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.

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.

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

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.

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.

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.

Arbitrarily accurate twin composite π -pulse sequences

NASA Astrophysics Data System (ADS)

Torosov, Boyan T.; Vitanov, Nikolay V.

2018-04-01

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

Analytical pricing formulas for hybrid variance swaps with regime-switching

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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.

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.

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

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

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

1980-09-01

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

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.

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.…

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.

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.

Simplified analysis about horizontal displacement of deep soil under tunnel excavation

NASA Astrophysics Data System (ADS)

Tian, Xiaoyan; Gu, Shuancheng; Huang, Rongbin

2017-11-01

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

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.

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".

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.

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

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

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

2008-07-30

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

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.)

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.

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

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.

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.

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.

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.

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.

Point spread functions and deconvolution of ultrasonic images.

PubMed

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

2015-03-01

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

A 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…

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.

A simple method for estimating frequency response corrections for eddy covariance systems

Treesearch

W. J. Massman

2000-01-01

A simple analytical formula is developed for estimating the frequency attenuation of eddy covariance fluxes due to sensor response, path-length averaging, sensor separation, signal processing, and flux averaging periods. Although it is an approximation based on flat terrain cospectra, this analytical formula should have broader applicability than just flat-terrain...

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.

Theory of the control of structures by low authority controllers

NASA Technical Reports Server (NTRS)

Aubrun, J. N.

1978-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

Bending elasticity of macromolecules: analytic predictions from the wormlike chain model.

PubMed

Polley, Anirban; Samuel, Joseph; Sinha, Supurna

2013-01-01

We present a study of the bend angle distribution of semiflexible polymers of short and intermediate lengths within the wormlike chain model. This enables us to calculate the elastic response of a stiff molecule to a bending moment. Our results go beyond the Hookean regime and explore the nonlinear elastic behavior of a single molecule. We present analytical formulas for the bend angle distribution and for the moment-angle relation. Our analytical study is compared against numerical Monte Carlo simulations. The functional forms derived here can be applied to fluorescence microscopic studies on actin and DNA. Our results are relevant to recent studies of "kinks" and cyclization in short and intermediate length DNA strands.

Analytical 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.

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.

Unified semiclassical theory for the two-state system: an analytical solution for general nonadiabatic tunneling.

PubMed

Zhu, Chaoyuan; Lin, Sheng Hsien

2006-07-28

Unified semiclasical solution for general nonadiabatic tunneling between two adiabatic potential energy surfaces is established by employing unified semiclassical solution for pure nonadiabatic transition [C. Zhu, J. Chem. Phys. 105, 4159 (1996)] with the certain symmetry transformation. This symmetry comes from a detailed analysis of the reduced scattering matrix for Landau-Zener type of crossing as a special case of nonadiabatic transition and nonadiabatic tunneling. Traditional classification of crossing and noncrossing types of nonadiabatic transition can be quantitatively defined by the rotation angle of adiabatic-to-diabatic transformation, and this rotational angle enters the analytical solution for general nonadiabatic tunneling. The certain two-state exponential potential models are employed for numerical tests, and the calculations from the present general nonadiabatic tunneling formula are demonstrated in very good agreement with the results from exact quantum mechanical calculations. The present general nonadiabatic tunneling formula can be incorporated with various mixed quantum-classical methods for modeling electronically nonadiabatic processes in photochemistry.

Mathematical developments regarding the general theory of the Earth magnetism

NASA Technical Reports Server (NTRS)

Schmidt, A.

1983-01-01

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

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.

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

PubMed

Bauer, P; Attinger, S; Kinzelbach, W

2001-06-01

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

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.

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

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.

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.

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

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.

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

PubMed

Gilliland, Don

2016-01-01

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

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

PubMed

Arrizón, V; Rojo-Velázquez, G

2001-06-01

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

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.

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.

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

A simple calculation method for determination of equivalent square field.

PubMed

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

2012-04-01

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

Hollow Gaussian Schell-model beam and its propagation

NASA Astrophysics Data System (ADS)

Wang, Li-Gang; Wang, Li-Qin

2008-03-01

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

Lattice QCD and the timelike pion form factor.

PubMed

Meyer, Harvey B

2011-08-12

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

Sound velocity in five-component air mixtures of various densities

NASA Astrophysics Data System (ADS)

Bogdanova, N. V.; Rydalevskaya, M. A.

2018-05-01

The local equilibrium flows of five-component air mixtures are considered. Gas dynamic equations are derived from the kinetic equations for aggregate values of collision invariants. It is shown that the traditional formula for sound velocity is true in air mixtures considered with the chemical reactions and the internal degrees of freedom. This formula connects the square of sound velocity with pressure and density. However, the adiabatic coefficient is not constant under existing conditions. The analytical expression for this coefficient is obtained. The examples of its calculation in air mixtures of various densities are presented.

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)].

A numerical test of the topographic bias

NASA Astrophysics Data System (ADS)

Sjöberg, L. E.; Joud, M. S. S.

2018-02-01

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

Design of a Ku band miniature multiple beam klystron

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

Bandyopadhyay, Ayan Kumar, E-mail: ayan.bandyopadhyay@gmail.com; Pal, Debasish; Kant, Deepender

2016-03-09

The design of a miniature multiple beam klystron (MBK) working in the Ku-band frequency range is presented in this article. Starting from the main design parameters, design of the electron gun, the input and output couplers and radio frequency section (RF-section) are presented. The design methodology using state of the art commercial electromagnetic design tools, analytical formulae as well as noncommercial design tools are briefly presented in this article.

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

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.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

A 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

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

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 Stochastic Super-Exponential Growth Model for Population Dynamics

NASA Astrophysics Data System (ADS)

Avila, P.; Rekker, A.

2010-11-01

A super-exponential growth model with environmental noise has been studied analytically. Super-exponential growth rate is a property of dynamical systems exhibiting endogenous nonlinear positive feedback, i.e., of self-reinforcing systems. Environmental noise acts on the growth rate multiplicatively and is assumed to be Gaussian white noise in the Stratonovich interpretation. An analysis of the stochastic super-exponential growth model with derivations of exact analytical formulae for the conditional probability density and the mean value of the population abundance are presented. Interpretations and various applications of the results are discussed.

One-dimensional magnetohydrodynamics of a cylindrical liner imploded by an azimuthal magnetic field and compressing an axial field

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

Hamann, F., E-mail: franck.hamann@cea.fr; Combis, P.; Videau, L.

The one-dimensional magnetohydrodynamics of a plasma cylindrical liner is addressed in the case of a two components magnetic field. The azimuthal component is responsible for the implosion of the liner and the axial field is compressed inside the liner. A complete set of analytical profiles for the magnetic field components, the density, and the local velocity are proposed at the scale of the liner thickness. Numerical simulations are also presented to test the validity of the analytical formulas.

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)].

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.

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.

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

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.

An invariant asymptotic formula for solutions of second-order linear ODE's

NASA Technical Reports Server (NTRS)

Gingold, H.

1988-01-01

An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).

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].

High-Contrast Gratings based Spoof Surface Plasmons

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

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

PubMed Central

Haghighi, Maryam; Rezaei, Karamatollah

2012-01-01

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

Leading non-Gaussian corrections for diffusion orientation distribution function.

PubMed

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

2014-02-01

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

Leading Non-Gaussian Corrections for Diffusion Orientation Distribution Function

PubMed Central

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

2014-01-01

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

An analytic formula for heating due to ozone absorption

NASA Technical Reports Server (NTRS)

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

1972-01-01

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

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.

Effective diffusion of confined active Brownian swimmers.

PubMed

Sandoval, Mario; Dagdug, Leornardo

2014-12-01

We theoretically find the effect of confinement and thermal fluctuations on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian dynamics simulations and we obtain excellent agreement.

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

NASA Astrophysics Data System (ADS)

Sadeghi, F.; Ansari, R.

2017-07-01

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

Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function

NASA Technical Reports Server (NTRS)

King, H. F.; Komornicki, A.

1986-01-01

Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.

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.

Reemission spectra and inelastic processes at interaction of attosecond and shorter duration electromagnetic pulses with atoms

NASA Astrophysics Data System (ADS)

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

2017-01-01

Inelastic processes and the reemission of attosecond and shorter electromagnetic pulses by atoms have been considered within the analytical solution of the Schrödinger equation in the sudden perturbation approximation. A method of calculations with the exact inclusion of spatial inhomogeneity of the field of an ultrashort pulse and the momenta of photons in the reemission processes has been developed. The probabilities of inelastic processes and spectra of reemission of ultrashort electromagnetic pulses by one- and many-electron atoms have been calculated. The results have been presented in the form of analytical formulas.

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.

A two-dimensional solution of the FW-H equation for rectilinear motion of sources

NASA Astrophysics Data System (ADS)

Bozorgi, Alireza; Siozos-Rousoulis, Leonidas; Nourbakhsh, Seyyed Ahmad; Ghorbaniasl, Ghader

2017-02-01

In this paper, a subsonic solution of the two-dimensional Ffowcs Williams and Hawkings (FW-H) equation is presented for calculation of noise generated by sources moving with constant velocity in a medium at rest or in a moving medium. The solution is represented in the frequency domain and is valid for observers located far from the noise sources. In order to verify the validity of the derived formula, three test cases are considered, namely a monopole, a dipole, and a quadrupole source in a medium at rest or in motion. The calculated results well coincide with the analytical solutions, validating the applicability of the formula to rectilinear subsonic motion problems.

Resonant behaviour of MHD waves on magnetic flux tubes. I - Connection formulae at the resonant surfaces. II - Absorption of sound waves by sunspots

NASA Technical Reports Server (NTRS)

Sakurai, Takashi; Goossens, Marcel; Hollweg, Joseph V.

1991-01-01

The present method of addressing the resonance problems that emerge in such MHD phenomena as the resonant absorption of waves at the Alfven resonance point avoids solving the fourth-order differential equation of dissipative MHD by recourse to connection formulae across the dissipation layer. In the second part of this investigation, the absorption of solar 5-min oscillations by sunspots is interpreted as the resonant absorption of sounds by a magnetic cylinder. The absorption coefficient is interpreted (1) analytically, under certain simplifying assumptions, and numerically, under more general conditions. The observed absorption coefficient magnitude is explained over suitable parameter ranges.

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

NASA Astrophysics Data System (ADS)

Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

2017-11-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

Leading multi-soft limits from scattering equations

NASA Astrophysics Data System (ADS)

Zlotnikov, Michael

2017-10-01

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

Bulk diffusion in a kinetically constrained lattice gas

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

Pressure Distribution in a Squeeze Film Spherical Bearing with Rough Surfaces Lubricated by an Ellis Fluid

NASA Astrophysics Data System (ADS)

Jurczak, P.; Falicki, J.

2016-08-01

In this paper, the solution to a problem of pressure distribution in a curvilinear squeeze film spherical bearing is considered. The equations of motion of an Ellis pseudo-plastic fluid are presented. Using Christensen's stochastic model of rough surfaces, different forms of Reynolds equation for various types of surface roughness pattern are obtained. The analytical solutions of these equations for the cases of externally pressurized bearing and squeeze film bearing are presented. Analytical solutions for the film pressure are found for the longitudinal and circumferential roughness patterns. As a result the formulae expressing pressure distribution in the clearance of bearing lubricated by an Ellis fluid was obtained. The numerical considerations for a spherical bearing are given in detail.

Spatiotemporal behaviour of isodiffracting hollow Gaussian pulsed beams

NASA Astrophysics Data System (ADS)

Xu, Yanbing; Lü, Baida

2007-05-01

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

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

PubMed

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

2010-05-07

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

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

PubMed Central

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

2010-01-01

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

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

PubMed

Fetterly, Kenneth A; Favazza, Christopher P

2016-08-07

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

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

Energy deposition at the bone-tissue interface from nuclear fragments produced by high-energy nucleons

NASA Technical Reports Server (NTRS)

Cucinotta, Francis A.; Hajnal, Ferenc; Wilson, John W.

1990-01-01

The transport of nuclear fragmentation recoils produced by high-energy nucleons in the region of the bone-tissue interface is considered. Results for the different flux and absorbed dose for recoils produced by 1 GeV protons are presented in a bidirectional transport model. The energy deposition in marrow cavities is seen to be enhanced by recoils produced in bone. Approximate analytic formulae for absorbed dose near the interface region are also presented for a simplified range-energy model.

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.

Analytic study of the effect of dark energy-dark matter interaction on the growth of structures

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

Marcondes, Rafael J.F.; Landim, Ricardo C.G.; Costa, André A.

2016-12-01

Large-scale structure has been shown as a promising cosmic probe for distinguishing and constraining dark energy models. Using the growth index parametrization, we obtain an analytic formula for the growth rate of structures in a coupled dark energy model in which the exchange of energy-momentum is proportional to the dark energy density. We find that the evolution of f σ{sub 8} can be determined analytically once we know the coupling, the dark energy equation of state, the present value of the dark energy density parameter and the current mean amplitude of dark matter fluctuations. After correcting the growth function formore » the correspondence with the velocity field through the continuity equation in the interacting model, we use our analytic result to compare the model's predictions with large-scale structure observations.« less

Analytic solution for quasi-Lambertian radiation transfer.

PubMed

Braun, Avi; Gordon, Jeffrey M

2010-02-10

An analytic solution is derived for radiation transfer between flat quasi-Lambertian surfaces of arbitrary orientation, i.e., surfaces that radiate in a Lambertian fashion but within a numerical aperture smaller than unity. These formulas obviate the need for ray trace simulations and provide exact, physically transparent results. Illustrative examples that capture the salient features of the flux maps and the efficiency of flux transfer are presented for a few configurations of practical interest. There is also a fundamental reciprocity relation for quasi-Lambertian exchange, akin to the reciprocity theorem for fully Lambertian surfaces. Applications include optical fiber coupling, fiber-optic biomedical procedures, and solar concentrators.

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

Analysis of random point images with the use of symbolic computation codes and generalized Catalan numbers

NASA Astrophysics Data System (ADS)

Reznik, A. L.; Tuzikov, A. V.; Solov'ev, A. A.; Torgov, A. V.

2016-11-01

Original codes and combinatorial-geometrical computational schemes are presented, which are developed and applied for finding exact analytical formulas that describe the probability of errorless readout of random point images recorded by a scanning aperture with a limited number of threshold levels. Combinatorial problems encountered in the course of the study and associated with the new generalization of Catalan numbers are formulated and solved. An attempt is made to find the explicit analytical form of these numbers, which is, on the one hand, a necessary stage of solving the basic research problem and, on the other hand, an independent self-consistent problem.

(U) Analytic First and Second Derivatives of the Uncollided Leakage for a Homogeneous Sphere

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

Favorite, Jeffrey A.

2017-04-26

The second-order adjoint sensitivity analysis methodology (2nd-ASAM), developed by Cacuci, has been applied by Cacuci to derive second derivatives of a response with respect to input parameters for uncollided particles in an inhomogeneous transport problem. In this memo, we present an analytic benchmark for verifying the derivatives of the 2nd-ASAM. The problem is a homogeneous sphere, and the response is the uncollided total leakage. This memo does not repeat the formulas given in Ref. 2. We are preparing a journal article that will include the derivation of Ref. 2 and the benchmark of this memo.

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.

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.

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.

On the Gompertzian growth in the fractal space-time.

PubMed

Molski, Marcin; Konarski, Jerzy

2008-06-01

An analytical approach to determination of time-dependent temporal fractal dimension b(t)(t) and scaling factor a(t)(t) for the Gompertzian growth in the fractal space-time is presented. The derived formulae take into account the proper boundary conditions and permit a calculation of the mean values b(t)(t) and a(t)(t) at any period of time. The formulae derived have been tested on experimental data obtained by Schrek for the Brown-Pearce rabbit's tumor growth. The results obtained confirm a possibility of successful mapping of the experimental Gompertz curve onto the fractal power-law scaling function y(t)=a(t)tb(t) and support a thesis that Gompertzian growth is a self-similar and allometric process of a holistic nature.

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.

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.

Rapidity window dependences of higher order cumulants and diffusion master equation

NASA Astrophysics Data System (ADS)

Kitazawa, Masakiyo

2015-10-01

We study the rapidity window dependences of higher order cumulants of conserved charges observed in relativistic heavy ion collisions. The time evolution and the rapidity window dependence of the non-Gaussian fluctuations are described by the diffusion master equation. Analytic formulas for the time evolution of cumulants in a rapidity window are obtained for arbitrary initial conditions. We discuss that the rapidity window dependences of the non-Gaussian cumulants have characteristic structures reflecting the non-equilibrium property of fluctuations, which can be observed in relativistic heavy ion collisions with the present detectors. It is argued that various information on the thermal and transport properties of the hot medium can be revealed experimentally by the study of the rapidity window dependences, especially by the combined use, of the higher order cumulants. Formulas of higher order cumulants for a probability distribution composed of sub-probabilities, which are useful for various studies of non-Gaussian cumulants, are also presented.

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.

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.

Double diffusive magnetohydrodynamic (MHD) mixed convective slip flow along a radiating moving vertical flat plate with convective boundary condition.

PubMed

Rashidi, Mohammad M; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J; Freidoonimehr, Navid

2014-01-01

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, [Formula: see text], local Nusselt number, [Formula: see text], and local Sherwood number [Formula: see text] are shown and explained through tables.

Corneal aberrations in keratoconic eyes: influence of pupil size and centering

NASA Astrophysics Data System (ADS)

Comastri, S. A.; Perez, L. I.; Pérez, G. D.; Martin, G.; Bianchetti, A.

2011-01-01

Ocular aberrations vary among subjects and under different conditions and are commonly analyzed expanding the wavefront aberration function in Zernike polynomials. In previous articles, explicit analytical formulas to transform Zernike coefficients of up to 7th order corresponding to an original pupil into those related to a contracted displaced new pupil are obtained. In the present paper these formulas are applied to 20 keratoconic corneas of varying severity. Employing the SN CT1000 topographer, aberrations of the anterior corneal surface for a pupil of semi-diameter 3 mm centered on the keratometric axis are evaluated, the relation between the higher-order root mean square wavefront error and the index KISA% characterizing keratoconus is studied and the size and centering of the ocular photopic natural pupil are determined. Using these data and the transformation formulas, new coefficients associated to the photopic pupil size are computed and their variation when coordinates origin is shifted from the keratometric axis to the ocular pupil centre is analyzed.

CMOS Amperometric ADC With High Sensitivity, Dynamic Range and Power Efficiency for Air Quality Monitoring.

PubMed

Li, Haitao; Boling, C Sam; Mason, Andrew J

2016-08-01

Airborne pollutants are a leading cause of illness and mortality globally. Electrochemical gas sensors show great promise for personal air quality monitoring to address this worldwide health crisis. However, implementing miniaturized arrays of such sensors demands high performance instrumentation circuits that simultaneously meet challenging power, area, sensitivity, noise and dynamic range goals. This paper presents a new multi-channel CMOS amperometric ADC featuring pixel-level architecture for gas sensor arrays. The circuit combines digital modulation of input currents and an incremental Σ∆ ADC to achieve wide dynamic range and high sensitivity with very high power efficiency and compact size. Fabricated in 0.5 [Formula: see text] CMOS, the circuit was measured to have 164 dB cross-scale dynamic range, 100 fA sensitivity while consuming only 241 [Formula: see text] and 0.157 [Formula: see text] active area per channel. Electrochemical experiments with liquid and gas targets demonstrate the circuit's real-time response to a wide range of analyte concentrations.

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.

Alpha decay calculations with a new formula

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Semiclassical Dynamicswith Exponentially Small Error Estimates

NASA Astrophysics Data System (ADS)

Hagedorn, George A.; Joye, Alain

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

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

NASA Astrophysics Data System (ADS)

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

1989-01-01

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

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

NASA Astrophysics Data System (ADS)

Cai, Yangjian; Zhang, Lei

2006-07-01

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

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.

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.

Reconstruction of primary vertices at the ATLAS experiment in Run 1 proton-proton collisions at the LHC.

PubMed

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Sultansoy, S; Sumida, T; Sun, S; Sun, X; Sundermann, J E; Suruliz, K; Susinno, G; Sutton, M R; Suzuki, S; Svatos, M; Swiatlowski, M; Sykora, I; Sykora, T; Ta, D; Taccini, C; Tackmann, K; Taenzer, J; Taffard, A; Tafirout, R; Taiblum, N; Takai, H; Takashima, R; Takeshita, T; Takubo, Y; Talby, M; Talyshev, A A; Tan, K G; Tanaka, J; Tanaka, R; Tanaka, S; Tannenwald, B B; Araya, S Tapia; Tapprogge, S; Tarem, S; Tartarelli, G F; Tas, P; Tasevsky, M; Tashiro, T; Tassi, E; Delgado, A Tavares; Tayalati, Y; Taylor, A C; Taylor, G N; Taylor, P T E; Taylor, W; Teischinger, F A; Teixeira-Dias, P; Temple, D; Kate, H Ten; Teng, P K; Teoh, J J; Tepel, F; Terada, S; Terashi, K; Terron, J; Terzo, S; Testa, M; Teuscher, R J; Theveneaux-Pelzer, T; Thomas, J P; Thomas-Wilsker, J; Thompson, E N; Thompson, P D; Thompson, A S; Thomsen, L A; Thomson, E; Thomson, M; Tibbetts, M J; Torres, R E Ticse; Tikhomirov, V O; Tikhonov, Yu A; Timoshenko, S; Tipton, P; Tisserant, S; Todome, K; Todorov, T; Todorova-Nova, S; Tojo, J; Tokár, S; Tokushuku, K; Tolley, E; Tomlinson, L; Tomoto, M; Tompkins, L; Toms, K; Tong, B; Torrence, E; Torres, H; Pastor, E Torró; Toth, J; Touchard, F; Tovey, D R; Trefzger, T; Tricoli, A; Trigger, I M; Trincaz-Duvoid, S; Tripiana, M F; Trischuk, W; Trocmé, B; Trofymov, A; Troncon, C; Trottier-McDonald, M; Trovatelli, M; Truong, L; Trzebinski, M; Trzupek, A; Tseng, J C-L; Tsiareshka, P V; Tsipolitis, G; Tsirintanis, N; Tsiskaridze, S; Tsiskaridze, V; Tskhadadze, E G; Tsui, K M; Tsukerman, I I; Tsulaia, V; Tsuno, S; Tsybychev, D; Tudorache, A; Tudorache, V; Tuna, A N; Tupputi, S A; Turchikhin, S; Turecek, D; Turgeman, D; Turra, R; Turvey, A J; Tuts, P M; Tyndel, M; Ucchielli, G; Ueda, I; Ughetto, M; Ukegawa, F; Unal, G; Undrus, A; Unel, G; Ungaro, F C; Unno, Y; Unverdorben, C; Urban, J; Urquijo, P; Urrejola, P; Usai, G; Usanova, A; Vacavant, L; Vacek, V; Vachon, B; Valderanis, C; Santurio, E Valdes; Valencic, N; Valentinetti, S; Valero, A; Valéry, L; Valkar, S; Vallecorsa, S; Ferrer, J A Valls; Van Den Wollenberg, W; Van Der Deijl, P C; van der Geer, R; van der Graaf, H; van Eldik, N; van Gemmeren, P; Van Nieuwkoop, J; van Vulpen, I; van Woerden, M C; Vanadia, M; Vandelli, W; Vanguri, R; Vaniachine, A; Vankov, P; Vardanyan, G; Vari, R; Varnes, E W; Varol, T; Varouchas, D; Vartapetian, A; Varvell, K E; Vasquez, J G; Vazeille, F; Schroeder, T Vazquez; Veatch, J; Veloce, L M; Veloso, F; Veneziano, S; Ventura, A; Venturi, M; Venturi, N; Venturini, A; Vercesi, V; Verducci, M; Verkerke, W; Vermeulen, J C; Vest, A; Vetterli, M C; Viazlo, O; Vichou, I; Vickey, T; Boeriu, O E Vickey; Viehhauser, G H A; Viel, S; Vigani, L; Vigne, R; Villa, M; Perez, M Villaplana; Vilucchi, E; Vincter, M G; Vinogradov, V B; Vittori, C; Vivarelli, I; Vlachos, S; Vlasak, M; Vogel, M; Vokac, P; Volpi, G; Volpi, M; von der Schmitt, H; von Toerne, E; Vorobel, V; Vorobev, K; Vos, M; Voss, R; Vossebeld, J H; Vranjes, N; Milosavljevic, M Vranjes; Vrba, V; Vreeswijk, M; Vuillermet, R; Vukotic, I; Vykydal, Z; Wagner, P; Wagner, W; Wahlberg, H; Wahrmund, S; Wakabayashi, J; Walder, J; Walker, R; Walkowiak, W; Wallangen, V; Wang, C; Wang, C; Wang, F; Wang, H; Wang, H; Wang, J; Wang, J; Wang, K; Wang, R; Wang, S M; Wang, T; Wang, T; Wang, W; Wang, X; Wanotayaroj, C; Warburton, A; Ward, C P; Wardrope, D R; Washbrook, A; Watkins, P M; Watson, A T; Watson, M F; Watts, G; Watts, S; Waugh, B M; Webb, S; Weber, M S; Weber, S W; Webster, J S; Weidberg, A R; Weinert, B; Weingarten, J; Weiser, C; Weits, H; Wells, P S; Wenaus, T; Wengler, T; Wenig, S; Wermes, N; Werner, M; Werner, M D; Werner, P; Wessels, M; Wetter, J; Whalen, K; Whallon, N L; Wharton, A M; White, A; White, M J; White, R; Whiteson, D; Wickens, F J; Wiedenmann, W; Wielers, M; Wienemann, P; Wiglesworth, C; Wiik-Fuchs, L A M; Wildauer, A; Wilk, F; Wilkens, H G; Williams, H H; Williams, S; Willis, C; Willocq, S; Wilson, J A; Wingerter-Seez, I; Winklmeier, F; Winston, O J; Winter, B T; Wittgen, M; Wittkowski, J; Wolter, M W; Wolters, H; Worm, S D; Wosiek, B K; Wotschack, J; Woudstra, M J; Wozniak, K W; Wu, M; Wu, M; Wu, S L; Wu, X; Wu, Y; Wyatt, T R; Wynne, B M; Xella, S; Xu, D; Xu, L; Yabsley, B; Yacoob, S; Yakabe, R; Yamaguchi, D; Yamaguchi, Y; Yamamoto, A; Yamamoto, S; Yamanaka, T; Yamauchi, K; Yamazaki, Y; Yan, Z; Yang, H; Yang, H; Yang, Y; Yang, Z; Yao, W-M; Yap, Y C; Yasu, Y; Yatsenko, E; Wong, K H Yau; Ye, J; Ye, S; Yeletskikh, I; Yen, A L; Yildirim, E; Yorita, K; Yoshida, R; Yoshihara, K; Young, C; Young, C J S; Youssef, S; Yu, D R; Yu, J; Yu, J M; Yu, J; Yuan, L; Yuen, S P Y; Yusuff, I; Zabinski, B; Zaidan, R; Zaitsev, A M; Zakharchuk, N; Zalieckas, J; Zaman, A; Zambito, S; Zanello, L; Zanzi, D; Zeitnitz, C; Zeman, M; Zemla, A; Zeng, J C; Zeng, Q; Zengel, K; Zenin, O; Ženiš, T; Zerwas, D; Zhang, D; Zhang, F; Zhang, G; Zhang, H; Zhang, J; Zhang, L; Zhang, R; Zhang, R; Zhang, X; Zhang, Z; Zhao, X; Zhao, Y; Zhao, Z; Zhemchugov, A; Zhong, J; Zhou, B; Zhou, C; Zhou, L; Zhou, L; Zhou, M; Zhou, N; Zhu, C G; Zhu, H; Zhu, J; Zhu, Y; Zhuang, X; Zhukov, K; Zibell, A; Zieminska, D; Zimine, N I; Zimmermann, C; Zimmermann, S; Zinonos, Z; Zinser, M; Ziolkowski, M; Živković, L; Zobernig, G; Zoccoli, A; Nedden, M Zur; Zwalinski, L

2017-01-01

This paper presents the method and performance of primary vertex reconstruction in proton-proton collision data recorded by the ATLAS experiment during Run 1 of the LHC. The studies presented focus on data taken during 2012 at a centre-of-mass energy of [Formula: see text] TeV. The performance has been measured as a function of the number of interactions per bunch crossing over a wide range, from one to seventy. The measurement of the position and size of the luminous region and its use as a constraint to improve the primary vertex resolution are discussed. A longitudinal vertex position resolution of about [Formula: see text] is achieved for events with high multiplicity of reconstructed tracks. The transverse position resolution is better than [Formula: see text] and is dominated by the precision on the size of the luminous region. An analytical model is proposed to describe the primary vertex reconstruction efficiency as a function of the number of interactions per bunch crossing and of the longitudinal size of the luminous region. Agreement between the data and the predictions of this model is better than 3% up to seventy interactions per bunch crossing.

