theoretical demagnetizing factors of two magnetic discs that interact together in parallel magnetic structures were derived from an analytical calculation based on a superposition method. These factors were introduced in ME voltage calculations which take account of the demagnetizing effect. To fit the experimental results, a mechanical coupling factor was also introduced in the theoretical formula. This reflects the differential strain that exists in the ferrite and PZT layers due to shear effects near the edge of the ME samples and within the bonding epoxy layers. From this study, an optimization in magnitude of the ME voltage is obtained. Lastly, an analytical calculation of demagnetizing effect was conducted for layered ME composites containing higher numbers of alternated layers (n ≥ 5). The advantage of such a structure is then discussed.

An explicit closed-form analytical solution for European options under the CGMY model

NASA Astrophysics Data System (ADS)

Chen, Wenting; Du, Meiyu; Xu, Xiang

2017-01-01

In this paper, we consider the analytical pricing of European path-independent options under the CGMY model, which is a particular type of pure jump Le´vy process, and agrees well with many observed properties of the real market data by allowing the diffusions and jumps to have both finite and infinite activity and variation. It is shown that, under this model, the option price is governed by a fractional partial differential equation (FPDE) with both the left-side and right-side spatial-fractional derivatives. In comparison to derivatives of integer order, fractional derivatives at a point not only involve properties of the function at that particular point, but also the information of the function in a certain subset of the entire domain of definition. This ;globalness; of the fractional derivatives has added an additional degree of difficulty when either analytical methods or numerical solutions are attempted. Albeit difficult, we still have managed to derive an explicit closed-form analytical solution for European options under the CGMY model. Based on our solution, the asymptotic behaviors of the option price and the put-call parity under the CGMY model are further discussed. Practically, a reliable numerical evaluation technique for the current formula is proposed. With the numerical results, some analyses of impacts of four key parameters of the CGMY model on European option prices are also provided.

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

Bencze, G.; Chandler, C.

It is shown that the electric polarizability of the deuteron produces negligible effect on the cross section of deuteron induced rearrangement reactions even at extremely low energies. This assessment is based on simple analytical formulas, derived on the basis of {ital N}-particle scattering theory by means of the general two-potential formalism, including Coulomb and exchange effects. It is shown on the basis of general physical arguments that the polarizability effects at very low energies are entirely contained in a multiplicative enhancement factor that differs from 1 by at most a few percent. As a result enhancement of ({ital d},{ital p})more » relative to ({ital d},{ital n}) reactions is not possible by the Oppenheimer-Phillips mechanism.« less

Direct S -matrix calculation for diffractive structures and metasurfaces

NASA Astrophysics Data System (ADS)

Shcherbakov, Alexey A.; Stebunov, Yury V.; Baidin, Denis F.; Kämpfe, Thomas; Jourlin, Yves

2018-06-01

The paper presents a derivation of analytical components of S matrices for arbitrary planar diffractive structures and metasurfaces in the Fourier domain. The attained general formulas for S -matrix components can be applied within both formulations in the Cartesian and curvilinear metric. A numerical method based on these results can benefit from all previous improvements of the Fourier domain methods. In addition, we provide expressions for S -matrix calculation in the case of periodically corrugated layers of two-dimensional materials, which are valid for arbitrary corrugation depth-to-period ratios. As an example, the derived equations are used to simulate resonant grating excitation of graphene plasmons and the impact of a silica interlayer on corresponding reflection curves.

Elastic properties of spherically anisotropic piezoelectric composites

NASA Astrophysics Data System (ADS)

Wei, En-Bo; Gu, Guo-Qing; Poon, Ying-Ming

2010-09-01

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.

Spin-squeezing and Dicke-state preparation by heterodyne measurement

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

Vanderbruggen, T.; Bernon, S.; Bertoldi, A.

2011-01-15

We investigate the quantum nondemolition (QND) measurement of an atomic population based on a heterodyne detection and show that the induced back-action allows for the preparation of both spin-squeezed and Dicke states. We use a wave-vector formalism to describe the stochastic process of the measurement and the associated atomic evolution. Analytical formulas of the atomic distribution momenta are derived in the weak-coupling regime both for short- and long-time behavior, and they are in good agreement with those obtained by a Monte Carlo simulation. The experimental implementation of the proposed heterodyne detection scheme is discussed. The role played in the squeezingmore » process by the spontaneous emission is considered.« less

Was the Big Bang hot?

NASA Technical Reports Server (NTRS)

Wright, E. L.

1983-01-01

Techniques for verifying the spectrum defined by Woody and Richards (WR, 1981), which serves as a base for dust-distorted models of the 3 K background, are discussed. WR detected a sharp deviation from the Planck curve in the 3 K background. The absolute intensity of the background may be determined by the frequency dependence of the dipole anisotropy of the background or the frequency dependence effect in galactic clusters. Both methods involve the Doppler shift; analytical formulae are defined for characterization of the dipole anisotropy. The measurement of the 30-300 GHz spectra of cold galactic dust may reveal the presence of significant amounts of needle-shaped grains, which would in turn support a theory of a cold Big Bang.

Development and validation of a solid-phase extraction method coupled to liquid chromatography with fluorescence detection for the determination of fluoroquinolone residues in powdered infant formulae. Application to the analysis of samples from the Spanish and Latin American market.

