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.

Phonon scattering in nanoscale systems: lowest order expansion of the current and power expressions

NASA Astrophysics Data System (ADS)

Paulsson, Magnus; Frederiksen, Thomas; Brandbyge, Mads

2006-04-01

We use the non-equilibrium Green's function method to describe the effects of phonon scattering on the conductance of nano-scale devices. Useful and accurate approximations are developed that both provide (i) computationally simple formulas for large systems and (ii) simple analytical models. In addition, the simple models can be used to fit experimental data and provide physical parameters.

SU-E-T-439: An Improved Formula of Scatter-To-Primary Ratio for Photon Dose Calculation

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

Zhu, T

2014-06-01

Purpose: Scatter-to-primary ratio (SPR) is an important dosimetric quantity that describes the contribution from the scatter photons in an external photon beam. The purpose of this study is to develop an improved analytical formula to describe SPR as a function of circular field size (r) and depth (d) using Monte Carlo (MC) simulation. Methods: MC simulation was performed for Mohan photon spectra (Co-60, 4, 6, 10, 15, 23 MV) using EGSNRC code. Point-spread scatter dose kernels in water are generated. The scatter-to-primary ratio (SPR) is also calculated using MC simulation as a function of field size for circular field sizemore » with radius r and depth d. The doses from forward scatter and backscatter photons are calculated using a convolution of the point-spread scatter dose kernel and by accounting for scatter photons contributing to dose before (z'd) reaching the depth of interest, d, where z' is the location of scatter photons, respectively. The depth dependence of the ratio of the forward scatter and backscatter doses is determined as a function of depth and field size. Results: We are able to improve the existing 3-parameter (a, w, d0) empirical formula for SPR by introducing depth dependence for one of the parameter d0, which becomes 0 for deeper depths. The depth dependence of d0 can be directly calculated as a ratio of backscatter-to-forward scatter doses for otherwise the same field and depth. With the improved empirical formula, we can fit SPR for all megavoltage photon beams to within 2%. Existing 3-parameter formula cannot fit SPR data for Co-60 to better than 3.1%. Conclusion: An improved empirical formula is developed to fit SPR for all megavoltage photon energies to within 2%.« less

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

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

Kawaguchi, Kyohei; Shibata, Masaru; Kyutoku, Koutarou

2016-07-01

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

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

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.

Fitting Higgs data with nonlinear effective theory.

PubMed

Buchalla, G; Catà, O; Celis, A; Krause, C

2016-01-01

In a recent paper we showed that the electroweak chiral Lagrangian at leading order is equivalent to the conventional [Formula: see text] formalism used by ATLAS and CMS to test Higgs anomalous couplings. Here we apply this fact to fit the latest Higgs data. The new aspect of our analysis is a systematic interpretation of the fit parameters within an EFT. Concentrating on the processes of Higgs production and decay that have been measured so far, six parameters turn out to be relevant: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. A global Bayesian fit is then performed with the result [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. Additionally, we show how this leading-order parametrization can be generalized to next-to-leading order, thus improving the [Formula: see text] formalism systematically. The differences with a linear EFT analysis including operators of dimension six are also discussed. One of the main conclusions of our analysis is that since the conventional [Formula: see text] formalism can be properly justified within a QFT framework, it should continue to play a central role in analyzing and interpreting Higgs data.

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

PubMed

Minin, Serge; Kamalabadi, Farzad

2009-12-20

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

A new world survey expression for cosmic ray vertical intensity vs. depth in standard rock

NASA Technical Reports Server (NTRS)

Crouch, M.

1985-01-01

The cosmic ray data on vertical intensity versus depth below 10 to the 5th power g sq cm is fitted to a 5 parameter empirical formula to give an analytical expression for interpretation of muon fluxes in underground measurements. This expression updates earlier published results and complements the more precise curves obtained by numerical integration or Monte Carlo techniques in which the fit is made to an energy spectrum at the top of the atmosphere. The expression is valid in the transitional region where neutrino induced muons begin to be important, as well as at great depths where this component becomes dominant.