Sensitivity analysis of non-cohesive sediment transport formulae

NASA Astrophysics Data System (ADS)

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

2006-10-01

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

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

A mystery of black-hole gravitational resonances

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

Hod, Shahar; The Hadassah Academic College, Jerusalem 91010

More than three decades ago, Detweiler provided an analytical formula for the gravitational resonant frequencies of rapidly-rotating Kerr black holes. In the present work we shall discuss an important discrepancy between the famous analytical prediction of Detweiler and the recent numerical results of Zimmerman et al. In addition, we shall refute the claim that recently appeared in the physics literature that the Detweiler-Teukolsky-Press resonance equation for the characteristic gravitational eigenfrequencies of rapidly-rotating Kerr black holes is not valid in the regime of damped quasinormal resonances with ℑω/T{sub BH}≫1 (here ω and T{sub BH} are respectively the characteristic quasinormal resonant frequencymore » of the Kerr black hole and its Bekenstein-Hawking temperature). The main goal of the present paper is to highlight and expose this important black-hole quasinormal mystery (that is, the intriguing discrepancy between the analytical and numerical results regarding the gravitational quasinormal resonance spectra of rapidly-rotating Kerr black holes).« less

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

PubMed

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

2014-01-01

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

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.

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.

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.

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…

Design sensitivity analysis of nonlinear structural response

NASA Technical Reports Server (NTRS)

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

1987-01-01

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

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.

Analytical model for effect of temperature variation on PSF consistency in wavefront coding infrared imaging system

NASA Astrophysics Data System (ADS)

Feng, Bin; Shi, Zelin; Zhang, Chengshuo; Xu, Baoshu; Zhang, Xiaodong

2016-05-01

The point spread function (PSF) inconsistency caused by temperature variation leads to artifacts in decoded images of a wavefront coding infrared imaging system. Therefore, this paper proposes an analytical model for the effect of temperature variation on the PSF consistency. In the proposed model, a formula for the thermal deformation of an optical phase mask is derived. This formula indicates that a cubic optical phase mask (CPM) is still cubic after thermal deformation. A proposed equivalent cubic phase mask (E-CPM) is a virtual and room-temperature lens which characterizes the optical effect of temperature variation on the CPM. Additionally, a calculating method for PSF consistency after temperature variation is presented. Numerical simulation illustrates the validity of the proposed model and some significant conclusions are drawn. Given the form parameter, the PSF consistency achieved by a Ge-material CPM is better than the PSF consistency by a ZnSe-material CPM. The effect of the optical phase mask on PSF inconsistency is much slighter than that of the auxiliary lens group. A large form parameter of the CPM will introduce large defocus-insensitive aberrations, which improves the PSF consistency but degrades the room-temperature MTF.

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.

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.

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

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.

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.

Bifurcation analysis and global dynamics of a mathematical model of antibiotic resistance in hospitals.

PubMed

Cen, Xiuli; Feng, Zhilan; Zheng, Yiqiang; Zhao, Yulin

2017-12-01

Antibiotic-resistant bacteria have posed a grave threat to public health by causing a number of nosocomial infections in hospitals. Mathematical models have been used to study transmission dynamics of antibiotic-resistant bacteria within a hospital and the measures to control antibiotic resistance in nosocomial pathogens. Studies presented in Lipstich et al. (Proc Natl Acad Sci 97(4):1938-1943, 2000) and Lipstich and Bergstrom (Infection control in the ICU environment. Kluwer, Boston, 2002) have provided valuable insights in understanding the transmission of antibiotic-resistant bacteria in a hospital. However, their results are limited to numerical simulations of a few different scenarios without analytical analyses of the models in broader parameter regions that are biologically feasible. Bifurcation analysis and identification of the global stability conditions can be very helpful for assessing interventions that are aimed at limiting nosocomial infections and stemming the spread of antibiotic-resistant bacteria. In this paper we study the global dynamics of the mathematical model of antibiotic resistance in hospitals considered in Lipstich et al. (2000) and Lipstich and Bergstrom (2002). The invasion reproduction number [Formula: see text] of antibiotic-resistant bacteria is derived, and the relationship between [Formula: see text] and two control reproduction numbers of sensitive bacteria and resistant bacteria ([Formula: see text] and [Formula: see text]) is established. More importantly, we prove that a backward bifurcation may occur at [Formula: see text] when the model includes superinfection, which is not mentioned in Lipstich and Bergstrom (2002). More specifically, there exists a new threshold [Formula: see text], such that if [Formula: see text], then the system can have two positive interior equilibria, which leads to an interesting bistable phenomenon. This may have critical implications for controlling the antibiotic-resistance in a hospital.

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.

Analytical study of mixed electroosmotic-pressure-driven flow in rectangular micro-channels

NASA Astrophysics Data System (ADS)

Movahed, Saeid; Kamali, Reza; Eghtesad, Mohammad; Khosravifard, Amir

2013-09-01

Operational state of many miniaturized devices deals with flow field in microchannels. Pressure-driven flow (PDF) and electroosmotic flow (EOF) can be recognized as the two most important types of the flow field in such channels. EOF has many advantages in comparison with PDF, such as being vibration free and not requiring any external mechanical pumps or moving parts. However, the disadvantages of this type of flow such as Joule heating, electrophoresis demixing, and not being suitable for mobile devices must be taken into consideration carefully. By using mixed electroosmotic/pressure-driven flow, the role of EOF in producing desired velocity profile will be reduced. In this way, the advantages of EOF can be exploited, and its disadvantages can be prevented. Induced pressure gradient can be utilized in order to control the separation in the system. Furthermore, in many complicated geometries such as T-shape microchannels, turns may induce pressure gradient to the electroosmotic velocity. While analytical formulas are completely essential for analysis and control of any industrial and laboratory microdevices, lack of such formulas in the literature for solving Poisson-Boltzmann equation and predicting electroosmotic velocity field in rectangular domains is evident. In the present study, first a novel method is proposed to solve Poisson-Boltzmann equation (PBE). Subsequently, this solution is utilized to find the electroosmotic and the mixed electroosmotic/pressure-driven velocity profile in a rectangular domain of the microchannels. To demonstrate the accuracy of the presented analytical method in solving PBE and finding electroosmotic velocity, a general nondimensional example is analyzed, and the results are compared with the solution of boundary element method. Additionally, the effects of different nondimensional parameters and also aspect ratio of channels on the electroosmotic part of the flow field will be investigated.

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

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

NASA Technical Reports Server (NTRS)

Ng, C. F.

1988-01-01

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

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.

An analytical reconstruction model of the spread-out Bragg peak using laser-accelerated proton beams.

PubMed

Tao, Li; Zhu, Kun; Zhu, Jungao; Xu, Xiaohan; Lin, Chen; Ma, Wenjun; Lu, Haiyang; Zhao, Yanying; Lu, Yuanrong; Chen, Jia-Er; Yan, Xueqing

2017-07-07

With the development of laser technology, laser-driven proton acceleration provides a new method for proton tumor therapy. However, it has not been applied in practice because of the wide and decreasing energy spectrum of laser-accelerated proton beams. In this paper, we propose an analytical model to reconstruct the spread-out Bragg peak (SOBP) using laser-accelerated proton beams. Firstly, we present a modified weighting formula for protons of different energies. Secondly, a theoretical model for the reconstruction of SOBPs with laser-accelerated proton beams has been built. It can quickly calculate the number of laser shots needed for each energy interval of the laser-accelerated protons. Finally, we show the 2D reconstruction results of SOBPs for laser-accelerated proton beams and the ideal situation. The final results show that our analytical model can give an SOBP reconstruction scheme that can be used for actual tumor therapy.

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

PubMed

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

2000-08-20

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

Analytical mass formula and nuclear surface properties in the ETF approximation. Part II: asymmetric nuclei

NASA Astrophysics Data System (ADS)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

2016-08-01

We have recently addressed the problem of the determination of the nuclear surface energy for symmetric nuclei in the framework of the extended Thomas-Fermi (ETF) approximation using Skyrme functionals. We presently extend this formalism to the case of asymmetric nuclei and the question of the surface symmetry energy. We propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves previous models and leads to a precision of better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.

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

PubMed

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

2013-10-15

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

Light distribution in diffractive multifocal optics and its optimization.

PubMed

Portney, Valdemar

2011-11-01

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

Global stability for epidemic models on multiplex networks.

PubMed

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

2018-05-01

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

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

PubMed Central

Lin, Chen-Yen; Halabi, Susan

2017-01-01

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

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

PubMed

Lin, Chen-Yen; Halabi, Susan

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Thin-plate spline quadrature of geodetic integrals

NASA Technical Reports Server (NTRS)

Vangysen, Herman

1989-01-01

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

A generalized Uhlenbeck and Beth formula for the third cluster coefficient

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

Larsen, Sigurd Yves; Lassaut, Monique; Amaya-Tapia, Alejandro, E-mail: jano@icf.unam.mx

2016-11-15

Relatively recently (Amaya-Tapia et al., 2011), we presented a formula for the evaluation of the third Bose fugacity coefficient–leading to the third virial coefficient–in terms of three-body eigenphase shifts, for particles subject to repulsive forces. An analytical calculation for a 1-dim. model, for which the result is known, confirmed the validity of this approach. We now extend the formalism to particles with attractive forces, and therefore must allow for the possibility that the particles have bound states. We thus obtain a true generalization of the famous formula of Uhlenbeck and Beth (Uhlenbeck and Beth, 1936; Beth and Uhlenbeck, 1937) and ofmore » Gropper (Gropper, 1936, 1937) for the second virial. We illustrate our formalism by a calculation, in an adiabatic approximation, of the third cluster in one dimension, using McGuire’s model as in our previous paper, but with attractive forces. The inclusion of three-body bound states is trivial; taking into account states having asymptotically two particles bound, and one free, is not.« less

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.

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

ERIC Educational Resources Information Center

Douvropoulos, Theodosios G.

2012-01-01

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

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.

Influence of changes in an eye's optical system on refraction

NASA Astrophysics Data System (ADS)

Bartkowska, Janina

1998-10-01

The optical system of eye is composed of cornea, lens, anterior chamber, and vitreous body. In the standard schematic eye there are 6 refracting surfaces. The changes of the curvature radii, of the distances between them, of the refractive indices influence the ametropia, refractive power of the eye and retinal image size. The influence of these changes can be appreciated by ray tracing or by an analytical method. There are presented simplified formulae for the differentials of ametropia and refractive power of the eye with respect to the surfaces curvatures, refracting power of cornea and lens, refractive indices. The relations are valid too for bigger changes if ametropia is measured in the cornea vertex. The formulae for the differentials with respect to distances, lens translation, eye axis length are valid if ametropia is measured in the object focus of the eye.

Probability of lensing magnification by cosmologically distributed galaxies

NASA Technical Reports Server (NTRS)

Pei, Yichuan C.

1993-01-01

We present the analytical formulae for computing the magnification probability caused by cosmologically distributed galaxies. The galaxies are assumed to be singular, truncated-isothermal spheres without both evolution and clustering in redshift. We find that, for a fixed total mass, extended galaxies produce a broader shape in the magnification probability distribution and hence are less efficient as gravitational lenses than compact galaxies. The high-magnification tail caused by large galaxies is well approximated by an A exp -3 form, while the tail by small galaxies is slightly shallower. The mean magnification as a function of redshift is, however, found to be independent of the size of the lensing galaxies. In terms of the flux conservation, our formulae for the isothermal galaxy model predict a mean magnification to within a few percent with the Dyer-Roeder model of a clumpy universe.

Turbulent equipartition pinch of toroidal momentum in spherical torus

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

An analytical computation of magnetic field generated from a cylinder ferromagnet

NASA Astrophysics Data System (ADS)

Taniguchi, Tomohiro

2018-04-01

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

Computer modeling of the mechanical behavior of composites -- Interfacial cracks in fiber-reinforced materials

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

Schmauder, S.; Haake, S.; Mueller, W.H.

Computer modeling of materials and especially modeling the mechanical behavior of composites became increasingly popular in the past few years. Among them are examples of micromechanical modeling of real structures as well as idealized model structures of linear elastic and elasto-plastic material response. In this paper, Erdogan`s Integral Equation Method (IEM) is chosen as an example for a powerful method providing principle insight into elastic fracture mechanical situations. IEM or, alternatively, complex function techniques sometimes even allow for deriving analytical solutions such as in the case of a circumferential crack along a fiber/matrix interface. The analytical formulae of this interfacemore » crack will be analyzed numerically and typical results will be presented graphically.« less

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Error analysis in some Gauss-Turan-Radau and Gauss-Turan-Lobatto quadratures for analytic functions

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2004-03-01

We consider the generalized Gauss-Turan quadrature formulae of Radau and Lobatto type for approximating . The aim of this paper is to analyze the remainder term in the case when f is an analytic function in some region of the complex plane containing the interval [-1,1] in its interior. The remainder term is presented in the form of a contour integral over confocal ellipses (cf. SIAM J. Numer. Anal. 80 (1983) 1170). Sufficient conditions on the convergence for some of such quadratures, associated with the generalized Chebyshev weight functions, are found. Using some ideas from Hunter (BIT 35 (1995) 64) we obtain new estimates of the remainder term, which are very exact. Some numerical results and illustrations are shown.

Dynamics of nanoparticle-protein corona complex formation: analytical results from population balance equations.

PubMed

Darabi Sahneh, Faryad; Scoglio, Caterina; Riviere, Jim

2013-01-01

Nanoparticle-protein corona complex formation involves absorption of protein molecules onto nanoparticle surfaces in a physiological environment. Understanding the corona formation process is crucial in predicting nanoparticle behavior in biological systems, including applications of nanotoxicology and development of nano drug delivery platforms. This paper extends the modeling work in to derive a mathematical model describing the dynamics of nanoparticle corona complex formation from population balance equations. We apply nonlinear dynamics techniques to derive analytical results for the composition of nanoparticle-protein corona complex, and validate our results through numerical simulations. The model presented in this paper exhibits two phases of corona complex dynamics. In the first phase, proteins rapidly bind to the free surface of nanoparticles, leading to a metastable composition. During the second phase, continuous association and dissociation of protein molecules with nanoparticles slowly changes the composition of the corona complex. Given sufficient time, composition of the corona complex reaches an equilibrium state of stable composition. We find analytical approximate formulae for metastable and stable compositions of corona complex. Our formulae are very well-structured to clearly identify important parameters determining corona composition. The dynamics of biocorona formation constitute vital aspect of interactions between nanoparticles and living organisms. Our results further understanding of these dynamics through quantitation of experimental conditions, modeling results for in vitro systems to better predict behavior for in vivo systems. One potential application would involve a single cell culture medium related to a complex protein medium, such as blood or tissue fluid.

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

PubMed

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

2018-05-07

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

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.

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.

Orbital and spin parts of energy currents for electromagnetic waves through spatially inhomogeneous media

NASA Astrophysics Data System (ADS)

Lee, Hyoung-In; Mok, Jinsik

2018-05-01

We investigate electromagnetic waves propagating through non-magnetic and loss-free dielectric media, but with spatially inhomogeneous refractive indices. We derive hence a set of analytic formulae for conservation laws and energy-current (Poynting) vector. As a result, we deduce that the energy-current vector cannot be neatly separated into its orbital and spin parts in contrast to the cases with spatially homogeneous media. In addition, we present physical interpretations of the two additional terms due to spatial material inhomogeneity.

A study of space shuttle energy management, approach and landing analysis

NASA Technical Reports Server (NTRS)

Morth, R.

1973-01-01

The steering system of the space shuttle vehicle is presented for the several hundred miles of flight preceding landing. The guidance scheme is characterized by a spiral turn to dissipate excess potential energy (altitude) prior to a standard straight-in final approach. In addition, the system features pilot oriented control, drag brakes, phugoid damping, and a navigational capacity founded upon an inertial measurement unit and an on-board computer. Analytic formulas are used to calculate, represent, and insure the workability of the system's specifications

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.

The tightly bound nuclei in the liquid drop model

NASA Astrophysics Data System (ADS)

Sree Harsha, N. R.

2018-05-01

In this paper, we shall maximise the binding energy per nucleon function in the semi-empirical mass formula of the liquid drop model of the atomic nuclei to analytically prove that the mean binding energy per nucleon curve has local extrema at A ≈ 58.6960, Z ≈ 26.3908 and at A ≈ 62.0178, Z ≈ 27.7506. The Lagrange method of multipliers is used to arrive at these results, while we have let the values of A and Z take continuous fractional values. The shell model that shows why 62Ni is the most tightly bound nucleus is outlined. A brief account on stellar nucleosynthesis is presented to show why 56Fe is more abundant than 62Ni and 58Fe. We believe that the analytical proof presented in this paper can be a useful tool to the instructors to introduce the nucleus with the highest mean binding energy per nucleon.

Metric of two balancing Kerr particles in physical parametrization

NASA Astrophysics Data System (ADS)

Manko, V. S.; Ruiz, E.

2015-11-01

The present paper aims at elaborating a completely physical representation for the general 4-parameter family of the extended double-Kerr spacetimes describing two spinning sources in gravitational equilibrium. This involved problem is solved in a concise analytical form by using the individual Komar masses and angular momenta as arbitrary parameters, and the simplest equatorially symmetric specialization of the general expressions obtained by us yields the physical representation for the well-known Dietz-Hoenselaers superextreme case of two balancing identical Kerr constituents. The existence of the physically meaningful "black-hole-superextreme-object" equilibrium configurations permitted by the general solution may be considered as a clear indication that the spin-spin repulsion force might actually be by far stronger than expected earlier, when only the balance between two superextreme Kerr sources was thought possible. We also present the explicit analytical formulas relating the equilibrium states in the double-Kerr and double-Reissner-Nordström configurations.

Collective relaxation dynamics of small-world networks

NASA Astrophysics Data System (ADS)

Grabow, Carsten; Grosskinsky, Stefan; Kurths, Jürgen; Timme, Marc

2015-05-01

Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph Laplacian, or a similar linear operator. The structure of networks with regular, small-world, and random connectivities are reasonably well understood, but their collective dynamical properties remain largely unknown. Here we present a two-stage mean-field theory to derive analytic expressions for network spectra. A single formula covers the spectrum from regular via small-world to strongly randomized topologies in Watts-Strogatz networks, explaining the simultaneous dependencies on network size N , average degree k , and topological randomness q . We present simplified analytic predictions for the second-largest and smallest eigenvalue, and numerical checks confirm our theoretical predictions for zero, small, and moderate topological randomness q , including the entire small-world regime. For large q of the order of one, we apply standard random matrix theory, thereby overarching the full range from regular to randomized network topologies. These results may contribute to our analytic and mechanistic understanding of collective relaxation phenomena of network dynamical systems.

Collective relaxation dynamics of small-world networks.

PubMed

Grabow, Carsten; Grosskinsky, Stefan; Kurths, Jürgen; Timme, Marc

2015-05-01

Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph Laplacian, or a similar linear operator. The structure of networks with regular, small-world, and random connectivities are reasonably well understood, but their collective dynamical properties remain largely unknown. Here we present a two-stage mean-field theory to derive analytic expressions for network spectra. A single formula covers the spectrum from regular via small-world to strongly randomized topologies in Watts-Strogatz networks, explaining the simultaneous dependencies on network size N, average degree k, and topological randomness q. We present simplified analytic predictions for the second-largest and smallest eigenvalue, and numerical checks confirm our theoretical predictions for zero, small, and moderate topological randomness q, including the entire small-world regime. For large q of the order of one, we apply standard random matrix theory, thereby overarching the full range from regular to randomized network topologies. These results may contribute to our analytic and mechanistic understanding of collective relaxation phenomena of network dynamical systems.

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.

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

TTVFaster: First order eccentricity transit timing variations (TTVs)

NASA Astrophysics Data System (ADS)

Agol, Eric; Deck, Katherine

2016-04-01

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

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

NASA Astrophysics Data System (ADS)

Doha, E. H.

2003-05-01

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

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

NASA Astrophysics Data System (ADS)

Doha, E. H.

2004-01-01

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

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.

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…

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

NASA Astrophysics Data System (ADS)

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

2004-08-01

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

The mean and variance of phylogenetic diversity under rarefaction

PubMed Central

Matsen, Frederick A.

2013-01-01

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

The mean and variance of phylogenetic diversity under rarefaction.

PubMed

Nipperess, David A; Matsen, Frederick A

2013-06-01

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

Novel design configurations for permanent magnet wind generators

NASA Astrophysics Data System (ADS)

Chen, Yicheng

2004-12-01

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

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

NASA Astrophysics Data System (ADS)

Andréassian, Vazken; Lebecherel, Laure

2013-04-01

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

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.

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.

Probing-models for interdigitated electrode systems with ferroelectric thin films

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

PubMed

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

2015-01-01

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

Cutting solid figures by plane - analytical solution and spreadsheet implementation

NASA Astrophysics Data System (ADS)

Benacka, Jan

2012-07-01

In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and cosine rules. The basic problem is to find the section of the figure by a plane that is defined by three points related to the figure. In this article, a formula is derived that gives the positions of the intersection points of such a plane and the figure edges, that is, the vertices of the section polygon. Spreadsheet implementations of the formula for cuboid and right rectangular pyramids are presented. The user can check his/her graphical solution, or proceed if he/she is not able to complete the section.

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

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.

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

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.

Relationship of attenuation in a vegetation canopy to physical parameters of the canopy

NASA Technical Reports Server (NTRS)

Karam, M. A.; Levine, D. M.

1993-01-01

A discrete scatter model is employed to compute the radiometric response (i.e. emissivity) of a layer of vegetation over a homogeneous ground. This was done to gain insight into empirical formulas for the emissivity which have recently appeared in the literature and which indicate that the attenuation through the canopy is proportional to the water content of the vegetation and inversely proportional to wavelength raised to a power around unity. The analytical result assumes that the vegetation can be modeled by a sparse layer of discrete, randomly oriented particles (leaves, stalks, etc.). The attenuation is given by the effective wave number of the layer obtained from the solution for the mean wave using the effective field approximation. By using the Ulaby-El Rayes formula to relate the dielectric constant of the vegetation to its water content, it can be shown that the attenuation is proportional to water content. The analytical form offers insight into the dependence of the empirical parameters on other variables of the canopy, including plant geometry (i.e. shape and orientation of the leaves and stalks of which the vegetation is comprised), frequency of the measurement and even the physical temperature of the vegetation. Solutions are presented for some special cases including layers consisting of cylinders (stalks) and disks (leaves).

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

PubMed

McClure, Foster D; Lee, Jung K

2005-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

PubMed

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

2017-10-25

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

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

PubMed

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

2018-06-01

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

New aspects in single-body meteor physics

NASA Astrophysics Data System (ADS)

Pecina, P.; Ceplecha, Z.

1983-03-01

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

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.

Evaluation of occupational factors on continuation of breastfeeding and formula initiation in employed mothers.

PubMed

Ahmadi, Mahshid; Moosavi, Seyyed Mohammad

2013-09-25

During recent decades, women have been increasingly involved in social activities. Despite the fact that mothers prefer to breastfeed, their return to work is associated with a reduction in breastfeeding frequency and duration. The present study evaluates the impact of occupational factors on continuation of breastfeeding and formula initiation in employed mothers with infants aged 6-12 months in Bandar-Abbas, Iran in 2010. This is a descriptive-analytic study on employed mothers with infants aged 6-12 months referring to healthcare centers of Bandar-Abbas in 2010. Data were collected through a questionnaire dealing with work-related factors in mothers' workplace. Out of 212 mothers who responded, 52.38% used formula to feed their children, and 27.36% had discontinued breastfeeding. The rate of formula use was significantly higher in mothers who had less than 6 months of maternity leave, those who did not have a suitable nursery or place to milk themselves and preserve the milk in their workplace, those working more than 6 hours per day, and those who could not take a breastfeeding break. It is essential to identify and support breastfeeding employed women. The employers should provide facilities such as nurseries, a suitable physical space for milking, as well as the equipment necessary for milk preservation. Also, such mothers should be granted breastfeeding breaks to feed their child or milk their breasts.

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.

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.

Asymmetric spin-wave dispersion in ferromagnetic nanotubes induced by surface curvature

NASA Astrophysics Data System (ADS)

Otálora, Jorge A.; Yan, Ming; Schultheiss, Helmut; Hertel, Riccardo; Kákay, Attila

2017-05-01

We present a detailed analytical derivation of the spin wave (SW) dispersion relation in magnetic nanotubes with magnetization along the azimuthal direction. The obtained formula can be used to calculate the dispersion relation for any longitudinal and azimuthal mode. The obtained dispersion is asymmetric for all azimuthal modes traveling along the axial direction. As reported in our recent publication [Phys. Rev. Lett. 117, 227203 (2016), 10.1103/PhysRevLett.117.227203], the asymmetry is a curvature-induced effect originating from the dipole-dipole interaction. Here, we discuss the asymmetry of the dispersion for azimuthal modes by analyzing the SW asymmetry Δ f (kz) =fn(kz) -fn(-kz) , where fn(kz) is the eigenfrequency of a magnon with a longitudinal and azimuthal wave vectors, kz and n , respectively; and the dependence of the maximum asymmetry with the nanotube radius R . The analytical results are in perfect agreement with micromagnetic simulations. Furthermore, we show that the dispersion relation simplifies to the thin-film dispersion relation with in-plane magnetization when analyzing the three limiting cases: (i) kz=0 , (ii) kz≫1 /R , and (iii) kz≪1 /R . In the first case, for the zeroth-order modes the thin-film Kittel formula is obtained. For modes with higher order the dispersion relation for the Backward-Volume geometry is recovered. In the second case, for the zeroth-order mode the exchange dominated dispersion relation for SW in Damon-Esbach configuration is obtained. For the case kz≪1 /R , we find that the dispersion relation can be reduced to a formula similar to the Kalinikos-Slavin [J. Phys. C: Sol. State Phys. 19, 7013 (1986), 10.1088/0022-3719/19/35/014] type.

Dynamics of Nanoparticle-Protein Corona Complex Formation: Analytical Results from Population Balance Equations

PubMed Central

Darabi Sahneh, Faryad; Scoglio, Caterina; Riviere, Jim

2013-01-01

Background Nanoparticle-protein corona complex formation involves absorption of protein molecules onto nanoparticle surfaces in a physiological environment. Understanding the corona formation process is crucial in predicting nanoparticle behavior in biological systems, including applications of nanotoxicology and development of nano drug delivery platforms. Method This paper extends the modeling work in to derive a mathematical model describing the dynamics of nanoparticle corona complex formation from population balance equations. We apply nonlinear dynamics techniques to derive analytical results for the composition of nanoparticle-protein corona complex, and validate our results through numerical simulations. Results The model presented in this paper exhibits two phases of corona complex dynamics. In the first phase, proteins rapidly bind to the free surface of nanoparticles, leading to a metastable composition. During the second phase, continuous association and dissociation of protein molecules with nanoparticles slowly changes the composition of the corona complex. Given sufficient time, composition of the corona complex reaches an equilibrium state of stable composition. We find analytical approximate formulae for metastable and stable compositions of corona complex. Our formulae are very well-structured to clearly identify important parameters determining corona composition. Conclusion The dynamics of biocorona formation constitute vital aspect of interactions between nanoparticles and living organisms. Our results further understanding of these dynamics through quantitation of experimental conditions, modeling results for in vitro systems to better predict behavior for in vivo systems. One potential application would involve a single cell culture medium related to a complex protein medium, such as blood or tissue fluid. PMID:23741371

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

PubMed

Pipe, James G; Zwart, Nicholas R

2014-01-01

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

A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization

NASA Astrophysics Data System (ADS)

Sulyok, G.

2017-07-01

Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the ultraviolet (UV-)divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast to existing recursion schemes, we are able to present a general analytic result in closed form that enables direct determination of the UV-divergent part of any one-loop tensor N-point coefficient independent from UV-divergent parts of other one-loop tensor N-point coefficients. Simplified formulas and explicit expressions are presented for A-, B-, C-, D-, E-, and F-functions.

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.

Nonparaxial and paraxial focusing of azimuthal-variant vector beams.

PubMed

Gu, Bing; Cui, Yiping

2012-07-30

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

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.

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.

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.

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.

Higher-order jump conditions for conservation laws

NASA Astrophysics Data System (ADS)

Oksuzoglu, Hakan

2018-04-01

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

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

ERIC Educational Resources Information Center

Johannessen, Kim

2010-01-01

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

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.

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.

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.

Extended adiabatic blast waves and a model of the soft X-ray background. [interstellar matter

NASA Technical Reports Server (NTRS)

Cox, D. P.; Anderson, P. R.

1981-01-01

An analytical approximation is generated which follows the development of an adiabatic spherical blast wave in a homogeneous ambient medium of finite pressure. An analytical approximation is also presented for the electron temperature distribution resulting from coulomb collisional heating. The dynamical, thermal, ionization, and spectral structures are calculated for blast waves of energy E sub 0 = 5 x 10 to the 50th power ergs in a hot low-density interstellar environment. A formula is presented for estimating the luminosity evolution of such explosions. The B and C bands of the soft X-ray background, it is shown, are reproduced by such a model explosion if the ambient density is about .000004 cm, the blast radius is roughly 100 pc, and the solar system is located inside the shocked region. Evolution in a pre-existing cavity with a strong density gradient may, it is suggested, remove both the M band and OVI discrepancies.