PubMed

Rodriguez, E; Moreno-Bondi, M C; Marazuela, M D

2008-10-31

This paper describes a new method for the effective extraction, clean-up and chromatographic analysis of residues of four fluoroquinolones (ciprofloxacin, enrofloxacin, danofloxacin and sarafloxacin) in powdered infant formulae and follow-on preparations. Samples were reconstituted following the manufacturer's recommendations and treated with trichloroacetic acid in methanol 10% (w/v) for deproteinization. Two solid-phase extraction cartridges have been evaluated for sample clean-up and preconcentration, Strata Screen A and Strata X and the later provided the best recoveries for all the analytes tested. Chromatographic analysis has been carried out using a polar endcapped column (AQUA C(18)) and fluorescence detection, with lomefloxacin (LOME) as internal standard. Method validation has been performed according to European Commission Decision 2002/657/EC criteria, in terms of linearity, recovery, precision, specificity, decision limit (CC(alpha)) and detection capability (CC(beta)). Typical recoveries ranged between 70 and 110% at levels below and above the maximum residue limits of the target analytes in bovine milk, with an excellent intralab reproducibility (RSDs<7%). Matrix effects did not significantly affect method accuracy, as evidenced by analyzing different brands of milk. The method has been successfully applied to the analysis of 100 samples of infant and follow-on formulae of the Spanish and Latin American market, using LC-MS/MS as confirmatory technique.

Estimation of Right-Lobe Graft Weight From Computed Tomographic Volumetry for Living Donor Liver Transplantation.

PubMed

Yang, X; Chu, C W; Yang, J D; Yang, K H; Yu, H C; Cho, B H; You, H

2017-03-01

The objective of the study was to establish a right-lobe graft weight (GW) estimation formula for living donor liver transplantation (LDLT) from right-lobe graft volume without veins (GV w/o_veins ), including portal vein and hepatic vein measured by computed tomographic (CT) volumetry, and to compare its estimation accuracy with those of existing formulas. Right-lobe GW estimation formulas established with the use of graft volume with veins (GV w_veins ) sacrifice accuracy because GW measured intra-operatively excludes the weight of blood in the veins. Right-lobe GW estimation formulas have been established with the use of right-lobe GV w/o_veins , but a more accurate formula must be developed. The present study developed right-lobe GW estimation formulas based on GV w/o_veins as well as GV w_veins , using 40 cases of Korean donors: GW = 29.1 + 0.943 × GV w/o_veins (adjusted R 2  = 0.94) and GW = 74.7 + 0.773 × GV w_veins (adjusted R 2  = 0.87). The proposed GW estimation formulas were compared with existing GV w_veins - and GV w/o_veins -based models, using 43 cases additionally obtained from two medical centers for cross-validation. The GV w/o_veins -based formula developed in the present study was most preferred (absolute error = 21.5 ± 16.5 g and percentage of absolute error = 3.0 ± 2.3%). The GV w/o_veins -based formula is preferred to the GV w_veins -based formula in GW estimation. Accurate CT volumetry and alignment between planned and actual surgical cutting lines are crucial in the establishment of a better GW estimation formula. Copyright © 2016 Elsevier Inc. All rights reserved.

Parasitic current collection by PASP Plus solar arrays

NASA Technical Reports Server (NTRS)

Davis, Victoria Ann; Gardner, Barbara M.

1995-01-01

Solar cells at potentials positive with respect to a surrounding plasma collect electrons. Current is collected by the exposed high voltage surfaces: the interconnects and the sides of the solar cells. This current is a drain on the array power that can be significant for high-power arrays. In addition, this current influences the current balance that determines the floating potential of the spacecraft. One of the objectives of the Air Force (PL/GPS) PASP Plus (Photovoltaic Array Space Power Plus Diagnostics) experiment is an improved understanding fo parasitic current collection. We have done computer modeling of parasitic current collection and have examined current collection flight data from the first year of operations. Prior to the flight we did computer modeling to improve our understanding of the physical processes that control parasitic current collection. At high potentials, the current rapidly rises due to a phenomenon called snapover. Under snapover conditions, the equilibrium potential distribution across the dielectric surface is such that part of the area is at potentials greater than the first crossover of the secondary yield curve. Therefore, each incident electron generates more than one secondary electron. The net effect is that the high potential area and the collecting area increase. We did two-dimensional calculations for the various geometries to be flown. The calculations span the space of anticipated plasma conditions, applied potential, and material parameters. We used the calculations and early flight data to develop an analytic formula for the dependence of the current on the primary problem variables. The analytic formula was incorporated into the EPSAT computer code. EPSAT allows us to easily extend the results to other conditions. PASP Plus is the principal experiment integrated onto the Advanced Photovoltaic and Electronics Experiments (APEX) satellite bus. The experiment is testing twelve different solar array designs. Parasitic current collection is being measured for eight of the designs under various operational and environment conditions. We examined the current collected as a function of the various parameters for the six non-concentrator designs. The results are similar to those obtained in previous experiments and predicted by the calculations. We are using the flight data to validate the analytic formula developed. The formula can be used to quantify the parasitic current collected. Anticipating the parasitic current value allows the spacecraft designer to include this interaction when developing the design.