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

INTERNATIONAL CONFERENCE ON SEMICONDUCTOR INJECTION LASERS SELCO-87: Simple formula for the thermal conductivity of a quaternary solid solution

NASA Astrophysics Data System (ADS)

Nakwaski, W.

1988-11-01

An analysis is made of the thermal conductivity of quaternary solid solutions (alloys) allowing for their disordered structure on the basis of a phenomenological analysis proposed by Abeles. This method is applied to a quaternary solid solution In1 - xGaxAsyP1 - y. A simple analytic expression is derived for the thermal conductivity of this material.

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.

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

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

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.

A simple formula for the effective complex conductivity of periodic fibrous composites with interfacial impedance and applications to biological tissues

NASA Astrophysics Data System (ADS)

Bisegna, Paolo; Caselli, Federica

2008-06-01

This paper presents a simple analytical expression for the effective complex conductivity of a periodic hexagonal arrangement of conductive circular cylinders embedded in a conductive matrix, with interfaces exhibiting a capacitive impedance. This composite material may be regarded as an idealized model of a biological tissue comprising tubular cells, such as skeletal muscle. The asymptotic homogenization method is adopted, and the corresponding local problem is solved by resorting to Weierstrass elliptic functions. The effectiveness of the present analytical result is proved by convergence analysis and comparison with finite-element solutions and existing models.

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

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.

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.

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.

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

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

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.

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.

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.

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.

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.

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.

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.

Conditions and Linear Stability Analysis at the Transition to Synchronization of Three Coupled Phase Oscillators in a Ring

NASA Astrophysics Data System (ADS)

El-Nashar, Hassan F.

2017-06-01

We consider a system of three nonidentical coupled phase oscillators in a ring topology. We explore the conditions that must be satisfied in order to obtain the phases at the transition to a synchrony state. These conditions lead to the correct mathematical expressions of phases that aid to find a simple analytic formula for critical coupling when the oscillators transit to a synchronization state having a common frequency value. The finding of a simple expression for the critical coupling allows us to perform a linear stability analysis at the transition to the synchronization stage. The obtained analytic forms of the eigenvalues show that the three coupled phase oscillators with periodic boundary conditions transit to a synchrony state when a saddle-node bifurcation occurs.

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.

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

Rapid Equipping Force (REF) Analytical Support

DTIC Science & Technology

2007-06-01

document contains color images. 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER OF PAGES 44...interface and performs actions via Excel formulae, ActiveX controls, and VBA code. – Plan to provide both simple and complex weighting and scoring methods...Requirements Quad Chart. –Solution Set Information Worksheet: A spreadsheet containing detailed information concerning every potential solution considered

Q-controlled amplitude modulation atomic force microscopy in liquids: An analysis

NASA Astrophysics Data System (ADS)

Hölscher, H.; Schwarz, U. D.

2006-08-01

An analysis of amplitude modulation atomic force microscopy in liquids is presented with respect to the application of the Q-Control technique. The equation of motion is solved by numerical and analytic methods with and without Q-Control in the presence of a simple model interaction force adequate for many liquid environments. In addition, the authors give an explicit analytical formula for the tip-sample indentation showing that higher Q factors reduce the tip-sample force. It is found that Q-Control suppresses unwanted deformations of the sample surface, leading to the enhanced image quality reported in several experimental studies.

Study of the initial transient in the one-dimensional analytical models of impurity segregation during melt crystallization in the presence of convection

NASA Astrophysics Data System (ADS)

Voloshin, A. E.

2013-11-01

The well-known one-dimensional Burton-Prim-Slichter and Ostrogorsky-Müller analytical models obtained for the stationary mass transfer regime describe in a simple form the dependence of the effective impurity segregation coefficient on the ratio of the crystal growth and convective flow rates. Solutions for the initial transient regime are found in both models. It is shown that the formulas obtained make it possible to determine both the crystal growth rate and the convective mixing intensity on the basis of the analysis of impurity segregation in crystal.

Upper and lower bounds for the speed of pulled fronts with a cut-off

NASA Astrophysics Data System (ADS)

Benguria, R. D.; Depassier, M. C.; Loss, M.

2008-02-01

We establish rigorous upper and lower bounds for the speed of pulled fronts with a cut-off. For all reaction terms of KPP type a simple analytic upper bound is given. The lower bounds however depend on details of the reaction term. For a small cut-off parameter the two leading order terms in the asymptotic expansion of the upper and lower bounds coincide and correspond to the Brunet-Derrida formula. For large cut-off parameters the bounds do not coincide and permit a simple estimation of the speed of the front.

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.

Parameterized spectral distributions for meson production in proton-proton collisions

NASA Technical Reports Server (NTRS)

Schneider, John P.; Norbury, John W.; Cucinotta, Francis A.

1995-01-01

Accurate semiempirical parameterizations of the energy-differential cross sections for charged pion and kaon production from proton-proton collisions are presented at energies relevant to cosmic rays. The parameterizations, which depend on both the outgoing meson parallel momentum and the incident proton kinetic energy, are able to be reduced to very simple analytical formulas suitable for cosmic ray transport through spacecraft walls, interstellar space, the atmosphere, and meteorites.

Investigation of Truncated Waveguides

NASA Technical Reports Server (NTRS)

Lourie, Nathan P.; Chuss, David T.; Henry, Ross M.; Wollack, Edward J.

2013-01-01

The design, fabrication, and performance of truncated circular and square waveguide cross-sections are presented. An emphasis is placed upon numerical and experimental validation of simple analytical formulae that describe the propagation properties of these structures. A test component, a 90-degree phase shifter, was fabricated and tested at 30 GHz. The concepts explored can be directly applied in the design, synthesis and optimization of components in the microwave to sub-millimeter wavebands.

Analytical theory of the space-charge region of lateral p-n junctions in nanofilms

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

Gurugubelli, Vijaya Kumar, E-mail: vkgurugubelli@gmail.com; Karmalkar, Shreepad

There is growing interest in fabricating conventional semiconductor devices in a nanofilm which could be a 3D material with one reduced dimension (e.g., silicon-on-insulator (SOI) film), or single/multiple layers of a 2D material (e.g., MoS{sub 2}), or a two dimensional electron gas/two dimensional hole gas (2DEG/2DHG) layer. Lateral p-n junctions are essential parts of these devices. The space-charge region electrostatics in these nanofilm junctions is strongly affected by the surrounding field, unlike in bulk junctions. Current device physics of nanofilms lacks a simple analytical theory of this 2D electrostatics of lateral p-n junctions. We present such a theory taking intomore » account the film's thickness, permittivity, doping, interface charge, and possibly different ambient permittivities on film's either side. In analogy to the textbook theory of the 1D electrostatics of bulk p-n junctions, our theory yields simple formulas for the depletion width, the extent of space-charge tails beyond this width, and the screening length associated with the space-charge layer in nanofilm junctions; these formulas agree with numerical simulations and measurements. Our theory introduces an electrostatic thickness index to classify nanofilms into sheets, bulk and intermediate sized.« less

Variational method enabling simplified solutions to the linearized Boltzmann equation for oscillatory gas flows

NASA Astrophysics Data System (ADS)

Ladiges, Daniel R.; Sader, John E.

2018-05-01

Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, J. Stat. Phys. 1, 297 (1969), 10.1007/BF01007482] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two canonical flow problems: oscillatory Couette flow and Stokes' second problem. Approximate analytical formulas giving the bulk velocity and shear stress, valid for arbitrary oscillation frequency, are obtained for Couette flow. For Stokes' second problem, a simple system of ordinary differential equations is derived which may be solved to obtain the desired flow fields. Using this framework, a simple and accurate formula is provided for the shear stress at the oscillating boundary, again for arbitrary frequency, which may prove useful in application. These solutions are easily implemented on any symbolic or numerical package, such as Mathematica or matlab, facilitating the characterization of flows produced by nanomechanical devices and providing insight into the underlying flow physics.

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.

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".

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.

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

A one-parametric formula relating the frequencies of twin-peak quasi-periodic oscillations

NASA Astrophysics Data System (ADS)

Török, Gabriel; Goluchová, Kateřina; Šrámková, Eva; Horák, Jiří; Bakala, Pavel; Urbanec, Martin

2017-12-01

Timing analysis of X-ray flux in more than a dozen low-mass X-ray binary systems containing a neutron star reveals remarkable correlations between frequencies of two characteristic peaks present in the power-density spectra. We find a simple analytic relation that well reproduces all these individual correlations. We link this relation to a physical model which involves accretion rate modulation caused by an oscillating torus.

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.

Analyticity in Time and Smoothing Effect of Solutions to Nonlinear Schrödinger Equations

NASA Astrophysics Data System (ADS)

Hayashi, Nakao; Kato, Keiichi

In this paper we consider analyticity in time and smoothing effect of solutions to nonlinear Schrödinger equations where . We prove that if φ satisfies then there exists a unique solution of (1) and positive constants T, C0, C1 such that is analytic in time and space variables for and and has an analytic continuation on and In the case the condition (2) can be relaxed as follows: where m= 0 if n= 1, p= 1, m= 1 if n= 2, and m= 1 if n= 3, p= 1.

On a product-type operator from weighted Bergman-Orlicz space to some weighted type spaces.

PubMed

Jiang, Zhi-Jie

2015-04-01

Let [Formula: see text] be the open unit disk, [Formula: see text] an analytic self-map of [Formula: see text] and [Formula: see text] an analytic function on [Formula: see text]. Let D be the differentiation operator and [Formula: see text] the weighted composition operator. The boundedness and compactness of the product-type operator [Formula: see text] from the weighted Bergman-Orlicz space to the Bers type space, weighted Bloch space and weighted Zygmund space on [Formula: see text] are characterized.

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.

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.

Why does the sign problem occur in evaluating the overlap of HFB wave functions?

NASA Astrophysics Data System (ADS)

Mizusaki, Takahiro; Oi, Makito; Shimizu, Noritaka

2018-04-01

For the overlap matrix element between Hartree-Fock-Bogoliubov states, there are two analytically different formulae: one with the square root of the determinant (the Onishi formula) and the other with the Pfaffian (Robledo's Pfaffian formula). The former formula is two-valued as a complex function, hence it leaves the sign of the norm overlap undetermined (i.e., the so-called sign problem of the Onishi formula). On the other hand, the latter formula does not suffer from the sign problem. The derivations for these two formulae are so different that the reasons are obscured why the resultant formulae possess different analytical properties. In this paper, we discuss the reason why the difference occurs by means of the consistent framework, which is based on the linked cluster theorem and the product-sum identity for the Pfaffian. Through this discussion, we elucidate the source of the sign problem in the Onishi formula. We also point out that different summation methods of series expansions may result in analytically different formulae.

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

Cottam, Joseph A.; Blaha, Leslie M.

Systems have biases. Their interfaces naturally guide a user toward specific patterns of action. For example, modern word-processors and spreadsheets are both capable of taking word wrapping, checking spelling, storing tables, and calculating formulas. You could write a paper in a spreadsheet or could do simple business modeling in a word-processor. However, their interfaces naturally communicate which function they are designed for. Visual analytic interfaces also have biases. In this paper, we outline why simple Markov models are a plausible tool for investigating that bias and how they might be applied. We also discuss some anticipated difficulties in such modelingmore » and touch briefly on what some Markov model extensions might provide.« less

5 CFR 1315.17 - Formulas.

Code of Federal Regulations, 2010 CFR

2010-01-01

...) Daily simple interest formula. (1) To calculate daily simple interest the following formula may be used... a payment is due on April 1 and the payment is not made until April 11, a simple interest... equation calculates simple interest on any additional days beyond a monthly increment. (3) For example, if...

Quasiclassical calculations of blackbody-radiation-induced depopulation rates and effective lifetimes of Rydberg nS, nP, and nD alkali-metal atoms with n{<=}80

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

Beterov, I. I.; Ryabtsev, I. I.; Tretyakov, D. B.

2009-05-15

Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal nS, nP, and nD Rydberg states have been calculated in a wide range of principal quantum numbers n{<=}80 at the ambient temperatures of 77, 300, and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-induced depopulation rates, which well agree with the numerical data.

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

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.

An explicit analytical solution for sound propagation in a three-dimensional penetrable wedge with small apex angle.

PubMed

Petrov, Pavel S; Sturm, Frédéric

2016-03-01

A problem of sound propagation in a shallow-water waveguide with a weakly sloping penetrable bottom is considered. The adiabatic mode parabolic equations are used to approximate the solution of the three-dimensional (3D) Helmholtz equation by modal decomposition of the acoustic pressure field. The mode amplitudes satisfy parabolic equations that admit analytical solutions in the special case of the 3D wedge. Using the analytical formula for modal amplitudes, an explicit and remarkably simple expression for the acoustic pressure in the wedge is obtained. The proposed solution is validated by the comparison with a solution of the 3D penetrable wedge problem obtained using a fully 3D parabolic equation that includes a leading-order cross term correction.

A predictive analytic model for the solar modulation of cosmic rays

DOE PAGES

Cholis, Ilias; Hooper, Dan; Linden, Tim

2016-02-23

An important factor limiting our ability to understand the production and propagation of cosmic rays pertains to the effects of heliospheric forces, commonly known as solar modulation. The solar wind is capable of generating time- and charge-dependent effects on the spectrum and intensity of low-energy (≲10 GeV) cosmic rays reaching Earth. Previous analytic treatments of solar modulation have utilized the force-field approximation, in which a simple potential is adopted whose amplitude is selected to best fit the cosmic-ray data taken over a given period of time. Making use of recently available cosmic-ray data from the Voyager 1 spacecraft, along withmore » measurements of the heliospheric magnetic field and solar wind, we construct a time-, charge- and rigidity-dependent model of solar modulation that can be directly compared to data from a variety of cosmic-ray experiments. Here, we provide a simple analytic formula that can be easily utilized in a variety of applications, allowing us to better predict the effects of solar modulation and reduce the number of free parameters involved in cosmic-ray propagation models.« less

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.

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.

The predictive accuracy of analytical formulas and semiclassical approaches for α decay half-lives of superheavy nuclei

NASA Astrophysics Data System (ADS)

Zhao, T. L.; Bao, X. J.; Guo, S. Q.

2018-02-01

Systematic calculations on the α decay half-lives are performed by using three analytical formulas and two semiclassical approaches. For the three analytical formulas, the experimental α decay half-lives and {Q}α values of the 66 reference nuclei have been used to obtain the coefficients. We get only four adjustable parameters to describe α decay half-lives for even-even, odd-A, and odd-odd nuclei. By comparison between the calculated values from ten analytical formulas and experimental data, it is shown that the new universal decay law (NUDL) foumula is the most accurate one to reproduce the experimental α decay half-lives of the superheavy nuclei (SHN). Meanwhile it is found that the experimental α decay half-lives of SHN are well reproduced by the Royer formula although many parameters are contained. The results show that the NUDL formula and the generalized liquid drop model (GLDM2) with consideration of the preformation factor can give fairly equivalent results for the superheavy nuclei.

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.

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

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.

Statistical power for nonequivalent pretest-posttest designs. The impact of change-score versus ANCOVA models.

PubMed

Oakes, J M; Feldman, H A

2001-02-01

Nonequivalent controlled pretest-posttest designs are central to evaluation science, yet no practical and unified approach for estimating power in the two most widely used analytic approaches to these designs exists. This article fills the gap by presenting and comparing useful, unified power formulas for ANCOVA and change-score analyses, indicating the implications of each on sample-size requirements. The authors close with practical recommendations for evaluators. Mathematical details and a simple spreadsheet approach are included in appendices.

Comparison of Alcator C data with the Rebut-Lallia-Watkins critical gradient scaling

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

Hutchinson, I.H.

The critical temperature gradient model of Rebut, Lallia and Watkins is compared with data from Alcator C. The predicted central electron temperature is derived from the model, and a simple analytic formula is given. It is found to be in quite good agreement with the observed temperatures on Alcator C under ohmic heating conditions. However, the thermal diffusivity postulated in the model for gradients that exceed the critical is not consistent with the observed electron heating by Lower Hybrid waves.

Franck-Condon factor formulae for astrophysical and other molecules

NASA Technical Reports Server (NTRS)

Nicholls, R. W.

1981-01-01

Simple closed-form, approximate, analytic expressions for Franck-Condon factors are given. They provide reliable estimates for Franck-Condon factor arrays for molecular band systems for which only vibrational-frequency, equilibrium internuclear separation and reduced mass values are known, as is often the case for astrophysically interesting molecules such as CeO, CoH, CrH, CrO, CuH, GeH, LaO, NiH, SnH, and ZnH for band systems of which Franck-Condon arrays have been calculated.

Optical response of photopolymer materials for holographic data storage applications.

PubMed

Sheridan, J T; Gleeson, M R; Close, C E; Kelly, J V

2007-01-01

We briefly review the application of photopolymer recording materials in the area of holographic data storage. In particular we discuss the recent development of the Non-local Polymerisation Driven Diffusion model. Applying this model we develop simple first-order analytic expressions describing the spatial frequency response of photopolymer materials. The assumptions made in the derivation of these formulae are described and their ranges of validity are examined. The effects of particular physical parameters of a photopolymer on the material response are discussed.

Determination of Total Biotin by Liquid Chromatography Coupled with Immunoaffinity Column Cleanup Extraction: Multilaboratory Testing, Final Action 2016.02.

PubMed

Joseph, George; Devi, Ranjani; Marley, Elaine C; Leeman, David

2018-05-01

Single- and multilaboratory testing data have provided systematic scientific evidence that a simple, selective, accurate, and precise method can be used as a potential candidate reference method for dispute resolution in determining total biotin in all forms of infant, adult, and/or pediatric formula. Using LC coupled with immunoaffinity column cleanup extraction, the method fully meets the intended purpose and applicability statement in AOAC Standard Method Performance Requirement 2014.005. The method was applied to a cross-section of infant formula and adult nutritional matrixes, and acceptable precision and accuracy were established. The analytical platform is inexpensive, and the method can be used in almost any laboratory worldwide with basic facilities. The immunoaffinity column cleanup extraction is the key step to successful analysis.

All two-loop maximally helicity-violating amplitudes in multi-Regge kinematics from applied symbology

NASA Astrophysics Data System (ADS)

Prygarin, Alexander; Spradlin, Marcus; Vergu, Cristian; Volovich, Anastasia

2012-04-01

Recent progress on scattering amplitudes has benefited from the mathematical technology of symbols for efficiently handling the types of polylogarithm functions which frequently appear in multiloop computations. The symbol for all two-loop maximally helicity violating amplitudes in planar supersymmetric Yang-Mills theory is known, but explicit analytic formulas for the amplitudes are hard to come by except in special limits where things simplify, such as multi-Regge kinematics. By applying symbology we obtain a formula for the leading behavior of the imaginary part (the Mandelstam cut contribution) of this amplitude in multi-Regge kinematics for any number of gluons. Our result predicts a simple recursive structure which agrees with a direct Balitsky-Fadin-Kuraev-Lipatov computation carried out in a parallel publication.

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.

How accurate is the Pearson r-from-Z approximation? A Monte Carlo simulation study.

PubMed

Hittner, James B; May, Kim

2012-01-01

The Pearson r-from-Z approximation estimates the sample correlation (as an effect size measure) from the ratio of two quantities: the standard normal deviate equivalent (Z-score) corresponding to a one-tailed p-value divided by the square root of the total (pooled) sample size. The formula has utility in meta-analytic work when reports of research contain minimal statistical information. Although simple to implement, the accuracy of the Pearson r-from-Z approximation has not been empirically evaluated. To address this omission, we performed a series of Monte Carlo simulations. Results indicated that in some cases the formula did accurately estimate the sample correlation. However, when sample size was very small (N = 10) and effect sizes were small to small-moderate (ds of 0.1 and 0.3), the Pearson r-from-Z approximation was very inaccurate. Detailed figures that provide guidance as to when the Pearson r-from-Z formula will likely yield valid inferences are presented.

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

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.

Simple and Clear Proofs of Stirling's Formula

ERIC Educational Resources Information Center

Niizeki, Shozo; Araki, Makoto

2010-01-01

The purpose of our article is to show two simpler and clearer methods of proving Stirling's formula than the traditional and conventional ones. The distinction of our method is to use the simple trapezoidal formula.

Note on the coefficient of variations of neuronal spike trains.

PubMed

Lengler, Johannes; Steger, Angelika

2017-08-01

It is known that many neurons in the brain show spike trains with a coefficient of variation (CV) of the interspike times of approximately 1, thus resembling the properties of Poisson spike trains. Computational studies have been able to reproduce this phenomenon. However, the underlying models were too complex to be examined analytically. In this paper, we offer a simple model that shows the same effect but is accessible to an analytic treatment. The model is a random walk model with a reflecting barrier; we give explicit formulas for the CV in the regime of excess inhibition. We also analyze the effect of probabilistic synapses in our model and show that it resembles previous findings that were obtained by simulation.

Exact analysis of surface field reduction due to field-emitted vacuum space charge, in parallel-plane geometry, using simple dimensionless equations

NASA Astrophysics Data System (ADS)

Forbes, Richard G.

2008-10-01

This paper reports (a) a simple dimensionless equation relating to field-emitted vacuum space charge (FEVSC) in parallel-plane geometry, namely 9ζ2θ2-3θ-4ζ+3=0, where ζ is the FEVSC "strength" and θ is the reduction in emitter surface field (θ =field-with/field-without FEVSC), and (b) the formula j =9θ2ζ/4, where j is the ratio of emitted current density JP to that predicted by Child's law. These equations apply to any charged particle, positive or negative, emitted with near-zero kinetic energy. They yield existing and additional basic formulas in planar FEVSC theory. The first equation also yields the well-known cubic equation describing the relationship between JP and applied voltage; a method of analytical solution is described. Illustrative FEVSC effects in a liquid metal ion source and in field electron emission are discussed. For Fowler-Nordheim plots, a "turn-over" effect is predicted in the high FEVSC limit. The higher the voltage-to-local-field conversion factor for the emitter concerned, then the higher is the field at which turn over occurs. Past experiments have not found complete turn over; possible reasons are noted. For real field emitters, planar theory is a worst-case limit; however, adjusting ζ on the basis of Monte Carlo calculations might yield formulae adequate for real situations.

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.

Improvements in the Approximate Formulae for the Period of the Simple Pendulum

ERIC Educational Resources Information Center

Turkyilmazoglu, M.

2010-01-01

This paper is concerned with improvements in some exact formulae for the period of the simple pendulum problem. Two recently presented formulae are re-examined and refined rationally, yielding more accurate approximate periods. Based on the improved expressions here, a particular new formula is proposed for the period. It is shown that the derived…

A simple derivation of the formula to calculated synthetic long-period seismograms in a heterogeneous Earth by normal mode summation

NASA Technical Reports Server (NTRS)

Tanimoto, T.

1983-01-01

A simple modification of Gilbert's formula to account for slight lateral heterogeneity of the Earth leads to a convenient formula to calculate synthetic long period seismograms. Partial derivatives are easily calculated, thus the formula is suitable for direct inversion of seismograms for lateral heterogeneity of the Earth.

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

Perturbation-theory analysis of ionization by a chirped few-cycle attosecond pulse

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

Pronin, E. A.; Starace, Anthony F.; Peng Liangyou

2011-07-15

The angular distribution of electrons ionized from an atom by a chirped few-cycle attosecond pulse is analyzed using perturbation theory (PT), keeping terms in the transition amplitude up to second order in the pulse electric field. The dependence of the asymmetry in the ionized electron distributions on both the chirp and the carrier-envelope phase (CEP) of the pulse are explained using a simple analytical formula that approximates the exact PT result. This approximate formula (in which the chirp dependence is explicit) reproduces reasonably well the chirp-dependent oscillations of the electron angular distribution asymmetries found numerically by Peng et al. [Phys.more » Rev. A 80, 013407 (2009)]. It can also be used to determine the chirp rate of the attosecond pulse from the measured electron angular distribution asymmetry.« less

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.

Tidally induced residual current over the Malin Sea continental slope

NASA Astrophysics Data System (ADS)

Stashchuk, Nataliya; Vlasenko, Vasiliy; Hosegood, Phil; Nimmo-Smith, W. Alex M.

2017-05-01

Tidally induced residual currents generated over shelf-slope topography are investigated analytically and numerically using the Massachusetts Institute of Technology general circulation model. Observational support for the presence of such a slope current was recorded over the Malin Sea continental slope during the 88-th cruise of the RRS ;James Cook; in July 2013. A simple analytical formula developed here in the framework of time-averaged shallow water equations has been validated against a fully nonlinear nonhydrostatic numerical solution. A good agreement between analytical and numerical solutions is found for a wide range of input parameters of the tidal flow and bottom topography. In application to the Malin Shelf area both the numerical model and analytical solution predicted a northward moving current confined to the slope with its core located above the 400 m isobath and with vertically averaged maximum velocities up to 8 cm s-1, which is consistent with the in-situ data recorded at three moorings and along cross-slope transects.

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.

Controlling the light shift of the CPT resonance by modulation technique

NASA Astrophysics Data System (ADS)

Tsygankov, E. A.; Petropavlovsky, S. V.; Vaskovskaya, M. I.; Zibrov, S. A.; Velichansky, V. L.; Yakovlev, V. P.

2017-12-01

Motivated by recent developments in atomic frequency standards employing the effect of coherent population trapping (CPT), we propose a theoretical framework for the frequency modulation spectroscopy of the CPT resonances. Under realistic assumptions we provide simple yet non-trivial analytical formulae for the major spectroscopic signals such as the CPT resonance line and the in-phase/quadrature responses. We discuss the influence of the light shift and, in particular, derive a simple expression for the displacement of the resonance as a function of modulation index. The performance of the model is checked against numerical simulations, the agreement is good to perfect. The obtained results can be used in more general models accounting for light absorption in the thick optical medium.

A Simple Approach to the Landau-Zener Formula

ERIC Educational Resources Information Center

Vutha, Amar C.

2010-01-01

The Landau-Zener formula provides the probability of non-adiabatic transitions occurring when two energy levels are swept through an avoided crossing. The formula is derived here in a simple calculation that emphasizes the physics responsible for non-adiabatic population transfer. (Contains 2 figures.)

A simple derivation of the formula to calculate synthetic long-period seismograms in a heterogeneous earth by normal mode summation

NASA Technical Reports Server (NTRS)

Tanimoto, T.

1984-01-01

A simple modification of Gilbert's formula to account for slight lateral heterogeneity of the earth leads to a convenient formula to calculate synthetic long period seismograms. Partial derivatives are easily calculated, thus the formula is suitable for direct inversion of seismograms for lateral heterogeneity of the earth. Previously announced in STAR as N83-29893

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.

Nonequilibrium electrophoresis of an ion-selective microgranule for weak and moderate external electric fields

NASA Astrophysics Data System (ADS)

Frants, E. A.; Ganchenko, G. S.; Shelistov, V. S.; Amiroudine, S.; Demekhin, E. A.

2018-02-01

Electrokinetics and the movement of charge-selective micro-granules in an electrolyte solution under the influence of an external electric field are investigated theoretically. Straightforward perturbation analysis is applied to a thin electric double layer and a weak external field, while a numerical solution is used for moderate electric fields. The asymptotic solution enables the determination of the salt concentration, electric charge distribution, and electro-osmotic velocity fields. It may also be used to obtain a simple analytical formula for the electrophoretic velocity in the case of quasi-equilibrium electrophoresis (electrophoresis of the first kind). This formula differs from the famous Helmholtz-Smoluchowski relation, which applies to dielectric microparticles, but not to ion-selective granules. Numerical calculations are used to validate the derived formula for weak external electric fields, but for moderate fields, nonlinear effects lead to a significant increase in electrophoretic mobility and to a transition from quasi-equilibrium electrophoresis of the first kind to nonequilibrium electrophoresis of the second kind. Theoretical results are successfully compared with experimental data.

An analytical formula for the longitudinal resonance frequencies of a fluid-filled crack

NASA Astrophysics Data System (ADS)

Maeda, Y.; Kumagai, H.

2013-12-01

The fluid-filled crack model (Chouet, 1986, JGR) simulates the resonances of a rectangular crack filled with an inviscid fluid embedded in a homogeneous isotropic elastic medium. The model demonstrates the existence of a slow wave, known as the crack wave, that propagates along the solid-fluid interfaces. The wave velocity depends on the crack stiffness. The model has been used to interpret the peak frequencies of long-period (LP) and very long period (VLP) seismic events at various volcanoes (Chouet and Matoza, 2013, JVGR). Up to now, crack model simulations have been performed using the finite difference (Chouet, 1986) and boundary integral (Yamamoto and Kawakatsu, 2008, GJI) methods. These methods require computationally extensive procedures to estimate the complex frequencies of crack resonance modes. Establishing an easier way to calculate the frequencies of crack resonances would help understanding of the observed frequencies. In this presentation, we propose a simple analytical formula for the longitudinal resonance frequencies of a fluid-filled crack. We first evaluated the analytical expression proposed by Kumagai (2009, Encyc. Complex. Sys. Sci.) through a comparison of the expression with the peak frequencies computed by a 2D version of the FDM code of Chouet (1986). Our comparison revealed that the equation of Kumagai (2009) shows discrepancies with the resonant frequencies computed by the FDM. We then modified the formula as fmL = (m-1)a/[2L(1+2ɛmLC)1/2], (1) where L is the crack length, a is the velocity of sound in the fluid, C is the crack stiffness, m is a positive integer defined such that the wavelength of the normal displacement on the crack surface is 2L/m, and ɛmL is a constant that depends on the longitudinal resonance modes. Excellent fits were obtained between the peak frequencies calculated by the FDM and by Eq. (1), suggesting that this equation is suitable for the resonant frequencies. We also performed 3D FDM computations of the longitudinal mode resonances. The peak frequencies computed by the FDM are well fitted by Eq. (1). The best-fit ɛmL values are different from those for 2D and depend on W/L, where W is the crack width. Eq. (1) shows that fmL is a simple analytical function of a/L and C given m and W/L. This enables simple and rapid interpretations of the source processes of LP events, including estimation of the fluid properties and crack geometries as well as identification of the resonance modes of the individual peak frequencies. LP events at volcanoes often exhibit peak frequency variations. In such cases, the frequency variations can be easily converted to variations in the fluid properties and crack geometries. We showed that Eq. (1) is consistent with the analytical solution for an infinite crack given by Ferrazzini and Aki (1987, JGR). Although a theoretical derivation of Eq. (1) was not obtained yet, Eq. (1) is consistent with the frequencies expected from the wavelengths of the fluid pressure variation.

No Impact of the Analytical Method Used for Determining Cystatin C on Estimating Glomerular Filtration Rate in Children.