An analytical study of physical models with inherited temporal and spatial memory

NASA Astrophysics Data System (ADS)

Jaradat, Imad; Alquran, Marwan; Al-Khaled, Kamel

2018-04-01

Du et al. (Sci. Reb. 3, 3431 (2013)) demonstrated that the fractional derivative order can be physically interpreted as a memory index by fitting the test data of memory phenomena. The aim of this work is to study analytically the joint effect of the memory index on time and space coordinates simultaneously. For this purpose, we introduce a novel bivariate fractional power series expansion that is accompanied by twofold fractional derivatives ordering α, β\\in(0,1]. Further, some convergence criteria concerning our expansion are presented and an analog of the well-known bivariate Taylor's formula in the sense of mixed fractional derivatives is obtained. Finally, in order to show the functionality and efficiency of this expansion, we employ the corresponding Taylor's series method to obtain closed-form solutions of various physical models with inherited time and space memory.

Nonclassical thermal-state superpositions: Analytical evolution law and decoherence behavior

NASA Astrophysics Data System (ADS)

Meng, Xiang-guo; Goan, Hsi-Sheng; Wang, Ji-suo; Zhang, Ran

2018-03-01

Employing the integration technique within normal products of bosonic operators, we present normal product representations of thermal-state superpositions and investigate their nonclassical features, such as quadrature squeezing, sub-Poissonian distribution, and partial negativity of the Wigner function. We also analytically and numerically investigate their evolution law and decoherence characteristics in an amplitude-decay model via the variations of the probability distributions and the negative volumes of Wigner functions in phase space. The results indicate that the evolution formulas of two thermal component states for amplitude decay can be viewed as the same integral form as a displaced thermal state ρ(V , d) , but governed by the combined action of photon loss and thermal noise. In addition, the larger values of the displacement d and noise V lead to faster decoherence for thermal-state superpositions.

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

PubMed

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

2014-01-20

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

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

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

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.

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

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.

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

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

Watanabe, Y; Dahlman, E

2014-06-01

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

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

PubMed

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

2014-11-01

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

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

PubMed

Olendski, Oleg

2015-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Comparative Evaluation of Diagnostic Tools for Oxidative Deterioration of Polyunsaturated Fatty Acid-Enriched Infant Formulas during Storage

PubMed Central

Siefarth, Caroline; Serfert, Yvonne; Drusch, Stephan; Buettner, Andrea

2013-01-01

The challenge in the development of infant formulas enriched with polyunsaturated fatty acids (PUFAs) is to meet the consumers’ expectations with regard to high nutritional and sensory value. In particular, PUFAs may be prone to fatty acid oxidation that can generate potential rancid, metallic and/or fishy off-flavors. Although such off-flavors pose no health risk, they can nevertheless lead to rejection of products by consumers. Thus, monitoring autoxidation at its early stages is of great importance and finding a suitable analytical tool to perform these evaluations is therefore of high interest in quality monitoring. Two formulations of infant formulas were varied systematically in their mineral composition and their presence of antioxidants to produce 18 model formulas. All models were aged under controlled conditions and their oxidative deterioration was monitored. A quantitative study was performed on seven characteristic odor-active secondary oxidation products in the formulations via two-dimensional high resolution gas chromatography-mass spectrometry/olfactometry (2D-HRGC-MS/O). The sensitivity of the multi-dimensional GC-MS/O analysis was supported by two additional analytical tools for monitoring autoxidation, namely the analysis of lipid hydroperoxides and conjugated dienes. Furthermore, an aroma profile analysis (APA) was performed to reveal the presence and intensities of typical odor qualities generated in the course of fatty acid oxidation. The photometrical analyses of lipid hydroperoxides and conjugated dienes were found to be too insensitive for early indication of the development of sensory defects. By comparison, the 2D-HRGC-MS/O was capable of monitoring peroxidation of PUFAs at low ppb-level in its early stages. Thereby, it was possible to screen oxidative variances on the basis of such volatile markers already within eight weeks after production of the products, which is an earlier indication of oxidative deterioration than achievable via conventional methods. In detail, oxidative variances between the formulations revealed that lipid oxidation was low when copper was administered in an encapsulated form and when antioxidants (vitamin E, ascorbyl palmitate) were present. PMID:28234303

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.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-01

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-14

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

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.

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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.

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

NASA Astrophysics Data System (ADS)

Alexandrov, A.; Zhdanov, V.

2016-12-01

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

Unified semiclassical approach to electronic transport from diffusive to ballistic regimes

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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...

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

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

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

Lee, Teck-Ghee; Wong, Cheuk-Yin

2014-01-01

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

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.

Sterols in Infant Formulas: A Bioaccessibility Study.

PubMed

Hamdan, Islam J A; Sanchez-Siles, Luis Manuel; Garcia-Llatas, Guadalupe; Lagarda, María Jesús

2018-02-14

The design of infant formulas (IFs) seeks to resemble human milk (HM) composition and functionality. The fat sources used usually comprise vegetable oil blends to mimic the fatty acid composition of HM and introduce changes in the animal/plant sterol ratio. In contrast, the use of milk fat globule membrane (MFGM)-rich ingredients could improve this aspect by increasing the ratio. The present study evaluates the bioaccessibility (BA) of sterols (cholesterol, desmosterol, brassicasterol, campesterol, stigmasterol, and β-sitosterol) in three IFs (with or without MFGM) using an in vitro digestion method simulating infant conditions. Analytical parameters confirmed the suitability of the method for all of these sterols. Results showed the presence of MFGM to increase cholesterol content (6-7 vs 2 mg/100 mL), this being the most bioaccessible sterol in the IFs. Although the BA of cholesterol was reduced in MFGM-enriched IF (65.6-80.4% vs 99.7%), the intake of bioaccessible cholesterol from these IFs was higher.

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.

Study on characteristics of the aperture-averaging factor of atmospheric scintillation in terrestrial optical wireless communication

NASA Astrophysics Data System (ADS)

Shen, Hong; Liu, Wen-xing; Zhou, Xue-yun; Zhou, Li-ling; Yu, Long-Kun

2018-02-01

In order to thoroughly understand the characteristics of the aperture-averaging effect of atmospheric scintillation in terrestrial optical wireless communication and provide references for engineering design and performance evaluation of the optics system employed in the atmosphere, we have theoretically deduced the generally analytic expression of the aperture-averaging factor of atmospheric scintillation, and numerically investigated characteristics of the apertureaveraging factor under different propagation conditions. The limitations of the current commonly used approximate calculation formula of aperture-averaging factor have been discussed, and the results showed that the current calculation formula is not applicable for the small receiving aperture under non-uniform turbulence link. Numerical calculation has showed that aperture-averaging factor of atmospheric scintillation presented an exponential decline model for the small receiving aperture under non-uniform turbulent link, and the general expression of the model was given. This model has certain guiding significance for evaluating the aperture-averaging effect in the terrestrial optical wireless communication.

Thermodynamics of strong coupling superconductors including the effect of anisotropy

NASA Astrophysics Data System (ADS)

Daams, J. M.; Carbotte, J. P.

1981-05-01

The thermodynamics of several elemental superconductors is computed from isotropic Eliashberg theory formulated on the imaginary frequency axis. A symmary of the available experimental literature is presented and a comparison with theory is given. The small disagreements that are found are all in the direction expected from anisotropy effects. We calculate the effect of a small amount of model anisotropy on the critical temperature, critical field, and high-temperature specific heat from an exact solution of the anisotropic Eliashberg equations. These are the first such results below the critical temperature; unlike previous analytical work, we include retardation, anisotropy in the mass enhancement, and the effect of the Coulomb repulsion in enhancing anisotropy, all of which are significant. We derive a new formula independent of any model anisotropy for the rate of decrease with impurity lifetime of the critical temperature. Finally we demonstrate how the commonly used formulas of Markowitz and Kadanoff and of Clem may give entirely misleading estimates of the gap anisotropy when used to interpret certain experiments.

Lower bounds of concurrence for N-qubit systems and the detection of k-nonseparability of multipartite quantum systems

NASA Astrophysics Data System (ADS)

Qi, Xianfei; Gao, Ting; Yan, Fengli

2017-01-01

Concurrence, as one of the entanglement measures, is a useful tool to characterize quantum entanglement in various quantum systems. However, the computation of the concurrence involves difficult optimizations and only for the case of two qubits, an exact formula was found. We investigate the concurrence of four-qubit quantum states and derive analytical lower bound of concurrence using the multiqubit monogamy inequality. It is shown that this lower bound is able to improve the existing bounds. This approach can be generalized to arbitrary qubit systems. We present an exact formula of concurrence for some mixed quantum states. For even-qubit states, we derive an improved lower bound of concurrence using a monogamy equality for qubit systems. At the same time, we show that a multipartite state is k-nonseparable if the multipartite concurrence is larger than a constant related to the value of k, the qudit number and the dimension of the subsystems. Our results can be applied to detect the multipartite k-nonseparable states.

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.

The Investigation of Optimal Discrete Approximations for Real Time Flight Simulations

NASA Technical Reports Server (NTRS)

Parrish, E. A.; Mcvey, E. S.; Cook, G.; Henderson, K. C.

1976-01-01

The results are presented of an investigation of discrete approximations for real time flight simulation. Major topics discussed include: (1) consideration of the particular problem of approximation of continuous autopilots by digital autopilots; (2) use of Bode plots and synthesis of transfer functions by asymptotic fits in a warped frequency domain; (3) an investigation of the various substitution formulas, including the effects of nonlinearities; (4) use of pade approximation to the solution of the matrix exponential arising from the discrete state equations; and (5) an analytical integration of the state equation using interpolated input.

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

PubMed Central

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

2017-01-01

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

Prebreakdown characteristics of weakly ionized liquid and gaseous media in the strongly nonuniform electric field

NASA Astrophysics Data System (ADS)

Apfelbaum, M. S.; Syrovatka, R. A.; Vladimirov, V. I.

2018-01-01

A theoretical model of electrohydrodynamic prebreakdown phenomena in slightly ionized (weakly conductive) media is proposed. The electric high voltage conduction of weakly conductive liquids and slightly ionized gases in intense electric fields using this model is considered. The formula for the calculations of volt-ampere characteristics under high voltage spherical capacitor field is analytically obtained. The experimental corona discharge volt-ampere characteristics of air are presented. It was found that the size of the ionization region in the case of corona discharge in air increases monotonically with increasing discharge voltage.

Quantitative photoacoustic imaging in the acoustic regime using SPIM

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Performance of field-emitting resonating carbon nanotubes as radio-frequency demodulators

NASA Astrophysics Data System (ADS)

Vincent, P.; Poncharal, P.; Barois, T.; Perisanu, S.; Gouttenoire, V.; Frachon, H.; Lazarus, A.; de Langre, E.; Minoux, E.; Charles, M.; Ziaei, A.; Guillot, D.; Choueib, M.; Ayari, A.; Purcell, S. T.

2011-04-01

We report on a systematic study of the use of resonating nanotubes in a field emission (FE) configuration to demodulate radio frequency signals. We particularly concentrate on how the demodulation depends on the variation of the field amplification factor during resonance. Analytical formulas describing the demodulation are derived as functions of the system parameters. Experiments using AM and FM demodulations in a transmission electron microscope are also presented with a determination of all the pertinent experimental parameters. Finally we discuss the use of CNTs undergoing FE as nanoantennae and the different geometries that could be used for optimization and implementation.

Effective diffusion of confined active Brownian swimmers

NASA Astrophysics Data System (ADS)

Sandoval, Mario; Dagdug, Leonardo

2014-11-01

We find theoretically the effect of confinement and thermal fluctuations, on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian Dynamics simulations and we obtain excellent agreement. L.D. thanks Consejo Nacional de Ciencia y Tecnologia (CONACyT) Mexico, for partial support by Grant No. 176452. M. S. thanks CONACyT and Programa de Mejoramiento de Profesorado (PROMEP) for partially funding this work under Grant No. 103.5/13/6732.

Modeling of meteoroid streams: The velocity of ejection of meteoroids from comets (a review)

NASA Astrophysics Data System (ADS)

Ryabova, G. O.

2013-05-01

An analytical review of the models of ejection of meteoroids from cometary nuclei is presented. Different formulas for the ejection velocity of meteoroids and the corresponding parameters are discussed and compared with the use of comet Halley and the Geminids meteoroid stream as examples. The ejection velocities obtained from observations of the dust trails of comets are discussed, and the values for comets 2P/Encke, 4P/Faye, 17P/Holmes, 22P/Kopff, and 67P/Churyumov-Gerasimenko are compared to the velocities yielded by Whipple's model. The uncertainty intervals of the results are estimated.

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.

Anatomy of the binary black hole recoil: A multipolar analysis

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

Schnittman, Jeremy D.; Buonanno, Alessandra; Meter, James R. van

2008-02-15

We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole coalescence, for both unequal masses and nonzero, nonprecessing spins. We show that multipole moments up to and including l=4 are sufficient to accurately reproduce the final recoil velocity (within {approx_equal}2%) and that only a few dominant modes contribute significantly to it (within {approx_equal}5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical resultsmore » can be reproduced by an 'effective Newtonian' formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulas with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasinormal modes. Analytic formulas, obtained by expressing the multipole moments in terms of the fundamental quasinormal modes of a Kerr black hole, are able to explain the onset and amount of 'antikick' for each of the simulations. Lastly, we apply this multipolar analysis to help explain the remarkable difference between the amplitudes of planar and nonplanar kicks for equal-mass spinning black holes.« less

Anatomy of the Binary Black Hole Recoil: A Multipolar Analysis

NASA Technical Reports Server (NTRS)

Schnittman, Jeremy; Buonanno, Alessandra; vanMeter, James R.; Baker, John G.; Boggs, William D.; Centrella, Joan; Kelly, Bernard J.; McWilliams, Sean T.

2007-01-01

We present a multipolar analysis of the recoil velocity computed in recent numerical simulations of binary black hole coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including 1 = 4 are sufficient to accurately reproduce the final recoil velocity (= 98%) and that only a few dominant modes contribute significantly to it (2 95%). We describe how the relative amplitude, and more importantly, the relative phase, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ring-down phases. We also find that the numerical results can be reproduced, to a high level of accuracy, by an effective Newtonian formula for the multipole moments obtained by replacing in the Newtonian formula the radial separation with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasi-normal modes. Analytic formulae, obtained by expressing the multipole moments in terms of the fundamental QNMs of a Kerr BH, are able to explain the onset and amount of '.anti-kick" for each of the simulations. Lastly, we apply this multipolar analysis to understand the remarkable difference between the amplitudes of planar and non-planar kicks for equal-mass spinning black holes.

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.

Analytic solution for American strangle options using Laplace-Carson transforms

NASA Astrophysics Data System (ADS)

Kang, Myungjoo; Jeon, Junkee; Han, Heejae; Lee, Somin

2017-06-01

A strangle has been important strategy for options when the trader believes there will be a large movement in the underlying asset but are uncertain of which way the movement will be. In this paper, we derive analytic formula for the price of American strangle options. American strangle options can be mathematically formulated into the free boundary problems involving two early exercise boundaries. By using Laplace-Carson Transform(LCT), we can derive the nonlinear system of equations satisfied by the transformed value of two free boundaries. We then solve this nonlinear system using Newton's method and finally get the free boundaries and option values using numerical Laplace inversion techniques. We also derive the Greeks for the American strangle options as well as the value of perpetual American strangle options. Furthermore, we present various graphs for the free boundaries and option values according to the change of parameters.

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

Descendants of the first stars: the distinct chemical signature of second generation stars

NASA Astrophysics Data System (ADS)

Hartwig, Tilman; Yoshida, Naoki; Magg, Mattis; Frebel, Anna; Glover, Simon C. O.; Gómez, Facundo A.; Griffen, Brendan; Ishigaki, Miho N.; Ji, Alexander P.; Klessen, Ralf S.; O'Shea, Brian W.; Tominaga, Nozomu

2018-05-01

Extremely metal-poor (EMP) stars in the Milky Way (MW) allow us to infer the properties of their progenitors by comparing their chemical composition to the metal yields of the first supernovae. This method is most powerful when applied to mono-enriched stars, i.e. stars that formed from gas that was enriched by only one previous supernova. We present a novel diagnostic to identify this subclass of EMP stars. We model the first generations of star formation semi-analytically, based on dark matter halo merger trees that yield MW-like halos at the present day. Radiative and chemical feedback are included self-consistently and we trace all elements up to zinc. Mono-enriched stars account for only ˜1% of second generation stars in our fiducial model and we provide an analytical formula for this probability. We also present a novel analytical diagnostic to identify mono-enriched stars, based on the metal yields of the first supernovae. This new diagnostic allows us to derive our main results independently from the specific assumptions made regarding Pop III star formation, and we apply it to a set of observed EMP stars to demonstrate its strengths and limitations. Our results may provide selection criteria for current and future surveys and therefore contribute to a deeper understanding of EMP stars and their progenitors.

The Spectral Shift Function and Spectral Flow

NASA Astrophysics Data System (ADS)

Azamov, N. A.; Carey, A. L.; Sukochev, F. A.

2007-11-01

At the 1974 International Congress, I. M. Singer proposed that eta invariants and hence spectral flow should be thought of as the integral of a one form. In the intervening years this idea has lead to many interesting developments in the study of both eta invariants and spectral flow. Using ideas of [24] Singer’s proposal was brought to an advanced level in [16] where a very general formula for spectral flow as the integral of a one form was produced in the framework of noncommutative geometry. This formula can be used for computing spectral flow in a general semifinite von Neumann algebra as described and reviewed in [5]. In the present paper we take the analytic approach to spectral flow much further by giving a large family of formulae for spectral flow between a pair of unbounded self-adjoint operators D and D + V with D having compact resolvent belonging to a general semifinite von Neumann algebra {mathcal{N}} and the perturbation V in {mathcal{N}} . In noncommutative geometry terms we remove summability hypotheses. This level of generality is made possible by introducing a new idea from [3]. There it was observed that M. G. Krein’s spectral shift function (in certain restricted cases with V trace class) computes spectral flow. The present paper extends Krein’s theory to the setting of semifinite spectral triples where D has compact resolvent belonging to {mathcal{N}} and V is any bounded self-adjoint operator in {mathcal{N}} . We give a definition of the spectral shift function under these hypotheses and show that it computes spectral flow. This is made possible by the understanding discovered in the present paper of the interplay between spectral shift function theory and the analytic theory of spectral flow. It is this interplay that enables us to take Singer’s idea much further to create a large class of one forms whose integrals calculate spectral flow. These advances depend critically on a new approach to the calculus of functions of non-commuting operators discovered in [3] which generalizes the double operator integral formalism of [8-10]. One surprising conclusion that follows from our results is that the Krein spectral shift function is computed, in certain circumstances, by the Atiyah-Patodi-Singer index theorem [2].

Asymptotic co- and post-seismic displacements in a homogeneous Maxwell sphere

NASA Astrophysics Data System (ADS)

Tang, He; Sun, Wenke

2018-07-01

The deformations of the Earth caused by internal and external forces are usually expressed through Green's functions or the superposition of normal modes, that is, via numerical methods, which are applicable for computing both co- and post-seismic deformations. It is difficult to express these deformations in an analytical form, even for a uniform viscoelastic sphere. In this study, we present a set of asymptotic solutions for computing co- and post-seismic displacements; these solutions can be further applied to solving co- and post-seismic geoid, gravity and strain changes. Expressions are derived for a uniform Maxwell Earth by combining the reciprocity theorem, which links earthquake, tidal, shear and loading deformations, with the asymptotic solutions of these three external forces (tidal, shear and loading) and analytical inverse Laplace transformation formulae. Since the asymptotic solutions are given in a purely analytical form without series summations or extra convergence skills, they can be practically applied in an efficient way, especially when computing post-seismic deformations and glacial isotactic adjustments of the Earth over long timescales.

Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory

NASA Astrophysics Data System (ADS)

Raymond Ooi, C. H.; Sun, Qingqing; Zubairy, M. Suhail; Scully, Marlan O.

2007-01-01

We present a largely analytical theory for two-photon correlations G(2) between Stokes (s) and anti-Stokes (a) photon pairs from an extended medium (amplifier) composed of double- Λ atoms in counterpropagating geometry. We generalize the parametric coupled equations with quantum Langevin noise given in a beautiful experimental paper of Balic [Phys. Rev. Lett. 94, 183601 (2005)] beyond adiabatic approximation and valid for arbitrary strength and detuning of laser fields. We derive an analytical formula for cross correlation Gas(2)=⟨Ês†(L)Êa†(0,τ)Êa(0,τ)Ês(L)⟩ and use it to obtain results that are in good quantitative agreement with the experimental data. Results for Gas(2) obtained using our coupled equations are in good quantitative agreement with the results using the equations of Balic , while perfect agreement is obtained for sufficiently large detuning. We also compute the reverse correlation Gsa(2) which turns out to be negligibly small and remains classical while the cross correlation violates the Cauchy-Schwartz inequality by a factor of more than a hundred.

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.

Asymptotic Co- and Post-seismic displacements in a homogeneous Maxwell sphere

NASA Astrophysics Data System (ADS)

Tang, He; Sun, Wenke

2018-05-01

The deformations of the Earth caused by internal and external forces are usually expressed through Green's functions or the superposition of normal modes, i.e. via numerical methods, which are applicable for computing both co- and post-seismic deformations. It is difficult to express these deformations in an analytical form, even for a uniform viscoelastic sphere. In this study, we present a set of asymptotic solutions for computing co- and post-seismic displacements; these solutions can be further applied to solving co- and post-seismic geoid, gravity, and strain changes. Expressions are derived for a uniform Maxwell Earth by combining the reciprocity theorem, which links earthquake, tidal, shear and loading deformations, with the asymptotic solutions of these three external forces (tidal, shear and loading) and analytical inverse Laplace transformation formulae. Since the asymptotic solutions are given in a purely analytical form without series summations or extra convergence skills, they can be practically applied in an efficient way, especially when computing post-seismic deformations and glacial isotactic adjustments of the Earth over long timescales.

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

PubMed

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

2010-06-25

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

Barycentric parameterizations for isotropic BRDFs.

PubMed

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

2005-01-01

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

Updated hazard rate equations for dual safeguard systems.

PubMed

Rothschild, Marc

2007-04-11

A previous paper by this author [M.J. Rothschild, Updated hazard rate equation for single safeguards, J. Hazard. Mater. 130 (1-2) (2006) 15-20] showed that commonly used analytical methods for quantifying failure rates overestimates the risk in some circumstances. This can lead the analyst to mistakenly believe that a given operation presents an unacceptable risk. For a single safeguard system, a formula was presented in that paper that accurately evaluates the risk over a wide range of conditions. This paper expands on that analysis by evaluating the failure rate for dual safeguard systems. The safeguards can be activated at the same time or at staggered times, and the safeguard may provide an indication whether it was successful upon a challenge, or its status may go undetected. These combinations were evaluated using a Monte Carlo simulation. Empirical formulas for evaluating the hazard rate were developed from this analysis. It is shown that having the safeguards activate at the same time while providing positive feedback of their individual actions is the most effective arrangement in reducing the hazard rate. The hazard rate can also be reduced by staggering the testing schedules of the safeguards.

Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant-Exner morphodynamic model

NASA Astrophysics Data System (ADS)

Carraro, F.; Valiani, A.; Caleffi, V.

2018-03-01

Within the framework of the de Saint Venant equations coupled with the Exner equation for morphodynamic evolution, this work presents a new efficient implementation of the Dumbser-Osher-Toro (DOT) scheme for non-conservative problems. The DOT path-conservative scheme is a robust upwind method based on a complete Riemann solver, but it has the drawback of requiring expensive numerical computations. Indeed, to compute the non-linear time evolution in each time step, the DOT scheme requires numerical computation of the flux matrix eigenstructure (the totality of eigenvalues and eigenvectors) several times at each cell edge. In this work, an analytical and compact formulation of the eigenstructure for the de Saint Venant-Exner (dSVE) model is introduced and tested in terms of numerical efficiency and stability. Using the original DOT and PRICE-C (a very efficient FORCE-type method) as reference methods, we present a convergence analysis (error against CPU time) to study the performance of the DOT method with our new analytical implementation of eigenstructure calculations (A-DOT). In particular, the numerical performance of the three methods is tested in three test cases: a movable bed Riemann problem with analytical solution; a problem with smooth analytical solution; a test in which the water flow is characterised by subcritical and supercritical regions. For a given target error, the A-DOT method is always the most efficient choice. Finally, two experimental data sets and different transport formulae are considered to test the A-DOT model in more practical case studies.

Parametric Improper Integrals, Wallis Formula and Catalan Numbers

ERIC Educational Resources Information Center

Dana-Picard, Thierry; Zeitoun, David G.

2012-01-01

We present a sequence of improper integrals, for which a closed formula can be computed using Wallis formula and a non-straightforward recurrence formula. This yields a new integral presentation for Catalan numbers.

Parametric improper integrals, Wallis formula and Catalan numbers

NASA Astrophysics Data System (ADS)

Dana-Picard, Thierry; Zeitoun, David G.

2012-06-01

We present a sequence of improper integrals, for which a closed formula can be computed using Wallis formula and a non-straightforward recurrence formula. This yields a new integral presentation for Catalan numbers.

Degenerate limit thermodynamics beyond leading order for models of dense matter

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

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

2015-12-15

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

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

PubMed

Hošek, Lukáš; Wilkie, Alexander

2013-01-01

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

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

PubMed

Dutta, Annwesha; Chowdhury, Debashish

2017-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

PubMed

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

2012-01-01

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

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

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

Fukushima, Takuma; Fujita, Yutaka; To, Sho

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

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

PubMed

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

2008-01-01

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

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

PubMed

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

2005-10-22

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

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.

Measurement of the muon reconstruction performance of the ATLAS detector using 2011 and 2012 LHC proton-proton collision data.

PubMed

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Sugaya, Y; Suhr, C; Suk, M; Sulin, V V; Sultansoy, S; Sumida, T; Sun, S; Sun, X; Sundermann, J E; Suruliz, K; Susinno, G; Sutton, M R; Suzuki, Y; Svatos, M; Swedish, S; Swiatlowski, M; Sykora, I; Sykora, T; Ta, D; Taccini, C; Tackmann, K; Taenzer, J; Taffard, A; Tafirout, R; Taiblum, N; Takai, H; Takashima, R; Takeda, H; Takeshita, T; Takubo, Y; Talby, M; Talyshev, A A; Tam, J Y C; Tan, K G; Tanaka, J; Tanaka, R; Tanaka, S; Tanaka, S; Tanasijczuk, A J; Tannenwald, B B; Tannoury, N; Tapprogge, S; Tarem, S; Tarrade, F; Tartarelli, G F; Tas, P; Tasevsky, M; Tashiro, T; Tassi, E; Tavares Delgado, A; Tayalati, Y; Taylor, F E; Taylor, G N; Taylor, W; Teischinger, F A; Teixeira Dias Castanheira, M; Teixeira-Dias, P; Temming, K K; Ten Kate, H; Teng, P K; Teoh, J J; Terada, S; Terashi, K; Terron, J; Terzo, S; Testa, M; Teuscher, R J; Therhaag, J; Theveneaux-Pelzer, T; Thomas, J P; Thomas-Wilsker, J; Thompson, E N; Thompson, P D; Thompson, P D; Thompson, R J; Thompson, A S; Thomsen, L A; Thomson, E; Thomson, M; Thong, W M; Thun, R P; Tian, F; Tibbetts, M J; Tikhomirov, V O; Tikhonov, Yu A; Timoshenko, S; Tiouchichine, E; Tipton, P; Tisserant, S; Todorov, T; Todorova-Nova, S; Toggerson, B; Tojo, J; Tokár, S; Tokushuku, K; Tollefson, K; Tomlinson, L; Tomoto, M; Tompkins, L; Toms, K; Topilin, N D; Torrence, E; Torres, H; Torró Pastor, E; Toth, J; Touchard, F; Tovey, D R; Tran, H L; Trefzger, T; Tremblet, L; Tricoli, A; Trigger, I M; Trincaz-Duvoid, S; Tripiana, M F; Trischuk, W; Trocmé, B; Troncon, C; Trottier-McDonald, M; Trovatelli, M; True, P; Trzebinski, M; Trzupek, A; Tsarouchas, C; Tseng, J C-L; Tsiareshka, P V; Tsionou, D; Tsipolitis, G; Tsirintanis, N; Tsiskaridze, S; Tsiskaridze, V; Tskhadadze, E G; Tsukerman, I I; Tsulaia, V; Tsuno, S; Tsybychev, D; Tudorache, A; Tudorache, V; Tuna, A N; Tupputi, S A; Turchikhin, S; Turecek, D; Turk Cakir, I; Turra, R; Tuts, P M; Tykhonov, A; Tylmad, M; Tyndel, M; Uchida, K; Ueda, I; Ueno, R; Ughetto, M; Ugland, M; Uhlenbrock, M; Ukegawa, F; 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Young, C J S; Youssef, S; Yu, D R; Yu, J; Yu, J M; Yu, J; Yuan, L; Yurkewicz, A; Yusuff, I; Zabinski, B; Zaidan, R; Zaitsev, A M; Zaman, A; Zambito, S; Zanello, L; Zanzi, D; Zeitnitz, C; Zeman, M; Zemla, A; Zengel, K; Zenin, O; Ženiš, T; Zerwas, D; Zevi Della Porta, G; Zhang, D; Zhang, F; Zhang, H; Zhang, J; Zhang, L; Zhang, X; Zhang, Z; Zhao, Z; Zhemchugov, A; Zhong, J; Zhou, B; Zhou, L; Zhou, N; Zhu, C G; Zhu, H; Zhu, J; Zhu, Y; Zhuang, X; Zhukov, K; Zibell, A; Zieminska, D; Zimine, N I; Zimmermann, C; Zimmermann, R; Zimmermann, S; Zimmermann, S; Zinonos, Z; Ziolkowski, M; Zobernig, G; Zoccoli, A; Zur Nedden, M; Zurzolo, G; Zutshi, V; Zwalinski, L

This paper presents the performance of the ATLAS muon reconstruction during the LHC run with [Formula: see text] collisions at [Formula: see text]-8 TeV in 2011-2012, focusing mainly on data collected in 2012. Measurements of the reconstruction efficiency and of the momentum scale and resolution, based on large reference samples of [Formula: see text], [Formula: see text] and [Formula: see text] decays, are presented and compared to Monte Carlo simulations. Corrections to the simulation, to be used in physics analysis, are provided. Over most of the covered phase space (muon [Formula: see text] and [Formula: see text] GeV) the efficiency is above [Formula: see text] and is measured with per-mille precision. The momentum resolution ranges from [Formula: see text] at central rapidity and for transverse momentum [Formula: see text] GeV, to [Formula: see text] at large rapidity and [Formula: see text] GeV. The momentum scale is known with an uncertainty of [Formula: see text] to [Formula: see text] depending on rapidity. A method for the recovery of final state radiation from the muons is also presented.