Crossing fitness canyons by a finite population

NASA Astrophysics Data System (ADS)

Saakian, David B.; Bratus, Alexander S.; Hu, Chin-Kun

2017-06-01

We consider the Wright-Fisher model of the finite population evolution on a fitness landscape defined in the sequence space by a path of nearly neutral mutations. We study a specific structure of the fitness landscape: One of the intermediate mutations on the mutation path results in either a large fitness value (climbing up a fitness hill) or a low fitness value (crossing a fitness canyon), the rest of the mutations besides the last one are neutral, and the last sequence has much higher fitness than any intermediate sequence. We derive analytical formulas for the first arrival time of the mutant with two point mutations. For the first arrival problem for the further mutants in the case of canyon crossing, we analytically deduce how the mean first arrival time scales with the population size and fitness difference. The location of the canyon on the path of sequences has a crucial role. If the canyon is at the beginning of the path, then it significantly prolongs the first arrival time; otherwise it just slightly changes it. Furthermore, the fitness hill at the beginning of the path strongly prolongs the arrival time period; however, the hill located near the end of the path shortens it. We optimize the first arrival time by applying a nonzero selection to the intermediate sequences. We extend our results and provide a scaling for the valley crossing time via the depth of the canyon and population size in the case of a fitness canyon at the first position. Our approach is useful for understanding some complex evolution systems, e.g., the evolution of cancer.

Tensor hypercontraction. II. Least-squares renormalization

NASA Astrophysics Data System (ADS)

Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

2012-12-01

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

Tensor hypercontraction. II. Least-squares renormalization.

PubMed

Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David

2012-12-14

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)]. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1∕r(12) operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N(5)) effort if exact integrals are decomposed, or O(N(4)) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N(4)) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

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

NASA Astrophysics Data System (ADS)

Hayashi, Nakao; Kato, Keiichi

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

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

PubMed

Jiang, Zhi-Jie

2015-04-01

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

Partially ionized hydrogen plasma in strong magnetic fields.

PubMed

Potekhin, A Y; Chabrier, G; Shibanov, Y A

1999-08-01

We study the thermodynamic properties of a partially ionized hydrogen plasma in strong magnetic fields, B approximately 10(12)-10(13) G, typical of neutron stars. The properties of the plasma depend significantly on the quantum-mechanical sizes and binding energies of the atoms, which are strongly modified by thermal motion across the field. We use new fitting formulas for the atomic binding energies and sizes, based on accurate numerical calculations and valid for any state of motion of the atom. In particular, we take into account decentered atomic states, neglected in previous studies of thermodynamics of magnetized plasmas. We also employ analytic fits for the thermodynamic functions of nonideal fully ionized electron-ion Coulomb plasmas. This enables us to construct an analytic model of the free energy. An ionization equilibrium equation is derived, taking into account the strong magnetic field effects and the nonideality effects. This equation is solved by an iteration technique. Ionization degrees, occupancies, and the equation of state are calculated.

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

NASA Astrophysics Data System (ADS)

Mizusaki, Takahiro; Oi, Makito; Shimizu, Noritaka

2018-04-01

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

Extended analytical formulas for the perturbed Keplerian motion under a constant control acceleration

NASA Astrophysics Data System (ADS)

Zuiani, Federico; Vasile, Massimiliano

2015-03-01

This paper presents a set of analytical formulae for the perturbed Keplerian motion of a spacecraft under the effect of a constant control acceleration. The proposed set of formulae can treat control accelerations that are fixed in either a rotating or inertial reference frame. Moreover, the contribution of the zonal harmonic is included in the analytical formulae. It will be shown that the proposed analytical theory allows for the fast computation of long, multi-revolution spirals while maintaining good accuracy. The combined effect of different perturbations and of the shadow regions due to solar eclipse is also included. Furthermore, a simplified control parameterisation is introduced to optimise thrusting patterns with two thrust arcs and two cost arcs per revolution. This simple parameterisation is shown to ensure enough flexibility to describe complex low thrust spirals. The accuracy and speed of the proposed analytical formulae are compared against a full numerical integration with different integration schemes. An averaging technique is then proposed as an application of the analytical formulae. Finally, the paper presents an example of design of an optimal low-thrust spiral to transfer a spacecraft from an elliptical to a circular orbit around the Earth.

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

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.

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.

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

PubMed

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

2014-10-01

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

Event generator tunes obtained from underlying event and multiparton scattering measurements.