PubMed

Alberer, Martin; Hoefele, Julia; Benz, Marcus R; Bökenkamp, Arend; Weber, Lutz T

2017-01-01

Measurement of inulin clearance is considered to be the gold standard for determining kidney function in children, but this method is time consuming and expensive. The glomerular filtration rate (GFR) is on the other hand easier to calculate by using various creatinine- and/or cystatin C (Cys C)-based formulas. However, for the determination of serum creatinine (Scr) and Cys C, different and non-interchangeable analytical methods exist. Given the fact that different analytical methods for the determination of creatinine and Cys C were used in order to validate existing GFR formulas, clinicians should be aware of the type used in their local laboratory. In this study, we compared GFR results calculated on the basis of different GFR formulas and either used Scr and Cys C values as determined by the analytical method originally employed for validation or values obtained by an alternative analytical method to evaluate any possible effects on the performance. Cys C values determined by means of an immunoturbidimetric assay were used for calculating the GFR using equations in which this analytical method had originally been used for validation. Additionally, these same values were then used in other GFR formulas that had originally been validated using a nephelometric immunoassay for determining Cys C. The effect of using either the compatible or the possibly incompatible analytical method for determining Cys C in the calculation of GFR was assessed in comparison with the GFR measured by creatinine clearance (CrCl). Unexpectedly, using GFR equations that employed Cys C values derived from a possibly incompatible analytical method did not result in a significant difference concerning the classification of patients as having normal or reduced GFR compared to the classification obtained on the basis of CrCl. Sensitivity and specificity were adequate. On the other hand, formulas using Cys C values derived from a compatible analytical method partly showed insufficient performance when compared to CrCl. Although clinicians should be aware of applying a GFR formula that is compatible with the locally used analytical method for determining Cys C and creatinine, other factors might be more crucial for the calculation of correct GFR values.

A Simple Method for Assessing Upper-Limb Force-Velocity Profile in Bench Press.

PubMed

Rahmani, Abderrahmane; Samozino, Pierre; Morin, Jean-Benoit; Morel, Baptiste

2018-02-01

To analyze the reliability and validity of a field computation method based on easy-to-measure data to assess the mean force ([Formula: see text]) and velocity ([Formula: see text]) produced during a ballistic bench-press movement and to verify that the force-velocity profile (F-v) obtained with multiple loaded trials is accurately described. Twelve participants performed ballistic bench presses against various lifted mass from 30% to 70% of their body mass. For each trial, [Formula: see text] and [Formula: see text] were determined from an accelerometer (sampling rate 500 Hz; reference method) and a simple computation method based on upper-limb mass, barbell flight height, and push-off distance. These [Formula: see text] and [Formula: see text] data were used to establish the F-v relationship for each individual and method. A strong to almost perfect reliability was observed between the 2 trials (ICC > .90 for [Formula: see text] and .80 for [Formula: see text], CV% < 10%), whatever the considered method. The mechanical variables ([Formula: see text], [Formula: see text]) measured with the 2 methods and all the variables extrapolated from the F-v relationships were strongly correlated (r 2  > .80, P < .001). The practical differences between the methods for the extrapolated mechanical parameters were all <5%, indicating very probably no differences. The findings suggest that the simple computation method used here provides valid and reliable information on force and velocity produced during ballistic bench press, in line with that observed in laboratory conditions. This simple method is thus a practical tool, requiring only 3 simple parameters (upper-limb mass, barbell flight height, and push-off distance).

Approximate Analytical Time-Dependent Solutions to Describe Large-Amplitude Local Calcium Transients in the Presence of Buffers

PubMed Central

Mironova, Lidia A.; Mironov, Sergej L.

2008-01-01

Local Ca2+ signaling controls many neuronal functions, which is often achieved through spatial localization of Ca2+ signals. These nanodomains are formed due to combined effects of Ca2+ diffusion and binding to the cytoplasmic buffers. In this article we derived simple analytical expressions to describe Ca2+ diffusion in the presence of mobile and immobile buffers. A nonlinear character of the reaction-diffusion problem was circumvented by introducing a logarithmic approximation of the concentration term. The obtained formulas reproduce free Ca2+ levels up to 50 μM and their changes in the millisecond range. Derived equations can be useful to predict spatiotemporal profiles of large-amplitude [Ca2+] transients, which participate in various physiological processes. PMID:17872951

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.

Haldane, Waddington and recombinant inbred lines: extension of their work to any number of genes.

PubMed

Samal, Areejit; Martin, Olivier C

2017-11-01

In the early 1930s, J. B. S. Haldane and C. H. Waddington collaborated on the consequences of genetic linkage and inbreeding. One elegant mathematical genetics problem solved by them concerns recombinant inbred lines (RILs) produced via repeated self or brother-sister mating. In this classic contribution, Haldane and Waddington derived an analytical formula for the probabilities of 2-locus and 3-locus RIL genotypes. Specifically, the Haldane-Waddington formula gives the recombination rate R in such lines as a simple function of the per generation recombination rate r. Interestingly, for more than 80 years, an extension of this result to four or more loci remained elusive. In 2015, we generalized the Haldane-Waddington self-mating result to any number of loci. Our solution used self-consistent equations of the multi-locus probabilities 'for an infinite number of generations' and solved these by simple algebraic operations. In practice, our approach provides a quantum leap in the systems that can be handled: the cases of up to six loci can be solved by hand while a computer program implementing our mathematical formalism tackles up to 20 loci on standard desktop computers.

Perihelion precession from power law central force and magnetic-like force

NASA Astrophysics Data System (ADS)

Xu, Feng

2011-04-01

By the Laplace-Runge-Lenz (LRL) vector, we analyzed perihelion precessions of orbit with arbitrary eccentricity from perturbations of 1) power law central force and 2) fThusmagnetic-like force. Exact and analytically closed expressions for the precession rate are derived in both cases. In the central force case, we give a further expansion expression of precession rate in orders of eccentricity, and a rule judging pro- or retrograde precession is also given. We applied the result of central force to precessions of a planet in 1) Schwarzschild space-time, for which the formula for the Mercury’s 43”/century is reproduced, and 2) spherically distributed dark matter, for which we find a formula that is a generalization of the result derived by others for circular orbit. In the magnetic case, the use of the LRL vector proves to be simple and efficient. An example of magnetic-like perturbation is also discussed.

Perihelion precession from power law central force and magnetic-like force

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

Xu Feng

2011-04-15

By the Laplace-Runge-Lenz (LRL) vector, we analyzed perihelion precessions of orbit with arbitrary eccentricity from perturbations of 1) power law central force and 2) fThusmagnetic-like force. Exact and analytically closed expressions for the precession rate are derived in both cases. In the central force case, we give a further expansion expression of precession rate in orders of eccentricity, and a rule judging pro- or retrograde precession is also given. We applied the result of central force to precessions of a planet in 1) Schwarzschild space-time, for which the formula for the Mercury's 43''/century is reproduced, and 2) spherically distributed darkmore » matter, for which we find a formula that is a generalization of the result derived by others for circular orbit. In the magnetic case, the use of the LRL vector proves to be simple and efficient. An example of magnetic-like perturbation is also discussed.« less

Anomalous photo-ionization of 4d shell in medium-Z ionized atoms

NASA Astrophysics Data System (ADS)

Klapisch, M.; Busquet, M.

2013-09-01

Photoionization (PI) cross sections (PICS) are necessary for the simulation of astrophysical and ICF plasmas. In order to be used in plasma modeling, the PICS are usually fit to simple analytical formulas. We observed an unusual spectral shape of the PICS of the 4d shell of ionized Xe and other elements, computed with different codes: a local minimum occurs around twice the threshold energy. We explain this phenomenon as interference between the bound 4d wavefunction and the free electron wavefunction, which is similar to the Cooper minima for neutral atoms. Consequently, the usual fitting formulas, which consist of a combination of inverse powers of the frequency beyond threshold, may yield rates for PI and radiative recombination (RR) that are incorrect by orders of magnitude. A new fitting algorithm is proposed and is included in the latest version of HULLAC.v9.5.

Modeling direct interband tunneling. I. Bulk semiconductors

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

Interband tunneling is frequently studied using the semiclassical Kane model, despite uncertainty about its validity. Revisiting the physical basis of this formula, we find that it neglects coupling to other bands and underestimates transverse tunneling. As a result, significant errors can arise at low and high fields for small and large gap materials, respectively. We derive a simple multiband tunneling model to correct these defects analytically without arbitrary parameters. Through extensive comparison with band structure and quantum transport calculations for bulk InGaAs, InAs, and InSb, we probe the accuracy of the Kane and multiband formulas and establish the superiority ofmore » the latter. We also show that the nonlocal average electric field should be used when applying either of these models to nonuniform potentials. Our findings are important for efficient analysis and simulation of bulk semiconductor devices involving tunneling.« less

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

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.

Simple formula for the surface area of the body and a simple model for anthropometry.

PubMed

Reading, Bruce D; Freeman, Brian

2005-03-01

The body surface area (BSA) of any adult, when derived from the arithmetic mean of the different values calculated from four independent accepted formulae, can be expressed accurately in Systeme International d'Unites (SI) units by the simple equation BSA = 1/6(WH)0.5, where W is body weight in kg, H is body height in m, and BSA is in m2. This formula, which is derived in part by modeling the body as a simple solid of revolution or a prolate spheroid (i.e., a stretched ellipsoid of revolution) gives students, teachers, and clinicians a simple rule for the rapid estimation of surface area using rational units. The formula was tested independently for human subjects by using it to predict body volume and then comparing this prediction against the actual volume measured by Archimedes' principle. Copyright 2005 Wiley-Liss, Inc.

Modeling, Modal Properties, and Mesh Stiffness Variation Instabilities of Planetary Gears

NASA Technical Reports Server (NTRS)

Parker, Robert G.; Lin, Jian; Krantz, Timothy L. (Technical Monitor)

2001-01-01

Planetary gear noise and vibration are primary concerns in their applications in helicopters, automobiles, aircraft engines, heavy machinery and marine vehicles. Dynamic analysis is essential to the noise and vibration reduction. This work analytically investigates some critical issues and advances the understanding of planetary gear dynamics. A lumped-parameter model is built for the dynamic analysis of general planetary gears. The unique properties of the natural frequency spectra and vibration modes are rigorously characterized. These special structures apply for general planetary gears with cyclic symmetry and, in practically important case, systems with diametrically opposed planets. The special vibration properties are useful for subsequent research. Taking advantage of the derived modal properties, the natural frequency and vibration mode sensitivities to design parameters are investigated. The key parameters include mesh stiffnesses, support/bearing stiffnesses, component masses, moments of inertia, and operating speed. The eigen-sensitivities are expressed in simple, closed-form formulae associated with modal strain and kinetic energies. As disorders (e.g., mesh stiffness variation. manufacturing and assembling errors) disturb the cyclic symmetry of planetary gears, their effects on the free vibration properties are quantitatively examined. Well-defined veering rules are derived to identify dramatic changes of natural frequencies and vibration modes under parameter variations. The knowledge of free vibration properties, eigen-sensitivities, and veering rules provide important information to effectively tune the natural frequencies and optimize structural design to minimize noise and vibration. Parametric instabilities excited by mesh stiffness variations are analytically studied for multi-mesh gear systems. The discrepancies of previous studies on parametric instability of two-stage gear chains are clarified using perturbation and numerical methods. The operating conditions causing parametric instabilities are expressed in closed-form suitable for design guidance. Using the well-defined modal properties of planetary gears, the effects of mesh parameters on parametric instability are analytically identified. Simple formulae are obtained to suppress particular instabilities by adjusting contact ratios and mesh phasing.

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.

Simple, accurate formula for the average bit error probability of multiple-input multiple-output free-space optical links over negative exponential turbulence channels.

PubMed

Peppas, Kostas P; Lazarakis, Fotis; Alexandridis, Antonis; Dangakis, Kostas

2012-08-01

In this Letter we investigate the error performance of multiple-input multiple-output free-space optical communication systems employing intensity modulation/direct detection and operating over strong atmospheric turbulence channels. Atmospheric-induced strong turbulence fading is modeled using the negative exponential distribution. For the considered system, an approximate yet accurate analytical expression for the average bit error probability is derived and an efficient method for its numerical evaluation is proposed. Numerically evaluated and computer simulation results are further provided to demonstrate the validity of the proposed mathematical analysis.

Evaluation of geopotential and luni-solar perturbations by a recursive algorithm

NASA Technical Reports Server (NTRS)

Giacaglia, G. E. O.

1975-01-01

The disturbing functions due to the geopotential and Luni-solar attractions are linear and bilinear forms in spherical harmonics. Making use of recurrence relations for the solid spherical harmonics and their derivatives, recurrence formulas are obtained for high degree terms as function of lower degree for any term of those disturbing functions and their derivative with respect to any element. The equations obtained are effective when a numerical integration of the equations of motion is appropriate. In analytical theories, they provide a fast way of obtaining high degree terms starting from initial very simple functions.

Calculation of the time resolution of the J-PET tomograph using kernel density estimation

NASA Astrophysics Data System (ADS)

Raczyński, L.; Wiślicki, W.; Krzemień, W.; Kowalski, P.; Alfs, D.; Bednarski, T.; Białas, P.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Gajos, A.; Głowacz, B.; Gorgol, M.; Hiesmayr, B.; Jasińska, B.; Kamińska, D.; Korcyl, G.; Kozik, T.; Krawczyk, N.; Kubicz, E.; Mohammed, M.; Pawlik-Niedźwiecka, M.; Niedźwiecki, S.; Pałka, M.; Rudy, Z.; Rundel, O.; Sharma, N. G.; Silarski, M.; Smyrski, J.; Strzelecki, A.; Wieczorek, A.; Zgardzińska, B.; Zieliński, M.; Moskal, P.

2017-06-01

In this paper we estimate the time resolution of the J-PET scanner built from plastic scintillators. We incorporate the method of signal processing using the Tikhonov regularization framework and the kernel density estimation method. We obtain simple, closed-form analytical formulae for time resolution. The proposed method is validated using signals registered by means of the single detection unit of the J-PET tomograph built from a 30 cm long plastic scintillator strip. It is shown that the experimental and theoretical results obtained for the J-PET scanner equipped with vacuum tube photomultipliers are consistent.

Dielectronic recombination of the 4p and 4d open sub-shell tungsten ions

NASA Astrophysics Data System (ADS)

Li, M. J.; Fu, Y. B.; Zhang, G. D.; Zhang, Y. Z.; Dong, C. Z.; Koike, F.

2014-04-01

Dielectronic recombination rate coefficients are given theoretically for several highly charged tungsten ions. As 4p open sub-shell ions, Ga-, Ge-, As-, Br-, Kr-like ions are considered. Rb-like ion is further considered as a 4d open sub-shell ion. Theoretical calculations are carried out using a relativistic atomic code FAC. The effect of configuration interaction is taking into account. Inner-shell electron excitations play a significant role for the dielectronic recombination process. Simple analytical formulae are given for the total rate coefficients by fitting to the presently obtained numerical results.

Valid analytical performance specifications for combined analytical bias and imprecision for the use of common reference intervals.

PubMed

Hyltoft Petersen, Per; Lund, Flemming; Fraser, Callum G; Sandberg, Sverre; Sölétormos, György

2018-01-01

Background Many clinical decisions are based on comparison of patient results with reference intervals. Therefore, an estimation of the analytical performance specifications for the quality that would be required to allow sharing common reference intervals is needed. The International Federation of Clinical Chemistry (IFCC) recommended a minimum of 120 reference individuals to establish reference intervals. This number implies a certain level of quality, which could then be used for defining analytical performance specifications as the maximum combination of analytical bias and imprecision required for sharing common reference intervals, the aim of this investigation. Methods Two methods were investigated for defining the maximum combination of analytical bias and imprecision that would give the same quality of common reference intervals as the IFCC recommendation. Method 1 is based on a formula for the combination of analytical bias and imprecision and Method 2 is based on the Microsoft Excel formula NORMINV including the fractional probability of reference individuals outside each limit and the Gaussian variables of mean and standard deviation. The combinations of normalized bias and imprecision are illustrated for both methods. The formulae are identical for Gaussian and log-Gaussian distributions. Results Method 2 gives the correct results with a constant percentage of 4.4% for all combinations of bias and imprecision. Conclusion The Microsoft Excel formula NORMINV is useful for the estimation of analytical performance specifications for both Gaussian and log-Gaussian distributions of reference intervals.

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.

The effect of massive neutrinos on the BAO peak

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

Peloso, Marco; Pietroni, Massimo; Viel, Matteo

2015-07-01

We study the impact of neutrino masses on the shape and height of the BAO peak of the matter correlation function, both in real and redshift space. In order to describe the nonlinear evolution of the BAO peak we run N-body simulations and compare them with simple analytic formulae. We show that the evolution with redshift of the correlation function and its dependence on the neutrino masses is well reproduced in a simplified version of the Zel'dovich approximation, in which the mode-coupling contribution to the power spectrum is neglected. While in linear theory the BAO peak decreases for increasing neutrinomore » masses, the effect of nonlinear structure formation goes in the opposite direction, since the peak broadening by large scale flows is less effective. As a result of this combined effect, the peak decreases by ∼ 0.6 % for  ∑ m{sub ν} = 0.15 eV and increases by ∼1.2% for  ∑ m{sub ν} = 0.3 eV, with respect to a massless neutrino cosmology with equal value of the other cosmological parameters. We extend our analysis to redshift space and to halos, and confirm the agreement between simulations and the analytic formulae. We argue that all analytical approaches having the Zel'dovich propagator in their lowest order approximation should give comparable performances, irrespectively to their formulation in Lagrangian or in Eulerian space.« less

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

Evaluation of generalized degrees of freedom for sparse estimation by replica method

NASA Astrophysics Data System (ADS)

Sakata, A.

2016-12-01

We develop a method to evaluate the generalized degrees of freedom (GDF) for linear regression with sparse regularization. The GDF is a key factor in model selection, and thus its evaluation is useful in many modelling applications. An analytical expression for the GDF is derived using the replica method in the large-system-size limit with random Gaussian predictors. The resulting formula has a universal form that is independent of the type of regularization, providing us with a simple interpretation. Within the framework of replica symmetric (RS) analysis, GDF has a physical meaning as the effective fraction of non-zero components. The validity of our method in the RS phase is supported by the consistency of our results with previous mathematical results. The analytical results in the RS phase are calculated numerically using the belief propagation algorithm.

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…

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.

Origin of the Formulas of Dihydrogen and Other Simple Molecules

ERIC Educational Resources Information Center

Williams, Andrew

2007-01-01

The logic and experimental data are described with which chemists originally deduced the formulas of the fundamental compounds such as H[subscript 2], H[subscript 2]O, Cl[subscript 2], NH[subscript 3], CH[subscript 4], and HCl. This information is never provided in current texts at any level and the formulas of such simple compounds are taken as…

High-latitude analytical formulas for scintillation levels

NASA Astrophysics Data System (ADS)

Aarons, J.; MacKenzie, E.; Bhavnani, K.

The paper deals with the seasonal, solar flux, and magnetic dependence at auroral and subauroral latitudes as well as at a mid-latitude station. Analytical formulas are developed from a large data base. The data base used is a series of measurements of the scintillations of one synchronous satellite beacon, ATS 3, transmitting at 137 MHz. The analytical terms provide mean scintillation excursions as a function of time of day, month, solar flux, and magnetic index.

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.

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.

Quasi-linear diffusion coefficients for highly oblique whistler mode waves

NASA Astrophysics Data System (ADS)

Albert, J. M.

2017-05-01

Quasi-linear diffusion coefficients are considered for highly oblique whistler mode waves, which exhibit a singular "resonance cone" in cold plasma theory. The refractive index becomes both very large and rapidly varying as a function of wave parameters, making the diffusion coefficients difficult to calculate and to characterize. Since such waves have been repeatedly observed both outside and inside the plasmasphere, this problem has received renewed attention. Here the diffusion equations are analytically treated in the limit of large refractive index μ. It is shown that a common approximation to the refractive index allows the associated "normalization integral" to be evaluated in closed form and that this can be exploited in the numerical evaluation of the exact expression. The overall diffusion coefficient formulas for large μ are then reduced to a very simple form, and the remaining integral and sum over resonances are approximated analytically. These formulas are typically written for a modeled distribution of wave magnetic field intensity, but this may not be appropriate for highly oblique whistlers, which become quasi-electrostatic. Thus, the analysis is also presented in terms of wave electric field intensity. The final results depend strongly on the maximum μ (or μ∥) used to model the wave distribution, so realistic determination of these limiting values becomes paramount.

A Statistical Physicist's Approach to Biological Motion: From the the Kinesin Walk to Muscle Contraction

NASA Astrophysics Data System (ADS)

Vicsek, Tamas

1997-03-01

It is demonstrated that a wide range of experimental results on biological motion can be successfully interpreted in terms of statistical physics motivated models taking into account the relevant microscopic details of motor proteins and allowing analytic solutions. Two important examples are considered, i) the motion of a single kinesin molecule along microtubules inside individual cells and ii) muscle contraction which is a macroscopic phenomenon due to the collective action of a large number of myosin heads along actin filaments. i) Recently individual two-headed kinesin molecules have been studied in in vitro motility assays revealing a number of their peculiar transport properties. Here we propose a simple and robust model for the kinesin stepping process with elastically coupled Brownian heads showing all of these properties. The analytic treatment of our model results in a very good fit to the experimental data and practically has no free parameters. ii) Myosin is an ATPase enzyme that converts the chemical energy stored in ATP molecules into mechanical work. During muscle contraction, the myosin cross-bridges attach to the actin filaments and exert force on them yielding a relative sliding of the actin and myosin filaments. In this paper we present a simple mechanochemical model for the cross-bridge interaction involving the relevant kinetic data and providing simple analytic solutions for the mechanical properties of muscle contraction, such as the force-velocity relationship or the relative number of the attached cross-bridges. So far the only analytic formula which could be fitted to the measured force-velocity curves has been the well known Hill equation containing parameters lacking clear microscopic origin. The main advantages of our new approach are that it explicitly connects the mechanical data with the kinetic data and the concentration of the ATP and ATPase products and as such it leads to new analytic solutions which agree extremely well with a wide range of experimental curves, while the parameters of the corresponding expressions have well defined microscopic meaning.

Scaling of drizzle virga depth with cloud thickness for marine stratocumulus clouds

DOE PAGES

Yang, Fan; Luke, Edward P.; Kollias, Pavlos; ...

2018-04-20

Drizzle plays a crucial role in cloud lifetime and radiation properties of marine stratocumulus clouds. Understanding where drizzle exists in the sub-cloud layer, which depends on drizzle virga depth, can help us better understand where below-cloud scavenging and evaporative cooling and moisturizing occur. In this study, we examine the statistical properties of drizzle frequency and virga depth of marine stratocumulus based on unique ground-based remote sensing data. Results show that marine stratocumulus clouds are drizzling nearly all the time. In addition, we derive a simple scaling analysis between drizzle virga thickness and cloud thickness. Our analytical expression agrees with themore » observational data reasonable well, which suggests that our formula provides a simple parameterization for drizzle virga of stratocumulus clouds suitable for use in other models.« less

A simple model to quantitatively account for periodic outbreaks of the measles in the Dutch Bible Belt

NASA Astrophysics Data System (ADS)

Bier, Martin; Brak, Bastiaan

2015-04-01

In the Netherlands there has been nationwide vaccination against the measles since 1976. However, in small clustered communities of orthodox Protestants there is widespread refusal of the vaccine. After 1976, three large outbreaks with about 3000 reported cases of the measles have occurred among these orthodox Protestants. The outbreaks appear to occur about every twelve years. We show how a simple Kermack-McKendrick-like model can quantitatively account for the periodic outbreaks. Approximate analytic formulae to connect the period, size, and outbreak duration are derived. With an enhanced model we take the latency period in account. We also expand the model to follow how different age groups are affected. Like other researchers using other methods, we conclude that large scale underreporting of the disease must occur.

Scaling of drizzle virga depth with cloud thickness for marine stratocumulus clouds

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

Yang, Fan; Luke, Edward P.; Kollias, Pavlos

Drizzle plays a crucial role in cloud lifetime and radiation properties of marine stratocumulus clouds. Understanding where drizzle exists in the sub-cloud layer, which depends on drizzle virga depth, can help us better understand where below-cloud scavenging and evaporative cooling and moisturizing occur. In this study, we examine the statistical properties of drizzle frequency and virga depth of marine stratocumulus based on unique ground-based remote sensing data. Results show that marine stratocumulus clouds are drizzling nearly all the time. In addition, we derive a simple scaling analysis between drizzle virga thickness and cloud thickness. Our analytical expression agrees with themore » observational data reasonable well, which suggests that our formula provides a simple parameterization for drizzle virga of stratocumulus clouds suitable for use in other models.« less

Retrieval of the aerosol size distribution in the complex anomalous diffraction approximation

NASA Astrophysics Data System (ADS)

Franssens, Ghislain R.

This contribution reports some recently achieved results in aerosol size distribution retrieval in the complex anomalous diffraction approximation (ADA) to MIE scattering theory. This approximation is valid for spherical particles that are large compared to the wavelength and have a refractive index close to 1. The ADA kernel is compared with the exact MIE kernel. Despite being a simple approximation, the ADA seems to have some practical value for the retrieval of the larger modes of tropospheric and lower stratospheric aerosols. The ADA has the advantage over MIE theory that an analytic inversion of the associated Fredholm integral equation becomes possible. In addition, spectral inversion in the ADA can be formulated as a well-posed problem. In this way, a new inverse formula was obtained, which allows the direct computation of the size distribution as an integral over the spectral extinction function. This formula is valid for particles that both scatter and absorb light and it also takes the spectral dispersion of the refractive index into account. Some details of the numerical implementation of the inverse formula are illustrated using a modified gamma test distribution. Special attention is given to the integration of spectrally truncated discrete extinction data with errors.

Official Methods for the Determination of Minerals and Trace Elements in Infant Formula and Milk Products: A Review.

PubMed

Poitevin, Eric

2016-01-01

The minerals and trace elements that account for about 4% of total human body mass serve as materials and regulators in numerous biological activities in body structure building. Infant formula and milk products are important sources of endogenic and added minerals and trace elements and hence, must comply with regulatory as well as nutritional and safety requirements. In addition, reliable analytical data are necessary to support product content and innovation, health claims, or declaration and specific safety issues. Adequate analytical platforms and methods must be implemented to demonstrate both the compliance and safety assessment of all declared and regulated minerals and trace elements, especially trace-element contaminant surveillance. The first part of this paper presents general information on the mineral composition of infant formula and milk products and their regulatory status. In the second part, a survey describes the main techniques and related current official methods determining minerals and trace elements in infant formula and milk products applied for by various international organizations (AOAC INTERNATIONAL, the International Organization for Standardization, the International Dairy Federation, and the European Committe for Standardization). The third part summarizes method officialization activities by Stakeholder Panels on Infant Formula and Adult Nutritionals and Stakeholder Panel on Strategic Food Analytical Methods. The final part covers a general discussion focusing on analytical gaps and future trends in inorganic analysis that have been applied for in infant formula and milk-based products.

A simple formula for estimating Stark widths of neutral lines. [of stellar atmospheres

NASA Technical Reports Server (NTRS)

Freudenstein, S. A.; Cooper, J.

1978-01-01

A simple formula for the prediction of Stark widths of neutral lines similar to the semiempirical method of Griem (1968) for ion lines is presented. This formula is a simplification of the quantum-mechanical classical path impact theory and can be used for complicated atoms for which detailed calculations are not readily available, provided that the effective position of the closest interacting level is known. The expression does not require the use of a computer. The formula has been applied to a limited number of neutral lines of interest, and the width obtained is compared with the much more complete calculations of Bennett and Griem (1971). The agreement generally is well within 50% of the published value for the lines investigated. Comparisons with other formulas are also made. In addition, a simple estimate for the ion-broadening parameter is given.

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.

Entanglement transitions induced by large deviations

NASA Astrophysics Data System (ADS)

Bhosale, Udaysinh T.

2017-12-01

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B , is computed analytically using a Coulomb gas method. It is shown that this probability, for large N , goes as exp[-β N2Φ (ζ ) ] , where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ (ζ ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A , using the properties of the density matrix's partial transpose ρ12Γ. The density of states of ρ12Γ is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ . Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.

Entanglement transitions induced by large deviations.

PubMed

Bhosale, Udaysinh T

2017-12-01

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B, is computed analytically using a Coulomb gas method. It is shown that this probability, for large N, goes as exp[-βN^{2}Φ(ζ)], where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ(ζ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A, using the properties of the density matrix's partial transpose ρ_{12}^{Γ}. The density of states of ρ_{12}^{Γ} is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ. Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.

Tunneling of heat: Beyond linear response regime

NASA Astrophysics Data System (ADS)

Walczak, Kamil; Saroka, David

2018-02-01

We examine nanoscale processes of heat (energy) transfer as carried by electrons tunneling via potential barriers and molecular interconnects between two heat reservoirs (thermal baths). For that purpose, we use Landauer-type formulas to calculate thermal conductance and quadratic correction to heat flux flowing via quantum systems. As an input, we implement analytical expressions for transmission functions related to simple potential barriers and atomic bridges. Our results are discussed with respect to energy of tunneling electrons, temperature, the presence of resonant states, and specific parameters characterizing potential barriers as well as heat carriers. The simplicity of semi-analytical models developed by us allows to fit experimental data and extract crucial information about the values of model parameters. Further investigations are expected for more realistic transmission functions, while time-dependent aspects of nanoscale heat transfer may be addressed by using the concept of wave packets scattered on potential barriers and point-like defects within regular (periodic) nanostructures.

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.

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.

Broadband Noise Prediction When Turbulence Simulation Is Available - Derivation of Formulation 2B and Its Statistical Analysis

NASA Technical Reports Server (NTRS)

Farassat, Fereidoun; Casper, Jay H.

2012-01-01

We show that a simple modification of Formulation 1 of Farassat results in a new analytic expression that is highly suitable for broadband noise prediction when extensive turbulence simulation is available. This result satisfies all the stringent requirements, such as permitting the use of the exact geometry and kinematics of the moving body, that we have set as our goal in the derivation of useful acoustic formulas for the prediction of rotating blade and airframe noise. We also derive a simple analytic expression for the autocorrelation of the acoustic pressure that is valid in the near and far fields. Our analysis is based on the time integral of the acoustic pressure that can easily be obtained at any resolution for any observer time interval and digitally analyzed for broadband noise prediction. We have named this result as Formulation 2B of Farassat. One significant consequence of Formulation 2B is the derivation of the acoustic velocity potential for the thickness and loading terms of the Ffowcs Williams-Hawkings (FW-H) equation. This will greatly enhance the usefulness of the Fast Scattering Code (FSC) by providing a high fidelity boundary condition input for scattering predictions.

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.

Self-sustained peristaltic waves: Explicit asymptotic solutions

NASA Astrophysics Data System (ADS)

Dudchenko, O. A.; Guria, G. Th.

2012-02-01

A simple nonlinear model for the coupled problem of fluid flow and contractile wall deformation is proposed to describe peristalsis. In the context of the model the ability of a transporting system to perform autonomous peristaltic pumping is interpreted as the ability to propagate sustained waves of wall deformation. Piecewise-linear approximations of nonlinear functions are used to analytically demonstrate the existence of traveling-wave solutions. Explicit formulas are derived which relate the speed of self-sustained peristaltic waves to the rheological properties of the transporting vessel and the transported fluid. The results may contribute to the development of diagnostic and therapeutic procedures for cases of peristaltic motility disorders.

Assay of the Martian Regolith with Neutrons

NASA Technical Reports Server (NTRS)

Drake, Darrell M.; Reedy, R.; Jakowsky, B.; Clark, B.; Squyres, S.

1998-01-01

Different aspects of assaying Martian regolith using neutrons have been investigated. The epithermal portion of moderated neutrons spectra is dramatically effected by the presence of hydrogen (usually in the form of water). A simple analytic formula has been derived to describe the amplitude of this portion of the neutron spectrum as a function of water concentration. Several demonstration experiments have been performed and modeled with a Monte Carlo code. Results of these experiments generally agreed with the calculations to within 20%. In addition to He-3 detectors, lithium-glass scintillators and U-238 fission ion chambers were investigated to determine their applicability to space experiments.