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

A Malaria Transmission Model with Temperature-Dependent Incubation Period.

PubMed

Wang, Xiunan; Zhao, Xiao-Qiang

2017-05-01

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

α -decay chains of the superheavy nuclei Rg-350255

NASA Astrophysics Data System (ADS)

Santhosh, K. P.; Nithya, C.

2017-05-01

The decay modes and half-lives of 96 isotopes of the superheavy element roentgenium (Rg) within the range of 255 ≤A ≤350 come under investigation in the present paper. The isotopes which lie beyond the proton drip line are identified by calculating the one-proton and two-proton separation energies. The α -decay half-lives are calculated using the Coulomb and proximity potential model for deformed nuclei (CPPMDN). For a theoretical comparison the α half-lives are also evaluated using the Viola-Seaborg semiempirical relation, the universal curve of Poenaru et al., the analytical formula of Royer, and the universal decay law of Qi et al. Spontaneous fission half-lives are computed with the shell-effect-dependent formula of Santhosh and Nithya and the semiempirical formula of Xu et al. The decay modes are predicted by comparing the α -decay half-lives within the CPPMDN with the corresponding spontaneous fission half-lives computed by the shell-effect-dependent formula of Santhosh and Nithya. In our paper it is seen that the isotopes 255-271,273Rg lie beyond the proton drip line and hence decay through proton emission. The isotopes 272,274-277Rg exhibit long α chains. Three α chains are predicted from the isotopes Rg-282278. The isotopes Rg-345283 decay through spontaneous fission. The isotopes Rg-350346 are found to be stable against α decay. The theoretical results are compared with the available experimental results and are seen to be matching well. We hope that our predictions will be useful in future experimental investigations.

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

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

Numerical methods on European option second order asymptotic expansions for multiscale stochastic volatility

NASA Astrophysics Data System (ADS)

Canhanga, Betuel; Ni, Ying; Rančić, Milica; Malyarenko, Anatoliy; Silvestrov, Sergei

2017-01-01

After Black-Scholes proposed a model for pricing European Options in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption made by Black-Scholes was one of the main reasons for the model to be unable to capture some market details. Instead of constant volatilities, they introduced stochastic volatilities to the asset dynamic modeling. In 2009, Christoffersen empirically showed "why multifactor stochastic volatility models work so well". Four years later, Chiarella and Ziveyi solved the model proposed by Christoffersen. They considered an underlying asset whose price is governed by two factor stochastic volatilities of mean reversion type. Applying Fourier transforms, Laplace transforms and the method of characteristics they presented a semi-analytical formula to compute an approximate price for American options. The huge calculation involved in the Chiarella and Ziveyi approach motivated the authors of this paper in 2014 to investigate another methodology to compute European Option prices on a Christoffersen type model. Using the first and second order asymptotic expansion method we presented a closed form solution for European option, and provided experimental and numerical studies on investigating the accuracy of the approximation formulae given by the first order asymptotic expansion. In the present paper we will perform experimental and numerical studies for the second order asymptotic expansion and compare the obtained results with results presented by Chiarella and Ziveyi.

Curvilinear Squeeze Film Bearing with Porous Wall Lubricated by a Rabinowitsch Fluid

NASA Astrophysics Data System (ADS)

Walicka, A.; Walicki, E.; Jurczak, P.; Falicki, J.

2017-05-01

The present theoretical analysis is to investigate the effect of non-Newtonian lubricant modelled by a Rabinowitsch fluid on the performance of a curvilinear squeeze film bearing with one porous wall. The equations of motion of a Rabinowitsch fluid are used to derive the Reynolds equation. After general considerations on the flow in a bearing clearance and in a porous layer using the Morgan-Cameron approximation the modified Reynolds equation is obtained. The analytical solution of this equation for the case of a squeeze film bearing is presented. As a result one obtains the formulae expressing pressure distribution and load-carrying capacity. Thrust radial bearing and spherical bearing with a squeeze film are considered as numerical examples.

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

PubMed

Schwabl, Herbert; Vennos, Cécile

2015-06-05

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

Analysis of Stress in Steel and Concrete in Cfst Push-Out Test Samples

NASA Astrophysics Data System (ADS)

Grzeszykowski, Bartosz; Szadkowska, Magdalena; Szmigiera, Elżbieta

2017-09-01

The paper presents the analysis of stress in steel and concrete in CFST composite elements subjected to push-out tests. Two analytical models of stress distribution are presented. The bond at the interface between steel and concrete in the initial phase of the push-out test is provided by the adhesion. Until the force reach a certain value, the slip between both materials does not occur or it is negligibly small, what ensures full composite action of the specimen. In the first analytical model the full bond between both materials was assumed. This model allows to estimate value of the force for which the local loss of adhesion in given cross section begins. In the second model it was assumed that the bond stress distribution is constant along the shear transfer length of the specimen. Based on that the formulas for triangle distribution of stress in steel and concrete for the maximum push-out force were derived and compared with the experimental results. Both models can be used to better understand the mechanisms of interaction between steel and concrete in composite steel-concrete columns.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

A Finite Layer Formulation for Groundwater Flow to Horizontal Wells.

PubMed

Xu, Jin; Wang, Xudong

2016-09-01

A finite layer approach for the general problem of three-dimensional (3D) flow to horizontal wells in multilayered aquifer systems is presented, in which the unconfined flow can be taken into account. The flow is approximated by an integration of the standard finite element method in vertical direction and the analytical techniques in the other spatial directions. Because only the vertical discretization is involved, the horizontal wells can be completely contained in one specific nodal plane without discretization. Moreover, due to the analytical eigenfunctions introduced in the formulation, the weighted residual equations can be decoupled, and the formulas for the global matrices and flow vector corresponding to horizontal wells can be obtained explicitly. Consequently, the bandwidth of the global matrices and computational cost rising from 3D analysis can be significantly reduced. Two comparisons to the existing solutions are made to verify the validity of the formulation, including transient flow to horizontal wells in confined and unconfined aquifers. Furthermore, an additional numerical application to horizontal wells in three-layered systems is presented to demonstrate the applicability of the present method in modeling flow in more complex aquifer systems. © 2016, National Ground Water Association.

A "three-in-one" sample preparation method for simultaneous determination of B-group water-soluble vitamins in infant formula using VitaFast(®) kits.

PubMed

Zhang, Heng; Lan, Fang; Shi, Yupeng; Wan, Zhi-Gang; Yue, Zhen-Feng; Fan, Fang; Lin, Yan-Kui; Tang, Mu-Jin; Lv, Jing-Zhang; Xiao, Tan; Yi, Changqing

2014-06-15

VitaFast(®) test kits designed for the microbiological assay in microtiter plate format can be applied to quantitative determination of B-group water-soluble vitamins such as vitamin B12, folic acid and biotin, et al. Compared to traditional microbiological methods, VitaFast(®) kits significantly reduce sample processing time and provide greater reliability, higher productivity and better accuracy. Recently, simultaneous determination of vitamin B12, folic acid and biotin in one sample is urgently required when evaluating the quality of infant formulae in our practical work. However, the present sample preparation protocols which are developed for individual test systems, are incompatible with simultaneous determination of several analytes. To solve this problem, a novel "three-in-one" sample preparation method is herein developed for simultaneous determination of B-group water-soluble vitamins using VitaFast(®) kits. The performance of this novel "three-in-one" sample preparation method was systematically evaluated through comparing with individual sample preparation protocols. The experimental results of the assays which employed "three-in-one" sample preparation method were in good agreement with those obtained from conventional VitaFast(®) extraction methods, indicating that the proposed "three-in-one" sample preparation method is applicable to the present three VitaFast(®) vitamin test systems, thus offering a promising alternative for the three independent sample preparation methods. The proposed new sample preparation method will significantly improve the efficiency of infant formulae inspection. Copyright © 2013 Elsevier Ltd. 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 Central

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

2018-01-01

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

Phonon dispersion on Ag (100) surface: A modified analytic embedded atom method study

NASA Astrophysics Data System (ADS)

Xiao-Jun, Zhang; Chang-Le, Chen

2016-01-01

Within the harmonic approximation, the analytic expression of the dynamical matrix is derived based on the modified analytic embedded atom method (MAEAM) and the dynamics theory of surface lattice. The surface phonon dispersions along three major symmetry directions , and X¯M¯ are calculated for the clean Ag (100) surface by using our derived formulas. We then discuss the polarization and localization of surface modes at points X¯ and M¯ by plotting the squared polarization vectors as a function of the layer index. The phonon frequencies of the surface modes calculated by MAEAM are compared with the available experimental and other theoretical data. It is found that the present results are generally in agreement with the referenced experimental or theoretical results, with a maximum deviation of 10.4%. The agreement shows that the modified analytic embedded atom method is a reasonable many-body potential model to quickly describe the surface lattice vibration. It also lays a significant foundation for studying the surface lattice vibration in other metals. Project supported by the National Natural Science Foundation of China (Grant Nos. 61471301 and 61078057), the Scientific Research Program Funded by Shaanxi Provincial Education Department, China (Grant No. 14JK1301), and the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20126102110045).

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.

Investigation of plasmonic resonances in the two-dimensional electron gas of an InGaAs/InP high electron mobility transistor

NASA Astrophysics Data System (ADS)

Cleary, Justin W.; Peale, Robert E.; Saxena, Himanshu; Buchwald, Walter R.

2011-05-01

The observation of THz regime transmission resonances in an InGaAs/InP high electron mobility transistor (HEMT) can be attributed to excitation of plasmons in its two-dimensional electron gas (2DEG). Properties of grating-based, gate-voltage tunable resonances are shown to be adequately modeled using commercial finite element method (FEM) software when the HEMT layer structure, gate geometry and sheet charge concentration are taken into account. The FEM results are shown to produce results consistent with standard analytical theories in the 10-100 cm-1 wavenumber range. An original analytic formula presented here describes how the plasmonic resonance may change in the presence of a virtual gate, or region of relatively high free charge carriers that lies in the HEMT between the physical grating gate and the 2DEG. The virtual gate and corresponding analytic formulation are able to account for the red-shifting experimentally observed in plasmonic resonances. The calculation methods demonstrated here have the potential to greatly aid in the design of future detection devices that require specifically tuned plasmonic modes in the 2DEG of a HEMT, as well as giving new insights to aid in the development of more complete analytic theories.

A direct method for nonlinear ill-posed problems

NASA Astrophysics Data System (ADS)

Lakhal, A.

2018-02-01

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

Minimum-Cost Aircraft Descent Trajectories with a Constrained Altitude Profile

NASA Technical Reports Server (NTRS)

Wu, Minghong G.; Sadovsky, Alexander V.

2015-01-01

An analytical formula for solving the speed profile that accrues minimum cost during an aircraft descent with a constrained altitude profile is derived. The optimal speed profile first reaches a certain speed, called the minimum-cost speed, as quickly as possible using an appropriate extreme value of thrust. The speed profile then stays on the minimum-cost speed as long as possible, before switching to an extreme value of thrust for the rest of the descent. The formula is applied to an actual arrival route and its sensitivity to winds and airlines' business objectives is analyzed.

Spatial derivatives of flow quantities behind curved shocks of all strengths

NASA Technical Reports Server (NTRS)

Darden, C. M.

1984-01-01

Explicit formulas in terms of shock curvature are developed for spatial derivatives of flow quantities behind a curved shock for two-dimensional inviscid steady flow. Factors which yield the equations indeterminate as the shock strength approaches 0 have been cancelled analytically so that formulas are valid for shocks of any strength. An application for the method is shown in the solution of shock coalescence when nonaxisymmetric effects are felt through derivatives in the circumferential direction. The solution of this problem requires flow derivatives behind the shock in both the axial and radial direction.

Analytical theory of coherent synchrotron radiation wakefield of short bunches shielded by conducting parallel plates

NASA Astrophysics Data System (ADS)

Stupakov, Gennady; Zhou, Demin

2016-04-01

We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. All our formulas are benchmarked against numerical simulations with the CSRZ computer code.

Analytical effective tensor for flow-through composites

DOEpatents

Sviercoski, Rosangela De Fatima [Los Alamos, NM

2012-06-19

A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective tensor K.sup.a suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.

Analytical theory of coherent synchrotron radiation wakefield of short bunches shielded by conducting parallel plates

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

Stupakov, Gennady; Zhou, Demin

2016-04-21

We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. All our formulas are benchmarked against numerical simulations with the CSRZ computer code.

Determination of Free and Total Choline and Carnitine in Infant Formula and Adult/Pediatric Nutritional Formula by Liquid Chromatography/Tandem Mass Spectrometry (LC/MS/MS): Single-Laboratory Validation, First Action 2015.10.

PubMed

Ellingson, David J; Shippar, Jeffrey J; Gilmore, Justin M

2016-01-01

Analytical methods for the analysis of both L-carnitine and choline are needed for reliable and accurate determination in infant formula and adult/pediatric nutritional formula. These compounds are different in how they are utilized by the human body, but are structurally similar. L-carnitine and choline are quaternary ammonium compounds, enabling both to be retained under acidic conditions with strong cation exchange (SCX) chromatography. This method analyzes both compounds simultaneously as either the free forms or as a total amount that includes bound sources such as phosphatidylcholine or acetylcarnitine. The free analysis consists of water extraction and analysis by LC/MS/MS, while the total analysis consists of extraction by acid assisted microwave hydrolysis and analysis by LC/MS/MS. Calibration standards used for calculations are extracted with all samples in the batch. A single laboratory validation (SLV) was performed following the guidelines of the AOAC Stakeholder Panel on Infant Formula and Adult Nutritionals (SPIFAN) utilizing the kit of materials provided. The results achieved meet the requirements of SMPR 2012.010 and 2012.013 for L-carnitine and total choline, respectively.

Comparison of PSF maxima and minima of multiple annuli coded aperture (MACA) and complementary multiple annuli coded aperture (CMACA) systems

NASA Astrophysics Data System (ADS)

Ratnam, Challa; Lakshmana Rao, Vadlamudi; Lachaa Goud, Sivagouni

2006-10-01

In the present paper, and a series of papers to follow, the Fourier analytical properties of multiple annuli coded aperture (MACA) and complementary multiple annuli coded aperture (CMACA) systems are investigated. First, the transmission function for MACA and CMACA is derived using Fourier methods and, based on the Fresnel-Kirchoff diffraction theory, the formulae for the point spread function are formulated. The PSF maxima and minima are calculated for both the MACA and CMACA systems. The dependence of these properties on the number of zones is studied and reported in this paper.

Cyclic plasticity models and application in fatigue analysis

NASA Technical Reports Server (NTRS)

Kalev, I.

1981-01-01

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

Cosmic muon flux measurements at the Kimballton Underground Research Facility

NASA Astrophysics Data System (ADS)

Kalousis, L. N.; Guarnaccia, E.; Link, J. M.; Mariani, C.; Pelkey, R.

2014-08-01

In this article, the results from a series of muon flux measurements conducted at the Kimballton Underground Research Facility (KURF), Virginia, United States, are presented. The detector employed for these investigations, is made of plastic scintillator bars readout by wavelength shifting fibers and multianode photomultiplier tubes. Data was taken at several locations inside KURF, spanning rock overburden values from ~ 200 to 1450 m.w.e. From the extracted muon rates an empirical formula was devised, that estimates the muon flux inside the mine as a function of the overburden. The results are in good agreement with muon flux calculations based on analytical models and MUSIC.

Path-integral approach to the Wigner-Kirkwood expansion.

PubMed

Jizba, Petr; Zatloukal, Václav

2014-01-01

We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones, we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation, are discussed.

Universal lineshapes at the crossover between weak and strong critical coupling in Fano-resonant coupled oscillators

NASA Astrophysics Data System (ADS)

Zanotto, Simone; Tredicucci, Alessandro

2016-04-01

In this article we discuss a model describing key features concerning the lineshapes and the coherent absorption conditions in Fano-resonant dissipative coupled oscillators. The model treats on the same footing the weak and strong coupling regimes, and includes the critical coupling concept, which is of great relevance in numerous applications; in addition, the role of asymmetry is thoroughly analyzed. Due to the wide generality of the model, which can be adapted to various frameworks like nanophotonics, plasmonics, and optomechanics, we envisage that the analytical formulas presented here will be crucial to effectively design devices and to interpret experimental results.

Analytical dose evaluation of neutron and secondary gamma-ray skyshine from nuclear facilities

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

Hayashi, K.; Nakamura, T.

1985-11-01

The skyshine dose distributions of neutron and secondary gamma rays were calculated systematically using the Monte Carlo method for distances up to 2 km from the source. The energy of source neutrons ranged from thermal to 400 MeV; their emission angle from 0 to 90 deg from the ver tical was treated with a distribution of the direction cosine containing five equal intervals. Calculated dose distributions D(r) were fitted to the formula; D(r) = Q exp (-r/lambda)/r. The value of Q and lambda are slowly varied functions of energy. This formula was applied to the benchmark problems of neutron skyshinemore » from fission, fusion, and accelerator facilities, and good agreement was achieved. This formula will be quite useful for shielding designs of various nuclear facilities.« less

Cloud effects on ultraviolet photoclimatology

NASA Technical Reports Server (NTRS)

Green, A. E. S.; Spinhirne, J. D.

1978-01-01

The purpose of this study is to quantify for the needs of photobiology the influence of clouds upon the ultraviolet spectral irradiance reaching the ground. Towards this end, analytic formulas are developed which approximately characterize the influence of clouds upon total solar radiation. These may be used in conjunction with a solar pyranometer to assign an effective visual optical depth for the cloud cover. A formula is also developed which characterizes the influence of the optical depth of clouds upon the UV spectral irradiance in the 280-340 nm region. Thus total solar energy observations to assign cloud optical properties can be used to calculate the UV spectral irradiance at the ground in the presence of these clouds. As incidental by-products of this effort, convenient formulas are found for the direct and diffuse components of total solar energy.

Delving Deeper: Transforming Shapes Physically and Analytically

ERIC Educational Resources Information Center

Rathouz, Margaret; Novak, Christopher; Clifford, John

2013-01-01

Constructing formulas "from scratch" for calculating geometric measurements of shapes--for example, the area of a triangle--involves reasoning deductively and drawing connections between different methods (Usnick, Lamphere, and Bright 1992). Visual and manipulative models also play a role in helping students understand the underlying…

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

Bassi, Gabriele; Blednykh, Alexei; Smalyuk, Victor

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

An invariance property of generalized Pearson random walks in bounded geometries

NASA Astrophysics Data System (ADS)

Mazzolo, Alain

2009-03-01

Invariance properties of random walks in bounded domains are a topic of growing interest since they contribute to improving our understanding of diffusion in confined geometries. Recently, limited to Pearson random walks with exponentially distributed straight paths, it has been shown that under isotropic uniform incidence, the average length of the trajectories through the domain is independent of the random walk characteristic and depends only on the ratio of the volume's domain over its surface. In this paper, thanks to arguments of integral geometry, we generalize this property to any isotropic bounded stochastic process and we give the conditions of its validity for isotropic unbounded stochastic processes. The analytical form for the traveled distance from the boundary to the first scattering event that ensures the validity of the Cauchy formula is also derived. The generalization of the Cauchy formula is an analytical constraint that thus concerns a very wide range of stochastic processes, from the original Pearson random walk to a Rayleigh distribution of the displacements, covering many situations of physical importance.

Pricing foreign equity option under stochastic volatility tempered stable Lévy processes

NASA Astrophysics Data System (ADS)

Gong, Xiaoli; Zhuang, Xintian

2017-10-01

Considering that financial assets returns exhibit leptokurtosis, asymmetry properties as well as clustering and heteroskedasticity effect, this paper substitutes the logarithm normal jumps in Heston stochastic volatility model by the classical tempered stable (CTS) distribution and normal tempered stable (NTS) distribution to construct stochastic volatility tempered stable Lévy processes (TSSV) model. The TSSV model framework permits infinite activity jump behaviors of return dynamics and time varying volatility consistently observed in financial markets through subordinating tempered stable process to stochastic volatility process, capturing leptokurtosis, fat tailedness and asymmetry features of returns. By employing the analytical characteristic function and fast Fourier transform (FFT) technique, the formula for probability density function (PDF) of TSSV returns is derived, making the analytical formula for foreign equity option (FEO) pricing available. High frequency financial returns data are employed to verify the effectiveness of proposed models in reflecting the stylized facts of financial markets. Numerical analysis is performed to investigate the relationship between the corresponding parameters and the implied volatility of foreign equity option.

Simultaneous determination of water-soluble vitamins in SRM 1849 Infant/Adult Nutritional Formula powder by liquid chromatography-isotope dilution mass spectrometry.

PubMed

Goldschmidt, Robert J; Wolf, Wayne R

2010-05-01

Assessing dietary intake of vitamins from all sources, including foods, dietary supplements, and fortified foods, would be aided considerably by having analytical methodologies that are capable of simultaneous determination of several vitamins. Vitamins naturally present in foods may occur in different chemical forms, with levels ranging over several orders of magnitude. Vitamins in dietary supplements and fortified foods, however, are typically added in a single chemical form, and matrix issues are usually not as complex. These sources should thus be relatively amenable to approaches that aim for simultaneous determination of multiple vitamins. Our recent work has focused on development of liquid chromatography (LC)-UV/fluorescence and LC-tandem mass spectrometry methods for the simultaneous determination of water-soluble vitamins (thiamine, niacin, pyridoxine, pantothenic acid, folic acid, biotin, and riboflavin) in dietary supplement tablets and fortified foods, such as formula powders and breakfast cereals. As part of the validation of our methods and collaboration in characterization of a new NIST SRM 1849 Infant/Adult Nutritional Formula powder, we report data on SRM 1849 using isotope dilution mass spectrometric methods. Use of available NIST Standard Reference Materials(R) as test matrices in our method development and validation gives a benchmark for future application of these methods. We compare three chromatographic approaches and provide data on stability of vitamin standard solutions for LC-based multiple vitamin determinations.

High-performance liquid chromatography coupled with tandem mass spectrometry technology in the analysis of Chinese Medicine Formulas: A bibliometric analysis (1997-2015).

PubMed

He, Xi-Ran; Li, Chun-Guang; Zhu, Xiao-Shu; Li, Yuan-Qing; Jarouche, Mariam; Bensoussan, Alan; Li, Ping-Ping

2017-01-01

There is a recognized challenge in analyzing traditional Chinese medicine formulas because of their complex chemical compositions. The application of modern analytical techniques such as high-performance liquid chromatography coupled with a tandem mass spectrometry has improved the characterization of various compounds from traditional Chinese medicine formulas significantly. This study aims to conduct a bibliometric analysis to recognize the overall trend of high-performance liquid chromatography coupled with tandem mass spectrometry approaches in the analysis of traditional Chinese medicine formulas, its significance and possible underlying interactions between individual herbs in these formulas. Electronic databases were searched systematically, and the identified studies were collected and analyzed using Microsoft Access 2010, Graph Pad 5.0 software and Ucinet software package. 338 publications between 1997 and 2015 were identified, and analyzed in terms of annual growth and accumulated publications, top journals, forms of traditional Chinese medicine preparations and highly studied formulas and single herbs, as well as social network analysis of single herbs. There is a significant increase trend in using high-performance liquid chromatography coupled with tandem mass spectrometry related techniques in analysis of commonly used forms of traditional Chinese medicine formulas in the last 3 years. Stringent quality control is of great significance for the modernization and globalization of traditional Chinese medicine, and this bibliometric analysis provided the first and comprehensive summary within this field. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Analytic theory of high-order-harmonic generation by an intense few-cycle laser pulse

NASA Astrophysics Data System (ADS)

Frolov, M. V.; Manakov, N. L.; Popov, A. M.; Tikhonova, O. V.; Volkova, E. A.; Silaev, A. A.; Vvedenskii, N. V.; Starace, Anthony F.

2012-03-01

We present a theoretical model for describing the interaction of an electron, weakly bound in a short-range potential, with an intense, few-cycle laser pulse. General definitions for the differential probability of above-threshold ionization and for the yield of high-order-harmonic generation (HHG) are presented. For HHG we then derive detailed analytic expressions for the spectral density of generated radiation in terms of the key laser parameters, including the number N of optical cycles in the pulse and the carrier-envelope phase (CEP). In particular, in the tunneling approximation, we provide detailed derivations of the closed-form formulas presented briefly by M. V. Frolov [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.83.021405 83, 021405(R) (2011)], which were used to describe key features of HHG by both H and Xe atom targets in an intense, few-cycle laser pulse. We then provide a complete analysis of the dependence of the HHG spectrum on both N and the CEP φ of an N-cycle laser pulse. Most importantly, we show analytically that the structure of the HHG spectrum stems from interference between electron wave packets originating from electron ionization from neighboring half-cycles near the peak of the intensity envelope of the few-cycle laser pulse. Such interference is shown to be very sensitive to the CEP. The usual HHG spectrum for a monochromatic driving laser field (comprising harmonic peaks at odd multiples of the carrier frequency and spaced by twice the carrier frequency) is shown analytically to occur only in the limit of very large N, and begins to form, as N increases, in the energy region beyond the HHG plateau cutoff.

Two-component Jaffe models with a central black hole - I. The spherical case

NASA Astrophysics Data System (ADS)

Ciotti, Luca; Ziaee Lorzad, Azadeh

2018-02-01

Dynamical properties of spherically symmetric galaxy models where both the stellar and total mass density distributions are described by the Jaffe (1983) profile (with different scalelengths and masses) are presented. The orbital structure of the stellar component is described by Osipkov-Merritt anisotropy, and a black hole (BH) is added at the centre of the galaxy; the dark matter halo is isotropic. First, the conditions required to have a nowhere negative and monotonically decreasing dark matter halo density profile are derived. We then show that the phase-space distribution function can be recovered by using the Lambert-Euler W function, while in absence of the central BH only elementary functions appears in the integrand of the inversion formula. The minimum value of the anisotropy radius for consistency is derived in terms of the galaxy parameters. The Jeans equations for the stellar component are solved analytically, and the projected velocity dispersion at the centre and at large radii are also obtained analytically for generic values of the anisotropy radius. Finally, the relevant global quantities entering the Virial Theorem are computed analytically, and the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability is determined as a function of the galaxy parameters. The presented models, even though highly idealized, represent a substantial generalization of the models presented in Ciotti, and can be useful as starting point for more advanced modelling, the dynamics and the mass distribution of elliptical galaxies.

Infant dietary exposure to dioxins and dioxin-like compounds in Greece.

PubMed

Costopoulou, Danae; Vassiliadou, Irene; Leondiadis, Leondios

2013-09-01

The dietary exposure of infants to polychlorinated dibenzo dioxins and furans (PCDD/Fs) and dioxin like polychlorinated biphenyls (dl-PCBs) is an issue of great social impact. We investigated for the first time the dietary intake of these compounds in infants living in Greece. We included in our study two age groups: 0-6 months, when infants are fed exclusively by human milk and/or formula milk, and 6 to 12 months, when solid food is introduced to nutrition. We took into consideration analytical results for PCDD/Fs and dl-PCBs concentrations in the most popular infant formulae in the Greek market, previous data for mother milk concentrations of PCDD/Fs and dl-PCBs from Greece, and finally analytical data for fat-containing food products from the Greek market. In the first study group, it was found than in infants exclusively fed by breast milk, the calculated sum of PCDD/Fs and dioxin-like PCBs (60.3-80.4 TEQ pg/kg body weight) was significantly higher than that of infants that consume a combination of human milk and formula (31.2-41.6 TEQ pg/kg body weight). In the second study group, separate daily intake estimations were performed for babies receiving human milk (estimated total daily intake 19.76-24.95 TEQ pg/kg body weight) and formula milk (estimated total daily intake 1.60-2.24 TEQ pg/kg body weight). The risks of this exposure should not be overestimated because nursing is restricted to a limited period of human life and besides, the potential consumption of higher levels of dioxin-like compounds is fully compensated by the significant benefits of breast-feeding. Copyright © 2013 Elsevier Ltd. All rights reserved.