PubMed

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Renker, D; Rohe, T; Bachmair, F; Bäni, L; Bianchini, L; Casal, B; Dissertori, G; Dittmar, M; Donegà, M; Eller, P; Grab, C; Heidegger, C; Hits, D; Hoss, J; Kasieczka, G; Lustermann, W; Mangano, B; Marionneau, M; Martinez Ruiz Del Arbol, P; Masciovecchio, M; Meister, D; Micheli, F; Musella, P; Nessi-Tedaldi, F; Pandolfi, F; Pata, J; Pauss, F; Perrozzi, L; Quittnat, M; Rossini, M; Starodumov, A; Takahashi, M; Tavolaro, V R; Theofilatos, K; Wallny, R; Aarrestad, T K; Amsler, C; Caminada, L; Canelli, M F; Chiochia, V; De Cosa, A; Galloni, C; Hinzmann, A; Hreus, T; Kilminster, B; Lange, C; Ngadiuba, J; Pinna, D; Robmann, P; Ronga, F J; Salerno, D; Yang, Y; Cardaci, M; Chen, K H; Doan, T H; Jain, Sh; Khurana, R; Konyushikhin, M; Kuo, C M; Lin, W; Lu, Y J; Yu, S S; Kumar, Arun; Bartek, R; Chang, P; Chang, Y H; Chao, Y; Chen, K F; Chen, P H; Dietz, C; Fiori, F; Grundler, U; Hou, W-S; Hsiung, Y; Liu, Y F; Lu, R-S; Miñano Moya, M; Petrakou, E; Tsai, J F; Tzeng, Y M; Asavapibhop, B; Kovitanggoon, K; 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Campagnari, C; Dishaw, A; Dutta, V; Flowers, K; Franco Sevilla, M; Geffert, P; George, C; Golf, F; Gouskos, L; Gran, J; Incandela, J; Mccoll, N; Mullin, S D; Mullin, S D; Richman, J; Stuart, D; Suarez, I; West, C; Yoo, J; Anderson, D; Apresyan, A; Bornheim, A; Bunn, J; Chen, Y; Duarte, J; Mott, A; Newman, H B; Pena, C; Pierini, M; Spiropulu, M; Vlimant, J R; Xie, S; Zhu, R Y; Andrews, M B; Azzolini, V; Calamba, A; Carlson, B; Ferguson, T; Paulini, M; Russ, J; Sun, M; Vogel, H; Vorobiev, I; Cumalat, J P; Ford, W T; Gaz, A; Jensen, F; Johnson, A; Krohn, M; Mulholland, T; Nauenberg, U; Stenson, K; Wagner, S R; Alexander, J; Chatterjee, A; Chaves, J; Chu, J; Dittmer, S; Eggert, N; Mirman, N; Nicolas Kaufman, G; Patterson, J R; Rinkevicius, A; Ryd, A; Skinnari, L; Soffi, L; Sun, W; Tan, S M; Teo, W D; Thom, J; Thompson, J; Tucker, J; Weng, Y; Wittich, P; Abdullin, S; Albrow, M; Apollinari, G; Banerjee, S; Bauerdick, L A T; Beretvas, A; Berryhill, J; Bhat, P C; Bolla, G; Burkett, K; Butler, J N; Cheung, H W K; Chlebana, F; Cihangir, S; Elvira, V D; Fisk, I; Freeman, J; Gottschalk, E; Gray, L; Green, D; Grünendahl, S; Gutsche, O; Hanlon, J; Hare, D; Harris, R M; Hasegawa, S; Hirschauer, J; Hu, Z; Jayatilaka, B; Jindariani, S; Johnson, M; Joshi, U; Jung, A W; Klima, B; Kreis, B; Lammel, S; Linacre, J; Lincoln, D; Lipton, R; Liu, T; Lopes De Sá, R; Lykken, J; Maeshima, K; Marraffino, J M; Martinez Outschoorn, V I; Maruyama, S; Mason, D; McBride, P; Merkel, P; Mishra, K; Mrenna, S; Nahn, S; Newman-Holmes, C; O'Dell, V; Pedro, K; Prokofyev, O; Rakness, G; Sexton-Kennedy, E; Soha, A; Spalding, W J; Spiegel, L; Strobbe, N; Taylor, L; Tkaczyk, S; Tran, N V; Uplegger, L; Vaandering, E W; Vernieri, C; Verzocchi, M; Vidal, R; Weber, H A; Whitbeck, A; Acosta, D; Avery, P; Bortignon, P; Bourilkov, D; Carnes, A; Carver, M; Curry, D; Das, S; Field, R D; Furic, I K; Gleyzer, S V; Hugon, J; Konigsberg, J; Korytov, A; Kotov, K; Low, J