A method of determining attitude from magnetometer data only

NASA Technical Reports Server (NTRS)

Natanson, G. A.; Mclaughlin, S. F.; Nicklas, R. C.

1990-01-01

Presented here is a new algorithm to determine attitude using only magnetometer data under the following conditions: (1) internal torques are known and (2) external torques are negligible. Torque-free rotation of a spacecraft in thruster firing acquisition phase and its magnetic despin in the B-dot mode give typical examples of such situations. A simple analytical formula has been derived in the limiting case of a spacecraft rotating with constant angular velocity. The formula has been tested using low-frequency telemetry data for the Earth Radiation Budget Satellite (ERBS) under normal conditions. Observed small oscillation of body-fixed components of the angular velocity vector near their mean values result in relatively minor errors of approximately 5 degrees. More significant errors come from processing digital magnetometer data. Higher resolution of digitized magnetometer measurements would significantly improve the accuracy of this deterministic scheme. Tests of the general version of the developed algorithm for a free-rotating spacecraft and for the B-dot mode are in progress.

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.

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

Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory

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

Dixon, Lance J.; /SLAC; Drummond, James M.

2012-02-15

We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parametersmore » uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.« less

The theoretical link between voltage loss, reduction in field enhancement factor, and Fowler-Nordheim-plot saturation

NASA Astrophysics Data System (ADS)

Forbes, Richard G.

2017-03-01

With a large-area field electron emitter, when an individual post-like emitter is sufficiently resistive, and current through it is sufficiently large, then voltage loss occurs along it. This letter provides a simple analytical and conceptual demonstration that this voltage loss is directly and inextricably linked to a reduction in the field enhancement factor (FEF) at the post apex. A formula relating apex-FEF reduction to this voltage loss was obtained in the paper by Minoux et al. [Nano Lett. 5, 2135 (2005)] by fitting to numerical results from a Laplace solver. This letter derives the same formula analytically, by using a "floating sphere" model. The analytical proof brings out the underlying physics more clearly and shows that the effect is a general phenomenon, related to reduction in the magnitude of the surface charge in the most protruding parts of an emitter. Voltage-dependent FEF-reduction is one cause of "saturation" in Fowler-Nordheim (FN) plots. Another is a voltage-divider effect, due to measurement-circuit resistance. An integrated theory of both effects is presented. Both together, or either by itself, can cause saturation. Experimentally, if saturation occurs but voltage loss is small (<20 V, say), then saturation is more probably due to FEF-reduction than voltage division. In this case, existing treatments of electrostatic interaction ("shielding") between closely spaced emitters may need modification. Other putative causes of saturation exist, so the present theory is a partial story. Its extension seems possible and could lead to a more general physical understanding of the causes of FN-plot saturation.

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

Nomogram for sample size calculation on a straightforward basis for the kappa statistic.

PubMed

Hong, Hyunsook; Choi, Yunhee; Hahn, Seokyung; Park, Sue Kyung; Park, Byung-Joo

2014-09-01

Kappa is a widely used measure of agreement. However, it may not be straightforward in some situation such as sample size calculation due to the kappa paradox: high agreement but low kappa. Hence, it seems reasonable in sample size calculation that the level of agreement under a certain marginal prevalence is considered in terms of a simple proportion of agreement rather than a kappa value. Therefore, sample size formulae and nomograms using a simple proportion of agreement rather than a kappa under certain marginal prevalences are proposed. A sample size formula was derived using the kappa statistic under the common correlation model and goodness-of-fit statistic. The nomogram for the sample size formula was developed using SAS 9.3. The sample size formulae using a simple proportion of agreement instead of a kappa statistic and nomograms to eliminate the inconvenience of using a mathematical formula were produced. A nomogram for sample size calculation with a simple proportion of agreement should be useful in the planning stages when the focus of interest is on testing the hypothesis of interobserver agreement involving two raters and nominal outcome measures. Copyright © 2014 Elsevier Inc. All rights reserved.

Semi-empirical formulation of multiple scattering for the Gaussian beam model of heavy charged particles stopping in tissue-like matter.

PubMed

Kanematsu, Nobuyuki

2009-03-07

Dose calculation for radiotherapy with protons and heavier ions deals with a large volume of path integrals involving a scattering power of body tissue. This work provides a simple model for such demanding applications. There is an approximate linearity between RMS end-point displacement and range of incident particles in water, empirically found in measurements and detailed calculations. This fact was translated into a simple linear formula, from which the scattering power that is only inversely proportional to the residual range was derived. The simplicity enabled the analytical formulation for ions stopping in water, which was designed to be equivalent with the extended Highland model and agreed with measurements within 2% or 0.02 cm in RMS displacement. The simplicity will also improve the efficiency of numerical path integrals in the presence of heterogeneity.

On an example of a system of differential equations that are integrated in Abelian functions

NASA Astrophysics Data System (ADS)

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

2017-12-01

The short review of the theory of Abelian functions and its applications in mechanics and analytical theory of differential equations is given. We think that Abelian functions are the natural generalization of commonly used functions because if the general solution of the 2nd order differential equation depends algebraically on the constants of integration, then integrating this equation does not lead out of the realm of commonly used functions complemented by the Abelian functions (Painlevé theorem). We present a relatively simple example of a dynamical system that is integrated in Abelian integrals by “pairing” two copies of a hyperelliptic curve. Unfortunately, initially simple formulas unfold into very long ones. Apparently the theory of Abelian functions hasn’t been finished in the last century because without computer algebra systems it was impossible to complete the calculations to the end. All calculations presented in our report are performed in Sage.

How Many Peripheral Solder Joints in a Surface Mounted Design Experience Inelastic Strains?

NASA Astrophysics Data System (ADS)

Suhir, E.; Yi, S.; Ghaffarian, R.

2017-03-01

It has been established that it is the peripheral solder joints that are the most vulnerable in the ball-grid-array (BGA) and column-grid-array (CGA) designs and most often fail. As far as the long-term reliability of a soldered microelectronics assembly as a whole is concerned, it makes a difference, if just one or more peripheral joints experience inelastic strains. It is clear that the low cycle fatigue lifetime of the solder system is inversely proportional to the number of joints that simultaneously experience inelastic strains. A simple and physically meaningful analytical expression (formula) is obtained for the prediction, at the design stage, of the number of such joints, if any, for the given effective thermal expansion (contraction) mismatch of the package and PCB; materials and geometrical characteristics of the package/PCB assembly; package size; and, of course, the level of the yield stress in the solder material. The suggested formula can be used to determine if the inelastic strains in the solder material could be avoided by the proper selection of the above characteristics and, if not, how many peripheral joints are expected to simultaneously experience inelastic strains. The general concept is illustrated by a numerical example carried out for a typical BGA package. The suggested analytical model (formula) is applicable to any soldered microelectronics assembly. The roles of other important factors, such as, e.g., solder material anisotropy, grain size, and their random orientation within a joint, are viewed in this analysis as less important factors than the level of the interfacial stress. The roles of these factors will be accounted for in future work and considered, in addition to the location of the joint, in a more complicated, more sophisticated, and more comprehensive reliability/fatigue model.

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.

A strategy for reducing gross errors in the generalized Born models of implicit solvation

PubMed Central

Onufriev, Alexey V.; Sigalov, Grigori

2011-01-01

The “canonical” generalized Born (GB) formula [C. Still, A. Tempczyk, R. C. Hawley, and T. Hendrickson, J. Am. Chem. Soc. 112, 6127 (1990)] is known to provide accurate estimates for total electrostatic solvation energies ΔGel of biomolecules if the corresponding effective Born radii are accurate. Here we show that even if the effective Born radii are perfectly accurate, the canonical formula still exhibits significant number of gross errors (errors larger than 2kBT relative to numerical Poisson equation reference) in pairwise interactions between individual atomic charges. Analysis of exact analytical solutions of the Poisson equation (PE) for several idealized nonspherical geometries reveals two distinct spatial modes of the PE solution; these modes are also found in realistic biomolecular shapes. The canonical GB Green function misses one of two modes seen in the exact PE solution, which explains the observed gross errors. To address the problem and reduce gross errors of the GB formalism, we have used exact PE solutions for idealized nonspherical geometries to suggest an alternative analytical Green function to replace the canonical GB formula. The proposed functional form is mathematically nearly as simple as the original, but depends not only on the effective Born radii but also on their gradients, which allows for better representation of details of nonspherical molecular shapes. In particular, the proposed functional form captures both modes of the PE solution seen in nonspherical geometries. Tests on realistic biomolecular structures ranging from small peptides to medium size proteins show that the proposed functional form reduces gross pairwise errors in all cases, with the amount of reduction varying from more than an order of magnitude for small structures to a factor of 2 for the largest ones. PMID:21528947

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.

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.

Phosphorescence Kinetics of Singlet Oxygen Produced by Photosensitization in Spherical Nanoparticles. Part I. Theory.

PubMed

Hovan, Andrej; Datta, Shubhashis; Kruglik, Sergei G; Jancura, Daniel; Miskovsky, Pavol; Bánó, Gregor

2018-05-24

The singlet oxygen produced by energy transfer between an excited photosensitizer (pts) and ground-state oxygen molecules plays a key role in photodynamic therapy. Different nanocarrier systems are extensively studied to promote targeted pts delivery in a host body. The phosphorescence kinetics of the singlet oxygen produced by the short laser pulse photosensitization of pts inside nanoparticles is influenced by singlet oxygen diffusion from the particles to the surrounding medium. Two theoretical models are presented in this work: a more complex numerical one and a simple analytical one. Both the models predict the time course of singlet oxygen concentration inside and outside of the spherical particles following short-pulse excitation of pts. On the basis of the comparison of the numerical and analytical results, a semiempirical analytical formula is derived to calculate the characteristic diffusion time of singlet oxygen from the nanoparticles to the surrounding solvent. The phosphorescence intensity of singlet oxygen produced in pts-loaded nanocarrier systems can be calculated as a linear combination of the two concentrations (inside and outside the particles), taking the different phosphorescence emission rate constants into account.

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.

A Fast Method of Deriving the Kirchhoff Formula for Moving Surfaces

NASA Technical Reports Server (NTRS)

Farassat, F.; Posey, Joe W.

2007-01-01

The Kirchhoff formula for a moving surface is very useful in many wave propagation problems, particularly in the prediction of noise from rotating machinery. Several publications in the last two decades have presented derivations of the Kirchhoff formula for moving surfaces in both time and frequency domains. Here we present a method originally developed by Farassat and Myers in time domain that is both simple and direct. It is based on generalized function theory and the useful concept of imbedding the problem in the unbounded three-dimensional space. We derive an inhomogeneous wave equation with the source terms that involve Dirac delta functions with their supports on the moving data surface. This wave equation is then solved using the simple free space Green's function of the wave equation resulting in the Kirchhoff formula. The algebraic manipulations are minimal and simple. We do not need the Green's theorem in four dimensions and there is no ambiguity in the interpretation of any terms in the final formulas. Furthermore, this method also gives the simplest derivation of the classical Kirchhoff formula which has a fairly lengthy derivation in physics and applied mathematics books. The Farassat-Myers method can be used easily in frequency domain.

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

Analytical probabilistic modeling of RBE-weighted dose for ion therapy.

PubMed

Wieser, H P; Hennig, P; Wahl, N; Bangert, M

2017-11-10

Particle therapy is especially prone to uncertainties. This issue is usually addressed with uncertainty quantification and minimization techniques based on scenario sampling. For proton therapy, however, it was recently shown that it is also possible to use closed-form computations based on analytical probabilistic modeling (APM) for this purpose. APM yields unique features compared to sampling-based approaches, motivating further research in this context. This paper demonstrates the application of APM for intensity-modulated carbon ion therapy to quantify the influence of setup and range uncertainties on the RBE-weighted dose. In particular, we derive analytical forms for the nonlinear computations of the expectation value and variance of the RBE-weighted dose by propagating linearly correlated Gaussian input uncertainties through a pencil beam dose calculation algorithm. Both exact and approximation formulas are presented for the expectation value and variance of the RBE-weighted dose and are subsequently studied in-depth for a one-dimensional carbon ion spread-out Bragg peak. With V and B being the number of voxels and pencil beams, respectively, the proposed approximations induce only a marginal loss of accuracy while lowering the computational complexity from order [Formula: see text] to [Formula: see text] for the expectation value and from [Formula: see text] to [Formula: see text] for the variance of the RBE-weighted dose. Moreover, we evaluated the approximated calculation of the expectation value and standard deviation of the RBE-weighted dose in combination with a probabilistic effect-based optimization on three patient cases considering carbon ions as radiation modality against sampled references. The resulting global γ-pass rates (2 mm,2%) are [Formula: see text]99.15% for the expectation value and [Formula: see text]94.95% for the standard deviation of the RBE-weighted dose, respectively. We applied the derived analytical model to carbon ion treatment planning, although the concept is in general applicable to other ion species considering a variable RBE.

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.

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)].

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

Richtmyer-Meshkov flow in elastic solids.

PubMed

Piriz, A R; López Cela, J J; Tahir, N A; Hoffmann, D H H

2006-09-01

Richtmyer-Meshkov flow is studied by means of an analytical model which describes the asymptotic oscillations of a corrugated interface between two perfectly elastic solids after the interaction with a shock wave. The model shows that the flow stability is due to the restoring effect of the elastic force. It provides a simple approximate but still very accurate formula for the oscillation period. It also shows that as it is observed in numerical simulations, the amplitude oscillates around a mean value equal to the post-shock amplitude, and that this is a consequence of the stress free conditions of the material immediately after the shock interaction. Extensive numerical simulations are presented to validate the model results.

Susceptibility of a Magnetic Impurity in Weakly Localized Regime

NASA Astrophysics Data System (ADS)

Suga, Seiichiro; Kasai, Hideaki; Okiji, Ayao

1987-12-01

Interplay between the randomness and the s-d exchange interaction is investigated theoretically in the weakly localized regime through the temperature dependence of the susceptibility. In the first half the analytic calculations are performed perturbatively in terms of the s-d exchange coupling constant. It is shown that the quantum corrections to the susceptibility construct geometric series and can be summed up as simple formulae within the framework of the most divergent approximation. In the second half the numerical calculations are performed with the use of the self-consistent ladder approximation. It is shown that the effective Curie constant decreases more rapidly with decreasing the temperature than that in the usual Kondo systems.

Structure of the screening layer near a plane isolated body in the deep vacuum. Part 2. Monoenergetic isotropic flow

NASA Astrophysics Data System (ADS)

Gunko, Yuri F.; Gunko, Natalia A.

2018-05-01

In this paper we consider the problem of determining the structure of the electric field near the surface of a flat insulated body under conditions of a deep vacuum. It is assumed that the emitted particles are electrons leaving the body surface under the influence of ionizing radiation whose velocities distribution near the surface is isotropic. It is estimated the thickness of the screening layer under conditions of stationary emission from a flat surface. The solutio of the problem of determining a stationary self-consistent electric field near the surface is found in a simple analytical form. The thickness of the screening layer is calculated from this formula.

New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs

NASA Astrophysics Data System (ADS)

Csörgő, Tamás; Kasza, Gábor; Csanád, Máté; Jiang, Zefang

2018-06-01

We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision data at RHIC and LHC. In the longitudinally boost-invariant limit, these new solutions approach the Hwa-Bjorken solution and the corresponding rapidity distributions approach a rapidity plateaux.

A simple equation to estimate body fat percentage in children with overweightness or obesity: a retrospective study.

PubMed

Cortés-Castell, Ernesto; Juste, Mercedes; Palazón-Bru, Antonio; Monge, Laura; Sánchez-Ferrer, Francisco; Rizo-Baeza, María Mercedes

2017-01-01

Dual-energy X-ray absorptiometry (DXA) provides separate measurements of fat mass, fat-free mass and bone mass, and is a quick, accurate, and safe technique, yet one that is not readily available in routine clinical practice. Consequently, we aimed to develop statistical formulas to predict fat mass (%) and fat mass index (FMI) with simple parameters (age, sex, weight and height). We conducted a retrospective observational cross-sectional study in 416 overweight or obese patients aged 4-18 years that involved assessing adiposity by DXA (fat mass percentage and FMI), body mass index (BMI), sex and age. We randomly divided the sample into two parts (construction and validation). In the construction sample, we developed formulas to predict fat mass and FMI using linear multiple regression models. The formulas were validated in the other sample, calculating the intraclass correlation coefficient via bootstrapping. The fat mass percentage formula had a coefficient of determination of 0.65. This value was 0.86 for FMI. In the validation, the constructed formulas had an intraclass correlation coefficient of 0.77 for fat mass percentage and 0.92 for FMI. Our predictive formulas accurately predicted fat mass and FMI with simple parameters (BMI, sex and age) in children with overweight and obesity. The proposed methodology could be applied in other fields. Further studies are needed to externally validate these formulas.

Interatomic potential at small internuclear distances. A simple formula for the screening constant

NASA Astrophysics Data System (ADS)

Zinoviev, A. N.

2017-09-01

A simple formula for estimating the screening constant has been proposed. This formula fits well experimental data on the interaction potentials. Quantitative description of the experiment for the effect of electronic screening on the nuclear synthesis reaction cross-section for the D+-D system has been obtained. A conclusion has been made that the differences between the measured cross-sections and their theoretically predicted values, which take place in more complicated cases nuclear synthesis reactions, are not caused by uncertainties in the knowledge of potentials.

Einstein versus the Simple Pendulum Formula: Does Gravity Slow All Clocks?

ERIC Educational Resources Information Center

Puri, Avinash

2015-01-01

According to the Newtonian formula for a simple pendulum, the period of a pendulum is inversely proportional to the square root of "g", the gravitational field strength. Einstein's theory of general relativity leads to the result that time slows down where gravity is intense. The two claims look contradictory and can muddle student and…

12 CFR Appendix A to Part 230 - Annual Percentage Yield Calculation

Code of Federal Regulations, 2010 CFR

2010-01-01

... following simple formula: APY=100 (Interest/Principal) Examples (1) If an institution pays $61.68 in... percentage yield is 5.39%, using the simple formula: APY=100(134.75/2,500) APY=5.39% For $15,000, interest is... Yield Calculation The annual percentage yield measures the total amount of interest paid on an account...

The equivalent thermal properties of a single fracture

NASA Astrophysics Data System (ADS)

Sangaré, D.; Thovert, J.-F.; Adler, P. M.

2008-10-01

The normal resistance and the tangential conductivity of a single fracture with Gaussian or self-affine surfaces are systematically studied as functions of the nature of the materials in contact and of the geometrical parameters. Analytical formulas are provided in the lubrication limit for fractures with sinusoidal apertures; these formulas are used to substantiate empirical formulas for resistance and conductivity. Other approximations based on the combination of series and parallel formulas are tested.

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

The Preferential Tidal Stripping of Dark Matter versus Stars in Galaxies

NASA Astrophysics Data System (ADS)

Smith, Rory; Choi, Hoseung; Lee, Jaehyun; Rhee, Jinsu; Sanchez-Janssen, Ruben; Yi, Sukyoung K.

2016-12-01

Using high-resolution hydrodynamical cosmological simulations, we conduct a comprehensive study of how tidal stripping removes dark matter and stars from galaxies. We find that dark matter is always stripped far more significantly than the stars—galaxies that lose ˜80% of their dark matter, typically lose only 10% of their stars. This is because the dark matter halo is initially much more extended than the stars. As such, we find that the stellar-to-halo size-ratio (measured using r eff/r vir) is a key parameter controlling the relative amounts of dark matter and stellar stripping. We use simple fitting formulae to measure the relation between the fraction of bound dark matter and the fraction of bound stars. We measure a negligible dependence on cluster mass or galaxy mass. Therefore, these formulae have general applicability in cosmological simulations, and are ideal to improve stellar stripping recipes in semi-analytical models, and/or to estimate the impact that tidal stripping would have on galaxies when only their halo mass evolution is known.

Ionization of nS, nP, and nD lithium, potassium, and cesium Rydberg atoms by blackbody radiation

NASA Astrophysics Data System (ADS)

Beterov, I. I.; Ryabtsev, I. I.; Tretyakov, D. B.; Bezuglov, N. N.; Ékers, A.

2008-07-01

The results of theoretical calculations of the blackbody ionization rates of lithium, potassium, and cesium atoms residing in Rydberg states are presented. The calculations are performed for nS, nP, and nD states in a wide range of principal quantum numbers, n = 8-65, for blackbody radiation temperatures T = 77, 300, and 600 K. The calculations are performed using the known quasi-classical formulas for the photoionization cross sections and for the radial matrix elements of transitions in the discrete spectrum. The effect of the blackbody-radiation-induced population redistribution between Rydberg states on the blackbody ionization rates measured under laboratory conditions is quantitatively analyzed. Simple analytical formulas that approximate the numerical results and that can be used to estimate the blackbody ionization rates of Rydberg atoms are presented. For the S series of lithium, the rate of population of high-lying Rydberg levels by blackbody radiation is found to anomalously behave as a function of n. This anomaly is similar to the occurrence of the Cooper minimum in the discrete spectrum.

Shear viscosity of an ultrarelativistic Boltzmann gas with isotropic inelastic scattering processes

NASA Astrophysics Data System (ADS)

El, A.; Lauciello, F.; Wesp, C.; Bouras, I.; Xu, Z.; Greiner, C.

2014-05-01

We derive an analytic expression for the shear viscosity of an ultra-relativistic gas in presence of both elastic 2→2 and inelastic 2↔3 processes with isotropic differential cross sections. The derivation is based on the entropy principle and Grad's approximation for the off-equilibrium distribution function. The obtained formula relates the shear viscosity coefficient η to the total cross sections σ22 and σ23 of the elastic resp. inelastic processes. The values of shear viscosity extracted using the Green-Kubo formula from kinetic transport calculations are shown to be in excellent agreement with the analytic results which demonstrates the validity of the derived formula.

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)].

Electron-cyclotron absorption in high-temperature plasmas: quasi-exact analytical evaluation and comparative numerical analysis

NASA Astrophysics Data System (ADS)

Albajar, F.; Bertelli, N.; Bornatici, M.; Engelmann, F.

2007-01-01

On the basis of the electromagnetic energy balance equation, a quasi-exact analytical evaluation of the electron-cyclotron (EC) absorption coefficient is performed for arbitrary propagation (with respect to the magnetic field) in a (Maxwellian) magneto-plasma for the temperature range of interest for fusion reactors (in which EC radiation losses tend to be important in the plasma power balance). The calculation makes use of Bateman's expansion for the product of two Bessel functions, retaining the lowest-order contribution. The integration over electron momentum can then be carried out analytically, fully accounting for finite Larmor radius effects in this approximation. On the basis of the analytical expressions for the EC absorption coefficients of both the extraordinary and ordinary modes thus obtained, (i) for the case of perpendicular propagation simple formulae are derived for both modes and (ii) a numerical analysis of the angular distribution of EC absorption is carried out. An assessment of the accuracy of asymptotic expressions that have been given earlier is also performed, showing that these approximations can be usefully applied for calculating EC power losses from reactor-grade plasmas. Presented in part at the 14th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Resonance Heating, Santorini, Greece, 9-12 May 2006.

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.

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.

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

Photoionization of the hydrogen atom in strong magnetic fields

NASA Technical Reports Server (NTRS)

Potekhin, Aleksandr IU.; Pavlov, George G.

1993-01-01

The photoionization of the hydrogen atom in magnetic fields B about 10 exp 11 - 10 exp 13 G typical of the surface layers of neutron stars is investigated analytically and numerically. We consider the photoionization from various tightly bound and hydrogen-like states of the atom for photons with arbitrary polarizations and wave-vector directions. It is shown that the length form of the interaction matrix elements is more appropriate in the adiabatic approximation than the velocity form, at least in the most important frequency range omega much less than omega(B), where omega(B) is the electron cyclotron frequency. Use of the length form yields nonzero cross sections for photon polarizations perpendicular to the magnetic field at omega less than omega(B); these cross sections are the ones that most strongly affect the properties of the radiation escaping from an optically thick medium, e.g., from the atmosphere of a neutron star. The results of the numerical calculations are fitted by simple analytical formulas.

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.

Evaluation of bed load transport subject to high shear stress fluctuations

NASA Astrophysics Data System (ADS)

Cheng, Nian-Sheng; Tang, Hongwu; Zhu, Lijun

2004-05-01

Many formulas available in the literature for computing sediment transport rates are often expressed in terms of time mean variables such as time mean bed shear stress or flow velocity, while effects of turbulence intensity, e.g., bed shear stress fluctuation, on sediment transport were seldom considered. This may be due to the fact that turbulence fluctuation is relatively limited in laboratory open-channel flows, which are often used for conducting sediment transport experiments. However, turbulence intensity could be markedly enhanced in practice. This note presents an analytical method to compute bed load transport by including effects of fluctuations in the bed shear stress. The analytical results obtained show that the transport rate enhanced by turbulence can be expressed as a simple function of the relative fluctuation of the bed shear stress. The results are also verified using data that were collected recently from specifically designed laboratory experiments. The present analysis is applicable largely for the condition of a flat bed that is comprised of uniform sand particles subject to unidirectional flows.

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].

Good cash flow = come in fast, go out slow!

PubMed

Garvey, Sherill

2002-07-01

The formula for successful cash management in home care is a simple one: The agency must bring cash in as quickly as possible, while keeping expenditures at as low and slow a pace as possible. However, while the formula may be simple, success may be elusive unless agency administrators have a well-thought-out plan to handle cash management.

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

Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian

DOE PAGES

Shi, Yuan; Qin, Hong; Fisch, Nathaniel J.

2017-08-14

Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via three-wave interactions. While three-wave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this study, we overcome this analytical difficulty and find a convenient formula for three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell model to second order using a multiscale perturbative expansion. Themore » general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of three-wave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to what happens in unmagnetized plasmas. Finally, our approach gives a more complete picture, beyond the simple collimated geometry, of how injected waves can decay in magnetic confinement devices, as well as how lasers can be scattered in magnetized plasma targets.« less

Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian.

PubMed

Shi, Yuan; Qin, Hong; Fisch, Nathaniel J

2017-08-01

Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via three-wave interactions. While three-wave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this paper, we overcome this analytical difficulty and find a convenient formula for three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell model to second order using a multiscale perturbative expansion. The general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of three-wave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to what happens in unmagnetized plasmas. Our approach gives a more complete picture, beyond the simple collimated geometry, of how injected waves can decay in magnetic confinement devices, as well as how lasers can be scattered in magnetized plasma targets.

Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian

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

Shi, Yuan; Qin, Hong; Fisch, Nathaniel J.

Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via three-wave interactions. While three-wave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this study, we overcome this analytical difficulty and find a convenient formula for three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell model to second order using a multiscale perturbative expansion. Themore » general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of three-wave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to what happens in unmagnetized plasmas. Finally, our approach gives a more complete picture, beyond the simple collimated geometry, of how injected waves can decay in magnetic confinement devices, as well as how lasers can be scattered in magnetized plasma targets.« less

Statistics Using Just One Formula

ERIC Educational Resources Information Center

Rosenthal, Jeffrey S.

2018-01-01

This article advocates that introductory statistics be taught by basing all calculations on a single simple margin-of-error formula and deriving all of the standard introductory statistical concepts (confidence intervals, significance tests, comparisons of means and proportions, etc) from that one formula. It is argued that this approach will…

Stationary echo canceling in velocity estimation by time-domain cross-correlation.

PubMed

Jensen, J A

1993-01-01

The application of stationary echo canceling to ultrasonic estimation of blood velocities using time-domain cross-correlation is investigated. Expressions are derived that show the influence from the echo canceler on the signals that enter the cross-correlation estimator. It is demonstrated that the filtration results in a velocity-dependent degradation of the signal-to-noise ratio. An analytic expression is given for the degradation for a realistic pulse. The probability of correct detection at low signal-to-noise ratios is influenced by signal-to-noise ratio, transducer bandwidth, center frequency, number of samples in the range gate, and number of A-lines employed in the estimation. Quantitative results calculated by a simple simulation program are given for the variation in probability from these parameters. An index reflecting the reliability of the estimate at hand can be calculated from the actual cross-correlation estimate by a simple formula and used in rejecting poor estimates or in displaying the reliability of the velocity estimated.

Binary dislocation junction formation and strength in hexagonal close-packed crystals

DOE PAGES

Wu, Chi -Chin; Aubry, Sylvie; Arsenlis, Athanasios; ...

2015-12-17

This work examines binary dislocation interactions, junction formation and junction strengths in hexagonal close-packed ( hcp ) crystals. Through a line-tension model and dislocation dynamics (DD) simulations, the interaction and dissociation of different sets of binary junctions are investigated involving one dislocation on the (011¯0) prismatic plane and a second dislocation on one of the following planes: (0001) basal, (11¯00) prismatic, (11¯01) primary pyramidal, or (2¯112) secondary pyramidal. Varying pairs of Burgers vectors are chosen from among the common types the basal type < a > 1/3 < 112¯0 >, prismatic type < c > <0001>, and pyramidal type 1/3 < 112¯3¯ >. For binary interaction due to dislocation intersection, both the analytical results and DD-simulations indicate a relationship between symmetry of interaction maps and the relative magnitude of the Burgers vectors that constitute the junction. Using analytical formulae, a simple regressive model is also developed to represent the junction yield surface. The equation is treated as a degenerated super elliptical equation to quantify the aspect ratio and tilting angle. Lastly, the results provide analytical insights on binary dislocation interactions that may occur in general hcp metals.« less

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.

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.

Optimal low thrust geocentric transfer. [mission analysis computer program

NASA Technical Reports Server (NTRS)

Edelbaum, T. N.; Sackett, L. L.; Malchow, H. L.

1973-01-01

A computer code which will rapidly calculate time-optimal low thrust transfers is being developed as a mission analysis tool. The final program will apply to NEP or SEP missions and will include a variety of environmental effects. The current program assumes constant acceleration. The oblateness effect and shadowing may be included. Detailed state and costate equations are given for the thrust effect, oblateness effect, and shadowing. A simple but adequate model yields analytical formulas for power degradation due to the Van Allen radiation belts for SEP missions. The program avoids the classical singularities by the use of equinoctial orbital elements. Kryloff-Bogoliuboff averaging is used to facilitate rapid calculation. Results for selected cases using the current program are given.

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

Kim, K. S.; Nakae, L. F.; Prasad, M. K.

Here, we solve a simple theoretical model of time evolving fission chains due to Feynman that generalizes and asymptotically approaches the point model theory. The point model theory has been used to analyze thermal neutron counting data. This extension of the theory underlies fast counting data for both neutrons and gamma rays from metal systems. Fast neutron and gamma-ray counting is now possible using liquid scintillator arrays with nanosecond time resolution. For individual fission chains, the differential equations describing three correlated probability distributions are solved: the time-dependent internal neutron population, accumulation of fissions in time, and accumulation of leaked neutronsmore » in time. Explicit analytic formulas are given for correlated moments of the time evolving chain populations. The equations for random time gate fast neutron and gamma-ray counting distributions, due to randomly initiated chains, are presented. Correlated moment equations are given for both random time gate and triggered time gate counting. There are explicit formulas for all correlated moments are given up to triple order, for all combinations of correlated fast neutrons and gamma rays. The nonlinear differential equations for probabilities for time dependent fission chain populations have a remarkably simple Monte Carlo realization. A Monte Carlo code was developed for this theory and is shown to statistically realize the solutions to the fission chain theory probability distributions. Combined with random initiation of chains and detection of external quanta, the Monte Carlo code generates time tagged data for neutron and gamma-ray counting and from these data the counting distributions.« less

Information Based Numerical Practice.