Loading-unloading response of circular GLARE fiber-metal laminates under lateral indentation

NASA Astrophysics Data System (ADS)

Tsamasphyros, George J.; Bikakis, George S.

2015-01-01

GLARE is a Fiber-Metal laminated material used in aerospace structures which are frequently subjected to various impact damages. Hence, the response of GLARE plates subjected to lateral indentation is very important. In this paper, analytical expressions are derived and a non-linear finite element modeling procedure is proposed in order to predict the static load-indentation curves of circular GLARE plates during loading and unloading by a hemispherical indentor. We have recently published analytical formulas and a finite element procedure for the static indentation of circular GLARE plates which are now used during the loading stage. Here, considering that aluminum layers are in a state of membrane yield and employing energy balance during unloading, the unloading path is determined. Using this unloading path, an algebraic equation is derived for calculating the permanent dent depth of the GLARE plate after the indentor's withdrawal. Furthermore, our finite element procedure is modified in order to simulate the unloading stage as well. The derived formulas and the proposed finite element modeling procedure are applied successfully to GLARE 2-2/1-0.3 and to GLARE 3-3/2-0.4 circular plates. The analytical results are compared with corresponding FEM results and a good agreement is found. The analytically calculated permanent dent depth is within 6 % for the GLARE 2 plate, and within 7 % for the GLARE 3 plate, of the corresponding numerically calculated result. No other solution of this problem is known to the authors.

Plasma Properties in the Plume of a Hall Thruster Cluster

DTIC Science & Technology

2003-06-04

The Hall thruster cluster is an attractive propulsion approach for spacecraft requiring very high-power electric propulsion systems. This article...probes in the plume of a low-power, four-engine Hall thruster cluster. Simple analytical formulas are introduced that allow these quantities to be

Virtual photon impact factors with exact gluon kinematics

NASA Astrophysics Data System (ADS)

Bialas, A.; Navelet, H.; Peschanski, R.

2001-06-01

An explicit analytic formula for the transverse and longitudinal impact factors ST, L( N, γ) of the photon using kT factorization with exact gluon kinematics is given. Applications to the QCD dipole model and the extraction of the unintegrated gluon structure function from data are proposed.

The thermoelectric properties of strongly correlated systems

NASA Astrophysics Data System (ADS)

Cai, Jianwei

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

Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

NASA Astrophysics Data System (ADS)

Šprlák, Michal; Novák, Pavel

2017-02-01

New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.

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

PubMed

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

2009-01-01

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

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.

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.

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.

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

PubMed

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

2015-08-15

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

Finite word length effects on digital filter implementation.

NASA Technical Reports Server (NTRS)

Bowman, J. D.; Clark, F. H.

1972-01-01

This paper is a discussion of two known techniques to analyze finite word length effects on digital filters. These techniques are extended to several additional programming forms and the results verified experimentally. A correlation of the analytical weighting functions for the two methods is made through the Mason Gain Formula.

Testing Understanding and Understanding Testing.

ERIC Educational Resources Information Center

Pedersen, Jean; Ross, Peter

1985-01-01

Provides examples in which graphs are used in the statements of problems or in their solutions as a means of testing understanding of mathematical concepts. Examples (appropriate for a beginning course in calculus and analytic geometry) include slopes of lines and curves, quadratic formula, properties of the definite integral, and others. (JN)

Universality in volume-law entanglement of scrambled pure quantum states.

PubMed

Nakagawa, Yuya O; Watanabe, Masataka; Fujita, Hiroyuki; Sugiura, Sho

2018-04-24

A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. The thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases, however, quantum correlations break the correspondence and mandate a correction to this simple volume law. The elucidation of the size dependence of the entanglement entropy is thus essentially important in linking quantum physics with thermodynamics. Here we derive an analytic formula of the entanglement entropy for a class of pure states called cTPQ states representing equilibrium. We numerically find that our formula applies universally to any sufficiently scrambled pure state representing thermal equilibrium, i.e., energy eigenstates of non-integrable models and states after quantum quenches. Our formula is exploited as diagnostics for chaotic systems; it can distinguish integrable models from non-integrable models and many-body localization phases from chaotic phases.

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

PubMed

Zhao, Chengliang; Cai, Yangjian

2010-03-01

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

Current matrix element in HAL QCD's wavefunction-equivalent potential method

NASA Astrophysics Data System (ADS)

Watanabe, Kai; Ishii, Noriyoshi

2018-04-01

We give a formula to calculate a matrix element of a conserved current in the effective quantum mechanics defined by the wavefunction-equivalent potentials proposed by the HAL QCD collaboration. As a first step, a non-relativistic field theory with two-channel coupling is considered as the original theory, with which a wavefunction-equivalent HAL QCD potential is obtained in a closed analytic form. The external field method is used to derive the formula by demanding that the result should agree with the original theory. With this formula, the matrix element is obtained by sandwiching the effective current operator between the left and right eigenfunctions of the effective Hamiltonian associated with the HAL QCD potential. In addition to the naive one-body current, the effective current operator contains an additional two-body term emerging from the degrees of freedom which has been integrated out.

Acoustic sounding of wind velocity profiles in a stratified moving atmosphere.

PubMed

Ostashev, V E; Georges, T M; Clifford, S F; Goedecke, G H

2001-06-01

The paper deals with analytical and numerical studies of the effects of atmospheric stratification on acoustic remote sensing of wind velocity profiles by sodars. Both bistatic and monostatic schemes are considered. Formulas for the Doppler shift of an acoustic echo signal scattered by atmospheric turbulence advected with the mean wind in a stratified moving atmosphere are derived. Numerical studies of these formulas show that errors in retrieving wind velocity can be of the order of 1 m/s if atmospheric stratification is ignored. Formulas for the height at which wind velocity is retrieved are also derived. Approaches are proposed which allow one to take into account the effects of atmospheric stratification when restoring the wind velocity profile from measured values of the Doppler shift and the time interval of acoustic impulse propagation from a sodar to the scattering volume and back to the ground.

Estimating the Gibbs energy of hydration from molecular dynamics trajectories obtained by integral equations of the theory of liquids in the RISM approximation

NASA Astrophysics Data System (ADS)

Tikhonov, D. A.; Sobolev, E. V.

2011-04-01

A method of integral equations of the theory of liquids in the reference interaction site model (RISM) approximation is used to estimate the Gibbs energy averaged over equilibrium trajectories computed by molecular mechanics. Peptide oxytocin is selected as the object of interest. The Gibbs energy is calculated using all chemical potential formulas introduced in the RISM approach for the excess chemical potential of solvation and is compared with estimates by the generalized Born model. Some formulas are shown to give the wrong sign of Gibbs energy changes when peptide passes from the gas phase into water environment; the other formulas give overestimated Gibbs energy changes with the right sign. Note that allowance for the repulsive correction in the approximate analytical expressions for the Gibbs energy derived by thermodynamic perturbation theory is not a remedy.

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

PubMed

McClure, Foster D; Lee, Jung K

2012-01-01

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

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.

Analytical model for viscous damping and the spring force for perforated planar microstructures acting at both audible and ultrasonic frequencies

PubMed Central

Homentcovschi, Dorel; Miles, Ronald N.

2008-01-01

The paper presents a model for the squeezed film damping, the resistance of the holes, and the corresponding spring forces for a periodic perforated microstructure including the effects of compressibility, inertia, and rarefied gas. The viscous damping and spring forces are obtained by using the continuity equation. The analytical formula for the squeezed film damping is applied to analyze the response of an ultrasonic transducer. The inclusion of these effects in a model significantly improves the agreement with measured results. Finally, it is shown that the frequency dependence of the total damping and total spring force for a cell are very similar to those corresponding to a rectangular open microstructure without holes. A separate analysis reveals the importance of each particular correction. The most important is the compressibility correction; the inertia has to be considered only for determining the spring force and the damping force for sufficiently high frequencies. PMID:18646964

Back to Normal! Gaussianizing posterior distributions for cosmological probes

NASA Astrophysics Data System (ADS)

Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.

2014-05-01

We present a method to map multivariate non-Gaussian posterior probability densities into Gaussian ones via nonlinear Box-Cox transformations, and generalizations thereof. This is analogous to the search for normal parameters in the CMB, but can in principle be applied to any probability density that is continuous and unimodal. The search for the optimally Gaussianizing transformation amongst the Box-Cox family is performed via a maximum likelihood formalism. We can judge the quality of the found transformation a posteriori: qualitatively via statistical tests of Gaussianity, and more illustratively by how well it reproduces the credible regions. The method permits an analytical reconstruction of the posterior from a sample, e.g. a Markov chain, and simplifies the subsequent joint analysis with other experiments. Furthermore, it permits the characterization of a non-Gaussian posterior in a compact and efficient way. The expression for the non-Gaussian posterior can be employed to find analytic formulae for the Bayesian evidence, and consequently be used for model comparison.

Role of polarizer-tilting-angle in zero-field spin-transfer nano-oscillators with perpendicular anisotropy

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

Gonzalez-Fuentes, C.; Gallardo, R. A., E-mail: rodolfo.gallardo@usm.cl; Landeros, P.

2015-10-05

An analytical model for studying the stability of a single domain ferromagnetic layer under the influence of a spin-polarized current is presented. The theory is applied to bias-field-free nano-oscillators with perpendicular anisotropy, which allows to obtain a polarizer-angle vs. current phase diagram that describes the stability of magnetic states. Explicit formulae for the critical current densities unveil the influence of the relative orientation between free and polarizer layers, allowing the emergence of precessional steady-states, and also the possibility to reduce the magnitude of the threshold current density to produce microwave oscillations. It is shown that oscillating steady-states arise in amore » broad angular region, and the dependence of their boundaries is fully specified by the model. The reliability of the analytical results has been corroborated by comparison to numerical calculations. Such structures are currently under intense research because of remarkable properties offering new prospects for microwave applications in communication technologies.« less

Nonlinearity in bacterial population dynamics: Proposal for experiments for the observation of abrupt transitions in patches

PubMed Central

Kenkre, V. M.; Kumar, Niraj

2008-01-01

An explicit proposal for experiments leading to abrupt transitions in spatially extended bacterial populations in a Petri dish is presented on the basis of an exact formula obtained through an analytic theory. The theory provides accurately the transition expressions despite the fact that the actual solutions, which involve strong nonlinearity, are inaccessible to it. The analytic expressions are verified through numerical solutions of the relevant nonlinear equation. The experimental setup suggested uses opaque masks in a Petri dish bathed in ultraviolet radiation [Lin A-L, et al. (2004) Biophys J 87:75–80 and Perry N (2005) J R Soc Interface 2:379–387], but is based on the interplay of two distances the bacteria must traverse, one of them favorable and the other adverse. As a result of this interplay feature, the experiments proposed introduce highly enhanced reliability in interpretation of observations and in the potential for extraction of system parameters. PMID:19033185

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

PubMed

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

2016-07-01

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

Synthesis and Characterization of Hydroxyapatite Powder by Wet Precipitation Method

NASA Astrophysics Data System (ADS)

Cahyaningrum, S. E.; Herdyastuty, N.; Devina, B.; Supangat, D.

2018-01-01

Hydroxyapatite is main inorganic component of the bone with formula Ca10(PO4)6(OH)2. Hydroxyapatite can be used as substituted bone biomaterial because biocompatible, non toxic, and osteoconductive. In this study, hydroxyapatite is synthesized using wet precipitation method from egg shell. The product was sintered at different temperatures of 800°C to 1000°C to improve its crystallinity. The hydroxyapatite was characterized by X-ray analysis, Scanning Electron Microscopy (SEM) and Fourier Transform Infrared Spectroscopy (FTIR) to reveal its phase content, morphology and types of bond present within it. The analytical results showed hydroxyapatite had range in crystallinity from 85.527 to 98.753%. The analytical functional groups showed that presence of functional groups such as OH, (PO4)3 2-, and CO3 2- that indicated as hydroxyapatite. The result of characterization SEM indicated that hydroxyapatite without sintering and HAp sintering at 800 °C were irregular shape without pore. The best hydroxyapatite with temperature sintering at 900 °C showed oval shaped with pores without agglomerated.

On the superposition principle in interference experiments.

PubMed

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

2015-05-14

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

Analytical theory of coherent synchrotron radiation wakefield of short bunches shielded by conducting parallel plates

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

Stupakov, Gennady; Zhou, Demin

2016-04-21

We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. Furthermore, all our formulas are benchmarked against numerical simulations with the CSRZ computermore » code.« less

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

PubMed

Vorob'ev, V S; Martynov, G A

2007-07-14

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

Measurement of third-order nonlinear susceptibility tensor in InP using extended Z-scan technique with elliptical polarization

NASA Astrophysics Data System (ADS)

Oishi, Masaki; Shinozaki, Tomohisa; Hara, Hikaru; Yamamoto, Kazunuki; Matsusue, Toshio; Bando, Hiroyuki

2018-05-01

The elliptical polarization dependence of the two-photon absorption coefficient β in InP has been measured by the extended Z-scan technique for thick materials in the wavelength range from 1640 to 1800 nm. The analytical formula of the Z-scan technique has been extended with consideration of multiple reflections. The Z-scan results have been fitted very well by the formula and β has been evaluated accurately. The three independent elements of the third-order nonlinear susceptibility tensor in InP have also been determined accurately from the elliptical polarization dependence of β.

Capacity of a quantum memory channel correlated by matrix product states

NASA Astrophysics Data System (ADS)

Mulherkar, Jaideep; Sunitha, V.

2018-04-01

We study the capacity of a quantum channel where channel acts like controlled phase gate with the control being provided by a one-dimensional quantum spin chain environment. Due to the correlations in the spin chain, we get a quantum channel with memory. We derive formulas for the quantum capacity of this channel when the spin state is a matrix product state. Particularly, we derive exact formulas for the capacity of the quantum memory channel when the environment state is the ground state of the AKLT model and the Majumdar-Ghosh model. We find that the behavior of the capacity for the range of the parameters is analytic.

Broadband impedance calculations and single bunch instabilities estimations of of the HLS-II storage ring

NASA Astrophysics Data System (ADS)

Zhang, Qing-Kun; Wang, Lin; Li, Wei-Min; Gao, Wei-Wei

2015-12-01

The upgrade project of the Hefei Light Source storage ring is under way. In this paper, the broadband impedances of resistive wall and coated ceramic vacuum chamber are calculated using the analytic formula, and the wake fields and impedances of other designed vacuum chambers are simulated by CST code, and then a broadband impedance model is obtained. Using the theoretical formula, longitudinal and transverse single bunch instabilities are discussed. With the carefully-designed vacuum chamber, we find that the thresholds of the beam instabilities are higher than the beam current goal. Supported by Natural Science Foundation of China (11175182, 11175180)

Periodic Orbits and Semiclassical Form Factor in Barrier Billiards

NASA Astrophysics Data System (ADS)

Giraud, O.

2005-11-01

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

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

USGS Publications Warehouse

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

2006-01-01

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

Squeezing and its graphical representations in the anharmonic oscillator model

NASA Astrophysics Data System (ADS)

Tanaś, R.; Miranowicz, A.; Kielich, S.

1991-04-01

The problem of squeezing and its graphical representations in the anharmonic oscillator model is considered. Explicit formulas for squeezing, principal squeezing, and the quasiprobability distribution (QPD) function are given and illustrated graphically. Approximate analytical formulas for the variances, extremal variances, and QPD are obtained for the case of small nonlinearities and large numbers of photons. The possibility of almost perfect squeezing in the model is demonstrated and its graphical representations in the form of variance lemniscates and QPD contours are plotted. For large numbers of photons the crescent shape of the QPD contours is hardly visible and quite regular ellipses are obtained.

Semi empirical formula for exposure buildup factors

NASA Astrophysics Data System (ADS)

Seenappa, L.; Manjunatha, H. C.; Sridhar, K. N.; Hanumantharayappa, Chikka

2017-10-01

The nuclear data of photon buildup factor is an important concept that must be considered in nuclear safety aspects such as radiation shielding and dosimetry. The buildup factor is a coefficient that represents the contribution of collided photons with the target medium. Present work formulated a semi empirical formulae for exposure buildup factors (EBF) in the energy region 0.015-15 MeV, atomic number range 1 ≤ Z ≤ 92 and for mean free path up to 40 mfp. The EBFs produced by the present formula are compared with that of data available in the literature. It is found that present work agree with literature. This formula is first of its kind to calculate EBFs without using geometric progression fitting parameters. This formula may also use to calculate EBFs for compounds/mixtures/Biological samples. The present formula is useful in producing EBFs for elements and mixtures quickly. This semi empirical formula finds importance in the calculations of EBFs which intern helps in the radiation protection and dosimetry.

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

PubMed Central

Wang, Ying; Zhou, Yu; Zhou, Shuyu

2016-01-01

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

Radiation-driven winds of hot stars. VI - Analytical solutions for wind models including the finite cone angle effect

NASA Technical Reports Server (NTRS)

Kudritzki, R. P.; Pauldrach, A.; Puls, J.; Abbott, D. C.

1989-01-01

Analytical solutions for radiation-driven winds of hot stars including the important finite cone angle effect (see Pauldrach et al., 1986; Friend and Abbott, 1986) are derived which approximate the detailed numerical solutions of the exact wind equation of motion very well. They allow a detailed discussion of the finite cone angle effect and provide for given line force parameters k, alpha, delta definite formulas for mass-loss rate M and terminal velocity v-alpha as function of stellar parameters.

Distance numbers and Wiener indices of IPR fullerenes with formula C10(n-2) (n ≥ 8) in analytical forms

NASA Astrophysics Data System (ADS)

Ghosh, Tapanendu; Mondal, Sukanya; Mondal, Swapnadeep; Mandal, Bholanath

2018-06-01

The IPR fullerenes C10(n-2) with n ≥ 8 have been considered for obtaining their distance numbers and hence the Wiener indices in analytical forms for both even and odd n. The distance numbers along with their patterns have been found to give the number of 13C NMR signals with their respective intensity ratios. Logarithms of Wiener indices have been found to correlate well with the band (HOMO-LUMO) gaps and resonance energies of the respective fullerenes.

Satellite Orbit Under Influence of a Drag - Analytical Approach

NASA Astrophysics Data System (ADS)

Martinović, M. M.; Šegan, S. D.

2017-12-01

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

Fractional Fourier transform of truncated elliptical Gaussian beams.

PubMed

Du, Xinyue; Zhao, Daomu

2006-12-20

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

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.

Reference Materials: Critical Importance to the Infant Formula Industry.

PubMed

Wargo, Wayne F

2017-09-01

Infant formula is one of the most regulated foods in the world. It has advanced in complexity over the years as a result of numerous research innovations. To ensure product safety and quality, analytical technologies have also had to advance to keep pace. Given the rigorous performance demands expected of these methods and the ever-growing array of complex matrixes, there is the potential for gaps to exist in current Official MethodsSM and other recognized international methods for infant formula and adult nutritionals. Food safety concerns, particularly for infants, drive the need for extensive testing by manufacturers and regulators. The net effect is the potential for an increase in time- and resource-consuming regulatory disputes. In an effort to mitigate such costly activities, AOAC INTERNATIONAL, under the direction of the Infant Formula Council of America-a trade association of manufacturers and marketers of formulated nutritional products-agreed to establish voluntary consensus Standard Method Performance Requirements, and, ultimately, to identify and publish globally recognized, fit-for-purpose standard methods. To accomplish this task, nutritional reference materials (RMs), representing all major commercially available nutritional formulations, were (and continue to be) a critical necessity. In this paper, various types of RMs will be defined, followed by review and discussion of their importance to the infant formula industry.

Intervening on risk factors for coronary heart disease: an application of the parametric g-formula.

PubMed

Taubman, Sarah L; Robins, James M; Mittleman, Murray A; Hernán, Miguel A

2009-12-01

Estimating the population risk of disease under hypothetical interventions--such as the population risk of coronary heart disease (CHD) were everyone to quit smoking and start exercising or to start exercising if diagnosed with diabetes--may not be possible using standard analytic techniques. The parametric g-formula, which appropriately adjusts for time-varying confounders affected by prior exposures, is especially well suited to estimating effects when the intervention involves multiple factors (joint interventions) or when the intervention involves decisions that depend on the value of evolving time-dependent factors (dynamic interventions). We describe the parametric g-formula, and use it to estimate the effect of various hypothetical lifestyle interventions on the risk of CHD using data from the Nurses' Health Study. Over the period 1982-2002, the 20-year risk of CHD in this cohort was 3.50%. Under a joint intervention of no smoking, increased exercise, improved diet, moderate alcohol consumption and reduced body mass index, the estimated risk was 1.89% (95% confidence interval: 1.46-2.41). We discuss whether the assumptions required for the validity of the parametric g-formula hold in the Nurses' Health Study data. This work represents the first large-scale application of the parametric g-formula in an epidemiologic cohort study.

The Processing on Different Types of English Formulaic Sequences

ERIC Educational Resources Information Center

Qian, Li

2015-01-01

Formulaic sequences are found to be processed faster than their matched novel phrases in previous studies. Given the variety of formulaic types, few studies have compared processing on different types of formulaic sequences. The present study explored the processing among idioms, speech formulae and written formulae. It has been found that in…

Analytical approach for modeling and performance analysis of microring resonators as optical filters with multiple output bus waveguides

NASA Astrophysics Data System (ADS)

Lakra, Suchita; Mandal, Sanjoy

2017-06-01

A quadruple micro-optical ring resonator (QMORR) with multiple output bus waveguides is mathematically modeled and analyzed by making use of the delay-line signal processing approach in Z-domain and Mason's gain formula. The performances of QMORR with two output bus waveguides with vertical coupling are analyzed. This proposed structure is capable of providing wider free spectral response from both the output buses with appreciable cross talk. Thus, this configuration could provide increased capacity to insert a large number of communication channels. The simulated frequency response characteristic and its dispersion and group delay characteristics are graphically presented using the MATLAB environment.

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.

Scattering amplitude and bosonization duality in general Chern-Simons vector models

NASA Astrophysics Data System (ADS)

Yokoyama, Shuichi

2016-09-01

We present the exact large N calculus of four point functions in general Chern-Simons bosonic and fermionic vector models. Applying the LSZ formula to the four point function we determine the two body scattering amplitudes in these theories taking a special care for a non-analytic term to achieve unitarity in the singlet channel. We show that the S-matrix enjoys the bosonization duality, an unusual crossing relation and a non-relativistic reduction to Aharonov-Bohm scattering. We also argue that the S-matrix develops a pole in a certain range of coupling constants, which disappears in the range where the theory reduces to the Chern-Simons theory interacting with free fermions.

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.

Aerodynamics Via Acoustics: Application of Acoustic Formulas for Aerodynamic Calculations

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.

1986-01-01

Prediction of aerodynamic loads on bodies in arbitrary motion is considered from an acoustic point of view, i.e., in a frame of reference fixed in the undisturbed medium. An inhomogeneous wave equation which governs the disturbance pressure is constructed and solved formally using generalized function theory. When the observer is located on the moving body surface there results a singular linear integral equation for surface pressure. Two different methods for obtaining such equations are discussed. Both steady and unsteady aerodynamic calculations are considered. Two examples are presented, the more important being an application to propeller aerodynamics. Of particular interest for numerical applications is the analytical behavior of the kernel functions in the various integral equations.

Comment on ‘Monogamy of multi-qubit entanglement using Rényi entropy’

NASA Astrophysics Data System (ADS)

Yu, Long-Bao; Zhang, Li-Hua; Zhao, Jun-Long; Tang, Yong-Sheng

2018-02-01

In an article in 2010, Kim et al introduced the definition of Rényi-α entanglement for bipartite quantum states and established an analytic formula of Rényi-α entanglement for arbitrary two-qubit states with α≥slant 1 . They also derived a monogamy of entanglement in multi-qubit systems in terms of Rényi-α entanglement for α≥slant 2 Kim et al (2010 J. Phys. A: Math. Theor. 43 445305). We find the proofs of theorems 2 and 3 contain some errors and we also present an improved derivation to overcome this flaw. The alternative derivation shows that the main conclusions remain valid despite the invalidity of the proofs.

Direct S -matrix calculation for diffractive structures and metasurfaces

NASA Astrophysics Data System (ADS)

Shcherbakov, Alexey A.; Stebunov, Yury V.; Baidin, Denis F.; Kämpfe, Thomas; Jourlin, Yves

2018-06-01

The paper presents a derivation of analytical components of S matrices for arbitrary planar diffractive structures and metasurfaces in the Fourier domain. The attained general formulas for S -matrix components can be applied within both formulations in the Cartesian and curvilinear metric. A numerical method based on these results can benefit from all previous improvements of the Fourier domain methods. In addition, we provide expressions for S -matrix calculation in the case of periodically corrugated layers of two-dimensional materials, which are valid for arbitrary corrugation depth-to-period ratios. As an example, the derived equations are used to simulate resonant grating excitation of graphene plasmons and the impact of a silica interlayer on corresponding reflection curves.

A note on the bounds of the error of Gauss-Turan-type quadratures

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2007-03-01

This note is concerned with estimates for the remainder term of the Gauss-Turan quadrature formula,where is the Gori-Michelli weight function, with Un-1(t) denoting the (n-1)th degree Chebyshev polynomial of the second kind, and f is a function analytic in the interior of and continuous on the boundary of an ellipse with foci at the points +/-1 and sum of semiaxes [varrho]>1. The present paper generalizes the results in [G.V. Milovanovic, M.M. Spalevic, Bounds of the error of Gauss-Turan-type quadratures, J. Comput. Appl. Math. 178 (2005) 333-346], which is concerned with the same problem when s=1.

Interface stability in a slowly rotating, low gravity tank Experiments

NASA Technical Reports Server (NTRS)

Leslie, F.; Gans, R. F.

1986-01-01

Analytical models of liquid in partially-filled rotating tanks predict both the shape of the interface between the liquid and its vapor, and the stability of that interface. The models are of necessity incomplete and experimental data are needed to assess the approximations made. Presented are preliminary experimental studies both in the laboratory and in the low-gravity environment of a free-falling aircraft. Emphasis is placed on bubbles which intersect the container boundaries. Measurements of rotating equilibrium bubble shapes are in agreement with theoretical profiles derived from Laplace's formula. The interface shape depends on the contact angle, the radius of intersection with container, and the ratio of centrifugal force to surface tension.

The circulation of a baroclinic ocean around planetary scale islands with topography

NASA Astrophysics Data System (ADS)

Pedlosky, J.

2010-12-01

The circulation around planetary-scale islands is considered for an island with a topographic skirt for a stratified ocean. The simplest model of the ocean is a two layer ocean in a circular domain with the island in the center. When the girdling topography is steep, closed geostrophic contours guide the flow in each of the two layers although that guiding occurs at different horizontal locations in each layer. For flows with weak dissipation, modeled as bottom and interfacial friction, explicit formulae are given for the dependence of the streamfunction in each layer on the ambient potential vorticity, f/(layer depth). Numerical model calculations will be presented to supplement the analytical results.

Energy dependence of forward-rapidity [Formula: see text] and [Formula: see text] production in pp collisions at the LHC.