F; Ma, P; Matchev, K; Mei, H; Milenovic, P; Mitselmakher, G; Rank, D; Rossin, R; Shchutska, L; Snowball, M; Sperka, D; Terentyev, N; Thomas, L; Wang, J; Wang, S; Yelton, J; Hewamanage, S; Linn, S; Markowitz, P; Martinez, G; Rodriguez, J L; Adams, J R; Ackert, A; Adams, T; Askew, A; Bein, S; Bochenek, J; Diamond, B; Haas, J; Hagopian, S; Hagopian, V; Johnson, K F; Khatiwada, A; Prosper, H; Weinberg, M; Baarmand, M M; Bhopatkar, V; Colafranceschi, S; Hohlmann, M; Kalakhety, H; Noonan, D; Roy, T; Yumiceva, F; Adams, M R; Apanasevich, L; Berry, D; Betts, R R; Bucinskaite, I; Cavanaugh, R; Evdokimov, O; Gauthier, L; Gerber, C E; Hofman, D J; Kurt, P; O'Brien, C; Sandoval Gonzalez, L D; Silkworth, C; Turner, P; Varelas, N; Wu, Z; Zakaria, M; Bilki, B; Clarida, W; Dilsiz, K; Durgut, S; Gandrajula, R P; Haytmyradov, M; Khristenko, V; Merlo, J-P; Mermerkaya, H; Mestvirishvili, A; Moeller, A; Nachtman, J; Ogul, H; Onel, Y; Ozok, F; Penzo, A; Snyder, C; Tiras, E; Wetzel, J; Yi, K; Anderson, I; Anderson, I; Barnett, B A; Blumenfeld, B; Eminizer, N; Fehling, D; Feng, L; Gritsan, A V; Maksimovic, P; Martin, C; Osherson, M; Roskes, J; Sady, A; Sarica, U; Swartz, M; Xiao, M; Xin, Y; You, C; Xiao, M; Baringer, P; Bean, A; Benelli, G; Bruner, C; Kenny, R P; Majumder, D; Majumder, D; Malek, M; Murray, M; Sanders, S; Stringer, R; Wang, Q; Ivanov, A; Kaadze, K; Khalil, S; Makouski, M; Maravin, Y; Mohammadi, A; Saini, L K; Skhirtladze, N; Toda, S; Lange, D; Rebassoo, F; Wright, D; Anelli, C; Baden, A; Baron, O; Belloni, A; Calvert, B; Eno, S C; Ferraioli, C; Gomez, J A; Hadley, N J; Jabeen, S; Jabeen, S; Kellogg, R G; Kolberg, T; Kunkle, J; Lu, Y; Mignerey, A C; Shin, Y H; Skuja, A; Tonjes, M B; Tonwar, S C; Apyan, A; Barbieri, R; Baty, A; Bierwagen, K; Brandt, S; Bierwagen, K; Busza, W; Cali, I A; Demiragli, Z; Di Matteo, L; Gomez Ceballos, G; Goncharov, M; Gulhan, D; Iiyama, Y; Innocenti, G M; Klute, M; Kovalskyi, D; Lai, Y S; Lee, Y-J; Levin, A; Luckey, P D; Marini, A C; Mcginn, C; Mironov, C; Narayanan, S; Niu, X; Paus, C; Ralph, D; Roland, C; Roland, G; 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New sets of parameters ("tunes") for the underlying-event (UE) modelling of the pythia8, pythia6 and herwig++ Monte Carlo event generators are constructed using different parton distribution functions. Combined fits to CMS UE proton-proton ([Formula: see text]) data at [Formula: see text] and to UE proton-antiproton ([Formula: see text]) data from the CDF experiment at lower [Formula: see text], are used to study the UE models and constrain their parameters, providing thereby improved predictions for proton-proton collisions at 13[Formula: see text]. In addition, it is investigated whether the values of the parameters obtained from fits to UE observables are consistent with the values determined from fitting observables sensitive to double-parton scattering processes. Finally, comparisons are presented of the UE tunes to "minimum bias" (MB) events, multijet, and Drell-Yan ([Formula: see text] lepton-antilepton+jets) observables at 7 and 8[Formula: see text], as well as predictions for MB and UE observables at 13[Formula: see text].