DTIC Science & Technology

1987-02-01

characterization by comparative computational studies of various benchmark problems. See e.g. [MacNeal, Harder (1985)], [Robinson, Blackham (1981)] any...FOR NONADAPTIVE METHODS 2.1. THE QUADRATURE FORMULA The simplest example studied in detail in the literature is the problem of the optimal quadrature...formulae and the functional analytic prerequisites for the study of optimal formulae, we refer to the large monography (808 p) of [Sobolev (1974)]. Let us

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.

Simple Formulas and Results for Buckling-Resistance and Stiffness Design of Compression-Loaded Laminated-Composite Cylinders

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Mikulas, Martin M., Jr.

2009-01-01

Simple formulas for the buckling stress of homogeneous, specially orthotropic, laminated-composite cylinders are presented. The formulas are obtained by using nondimensional parameters and equations that facilitate general validation, and are validated against the exact solution for a wide range of cylinder geometries and laminate constructions. Results are presented that establish the ranges of the nondimensional parameters and coefficients used. General results, given in terms of the nondimensional parameters, are presented that encompass a wide range of geometries and laminate constructions. These general results also illustrate a wide spectrum of behavioral trends. Design-oriented results are also presented that provide a simple, clear indication of laminate composition on critical stress, critical strain, and axial stiffness. An example is provided to demonstrate the application of these results to thin-walled column designs.

Theoretical and Numerical Investigations on Shallow Tunnelling in Unsaturated Soils

NASA Astrophysics Data System (ADS)

Soranzo, Enrico; Wu, Wei

2013-04-01

Excavation of shallow tunnels with the New Austrian Tunnelling Method (NATM) requires proper assessing of the tunnel face stability, to enable an open-face excavation, and the estimation of the correspondent surface settlements. Soils in a partially saturated condition exhibit a higher cohesion than in a fully saturated state, which can be taken into account when assessing the stability of the tunnel face. For the assessment of the face support pressure, different methods are used in engineering practice, varying from simple empirical and analytical formulations to advanced finite element analysis. Such procedures can be modified to account for the unsaturated state of soils. In this study a method is presented to incorporate the effect of partial saturation in the numerical analysis. The results are then compared with a simple analytical formulation derived from parametric studies. As to the numerical analysis, the variation of cohesion and of Young's modulus with saturation can be considered when the water table lies below the tunnel in a soil exhibiting a certain capillary rise, so that the tunnel is driven in a partially saturated layer. The linear elastic model with Mohr-Coulomb failure criterion can be extended to partially saturated states and calibrated with triaxial tests on unsaturated. In order to model both positive and negative pore water pressure (suction), Bishop's effective stress is incorporated into Mohr-Coulomb's failure criterion. The effective stress parameter in Bishop's formulation is related to the degree of saturation as suggested by Fredlund. If a linear suction distribution is assumed, the degree of saturation can be calculated from the Soil Water Characteristic Curve (SWCC). Expressions exist that relate the Young's modulus of unsaturated soils to the net mean stress and the matric suction. The results of the numerical computation can be compared to Vermeer & Ruse's closed-form formula that expresses the limit support pressure of the tunnel face. The expression is derived from parametric studies and predicts stability of the tunnel face when negative values are returned, suggesting that open-face tunnelling can be performed. The formula can be modified to account for the variation of cohesion along the tunnel face. The results obtained from both the numerical analysis and the analytical formulation are well in agreement and show that the stability of the tunnel face can greatly benefit from the enhanced cohesion of partially saturated soils.

Geometrical Simplification of the Dipole-Dipole Interaction Formula

ERIC Educational Resources Information Center

Kocbach, Ladislav; Lubbad, Suhail

2010-01-01

Many students meet dipole-dipole potential energy quite early on when they are taught electrostatics or magnetostatics and it is also a very popular formula, featured in encyclopedias. We show that by a simple rewriting of the formula it becomes apparent that, for example, by reorienting the two dipoles, their attraction can become exactly twice…

A More Intuitive Version of the Lorentz Velocity Addition Formula

ERIC Educational Resources Information Center

Devlin, John F.

2009-01-01

The Lorentz velocity addition formula for one-dimensional motion presents a number of problems for beginning students of special relativity. In this paper we suggest a simple rewrite of the formula that is easier for students to memorize and manipulate, and furthermore is more intuitive in understanding the correction necessary when adding…

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.

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.

Ray Tracing and Modal Methods for Modeling Radio Propagation in Tunnels With Rough Walls

PubMed Central

Zhou, Chenming

2017-01-01

At the ultrahigh frequencies common to portable radios, tunnels such as mine entries are often modeled by hollow dielectric waveguides. The roughness condition of the tunnel walls has an influence on radio propagation, and therefore should be taken into account when an accurate power prediction is needed. This paper investigates how wall roughness affects radio propagation in tunnels, and presents a unified ray tracing and modal method for modeling radio propagation in tunnels with rough walls. First, general analytical formulas for modeling the influence of the wall roughness are derived, based on the modal method and the ray tracing method, respectively. Second, the equivalence of the ray tracing and modal methods in the presence of wall roughnesses is mathematically proved, by showing that the ray tracing-based analytical formula can converge to the modal-based formula through the Poisson summation formula. The derivation and findings are verified by simulation results based on ray tracing and modal methods. PMID:28935995

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.

Analysis of microbial community and nitrogen transition with enriched nitrifying soil microbes for organic hydroponics.

PubMed

Saijai, Sakuntala; Ando, Akinori; Inukai, Ryuya; Shinohara, Makoto; Ogawa, Jun

2016-06-27

Nitrifying microbial consortia were enriched from bark compost in a water system by regulating the amounts of organic nitrogen compounds and by controlling the aeration conditions with addition of CaCO 3 for maintaining suitable pH. Repeated enrichment showed reproducible mineralization of organic nitrogen via the conversion of ammonium ions ([Formula: see text]) and nitrite ions ([Formula: see text]) into nitrate ions ([Formula: see text]). The change in microbial composition during the enrichment was investigated by PCR-DGGE analysis with a focus on prokaryote, ammonia-oxidizing bacteria, nitrite-oxidizing bacteria, and eukaryote cell types. The microbial transition had a simple profile and showed clear relation to nitrogen ions transition. Nitrosomonas and Nitrobacter were mainly detected during [Formula: see text] and [Formula: see text] oxidation, respectively. These results revealing representative microorganisms acting in each ammonification and nitrification stages will be valuable for the development of artificial simple microbial consortia for organic hydroponics that consisted of identified heterotrophs and autotrophic nitrifying bacteria.

Genetics Home Reference: glucose-galactose malabsorption

MedlinePlus

... down into glucose and another simple sugar called fructose, and lactose is broken down into glucose and ... infant formulas. However, they are able to digest fructose-based formulas that do not contain glucose or ...

The generation of simple compliance boundaries for mobile communication base station antennas using formulae for SAR estimation.

PubMed

Thors, B; Hansson, B; Törnevik, C

2009-07-07

In this paper, a procedure is proposed for generating simple and practical compliance boundaries for mobile communication base station antennas. The procedure is based on a set of formulae for estimating the specific absorption rate (SAR) in certain directions around a class of common base station antennas. The formulae, given for both whole-body and localized SAR, require as input the frequency, the transmitted power and knowledge of antenna-related parameters such as dimensions, directivity and half-power beamwidths. With knowledge of the SAR in three key directions it is demonstrated how simple and practical compliance boundaries can be generated outside of which the exposure levels do not exceed certain limit values. The conservativeness of the proposed procedure is discussed based on results from numerical radio frequency (RF) exposure simulations with human body phantoms from the recently developed Virtual Family.

A one-pot synthesis of bis(phenylimino)thiazolidines from ketene N,S-acetals and [Formula: see text],[Formula: see text]-diphenyloxalimidoyl dichloride.

PubMed

Yavari, Issa; Zahedi, Nooshin; Baoosi, Leila; Skoulika, Stavroula

2018-02-01

A synthesis of functionalized 4,5-bis(phenylimino)-1,3-thiazolidine-2-ylidenes via a simple reaction between ketene [Formula: see text]-acetals (derived from isothiocyanates and acetonitrile derivatives) with N,[Formula: see text]-diphenyloxalimidoyl dichloride in the presence of KOH in DMF is described. When CS[Formula: see text] was used as the heterocumulene component, the reaction led to the formation of 4,5-bis(phenylimino)-1,3-dithiolan-2-ylidene derivatives, in moderate to good yields.

[Influences of Confucianism, Taoism and Buddhism on Chinese Medical Formulas in Jin-Tang Dynasties].

PubMed

Wu, Xiao-xiang

2006-04-01

In the Jin-Tang Dynasties, when Confucianism, Taoism and Buddhism contended, conflicted and well blent, forming a state of mingled thoughts of the three sects. It exerted profound influences on Chinese Medical Formulas and promoted the academic fashion of compiling books about medical formulas characterized by collecting various formulas especially the simple and proved recipes. This plays a role in the formation of the formulas used in the Jin-Tang Dynasties, featuring simplicity, convenience, cheapness, and effectiveness, different from those of other periods.

The accuracy of peres’ formula and topography anatomy in predicting the depth of CVC for installation in the right subclavia

NASA Astrophysics Data System (ADS)

Kambey, B. I.; Perdana, A.; Pryambodho

2017-08-01

Central venous catheter (CVC) insertion is a routine procedure in either intensive care or in perioperative circumstances. A simple and accurate method or rule is needed to predict the optimum depth of the CVC. The aim of this study is to evaluate the position and depth of CVCs using Peres’ formula ([height/10]-2) and landmark measurements, as well as assessing the incidence of malpositions of CVC installation. This research was an analytic observational study. Fifty patients undergoing central venous catheter (CVC) installation with the right subclavian vein approach were divided into two groups: a Peres’ formula ([height/10]-2) and an anatomy topography measurement group. The results of the calculations were used to determine the boundary prediction of skin fixation. CVC depth was evaluated by measuring the distance between the distal end of the CVC and the carina, from chest radiographs. The measurement results were analyzed by a Bland and Altman plot. The patient’s characteristics were equal for both groups. In the Peres’ formula group we found that the mean of the distal CVC was 1.5 (0.82) cm under the carina (CI 95%: 1.2 to 1.9 cm), with the limit of agreement as 0.0 cm to 3.0 cm. The mean of the landmark group was 0.85 (0.73) cm (CI 95%: 0.5 to 1.1 cm) with the limit of agreement as -0.5 cm to 2.2 cm. The incidence of malposition was found to be similar in both groups. The results showed that both prediction methods are not accurate enough to predict the depth of CVC insertion in Indonesian people.

Shear thinning of the Lennard-Jones fluid by molecular dynamics

NASA Astrophysics Data System (ADS)

Heyes, David M.

1985-11-01

Extensive Molecular Dynamics, MD, calculations of the Lennard-Jones, LJ, rheological equation of state have been made. Non-equilibrium MD permits evaluation of shear thinning of the dense LJ liquid which adheres in behaviour quite closely with that of more complex “real molecules”. However, quantitative correspondence with simple analytic formulae for non-Newtonian behaviour used in the treatment of experimental data is hindered by poor prediction of certain key parameters. For example, at low shear rates, the equilibrium Newtonian viscosity and, at high shear rates, a limiting shear stress are often required. Both are difficult to obtain by simulation in the portion of the LJ phase diagram which exhibits significant shear thinning and using present techniques. Suggestions for improving the Eyring model for shear thinning are made.

Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem

NASA Astrophysics Data System (ADS)

Belinschi, Serban; Nowak, Maciej A.; Speicher, Roland; Tarnowski, Wojciech

2017-03-01

We extend the so-called ‘single ring theorem’ (Feinberg and Zee 1997 Nucl. Phys. B 504 579), also known as the Haagerup-Larsen theorem (Haagerup and Larsen 2000 J. Funct. Anal. 176 331). We do this by showing that in the limit when the size of the matrix goes to infinity a particular correlator between left and right eigenvectors of the relevant non-hermitian matrix X, being the spectral density weighted by the squared eigenvalue condition number, is given by a simple formula involving only the radial spectral cumulative distribution function of X. We show that this object allows the calculation of the conditional expectation of the squared eigenvalue condition number. We give examples and provide a cross-check of the analytic prediction by the large scale numerics.

Electromagnetic field generated in model of human head by simplified telephone transceiver

NASA Astrophysics Data System (ADS)

King, Ronold W. P.

1995-01-01

Possible adverse effects of electromagnetic fields on the human body and especially on the nervous system and the brain are of increasing concern, particularly with reference to cellular telephone transceivers held close to the head. An essential step in the study of this problem is the accurate determination of the complete electromagnetic field penetrating through the skull into the brain. Simple analytical formulas are derived from the theory of the horizontal electric dipole over a layered region. These give the components of the electric and magnetic fields on the air-head surface, in the skin-skull layer, and throughout the brain in terms of a planar model with the dimensions and average electrical properties of the human head. The specific absorption rate (SAR) is also determined.

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.

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.

Zero-crossing statistics for non-Markovian time series.

PubMed

Nyberg, Markus; Lizana, Ludvig; Ambjörnsson, Tobias

2018-03-01

In applications spanning from image analysis and speech recognition to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging, and therefore few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero crossings in a fixed time interval of a zero-mean Gaussian stationary process. In this study we use the so-called independent interval approximation to go beyond Rice's result and derive analytic expressions for all higher-order zero-crossing cumulants and moments. Our results agree well with simulations for the non-Markovian autoregressive model.

Pfirsch–Schlüter neoclassical heavy impurity transport in a rotating plasma

DOE PAGES

Belli, Emily A.; Candy, Jefferey M.; Angioni, C.

2014-11-07

In this paper, we extend previous analytic theories for the neoclassical transport of a trace heavy impurity in a rotating plasma in the Pfirsch-Schl¨uter regime. The complete diffusive and convective components of the ambipolar particle flux are derived. The solution is valid for arbitrary impurity charge and impurity Mach number and for general geometry. Inclusion of finite main ion temperature gradient effects is shown in the small ion Mach number limit. A simple interpolation formula is derived for the case of high impurity charge and circular geometry. While an enhancement of the diffusion coefficient is found for order one impuritymore » Mach number, a reduction due to the rotation-driven poloidal asymmetry in the density occurs for very large Mach number.« less

Vectorlike fermions and Higgs effective field theory revisited

DOE PAGES

Chen, Chien-Yi; Dawson, S.; Furlan, Elisabetta

2017-07-10

Heavy vectorlike quarks (VLQs) appear in many models of beyond the Standard Model physics. Direct experimental searches require these new quarks to be heavy, ≳ 800 – 1000 GeV . Here, we perform a global fit of the parameters of simple VLQ models in minimal representations of S U ( 2 ) L to precision data and Higgs rates. One interesting connection between anomalous Z bmore » $$\\bar{b}$$ interactions and Higgs physics in VLQ models is discussed. Finally, we present our analysis in an effective field theory (EFT) framework and show that the parameters of VLQ models are already highly constrained. Exact and approximate analytical formulas for the S and T parameters in the VLQ models we consider are available in the Supplemental Material as Mathematica files.« less

Ultrathin metasurface with high absorptance for waterborne sound

NASA Astrophysics Data System (ADS)

Mei, Jun; Zhang, Xiujuan; Wu, Ying

2018-03-01

We present a design for an acoustic metasurface which can efficiently absorb low-frequency sound energy in water. The metasurface has a simple structure and consists of only two common materials: i.e., water and silicone rubber. The optimized material and geometrical parameters of the designed metasurface are determined by an analytic formula in conjunction with an iterative process based on the retrieval method. Although the metasurface is as thin as 0.15 of the wavelength, it can absorb 99.7% of the normally incident sound wave energy. Furthermore, the metasurface maintains a substantially high absorptance over a relatively broad bandwidth, and also works well for oblique incidence with an incident angle of up to 50°. Potential applications in the field of underwater sound isolation are expected.

Zero-crossing statistics for non-Markovian time series

NASA Astrophysics Data System (ADS)

Nyberg, Markus; Lizana, Ludvig; Ambjörnsson, Tobias

2018-03-01

In applications spanning from image analysis and speech recognition to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging, and therefore few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero crossings in a fixed time interval of a zero-mean Gaussian stationary process. In this study we use the so-called independent interval approximation to go beyond Rice's result and derive analytic expressions for all higher-order zero-crossing cumulants and moments. Our results agree well with simulations for the non-Markovian autoregressive model.

FAST TRACK COMMUNICATION: Exact and simple results for the XYZ and strongly interacting fermion chains

NASA Astrophysics Data System (ADS)

Fendley, Paul; Hagendorf, Christian

2010-10-01

We conjecture exact and simple formulas for some physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to the chiral Potts models. We conjecture that analogous results occur in the XYZ chain when the couplings obey JxJy + JyJz + JxJz = 0, and in a related fermion chain with strong interactions and supersymmetry. We find exact formulas for the magnetization and gap in the former, and the staggered density in the latter, by exploiting the fact that certain quantities are independent of finite-size effects.

Accurate formulas for interaction force and energy in frequency modulation force spectroscopy

NASA Astrophysics Data System (ADS)

Sader, John E.; Jarvis, Suzanne P.

2004-03-01

Frequency modulation atomic force microscopy utilizes the change in resonant frequency of a cantilever to detect variations in the interaction force between cantilever tip and sample. While a simple relation exists enabling the frequency shift to be determined for a given force law, the required complementary inverse relation does not exist for arbitrary oscillation amplitudes of the cantilever. In this letter we address this problem and present simple yet accurate formulas that enable the interaction force and energy to be determined directly from the measured frequency shift. These formulas are valid for any oscillation amplitude and interaction force, and are therefore of widespread applicability in frequency modulation dynamic force spectroscopy.

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

A facile and regioselective one-pot synthesis of novel pyrazolo[1[Formula: see text],5[Formula: see text]:1,2]pyrrolo[3,4-b]quinoline-2,3-dicarboxylate hybrids via intramolecular Wittig reaction.

PubMed

Largani, Tahere Hosseyni; Imanzadeh, Gholamhasan; Pesyan, Nader Noroozi; Şahin, Ertan; Shamkhali, Amir Nasser; Notash, Behrouz

2018-02-01

The regioselective syntheses of novel pyrazolo[1[Formula: see text],5[Formula: see text]:1,2]pyrrolo[3,4-b]quinoline-2,3-dicarboxylates (6a-l) from pyrrolo([3,4-b]quinolin-2(3H)-yl)benzamides through an intramolecular Wittig reaction are described. This protocol takes advantages of mild conditions, simple workup and high yield which make this method attractive for the synthesis of these hybrid of pyrazolo[1[Formula: see text],5[Formula: see text]:1,2]pyrrolo[3,4-b]quinolines.

PEDIATRICIANS’ REPRESENTATIONS ON DAIRY ALTERNATIVES WHEN WEANING IS UNAVOIDABLE

PubMed Central

Sarubbi, Vicente; Muylaert, Camila Junqueira; Bastos, Isabella Teixeira; Gallo, Paulo Rogério; Leone, Claudio

2017-01-01

ABSTRACT Objective: To analyze pediatricians’ representations on the nutritional alternatives that are adopted when weaning becomes inevitable. Methods: This is a mixed cross-sectional analytical study with probabilistic sampling. Fifty-seven randomly selected pediatricians were interviewed with the use of a semi-structured script for thematic analysis. The technique of free evocations was used, and the terms were processed using software EVOC 2005. The thematic categories were established on software NVivo10, and their co-occurrence matrix was exported and analyzed in terms of their simple similarity hierarchy on software CHIC. Results: In the pediatricians’ representations, whole milk was cited as a foodstuff with high allergenic risk (35.1%) and nutritionally inappropriate, and they did not recommend its use if weaning occurred before 1 year of age. The infant formula, referred by 98.3% of the pediatricians as the best alternative at the moment of weaning, was cited by 38.1% of them owing to its nutritional adequacy. The points quoted as unfavorable to the use of the formula were the price, the possibility of causing allergy and the risk of the inadequate use of such a highly industrialized product. Conclusions: The pediatricians’ representations show that they are sensitive to the importance of breast-feeding and at the same time, to the sociocultural difficulties inherent in the practice. Generally speaking, the interviewed pediatricians recommend the use of milk formulas, and not of whole cow’s milk, if weaning occurs before the end of the first year of life. PMID:28977316

Quantifying wall turbulence via a symmetry approach: A Lie group theory

NASA Astrophysics Data System (ADS)

She, Zhen-Su; Chen, Xi; Hussain, Fazle

2017-11-01

We present a symmetry-based approach which yields analytic expressions for the mean velocity and kinetic energy profiles from a Lie-group analysis. After verifying the dilation-group invariance of the Reynolds averaged Navier-Stokes equation in the presence of a wall, we select a stress and energy length function as similarity variables which are assumed to have a simple dilation-invariant form. Three kinds of (local) invariant forms of the length functions are postulated, a combination of which yields a multi-layer formula giving its distribution in the entire flow region normal to the wall. The mean velocity profile is then predicted using the mean momentum equation, which yields, in particular, analytic expressions for the (universal) wall function and separate wake functions for pipe and channel - which are validated by data from direct numerical simulations (DNS). Future applications to a variety of wall flows such as flows around flat plate or airfoil, in a Rayleigh-Benard cell or Taylor-Couette system, etc., are discussed, for which the dilation group invariance is valid in the wall-normal direction.

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.

On the index of noncommutative elliptic operators over C*-algebras

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

Savin, Anton Yu; Sternin, Boris Yu

2010-05-11

We consider noncommutative elliptic operators over C*-algebras, associated with a discrete group of isometries of a manifold. The main result of the paper is a formula expressing the Chern characters of the index (Connes invariants) in topological terms. As a corollary to this formula a simple proof of higher index formulae for noncommutative elliptic operators is obtained. Bibliography: 36 titles.

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.

Simple Analytic Collisional Rates for non-LTE Vibrational Populations in Astrophysical Environments: the Cases of Circumstellar SiO Masers and Shocked H2

NASA Astrophysics Data System (ADS)

Bieniek, Ronald

2008-05-01

Rates for collisionally induced transitions between molecular vibrational levels are important in modeling a variety of non-LTE processes in astrophysical environments. Two examples are SiO masering in circumstellar envelopes in certain late-type stars [1] and the vibrational populations of molecular hydrogen in shocked interstellar medium [cf 2]. A simple exponential-potential model of molecular collisions leads to a two-parameter analytic expression for state-to-state and thermally averaged rates for collisionally induced vibrational-translational (VT) transitions in diatomic molecules [3,4]. The thermally averaged rates predicted by this formula have been shown to be in excellent numerical agreement with absolute experimental and quantum mechanical rates over large temperature ranges and initial vibrational excitation levels in a variety of species, e.g., OH, O2, N2 [3] and even for the rate of H2(v=1)+H2, which changes by five orders of magnitude in the temperature range 50-2000 K [4]. Analogous analytic rates will be reported for vibrational transitions in SiO due to collisions with H2 and compared to the numerical fit of quantum-mechanical rates calculated by Bieniek and Green [5]. [1] Palov, A.P., Gray, M.D., Field, D., & Balint-Kurti, G.G. 2006, ApJ, 639, 204. [2] Flower, D. 2007, Molecular Collisions in the Interstellar Medium (Cambridge: Cambridge Univ. Press) [3] Bieniek, R.J. & Lipson, S.J. 1996, Chem. Phys. Lett. 263, 276. [4] Bieniek, R.J. 2006, Proc. NASA LAW (Lab. Astrophys. Workshop) 2006, 299; http://www.physics.unlv.edu/labastro/nasalaw2006proceedings.pdf. [5] Bieniek, R.J., & Green, S. 1983, ApJ, 265, L29 and 1983, ApJ, 270, L101.

Charged reflecting stars supporting charged massive scalar field configurations

NASA Astrophysics Data System (ADS)

Hod, Shahar

2018-03-01

The recently published no-hair theorems of Hod, Bhattacharjee, and Sarkar have revealed the intriguing fact that horizonless compact reflecting stars cannot support spatially regular configurations made of scalar, vector and tensor fields. In the present paper we explicitly prove that the interesting no-hair behavior observed in these studies is not a generic feature of compact reflecting stars. In particular, we shall prove that charged reflecting stars can support charged massive scalar field configurations in their exterior spacetime regions. To this end, we solve analytically the characteristic Klein-Gordon wave equation for a linearized charged scalar field of mass μ , charge coupling constant q, and spherical harmonic index l in the background of a spherically symmetric compact reflecting star of mass M, electric charge Q, and radius R_{ {s}}≫ M,Q. Interestingly, it is proved that the discrete set {R_{ {s}}(M,Q,μ ,q,l;n)}^{n=∞}_{n=1} of star radii that can support the charged massive scalar field configurations is determined by the characteristic zeroes of the confluent hypergeometric function. Following this simple observation, we derive a remarkably compact analytical formula for the discrete spectrum of star radii in the intermediate regime M≪ R_{ {s}}≪ 1/μ . The analytically derived resonance spectrum is confirmed by direct numerical computations.

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.

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.

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.

Dimensional analysis using toric ideals: primitive invariants.

PubMed

Atherton, Mark A; Bates, Ronald A; Wynn, Henry P

2014-01-01

Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units [Formula: see text] etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer [Formula: see text] matrix from the initial integer [Formula: see text] matrix holding the exponents for the derived quantities. The [Formula: see text] matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups) is obtained directly from the toric ideal defined by [Formula: see text]. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of [Formula: see text], is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.

Using mean duration and variation of procedure times to plan a list of surgical operations to fit into the scheduled list time.

PubMed

Pandit, Jaideep J; Tavare, Aniket

2011-07-01

It is important that a surgical list is planned to utilise as much of the scheduled time as possible while not over-running, because this can lead to cancellation of operations. We wished to assess whether, theoretically, the known duration of individual operations could be used quantitatively to predict the likely duration of the operating list. In a university hospital setting, we first assessed the extent to which the current ad-hoc method of operating list planning was able to match the scheduled operating list times for 153 consecutive historical lists. Using receiver operating curve analysis, we assessed the ability of an alternative method to predict operating list duration for the same operating lists. This method uses a simple formula: the sum of individual operation times and a pooled standard deviation of these times. We used the operating list duration estimated from this formula to generate a probability that the operating list would finish within its scheduled time. Finally, we applied the simple formula prospectively to 150 operating lists, 'shadowing' the current ad-hoc method, to confirm the predictive ability of the formula. The ad-hoc method was very poor at planning: 50% of historical operating lists were under-booked and 37% over-booked. In contrast, the simple formula predicted the correct outcome (under-run or over-run) for 76% of these operating lists. The calculated probability that a planned series of operations will over-run or under-run was found useful in developing an algorithm to adjust the planned cases optimally. In the prospective series, 65% of operating lists were over-booked and 10% were under-booked. The formula predicted the correct outcome for 84% of operating lists. A simple quantitative method of estimating operating list duration for a series of operations leads to an algorithm (readily created on an Excel spreadsheet, http://links.lww.com/EJA/A19) that can potentially improve operating list planning.

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.

Pocket formula for nuclear deformations of actinides

NASA Astrophysics Data System (ADS)

Manjunatha, H. C.; Sridhar, K. N.

2018-06-01

We have formulated a pocket formula for quadrupole (β2), octupole (β3), hexadecapole (β4) and hexacontatetrapole (β6) deformation of the nuclear ground state of all isotopes of actinide nuclei (89 < Z < 103). This formula is first of its kind and produces a nuclear deformation of all isotopes actinide nuclei 89 < Z < 103 with simple inputs of Z and A. Hence, this formula is useful in the fields of nuclear physics to study the structure and interaction of nuclei.

Quantum Theories of Self-Localization

NASA Astrophysics Data System (ADS)

Bernstein, Lisa Joan

In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.

Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions

DOE PAGES

Kim, K. S.; Nakae, L. F.; Prasad, M. K.; ...

2015-11-01

Here, we solve a simple theoretical model of time evolving fission chains due to Feynman that generalizes and asymptotically approaches the point model theory. The point model theory has been used to analyze thermal neutron counting data. This extension of the theory underlies fast counting data for both neutrons and gamma rays from metal systems. Fast neutron and gamma-ray counting is now possible using liquid scintillator arrays with nanosecond time resolution. For individual fission chains, the differential equations describing three correlated probability distributions are solved: the time-dependent internal neutron population, accumulation of fissions in time, and accumulation of leaked neutronsmore » in time. Explicit analytic formulas are given for correlated moments of the time evolving chain populations. The equations for random time gate fast neutron and gamma-ray counting distributions, due to randomly initiated chains, are presented. Correlated moment equations are given for both random time gate and triggered time gate counting. There are explicit formulas for all correlated moments are given up to triple order, for all combinations of correlated fast neutrons and gamma rays. The nonlinear differential equations for probabilities for time dependent fission chain populations have a remarkably simple Monte Carlo realization. A Monte Carlo code was developed for this theory and is shown to statistically realize the solutions to the fission chain theory probability distributions. Combined with random initiation of chains and detection of external quanta, the Monte Carlo code generates time tagged data for neutron and gamma-ray counting and from these data the counting distributions.« less

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.

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.

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.

Implementing successful strategic plans: a simple formula.

PubMed

Blondeau, Whitney; Blondeau, Benoit

2015-01-01

Strategic planning is a process. One way to think of strategic planning is to envision its development and design as a framework that will help your hospital navigate through internal and external changing environments over time. Although the process of strategic planning can feel daunting, following a simple formula involving five steps using the mnemonic B.E.G.I.N. (Begin, Evaluate, Goals & Objectives, Integration, and Next steps) will help the planning process feel more manageable, and lead you to greater success.

s -wave scattering length of a Gaussian potential

NASA Astrophysics Data System (ADS)

Jeszenszki, Peter; Cherny, Alexander Yu.; Brand, Joachim

2018-04-01

We provide accurate expressions for the s -wave scattering length for a Gaussian potential well in one, two, and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of ultracold-atomic gases, where the s -wave scattering length is a physically relevant parameter. We first describe a numerical procedure to compute the value of the s -wave scattering length from the parameters of the Gaussian, but find that its accuracy is limited in the vicinity of singularities that result from the formation of new bound states. We then derive simple analytical expressions that capture the correct asymptotic behavior of the s -wave scattering length near the bound states. Expressions that are increasingly accurate in wide parameter regimes are found by a hierarchy of approximations that capture an increasing number of bound states. The small number of numerical coefficients that enter these expressions is determined from accurate numerical calculations. The approximate formulas combine the advantages of the numerical and approximate expressions, yielding an accurate and simple description from the weakly to the strongly interacting limit.

Accurate mass measurement by matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry. I. Measurement of positive radical ions using porphyrin standard reference materials.

PubMed

Griffiths, Nia W; Wyatt, Mark F; Kean, Suzanna D; Graham, Andrew E; Stein, Bridget K; Brenton, A Gareth

2010-06-15

A method for the accurate mass measurement of positive radical ions by matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI-TOFMS) is described. Initial use of a conjugated oligomeric calibration material was rejected in favour of a series of meso-tetraalkyl/tetraalkylaryl-functionalised porphyrins, from which the two calibrants required for a particular accurate mass measurement were chosen. While all measurements of monoisotopic species were within +/-5 ppm, and the method was rigorously validated using chemometrics, mean values of five measurements were used for extra confidence in the generation of potential elemental formulae. Potential difficulties encountered when measuring compounds containing multi-isotopic elements are discussed, where the monoisotopic peak is no longer the lowest mass peak, and a simple mass-correction solution can be applied. The method requires no significant expertise to implement, but care and attention is required to obtain valid measurements. The method is operationally simple and will prove useful to the analytical chemistry community. Copyright (c) 2010 John Wiley & Sons, Ltd.