PubMed

Acharya, S; Adamová, D; Aggarwal, M M; Aglieri Rinella, G; Agnello, M; Agrawal, N; Ahammed, Z; Ahmad, N; Ahn, S U; Aiola, S; Akindinov, A; Alam, S N; Albuquerque, D S D; Aleksandrov, D; Alessandro, B; Alexandre, D; Alfaro Molina, R; Alici, A; Alkin, A; Alme, J; Alt, T; Altsybeev, I; Alves Garcia Prado, C; An, M; Andrei, C; Andrews, H A; Andronic, A; Anguelov, V; Anson, C; Antičić, T; Antinori, F; Antonioli, P; Anwar, R; Aphecetche, L; Appelshäuser, H; Arcelli, S; Arnaldi, R; Arnold, O W; Arsene, I C; Arslandok, M; Audurier, B; Augustinus, A; Averbeck, R; Azmi, M D; Badalà, A; Baek, Y W; Bagnasco, S; Bailhache, R; Bala, R; Baldisseri, A; Ball, M; Baral, R C; Barbano, A M; Barbera, R; Barile, F; Barioglio, L; Barnaföldi, G G; Barnby, L S; Barret, V; Bartalini, P; Barth, K; Bartke, J; Bartsch, E; Basile, M; Bastid, N; Basu, S; Bathen, B; Batigne, G; Batista Camejo, A; Batyunya, B; Batzing, P C; Bearden, I G; Beck, H; Bedda, C; Behera, N K; Belikov, I; Bellini, F; Bello Martinez, H; Bellwied, R; 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Kurashvili, P; Kurepin, A; Kurepin, A B; Kuryakin, A; Kushpil, S; Kweon, M J; Kwon, Y; La Pointe, S L; La Rocca, P; Lagana Fernandes, C; Lakomov, I; Langoy, R; Lapidus, K; Lara, C; Lardeux, A; Lattuca, A; Laudi, E; Lavicka, R; Lazaridis, L; Lea, R; Leardini, L; Lee, S; Lehas, F; Lehner, S; Lehrbach, J; Lemmon, R C; Lenti, V; Leogrande, E; León Monzón, I; Lévai, P; Li, S; Li, X; Lien, J; Lietava, R; Lindal, S; Lindenstruth, V; Lippmann, C; Lisa, M A; Litichevskyi, V; Ljunggren, H M; Llope, W J; Lodato, D F; Loenne, P I; Loginov, V; Loizides, C; Loncar, P; Lopez, X; López Torres, E; Lowe, A; Luettig, P; Lunardon, M; Luparello, G; Lupi, M; Lutz, T H; Maevskaya, A; Mager, M; Mahajan, S; Mahmood, S M; Maire, A; Majka, R D; Malaev, M; Maldonado Cervantes, I; Malinina, L; Mal'Kevich, D; Malzacher, P; Mamonov, A; Manko, V; Manso, F; Manzari, V; Mao, Y; Marchisone, M; Mareš, J; Margagliotti, G V; Margotti, A; Margutti, J; Marín, A; Markert, C; Marquard, M; Martin, N A; Martinengo, P; Martinez, J A L; Martínez, M I; Martínez García, G; Martinez Pedreira, M; Mas, A; Masciocchi, S; Masera, M; Masoni, A; Mastroserio, A; Mathis, A M; Matyja, A; Mayer, C; Mazer, J; Mazzilli, M; Mazzoni, M A; Meddi, F; Melikyan, Y; Menchaca-Rocha, A; Meninno, E; Mercado Pérez, J; Meres, M; Mhlanga, S; Miake, Y; Mieskolainen, M M; Mihaylov, D L; Mikhaylov, K; Milano, L; Milosevic, J; Mischke, A; Mishra, A N; Miśkowiec, D; Mitra, J; Mitu, C M; Mohammadi, N; Mohanty, B; Montes, E; Moreira De Godoy, D A; Moreno, L A P; Moretto, S; Morreale, A; Morsch, A; Muccifora, V; Mudnic, E; Mühlheim, D; Muhuri, S; Mukherjee, M; Mulligan, J D; Munhoz, M G; Münning, K; Munzer, R H; Murakami, H; Murray, S; Musa, L; Musinsky, J; Myers, C J; Naik, B; Nair, R; Nandi, B K; Nania, R; Nappi, E; Naru, M U; Natal da Luz, H; Nattrass, C; Navarro, S R; Nayak, K; Nayak, R; Nayak, T K; Nazarenko, S; Nedosekin, A; Negrao De Oliveira, R A; Nellen, L; Nesbo, S V; Ng, F; Nicassio, M; Niculescu, M; Niedziela, J; Nielsen, B S; Nikolaev, S; Nikulin, S; Nikulin, V; Noferini, F; Nomokonov, P; Nooren, G; Noris, J C C; Norman, J; Nyanin, A; Nystrand, J; Oeschler, H; Oh, S; Ohlson, A; Okubo, T; Olah, L; Oleniacz, J; Oliveira Da Silva, A C; Oliver, M H; Onderwaater, J; Oppedisano, C; Orava, R; Oravec, M; Ortiz Velasquez, A; Oskarsson, A; Otwinowski, J; Oyama, K; Pachmayer, Y; Pacik, V; Pagano, D; Pagano, P; Paić, G; Palni, P; Pan, J; Pandey, A K; Panebianco, S; Papikyan, V; Pappalardo, G S; Pareek, P; Park, J; Park, W J; Parmar, S; Passfeld, A; Pathak, S P; Paticchio, V; Patra, R N; Paul, B; Pei, H; Peitzmann, T; Peng, X; Pereira, L G; Pereira Da Costa, H; Peresunko, D; Perez Lezama, E; Peskov, V; Pestov, Y; Petráček, V; Petrov, V; Petrovici, M; Petta, C; Pezzi, R P; Piano, S; Pikna, M; Pillot, P; Pimentel, L O D L; Pinazza, O; Pinsky, L; Piyarathna, D B; Płoskoń, M; Planinic, M; Pluta, J; Pochybova, S; Podesta-Lerma, P L M; Poghosyan, M G; Polichtchouk, B; Poljak, N; Poonsawat, W; Pop, A; Poppenborg, H; Porteboeuf-Houssais, S; Porter, J; Pospisil, J; Pozdniakov, V; Prasad, S K; Preghenella, R; Prino, F; Pruneau, C A; Pshenichnov, I; Puccio, M; Puddu, G; Pujahari, P; Punin, V; Putschke, J; Qvigstad, H; Rachevski, A; Raha, S; Rajput, S; Rak, J; Rakotozafindrabe, A; Ramello, L; Rami, F; Rana, D B; Raniwala, R; Raniwala, S; Räsänen, S S; Rascanu, B T; Rathee, D; Ratza, V; Ravasenga, I; Read, K F; Redlich, K; Rehman, A; Reichelt, P; Reidt, F; Ren, X; Renfordt, R; Reolon, A R; Reshetin, A; Reygers, K; Riabov, V; Ricci, R A; Richert, T; Richter, M; Riedler, P; Riegler, W; Riggi, F; Ristea, C; Rodríguez Cahuantzi, M; Røed, K; Rogochaya, E; Rohr, D; Röhrich, D; Rokita, P S; Ronchetti, F; Ronflette, L; Rosnet, P; Rossi, A; Rotondi, A; Roukoutakis, F; Roy, A; Roy, C; Roy, P; Rubio Montero, A J; Rueda, O V; Rui, R; Russo, R; Rustamov, A; Ryabinkin, E; Ryabov, Y; Rybicki, A; Saarinen, S; Sadhu, S; Sadovsky, S; Šafařík, K; Saha, S K; Sahlmuller, B; Sahoo, B; Sahoo, P; Sahoo, R; Sahoo, S; Sahu, P K; Saini, J; Sakai, S; Saleh, M A; Salzwedel, J; Sambyal, S; Samsonov, V; Sandoval, A; Sarkar, D; Sarkar, N; Sarma, P; Sas, M H P; Scapparone, E; Scarlassara, F; Scharenberg, R P; Scheid, H S; Schiaua, C; Schicker, R; Schmidt, C; Schmidt, H R; Schmidt, M O; Schmidt, M; Schuchmann, S; Schukraft, J; Schutz, Y; Schwarz, K; Schweda, K; Scioli, G; Scomparin, E; Scott, R; Šefčík, M; Seger, J E; Sekiguchi, Y; Sekihata, D; Selyuzhenkov, I; Senosi, K; Senyukov, S; Serradilla, E; Sett, P; Sevcenco, A; Shabanov, A; Shabetai, A; Shadura, O; Shahoyan, R; Shangaraev, A; Sharma, A; Sharma, A; Sharma, M; Sharma, M; Sharma, N; Sheikh, A I; Shigaki, K; Shou, Q; Shtejer, K; Sibiriak, Y; Siddhanta, S; Sielewicz, K M; Siemiarczuk, T; Silvermyr, D; Silvestre, C; Simatovic, G; Simonetti, G; Singaraju, R; Singh, R; Singhal, V; Sinha, T; Sitar, B; Sitta, M; Skaali, T B; Slupecki, M; Smirnov, N; Snellings, R J M; Snellman, T W; Song, J; Song, M; Soramel, F; Sorensen, S; Sozzi, F; Spiriti, E; Sputowska, I; Srivastava, B K; Stachel, J; Stan, I; Stankus, P; Stenlund, E; Stiller, J H; Stocco, D; Strmen, P; Suaide, A A P; Sugitate, T; Suire, C; Suleymanov, M; Suljic, M; Sultanov, R; Šumbera, M; Sumowidagdo, S; Suzuki, K; Swain, S; Szabo, A; Szarka, I; Szczepankiewicz, A; Szymanski, M; Tabassam, U; Takahashi, J; Tambave, G J; Tanaka, N; Tarhini, M; Tariq, M; Tarzila, M G; Tauro, A; Tejeda Muñoz, G; Telesca, A; Terasaki, K; Terrevoli, C; Teyssier, B; Thakur, D; Thakur, S; Thomas, D; Tieulent, R; Tikhonov, A; Timmins, A R; Toia, A; Tripathy, S; Trogolo, S; Trombetta, G; Trubnikov, V; Trzaska, W H; Trzeciak, B A; Tsuji, T; Tumkin, A; Turrisi, R; Tveter, T S; Ullaland, K; Umaka, E N; Uras, A; Usai, G L; Utrobicic, A; Vala, M; Van Der Maarel, J; Van Hoorne, J W; van Leeuwen, M; Vanat, T; Vande Vyvre, P; Varga, D; Vargas, A; Vargyas, M; Varma, R; Vasileiou, M; Vasiliev, A; Vauthier, A; Vázquez Doce, O; Vechernin, V; Veen, A M; Velure, A; Vercellin, E; Vergara Limón, S; Vernet, R; Vértesi, R; Vickovic, L; Vigolo, S; Viinikainen, J; Vilakazi, Z; Villalobos Baillie, O; Villatoro Tello, A; Vinogradov, A; Vinogradov, L; Virgili, T; Vislavicius, V; Vodopyanov, A; Völkl, M A; Voloshin, K; Voloshin, S A; Volpe, G; von Haller, B; Vorobyev, I; Voscek, D; Vranic, D; Vrláková, J; Wagner, B; Wagner, J; Wang, H; Wang, M; Watanabe, D; Watanabe, Y; Weber, M; Weber, S G; Weiser, D F; Wessels, J P; Westerhoff, U; Whitehead, A M; Wiechula, J; Wikne, J; Wilk, G; Wilkinson, J; Willems, G A; Williams, M C S; Windelband, B; Witt, W E; Yalcin, S; Yang, P; Yano, S; Yin, Z; Yokoyama, H; Yoo, I-K; Yoon, J H; Yurchenko, V; Zaccolo, V; Zaman, A; Zampolli, C; Zanoli, H J C; Zardoshti, N; Zarochentsev, A; Závada, P; Zaviyalov, N; Zbroszczyk, H; Zhalov, M; Zhang, H; Zhang, X; Zhang, Y; Zhang, C; Zhang, Z; Zhao, C; Zhigareva, N; Zhou, D; Zhou, Y; Zhou, Z; Zhu, H; Zhu, J; Zhu, X; Zichichi, A; Zimmermann, A; Zimmermann, M B; Zimmermann, S; Zinovjev, G; Zmeskal, J

2017-01-01

We present results on transverse momentum ([Formula: see text]) and rapidity ([Formula: see text]) differential production cross sections, mean transverse momentum and mean transverse momentum square of inclusive [Formula: see text] and [Formula: see text] at forward rapidity ([Formula: see text]) as well as [Formula: see text]-to-[Formula: see text] cross section ratios. These quantities are measured in pp collisions at center of mass energies [Formula: see text] and 13 TeV with the ALICE detector. Both charmonium states are reconstructed in the dimuon decay channel, using the muon spectrometer. A comprehensive comparison to inclusive charmonium cross sections measured at [Formula: see text], 7 and 8 TeV is performed. A comparison to non-relativistic quantum chromodynamics and fixed-order next-to-leading logarithm calculations, which describe prompt and non-prompt charmonium production respectively, is also presented. A good description of the data is obtained over the full [Formula: see text] range, provided that both contributions are summed. In particular, it is found that for [Formula: see text] GeV/ c the non-prompt contribution reaches up to 50% of the total charmonium yield.

Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian.

PubMed

Shen, Liejun

2018-01-01

The present study is concerned with the following fractional p -Laplacian equation involving a critical Sobolev exponent of Kirchhoff type: [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are constants, and [Formula: see text] is the fractional p -Laplacian operator with [Formula: see text] and [Formula: see text]. For suitable [Formula: see text], the above equation possesses at least two nontrivial solutions by variational method for any [Formula: see text]. Moreover, we regard [Formula: see text] and [Formula: see text] as parameters to obtain convergent properties of solutions for the given problem as [Formula: see text] and [Formula: see text], respectively.

Assessing significance in a Markov chain without mixing.

PubMed

Chikina, Maria; Frieze, Alan; Pegden, Wesley

2017-03-14

We present a statistical test to detect that a presented state of a reversible Markov chain was not chosen from a stationary distribution. In particular, given a value function for the states of the Markov chain, we would like to show rigorously that the presented state is an outlier with respect to the values, by establishing a [Formula: see text] value under the null hypothesis that it was chosen from a stationary distribution of the chain. A simple heuristic used in practice is to sample ranks of states from long random trajectories on the Markov chain and compare these with the rank of the presented state; if the presented state is a [Formula: see text] outlier compared with the sampled ranks (its rank is in the bottom [Formula: see text] of sampled ranks), then this observation should correspond to a [Formula: see text] value of [Formula: see text] This significance is not rigorous, however, without good bounds on the mixing time of the Markov chain. Our test is the following: Given the presented state in the Markov chain, take a random walk from the presented state for any number of steps. We prove that observing that the presented state is an [Formula: see text]-outlier on the walk is significant at [Formula: see text] under the null hypothesis that the state was chosen from a stationary distribution. We assume nothing about the Markov chain beyond reversibility and show that significance at [Formula: see text] is best possible in general. We illustrate the use of our test with a potential application to the rigorous detection of gerrymandering in Congressional districting.

Development of a Capital Allocations Formula.

ERIC Educational Resources Information Center

Thompson, I.; And Others.

A description is presented of the present state of development of a capital allocations formula for general building project costs at the University of Toronto. The first part of the paper is devoted to a discussion of the objectives and application of the formula in its present state. A detailed description of the available data and the…

Assessment of critical exposure and outcome windows in time-to-event analysis with application to air pollution and preterm birth study.

PubMed

Chang, Howard H; Warren, Joshua L; Darrow, Lnydsey A; Reich, Brian J; Waller, Lance A

2015-07-01

In reproductive epidemiology, there is a growing interest to examine associations between air pollution exposure during pregnancy and the risk of preterm birth (PTB). One important research objective is to identify critical periods of exposure and estimate the associated effects at different stages of pregnancy. However, population studies have reported inconsistent findings. This may be due to limitations from the standard analytic approach of treating PTB as a binary outcome without considering time-varying exposures together over the course of pregnancy. To address this research gap, we present a Bayesian hierarchical model for conducting a comprehensive examination of gestational air pollution exposure by estimating the joint effects of weekly exposures during different vulnerable periods. Our model also treats PTB as a time-to-event outcome to address the challenge of different exposure lengths among ongoing pregnancies. The proposed model is applied to a dataset of geocoded birth records in the Atlanta metropolitan area between 1999-2005 to examine the risk of PTB associated with gestational exposure to ambient fine particulate matter [Formula: see text]m in aerodynamic diameter (PM[Formula: see text]). We find positive associations between PM[Formula: see text] exposure during early and mid-pregnancy, and evidence that associations are stronger for PTBs occurring around week 30. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

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.

Systematic study on the competition between α-decay and spontaneous fission of superheavy nuclei

NASA Astrophysics Data System (ADS)

Zhang, Y. L.; Wang, Y. Z.

2017-10-01

The competition between α-decay and spontaneous fission (SF) of Z = 112 isotopes are studied. The α-decay half-lives are estimated by the generalized liquid-drop model (GLDM) and several sets of analytic formulas. These formulas include the Royer formula, Viola-Seaborg semiempirical (VSS) formula and universal decay law (UDL). For the SF, its half-lives are calculated by using the Xu, Ren, Karpov and Santhosh formulas. It is shown that the predicted α-decay half-lives by different approaches are more or less identical. However, the SF half-lives are highly sensitive to models. To test the accuracies of different SF formulas, the half-lives of 56 even-even heavy nuclei are calculated by these formulas. By comparing with the experimental data, it is found that the Xu formula is the most accurate one to reproduce the experimental SF half-lives. This allows us to make a systematic prediction on the competition between α-decay and SF of even-even superheavy nuclei (SHN) with Z = 104- 120 by using the Xu formula and the above mentioned models on α-decay. The calculations suggest that 258,260104, 268-276110, 270-280112, 272-286114, 274-294116, 284-302118 and 292-308120 have smaller α-decay half-lives than those of SF. Thus these nuclei can be synthesized and identified via α-decay in the laboratory. In addition, it is observed that N = 162, 178, 184 and 196 may be the submagic or magic numbers. Finally, an extensive study on the possible α-decay chains for Z = 120 isotopes is performed. It is predicted that six sequential α-decay chains can be observed from 292-296120, four α-decay chains from 298120, three α-decay chains from 300,302120, two α-decay chains from 304,306120, and only one α-decay chain from 308120. These nuclei are the most likely candidates to be synthesized experimentally via α-decay in the near future.

Biases and Standard Errors of Standardized Regression Coefficients

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Chan, Wai

2011-01-01

The paper obtains consistent standard errors (SE) and biases of order O(1/n) for the sample standardized regression coefficients with both random and given predictors. Analytical results indicate that the formulas for SEs given in popular text books are consistent only when the population value of the regression coefficient is zero. The sample…

Actuation of Piezoelectric Layered Beams With and Coupling.

PubMed

Nguyen, Cuong H; Hanke, Ulrik; Halvorsen, Einar

2018-05-01

In this paper, we derive and compare the linear static bending of piezoelectric actuators with transversal ( ) and longitudinal ( ) coupling. The transducers are, respectively, structures utilizing top and bottom electrodes (TBEs) and interdigitated electrodes (IDEs). While the theory is well developed for the TBE beam, governing equations for the bending of the piezoelectric beams with IDEs are far less developed. We improve on this by deriving the governing equation for the IDE beam with an arbitrary number of layers and with coupling consistently included. In addition, we introduce a phenomenological quadratic form for the nonuniform field that lets us derive a deflection formula with nontrivial effects of the field accounted for. The theory is applied to derive deflection formulas for both cantilever and clamped-clamped beams. All analytic results are validated with numerical simulations. From the analytic models, two different figures of merit (FOMs) are derived. We show that these FOMs are the same for cantilevers and doubly clamped beams. The analysis indicates the optimal transducer length for clamped-clamped beams and gives a criterion that can be used to determine which design concept ( or ) gives the largest deflection.

Application of the backward extrapolation method to pulsed neutron sources

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

Talamo, Alberto; Gohar, Yousry

We report particle detectors operated in pulse mode are subjected to the dead-time effect. When the average of the detector counts is constant over time, correcting for the dead-time effect is simple and can be accomplished by analytical formulas. However, when the average of the detector counts changes over time it is more difficult to take into account the dead-time effect. When a subcritical nuclear assembly is driven by a pulsed neutron source, simple analytical formulas cannot be applied to the measured detector counts to correct for the dead-time effect because of the sharp change of the detector counts overmore » time. This work addresses this issue by using the backward extrapolation method. The latter can be applied not only to a continuous (e.g. californium) external neutron source but also to a pulsed external neutron source (e.g. by a particle accelerator) driving a subcritical nuclear assembly. Finally, the backward extrapolation method allows to obtain from the measured detector counts both the dead-time value and the real detector counts.« less

Brownian aggregation rate of colloid particles with several active sites

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

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

2014-08-14

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

GEOS satellite tracking corrections for refraction in the ionosphere

NASA Technical Reports Server (NTRS)

Berbert, J. H.; Parker, H. C.

1970-01-01

The analytic formulations at different elevation angles and at a frequency of 2-GHz for the ionospheric refraction corrections used on the GEOS satellite tracking data are compared. The formulas and ray trace results for elevations greater than 10 deg, where most satellite tracking is done, differ in elevation, range, and range rate by less than 0.4 millidegrees (1.4 arc-seconds), 12 meters, and 12 cm/sec, respectively. In comparison to most operational requirements, this is insignificant. However, for the GEOS Observation Systems Intercomparison Investigation, these differences are equivalent in size to observed differences in system biases for some of the best electronic geodetic tracking systems and are probably contributing to the observed biases. The ray trace results and most of the more detailed analytic correction formulas show that the ionospheric refraction correction for range rate on an overhead pass is a maximum for elevation angles between 15 deg and 30 deg and falls off rapidly for both higher and lower elevation angles, contrary to the effect of the troposphere and to some reports in the literature.

Application of the backward extrapolation method to pulsed neutron sources

DOE PAGES

Talamo, Alberto; Gohar, Yousry

2017-09-23

We report particle detectors operated in pulse mode are subjected to the dead-time effect. When the average of the detector counts is constant over time, correcting for the dead-time effect is simple and can be accomplished by analytical formulas. However, when the average of the detector counts changes over time it is more difficult to take into account the dead-time effect. When a subcritical nuclear assembly is driven by a pulsed neutron source, simple analytical formulas cannot be applied to the measured detector counts to correct for the dead-time effect because of the sharp change of the detector counts overmore » time. This work addresses this issue by using the backward extrapolation method. The latter can be applied not only to a continuous (e.g. californium) external neutron source but also to a pulsed external neutron source (e.g. by a particle accelerator) driving a subcritical nuclear assembly. Finally, the backward extrapolation method allows to obtain from the measured detector counts both the dead-time value and the real detector counts.« less

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

DOE PAGES

Bassi, Gabriele; Blednykh, Alexei; Smalyuk, Victor

2016-02-24

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

Valuing options in shot noise market

NASA Astrophysics Data System (ADS)

Laskin, Nick

2018-07-01

A new exactly solvable option pricing model has been introduced and elaborated. It is assumed that a stock price follows a Geometric shot noise process. An arbitrage-free integro-differential option pricing equation has been obtained and solved. The new Greeks have been analytically calculated. It has been shown that in diffusion approximation the developed option pricing model incorporates the well-known Black-Scholes equation and its solution. The stochastic dynamic origin of the Black-Scholes volatility has been uncovered. To model the observed market stock price patterns consisting of high frequency small magnitude and low frequency large magnitude jumps, the superposition of two Geometric shot noises has been implemented. A new generalized option pricing equation has been obtained and its exact solution was found. Merton's jump-diffusion formula for option price was recovered in diffusion approximation. Despite the non-Gaussian nature of probability distributions involved, the new option pricing model has the same degree of analytical tractability as the Black-Scholes model and the Merton jump-diffusion model. This attractive feature allows one to derive exact formulas to value options and option related instruments in the market with jump-like price patterns.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Development and validation of a solid-phase extraction method coupled to liquid chromatography with fluorescence detection for the determination of fluoroquinolone residues in powdered infant formulae. Application to the analysis of samples from the Spanish and Latin American market.

PubMed

Rodriguez, E; Moreno-Bondi, M C; Marazuela, M D

2008-10-31

This paper describes a new method for the effective extraction, clean-up and chromatographic analysis of residues of four fluoroquinolones (ciprofloxacin, enrofloxacin, danofloxacin and sarafloxacin) in powdered infant formulae and follow-on preparations. Samples were reconstituted following the manufacturer's recommendations and treated with trichloroacetic acid in methanol 10% (w/v) for deproteinization. Two solid-phase extraction cartridges have been evaluated for sample clean-up and preconcentration, Strata Screen A and Strata X and the later provided the best recoveries for all the analytes tested. Chromatographic analysis has been carried out using a polar endcapped column (AQUA C(18)) and fluorescence detection, with lomefloxacin (LOME) as internal standard. Method validation has been performed according to European Commission Decision 2002/657/EC criteria, in terms of linearity, recovery, precision, specificity, decision limit (CC(alpha)) and detection capability (CC(beta)). Typical recoveries ranged between 70 and 110% at levels below and above the maximum residue limits of the target analytes in bovine milk, with an excellent intralab reproducibility (RSDs<7%). Matrix effects did not significantly affect method accuracy, as evidenced by analyzing different brands of milk. The method has been successfully applied to the analysis of 100 samples of infant and follow-on formulae of the Spanish and Latin American market, using LC-MS/MS as confirmatory technique.

Higgs physics at the CLIC electron-positron linear collider.

PubMed

Abramowicz, H; Abusleme, A; Afanaciev, K; Alipour Tehrani, N; Balázs, C; Benhammou, Y; Benoit, M; Bilki, B; Blaising, J-J; Boland, M J; Boronat, M; Borysov, O; Božović-Jelisavčić, I; Buckland, M; Bugiel, S; Burrows, P N; Charles, T K; Daniluk, W; Dannheim, D; Dasgupta, R; Demarteau, M; Díaz Gutierrez, M A; Eigen, G; Elsener, K; Felzmann, U; Firlej, M; Firu, E; Fiutowski, T; Fuster, J; Gabriel, M; Gaede, F; García, I; Ghenescu, V; Goldstein, J; Green, S; Grefe, C; Hauschild, M; Hawkes, C; Hynds, D; Idzik, M; Kačarević, G; Kalinowski, J; Kananov, S; Klempt, W; Kopec, M; Krawczyk, M; Krupa, B; Kucharczyk, M; Kulis, S; Laštovička, T; Lesiak, T; Levy, A; Levy, I; Linssen, L; Lukić, S; Maier, A A; Makarenko, V; Marshall, J S; Martin, V J; Mei, K; Milutinović-Dumbelović, G; Moroń, J; Moszczyński, A; Moya, D; Münker, R M; Münnich, A; Neagu, A T; Nikiforou, N; Nikolopoulos, K; Nürnberg, A; Pandurović, M; Pawlik, B; Perez Codina, E; Peric, I; Petric, M; Pitters, F; Poss, S G; Preda, T; Protopopescu, D; Rassool, R; Redford, S; Repond, J; Robson, A; Roloff, P; Ros, E; Rosenblat, O; Ruiz-Jimeno, A; Sailer, A; Schlatter, D; Schulte, D; Shumeiko, N; Sicking, E; Simon, F; Simoniello, R; Sopicki, P; Stapnes, S; Ström, R; Strube, J; Świentek, K P; Szalay, M; Tesař, M; Thomson, M A; Trenado, J; Uggerhøj, U I; van der Kolk, N; van der Kraaij, E; Vicente Barreto Pinto, M; Vila, I; Vogel Gonzalez, M; Vos, M; Vossebeld, J; Watson, M; Watson, N; Weber, M A; Weerts, H; Wells, J D; Weuste, L; Winter, A; Wojtoń, T; Xia, L; Xu, B; Żarnecki, A F; Zawiejski, L; Zgura, I-S

2017-01-01

The Compact Linear Collider (CLIC) is an option for a future [Formula: see text] collider operating at centre-of-mass energies up to [Formula: see text], providing sensitivity to a wide range of new physics phenomena and precision physics measurements at the energy frontier. This paper is the first comprehensive presentation of the Higgs physics reach of CLIC operating at three energy stages: [Formula: see text], 1.4 and [Formula: see text]. The initial stage of operation allows the study of Higgs boson production in Higgsstrahlung ([Formula: see text]) and [Formula: see text]-fusion ([Formula: see text]), resulting in precise measurements of the production cross sections, the Higgs total decay width [Formula: see text], and model-independent determinations of the Higgs couplings. Operation at [Formula: see text] provides high-statistics samples of Higgs bosons produced through [Formula: see text]-fusion, enabling tight constraints on the Higgs boson couplings. Studies of the rarer processes [Formula: see text] and [Formula: see text] allow measurements of the top Yukawa coupling and the Higgs boson self-coupling. This paper presents detailed studies of the precision achievable with Higgs measurements at CLIC and describes the interpretation of these measurements in a global fit.

A Closer Look at Formulaic Language: Prosodic Characteristics of Swedish Proverbs

ERIC Educational Resources Information Center

Hallin, Anna Eva; Van Lancker Sidtis, Diana

2017-01-01

Formulaic expressions (such as idioms, proverbs, and conversational speech formulas) are currently a topic of interest. Examination of prosody in formulaic utterances, a less explored property of formulaic expressions, has yielded controversial views. The present study investigates prosodic characteristics of proverbs, as one type of formulaic…

Low-coverage surface diffusion in complex periodic energy landscapes: Analytical solution for systems with symmetric hops and application to intercalation in topological insulators

NASA Astrophysics Data System (ADS)

Gosálvez, Miguel A.; Otrokov, Mikhail M.; Ferrando, Nestor; Ryabishchenkova, Anastasia G.; Ayuela, Andres; Echenique, Pedro M.; Chulkov, Evgueni V.

2016-02-01

This is the first of two papers that introduce a general expression for the tracer diffusivity in complex, periodic energy landscapes with M distinct hop rates in one-, two-, and three-dimensional diluted systems (low-coverage, single-tracer limit). The present report focuses on the analysis of diffusion in systems where the end sites of the hops are located symmetrically with respect to the hop origins (symmetric hops), as encountered in many ideal surfaces and bulk materials. For diffusion in two dimensions, a number of formulas are presented for complex combinations of the different hops in systems with triangular, rectangular, and square symmetry. The formulas provide values in excellent agreement with kinetic Monte Carlo simulations, concluding that the diffusion coefficient can be directly determined from the proposed expressions without performing the simulations. Based on the diffusion barriers obtained from first-principles calculations and a physically meaningful estimate of the attempt frequencies, the proposed formulas are used to analyze the diffusion of Cu, Ag, and Rb adatoms on the surface and within the van der Waals (vdW) gap of a model topological insulator, Bi2Se3 . Considering the possibility of adsorbate intercalation from the terraces to the vdW gaps at morphological steps, we infer that, at low coverage and room temperature, (i) a majority of the Rb atoms bounce back at the steps and remain on the terraces, (ii) Cu atoms mostly intercalate into the vdW gap, the remaining fraction staying at the steps, and (iii) Ag atoms essentially accumulate at the steps and gradually intercalate into the vdW gap. These conclusions are in good qualitative agreement with previous experiments. The companion report (M. A. Gosálvez et al., Phys. Rev. B, submitted] extends the present study to the description of systems that contain asymmetric hops.

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

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

Parasitic current collection by PASP Plus solar arrays

NASA Technical Reports Server (NTRS)

Davis, Victoria Ann; Gardner, Barbara M.