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.

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.

Personalized dynamic prediction of death according to tumour progression and high-dimensional genetic factors: Meta-analysis with a joint model.

PubMed

Emura, Takeshi; Nakatochi, Masahiro; Matsui, Shigeyuki; Michimae, Hirofumi; Rondeau, Virginie

2017-01-01

Developing a personalized risk prediction model of death is fundamental for improving patient care and touches on the realm of personalized medicine. The increasing availability of genomic information and large-scale meta-analytic data sets for clinicians has motivated the extension of traditional survival prediction based on the Cox proportional hazards model. The aim of our paper is to develop a personalized risk prediction formula for death according to genetic factors and dynamic tumour progression status based on meta-analytic data. To this end, we extend the existing joint frailty-copula model to a model allowing for high-dimensional genetic factors. In addition, we propose a dynamic prediction formula to predict death given tumour progression events possibly occurring after treatment or surgery. For clinical use, we implement the computation software of the prediction formula in the joint.Cox R package. We also develop a tool to validate the performance of the prediction formula by assessing the prediction error. We illustrate the method with the meta-analysis of individual patient data on ovarian cancer patients.

Using Spreadsheets to Produce Acid-Base Titration Curves.

ERIC Educational Resources Information Center

Cawley, Martin James; Parkinson, John

1995-01-01

Describes two spreadsheets for producing acid-base titration curves, one uses relatively simple cell formulae that can be written into the spreadsheet by inexperienced students and the second uses more complex formulae that are best written by the teacher. (JRH)

Visible and UV photo-detection in ZnO nanostructured thin films via simple tuning of solution method.

PubMed

Khokhra, Richa; Bharti, Bandna; Lee, Heung-No; Kumar, Rajesh

2017-11-08

This study demonstrates significant visible light photo-detection capability of pristine ZnO nanostructure thin films possessing substantially high percentage of oxygen vacancies [Formula: see text] and zinc interstitials [Formula: see text], introduced by simple tuning of economical solution method. The demonstrated visible light photo-detection capability, in addition to the inherent UV light detection ability of ZnO, shows great dependency of [Formula: see text] and [Formula: see text] with the nanostructure morphology. The dependency was evaluated by analyzing the presence/percentage of [Formula: see text] and [Formula: see text] using photoluminescence (PL) and X-ray photoelectron spectroscopy (XPS) measurements. Morphologies of ZnO viz. nanoparticles (NPs), nanosheets (NSs) and nanoflowers (NFs), as a result of tuning of synthesis method contended different concentrations of defects, demonstrated different photo-detection capabilities in the form of a thin film photodetector. The photo-detection capability was investigated under different light excitations (UV; 380~420 nm, white ; λ > 420 nm and green; 490~570 nm). The as fabricated NSs photodetector possessing comparatively intermediate percentage of [Formula: see text] ~ 47.7% and [Formula: see text] ~ 13.8% exhibited superior performance than that of NPs and NFs photodetectors, and ever reported photodetectors fabricated by using pristine ZnO nanostructures in thin film architecture. The adopted low cost and simplest approach makes the pristine ZnO-NSs applicable for wide-wavelength applications in optoelectronic devices.

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.

Kidney function estimating equations in patients with chronic kidney disease.

PubMed

Hojs, R; Bevc, S; Ekart, R; Gorenjak, M; Puklavec, L

2011-04-01

The current guidelines emphasise the need to assess kidney function using predictive equations rather than just serum creatinine. The present study compares serum cystatin C-based equations and serum creatinine-based equations in patients with chronic kidney disease (CKD). Seven hundred and sixty-four adult patients with CKD were enrolled. In each patient serum creatinine and serum cystatin C were determined. Their glomerular filtration rate (GFR) was estimated using three serum creatinine-based equations [Cockcroft-Gault (C&G), modification of diet in renal disease (MDRD) and the Chronic Kidney Disease Epidemiology Collaboration equation (CKD-EPI)] and two serum cystatin C-based equations [our own cystatin C formula (GFR=90.63 × cystatin C(-1.192) ) and simple cystatin C formula (GFR=100/cystatin C)]. The GFR was measured using (51) CrEDTA clearance. Statistically significant correlation between (51) CrEDTA clearance with serum creatinine, serum cystatin C and all observed formulas was found. The receiver operating characteristic curve analysis (cut-off for GFR 60 ml/min/1.73m(2)) showed that serum cystatin C and both cystatin C formulas had a higher diagnostic accuracy than C&G formula. Bland and Altman analysis for the same cut-off value showed that all formulas except simple cystatin C formula underestimated measured GFR. The accuracy within 30% of estimated (51) CrEDTA clearance values differs according to stages of CKD. Analysis of ability to correctly predict patient's GFR below or above 60 ml/min/1.73m(2) showed statistically significant higher ability for both cystatin C formulas compared to MDRD formula. Our results indicate that serum cystatin C-based equations are reliable markers of GFR comparable with creatinine-based formulas. © 2011 Blackwell Publishing Ltd.

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.

Coherent beam combination of fiber lasers with a strongly confined waveguide: numerical model.

PubMed

Tao, Rumao; Si, Lei; Ma, Yanxing; Zhou, Pu; Liu, Zejin

2012-08-20

Self-imaging properties of fiber lasers in a strongly confined waveguide (SCW) and their application in coherent beam combination (CBC) are studied theoretically. Analytical formulas are derived for the positions, amplitudes, and phases of the N images at the end of an SCW, which is important for quantitative analysis of waveguide CBC. The formulas are verified with experimental results and numerical simulation of a finite difference beam propagation method (BPM). The error of our analytical formulas is less than 6%, which can be reduced to less than 1.5% with Goos-Hahnchen penetration depth considered. Based on the theoretical model and BPM, we studied the combination of two laser beams based on an SCW. The effects of the waveguide refractive index and Gaussian beam waist are studied. We also simulated the CBC of nine and 16 fiber lasers, and a single beam without side lobes was achieved.

A simple formula for predicting claw volume of cattle.

PubMed

Scott, T D; Naylor, J M; Greenough, P R

1999-11-01

The object of this study was to develop a simple method for accurately calculating the volume of bovine claws under field conditions. The digits of 30 slaughterhouse beef cattle were examined and the following four linear measurements taken from each pair of claws: (1) the length of the dorsal surface of the claw (Toe); (2) the length of the coronary band (CorBand); (3) the length of the bearing surface (Base); and (4) the height of the claw at the abaxial groove (AbaxGr). Measurements of claw volume using a simple hydrometer were highly repeatable (r(2)= 0.999) and could be calculated from linear measurements using the formula:Claw Volume (cm(3)) = (17.192 x Base) + (7.467 x AbaxGr) + 45.270 x (CorBand) - 798.5This formula was found to be accurate (r(2)= 0.88) when compared to volume data derived from a hydrometer displacement procedure. The front claws occupied 54% of the total volume compared to 46% for the hind claws. Copyright 1999 Harcourt Publishers Ltd.

Landau-Zener transitions and Dykhne formula in a simple continuum model

NASA Astrophysics Data System (ADS)

Dunham, Yujin; Garmon, Savannah

The Landau-Zener model describing the interaction between two linearly driven discrete levels is useful in describing many simple dynamical systems; however, no system is completely isolated from the surrounding environment. Here we examine a generalizations of the original Landau-Zener model to study simple environmental influences. We consider a model in which one of the discrete levels is replaced with a energy continuum, in which we find that the survival probability for the initially occupied diabatic level is unaffected by the presence of the continuum. This result can be predicted by assuming that each step in the evolution for the diabatic state evolves independently according to the Landau-Zener formula, even in the continuum limit. We also show that, at least for the simplest model, this result can also be predicted with the natural generalization of the Dykhne formula for open systems. We also observe dissipation as the non-escape probability from the discrete levels is no longer equal to one.

Graphical representation of QT rate correction formulae: an aid facilitating the use of a given formula and providing a visual comparison of the impact of different formulae.

PubMed

Rowlands, Derek J

2012-01-01

The QT interval on the electrocardiogram is an increasingly important measurement, especially in relation to drug action and interaction. The QT interval varies inversely as the heart rate and numerous rate correction formulae have been proposed. It is difficult to compare the effect of applying different formulae at different heart rates and for different measured QT intervals. A simple graphical display of the results from different formulae is proposed. This display is dependent on the concept of the absolute correction factor. This graphical presentation is useful (a) in comparing the effect of the application of different formulae and (b) in directly reading the correction produced by any individual formula. Copyright © 2012 Elsevier Inc. All rights reserved.

New formulae between Jacobi polynomials and some fractional Jacobi functions generalizing some connection formulae

NASA Astrophysics Data System (ADS)

Abd-Elhameed, W. M.

2017-07-01

In this paper, a new formula relating Jacobi polynomials of arbitrary parameters with the squares of certain fractional Jacobi functions is derived. The derived formula is expressed in terms of a certain terminating hypergeometric function of the type _4F3(1) . With the aid of some standard reduction formulae such as Pfaff-Saalschütz's and Watson's identities, the derived formula can be reduced in simple forms which are free of any hypergeometric functions for certain choices of the involved parameters of the Jacobi polynomials and the Jacobi functions. Some other simplified formulae are obtained via employing some computer algebra algorithms such as the algorithms of Zeilberger, Petkovsek and van Hoeij. Some connection formulae between some Jacobi polynomials are deduced. From these connection formulae, some other linearization formulae of Chebyshev polynomials are obtained. As an application to some of the introduced formulae, a numerical algorithm for solving nonlinear Riccati differential equation is presented and implemented by applying a suitable spectral method.

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

On one-parametric formula relating the frequencies of twin-peak quasi-periodic oscillations

NASA Astrophysics Data System (ADS)

Török, Gabriel; Goluchová, Kateřina; Šrámková, Eva; Horák, Jiří; Bakala, Pavel; Urbanec, Martin

2018-01-01

Twin-peak quasi-periodic oscillations (QPOs) are observed in several low-mass X-ray binary systems containing neutron stars. Timing the analysis of X-ray fluxes of more than dozen of such systems reveals remarkable correlations between the frequencies of two characteristic peaks present in the power density spectra. The individual correlations clearly differ, but they roughly follow a common individual pattern. High values of measured QPO frequencies and strong modulation of the X-ray flux both suggest that the observed correlations are connected to orbital motion in the innermost part of an accretion disc. Several attempts to model these correlations with simple geodesic orbital models or phenomenological relations have failed in the past. We find and explore a surprisingly simple analytic relation that reproduces individual correlations for a group of several sources through a single parameter. When an additional free parameter is considered within our relation, it well reproduces the data of a large group of 14 sources. The very existence and form of this simple relation support the hypothesis of the orbital origin of QPOs and provide the key for further development of QPO models. We discuss a possible physical interpretation of our relation's parameters and their links to concrete QPO models.

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.

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.

EXTRACTING PLANET MASS AND ECCENTRICITY FROM TTV DATA

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

Lithwick, Yoram; Xie Jiwei; Wu Yanqin

2012-12-20

Most planet pairs in the Kepler data that have measured transit time variations (TTVs) are near first-order mean-motion resonances. We derive analytical formulae for their TTV signals. We separate planet eccentricity into free and forced parts, where the forced part is purely due to the planets' proximity to resonance. This separation yields simple analytical formulae. The phase of the TTV depends sensitively on the presence of free eccentricity: if the free eccentricity vanishes, the TTV will be in phase with the longitude of conjunctions. This effect is easily detectable in current TTV data. The amplitude of the TTV depends onmore » planet mass and free eccentricity, and it determines planet mass uniquely only when the free eccentricity is sufficiently small. We analyze the TTV signals of six short-period Kepler pairs. We find that three of these pairs (Kepler 18, 24, 25) have a TTV phase consistent with zero. The other three (Kepler 23, 28, 32) have small TTV phases, but ones that are distinctly non-zero. We deduce that the free eccentricities of the planets are small, {approx}< 0.01, but not always vanishing. Furthermore, as a consequence of this, we deduce that the true masses of the planets are fairly accurately determined by the TTV amplitudes, within a factor of {approx}< 2. The smallness of the free eccentricities suggests that the planets have experienced substantial dissipation. This is consistent with the hypothesis that the observed pile-up of Kepler pairs near mean-motion resonances is caused by resonant repulsion. But the fact that some of the planets have non-vanishing free eccentricity suggests that after resonant repulsion occurred there was a subsequent phase in the planets' evolution when their eccentricities were modestly excited, perhaps by interplanetary interactions.« less

On the solution of the complex eikonal equation in acoustic VTI media: A perturbation plus optimization scheme

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Jianguo; Greenhalgh, Stewart

2018-04-01

We present methods for obtaining numerical and analytic solutions of the complex eikonal equation in inhomogeneous acoustic VTI media (transversely isotropic media with a vertical symmetry axis). The key and novel point of the method for obtaining numerical solutions is to transform the problem of solving the highly nonlinear acoustic VTI eikonal equation into one of solving the relatively simple eikonal equation for the background (isotropic) medium and a system of linear partial differential equations. Specifically, to obtain the real and imaginary parts of the complex traveltime in inhomogeneous acoustic VTI media, we generalize a perturbation theory, which was developed earlier for solving the conventional real eikonal equation in inhomogeneous anisotropic media, to the complex eikonal equation in such media. After the perturbation analysis, we obtain two types of equations. One is the complex eikonal equation for the background medium and the other is a system of linearized partial differential equations for the coefficients of the corresponding complex traveltime formulas. To solve the complex eikonal equation for the background medium, we employ an optimization scheme that we developed for solving the complex eikonal equation in isotropic media. Then, to solve the system of linearized partial differential equations for the coefficients of the complex traveltime formulas, we use the finite difference method based on the fast marching strategy. Furthermore, by applying the complex source point method and the paraxial approximation, we develop the analytic solutions of the complex eikonal equation in acoustic VTI media, both for the isotropic and elliptical anisotropic background medium. Our numerical results demonstrate the effectiveness of our derivations and illustrate the influence of the beam widths and the anisotropic parameters on the complex traveltimes.

BRIEF REPORT: A simple interpolation formula for the spectra of power-law and log potentials

NASA Astrophysics Data System (ADS)

Hall, Richard L.

2000-06-01

Non-relativistic potential models are considered of the pure power V(r) = sgn(q) r q and logarithmic V(r) = ln (r) types. It is shown that, from the spectral viewpoint, these potentials are actually in a single family. The log spectra can be obtained from the power spectra by the limit q→0 taken in a smooth representation Pnl(q) for the eigenvalues Enl(q). A simple approximation formula is developed which yields the first 30 eigenvalues with an error less than 0.04%.

A Simple Formula to Calculate Shallow-Water Transmission Loss by Means of a Least-Squares Surface Fit Technique.

DTIC Science & Technology

1980-09-01

HASTRUP , T REAL UNCLASSIFIED SACLAATCEN- SM-139 N SACLANTCEN Memorandum SM -139 -LEFW SACLANT ASW RESEARCH CENTRE ~ MEMORANDUM A SIMPLE FORMULA TO...CALCULATE SHALLOW-WATER TRANSMISSION LOSS BY MEANS OF A LEAST- SQUARES SURFACE FIT TECHNIQUE 7-sallby OLE F. HASTRUP and TUNCAY AKAL I SEPTEMBER 1980 NORTH...JRANSi4ISSION LOSS/ BY MEANS OF A LEAST-SQUARES SURFACE fIT TECHNIQUE, C T ~e F./ Hastrup .0TnaAa ()1 Sep 8 This memorandum has been prepared within the

Analytical model for the radio-frequency sheath

NASA Astrophysics Data System (ADS)

Czarnetzki, Uwe

2013-12-01

A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.

Analytical model for the radio-frequency sheath.

PubMed

Czarnetzki, Uwe

2013-12-01

A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.

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.

An estimating formula for ion-atom association rates in gases

NASA Technical Reports Server (NTRS)

Chatterjee, B. K.; Johnsen, R.

1990-01-01

A simple estimating formula is derived for rate coefficients of three-body ion atom association in gases and compare its predictions to experimental data on ion association and three-body radiative charge transfer reactions of singly- and doubly-charged rare-gas ions. The formula appears to reproduce most experimental data quite well. It may be useful for estimating the rates of reactions that have not been studied in the laboratory.

An algorithm for the Baker-Campbell-Hausdorff formula

NASA Astrophysics Data System (ADS)

Matone, Marco

2015-05-01

A simple algorithm, which exploits the associativity of the BCH formula, and that can be generalized by iteration, extends the remarkable simplification of the BakerCampbell-Hausdorff (BCH) formula, recently derived by Van-Brunt and Visser. We show that if [ X, Y] = uX + vY + cI, [ Y, Z] = wY + zZ + dI, and, consistently with the Jacobi identity, [ X, Z] = mX + nY + pZ + eI, then

Calculating Strain Relief in Electronic-Component Leads

NASA Technical Reports Server (NTRS)

Snytsheuvel, H.

1985-01-01

Stress/strain formulas applicable to design of electronic-component leads compiled in report. Such things as factors of safety and whether or not lead is likely to fall in service determined in advance. Set of formulas is simple enough to be solved on programable hand-held calculator.

Real-Time Prediction of Temperature Elevation During Robotic Bone Drilling Using the Torque Signal.

PubMed

Feldmann, Arne; Gavaghan, Kate; Stebinger, Manuel; Williamson, Tom; Weber, Stefan; Zysset, Philippe

2017-09-01

Bone drilling is a surgical procedure commonly required in many surgical fields, particularly orthopedics, dentistry and head and neck surgeries. While the long-term effects of thermal bone necrosis are unknown, the thermal damage to nerves in spinal or otolaryngological surgeries might lead to partial paralysis. Previous models to predict the temperature elevation have been suggested, but were not validated or have the disadvantages of computation time and complexity which does not allow real time predictions. Within this study, an analytical temperature prediction model is proposed which uses the torque signal of the drilling process to model the heat production of the drill bit. A simple Green's disk source function is used to solve the three dimensional heat equation along the drilling axis. Additionally, an extensive experimental study was carried out to validate the model. A custom CNC-setup with a load cell and a thermal camera was used to measure the axial drilling torque and force as well as temperature elevations. Bones with different sets of bone volume fraction were drilled with two drill bits ([Formula: see text]1.8 mm and [Formula: see text]2.5 mm) and repeated eight times. The model was calibrated with 5 of 40 measurements and successfully validated with the rest of the data ([Formula: see text]C). It was also found that the temperature elevation can be predicted using only the torque signal of the drilling process. In the future, the model could be used to monitor and control the drilling process of surgeries close to vulnerable structures.

"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.

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.

Approximate Bayesian evaluations of measurement uncertainty

NASA Astrophysics Data System (ADS)

Possolo, Antonio; Bodnar, Olha

2018-04-01

The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

Rotationally and vibrationally inelastic scattering in the rotational IOS approximation. Ultrasimple calculation of total (differential, integral, and transport) cross sections for nonspherical molecules

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

Parker, G.A.; Pack, R.T

1978-02-15

A simple, direct derivation of the rotational infinite order sudden (IOS) approximation in molecular scattering theory is given. Connections between simple scattering amplitude formulas, choice of average partial wave parameter, and magnetic transitions are reviewed. Simple procedures for calculating cross sections for specific transitions are discussed and many older model formulas are given clear derivations. Total (summed over rotation) differential, integral, and transport cross sections, useful in the analysis of many experiments involving nonspherical molecules, are shown to be exceedingly simple: They are just averages over the potential angle of cross sections calculated using simple structureless spherical particle formulas andmore » programs. In the case of vibrationally inelastic scattering, the IOSA, without further approximation, provides a well-defined way to get fully three dimensional cross sections from calculations no more difficult than collinear calculations. Integral, differential, viscosity, and diffusion cross sections for He-CO/sub 2/ obtained from the IOSA and a realistic intermolecular potential are calculated as an example and compared with experiment. Agreement is good for the complete potential but poor when only its spherical part is used, so that one should never attempt to treat this system with a spherical model. The simplicity and accuracy of the IOSA make it a viable method for routine analysis of experiments involving collisions of nonspherical molecules.« less

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.

Formula for the rms blur circle radius of Wolter telescope based on aberration theory

NASA Technical Reports Server (NTRS)

Shealy, David L.; Saha, Timo T.

1990-01-01

A formula for the rms blur circle for Wolter telescopes has been derived using the transverse ray aberration expressions of Saha (1985), Saha (1984), and Saha (1986). The resulting formula for the rms blur circle radius over an image plane and a formula for the surface of best focus based on third-, fifth-, and seventh-order aberration theory predict results in good agreement with exact ray tracing. It has also been shown that one of the two terms in the empirical formula of VanSpeybroeck and Chase (1972), for the rms blur circle radius of a Wolter I telescope can be justified by the aberration theory results. Numerical results are given comparing the rms blur radius and the surface of best focus vs the half-field angle computed by skew ray tracing and from analytical formulas for grazing incidence Wolter I-II telescopes and a normal incidence Cassegrain telescope.

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…

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.

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.

Influence of water vapour and permanent gases on the atmospheric optical depths and transmittance

NASA Astrophysics Data System (ADS)

Badescu, V.

1991-05-01

The influence of the atmospheric state on the extinction of direct solar radiation has been studied by using a four layer atmospheric model. Simple analytical formulae are established for the spectral optical depths of permanent gases and water vapour. These formulae use the ground level values of air pressure, temperature and relative huniidity. An additional parameter, related to the vertical distribution of the hunmidity content, is used for a better estimation of the water vapour optical depth. Good agreement between theory and measurements is found. The paper shows the dependence of the atmospheric spectral transmittance on the above mentioned parameters. L'influence de l'état atmosphérique sur l'extinction de la radiation solaire directe a été étudiée à l'aide d'un modèle atmosphérique développé antérieurement par l'auteur. Des formules simples ont été établies pour l'épaisseur optique spectrale des gaz et de la vapeur d'eau. Ces formules utilisent les valeurs de la pression atmosphérique, de la température et de l'humidité relative, mesurées au niveau du sol. Un paramètre supplémentaire, lié à la distribution verticale du contenu d'humidité, est utilisé pour calculer l'épaisseur optique due à la vapeur d'eau. La théorie est en bon accord avec les résultats des mesures. Le travail montre la dépendance de la transmittance atmosphérique spectrale en fonction des paramètres spécifiés ci-dessus.

Reconstructing the primordial spectrum of fluctuations of the universe from the observed nonlinear clustering of galaxies

NASA Technical Reports Server (NTRS)

Hamilton, A. J. S.; Matthews, Alex; Kumar, P.; Lu, Edward

1991-01-01

It was discovered that the nonlinear evolution of the two point correlation function in N-body experiments of galaxy clustering with Omega = 1 appears to be described to good approximation by a simple general formula. The underlying form of the formula is physically motivated, but its detailed representation is obtained empirically by fitting to N-body experiments. In this paper, the formula is presented along with an inverse formula which converts a final, nonlinear correlation function into the initial linear correlation function. The inverse formula is applied to observational data from the CfA, IRAs, and APM galaxy surveys, and the initial spectrum of fluctuations of the universe, if Omega = 1.

Research Timeline: Formulaic language

ERIC Educational Resources Information Center

Wray, Alison

2013-01-01

Creating a timeline for formulaic language is far from simple, because several partially independent lines of research have contributed to the emerging picture. Each exhibits cycles of innovation and consolidation over time: domains take a leading role in developing new knowledge and then fall back, while another area comes to the fore. Thus, some…

Using Paperclips to Explain Empirical Formulas to Students

ERIC Educational Resources Information Center

Nassiff, Peter; Czerwinski, Wendy A.

2014-01-01

Early in their chemistry education, students learn to do empirical formula calculations by rote without an understanding of the historical context behind them or the reason why their calculations work. In these activities, students use paperclip "atoms", construct a series of simple compounds representing real molecules, and discover,…

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.

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

Theory and applications of a deterministic approximation to the coalescent model

PubMed Central

Jewett, Ethan M.; Rosenberg, Noah A.

2014-01-01

Under the coalescent model, the random number nt of lineages ancestral to a sample is nearly deterministic as a function of time when nt is moderate to large in value, and it is well approximated by its expectation E[nt]. In turn, this expectation is well approximated by simple deterministic functions that are easy to compute. Such deterministic functions have been applied to estimate allele age, effective population size, and genetic diversity, and they have been used to study properties of models of infectious disease dynamics. Although a number of simple approximations of E[nt] have been derived and applied to problems of population-genetic inference, the theoretical accuracy of the formulas and the inferences obtained using these approximations is not known, and the range of problems to which they can be applied is not well understood. Here, we demonstrate general procedures by which the approximation nt ≈ E[nt] can be used to reduce the computational complexity of coalescent formulas, and we show that the resulting approximations converge to their true values under simple assumptions. Such approximations provide alternatives to exact formulas that are computationally intractable or numerically unstable when the number of sampled lineages is moderate or large. We also extend an existing class of approximations of E[nt] to the case of multiple populations of time-varying size with migration among them. Our results facilitate the use of the deterministic approximation nt ≈ E[nt] for deriving functionally simple, computationally efficient, and numerically stable approximations of coalescent formulas under complicated demographic scenarios. PMID:24412419

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.

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).

An Analysis Model for Water Cone Subsidence in Bottom Water Drive Reservoirs

NASA Astrophysics Data System (ADS)

Wang, Jianjun; Xu, Hui; Wu, Shucheng; Yang, Chao; Kong, lingxiao; Zeng, Baoquan; Xu, Haixia; Qu, Tailai

2017-12-01

Water coning in bottom water drive reservoirs, which will result in earlier water breakthrough, rapid increase in water cut and low recovery level, has drawn tremendous attention in petroleum engineering field. As one simple and effective method to inhibit bottom water coning, shut-in coning control is usually preferred in oilfield to control the water cone and furthermore to enhance economic performance. However, most of the water coning researchers just have been done on investigation of the coning behavior as it grows up, the reported studies for water cone subsidence are very scarce. The goal of this work is to present an analytical model for water cone subsidence to analyze the subsidence of water cone when the well shut in. Based on Dupuit critical oil production rate formula, an analytical model is developed to estimate the initial water cone shape at the point of critical drawdown. Then, with the initial water cone shape equation, we propose an analysis model for water cone subsidence in bottom water reservoir reservoirs. Model analysis and several sensitivity studies are conducted. This work presents accurate and fast analytical model to perform the water cone subsidence in bottom water drive reservoirs. To consider the recent interests in development of bottom drive reservoirs, our approach provides a promising technique for better understanding the subsidence of water cone.

Stationary bound-state massive scalar field configurations supported by spherically symmetric compact reflecting stars

NASA Astrophysics Data System (ADS)

Hod, Shahar

2017-12-01

It has recently been demonstrated that asymptotically flat neutral reflecting stars are characterized by an intriguing no-hair property. In particular, it has been proved that these horizonless compact objects cannot support spatially regular static matter configurations made of scalar (spin-0) fields, vector (spin-1) fields and tensor (spin-2) fields. In the present paper we shall explicitly prove that spherically symmetric compact reflecting stars can support stationary (rather than static) bound-state massive scalar fields in their exterior spacetime regions. To this end, we solve analytically the Klein-Gordon wave equation for a linearized scalar field of mass μ and proper frequency ω in the curved background of a spherically symmetric compact reflecting star of mass M and radius R_{ {s}}. It is proved that the regime of existence of these stationary composed star-field configurations is characterized by the simple inequalities 1-2M/R_{ {s}}<(ω /μ )^2<1. Interestingly, in the regime M/R_{ {s}}≪ 1 of weakly self-gravitating stars we derive a remarkably compact analytical equation for the discrete spectrum {ω (M,R_{ {s}},μ )}^{n=∞}_{n=1} of resonant oscillation frequencies which characterize the stationary composed compact-reflecting-star-linearized-massive-scalar-field configurations. Finally, we verify the accuracy of the analytically derived resonance formula of the composed star-field configurations with direct numerical computations.

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.

Optimization of long circulating mixed polymeric micelles containing vinpocetine using simple lattice mixture design, in vitro and in vivo characterization.

PubMed

El-Dahmy, Rania Moataz; Elsayed, Ibrahim; Elshafeey, Ahmed Hassen; Gawad, Nabaweya Abdelaziz Abd El; El-Gazayerly, Omaima Naim

2014-12-30

The aim of this study was to increase the in vivo mean residence time of vinpocetine after IV injection utilizing long circulating mixed micellar systems. Mixed micelles were prepared using Pluronics L121, P123 and F127. The systems were characterized by testing their entrapment efficiency, particle size, polydispersity index, zeta potential, transmission electron microscopy and in vitro drug release. Simple lattice mixture design was planned for the optimization using Design-Expert(®) software. The optimized formula was lyophilized, sterilized and imaged by scanning electron microscope. Moreover, the in vivo behavior of the optimized formula was evaluated after IV injection in rabbits. The optimized formula, containing 68% w/w Pluronic L121 and 32% w/w Pluronic F127, had the highest desirability value (0.621). Entrapment efficiency, particle size, polydispersity index and zeta potential of the optimized formula were 50.74 ± 3.26%, 161.50 ± 7.39 nm, 0.21 ± 0.03 and -22.42 ± 1.72 mV, respectively. Lyophilization and sterilization did not affect the characteristics of the optimized formula. Upon in vivo investigation in rabbits, the optimized formula showed a significantly higher elimination half-life and mean residence time than the market product. Finally, mixed micelles could be considered as a promising long circulating nanocarrier for lipophilic drugs. Copyright © 2014 Elsevier B.V. All rights reserved.

SYSTEMATIZATION OF MASS LEVELS OF PARTICLES AND RESONANCES ON HEURISTIC BASIS

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

Takabayasi, T.

1963-12-16

Once more a scheme of simple mass rules and formulas for particles and resonant levels is investigated and organized, based on some general hypotheses. The essential ingredients in the scheme are, on one hand, the equalinterval rule governing the isosinglet meson series, associated with particularly simple mass ratio between the 2/sup ++/ level f and 0/sup ++/ level ABC, and on the other a new basic mass formula that unifies some of the meson and baryon levels. The whole baryon levels are arranged in a table analogous to the periodic table, and then correspondences between different series and equivalence betweenmore » spin and hypercharge, when properly applied, just fix the whole baryon mass spectrum in good agreement with observations. Connections with the scheme of mass formulas formerly given are also shown. (auth)« less

Simulation of fatigue crack growth under large scale yielding conditions

NASA Astrophysics Data System (ADS)

Schweizer, Christoph; Seifert, Thomas; Riedel, Hermann

2010-07-01

A simple mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack-tip opening displacement (ΔCTOD) and the crack growth increment (da/dN). The objective of this work is to compare analytical estimates of ΔCTOD with results of numerical calculations under large scale yielding conditions and to verify the physical basis of the model by comparing the predicted and the measured evolution of the crack length in a 10%-chromium-steel. The material is described by a rate independent cyclic plasticity model with power-law hardening and Masing behavior. During the tension-going part of the cycle, nodes at the crack-tip are released such that the crack growth increment corresponds approximately to the crack-tip opening. The finite element analysis performed in ABAQUS is continued for so many cycles until a stabilized value of ΔCTOD is reached. The analytical model contains an interpolation formula for the J-integral, which is generalized to account for cyclic loading and crack closure. Both simulated and estimated ΔCTOD are reasonably consistent. The predicted crack length evolution is found to be in good agreement with the behavior of microcracks observed in a 10%-chromium steel.