1995-01-01

Solar cells at potentials positive with respect to a surrounding plasma collect electrons. Current is collected by the exposed high voltage surfaces: the interconnects and the sides of the solar cells. This current is a drain on the array power that can be significant for high-power arrays. In addition, this current influences the current balance that determines the floating potential of the spacecraft. One of the objectives of the Air Force (PL/GPS) PASP Plus (Photovoltaic Array Space Power Plus Diagnostics) experiment is an improved understanding fo parasitic current collection. We have done computer modeling of parasitic current collection and have examined current collection flight data from the first year of operations. Prior to the flight we did computer modeling to improve our understanding of the physical processes that control parasitic current collection. At high potentials, the current rapidly rises due to a phenomenon called snapover. Under snapover conditions, the equilibrium potential distribution across the dielectric surface is such that part of the area is at potentials greater than the first crossover of the secondary yield curve. Therefore, each incident electron generates more than one secondary electron. The net effect is that the high potential area and the collecting area increase. We did two-dimensional calculations for the various geometries to be flown. The calculations span the space of anticipated plasma conditions, applied potential, and material parameters. We used the calculations and early flight data to develop an analytic formula for the dependence of the current on the primary problem variables. The analytic formula was incorporated into the EPSAT computer code. EPSAT allows us to easily extend the results to other conditions. PASP Plus is the principal experiment integrated onto the Advanced Photovoltaic and Electronics Experiments (APEX) satellite bus. The experiment is testing twelve different solar array designs. Parasitic current collection is being measured for eight of the designs under various operational and environment conditions. We examined the current collected as a function of the various parameters for the six non-concentrator designs. The results are similar to those obtained in previous experiments and predicted by the calculations. We are using the flight data to validate the analytic formula developed. The formula can be used to quantify the parasitic current collected. Anticipating the parasitic current value allows the spacecraft designer to include this interaction when developing the design.

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.

Measurement Model Nonlinearity in Estimation of Dynamical Systems

NASA Astrophysics Data System (ADS)

Majji, Manoranjan; Junkins, J. L.; Turner, J. D.

2012-06-01

The role of nonlinearity of the measurement model and its interactions with the uncertainty of measurements and geometry of the problem is studied in this paper. An examination of the transformations of the probability density function in various coordinate systems is presented for several astrodynamics applications. Smooth and analytic nonlinear functions are considered for the studies on the exact transformation of uncertainty. Special emphasis is given to understanding the role of change of variables in the calculus of random variables. The transformation of probability density functions through mappings is shown to provide insight in to understanding the evolution of uncertainty in nonlinear systems. Examples are presented to highlight salient aspects of the discussion. A sequential orbit determination problem is analyzed, where the transformation formula provides useful insights for making the choice of coordinates for estimation of dynamic systems.

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

NASA Astrophysics Data System (ADS)

Izacard, Olivier

2016-08-01

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

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

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

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

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

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

PubMed

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

2015-05-04

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

Alpha Decay Potential Barriers and Half-Lives and Analytical Formula Predictions for Superheavy Nuclei

NASA Astrophysics Data System (ADS)

Royer, Guy; Zhang, Hongfei

The α decay potential barriers are determined in the cluster-like shape path within a generalized liquid drop model including the proximity effects between the α particle and the daughter nucleus and adjusted to reproduce the experimental Qα. The α emission half-lives are determined within the WKB penetration probability. Calculations using previously proposed formulae depending only on the mass and charge of the alpha emitter and Qα are also compared with new experimental alpha-decay half-lives. The agreement allows to provide predictions for the α decay half-lives of other still unknown superheavy nuclei using the Qα determined from the 2003 atomic mass evaluation of Audi, Wapstra and Thibault.

Stress concentration factors for circular, reinforced penetrations in pressurized cylindrical shells. Ph.D. Thesis - Virginia Univ.

NASA Technical Reports Server (NTRS)

Ramsey, J. W., Jr.

1975-01-01

The effect on stresses in a cylindrical shell with a circular penetration subject to internal pressure was investigated in thin, shallow linearly, elastic cylindrical shells. Results provide numerical predictions of peak stress concentration factors around nonreinforced and reinforced penetrations in pressurized cylindrical shells. Analytical results were correlated with published formulas, as well as theoretical and experimental results. An accuracy study was made of the finite element program for each of the configurations considered important in pressure vessel technology. A formula is developed to predict the peak stress concentration factor for analysis and/or design in conjunction with the ASME Boiler and Pressure Vessel Code.

Time delay of critical images of a point source near the gravitational lens fold-caustic

NASA Astrophysics Data System (ADS)

Alexandrov, A.; Zhdanov, V.

2016-06-01

Within the framework of the analytical theory of the gravitational lensing we derive asymptotic formula for the time delay of critical images of apoint source, which is situated near a fold-caustic. We found corrections of the first and second order in powers of a parameter, which describescloseness of the source to the caustic. Our formula modifies earlier result by Congdon, Keeton &Nordgren (MNRAS, 2008) obtained in zero-orderapproximation. We have proved the hypothesis put forward by these authors that the first-order correction to the relative time delay of two criticalmages is identically zero. The contribution of the corrections is illustrated in model example by comparison with exact expression.

Quantum correlations for bipartite continuous-variable systems

NASA Astrophysics Data System (ADS)

Ma, Ruifen; Hou, Jinchuan; Qi, Xiaofei; Wang, Yangyang

2018-04-01

Two quantum correlations Q and Q_P for (m+n)-mode continuous-variable systems are introduced in terms of average distance between the reduced states under the local Gaussian positive operator-valued measurements, and analytical formulas of these quantum correlations for bipartite Gaussian states are provided. It is shown that the product states do not contain these quantum correlations, and conversely, all (m+n)-mode Gaussian states with zero quantum correlations are product states. Generally, Q≥ Q_{P}, but for the symmetric two-mode squeezed thermal states, these quantum correlations are the same and a computable formula is given. In addition, Q is compared with Gaussian geometric discord for symmetric squeezed thermal states.

Influence of Convection and Aerosol Pollution on Ice Cloud Particle Effective Radius

NASA Technical Reports Server (NTRS)

Jiang, J. H.; Su, H.; Zhai, C.; Massie, S. T.; Schoeberl, M. R.; Colarco, P. R.; Platnick, S.; Gu, Y.; Liou, K.-N.

2011-01-01

Satellite observations show that ice cloud effective radius (r(sub e)) increases with ice water content (IWC) but decreases with aerosol optical thickness (AOT). Using least-squares fitting to the observed data, we obtain an analytical formula to describe the variations of r(sub e) with IWC and AOT for several regions with distinct characteristics of r(sub e) -IWC-AOT relationships. As IWC directly relates to convective strength and AOT represents aerosol loading, our empirical formula provides a means to quantify the relative roles of dynamics and aerosols in controlling r(sub e) in different geographical regions, and to establish a framework for parameterization of aerosol effects on r(sub e) in climate models.

Time-dependent diffusive acceleration of test particles at shocks

NASA Astrophysics Data System (ADS)

Drury, L. O'C.

1991-07-01

A theoretical description is developed for the acceleration of test particles at a steady plane nonrelativistic shock. The mean and the variance of the acceleration-time distribution are expressed analytically for the condition under which the diffusion coefficient is arbitrarily dependent on position and momentum. The formula for an acceleration rate with arbitrary spatial variation in the diffusion coefficient developed by Drury (1987) is supplemented by a general theory of time dependence. An approximation scheme is developed by means of the analysis which permits the description of the spectral cutoff resulting from the finite shock age. The formulas developed in the analysis are also of interest for analyzing the observations of heliospheric shocks made from spacecraft.

Matrix Sturm-Liouville equation with a Bessel-type singularity on a finite interval

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia

2017-03-01

The matrix Sturm-Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with the prescribed behavior at the singular point and Birkhoff-type solutions with the known asymptotics for large values of the spectral parameter. The asymptotic formulas for Stokes multipliers, connecting these two fundamental systems of solutions, are derived. We also set boundary conditions and obtain asymptotic formulas for the spectral data (the eigenvalues and the weight matrices) of the boundary value problem. Our results will be useful in the theory of direct and inverse spectral problems.

Calculation of the Ionization Coefficient in the Townsend Discharge in the Mixture of Argon and Mercury Vapors with Temperature-Dependent Composition

NASA Astrophysics Data System (ADS)

Bondarenko, G. G.; Dubinina, M. S.; Fisher, M. R.; Kristya, V. I.

2018-04-01

For a hybrid model of the low-current discharge considering, along with direct ionization of the mixture components by electrons, the Penning ionization of mercury atoms by metastable argon atoms, the ionization coefficient in the argon-mercury mixture used in illuminating lamps is calculated. The analytical approximation formula describing the dependence of the ionization coefficient of the mixture on the reduced electric field strength and temperature is obtained for sufficiently wide ranges of their variations, and its accuracy is estimated. It is demonstrated that the discharge ignition voltage calculated using this formula is in agreement with the results of simulation and the available experimental data.

Quark flavour observables in the Littlest Higgs model with T-parity after LHC Run 1.

PubMed

Blanke, Monika; Buras, Andrzej J; Recksiegel, Stefan

2016-01-01

The Littlest Higgs model with T-parity (LHT) belongs to the simplest new physics scenarios with new sources of flavour and CP violation. The latter originate in the interactions of ordinary quarks and leptons with heavy mirror quarks and leptons that are mediated by new heavy gauge bosons. Also a heavy fermionic top partner is present in this model which communicates with the SM fermions by means of standard [Formula: see text] and [Formula: see text] gauge bosons. We present a new analysis of quark flavour observables in the LHT model in view of the oncoming flavour precision era. We use all available information on the CKM parameters, lattice QCD input and experimental data on quark flavour observables and corresponding theoretical calculations, taking into account new lower bounds on the symmetry breaking scale and the mirror quark masses from the LHC. We investigate by how much the branching ratios for a number of rare K and B decays are still allowed to depart from their SM values. This includes [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. Taking into account the constraints from [Formula: see text] processes, significant departures from the SM predictions for [Formula: see text] and [Formula: see text] are possible, while the effects in B decays are much smaller. In particular, the LHT model favours [Formula: see text], which is not supported by the data, and the present anomalies in [Formula: see text] decays cannot be explained in this model. With the recent lattice and large N input the imposition of the [Formula: see text] constraint implies a significant suppression of the branching ratio for [Formula: see text] with respect to its SM value while allowing only for small modifications of [Formula: see text]. Finally, we investigate how the LHT physics could be distinguished from other models by means of indirect measurements and discuss the consequences for quark flavour observables of not finding any LHT state in the coming years.

Production of [Formula: see text] and [Formula: see text] in p-Pb collisions at [Formula: see text] TeV.

PubMed

Adamová, D; Aggarwal, M M; Aglieri Rinella, G; Agnello, M; Agrawal, N; Ahammed, Z; Ahmad, S; Ahn, S U; Aiola, S; Akindinov, A; Alam, S N; Albuquerque, D S D; Aleksandrov, D; Alessandro, B; Alexandre, D; Alfaro Molina, R; Alici, A; Alkin, A; Alme, J; Alt, T; Altinpinar, S; Altsybeev, I; Alves Garcia Prado, C; An, M; Andrei, C; Andrews, H A; Andronic, A; Anguelov, V; Anson, C; Antičić, T; Antinori, F; Antonioli, P; Anwar, R; Aphecetche, L; Appelshäuser, H; Arcelli, S; Arnaldi, R; Arnold, O W; Arsene, I C; Arslandok, M; Audurier, B; Augustinus, A; Averbeck, R; Azmi, M D; Badalà, A; Baek, Y W; Bagnasco, S; Bailhache, R; Bala, R; Baldisseri, A; Ball, M; Baral, R C; Barbano, A M; Barbera, R; Barile, F; Barioglio, L; Barnaföldi, G G; Barnby, L S; Barret, V; Bartalini, P; Barth, K; Bartke, J; Bartsch, E; Basile, M; Bastid, N; Basu, S; Bathen, B; Batigne, G; Batista Camejo, A; Batyunya, B; Batzing, P C; Bearden, I G; Beck, H; Bedda, C; Behera, N K; Belikov, I; Bellini, F; Bello Martinez, H; Bellwied, R; Beltran, L G E; Belyaev, V; Bencedi, G; Beole, S; Bercuci, A; Berdnikov, Y; Berenyi, D; Bertens, R A; Berzano, D; Betev, L; Bhasin, A; Bhat, I R; Bhati, A K; Bhattacharjee, B; Bhom, J; Bianchi, L; Bianchi, N; Bianchin, C; Bielčík, J; Bielčíková, J; Bilandzic, A; Biro, G; Biswas, R; Biswas, S; Blair, J T; Blau, D; Blume, C; Boca, G; Bock, F; Bogdanov, A; Boldizsár, L; Bombara, M; Bonomi, G; Bonora, M; Book, J; Borel, H; Borissov, A; Borri, M; Botta, E; Bourjau, C; Braun-Munzinger, P; Bregant, M; Broker, T A; Browning, T A; Broz, M; Brucken, E J; Bruna, E; Bruno, G E; Budnikov, D; Buesching, H; Bufalino, S; Buhler, P; Buitron, S A I; Buncic, P; Busch, O; Buthelezi, Z; Butt, J B; Buxton, J T; Cabala, J; Caffarri, D; Caines, H; Caliva, A; Calvo Villar, E; Camerini, P; Capon, A A; Carena, F; Carena, W; Carnesecchi, F; Castillo Castellanos, J; Castro, A J; Casula, E A R; Ceballos Sanchez, C; Cerello, P; Chang, B; Chapeland, S; Chartier, M; Charvet, J L; Chattopadhyay, S; Chattopadhyay, S; Chauvin, A; Cherney, M; Cheshkov, C; Cheynis, B; Chibante Barroso, V; Chinellato, D D; Cho, S; Chochula, P; Choi, K; Chojnacki, M; Choudhury, S; Christakoglou, P; Christensen, C H; Christiansen, P; Chujo, T; Chung, S U; Cicalo, C; Cifarelli, L; Cindolo, F; Cleymans, J; Colamaria, F; Colella, D; Collu, A; Colocci, M; Conesa Balbastre, G; Conesa Del Valle, Z; Connors, M E; Contreras, J G; Cormier, T M; Corrales Morales, Y; Cortés Maldonado, I; Cortese, P; Cosentino, M R; Costa, F; Costanza, S; Crkovská, J; Crochet, P; Cuautle, E; Cunqueiro, L; Dahms, T; Dainese, A; Danisch, M C; Danu, A; Das, D; Das, I; Das, S; Dash, A; Dash, S; De, S; De Caro, A; de Cataldo, G; de Conti, C; de Cuveland, J; De Falco, A; De Gruttola, D; De Marco, N; De Pasquale, S; De Souza, R D; Degenhardt, H F; Deisting, A; Deloff, A; Deplano, C; Dhankher, P; Di Bari, D; Di Mauro, A; Di Nezza, P; Di Ruzza, B; Diaz Corchero, M A; Dietel, T; Dillenseger, P; Divià, R; Djuvsland, Ø; Dobrin, A; Domenicis Gimenez, D; Dönigus, B; Dordic, O; Drozhzhova, T; Dubey, A K; Dubla, A; Ducroux, L; Duggal, A K; Dupieux, P; Ehlers, R J; Elia, D; Endress, E; Engel, H; Epple, E; Erazmus, B; Erhardt, F; Espagnon, B; Esumi, S; Eulisse, G; Eum, J; Evans, D; Evdokimov, S; Fabbietti, L; Fabris, D; Faivre, J; Fantoni, A; Fasel, M; Feldkamp, L; Feliciello, A; Feofilov, G; Ferencei, J; Fernández Téllez, A; Ferreiro, E G; Ferretti, A; Festanti, A; Feuillard, V J G; Figiel, J; Figueredo, M A S; Filchagin, S; Finogeev, D; Fionda, F M; Fiore, E M; Floris, M; Foertsch, S; Foka, P; Fokin, S; Fragiacomo, E; Francescon, A; Francisco, A; Frankenfeld, U; Fronze, G G; Fuchs, U; Furget, C; Furs, A; Fusco Girard, M; Gaardhøje, J J; Gagliardi, M; Gago, A M; Gajdosova, K; Gallio, M; Galvan, C D; Gangadharan, D R; Ganoti, P; Gao, C; Garabatos, C; Garcia-Solis, E; Garg, K; Garg, P; Gargiulo, C; Gasik, P; Gauger, E F; Gay Ducati, M B; Germain, M; Ghosh, P; Ghosh, S K; Gianotti, P; Giubellino, P; Giubilato, P; Gladysz-Dziadus, E; Glässel, P; Goméz Coral, D M; Gomez Ramirez, A; Gonzalez, A S; Gonzalez, V; González-Zamora, P; Gorbunov, S; Görlich, L; Gotovac, S; Grabski, V; Graczykowski, L K; Graham, K L; Greiner, L; Grelli, A; Grigoras, C; Grigoriev, V; Grigoryan, A; Grigoryan, S; Grion, N; Gronefeld, J M; Grosa, F; Grosse-Oetringhaus, J F; Grosso, R; Gruber, L; Grull, F R; Guber, F; Guernane, R; Guerzoni, B; Gulbrandsen, K; Gunji, T; Gupta, A; Gupta, R; Guzman, I B; Haake, R; Hadjidakis, C; Hamagaki, H; Hamar, G; Hamon, J C; Harris, J W; Harton, A; Hatzifotiadou, D; Hayashi, S; Heckel, S T; Hellbär, E; Helstrup, H; Herghelegiu, A; Herrera Corral, G; Herrmann, F; Hess, B A; Hetland, K F; Hillemanns, H; Hippolyte, B; Hladky, J; Horak, D; Hosokawa, R; Hristov, P; Hughes, C; Humanic, T J; Hussain, N; Hussain, T; Hutter, D; Hwang, D S; Ilkaev, R; Inaba, M; Ippolitov, M; Irfan, M; Isakov, V; Islam, M S; Ivanov, M; Ivanov, V; Izucheev, V; Jacak, B; Jacazio, N; Jacobs, P M; Jadhav, M B; Jadlovska, S; Jadlovsky, J; Jahnke, C; Jakubowska, M J; Janik, M A; Jayarathna, P H S Y; Jena, C; Jena, S; Jercic, M; Jimenez Bustamante, R T; Jones, P G; Jusko, A; Kalinak, P; Kalweit, A; Kang, J H; Kaplin, V; Kar, S; Karasu Uysal, A; Karavichev, O; Karavicheva, T; Karayan, L; Karpechev, E; Kebschull, U; Keidel, R; Keijdener, D L D; Keil, M; Ketzer, B; Mohisin Khan, M; Khan, P; Khan, S A; Khanzadeev, A; Kharlov, Y; Khatun, A; Khuntia, A; Kielbowicz, M M; Kileng, B; Kim, D W; Kim, D J; Kim, D; Kim, H; Kim, J S; Kim, J; Kim, M; Kim, M; Kim, S; Kim, T; Kirsch, S; Kisel, I; Kiselev, S; Kisiel, A; Kiss, G; Klay, J L; Klein, C; Klein, J; Klein-Bösing, C; Klewin, S; Kluge, A; Knichel, M L; Knospe, A G; Kobdaj, C; Kofarago, M; Kollegger, T; Kolojvari, A; Kondratiev, V; Kondratyeva, N; Kondratyuk, E; Konevskikh, A; Kopcik, M; Kour, M; Kouzinopoulos, C; Kovalenko, O; Kovalenko, V; Kowalski, M; Koyithatta Meethaleveedu, G; Králik, I; Kravčáková, A; Krivda, M; Krizek, F; Kryshen, E; Krzewicki, M; Kubera, A M; Kučera, V; Kuhn, C; Kuijer, P G; Kumar, A; Kumar, J; Kumar, L; Kumar, S; Kundu, S; Kurashvili, P; Kurepin, A; Kurepin, A B; Kuryakin, A; Kushpil, S; Kweon, M J; Kwon, Y; La Pointe, S L; La Rocca, P; Lagana Fernandes, C; Lakomov, I; Langoy, R; Lapidus, K; Lara, C; Lardeux, A; Lattuca, A; Laudi, E; Lavicka, R; Lazaridis, L; Lea, R; Leardini, L; Lee, S; Lehas, F; Lehner, S; Lehrbach, J; Lemmon, R C; Lenti, V; Leogrande, E; León Monzón, I; Lévai, P; Li, S; Li, X; Lien, J; Lietava, R; Lindal, S; Lindenstruth, V; Lippmann, C; Lisa, M A; Litichevskyi, V; Ljunggren, H M; Llope, W J; Lodato, D F; Loenne, P I; Loginov, V; Loizides, C; Loncar, P; Lopez, X; López Torres, E; Lowe, A; Luettig, P; Lunardon, M; Luparello, G; Lupi, M; Lutz, T H; Maevskaya, A; Mager, M; Mahajan, S; Mahmood, S M; Maire, A; Majka, R D; Malaev, M; Maldonado Cervantes, I; Malinina, L; Mal'Kevich, D; Malzacher, P; Mamonov, A; Manko, V; Manso, F; Manzari, V; Mao, Y; Marchisone, M; Mareš, J; Margagliotti, G V; Margotti, A; Margutti, J; Marín, A; Markert, C; Marquard, M; Martin, N A; Martinengo, P; Martinez, J A L; Martínez, M I; Martínez García, G; Martinez Pedreira, M; Mas, A; Masciocchi, S; Masera, M; Masoni, A; Mastroserio, A; Mathis, A M; Matyja, A; Mayer, C; Mazer, J; Mazzilli, M; Mazzoni, M A; Meddi, F; Melikyan, Y; Menchaca-Rocha, A; Meninno, E; Mercado Pérez, J; Meres, M; Mhlanga, S; Miake, Y; Mieskolainen, M M; Mihaylov, D; Mikhaylov, K; Milano, L; Milosevic, J; Mischke, A; Mishra, A N; Miśkowiec, D; Mitra, J; Mitu, C M; Mohammadi, N; Mohanty, B; Montes, E; Moreira De Godoy, D A; Moreno, L A P; Moretto, S; Morreale, A; Morsch, A; Muccifora, V; Mudnic, E; Mühlheim, D; Muhuri, S; Mukherjee, M; Mulligan, J D; Munhoz, M G; Münning, K; Munzer, R H; Murakami, H; Murray, S; Musa, L; Musinsky, J; Myers, C J; Naik, B; Nair, R; Nandi, B K; Nania, R; Nappi, E; Naru, M U; Natal da Luz, H; Nattrass, C; Navarro, S R; Nayak, K; Nayak, R; Nayak, T K; Nazarenko, S; Nedosekin, A; Negrao De Oliveira, R A; Nellen, L; Nesbo, S V; Ng, F; Nicassio, M; Niculescu, M; Niedziela, J; Nielsen, B S; Nikolaev, S; Nikulin, S; Nikulin, V; Noferini, F; Nomokonov, P; Nooren, G; Noris, J C C; Norman, J; Nyanin, A; Nystrand, J; Oeschler, H; Oh, S; Ohlson, A; Okubo, T; Olah, L; Oleniacz, J; Oliveira Da Silva, A C; Oliver, M H; Onderwaater, J; Oppedisano, C; Orava, R; Oravec, M; Ortiz Velasquez, A; Oskarsson, A; Otwinowski, J; Oyama, K; Ozdemir, M; Pachmayer, Y; Pacik, V; Pagano, D; Pagano, P; Paić, G; Pal, S K; Palni, P; Pan, J; Pandey, A K; Panebianco, S; Papikyan, V; Pappalardo, G S; Pareek, P; Park, J; Park, W J; Parmar, S; Passfeld, A; Pathak, S P; Paticchio, V; Patra, R N; Paul, B; Pei, H; Peitzmann, T; Peng, X; Pereira, L G; Pereira Da Costa, H; Peresunko, D; Perez Lezama, E; Peskov, V; Pestov, Y; Petráček, V; Petrov, V; Petrovici, M; Petta, C; Pezzi, R P; Piano, S; Pikna, M; Pillot, P; Pimentel, L O D L; Pinazza, O; Pinsky, L; Piyarathna, D B; Płoskoń, M; Planinic, M; Pluta, J; Pochybova, S; Podesta-Lerma, P L M; Poghosyan, M G; Polichtchouk, B; Poljak, N; Poonsawat, W; Pop, A; Poppenborg, H; Porteboeuf-Houssais, S; Porter, J; Pospisil, J; Pozdniakov, V; Prasad, S K; Preghenella, R; Prino, F; Pruneau, C A; Pshenichnov, I; Puccio, M; Puddu, G; Pujahari, P; Punin, V; Putschke, J; Qvigstad, H; Rachevski, A; Raha, S; Rajput, S; Rak, J; Rakotozafindrabe, A; Ramello, L; Rami, F; Rana, D B; Raniwala, R; Raniwala, S; Räsänen, S S; Rascanu, B T; Rathee, D; Ratza, V; Ravasenga, I; Read, K F; Redlich, K; Rehman, A; Reichelt, P; Reidt, F; Ren, X; Renfordt, R; Reolon, A R; Reshetin, A; Reygers, K; Riabov, V; Ricci, R A; Richert, T; Richter, M; Riedler, P; Riegler, W; Riggi, F; Ristea, C; Rodríguez Cahuantzi, M; Røed, K; Rogochaya, E; Rohr, D; Röhrich, D; Rokita, P S; Ronchetti, F; Ronflette, L; Rosnet, P; Rossi, A; Rotondi, A; Roukoutakis, F; Roy, A; Roy, C; Roy, P; Rubio Montero, A J; Rui, R; Russo, R; Rustamov, A; Ryabinkin, E; Ryabov, Y; Rybicki, A; Saarinen, S; Sadhu, S; Sadovsky, S; Šafařík, K; Saha, S K; Sahlmuller, B; Sahoo, B; Sahoo, P; Sahoo, R; Sahoo, S; Sahu, P K; Saini, J; Sakai, S; Saleh, M A; Salzwedel, J; 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2017-01-01

The transverse momentum distributions of the strange and double-strange hyperon resonances ([Formula: see text], [Formula: see text]) produced in p-Pb collisions at [Formula: see text] TeV were measured in the rapidity range [Formula: see text] for event classes corresponding to different charged-particle multiplicity densities, [Formula: see text]d[Formula: see text]/d[Formula: see text]. The mean transverse momentum values are presented as a function of [Formula: see text]d[Formula: see text]/d[Formula: see text], as well as a function of the particle masses and compared with previous results on hyperon production. The integrated yield ratios of excited to ground-state hyperons are constant as a function of [Formula: see text]d[Formula: see text]/d[Formula: see text]. The equivalent ratios to pions exhibit an increase with [Formula: see text]d[Formula: see text]/d[Formula: see text], depending on their strangeness content.

Ratio-based estimators for a change point in persistence.

PubMed

Halunga, Andreea G; Osborn, Denise R

2012-11-01

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

Highly excited bound-state resonances of short-range inverse power-law potentials

NASA Astrophysics Data System (ADS)

Hod, Shahar

2017-11-01

We study analytically the radial Schrödinger equation with long-range attractive potentials whose asymptotic behaviors are dominated by inverse power-law tails of the form V(r)=-β _n r^{-n} with n>2. In particular, assuming that the effective radial potential is characterized by a short-range infinitely repulsive core of radius R, we derive a compact analytical formula for the threshold energy E^{ {max}}_l=E^{ {max}}_l(n,β _n,R), which characterizes the most weakly bound-state resonance (the most excited energy level) of the quantum system.

Explicit analytical expression for the condition number of polynomials in power form

NASA Astrophysics Data System (ADS)

Rack, Heinz-Joachim

2017-07-01

In his influential papers [1-3] W. Gautschi has defined and reshaped the condition number κ∞ of polynomials Pn of degree ≤ n which are represented in power form on a zero-symmetric interval [-ω, ω]. Basically, κ∞ is expressed as the product of two operator norms: an explicit factor times an implicit one (the l∞-norm of the coefficient vector of the n-th Chebyshev polynomial of the first kind relative to [-ω, ω]). We provide a new proof, economize the second factor and express it by an explicit analytical formula.

KAM Tori for 1D Nonlinear Wave Equationswith Periodic Boundary Conditions

NASA Astrophysics Data System (ADS)

Chierchia, Luigi; You, Jiangong

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

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.

Chemseal 3808-A2 penetration into small leak path

NASA Technical Reports Server (NTRS)

Carruth, M. R., Jr.; Dehaye, R. F.

1988-01-01

A possible fix to a leak in the oxidizer system of the Space Shuttle Discovery's attitude control system was proposed by MSFC. This fix involved the passing of a shuttlecock past the leaking Dynaflow fitting and sealing the vent tube containing the fitting with Chemseal 3808-A2. The question of whether the Chemseal 3808-A2 can flow into the leak path and provide a better seal was addressed analytically and by experiment to verify the analytical formula used. The results show that the equations are applicable and that the Chemseal will flow into the expected leak path and seal.

Calculation of phonon dispersion relation using new correlation functional

NASA Astrophysics Data System (ADS)

Jitropas, Ukrit; Hsu, Chung-Hao

2017-06-01

To extend the use of Local Density Approximation (LDA), a new analytical correlation functional is introduced. Correlation energy is an essential ingredient within density functional theory and used to determine ground state energy and other properties including phonon dispersion relation. Except for high and low density limit, the general expression of correlation energy is unknown. The approximation approach is therefore required. The accuracy of the modelling system depends on the quality of correlation energy approximation. Typical correlation functionals used in LDA such as Vosko-Wilk-Nusair (VWN) and Perdew-Wang (PW) were obtained from parameterizing the near-exact quantum Monte Carlo data of Ceperley and Alder. These functionals are presented in complex form and inconvenient to implement. Alternatively, the latest published formula of Chachiyo correlation functional provides a comparable result for those much more complicated functionals. In addition, it provides more predictive power based on the first principle approach, not fitting functionals. Nevertheless, the performance of Chachiyo formula for calculating phonon dispersion relation (a key to the thermal properties of materials) has not been tested yet. Here, the implementation of new correlation functional to calculate phonon dispersion relation is initiated. The accuracy and its validity will be explored.

Asymptotic solutions for flow in microchannels with ridged walls and arbitrary meniscus protrusion

NASA Astrophysics Data System (ADS)

Kirk, Toby

2017-11-01

Flow over structured surfaces exhibiting apparent slip, such as parallel ridges, have received much attention experimentally and numerically, but analytical and asymptotic solutions that account for the microstructure have so far been limited to unbounded geometries such as shear-driven flows. Analysis for channel flows has been limited to (close to) flat interfaces spanning the grooves between ridges, but in applications the interfaces (menisci) can highly protrude and have a significant impact on the apparent slip. In this presentation, we consider pressure-driven flow through a microchannel with longitudinal ridges patterning one or both walls. With no restriction on the meniscus protrusion, we develop explicit formulae for the slip length using a formal matched asymptotic expansion. Assuming the ratio of channel height to ridge period is large, the periodicity is confined to an inner layer close to the ridges, and the expansion is found to all algebraic orders. As a result, the error is exponentially small and, under a further ``diluteness'' assumption, the explicit formulae are compared to finite element solutions. They are found to have a very wide range of validity in channel height (even when the menisci can touch the opposing wall) and so are useful for practitioners.

First-principles study of the binding energy between nanostructures and its scaling with system size

NASA Astrophysics Data System (ADS)

Tao, Jianmin; Jiao, Yang; Mo, Yuxiang; Yang, Zeng-Hui; Zhu, Jian-Xin; Hyldgaard, Per; Perdew, John P.

2018-04-01

The equilibrium van der Waals binding energy is an important factor in the design of materials and devices. However, it presents great computational challenges for materials built up from nanostructures. Here we investigate the binding-energy scaling behavior from first-principles calculations. We show that the equilibrium binding energy per atom between identical nanostructures can scale up or down with nanostructure size, but can be parametrized for large N with an analytical formula (in meV/atom), Eb/N =a +b /N +c /N2+d /N3 , where N is the number of atoms in a nanostructure and a , b , c , and d are fitting parameters, depending on the properties of a nanostructure. The formula is consistent with a finite large-size limit of binding energy per atom. We find that there are two competing factors in the determination of the binding energy: Nonadditivities of van der Waals coefficients and center-to-center distance between nanostructures. To decode the detail, the nonadditivity of the static multipole polarizability is investigated from an accurate spherical-shell model. We find that the higher-order multipole polarizability displays ultrastrong intrinsic nonadditivity, no matter if the dipole polarizability is additive or not.

A Sommerfeld toolbox for colored dark sectors

NASA Astrophysics Data System (ADS)

El Hedri, Sonia; Kaminska, Anna; de Vries, Maikel

2017-09-01

We present analytical formulas for the Sommerfeld corrections to the annihilation of massive colored particles into quarks and gluons through the strong interaction. These corrections are essential to accurately compute the dark matter relic density for coannihilation with colored partners. Our formulas allow us to compute the Sommerfeld effect, not only for the lowest term in the angular momentum expansion of the amplitude, but for all orders in the partial wave expansion. In particular, we carefully account for the effects of the spin of the annihilating particle on the symmetry of the two-particle wave function. This work focuses on strongly interacting particles of arbitrary spin in the triplet, sextet and octet color representations. For typical velocities during freeze-out, we find that including Sommerfeld corrections on the next-to-leading order partial wave leads to modifications of up to 10 to 20 percent on the total annihilation cross section. Complementary to QCD, we generalize our results to particles charged under an arbitrary unbroken SU( N) gauge group, as encountered in dark glueball models. In connection with this paper a Mathematica notebook is provided to compute the Sommerfeld corrections for colored particles up to arbitrary order in the angular momentum expansion.

Computing Programs for Determining Traffic Flows from Roundabouts

NASA Astrophysics Data System (ADS)

Boroiu, A. A.; Tabacu, I.; Ene, A.; Neagu, E.; Boroiu, A.

2017-10-01

For modelling road traffic at the level of a road network it is necessary to specify the flows of all traffic currents at each intersection. These data can be obtained by direct measurements at the traffic light intersections, but in the case of a roundabout this is not possible directly and the literature as well as the traffic modelling software doesn’t offer ways to solve this issue. Two sets of formulas are proposed by which all traffic flows from the roundabouts with 3 or 4 arms are calculated based on the streams that can be measured. The objective of this paper is to develop computational programs to operate with these formulas. For each of the two sets of analytical relations, a computational program was developed in the Java operating language. The obtained results fully confirm the applicability of the calculation programs. The final stage for capitalizing these programs will be to make them web pages in HTML format, so that they can be accessed and used on the Internet. The achievements presented in this paper are an important step to provide a necessary tool for traffic modelling because these computational programs can be easily integrated into specialized software.

Experimental investigation of graphite/polyimide sandwich panels in edgewise compression

NASA Technical Reports Server (NTRS)

Camarda, C. J.

1980-01-01

The local and general buckling behavior of graphite/polyimide sandwich panels simply supported along all four edges and loaded in uniaxial edgewise compression was investigated. Material properties of adhesive and facings were determined from flatwise tension and sandwich beam flexure tests. Tensile and compressive material properties of the facings were determined at 116, R.T., and 589 K (-250, R.T., and 600 F) using the sandwich beam flexure test method. Results indicate that Gr/PI is a usable structural material for short term use at temperatures as high as 589 K (600 F). Buckling specimens were 30.5 X 33.0 cm (12 x 13 in.), had quasi-isotropic symmetric facings and a glass/polyimide honeycomb core. Core thicknesses varied and three panels of each thickness were tested in edgewise compression at room temperature to investigate failure modes and corresponding buckling formulas. Specimens 0.635 cm (0.25 in.) thick failed by overall buckling at loads close to the analytically predicted buckling load; all other panels failed by face wrinkling. Results of the winkling tests indicate that several buckling formulas were unconservative and therefore not suitable for design purposes; recommended wrinkling equations are presented.

Plasma Physics Approximations in Ares

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

Managan, R. A.

Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, F n( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A α (ζmore » ),A β (ζ ), ζ, f(ζ ) = (1 + e -μ/θ)F 1/2(μ/θ), F 1/2'/F 1/2, F c α, and F c β. In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.« less

Global parameter optimization of a Mather-type plasma focus in the framework of the Gratton-Vargas two-dimensional snowplow model

NASA Astrophysics Data System (ADS)

Auluck, S. K. H.

2014-12-01

Dense plasma focus (DPF) is known to produce highly energetic ions, electrons and plasma environment which can be used for breeding short-lived isotopes, plasma nanotechnology and other material processing applications. Commercial utilization of DPF in such areas would need a design tool that can be deployed in an automatic search for the best possible device configuration for a given application. The recently revisited (Auluck 2013 Phys. Plasmas 20 112501) Gratton-Vargas (GV) two-dimensional analytical snowplow model of plasma focus provides a numerical formula for dynamic inductance of a Mather-type plasma focus fitted to thousands of automated computations, which enables the construction of such a design tool. This inductance formula is utilized in the present work to explore global optimization, based on first-principles optimality criteria, in a four-dimensional parameter-subspace of the zero-resistance GV model. The optimization process is shown to reproduce the empirically observed constancy of the drive parameter over eight decades in capacitor bank energy. The optimized geometry of plasma focus normalized to the anode radius is shown to be independent of voltage, while the optimized anode radius is shown to be related to capacitor bank inductance.

The differential production cross section of the [Formula: see text](1020) meson in [Formula: see text] = 7 TeV [Formula: see text] collisions measured with the ATLAS detector.

PubMed

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Roe, A; Roe, S; Røhne, O; Rolli, S; Romaniouk, A; Romano, M; Romeo, G; Romero Adam, E; Rompotis, N; Roos, L; Ros, E; Rosati, S; Rosbach, K; Rose, A; Rose, M; Rosenbaum, G A; Rosenberg, E I; Rosendahl, P L; Rosenthal, O; Rosselet, L; Rossetti, V; Rossi, E; Rossi, L P; Rotaru, M; Roth, I; Rothberg, J; Rousseau, D; Royon, C R; Rozanov, A; Rozen, Y; Ruan, X; Rubbo, F; Rubinskiy, I; Ruckstuhl, N; Rud, V I; Rudolph, C; Rudolph, G; Rühr, F; Ruiz-Martinez, A; Rumyantsev, L; Rurikova, Z; Rusakovich, N A; Ruschke, A; Rutherfoord, J P; Ruzicka, P; Ryabov, Y F; Rybar, M; Rybkin, G; Ryder, N C; Saavedra, A F; Sadeh, I; Sadrozinski, H F-W; Sadykov, R; Safai Tehrani, F; Sakamoto, H; Salamanna, G; Salamon, A; Saleem, M; Salek, D; Salihagic, D; Salnikov, A; Salt, J; Salvachua Ferrando, B M; Salvatore, D; Salvatore, F; Salvucci, A; Salzburger, A; Sampsonidis, D; Samset, B H; Sanchez, A; Sanchez Martinez, V; Sandaker, H; Sander, H G; Sanders, M P; Sandhoff, M; Sandoval, T; Sandoval, C; Sandstroem, R; Sankey, D P C; Sansoni, A; Santamarina Rios, C; Santoni, C; Santonico, R; Santos, H; Santoyo Castillo, I; Saraiva, J G; Sarangi, T; Sarkisyan-Grinbaum, E; Sarri, F; Sartisohn, G; Sasaki, O; Sasaki, Y; Sasao, N; Satsounkevitch, I; Sauvage, G; Sauvan, E; Sauvan, J B; Savard, P; Savinov, V; Savu, D O; Sawyer, L; Saxon, D H; Saxon, J; Sbarra, C; Sbrizzi, A; Scannicchio, D A; Scarcella, M; Schaarschmidt, J; Schacht, P; Schaefer, D; Schäfer, U; Schaelicke, A; Schaepe, S; Schaetzel, S; Schaffer, A C; Schaile, D; Schamberger, R D; Schamov, A G; Scharf, V; Schegelsky, V A; Scheirich, D; Schernau, M; Scherzer, M I; Schiavi, C; Schieck, J; Schioppa, M; Schlenker, S; Schmidt, E; Schmieden, K; Schmitt, C; Schmitt, S; Schneider, B; Schnoor, U; Schoeffel, L; Schoening, A; Schorlemmer, A L S; Schott, M; Schouten, D; Schovancova, J; Schram, M; Schroeder, C; Schroer, N; Schultens, M J; Schultes, J; Schultz-Coulon, H-C; Schulz, H; Schumacher, M; Schumm, B A; Schune, Ph; Schwanenberger, C; Schwartzman, A; Schwegler, Ph; Schwemling, Ph; Schwienhorst, R; Schwierz, R; Schwindling, J; Schwindt, T; Schwoerer, M; Sciacca, F G; Sciolla, G; Scott, W G; Searcy, J; Sedov, G; Sedykh, E; Seidel, S C; Seiden, A; Seifert, F; Seixas, J M; Sekhniaidze, G; Sekula, S J; Selbach, K E; Seliverstov, D M; Sellden, B; Sellers, G; Seman, M; Semprini-Cesari, N; Serfon, C; Serin, L; Serkin, L; Seuster, R; Severini, H; Sfyrla, A; Shabalina, E; Shamim, M; Shan, L Y; Shank, J T; Shao, Q T; Shapiro, M; Shatalov, P B; Shaw, K; Sherman, D; Sherwood, P; Shimizu, S; Shimojima, M; Shin, T; Shiyakova, M; Shmeleva, A; Shochet, M J; Short, D; Shrestha, S; Shulga, E; Shupe, M A; Sicho, P; Sidoti, A; Siegert, F; Sijacki, Dj; Silbert, O; Silva, J; Silver, Y; Silverstein, D; Silverstein, S B; Simak, V; Simard, O; Simic, Lj; Simion, S; Simioni, E; Simmons, B; Simoniello, R; Simonyan, M; Sinervo, P; Sinev, N B; Sipica, V; Siragusa, G; Sircar, A; Sisakyan, A N; Sivoklokov, S Yu; Sjölin, J; Sjursen, T B; Skinnari, L A; Skottowe, H P; Skovpen, K; Skubic, P; Slater, M; Slavicek, T; Sliwa, K; Smakhtin, V; Smart, B H; Smestad, L; Smirnov, S Yu; Smirnov, Y; Smirnova, L N; Smirnova, O; Smith, B C; Smith, D; Smith, K M; Smizanska, M; Smolek, K; Snesarev, A A; Snow, S W; Snow, J; Snyder, S; Sobie, R; Sodomka, J; Soffer, A; Solans, C A; Solar, M; Solc, J; Soldatov, E Yu; Soldevila, U; Solfaroli Camillocci, E; Solodkov, A A; Solovyanov, O V; Solovyev, V; Soni, N; Sopko, V; Sopko, B; Sosebee, M; Soualah, R; Soukharev, A; Spagnolo, S; Spanò, F; Spighi, R; Spigo, G; Spiwoks, R; Spousta, M; Spreitzer, T; Spurlock, B; St Denis, R D; Stahlman, J; Stamen, R; Stanecka, E; Stanek, R W; Stanescu, C; Stanescu-Bellu, M; Stanitzki, M M; Stapnes, S; Starchenko, E A; Stark, J; Staroba, P; Starovoitov, P; Staszewski, R; Staude, A; Stavina, P; Steele, G; Steinbach, P; Steinberg, P; Stekl, I; Stelzer, B; Stelzer, H J; Stelzer-Chilton, O; Stenzel, H; Stern, S; Stewart, G A; Stillings, J A; Stockton, M C; Stoerig, K; Stoicea, G; Stonjek, S; Strachota, P; Stradling, A R; Straessner, A; Strandberg, J; Strandberg, S; Strandlie, A; Strang, M; Strauss, E; Strauss, M; Strizenec, P; Ströhmer, R; Strom, D M; Strong, J A; Stroynowski, R; Stugu, B; Stumer, I; Stupak, J; Sturm, P; Styles, N A; Soh, D A; Su, D; Subramania, H S; Subramaniam, R; Succurro, A; Sugaya, Y; Suhr, C; Suk, M; Sulin, V V; Sultansoy, S; Sumida, T; Sun, X; Sundermann, J E; Suruliz, K; Susinno, G; Sutton, M R; Suzuki, Y; Suzuki, Y; Svatos, M; Swedish, S; Sykora, I; Sykora, T; Sánchez, J; Ta, D; Tackmann, K; Taffard, A; Tafirout, R; Taiblum, N; Takahashi, Y; Takai, H; Takashima, R; Takeda, H; Takeshita, T; Takubo, Y; Talby, M; Talyshev, A; Tamsett, M C; Tan, K G; Tanaka, J; Tanaka, R; Tanaka, S; Tanaka, S; Tanasijczuk, A J; Tani, K; Tannoury, N; Tapprogge, S; Tardif, D; Tarem, S; Tarrade, F; Tartarelli, G F; Tas, P; Tasevsky, M; Tassi, E; Tayalati, Y; Taylor, C; Taylor, F E; Taylor, G N; Taylor, W; Teinturier, M; Teischinger, F A; Teixeira Dias Castanheira, M; Teixeira-Dias, P; Temming, K K; Ten Kate, H; Teng, P K; Terada, S; Terashi, K; Terron, J; Testa, M; Teuscher, R J; Therhaag, J; Theveneaux-Pelzer, T; Thoma, S; Thomas, J P; Thompson, E N; Thompson, P D; Thompson, P D; Thompson, A S; Thomsen, L A; Thomson, E; Thomson, M; Thong, W M; Thun, R P; Tian, F; Tibbetts, M J; Tic, T; Tikhomirov, V O; Tikhonov, Y A; Timoshenko, S; Tiouchichine, E; Tipton, P; Tisserant, S; Todorov, T; Todorova-Nova, S; Toggerson, B; Tojo, J; Tokár, S; Tokushuku, K; Tollefson, K; Tomoto, M; Tompkins, L; Toms, K; Tonoyan, A; Topfel, C; Topilin, N D; Torrence, E; Torres, H; Torró Pastor, E; Toth, J; Touchard, F; Tovey, D R; Trefzger, T; Tremblet, L; Tricoli, A; Trigger, I M; Trincaz-Duvoid, S; Tripiana, M F; Triplett, N; Trischuk, W; Trocmé, B; Troncon, C; Trottier-McDonald, M; True, P; Trzebinski, M; Trzupek, A; Tsarouchas, C; Tseng, J C-L; Tsiakiris, M; Tsiareshka, P V; Tsionou, D; Tsipolitis, G; Tsiskaridze, S; Tsiskaridze, V; Tskhadadze, E G; Tsukerman, I I; Tsulaia, V; Tsung, J-W; Tsuno, S; Tsybychev, D; Tua, A; Tudorache, A; Tudorache, V; Tuggle, J M; Turala, M; Turecek, D; Turk Cakir, I; Turlay, E; Turra, R; Tuts, P M; Tykhonov, A; Tylmad, M; Tyndel, M; Tzanakos, G; Uchida, K; Ueda, I; Ueno, R; Ugland, M; Uhlenbrock, M; Uhrmacher, M; Ukegawa, F; Unal, G; Undrus, A; Unel, G; Unno, Y; Urbaniec, D; Urquijo, P; Usai, G; Uslenghi, M; Vacavant, L; Vacek, V; Vachon, B; Vahsen, S; Valenta, J; Valentinetti, S; Valero, A; Valkar, S; Valladolid Gallego, E; Vallecorsa, S; Valls Ferrer, J A; Van Berg, R; Van Der Deijl, P C; van der Geer, R; van der Graaf, H; Van Der Leeuw, R; van der Poel, E; van der Ster, D; van Eldik, N; van Gemmeren, P; van Vulpen, I; Vanadia, M; Vandelli, W; Vaniachine, A; Vankov, P; Vannucci, F; Vari, R; Varnes, E W; Varol, T; Varouchas, D; Vartapetian, A; Varvell, K E; Vassilakopoulos, V I; Vazeille, F; Vazquez Schroeder, T; Vegni, G; Veillet, J J; Veloso, F; Veness, R; Veneziano, S; Ventura, A; Ventura, D; Venturi, M; Venturi, N; Vercesi, V; Verducci, M; Verkerke, W; Vermeulen, J C; Vest, A; Vetterli, M C; Vichou, I; Vickey, T; Vickey Boeriu, O E; Viehhauser, G H A; Viel, S; Villa, M; Villaplana Perez, M; Vilucchi, E; Vincter, M G; Vinek, E; Vinogradov, V B; Virchaux, M; Virzi, J; Vitells, O; Viti, M; Vivarelli, I; Vives Vaque, F; Vlachos, S; Vladoiu, D; Vlasak, M; Vogel, A; Vokac, P; Volpi, G; Volpi, M; Volpini, G; von der Schmitt, H; von Radziewski, H; von Toerne, E; Vorobel, V; Vorwerk, V; Vos, M; Voss, R; Voss, T T; Vossebeld, J H; Vranjes, N; Vranjes Milosavljevic, M; Vrba, V; Vreeswijk, M; Vu Anh, T; Vuillermet, R; Vukotic, I; Wagner, W; Wagner, P; Wahlen, H; Wahrmund, S; Wakabayashi, J; Walch, S; Walder, J; Walker, R; Walkowiak, W; Wall, R; Waller, P; Walsh, B; Wang, C; Wang, H; Wang, H; Wang, J; Wang, J; Wang, R; Wang, S M; Wang, T; Warburton, A; Ward, C P; Wardrope, D R; Warsinsky, M; Washbrook, A; Wasicki, C; Watanabe, I; Watkins, P M; Watson, A T; Watson, I J; Watson, M F; Watts, G; Watts, S; Waugh, A T; Waugh, B M; Weber, M S; Webster, J S; Weidberg, A R; Weigell, P; Weingarten, J; Weiser, C; Wells, P S; Wenaus, T; Wendland, D; Weng, Z; Wengler, T; Wenig, S; Wermes, N; Werner, M; Werner, P; Werth, M; Wessels, M; Wetter, J; Weydert, C; Whalen, K; White, A; White, M J; White, S; Whitehead, S R; Whiteson, D; Whittington, D; Wicek, F; Wicke, D; Wickens, F J; Wiedenmann, W; Wielers, M; Wienemann, P; Wiglesworth, C; Wiik-Fuchs, L A M; Wijeratne, P A; Wildauer, A; Wildt, M A; Wilhelm, I; Wilkens, H G; Will, J Z; Williams, E; Williams, H H; Willis, W; Willocq, S; Wilson, J A; Wilson, M G; Wilson, A; Wingerter-Seez, I; Winkelmann, S; Winklmeier, F; Wittgen, M; Wollstadt, S J; Wolter, M W; Wolters, H; Wong, W C; Wooden, G; Wosiek, B K; Wotschack, J; Woudstra, M J; Wozniak, K W; Wraight, K; Wright, M; Wrona, B; Wu, S L; Wu, X; Wu, Y; Wulf, E; Wynne, B M; Xella, S; Xiao, M; Xie, S; Xu, C; Xu, D; Xu, L; Yabsley, B; Yacoob, S; Yamada, M; Yamaguchi, H; Yamamoto, A; Yamamoto, K; Yamamoto, S; Yamamura, T; Yamanaka, T; Yamazaki, T; Yamazaki, Y; Yan, Z; Yang, H; Yang, U K; Yang, Y; Yang, Z; Yanush, S; Yao, L; Yao, Y; Yasu, Y; Ybeles Smit, G V; Ye, J; Ye, S; Yilmaz, M; Yoosoofmiya, R; Yorita, K; Yoshida, R; Yoshihara, K; Young, C; Young, C J; Youssef, S; Yu, D; Yu, J; Yu, J; Yuan, L; Yurkewicz, A; Zabinski, B; Zaidan, R; Zaitsev, A M; Zajacova, Z; Zanello, L; Zanzi, D; Zaytsev, A; Zeitnitz, C; Zeman, M; Zemla, A; Zendler, C; Zenin, O; Ženiš, T; Zinonos, Z; Zerwas, D; Zevi Della Porta, G; Zhang, D; Zhang, H; Zhang, J; Zhang, X; Zhang, Z; Zhao, L; Zhao, Z; Zhemchugov, A; Zhong, J; Zhou, B; Zhou, N; Zhou, Y; Zhu, C G; Zhu, H; Zhu, J; Zhu, Y; Zhuang, X; Zhuravlov, V; Zibell, A; Zieminska, D; Zimin, N I; Zimmermann, R; Zimmermann, S; Zimmermann, S; Ziolkowski, M; Zitoun, R; Živković, L; Zmouchko, V V; Zobernig, G; Zoccoli, A; Zur Nedden, M; Zutshi, V; Zwalinski, L

A measurement is presented of the [Formula: see text] production cross section at [Formula: see text] = 7 TeV using [Formula: see text] collision data corresponding to an integrated luminosity of 383 [Formula: see text], collected with the ATLAS experiment at the LHC. Selection of [Formula: see text](1020) mesons is based on the identification of charged kaons by their energy loss in the pixel detector. The differential cross section is measured as a function of the transverse momentum, [Formula: see text], and rapidity, [Formula: see text], of the [Formula: see text](1020) meson in the fiducial region 500 [Formula: see text] 1200 MeV, [Formula: see text] 0.8, kaon [Formula: see text] 230 MeV and kaon momentum [Formula: see text] 800 MeV. The integrated [Formula: see text]-meson production cross section in this fiducial range is measured to be [Formula: see text] = 570 [Formula: see text] 8 (stat) [Formula: see text] 66 (syst) [Formula: see text] 20 (lumi) [Formula: see text].

Analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric

NASA Astrophysics Data System (ADS)

Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

2017-09-01

We construct an analytical approximation for the numerical black hole metric of P. Kanti et al. [Phys. Rev. D 54, 5049 (1996), 10.1103/PhysRevD.54.5049] in the four-dimensional Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansion in terms of a compactified radial coordinate, used here, converges slowly when the dilaton coupling approaches its extremal values, but for a black hole far from the extremal state, the analytical formula has a maximal relative error of a fraction of one percent already within the third order of the continued fraction expansion. The suggested analytical representation of the numerical black hole metric is relatively compact and a good approximation in the whole space outside the black hole event horizon. Therefore, it can serve in the same way as an exact solution when analyzing particles' motion, perturbations, quasinormal modes, Hawking radiation, accreting disks, and many other problems in the vicinity of a black hole. In addition, we construct the approximate analytical expression for the dilaton field.

Improved formula for continuous-wave measurements of ultrasonic phase velocity

NASA Technical Reports Server (NTRS)

Chern, E. J.; Cantrell, J. H., Jr.; Heyman, J. S.

1981-01-01

An improved formula for continuous-wave ultrasonic phase velocity measurements using contact transducers is derived from the transmission line theory. The effect of transducer-sample coupling bonds is considered for measurements of solid samples even though it is often neglected because of the difficulty of accurately determining the bond thickness. Computer models show that the present formula is more accurate than previous expressions. Laboratory measurements using contacting transducers with the present formula are compared to measurements using noncontacting (hence effectively correction-free) capacitive transducers. The results of the experiments verify the validity and accuracy of the new formula.

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.

Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points

NASA Astrophysics Data System (ADS)

Shevchenko, I. I.

2008-05-01

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is designed so that normalization problems of high analytical complexity could be solved. It is used to obtain the Birkhoff normal form of the Hamiltonian in the given problem. The normalization is carried out up to the 6th order of expansion of the Hamiltonian in the coordinates and momenta. Analytical expressions for the coefficients of the normal form of the 6th order are derived. Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format. The analogue of the Deprit formula for the stability criterion is derived in the 6th order of normalization. The obtained floating-point numerical values for the normal form coefficients and the stability criterion confirm the results by Markeev (1969) and Coppola and Rand (1989), while the obtained analytical and exact numeric expressions confirm the results by Meyer and Schmidt (1986) and Schmidt (1989). The given computational problem is solved without constructing a specialized algebraic processor, i.e., the designed computer algebra package has a broad field of applicability.

The Adams formulas for numerical integration of differential equations from 1st to 20th order

NASA Technical Reports Server (NTRS)

Kirkpatrick, J. C.

1976-01-01

The Adams Bashforth predictor coefficients and the Adams Moulton corrector coefficients for the integration of differential equations are presented for methods of 1st to 20th order. The order of the method as presented refers to the highest order difference formula used in Newton's backward difference interpolation formula, on which the Adams method is based. The Adams method is a polynomial approximation method derived from Newton's backward difference interpolation formula. The Newton formula is derived and expanded to 20th order. The Adams predictor and corrector formulas are derived and expressed in terms of differences of the derivatives, as well as in terms of the derivatives themselves. All coefficients are given to 18 significant digits. For the difference formula only, the ratio coefficients are given to 10th order.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Firing rate of noisy integrate-and-fire neurons with synaptic current dynamics

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

Andrieux, David; Monnai, Takaaki; Department of Applied Physics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555

2009-08-15

We derive analytical formulas for the firing rate of integrate-and-fire neurons endowed with realistic synaptic dynamics. In particular, we include the possibility of multiple synaptic inputs as well as the effect of an absolute refractory period into the description. The latter affects the firing rate through its interaction with the synaptic dynamics.

Quantifying dispersal of southern pine beetles with mark-recapture experiments and a diffusion model

Treesearch

P. Turchin; W.T. Thoeny

1993-01-01

Pest management decisions should take into consideration quantitative information on dispersal of insect pests, but such information is often lacking.The goal of this study was to measure intraforest dispersal in the southern pine beetle (SPB).We developed an analytical formula for interpreting data from mark-recapture studies of insect dispersal.The proposed...

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

NASA Astrophysics Data System (ADS)

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

1999-11-01

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

Unsteady translational motion of a slip sphere in a viscous fluid using the fractional Navier-Stokes equation

NASA Astrophysics Data System (ADS)

Ashmawy, E. A.

2017-03-01

In this paper, we investigate the translational motion of a slip sphere with time-dependent velocity in an incompressible viscous fluid. The modified Navier-Stokes equation with fractional order time derivative is used. The linear slip boundary condition is applied on the spherical boundary. The integral Laplace transform technique is employed to solve the problem. The solution in the physical domain is obtained analytically by inverting the Laplace transform using the complex inversion formula together with contour integration. An exact formula for the drag force exerted by the fluid on the spherical object is deduced. This formula is applied to some flows, namely damping oscillation, sine oscillation and sudden motion. The numerical results showed that the order of the fractional derivative contributes considerably to the drag force. The increase in this parameter resulted in an increase in the drag force. In addition, the values of the drag force increased with the increase in the slip parameter.

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.