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.

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

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.

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.

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.

Simple expression for the quantum Fisher information matrix

NASA Astrophysics Data System (ADS)

Šafránek, Dominik

2018-04-01

Quantum Fisher information matrix (QFIM) is a cornerstone of modern quantum metrology and quantum information geometry. Apart from optimal estimation, it finds applications in description of quantum speed limits, quantum criticality, quantum phase transitions, coherence, entanglement, and irreversibility. We derive a surprisingly simple formula for this quantity, which, unlike previously known general expression, does not require diagonalization of the density matrix, and is provably at least as efficient. With a minor modification, this formula can be used to compute QFIM for any finite-dimensional density matrix. Because of its simplicity, it could also shed more light on the quantum information geometry in general.

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.

Subleading Regge limit from a soft anomalous dimension

NASA Astrophysics Data System (ADS)

Brüser, Robin; Caron-Huot, Simon; Henn, Johannes M.

2018-04-01

Wilson lines capture important features of scattering amplitudes, for example soft effects relevant for infrared divergences, and the Regge limit. Beyond the leading power approximation, corrections to the eikonal picture have to be taken into account. In this paper, we study such corrections in a model of massive scattering amplitudes in N=4 super Yang-Mills, in the planar limit, where the mass is generated through a Higgs mechanism. Using known three-loop analytic expressions for the scattering amplitude, we find that the first power suppressed term has a very simple form, equal to a single power law. We propose that its exponent is governed by the anomalous dimension of a Wilson loop with a scalar inserted at the cusp, and we provide perturbative evidence for this proposal. We also analyze other limits of the amplitude and conjecture an exact formula for a total cross-section at high energies.

Particles with nonlinear electric response: Suppressing van der Waals forces by an external field.

PubMed

Soo, Heino; Dean, David S; Krüger, Matthias

2017-01-01

We study the classical thermal component of Casimir, or van der Waals, forces between point particles with highly anharmonic dipole Hamiltonians when they are subjected to an external electric field. Using a model for which the individual dipole moments saturate in a strong field (a model that mimics the charges in a neutral, perfectly conducting sphere), we find that the resulting Casimir force depends strongly on the strength of the field, as demonstrated by analytical results. For a certain angle between the external field and center-to-center axis, the fluctuation force can be tuned and suppressed to arbitrarily small values. We compare the forces between these particles with those between particles with harmonic Hamiltonians and also provide a simple formula for asymptotically large external fields, which we expect to be generally valid for the case of saturating dipole moments.

Laplacian scale-space behavior of planar curve corners.

PubMed

Zhang, Xiaohong; Qu, Ying; Yang, Dan; Wang, Hongxing; Kymer, Jeff

2015-11-01

Scale-space behavior of corners is important for developing an efficient corner detection algorithm. In this paper, we analyze the scale-space behavior with the Laplacian of Gaussian (LoG) operator on a planar curve which constructs Laplacian Scale Space (LSS). The analytical expression of a Laplacian Scale-Space map (LSS map) is obtained, demonstrating the Laplacian Scale-Space behavior of the planar curve corners, based on a newly defined unified corner model. With this formula, some Laplacian Scale-Space behavior is summarized. Although LSS demonstrates some similarities to Curvature Scale Space (CSS), there are still some differences. First, no new extreme points are generated in the LSS. Second, the behavior of different cases of a corner model is consistent and simple. This makes it easy to trace the corner in a scale space. At last, the behavior of LSS is verified in an experiment on a digital curve.

Simulation of wind turbine wakes using the actuator line technique

PubMed Central

Sørensen, Jens N.; Mikkelsen, Robert F.; Henningson, Dan S.; Ivanell, Stefan; Sarmast, Sasan; Andersen, Søren J.

2015-01-01

The actuator line technique was introduced as a numerical tool to be employed in combination with large eddy simulations to enable the study of wakes and wake interaction in wind farms. The technique is today largely used for studying basic features of wakes as well as for making performance predictions of wind farms. In this paper, we give a short introduction to the wake problem and the actuator line methodology and present a study in which the technique is employed to determine the near-wake properties of wind turbines. The presented results include a comparison of experimental results of the wake characteristics of the flow around a three-bladed model wind turbine, the development of a simple analytical formula for determining the near-wake length behind a wind turbine and a detailed investigation of wake structures based on proper orthogonal decomposition analysis of numerically generated snapshots of the wake. PMID:25583862

Non-Linear Analysis of Mode II Fracture in the end Notched Flexure Beam

NASA Astrophysics Data System (ADS)

Rizov, V.

2016-03-01

Analysis is carried-out of fracture in the End Notched Flex- ure (ENF) beam configuration, taking into account the material nonlin- earity. For this purpose, the J-integral approach is applied. A non-linear model, based on the Classical beam theory is used. The mechanical be- haviour of the ENF configuration is described by the Ramberg-Osgood stress-strain curve. It is assumed that the material possesses the same properties in tension and compression. The influence is evaluated of the material constants in the Ramberg-Osgood stress-strain equation on the fracture behaviour. The effect of the crack length on the J-integral value is investigated, too. The analytical approach, developed in the present paper, is very useful for parametric analyses, since the simple formulae obtained capture the essentials of the non-linear fracture in the ENF con- figuration.

Critical asset and portfolio risk analysis: an all-hazards framework.

PubMed

Ayyub, Bilal M; McGill, William L; Kaminskiy, Mark

2007-08-01

This article develops a quantitative all-hazards framework for critical asset and portfolio risk analysis (CAPRA) that considers both natural and human-caused hazards. Following a discussion on the nature of security threats, the need for actionable risk assessments, and the distinction between asset and portfolio-level analysis, a general formula for all-hazards risk analysis is obtained that resembles the traditional model based on the notional product of consequence, vulnerability, and threat, though with clear meanings assigned to each parameter. Furthermore, a simple portfolio consequence model is presented that yields first-order estimates of interdependency effects following a successful attack on an asset. Moreover, depending on the needs of the decisions being made and available analytical resources, values for the parameters in this model can be obtained at a high level or through detailed systems analysis. Several illustrative examples of the CAPRA methodology are provided.

Computational expressions for signals in frequency-modulation spectroscopy.

PubMed

Di Rosa, Michael D; Reiten, M T

2015-06-01

General expressions for the signals in frequency-modulation spectroscopy (FMS) appear in the literature but are often reduced to simple analytical equations following the assumption of a weak modulation index. This is little help to the experimentalist who wants to predict signals for modulation depths of the order of unity or greater, where strong FMS signals reside. Here, we develop general formulas for FMS signals in the case of an absorber with a Voigt line shape and then link these expressions to an example and existing numerical code for the line shape. The resulting computational recipe is easy to implement and exercised here to show where the larger FMS signals are found over the coordinates of modulation index and modulation frequency. One can also estimate from provided curves the in-phase FMS signal over a wide range of modulation parameters at either the Lorentzian-broadening or Doppler-broadening limit, or anywhere in between by interpolation.

The propagation of a flattened circular Gaussian beam through an optical system in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Chu, X. X.; Liu, Z. J.; Wu, Y.

2008-07-01

Based on the Huygens-Fresnel integral, the properties of a circular flattened Gaussian beam through a stigmatic optical system in turbulent atmosphere are investigated. Analytical formulas for the average intensity are derived. As elementary examples, the average intensity distributions of a collimated circular flattened Gaussian beam and a focused circular flattened Gaussian beam through a simple optical system are studied. To see the effects of the optical system on the propagation, the average intensity distributions of the beam for direct propagation are also studied. From the analysis, comparison and numerical calculation we can see that there are many differences between the two propagations. These differences are due to the geometrical magnification of the optical system, different diffraction and different turbulence-induced spreading. Namely, an optical system not only affects the diffraction but also affects the turbulence-induced spreading.

Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals

NASA Astrophysics Data System (ADS)

Simonović, Marko; Baldauf, Tobias; Zaldarriaga, Matias; Carrasco, John Joseph; Kollmeier, Juna A.

2018-04-01

We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a ΛCDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved using an FFTLog algorithm. For power-law cosmologies, all loop integrals are formally equivalent to loop integrals of massless quantum field theory. These integrals have analytic solutions in terms of generalized hypergeometric functions. We provide explicit formulae for the one-loop and the two-loop power spectrum and the one-loop bispectrum. A chief advantage of our approach is that the difficult part of the calculation is cosmology independent, need be done only once, and can be recycled for any relevant predictions. Evaluation of standard loop diagrams then boils down to a simple matrix multiplication. We demonstrate the promise of this method for applications to higher multiplicity/loop correlation functions.

Electric field effect on the second-order nonlinear optical properties of parabolic and semiparabolic quantum wells

NASA Astrophysics Data System (ADS)

Zhang, Li; Xie, Hong-Jing

2003-12-01

By using the compact-density-matrix approach and iterative procedure, a detailed procedure for the calculation of the second-harmonic generation (SHG) susceptibility tensor is given in the electric-field-biased parabolic and semiparabolic quantum wells (QW’s). The simple analytical formula for the SHG susceptibility in the systems is also deduced. By adopting the methods of envelope wave function and displacement harmonic oscillation, the electronic states in parabolic and semi parabolic QW’s with applied electric fields are exactly solved. Numerical results on typical AlxGa1-xAl/GaAs materials show that, for the same effective widths, the SHG susceptibility in semiparabolic QW is larger than that in parabolic QW due to the self-asymmetry of the semiparabolic QW, and the applied electric field can make the SHG susceptibilities in both systems enhance remarkably. Moreover, the SHG susceptibility also sensitively depends on the relaxation rate of the systems.

The entrainment matrix of a superfluid nucleon mixture at finite temperatures

NASA Astrophysics Data System (ADS)

Leinson, Lev B.

2018-06-01

It is considered a closed system of non-linear equations for the entrainment matrix of a non-relativistic mixture of superfluid nucleons at arbitrary temperatures below the onset of neutron superfluidity, which takes into account the essential dependence of the superfluid energy gap in the nucleon spectra on the velocities of superfluid flows. It is assumed that the protons condense into the isotropic 1S0 state, and the neutrons are paired into the spin-triplet 3P2 state. It is derived an analytic solution to the non-linear equations for the entrainment matrix under temperatures just below the critical value for the neutron superfluidity onset. In general case of an arbitrary temperature of the superfluid mixture the non-linear equations are solved numerically and fitted by simple formulas convenient for a practical use with an arbitrary set of the Landau parameters.

Predictions and Observations of Two-Plasmon Decay on the NIKE Laser System

NASA Astrophysics Data System (ADS)

Phillips, Lee; Weaver, James; Oh, J.; Schmitt, A. J.; Obenschain, S.; Velikovich, A.

2011-10-01

NIKE is a Krf laser system at the Naval Research Laboratory used to explore hydrodynamic stability, equation of state, and other physics problems arising in IFE research. The short wavelength and large bandwidth of the NIKE laser is predicted to raise the threshold of parametric instabilities such as two-plasmon decay (TPD). We report on simulations performed using the FAST3d radiation hydrocode to design TPD experiments that have allowed us to explore the validity of simple threshold formulas and demonstrate the advantages of the KrF wavelength in suppressing LPI. We consider proposed high-gain shock ignition designs and show, through analytic estimates and simulations, that we can explore the relevant scalelength-temperature regime, providing an experimental method to study the LPI threat to these targets at a small fraction of their designed input energies. This research is funded by the US DOE, NRL, and ONR.

A simple algorithm for computing positively weighted straight skeletons of monotone polygons.

PubMed

Biedl, Therese; Held, Martin; Huber, Stefan; Kaaser, Dominik; Palfrader, Peter

2015-02-01

We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in [Formula: see text] time and [Formula: see text] space, where n denotes the number of vertices of the polygon.

A New Approach for Proving or Generating Combinatorial Identities

ERIC Educational Resources Information Center

Gonzalez, Luis

2010-01-01

A new method for proving, in an immediate way, many combinatorial identities is presented. The method is based on a simple recursive combinatorial formula involving n + 1 arbitrary real parameters. Moreover, this formula enables one not only to prove, but also generate many different combinatorial identities (not being required to know them "a…

On the Matrix Exponential Function

ERIC Educational Resources Information Center

Hou, Shui-Hung; Hou, Edwin; Pang, Wan-Kai

2006-01-01

A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.

An empirical relationship for homogenization in single-phase binary alloy systems

NASA Technical Reports Server (NTRS)

Unnam, J.; Tenney, D. R.; Stein, B. A.

1979-01-01

A semiempirical formula is developed for describing the extent of interaction between constituents in single-phase binary alloy systems with planar, cylindrical, or spherical interfaces. The formula contains two parameters that are functions of mean concentration and interface geometry of the couple. The empirical solution is simple, easy to use, and does not involve sequential calculations, thereby allowing quick estimation of the extent of interactions without lengthy calculations. Results obtained with this formula are in good agreement with those from a finite-difference analysis.

Improved Design Formulae for Buckling of Orthotropic Plates under Combined Loading

NASA Technical Reports Server (NTRS)

Weaver, Paul M.; Nemeth, Michael P.

2008-01-01

Simple, accurate buckling interaction formulae are presented for long orthotropic plates with either simply supported or clamped longitudinal edges and under combined loading that are suitable for design studies. The loads include 1) combined uniaxial compression (or tension) and shear, 2) combined pure inplane bending and 3) shear and combined uniaxial compression (or tension) and pure inplane bending. The interaction formulae are the results of detailed regression analysis of buckling data obtained from a very accurate Rayleigh-Ritz method.

A simple method for finding explicit analytic transition densities of diffusion processes with general diploid selection.

PubMed

Song, Yun S; Steinrücken, Matthias

2012-03-01

The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.

A Simple Method for Finding Explicit Analytic Transition Densities of Diffusion Processes with General Diploid Selection

PubMed Central

Song, Yun S.; Steinrücken, Matthias

2012-01-01

The transition density function of the Wright–Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright–Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation–selection balance. PMID:22209899

A simple analytical method for determining the atmospheric dispersion of upward-directed high velocity releases

NASA Astrophysics Data System (ADS)

Palazzi, E.

The evaluation of atmospheric dispersion of a cloud, arising from a sudden release of flammable or toxic materials, is an essential tool for properly designing flares, vents and other safety devices and to quantify the potential risk related to the existing ones or arising from the various kinds of accidents which can occur in chemical plants. Among the methods developed to treat the important case of upward-directed jets, Hoehne's procedure for determining the behaviour and extent of flammability zone is extensively utilized, particularly concerning petrochemical plants. In a previous study, a substantial simplification of the aforesaid procedure was achieved, by correlating the experimental data with an empirical formula, allowing to obtain a mathematical description of the boundaries of the flammable cloud. Following a theoretical approach, a most general model is developed in the present work, applicable to the various kinds of design problems and/or risk evaluation regarding upward-directed releases from high velocity sources. It is also demonstrated that the model gives conservative results, if applied outside the range of the Hoehne's experimental conditions. Moreover, with simple modifications, the same approach could be easily applied to deal with the atmospheric dispersion of anyhow directed releases.

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.

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.

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.

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.

Enhanced hyperuniformity from random reorganization.

PubMed

Hexner, Daniel; Chaikin, Paul M; Levine, Dov

2017-04-25

Diffusion relaxes density fluctuations toward a uniform random state whose variance in regions of volume [Formula: see text] scales as [Formula: see text] Systems whose fluctuations decay faster, [Formula: see text] with [Formula: see text], are called hyperuniform. The larger [Formula: see text], the more uniform, with systems like crystals achieving the maximum value: [Formula: see text] Although finite temperature equilibrium dynamics will not yield hyperuniform states, driven, nonequilibrium dynamics may. Such is the case, for example, in a simple model where overlapping particles are each given a small random displacement. Above a critical particle density [Formula: see text], the system evolves forever, never finding a configuration where no particles overlap. Below [Formula: see text], however, it eventually finds such a state, and stops evolving. This "absorbing state" is hyperuniform up to a length scale [Formula: see text], which diverges at [Formula: see text] An important question is whether hyperuniformity survives noise and thermal fluctuations. We find that hyperuniformity of the absorbing state is not only robust against noise, diffusion, or activity, but that such perturbations reduce fluctuations toward their limiting behavior, [Formula: see text], a uniformity similar to random close packing and early universe fluctuations, but with arbitrary controllable density.

Thermodynamics of atomic and ionized hydrogen: analytical results versus equation-of-state tables and Monte Carlo data.

PubMed

Alastuey, A; Ballenegger, V

2012-12-01

We compute thermodynamical properties of a low-density hydrogen gas within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential. Our calculations are done using the exact scaled low-temperature (SLT) expansion, which provides a rigorous extension of the well-known virial expansion-valid in the fully ionized phase-into the Saha regime where the system is partially or fully recombined into hydrogen atoms. After recalling the SLT expansion of the pressure [A. Alastuey et al., J. Stat. Phys. 130, 1119 (2008)], we obtain the SLT expansions of the chemical potential and of the internal energy, up to order exp(-|E_{H}|/kT) included (E_{H}≃-13.6 eV). Those truncated expansions describe the first five nonideal corrections to the ideal Saha law. They account exactly, up to the considered order, for all effects of interactions and thermal excitations, including the formation of bound states (atom H, ions H^{-} and H_{2}^{+}, molecule H_{2},⋯) and atom-charge and atom-atom interactions. Among the five leading corrections, three are easy to evaluate, while the remaining ones involve well-defined internal partition functions for the molecule H_{2} and ions H^{-} and H_{2}^{+}, for which no closed-form analytical formula exist currently. We provide accurate low-temperature approximations for those partition functions by using known values of rotational and vibrational energies. We compare then the predictions of the SLT expansion, for the pressure and the internal energy, with, on the one hand, the equation-of-state tables obtained within the opacity program at Livermore (OPAL) and, on the other hand, data of path integral quantum Monte Carlo (PIMC) simulations. In general, a good agreement is found. At low densities, the simple analytical SLT formulas reproduce the values of the OPAL tables up to the last digit in a large range of temperatures, while at higher densities (ρ∼10^{-2} g/cm^{3}), some discrepancies among the SLT, OPAL, and PIMC results are observed.

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.

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

Effect of blood flow on near-the-wall mass transport of drugs and other bioactive agents: a simple formula to estimate boundary layer concentrations.

PubMed

Rugonyi, Sandra

2008-04-01

Transport of bioactive agents through the blood is essential for cardiovascular regulatory processes and drug delivery. Bioactive agents and other solutes infused into the blood through the wall of a blood vessel or released into the blood from an area in the vessel wall spread downstream of the infusion/release region and form a thin boundary layer in which solute concentration is higher than in the rest of the blood. Bioactive agents distributed along the vessel wall affect endothelial cells and regulate biological processes, such as thrombus formation, atherogenesis, and vascular remodeling. To calculate the concentration of solutes in the boundary layer, researchers have generally used numerical simulations. However, to investigate the effect of blood flow, infusion rate, and vessel geometry on the concentration of different solutes, many simulations are needed, leading to a time-consuming effort. In this paper, a relatively simple formula to quantify concentrations in a tube downstream of an infusion/release region is presented. Given known blood-flow rates, tube radius, solute diffusivity, and the length of the infusion region, this formula can be used to quickly estimate solute concentrations when infusion rates are known or to estimate infusion rates when solute concentrations at a point downstream of the infusion region are known. The developed formula is based on boundary layer theory and physical principles. The formula is an approximate solution of the advection-diffusion equations in the boundary layer region when solute concentration is small (dilute solution), infusion rate is modeled as a mass flux, and there is no transport of solute through the wall or chemical reactions downstream of the infusion region. Wall concentrations calculated using the formula developed in this paper were compared to the results from finite element models. Agreement between the results was within 10%. The developed formula could be used in experimental procedures to evaluate drug efficacy, in the design of drug-eluting stents, and to calculate rates of release of bioactive substances at active surfaces using downstream concentration measurements. In addition to being simple and fast to use, the formula gives accurate quantifications of concentrations and infusion rates under steady-state and oscillatory flow conditions, and therefore can be used to estimate boundary layer concentrations under physiological conditions.

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.

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.

12 CFR Appendix A to Part 707 - Annual Percentage Yield Calculation

Code of Federal Regulations, 2010 CFR

2010-01-01

... the member to open, maintain, increase or renew an account. Dividends, interest or other earnings are... may or may not occur in the future. These formulas apply to both dividend-bearing and interest-bearing... not have a stated maturity), the APY can be calculated by use of the following simple formula: APY=100...

A Compact Formula for Rotations as Spin Matrix Polynomials

DOE PAGES

Curtright, Thomas L.; Fairlie, David B.; Zachos, Cosmas K.

2014-08-12

Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. Here, the simple explicit result exhibits connections between group theory, combinatorics, and Fourier analysis, especially in the large spin limit. Salient intuitive features of the formula are illustrated and discussed.

Programmable calculator uses equation to figure steady-state gas-pipeline flow

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

Holmberg, E.

Because it is accurate and consistent over a wide range of variables, the Colebrook-White (C-W) formula serves as the basis for many methods of calculating turbulent flow in gas pipelines. Oilconsult reveals a simple way to adapt the C-W formula to calculate steady-state pipeline flow using the TI-59 programmable calculator.

A Novel Instructional Approach to the Design of Standard Controllers: Using Inversion Formulae

ERIC Educational Resources Information Center

Ntogramatzidis, Lorenzo; Zanasi, Roberto; Cuoghi, Stefania

2014-01-01

This paper describes a range of design techniques for standard compensators (Lead-Lag networks and PID controllers) that have been applied to the teaching of many undergraduate control courses throughout Italy over the last twenty years, but that have received little attention elsewhere. These techniques hinge upon a set of simple formulas--herein…

WE-E-18A-05: Bremsstrahlung of Laser-Plasma Interaction at KeV Temperature: Forward Dose and Attenuation Factors

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

Saez-Beltran, M; Fernandez Gonzalez, F

2014-06-15

Purpose: To obtain an analytical empirical formula for the photon dose source term in forward direction from bremsstrahlung generated from laser-plasma accelerated electron beams in aluminum solid targets, with electron-plasma temperatures in the 10–100 keV energy range, and to calculate transmission factors for iron, aluminum, methacrylate, lead and concrete and air, materials most commonly found in vacuum chamber labs. Methods: Bremsstrahlung fluence is calculated from the convolution of thin-target bremsstrahlung spectrum for monoenergetic electrons and the relativistic Maxwell-Juettner energy distribution for the electron-plasma. Unattenuatted dose in tissue is calculated by integrating the photon spectrum with the mass-energy absorption coefficient. Formore » the attenuated dose, energy dependent absorption coefficient, build-up factors and finite shielding correction factors were also taken into account. For the source term we use a modified formula from Hayashi et al., and we fitted the proportionality constant from experiments with the aid of the previously calculated transmission factors. Results: The forward dose has a quadratic dependence on electron-plasma temperature: 1 joule of effective laser energy transferred to the electrons at 1 m in vacuum yields 0,72 Sv per MeV squared of electron-plasma temperature. Air strongly filters the softer part of the photon spectrum and reduce the dose to one tenth in the first centimeter. Exponential higher energy tail of maxwellian spectrum contributes mainly to the transmitted dose. Conclusion: A simple formula for forward photon dose from keV range temperature plasma is obtained, similar to those found in kilovoltage x-rays but with higher dose per dissipated electron energy, due to thin target and absence of filtration.« less

Calculation of the temporal gravity variation from spatially variable water storage change in soils and aquifers

NASA Astrophysics Data System (ADS)

Leirião, Sílvia; He, Xin; Christiansen, Lars; Andersen, Ole B.; Bauer-Gottwein, Peter

2009-02-01

SummaryTotal water storage change in the subsurface is a key component of the global, regional and local water balances. It is partly responsible for temporal variations of the earth's gravity field in the micro-Gal (1 μGal = 10 -8 m s -2) range. Measurements of temporal gravity variations can thus be used to determine the water storage change in the hydrological system. A numerical method for the calculation of temporal gravity changes from the output of hydrological models is developed. Gravity changes due to incremental prismatic mass storage in the hydrological model cells are determined to give an accurate 3D gravity effect. The method is implemented in MATLAB and can be used jointly with any hydrological simulation tool. The method is composed of three components: the prism formula, the MacMillan formula and the point-mass approximation. With increasing normalized distance between the storage prism and the measurement location the algorithm switches first from the prism equation to the MacMillan formula and finally to the simple point-mass approximation. The method was used to calculate the gravity signal produced by an aquifer pump test. Results are in excellent agreement with the direct numerical integration of the Theis well solution and the semi-analytical results presented in [Damiata, B.N., and Lee, T.-C., 2006. Simulated gravitational response to hydraulic testing of unconfined aquifers. Journal of Hydrology 318, 348-359]. However, the presented method can be used to forward calculate hydrology-induced temporal variations in gravity from any hydrological model, provided earth curvature effects can be neglected. The method allows for the routine assimilation of ground-based gravity data into hydrological models.

WE-E-18A-06: To Remove Or Not to Remove: Comfort Pads From Beneath Neonates for Radiography

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

Jiang, X; Baad, M; Reiser, I

2014-06-15

Purpose: To obtain an analytical empirical formula for the photon dose source term in forward direction from bremsstrahlung generated from laser-plasma accelerated electron beams in aluminum solid targets, with electron-plasma temperatures in the 10–100 keV energy range, and to calculate transmission factors for iron, aluminum, methacrylate, lead and concrete and air, materials most commonly found in vacuum chamber labs. Methods: Bremsstrahlung fluence is calculated from the convolution of thin-target bremsstrahlung spectrum for monoenergetic electrons and the relativistic Maxwell-Juettner energy distribution for the electron-plasma. Unattenuatted dose in tissue is calculated by integrating the photon spectrum with the mass-energy absorption coefficient. Formore » the attenuated dose, energy dependent absorption coefficient, build-up factors and finite shielding correction factors were also taken into account. For the source term we use a modified formula from Hayashi et al., and we fitted the proportionality constant from experiments with the aid of the previously calculated transmission factors. Results: The forward dose has a quadratic dependence on electron-plasma temperature: 1 joule of effective laser energy transferred to the electrons at 1 m in vacuum yields 0,72 Sv per MeV squared of electron-plasma temperature. Air strongly filters the softer part of the photon spectrum and reduce the dose to one tenth in the first centimeter. Exponential higher energy tail of maxwellian spectrum contributes mainly to the transmitted dose. Conclusion: A simple formula for forward photon dose from keV range temperature plasma is obtained, similar to those found in kilovoltage x-rays but with higher dose per dissipated electron energy, due to thin target and absence of filtration.« 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.

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.

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.…

Standard Errors of Equating for the Percentile Rank-Based Equipercentile Equating with Log-Linear Presmoothing

ERIC Educational Resources Information Center

Wang, Tianyou

2009-01-01

Holland and colleagues derived a formula for analytical standard error of equating using the delta-method for the kernel equating method. Extending their derivation, this article derives an analytical standard error of equating procedure for the conventional percentile rank-based equipercentile equating with log-linear smoothing. This procedure is…

Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement.

PubMed

Zhuang, Quntao; Zhu, Elton Yechao; Shor, Peter W

2017-05-19

We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver's preshared ancilla. Instead of a pure state, we consider the signal-ancilla pair in a mixed state, purified by a "witness." Thus, the signal-witness correlation limits the resource available from the signal-ancilla correlation. Our formula characterizes the utility of different forms of resources, including noisy or limited entanglement assistance, for classical communication. With separable encoding, the sender's signals across multiple channel uses are still allowed to be entangled, yet our capacity formula is additive. In particular, for generalized covariant channels, our capacity formula has a simple closed form. Moreover, our additive capacity formula upper bounds the general coherent attack's information gain in various two-way quantum key distribution protocols. For Gaussian protocols, the additivity of the formula indicates that the collective Gaussian attack is the most powerful.

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.

On the estimation variance for the specific Euler-Poincaré characteristic of random networks.

PubMed

Tscheschel, A; Stoyan, D

2003-07-01

The specific Euler number is an important topological characteristic in many applications. It is considered here for the case of random networks, which may appear in microscopy either as primary objects of investigation or as secondary objects describing in an approximate way other structures such as, for example, porous media. For random networks there is a simple and natural estimator of the specific Euler number. For its estimation variance, a simple Poisson approximation is given. It is based on the general exact formula for the estimation variance. In two examples of quite different nature and topology application of the formulas is demonstrated.

Some Simple Formulas for Posterior Convergence Rates

PubMed Central

2014-01-01

We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a “penalized divergence” of the prior, which measures the ability of the prior distribution to propose a nonnegligible set of working models to approximate the true model and a “norm complexity” of the prior, which measures the complexity of the prior support, weighted by the prior probability masses. These formulas are explicit and involve no essential assumptions and are easy to apply. We apply this approach to the case with model averaging and derive some useful oracle inequalities that can optimize the performance adaptively without knowing the true model. PMID:27379278

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.

Analytical Studies on the Synchronization of a Network of Linearly-Coupled Simple Chaotic Systems

NASA Astrophysics Data System (ADS)

Sivaganesh, G.; Arulgnanam, A.; Seethalakshmi, A. N.; Selvaraj, S.

2018-05-01

We present explicit generalized analytical solutions for a network of linearly-coupled simple chaotic systems. Analytical solutions are obtained for the normalized state equations of a network of linearly-coupled systems driven by a common chaotic drive system. Two parameter bifurcation diagrams revealing the various hidden synchronization regions, such as complete, phase and phase-lag synchronization are identified using the analytical results. The synchronization dynamics and their stability are studied using phase portraits and the master stability function, respectively. Further, experimental results for linearly-coupled simple chaotic systems are presented to confirm the analytical results. The synchronization dynamics of a network of chaotic systems studied analytically is reported for the first time.

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.

The calculation of force-free fields from discrete flux distributions. [for chromospheric magnetic fields

NASA Technical Reports Server (NTRS)

Sheeley, N. R., Jr.; Harvey, J. W.

1975-01-01

This paper presents particularly simple mathematical formulas for the calculation of force-free fields of constant alpha from the distribution of discrete sources on a flat surface. The advantage of these formulas lies in their physical simplicity and the fact that they can be easily used in practice to calculate the fields. The disadvantage is that they are limited to fields of 'sufficiently small alpha'. These formulas may be useful in the study of chromospheric magnetic fields by the comparison of high-resolution H-alpha photographs and photospheric magnetograms.

Formal verification of automated teller machine systems using SPIN

NASA Astrophysics Data System (ADS)

Iqbal, Ikhwan Mohammad; Adzkiya, Dieky; Mukhlash, Imam

2017-08-01

Formal verification is a technique for ensuring the correctness of systems. This work focuses on verifying a model of the Automated Teller Machine (ATM) system against some specifications. We construct the model as a state transition diagram that is suitable for verification. The specifications are expressed as Linear Temporal Logic (LTL) formulas. We use Simple Promela Interpreter (SPIN) model checker to check whether the model satisfies the formula. This model checker accepts models written in Process Meta Language (PROMELA), and its specifications are specified in LTL formulas.

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.

Comparative analysis of the main bioactive components of Xin-Sheng-Hua granule and its single herbs by ultrahigh performance liquid chromatography with tandem mass spectrometry.

PubMed

Pang, Hanqing; Wang, Jun; Tang, Yuping; Xu, Huiqin; Wu, Liang; Jin, Yi; Zhu, Zhenhua; Guo, Sheng; Shi, Xuqin; Huang, Shengliang; Sun, Dazheng; Duan, Jin-Ao

2016-11-01

Xin-Sheng-Hua granule, a representative formula for postpartum hemorrhage, has been used clinically to treat postpartum diseases. Its main bioactive components comprise aromatic acids, phthalides, alkaloids, flavonoids, and gingerols among others. To investigate the changes in main bioactive constituents in its seven single herbs before and after compatibility, a rapid, simple, and sensitive method was developed for comparative analysis of 27 main bioactive components by using ultrahigh-performance liquid chromatography with triple quadrupole electrospray tandem mass spectrometry for the first time. The sufficient separation of 27 target constituents was achieved on a Thermo Scientific Hypersil GOLD column (100 mm × 3 mm, 1.9 μm) within 20 min under the optimized chromatographic conditions. Compared with the theoretical content, the observed content of each analyte showed remarkable differences in Xin-Sheng-Hua granule except thymine, p-coumaric acid, senkyunolide I, senkyunolide H, and ligustilide; the total contents of 27 components increased significantly, and the content variation degrees for the different components were gingerols > flavonoids > aromatic acids > alkaloids > phthalides. The results could provide a good reference for the quality control of Xin-Sheng-Hua granule and might be helpful to interpret the drug interactions based on variation of bioactive components in formulae. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

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.

Can We Move beyond "Indigenous Good, Non-Indigenous Bad" in Thinking about People and the Environment?

ERIC Educational Resources Information Center

Zink, Robyn

2007-01-01

Bucknell & Mannion (2007) commented that student responses in the 2006 VCE Outdoor and Environmental Studies (OES) exam could be boiled down to the simple formula of "Indigenous good, non-Indigenous bad" (p. 8). They suggest that the subject of OES is to rich for such pat answers. This paper uses this formula of "Indigenous…

The algebra of complex 2 × 2 matrices and a general closed Baker-Campbell-Hausdorff formula

NASA Astrophysics Data System (ADS)

Foulis, D. L.

2017-07-01

We derive a closed formula for the Baker-Campbell-Hausdorff series expansion in the case of complex 2×2 matrices. For arbitrary matrices A and B, and a matrix Z such that \\exp Z = \\exp A \\exp B , our result expresses Z as a linear combination of A and B, their commutator [A, B] , and the identity matrix I. The coefficients in this linear combination are functions of the traces and determinants of A and B, and the trace of their product. The derivation proceeds purely via algebraic manipulations of the given matrices and their products, making use of relations developed here, based on the Cayley-Hamilton theorem, as well as a characterization of the consequences of [A, B] and/or its determinant being zero or otherwise. As a corollary of our main result we also derive a closed formula for the Zassenhaus expansion. We apply our results to several special cases, most notably the parametrization of the product of two SU(2) matrices and a verification of the recent result of Van-Brunt and Visser (2015 J. Phys. A: Math. Theor. 48 225207) for complex 2×2 matrices, in this latter case deriving also the related Zassenhaus formula which turns out to be quite simple. We then show that this simple formula should be valid for all matrices and operators.

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.

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.

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.

A Fractal Excursion.

ERIC Educational Resources Information Center

Camp, Dane R.

1991-01-01

After introducing the two-dimensional Koch curve, which is generated by simple recursions on an equilateral triangle, the process is extended to three dimensions with simple recursions on a regular tetrahedron. Included, for both fractal sequences, are iterative formulae, illustrations of the first several iterations, and a sample PASCAL program.…

Relaxation of structural parameters and potential coefficients of nonrigid molecules. General symmetry properties and application to ab initio study of 1,2-difluoroethane

NASA Astrophysics Data System (ADS)

Ha, T.-K.; Günthard, H. H.

1989-07-01

Structural parameters like bond length, bond angles, etc. and harmonic and anharmonic potential coefficients of molecules with internal rotation, inversion or puckering modes are generally assumed to vary with the large amplitude internal coordinates in a concerted manner (relaxation). Taking the coordinate vectors of the nuclear configuration of semirigid molecules with relaxation (SRMRs) as functions of relaxing structural parameters and finite amplitude internal coordinate, the isometric group of SRMRs is discussed and the irreducible representations of the latter are shown to classify into engendered and nonengendered ones. On this basis a concept of equivalent sets of nuclei SRMRs is introduced and an analytical expression is derived which defines the most general functional form of relaxation increments of all common types of structural parameters compatible with isometric symmetry. This formula is shown to be a close analog of an analytical expression defining the transformations induced by the isometric group of infinitesimal internal coordinates associated with typical structural parameters. Furthermore analogous formulae are given for the most general form of the relaxation of harmonic potential coefficients as a function of finite internal coordinates. The general relations are illustrated by ab initio calculations for 1,2-difluoroethane at the MP4/DZP//HF/4-31G* level for twelve values of the dihedral angle including complete structure optimization. The potential to internal rotation is found to be in essential agreement with experimentally derived data. For a complete set of ab initio structural parameters the associated relaxation increments are represented as Fourier series, which are shown to confirm the form predicted by the general formula and the isometric group of 1,2-difluoroethane. Depending on type of the structural parameters (bond length, bond angles, etc.), the associated relaxation increments appear to follow some simple rules. Similarly a complete set of harmonic potential coefficients derived from the ab initio calculations will be analyzed in terms of Fourier series and shown to conform to the symmetry requirements of the symmetry group. Relaxation of potential coefficients is found to amount to up to ≈5% for some types of diagonal and nondiagonal terms and to reflect certain "topological" rules similar to regularities of harmonic potential constants of quasi-rigid molecules found in empirical determinations of valence force fields.

Stress-stress fluctuation formula for elastic constants in the NPT ensemble

NASA Astrophysics Data System (ADS)

Lips, Dominik; Maass, Philipp

2018-05-01

Several fluctuation formulas are available for calculating elastic constants from equilibrium correlation functions in computer simulations, but the ones available for simulations at constant pressure exhibit slow convergence properties and cannot be used for the determination of local elastic constants. To overcome these drawbacks, we derive a stress-stress fluctuation formula in the NPT ensemble based on known expressions in the NVT ensemble. We validate the formula in the NPT ensemble by calculating elastic constants for the simple nearest-neighbor Lennard-Jones crystal and by comparing the results with those obtained in the NVT ensemble. For both local and bulk elastic constants we find an excellent agreement between the simulated data in the two ensembles. To demonstrate the usefulness of the formula, we apply it to determine the elastic constants of a simulated lipid bilayer.

Cooling of solar flares plasmas. 1: Theoretical considerations

NASA Technical Reports Server (NTRS)

Cargill, Peter J.; Mariska, John T.; Antiochos, Spiro K.

1995-01-01

Theoretical models of the cooling of flare plasma are reexamined. By assuming that the cooling occurs in two separate phase where conduction and radiation, respectively, dominate, a simple analytic formula for the cooling time of a flare plasma is derived. Unlike earlier order-of-magnitude scalings, this result accounts for the effect of the evolution of the loop plasma parameters on the cooling time. When the conductive cooling leads to an 'evaporation' of chromospheric material, the cooling time scales L(exp 5/6)/p(exp 1/6), where the coronal phase (defined as the time maximum temperature). When the conductive cooling is static, the cooling time scales as L(exp 3/4)n(exp 1/4). In deriving these results, use was made of an important scaling law (T proportional to n(exp 2)) during the radiative cooling phase that was forst noted in one-dimensional hydrodynamic numerical simulations (Serio et al. 1991; Jakimiec et al. 1992). Our own simulations show that this result is restricted to approximately the radiative loss function of Rosner, Tucker, & Vaiana (1978). for different radiative loss functions, other scaling result, with T and n scaling almost linearly when the radiative loss falls off as T(exp -2). It is shown that these scaling laws are part of a class of analytic solutions developed by Antiocos (1980).

Direct Analysis in Real Time Mass Spectrometry for Characterization of Large Saccharides.

PubMed

Ma, Huiying; Jiang, Qing; Dai, Diya; Li, Hongli; Bi, Wentao; Da Yong Chen, David

2018-03-06

Polysaccharide characterization posts the most difficult challenge to available analytical technologies compared to other types of biomolecules. Plant polysaccharides are reported to have numerous medicinal values, but their effect can be different based on the types of plants, and even regions of productions and conditions of cultivation. However, the molecular basis of the differences of these polysaccharides is largely unknown. In this study, direct analysis in real time mass spectrometry (DART-MS) was used to generate polysaccharide fingerprints. Large saccharides can break down into characteristic small fragments in the DART source via pyrolysis, and the products are then detected by high resolution MS. Temperature was shown to be a crucial parameter for the decomposition of large polysaccharide. The general behavior of carbohydrates in DART-MS was also studied through the investigation of a number of mono- and oligosaccharide standards. The chemical formula and putative ionic forms of the fragments were proposed based on accurate mass with less than 10 ppm mass errors. Multivariate data analysis shows the clear differentiation of different plant species. Intensities of marker ions compared among samples also showed obvious differences. The combination of DART-MS analysis and mechanochemical extraction method used in this work demonstrates a simple, fast, and high throughput analytical protocol for the efficient evaluation of molecular features in plant polysaccharides.

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

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.

A general power equation for predicting bed load transport rates in gravel bed rivers

Treesearch

Jeffrey J. Barry; John M. Buffington; John G. King

2004-01-01

A variety of formulae has been developed to predict bed load transport in gravel bed rivers, ranging from simple regressions to complex multiparameter formulations. The ability to test these formulae across numerous field sites has, until recently, been hampered by a paucity of bed load transport data for gravel bed rivers. We use 2104 bed load transport observations...

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.

Chemical Methods to Prepare [60]Fulleranes

NASA Astrophysics Data System (ADS)

Briggs, Jonathan B.; Miller, Glen P.

Most known chemical methods to prepare hydrogenated [60]fullerenes or [60]fulleranes are described with an emphasis on those methods that are of historical significance and/or convenient, scalable and high yielding. Separate sections are dedicated to C60H2, C60H4-16, C60H18, C60H36, and C60H>36. The simplest of all [60]fullerane derivatives, 1,2-C60H2, is prepared in good isolated yield using either a NaBH4 reduction (59% isolated) or a Zn(Cu) couple reduction (66% isolated). A few C60H4 (e.g., 1,2,3,4-C60H4) and C60H6 (e.g., 1,2,33,41,42,50-C60H6) isomers have been formed and identified using structure sensitive analytical techniques but evidence for [60]fulleranes of formula C60H8-16 is based largely upon structure insensitive mass spectrometry data. Crown shaped C 3v C60H18 is the only [60]fullerane species that can be produced in high yield using multiple synthetic methods. It is a stable, easily isolable species of limited solubility that persists for years. Of the synthetic methodologies available, the polyamine chemistries [conventional heating or microwave irradiation] are best because the yields are excellent, the reactions are scalable, only standard glassware is required, the work-up is simple, and no purification is required. Birch reductions, transfer hydrogenations and Zn-acid conditions all lead to mixtures of C60H36 isomers in good yield. Of these methods, the transfer hydrogenation reaction gives the cleanest product slate with formation of three isomers possessing C 1 symmetry (60-70%), C 3 symmetry (25-30%) and T symmetry (2-5%), respectively. The formation of [60]fulleranes with more than 36 hydrogens is well documented but the products have generally escaped characterization by structure sensitive analytical techniques. No single isomer of formula C60H>36 has ever been isolated.

Electroacoustic theory for concentrated colloids with overlapped DLs at arbitrary kappa alpha. I. Application to nanocolloids and nonaqueous colloids.

PubMed

Shilov, V N; Borkovskaja, Y B; Dukhin, A S

2004-09-15

Existing theories of electroacoustic phenomena in concentrated colloids neglect the possibility of double layer overlap and are valid mostly for the "thin double layer," when the double layer thickness is much less than the particle size. In this paper we present a new electroacoustic theory which removes this restriction. This would make this new theory applicable to characterizing a variety of aqueous nanocolloids and of nonaqueous dispersions. There are two versions of the theory leading to the analytical solutions. The first version corresponds to strongly overlapped diffuse layers (so-called quasi-homogeneous model). It yields a simple analytical formula for colloid vibration current (CVI), which is valid for arbitrary ultrasound frequency, but for restricted kappa alpha range. This version of the theory, as well the Smoluchowski theory for microelectrophoresis, is independent of particle shape and polydispersity. This makes it very attractive for practical use, with the hope that it might be as useful as classical Smoluchowski theory. In order to determine the kappa alpha range of the quasi-homogeneous model validity we develop the second version that limits ultrasound frequency, but applies no restriction on kappa alpha. The ultrasound frequency should substantially exceed the Maxwell-Wagner relaxation frequency. This limitation makes active conductivity related current negligible compared to the passive dielectric displacement current. It is possible to derive an expression for CVI in the concentrated dispersion as formulae inhering definite integrals with integrands depending on equilibrium potential distribution. This second version allowed us to estimate the ranges of the applicability of the first, quasi-homogeneous version. It turns out that the quasi-homogeneous model works for kappa alpha values up to almost 1. For instance, at volume fraction 30%, the highest kappa alpha limit of the quasi-homogeneous model is 0.65. Therefore, this version of the electroacoustic theory is valid for almost all nonaqueous dispersions and a wide variety of nanocolloids, especially with sizes under 100 nm.

Prediction of transmission loss through an aircraft sidewall using statistical energy analysis

NASA Astrophysics Data System (ADS)

Ming, Ruisen; Sun, Jincai

1989-06-01

The transmission loss of randomly incident sound through an aircraft sidewall is investigated using statistical energy analysis. Formulas are also obtained for the simple calculation of sound transmission loss through single- and double-leaf panels. Both resonant and nonresonant sound transmissions can be easily calculated using the formulas. The formulas are used to predict sound transmission losses through a Y-7 propeller airplane panel. The panel measures 2.56 m x 1.38 m and has two windows. The agreement between predicted and measured values through most of the frequency ranges tested is quite good.

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.

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.

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.

Evidence for the confinement of magnetic monopoles in quantum spin ice.

PubMed

Sarte, P M; Aczel, A A; Ehlers, G; Stock, C; Gaulin, B D; Mauws, C; Stone, M B; Calder, S; Nagler, S E; Hollett, J W; Zhou, H D; Gardner, J S; Attfield, J P; Wiebe, C R

2017-10-19

Magnetic monopoles are hypothesised elementary particles connected by Dirac strings that behave like infinitely thin solenoids (Dirac 1931 Proc. R. Soc. A 133 60). Despite decades of searching, free magnetic monopoles and their Dirac strings have eluded experimental detection, although there is substantial evidence for deconfined magnetic monopole quasiparticles in spin ice materials (Castelnovo et al 2008 Nature 326 411). Here we report the detection of a hierarchy of unequally-spaced magnetic excitations via high resolution inelastic neutron spectroscopic measurements on the quantum spin ice candidate [Formula: see text] [Formula: see text] [Formula: see text]. These excitations are well-described by a simple model of monopole pairs bound by a linear potential (Coldea et al Science 327 177) with an effective tension of 0.642(8) K [Formula: see text] at 1.65 K. The success of the linear potential model suggests that these low energy magnetic excitations are direct spectroscopic evidence for the confinement of magnetic monopole quasiparticles in the quantum spin ice candidate [Formula: see text] [Formula: see text] [Formula: see text].

A forecast for extinction debt in the presence of speciation.

PubMed

Sgardeli, Vasiliki; Iwasa, Yoh; Varvoglis, Harry; Halley, John M

2017-02-21

Predicting biodiversity relaxation following a disturbance is of great importance to conservation biology. Recently-developed models of stochastic community assembly allow us to predict the evolution of communities on the basis of mechanistic processes at the level of individuals. The neutral model of biodiversity, in particular, has provided closed-form solutions for the relaxation of biodiversity in isolated communities (no immigration or speciation). Here, we extend these results by deriving a relaxation curve for a neutral community in which new species are introduced through the mechanism of random fission speciation (RFS). The solution provides simple closed-form expressions for the equilibrium species richness, the relaxation time and the species-individual curve, which are good approximation to the more complicated formulas existing for the same model. The derivation of the relaxation curve is based on the assumption of a broken-stick species-abundance distribution (SAD) as an initial community configuration; yet for commonly observed SADs, the maximum deviation from the curve does not exceed 10%. Importantly, the solution confirms theoretical results and observations showing that the relaxation time increases with community size and thus habitat area. Such simple and analytically tractable models can help crystallize our ideas on the leading factors affecting biodiversity loss. Copyright © 2016 Elsevier Ltd. All rights reserved.

A Comprehensive Physical Impedance Model of Polymer Electrolyte Fuel Cell Cathodes in Oxygen-free Atmosphere.

PubMed

Obermaier, Michael; Bandarenka, Aliaksandr S; Lohri-Tymozhynsky, Cyrill

2018-03-21

Electrochemical impedance spectroscopy (EIS) is an indispensable tool for non-destructive operando characterization of Polymer Electrolyte Fuel Cells (PEFCs). However, in order to interpret the PEFC's impedance response and understand the phenomena revealed by EIS, numerous semi-empirical or purely empirical models are used. In this work, a relatively simple model for PEFC cathode catalyst layers in absence of oxygen has been developed, where all the equivalent circuit parameters have an entire physical meaning. It is based on: (i) experimental quantification of the catalyst layer pore radii, (ii) application of De Levie's analytical formula to calculate the response of a single pore, (iii) approximating the ionomer distribution within every pore, (iv) accounting for the specific adsorption of sulfonate groups and (v) accounting for a small H 2 crossover through ~15 μm ionomer membranes. The derived model has effectively only 6 independent fitting parameters and each of them has clear physical meaning. It was used to investigate the cathode catalyst layer and the double layer capacitance at the interface between the ionomer/membrane and Pt-electrocatalyst. The model has demonstrated excellent results in fitting and interpretation of the impedance data under different relative humidities. A simple script enabling fitting of impedance data is provided as supporting information.

TRIGRS - A Fortran Program for Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Analysis, Version 2.0

USGS Publications Warehouse

Baum, Rex L.; Savage, William Z.; Godt, Jonathan W.

2008-01-01

The Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Model (TRIGRS) is a Fortran program designed for modeling the timing and distribution of shallow, rainfall-induced landslides. The program computes transient pore-pressure changes, and attendant changes in the factor of safety, due to rainfall infiltration. The program models rainfall infiltration, resulting from storms that have durations ranging from hours to a few days, using analytical solutions for partial differential equations that represent one-dimensional, vertical flow in isotropic, homogeneous materials for either saturated or unsaturated conditions. Use of step-function series allows the program to represent variable rainfall input, and a simple runoff routing model allows the user to divert excess water from impervious areas onto more permeable downslope areas. The TRIGRS program uses a simple infinite-slope model to compute factor of safety on a cell-by-cell basis. An approximate formula for effective stress in unsaturated materials aids computation of the factor of safety in unsaturated soils. Horizontal heterogeneity is accounted for by allowing material properties, rainfall, and other input values to vary from cell to cell. This command-line program is used in conjunction with geographic information system (GIS) software to prepare input grids and visualize model results.

Vector-based model of elastic bonds for simulation of granular solids.

PubMed

Kuzkin, Vitaly A; Asonov, Igor E

2012-11-01

A model (further referred to as the V model) for the simulation of granular solids, such as rocks, ceramics, concrete, nanocomposites, and agglomerates, composed of bonded particles (rigid bodies), is proposed. It is assumed that the bonds, usually representing some additional gluelike material connecting particles, cause both forces and torques acting on the particles. Vectors rigidly connected with the particles are used to describe the deformation of a single bond. The expression for potential energy of the bond and corresponding expressions for forces and torques are derived. Formulas connecting parameters of the model with longitudinal, shear, bending, and torsional stiffnesses of the bond are obtained. It is shown that the model makes it possible to describe any values of the bond stiffnesses exactly; that is, the model is applicable for the bonds with arbitrary length/thickness ratio. Two different calibration procedures depending on bond length/thickness ratio are proposed. It is shown that parameters of the model can be chosen so that under small deformations the bond is equivalent to either a Bernoulli-Euler beam or a Timoshenko beam or short cylinder connecting particles. Simple analytical expressions, relating parameters of the V model with geometrical and mechanical characteristics of the bond, are derived. Two simple examples of computer simulation of thin granular structures using the V model are given.

Simple versus composite indicators of socioeconomic status in resource allocation formulae: the case of the district resource allocation formula in Malawi

PubMed Central

2010-01-01

Background The district resource allocation formula in Malawi was recently reviewed to include stunting as a proxy measure of socioeconomic status. In many countries where the concept of need has been incorporated in resource allocation, composite indicators of socioeconomic status have been used. In the Malawi case, it is important to ascertain whether there are differences between using single variable or composite indicators of socioeconomic status in allocations made to districts, holding all other factors in the resource allocation formula constant. Methods Principal components analysis was used to calculate asset indices for all districts from variables that capture living standards using data from the Malawi Multiple Indicator Cluster Survey 2006. These were normalized and used to weight district populations. District proportions of national population weighted by both the simple and composite indicators were then calculated for all districts and compared. District allocations were also calculated using the two approaches and compared. Results The two types of indicators are highly correlated, with a spearman rank correlation coefficient of 0.97 at the 1% level of significance. For 21 out of the 26 districts included in the study, proportions of national population weighted by the simple indicator are higher by an average of 0.6 percentage points. For the remaining 5 districts, district proportions of national population weighted by the composite indicator are higher by an average of 2 percentage points. Though the average percentage point differences are low and the actual allocations using both approaches highly correlated (ρ of 0.96), differences in actual allocations exceed 10% for 8 districts and have an average of 4.2% for the remaining 17. For 21 districts allocations based on the single variable indicator are higher. Conclusions Variations in district allocations made using either the simple or composite indicators of socioeconomic status are not statistically different to recommend one over the other. However, the single variable indicator is favourable for its ease of computation. PMID:20053274

The Torsion of Members Having Sections Common in Aircraft Construction

NASA Technical Reports Server (NTRS)

Trayer, George W; March, H W

1930-01-01

Within recent years a great variety of approximate torsion formulas and drafting-room processes have been advocated. In some of these, especially where mathematical considerations are involved, the results are extremely complex and are not generally intelligible to engineers. The principal object of this investigation was to determine by experiment and theoretical investigation how accurate the more common of these formulas are and on what assumptions they are founded and, if none of the proposed methods proved to be reasonable accurate in practice, to produce simple, practical formulas from reasonably correct assumptions, backed by experiment. A second object was to collect in readily accessible form the most useful of known results for the more common sections. Formulas for all the important solid sections that have yielded to mathematical treatment are listed. Then follows a discussion of the torsion of tubular rods with formulas both rigorous and approximate.

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

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.

Necessary and sufficient conditions for R₀ to be a sum of contributions of fertility loops.

PubMed

Rueffler, Claus; Metz, Johan A J

2013-03-01

Recently, de-Camino-Beck and Lewis (Bull Math Biol 69:1341-1354, 2007) have presented a method that under certain restricted conditions allows computing the basic reproduction ratio R₀ in a simple manner from life cycle graphs, without, however, giving an explicit indication of these conditions. In this paper, we give various sets of sufficient and generically necessary conditions. To this end, we develop a fully algebraic counterpart of their graph-reduction method which we actually found more useful in concrete applications. Both methods, if they work, give a simple algebraic formula that can be interpreted as the sum of contributions of all fertility loops. This formula can be used in e.g. pest control and conservation biology, where it can complement sensitivity and elasticity analyses. The simplest of the necessary and sufficient conditions is that, for irreducible projection matrices, all paths from birth to reproduction have to pass through a common state. This state may be visible in the state representation for the chosen sampling time, but the passing may also occur in between sampling times, like a seed stage in the case of sampling just before flowering. Note that there may be more than one birth state, like when plants in their first year can already have different sizes at the sampling time. Also the common state may occur only later in life. However, in all cases R₀ allows a simple interpretation as the expected number of new individuals that in the next generation enter the common state deriving from a single individual in this state. We end with pointing to some alternative algebraically simple quantities with properties similar to those of R₀ that may sometimes be used to good effect in cases where no simple formula for R₀ exists.

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.

Length filtration of the separable states.

PubMed

Chen, Lin; Ðoković, Dragomir Ž

2016-11-01

We investigate the separable states ρ of an arbitrary multi-partite quantum system with Hilbert space [Formula: see text] of dimension d . The length L ( ρ ) of ρ is defined as the smallest number of pure product states having ρ as their mixture. The length filtration of the set of separable states, [Formula: see text], is the increasing chain [Formula: see text], where [Formula: see text]. We define the maximum length, [Formula: see text], critical length, L crit , and yet another special length, L c , which was defined by a simple formula in one of our previous papers. The critical length indicates the first term in the length filtration whose dimension is equal to [Formula: see text]. We show that in general d ≤ L c ≤ L crit ≤ L max ≤ d 2 . We conjecture that the equality L crit = L c holds for all finite-dimensional multi-partite quantum systems. Our main result is that L crit = L c for the bipartite systems having a single qubit as one of the parties. This is accomplished by computing the rank of the Jacobian matrix of a suitable map having [Formula: see text] as its range.

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.

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.

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.

Detection of β-Thalassemia Carriers by Red Cell Parameters Obtained from Automatic Counters using Mathematical Formulas

PubMed Central

Roth, Idit Lachover; Lachover, Boaz; Koren, Guy; Levin, Carina; Zalman, Luci; Koren, Ariel

2018-01-01

Background β-thalassemia major is a severe disease with high morbidity. The world prevalence of carriers is around 1.5–7%. The present study aimed to find a reliable formula for detecting β-thalassemia carriers using an extensive database of more than 22,000 samples obtained from a homogeneous population of childbearing age women with 3161 (13.6%) of β-thalassemia carriers and to check previously published formulas. Methods We applied a mathematical method based on the support vector machine (SVM) algorithm in the search for a reliable formula that can differentiate between thalassemia carriers and non-carriers, including normal counts or counts suspected to belong to iron-deficient women. Results Shine’s formula and our SVM formula showed >98% sensitivity and >99.77% negative predictive value (NPV). All other published formulas gave inferior results. Conclusions We found a reliable formula that can be incorporated into any automatic blood counter to alert health providers to the possibility of a woman being a β-thalassemia carrier. A further simple hemoglobin characterization by HPLC analysis should be performed to confirm the diagnosis, and subsequent family studies should be carried out. Our SVM formula is currently limited to women of fertility age until further analysis in other groups can be performed. PMID:29326805

Estimation of standard liver volume in Chinese adult living donors.

PubMed

Fu-Gui, L; Lu-Nan, Y; Bo, L; Yong, Z; Tian-Fu, W; Ming-Qing, X; Wen-Tao, W; Zhe-Yu, C

2009-12-01

To determine a formula predicting the standard liver volume based on body surface area (BSA) or body weight in Chinese adults. A total of 115 consecutive right-lobe living donors not including the middle hepatic vein underwent right hemi-hepatectomy. No organs were used from prisoners, and no subjects were prisoners. Donor anthropometric data including age, gender, body weight, and body height were recorded prospectively. The weights and volumes of the right lobe liver grafts were measured at the back table. Liver weights and volumes were calculated from the right lobe graft weight and volume obtained at the back table, divided by the proportion of the right lobe on computed tomography. By simple linear regression analysis and stepwise multiple linear regression analysis, we correlated calculated liver volume and body height, body weight, or body surface area. The subjects had a mean age of 35.97 +/- 9.6 years, and a female-to-male ratio of 60:55. The mean volume of the right lobe was 727.47 +/- 136.17 mL, occupying 55.59% +/- 6.70% of the whole liver by computed tomography. The volume of the right lobe was 581.73 +/- 96.137 mL, and the estimated liver volume was 1053.08 +/- 167.56 mL. Females of the same body weight showed a slightly lower liver weight. By simple linear regression analysis and stepwise multiple linear regression analysis, a formula was derived based on body weight. All formulae except the Hong Kong formula overestimated liver volume compared to this formula. The formula of standard liver volume, SLV (mL) = 11.508 x body weight (kg) + 334.024, may be applied to estimate liver volumes in Chinese adults.

Analytical approximations for spatial stochastic gene expression in single cells and tissues

PubMed Central

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2016-01-01

Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686

Depletion region surface effects in electron beam induced current measurements.

PubMed

Haney, Paul M; Yoon, Heayoung P; Gaury, Benoit; Zhitenev, Nikolai B

2016-09-07

Electron beam induced current (EBIC) is a powerful characterization technique which offers the high spatial resolution needed to study polycrystalline solar cells. Current models of EBIC assume that excitations in the p - n junction depletion region result in perfect charge collection efficiency. However we find that in CdTe and Si samples prepared by focused ion beam (FIB) milling, there is a reduced and nonuniform EBIC lineshape for excitations in the depletion region. Motivated by this, we present a model of the EBIC response for excitations in the depletion region which includes the effects of surface recombination from both charge-neutral and charged surfaces. For neutral surfaces we present a simple analytical formula which describes the numerical data well, while the charged surface response depends qualitatively on the location of the surface Fermi level relative to the bulk Fermi level. We find the experimental data on FIB-prepared Si solar cells is most consistent with a charged surface, and discuss the implications for EBIC experiments on polycrystalline materials.

Quantum mechanical/molecular mechanical/continuum style solvation model: linear response theory, variational treatment, and nuclear gradients.

PubMed

Li, Hui

2009-11-14

Linear response and variational treatment are formulated for Hartree-Fock (HF) and Kohn-Sham density functional theory (DFT) methods and combined discrete-continuum solvation models that incorporate self-consistently induced dipoles and charges. Due to the variational treatment, analytic nuclear gradients can be evaluated efficiently for these discrete and continuum solvation models. The forces and torques on the induced point dipoles and point charges can be evaluated using simple electrostatic formulas as for permanent point dipoles and point charges, in accordance with the electrostatic nature of these methods. Implementation and tests using the effective fragment potential (EFP, a polarizable force field) method and the conductorlike polarizable continuum model (CPCM) show that the nuclear gradients are as accurate as those in the gas phase HF and DFT methods. Using B3LYP/EFP/CPCM and time-dependent-B3LYP/EFP/CPCM methods, acetone S(0)-->S(1) excitation in aqueous solution is studied. The results are close to those from full B3LYP/CPCM calculations.

Failsafe modes in incomplete minority game

NASA Astrophysics Data System (ADS)

Yao, Xiaobo; Wan, Shaolong; Chen, Wen

2009-09-01

We make a failsafe extension to the incomplete minority game model, give a brief analysis on how incompleteness will effect system efficiency. Simulations that limited incompleteness in strategies can improve the system efficiency. Among three failsafe modes, the “Back-to-Best” mode brings most significant improvement and keeps the system efficiency in a long range of incompleteness. A simple analytic formula has a trend which matches simulation results. The IMMG model is used to study the effect of distribution, and we find that there is one junction point in each series of curves, at which system efficiency is not influenced by the distribution of incompleteness. When pIbar > the concentration of incompleteness weakens the effect. On the other side of , concentration will be helpful. When pI is close to zero agents using incomplete strategies have on average better profits than those using standard strategies, and the “Back-to-Best” agents have a wider range of pI to win.

Storage Capacity of Generalized Palimpsests

NASA Astrophysics Data System (ADS)

Bonnaz, D.

1997-12-01

A simple analytical study of a short term memory model is performed. This model consists of a symmetric p-neuron interaction between N neurons. Learning is achieved by a generalized Hebb rule. Saturation is prevented by the introduction of a bound A to the couplings. At each time step, an input pattern is drawn at random, independently of the previous ones. The determination of the life time T of a memorized pattern viewed as a function of A and N is accomplished by a statistical study of the dynamic of the learning process which has been made possible under the assumption that the couplings evolve independently. This simplification reduces the determination of T to a one-dimensional problem, by considering energies rather than couplings. The choice of the optimal value A_opt of A is a compromise between the success of the learning process and the maximization of T. The essential results are expressed by the formulae Tpropto A^2 and A_optpropto N^{frac{p-1}{2}}.

Simulation of wind turbine wakes using the actuator line technique.

PubMed

Sørensen, Jens N; Mikkelsen, Robert F; Henningson, Dan S; Ivanell, Stefan; Sarmast, Sasan; Andersen, Søren J

2015-02-28

The actuator line technique was introduced as a numerical tool to be employed in combination with large eddy simulations to enable the study of wakes and wake interaction in wind farms. The technique is today largely used for studying basic features of wakes as well as for making performance predictions of wind farms. In this paper, we give a short introduction to the wake problem and the actuator line methodology and present a study in which the technique is employed to determine the near-wake properties of wind turbines. The presented results include a comparison of experimental results of the wake characteristics of the flow around a three-bladed model wind turbine, the development of a simple analytical formula for determining the near-wake length behind a wind turbine and a detailed investigation of wake structures based on proper orthogonal decomposition analysis of numerically generated snapshots of the wake. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

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

Kyriakou, Ioanna; Emfietzoglou, Dimitris; Nojeh, Alireza

A systematic study of electron-beam penetration and backscattering in multi-walled carbon nanotube (MWCNT) materials for beam energies of {approx}0.3 to 30 keV is presented based on event-by-event Monte Carlo simulation of electron trajectories using state-of-the-art scattering cross sections. The importance of different analytic approximations for computing the elastic and inelastic electron-scattering cross sections for MWCNTs is emphasized. We offer a simple parameterization for the total and differential elastic-scattering Mott cross section, using appropriate modifications to the Browning formula and the Thomas-Fermi screening parameter. A discrete-energy-loss approach to inelastic scattering based on dielectric theory is adopted using different descriptions of themore » differential cross section. The sensitivity of electron penetration and backscattering parameters to the underlying scattering models is examined. Our simulations confirm the recent experimental backscattering data on MWCNT forests and, in particular, the steep increase of the backscattering yield at sub-keV energies as well as the sidewalls escape effect at high-beam energies.« less

Optimization of single-base-pair mismatch discrimination in oligonucleotide microarrays

NASA Technical Reports Server (NTRS)

Urakawa, Hidetoshi; El Fantroussi, Said; Smidt, Hauke; Smoot, James C.; Tribou, Erik H.; Kelly, John J.; Noble, Peter A.; Stahl, David A.

2003-01-01

The discrimination between perfect-match and single-base-pair-mismatched nucleic acid duplexes was investigated by using oligonucleotide DNA microarrays and nonequilibrium dissociation rates (melting profiles). DNA and RNA versions of two synthetic targets corresponding to the 16S rRNA sequences of Staphylococcus epidermidis (38 nucleotides) and Nitrosomonas eutropha (39 nucleotides) were hybridized to perfect-match probes (18-mer and 19-mer) and to a set of probes having all possible single-base-pair mismatches. The melting profiles of all probe-target duplexes were determined in parallel by using an imposed temperature step gradient. We derived an optimum wash temperature for each probe and target by using a simple formula to calculate a discrimination index for each temperature of the step gradient. This optimum corresponded to the output of an independent analysis using a customized neural network program. These results together provide an experimental and analytical framework for optimizing mismatch discrimination among all probes on a DNA microarray.

Self-consistent approach for neutral community models with speciation

NASA Astrophysics Data System (ADS)

Haegeman, Bart; Etienne, Rampal S.

2010-03-01

Hubbell’s neutral model provides a rich theoretical framework to study ecological communities. By incorporating both ecological and evolutionary time scales, it allows us to investigate how communities are shaped by speciation processes. The speciation model in the basic neutral model is particularly simple, describing speciation as a point-mutation event in a birth of a single individual. The stationary species abundance distribution of the basic model, which can be solved exactly, fits empirical data of distributions of species’ abundances surprisingly well. More realistic speciation models have been proposed such as the random-fission model in which new species appear by splitting up existing species. However, no analytical solution is available for these models, impeding quantitative comparison with data. Here, we present a self-consistent approximation method for neutral community models with various speciation modes, including random fission. We derive explicit formulas for the stationary species abundance distribution, which agree very well with simulations. We expect that our approximation method will be useful to study other speciation processes in neutral community models as well.

Prediction of apparent extinction for optical transmission through rain

NASA Astrophysics Data System (ADS)

Vasseur, H.; Gibbins, C. J.

1996-12-01

At optical wavelengths, geometrical optics holds that the extinction efficiency of raindrops is equal to two. This approximation yields a wavelength-independent extinction coefficient that, however, can hardly be used to predict accurately rain extinction measured in optical transmissions. Actually, in addition to the extinct direct incoming light, a significant part of the power scattered by the rain particles reaches the receiver. This leads to a reduced apparent extinction that depends on both rain characteristics and link parameters. A simple method is proposed to evaluate this apparent extinction. It accounts for the additional scattered power that enters the receiver when one considers the forward-scattering pattern of the raindrops as well as the multiple-scattering effects using, respectively, the Fraunhofer diffraction and Twersky theory. It results in a direct analytical formula that enables a quick and accurate estimation of the rain apparent extinction and highlights the influence of the link parameters. Predictions of apparent extinction through rain are found in excellent agreement with measurements in the visible and IR regions.

Phase derivative method for reconstruction of slightly off-axis digital holograms.

PubMed

Guo, Cheng-Shan; Wang, Ben-Yi; Sha, Bei; Lu, Yu-Jie; Xu, Ming-Yuan

2014-12-15

A phase derivative (PD) method is proposed for reconstruction of off-axis holograms. In this method, a phase distribution of the tested object wave constrained within 0 to pi radian is firstly worked out by a simple analytical formula; then it is corrected to its right range from -pi to pi according to the sign characteristics of its first-order derivative. A theoretical analysis indicates that this PD method is particularly suitable for reconstruction of slightly off-axis holograms because it only requires the spatial frequency of the reference beam larger than spatial frequency of the tested object wave in principle. In addition, because the PD method belongs to a pure local method with no need of any integral operation or phase shifting algorithm in process of the phase retrieval, it could have some advantages in reducing computer load and memory requirements to the image processing system. Some experimental results are given to demonstrate the feasibility of the method.

Computational expressions for signals in frequency-modulation spectroscopy

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

Di Rosa, Michael D.; Reiten, M. T.

2015-05-25

In this study, general expressions for the signals in frequency-modulation spectroscopy (FMS) appear in the literature but are often reduced to simple analytical equations following the assumption of a weak modulation index. This is little help to the experimentalist who wants to predict signals for modulation depths of the order of unity or greater, where strong FMS signals reside. Here, we develop general formulas for FMS signals in the case of an absorber with a Voigt line shape and then link these expressions to an example and existing numerical code for the line shape. The resulting computational recipe is easymore » to implement and exercised here to show where the larger FMS signals are found over the coordinates of modulation index and modulation frequency. One can also estimate from provided curves the in-phase FMS signal over a wide range of modulation parameters at either the Lorentzian-broadening or Doppler-broadening limit, or anywhere in between by interpolation.« less

Universality of next-to-leading power threshold effects for colourless final states in hadronic collisions

NASA Astrophysics Data System (ADS)

Del Duca, V.; Laenen, E.; Magnea, L.; Vernazza, L.; White, C. D.

2017-11-01

We consider the production of an arbitrary number of colour-singlet particles near partonic threshold, and show that next-to-leading order cross sections for this class of processes have a simple universal form at next-to-leading power (NLP) in the energy of the emitted gluon radiation. Our analysis relies on a recently derived factorisation formula for NLP threshold effects at amplitude level, and therefore applies both if the leading-order process is tree-level and if it is loop-induced. It holds for differential distributions as well. The results can furthermore be seen as applications of recently derived next-to-soft theorems for gauge theory amplitudes. We use our universal expression to re-derive known results for the production of up to three Higgs bosons at NLO in the large top mass limit, and for the hadro-production of a pair of electroweak gauge bosons. Finally, we present new analytic results for Higgs boson pair production at NLO and NLP, with exact top-mass dependence.

Electron Cyclotron Current Drive Efficiency in General Tokamak Geometry and Its Application to Advanced Tokamak Plasmas

NASA Astrophysics Data System (ADS)

Lin-Liu, Y. R.; Chan, V. S.; Luce, T. C.; Prater, R.

1998-11-01

Owing to relativistic mass shift in the cyclotron resonance condition, a simple and accurate interpolation formula for estimating the current drive efficiency, such as those(S.C. Chiu et al.), Nucl. Fusion 29, 2175 (1989).^,(D.A. Ehst and C.F.F. Karney, Nucl. Fusion 31), 1933 (1991). commonly used in FWCD, is not available in the case of ECCD. In this work, we model ECCD using the adjoint techniques. A semi-analytic adjoint function appropriate for general tokamak geometry is obtained using Fisch's relativistic collision model. Predictions of off-axis ECCD qualitatively and semi-quantitatively agrees with those of Cohen,(R.H. Cohen, Phys. Fluids 30), 2442 (1987). currently implemented in the raytracing code TORAY. The dependences of the current drive efficiency on the wave launch configuration and the plasma parameters will be presented. Strong absorption of the wave away from the resonance layer is shown to be an important factor in optimizing the off-axis ECCD for application to advanced tokamak operations.

Reflection by absorbing periodically stratified media

NASA Astrophysics Data System (ADS)

Lekner, John

2014-03-01

Existing theory gives the optical properties of a periodically stratified medium in terms of a two by two matrix. This theory is valid also for absorbing media, because the matrix remains unimodular. The main effect of absorption is that the reflection (of either polarization) becomes independent of the number of periods N, and of the substrate properties, provided N exceeds a certain value which depends on the absorption. The s and p reflections are then given by simple formulae. The stop-band structure, which gives total reflection in bands of frequency and angle of incidence in the non-absorbing case, remains influential in weakly absorbing media, causing strong variations in reflectivity. The theory is applied to the frequency dependence of the normal-incidence reflectivity of a quarter-wave stack in which the high-index and low-index layers both absorb weakly. Analytical expressions are obtained for the frequency at which the reflectivity is maximum, the maximum reflectivity, and also for the reflectivity at the band edges of the stop band of the non-absorbing stack.

DECOMPOSITION OF THE PARTICLE AND CONNECTION OF PARTICLES IN THE TERMINI OF THE MOMENTUM SPACE

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

Chernikov, N.A.

1958-01-01

>Geometric and algebraic notions and ideas are used to obtain a geometric interpretation of the kinematics of nuclear reactions. Thus, extended analytic calculations combined with the transition from one reference system to another, are replaced by simple formulas of the hyperbolic trigonometry. Let a particle move with the velocity a in a reference system which moves with the velocity o. Then the modulus of the three-dimensional impulse of the particle is p/sub 0a/ = m c sh oa-bar/c, where m is the resting miss, c is the velocity of the light, oa-bar is the distance of the points o andmore » a in the momentum space. The kinetic energy epsilon /sub oa/ of the particle in the system o is epsilon / sub oa/=m c/sup 2/STAoa-bar/c-1!. Then the ratio epsilon /sub oa/m is the area divided by 2 pi of a circle of radius oa in the momentum space. (TCO)« less

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.

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.

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.

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.

An admissible level \\widehat{osp} ( 1 \\big \\vert 2 ) -model: modular transformations and the Verlinde formula

NASA Astrophysics Data System (ADS)

Snadden, John; Ridout, David; Wood, Simon

2018-05-01

The modular properties of the simple vertex operator superalgebra associated with the affine Kac-Moody superalgebra \\widehat{{osp}} (1|2) at level -5/4 are investigated. After classifying the relaxed highest-weight modules over this vertex operator superalgebra, the characters and supercharacters of the simple weight modules are computed and their modular transforms are determined. This leads to a complete list of the Grothendieck fusion rules by way of a continuous superalgebraic analog of the Verlinde formula. All Grothendieck fusion coefficients are observed to be non-negative integers. These results indicate that the extension to general admissible levels will follow using the same methodology once the classification of relaxed highest-weight modules is completed.

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.

Weight shifting operators and conformal blocks

NASA Astrophysics Data System (ADS)

Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David

2018-02-01

We introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involving operators with spin in conformal field theories. As an application, we derive a formula for a general conformal block (with arbitrary internal and external representations) in terms of derivatives of blocks for external scalars. In particular, our formula gives new expressions for "seed conformal blocks" in 3d and 4d CFTs. We also find simple derivations of identities between external-scalar blocks with different dimensions and internal spins. We comment on additional applications, including deriving recursion relations for general conformal blocks, reducing inversion formulae for spinning operators to inversion formulae for scalars, and deriving identities between general 6 j symbols (Racah-Wigner coefficients/"crossing kernels") of the conformal group.

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

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.

Geometrically derived difference formulae for the numerical integration of trajectory problems

NASA Technical Reports Server (NTRS)

Mcleod, R. J. Y.; Sanz-Serna, J. M.

1981-01-01

The term 'trajectory problem' is taken to include problems that can arise, for instance, in connection with contour plotting, or in the application of continuation methods, or during phase-plane analysis. Geometrical techniques are used to construct difference methods for these problems to produce in turn explicit and implicit circularly exact formulae. Based on these formulae, a predictor-corrector method is derived which, when compared with a closely related standard method, shows improved performance. It is found that this latter method produces spurious limit cycles, and this behavior is partly analyzed. Finally, a simple variable-step algorithm is constructed and tested.

Simplified formula for mean cycle-slip time of phase-locked loops with steady-state phase error.

NASA Technical Reports Server (NTRS)

Tausworthe, R. C.

1972-01-01

Previous work shows that the mean time from lock to a slipped cycle of a phase-locked loop is given by a certain double integral. Accurate numerical evaluation of this formula for the second-order loop is extremely vexing because the difference between exponentially large quantities is involved. The presented article demonstrates a method in which a much-reduced precision program can be used to obtain the mean first-cycle slip time for a loop of arbitrary degree tracking at a specified SNR and steady-state phase error. It also presents a simple approximate formula that is asymptotically tight at higher loop SNR.

Assessment of Simple Models for Molecular Simulation of Ethylene Carbonate and Propylene Carbonate as Solvents for Electrolyte Solutions.

PubMed

Chaudhari, Mangesh I; Muralidharan, Ajay; Pratt, Lawrence R; Rempe, Susan B

2018-02-12

Progress in understanding liquid ethylene carbonate (EC) and propylene carbonate (PC) on the basis of molecular simulation, emphasizing simple models of interatomic forces, is reviewed. Results on the bulk liquids are examined from the perspective of anticipated applications to materials for electrical energy storage devices. Preliminary results on electrochemical double-layer capacitors based on carbon nanotube forests and on model solid-electrolyte interphase (SEI) layers of lithium ion batteries are considered as examples. The basic results discussed suggest that an empirically parameterized, non-polarizable force field can reproduce experimental structural, thermodynamic, and dielectric properties of EC and PC liquids with acceptable accuracy. More sophisticated force fields might include molecular polarizability and Buckingham-model description of inter-atomic overlap repulsions as extensions to Lennard-Jones models of van der Waals interactions. Simple approaches should be similarly successful also for applications to organic molecular ions in EC/PC solutions, but the important case of Li[Formula: see text] deserves special attention because of the particularly strong interactions of that small ion with neighboring solvent molecules. To treat the Li[Formula: see text] ions in liquid EC/PC solutions, we identify interaction models defined by empirically scaled partial charges for ion-solvent interactions. The empirical adjustments use more basic inputs, electronic structure calculations and ab initio molecular dynamics simulations, and also experimental results on Li[Formula: see text] thermodynamics and transport in EC/PC solutions. Application of such models to the mechanism of Li[Formula: see text] transport in glassy SEI models emphasizes the advantage of long time-scale molecular dynamics studies of these non-equilibrium materials.

Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.

PubMed

Bratus, Alexander S; Novozhilov, Artem S; Semenov, Yuri S

2014-10-01

A particular case of the famous quasispecies model - the Crow-Kimura model with a permutation invariant fitness landscape - is investigated. Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special tridiagonal form, a change of the basis is suggested such that in the new coordinates a number of analytical results can be obtained. In particular, using the eigenvectors of the mutation matrix as the new basis, we show that the quasispecies distribution approaches a binomial one and give simple estimates for the speed of convergence. Another consequence of the suggested approach is a parametric solution to the system of equations determining the quasispecies. Using this parametric solution we show that our approach leads to exact asymptotic results in some cases, which are not covered by the existing methods. In particular, we are able to present not only the limit behavior of the leading eigenvalue (mean population fitness), but also the exact formulas for the limit quasispecies eigenvector for special cases. For instance, this eigenvector has a geometric distribution in the case of the classical single peaked fitness landscape. On the biological side, we propose a mathematical definition, based on the closeness of the quasispecies to the binomial distribution, which can be used as an operational definition of the notorious error threshold. Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs. Copyright © 2014 Elsevier Inc. All rights reserved.

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.

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).

Query Optimization by Semantic Reasoning.

DTIC Science & Technology

1981-05-01

condition holds, then formulas X and Y are said to be ,nerge-compatible. Let xi be the variable in X that corresponds to variable yj in Y (x is not...Davidson, Ramez EI-Masri, Sheldon Finkelstein, Hector Garcia, Mohammed Olumi, Tom Rogers, Neil Rowe, David Shaw, and Kyu-Young Whang . Special credit...for the simple queries, along with cost formulas and applicability conditions for the methods. Most recently has come the development of optimizers for

Alternatives to the Madison Formula, the Original Do-It Yourself Semitransparent Stain

Treesearch

Mark Knaebe

2013-01-01

The “Madison formula” was developed at the Forest Products Laboratory around 1950 as a simple linseed-oil-based finish that could be made from readily available components. It was one of the first formulations of its type—a penetrating finish that eliminated the problems with cracking and peeling commonly found with the oil-based paints available at that time. The...

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.

Simplified refracting technique in keratoconus.

PubMed

Gasset, A R

1975-01-01

A simple but effective technique to refract keratoconus patients is presented. The theoretical objection to these methods are discussed. In addition, a formula to calculate lenticular astigmatism is presented.

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.)

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.

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

A simple high-performance matrix-free biomass molten carbonate fuel cell without CO2 recirculation.

PubMed

Lan, Rong; Tao, Shanwen

2016-08-01

In previous reports, flowing CO2 at the cathode is essential for either conventional molten carbonate fuel cells (MCFCs) based on molten carbonate/LiAlO2 electrolytes or matrix-free MCFCs. For the first time, we demonstrate a high-performance matrix-free MCFC without CO2 recirculation. At 800°C, power densities of 430 and 410 mW/cm(2) are achieved when biomass-bamboo charcoal and wood, respectively-is used as fuel. At 600°C, a stable performance is observed during the measured 90 hours after the initial degradation. In this MCFC, CO2 is produced at the anode when carbon-containing fuels are used. The produced CO2 then dissolves and diffuses to the cathode to react with oxygen in open air, forming the required [Formula: see text] or [Formula: see text] ions for continuous operation. The dissolved [Formula: see text] ions may also take part in the cell reactions. This provides a simple new fuel cell technology to directly convert carbon-containing fuels such as carbon and biomass into electricity with high efficiency.

In Defense of the Formula Essay

ERIC Educational Resources Information Center

Haluska, Jan Charles

2007-01-01

In 1970, the author learned a simple step in making essays from his advisor. His advisor used a drawing of the Parthenon to illustrate the creation of a five-paragraph essay. It was obvious that his advisor was hesitant on teaching them a very simple concept of essay writing because it was pretty mechanical. Like his advisor, a lot of teachers…

TAKING THE LONG VIEW TOWARDS THE LONG WAR. Equipping General Purpose Force Leaders with Soft Power Tools for Irregular Warfare

DTIC Science & Technology

2009-02-12

equivalent to usual printing or typescript . Can read either representations of familiar formulaic verbal exchanges or simple language containing only...read simple, authentic written material in a form equivalent to usual printing or typescript on subjects within a familiar context. Able to read with

Reduction of chemical formulas from the isotopic peak distributions of high-resolution mass spectra.

PubMed

Roussis, Stilianos G; Proulx, Richard

2003-03-15

A method has been developed for the reduction of the chemical formulas of compounds in complex mixtures from the isotopic peak distributions of high-resolution mass spectra. The method is based on the principle that the observed isotopic peak distribution of a mixture of compounds is a linear combination of the isotopic peak distributions of the individual compounds in the mixture. All possible chemical formulas that meet specific criteria (e.g., type and number of atoms in structure, limits of unsaturation, etc.) are enumerated, and theoretical isotopic peak distributions are generated for each formula. The relative amount of each formula is obtained from the accurately measured isotopic peak distribution and the calculated isotopic peak distributions of all candidate formulas. The formulas of compounds in simple spectra, where peak components are fully resolved, are rapidly determined by direct comparison of the calculated and experimental isotopic peak distributions. The singular value decomposition linear algebra method is used to determine the contributions of compounds in complex spectra containing unresolved peak components. The principles of the approach and typical application examples are presented. The method is most useful for the characterization of complex spectra containing partially resolved peaks and structures with multiisotopic elements.

On the equivalent classification of three-dimensional competitive Leslie/Gower models via the boundary dynamics on the carrying simplex.

PubMed

Jiang, Jifa; Niu, Lei

2017-04-01

We study the asymptotic behavior of the competitive Leslie/Gower model (map) [Formula: see text]It is shown that T unconditionally admits a globally attracting 1-codimensional invariant hypersurface [Formula: see text], called carrying simplex, such that every nontrivial orbit is asymptotic to one in [Formula: see text]. More general and easily checked conditions to guarantee the existence of carrying simplex for competitive maps are provided. An equivalence relation is defined relative to local stability of fixed points on [Formula: see text] (the boundary of [Formula: see text]) on the space of all three-dimensional Leslie/Gower models. Using a formula on the sum of the indices of all fixed points on the carrying simplex for three-dimensional maps, we list the 33 stable equivalence classes in terms of simple inequalities on the parameters [Formula: see text] and [Formula: see text] and draw their orbits on [Formula: see text]. In classes 1-18, every nontrivial orbit tends to a fixed point on [Formula: see text]. In classes 19-25, each map possesses a unique positive fixed point which is a saddle on [Formula: see text], and hence Neimark-Sacker bifurcations do not occur. Neimark-Sacker bifurcation does occur within each of classes 26-31, while it does not occur in class 32. Each map from class 27 admits a heteroclinic cycle, which forms the boundary of [Formula: see text]. The criteria on the stability of heteroclinic cycles are also given. This classification makes it possible to further investigate various dynamical properties in respective class.

Elementary quantum mechanics of the neutron with an electric dipole moment.

PubMed

Baym, Gordon; Beck, D H

2016-07-05

The neutron, in addition to possibly having a permanent electric dipole moment as a consequence of violation of time-reversal invariance, develops an induced electric dipole moment in the presence of an external electric field. We present here a unified nonrelativistic description of these two phenomena, in which the dipole moment operator, [Formula: see text], is not constrained to lie along the spin operator. Although the expectation value of [Formula: see text] in the neutron is less than [Formula: see text] of the neutron radius, [Formula: see text], the expectation value of [Formula: see text] is of order [Formula: see text] We determine the spin motion in external electric and magnetic fields, as used in past and future searches for a permanent dipole moment, and show that the neutron electric polarizability, although entering the neutron energy in an external electric field, does not affect the spin motion. In a simple nonrelativistic model we show that the expectation value of the permanent dipole is, to lowest order, proportional to the product of the time-reversal-violating coupling strength and the electric polarizability of the neutron.

Iteration with Spreadsheets.

ERIC Educational Resources Information Center

Smith, Michael

1990-01-01

Presents several examples of the iteration method using computer spreadsheets. Examples included are simple iterative sequences and the solution of equations using the Newton-Raphson formula, linear interpolation, and interval bisection. (YP)

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

Validation of the replica trick for simple models

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-04-01

We discuss the replica analytic continuation using several simple models in order to prove mathematically the validity of the replica analysis, which is used in a wide range of fields related to large-scale complex systems. While replica analysis consists of two analytical techniques—the replica trick (or replica analytic continuation) and the thermodynamical limit (and/or order parameter expansion)—we focus our study on replica analytic continuation, which is the mathematical basis of the replica trick. We apply replica analysis to solve a variety of analytical models, and examine the properties of replica analytic continuation. Based on the positive results for these models we propose that replica analytic continuation is a robust procedure in replica analysis.

Fusion barrier characteristics of actinides

NASA Astrophysics Data System (ADS)

Manjunatha, H. C.; Sridhar, K. N.

2018-03-01

We have studied fusion barrier characteristics of actinide compound nuclei with atomic number range 89 ≤ Z ≤ 103 for all projectile target combinations. After the calculation of fusion barrier heights and positions, we have searched for their parameterization. We have achieved the empirical formula for fusion barrier heights (VB), positions (RB), curvature of the inverted parabola (ħω) of actinide compound nuclei with atomic number range 89 ≤ Z ≤ 103 for all projectile target combinations (6

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.

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.

Evolution of stochastic demography with life history tradeoffs in density-dependent age-structured populations.

PubMed

Lande, Russell; Engen, Steinar; Sæther, Bernt-Erik

2017-10-31

We analyze the stochastic demography and evolution of a density-dependent age- (or stage-) structured population in a fluctuating environment. A positive linear combination of age classes (e.g., weighted by body mass) is assumed to act as the single variable of population size, [Formula: see text], exerting density dependence on age-specific vital rates through an increasing function of population size. The environment fluctuates in a stationary distribution with no autocorrelation. We show by analysis and simulation of age structure, under assumptions often met by vertebrate populations, that the stochastic dynamics of population size can be accurately approximated by a univariate model governed by three key demographic parameters: the intrinsic rate of increase and carrying capacity in the average environment, [Formula: see text] and [Formula: see text], and the environmental variance in population growth rate, [Formula: see text] Allowing these parameters to be genetically variable and to evolve, but assuming that a fourth parameter, [Formula: see text], measuring the nonlinearity of density dependence, remains constant, the expected evolution maximizes [Formula: see text] This shows that the magnitude of environmental stochasticity governs the classical trade-off between selection for higher [Formula: see text] versus higher [Formula: see text] However, selection also acts to decrease [Formula: see text], so the simple life-history trade-off between [Formula: see text]- and [Formula: see text]-selection may be obscured by additional trade-offs between them and [Formula: see text] Under the classical logistic model of population growth with linear density dependence ([Formula: see text]), life-history evolution in a fluctuating environment tends to maximize the average population size. Published under the PNAS license.

Magnetic Helicity of Alfven Simple Waves

NASA Technical Reports Server (NTRS)

Webb, Gary M.; Hu, Q.; Dasgupta, B.; Zank, G. P.; Roberts, D.

2010-01-01

The magnetic helicity of fully nonlinear, multi-dimensional Alfven simple waves are investigated, by using relative helicity formulae and also by using an approach involving poloidal and toroidal decomposition of the magnetic field and magnetic vector potential. Different methods to calculate the magnetic vector potential are used, including the homotopy and Biot-Savart formulas. Two basic Alfven modes are identified: (a) the plane 1D Alfven simple wave given in standard texts, in which the Alfven wave propagates along the z-axis, with wave phase varphi=k_0(z-lambda t), where k_0 is the wave number and lambda is the group velocity of the wave, and (b)\\ the generalized Barnes (1976) simple Alfven wave in which the wave normal {bf n} moves in a circle in the xy-plane perpendicular to the mean field, which is directed along the z-axis. The plane Alfven wave (a) is analogous to the slab Alfven mode and the generalized Barnes solution (b) is analogous to the 2D mode in Alfvenic, incompressible turbulence. The helicity characteristics of these two basic Alfven modes are distinct. The helicity characteristics of more general multi-dimensional simple Alfven waves are also investigated. Applications to nonlinear Aifvenic fluctuations and structures observed in the solar wind are discussed.

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

[FQA: A method for floristic quality assessment based on conservatism of plant species].

PubMed

Cao, Li Juan; He, Ping; Wang, Mi; Xui, Jie; Ren, Ying

2018-04-01

FQA, which uses the conservatism of plant species for particular habitats and the species richness of plant communities, is a rapid method for the assessment of habitat quality. This method is based on species composition of quadrats and coefficients of conservatism for species which assigned by experts. Floristic Quality Index (FQI) that reflects vegetation integrity and degradation of a site can be calculated by a simple formula and be used for space-time comparison of habitat quality. It has been widely used in more than ten countries including the United States and Canada. This paper presented the principle, calculation formulas and application cases of this method, with the aim to provide a simple, repeatable and comparable method to assess habitat quality for ecological managers and researchers.

Development of a quantitative multi-compound method for the detection of 14 nitrogen-rich adulterants by LC-MS/MS in food materials.

PubMed

Frank, Nancy; Bessaire, Thomas; Tarres, Adrienne; Goyon, Alexandre; Delatour, Thierry

2017-11-01

The increasing number of food frauds using exogenous nitrogen-rich adulterants to artificially raise the protein content for economically motivated adulteration has demonstrated the need for a robust analytical methodology. This method should be applicable for quality control in operations covering a wide range of analyte concentrations to be able to analyse high levels as usually found in adulteration, as well as low levels due to contamination. The paper describes a LC-MS/MS method covering 14 nitrogen-rich adulterants using a simple and fast sample preparation based on dilution and clean-up by dispersive SPE. Quantification is carried out by isotopic dilution reaching LOQs of 0.05-0.20 mg/kg in a broad range of food matrices (infant formula, liquid milk, dairy ingredient, high protein meal, cereal, infant cereal, and meat/fish powder). Validation of seven commodity groups was performed according to SANCO 12571/2013, giving satisfactory results demonstrating the method's fitness for purpose at the validated range at contamination level. Method ruggedness was further assessed by transferring the developed method into another laboratory devoted to routine testing for quality control. Next to the method description, emphasis is placed on challenges and problems appearing during method development as well as validation. They are discussed in detail and solutions are provided.

TRAC, a collaborative computer tool for tracer-test interpretation

NASA Astrophysics Data System (ADS)

Gutierrez, A.; Klinka, T.; Thiéry, D.; Buscarlet, E.; Binet, S.; Jozja, N.; Défarge, C.; Leclerc, B.; Fécamp, C.; Ahumada, Y.; Elsass, J.

2013-05-01

Artificial tracer tests are widely used by consulting engineers for demonstrating water circulation, proving the existence of leakage, or estimating groundwater velocity. However, the interpretation of such tests is often very basic, with the result that decision makers and professionals commonly face unreliable results through hasty and empirical interpretation. There is thus an increasing need for a reliable interpretation tool, compatible with the latest operating systems and available in several languages. BRGM, the French Geological Survey, has developed a project together with hydrogeologists from various other organizations to build software assembling several analytical solutions in order to comply with various field contexts. This computer program, called TRAC, is very light and simple, allowing the user to add his own analytical solution if the formula is not yet included. It aims at collaborative improvement by sharing the tool and the solutions. TRAC can be used for interpreting data recovered from a tracer test as well as for simulating the transport of a tracer in the saturated zone (for the time being). Calibration of a site operation is based on considering the hydrodynamic and hydrodispersive features of groundwater flow as well as the amount, nature and injection mode of the artificial tracer. The software is available in French, English and Spanish, and the latest version can be downloaded from the web site http://trac.brgm.fr">http://trac.brgm.fr.