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

PubMed

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

2014-03-10

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

A mathematical description of the inclusive fitness theory.

PubMed

Wakano, Joe Yuichiro; Ohtsuki, Hisashi; Kobayashi, Yutaka

2013-03-01

Recent developments in the inclusive fitness theory have revealed that the direction of evolution can be analytically predicted in a wider class of models than previously thought, such as those models dealing with network structure. This paper aims to provide a mathematical description of the inclusive fitness theory. Specifically, we provide a general framework based on a Markov chain that can implement basic models of inclusive fitness. Our framework is based on the probability distribution of "offspring-to-parent map", from which the key concepts of the theory, such as fitness function, relatedness and inclusive fitness, are derived in a straightforward manner. We prove theorems showing that inclusive fitness always provides a correct prediction on which of two competing genes more frequently appears in the long run in the Markov chain. As an application of the theorems, we prove a general formula of the optimal dispersal rate in the Wright's island model with recurrent mutations. We also show the existence of the critical mutation rate, which does not depend on the number of islands and below which a positive dispersal rate evolves. Our framework can also be applied to lattice or network structured populations. Copyright © 2012 Elsevier Inc. All rights reserved.

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.

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.

Modeling of soil water retention from saturation to oven dryness

USGS Publications Warehouse

Rossi, Cinzia; Nimmo, John R.

1994-01-01

Most analytical formulas used to model moisture retention in unsaturated porous media have been developed for the wet range and are unsuitable for applications in which low water contents are important. We have developed two models that fit the entire range from saturation to oven dryness in a practical and physically realistic way with smooth, continuous functions that have few parameters. Both models incorporate a power law and a logarithmic dependence of water content on suction, differing in how these two components are combined. In one model, functions are added together (model “sum”); in the other they are joined smoothly together at a discrete point (model “junction”). Both models also incorporate recent developments that assure a continuous derivative and force the function to reach zero water content at a finite value of suction that corresponds to oven dryness. The models have been tested with seven sets of water retention data that each cover nearly the entire range. The three-parameter sum model fits all data well and is useful for extrapolation into the dry range when data for it are unavailable. The two-parameter junction model fits most data sets almost as well as the sum model and has the advantage of being analytically integrable for convenient use with capillary-bundle models to obtain the unsaturated hydraulic conductivity.

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

NASA Astrophysics Data System (ADS)

Wei, Huazhou; Fu, Shiwei

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

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

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

Ding, X; Bues, M

2015-06-15

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

The 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.

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.

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

NASA Technical Reports Server (NTRS)

Giesy, Daniel P.; Lim, Kyong B.

1992-01-01

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

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.

Substrate-Induced Formation of Ribosomal Decoding Center for Accurate and Rapid Genetic Code Translation.

PubMed

Pavlov, Michael Y; Ehrenberg, Måns

2018-05-20

Accurate translation of genetic information is crucial for synthesis of functional proteins in all organisms. We use recent experimental data to discuss how induced fit affects accuracy of initial codon selection on the ribosome by aminoacyl transfer RNA in ternary complex ( T 3 ) with elongation factor Tu (EF-Tu) and guanosine-5'-triphosphate (GTP). We define actual accuracy ([Formula: see text]) of a particular protein synthesis system as its current accuracy and the effective selectivity ([Formula: see text]) as [Formula: see text] in the limit of zero ribosomal binding affinity for T 3 . Intrinsic selectivity ([Formula: see text]), defined as the upper thermodynamic limit of [Formula: see text], is determined by the free energy difference between near-cognate and cognate T 3 in the pre-GTP hydrolysis state on the ribosome. [Formula: see text] is much larger than [Formula: see text], suggesting the possibility of a considerable increase in [Formula: see text] and [Formula: see text] at negligible kinetic cost. Induced fit increases [Formula: see text] and [Formula: see text] without affecting [Formula: see text], and aminoglycoside antibiotics reduce [Formula: see text] and [Formula: see text] at unaltered [Formula: see text].

Discrete stochastic analogs of Erlang epidemic models.

PubMed

Getz, Wayne M; Dougherty, Eric R

2018-12-01

Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

Application of the Calculating Formula for the Mean Neutron Exposure in CEPM-s and CEPM-r/s Stars %Kstars: AGB and post-AGB, nuclear reactions, nucleosynthesis, abundances, methods: analytical

NASA Astrophysics Data System (ADS)

Zhang, F. H.; Zhang, L.; Cui, W. Y.; Zhang, B.

2017-09-01

Recent studies have shown that, for the current s-process nucleosynthesis model for the low-mass asymptotic giant branch (AGB) stars with (13C) pocket radiative burning during the interpulse period, the neutron exposure distribution in the nucleosynthesis region can be regarded as an exponential function, and the relation between the mean neutron exposure (τ0) and the model parameters is τ0 = - Δ τ/ln [q/(1 - r + q)]), in which (Δ τ) is the exposure value of each neutron irradiation, (r) is the overlap factor, and (q) is the mass ratio of the (13C) shell to the He intershell. Using the published data resulted from fitting the observed abundances of neutron-capture elements in 20 CEMP (Carbon-Enhanced Metal-Poor)-s and CEMP-s/r stars with the parametric AGB stellar s-process model, the reliability of the derived formula is tested, and further more the application of the formula in the s-process nucleosynthesis study is explored preliminarily. Our results show that, under the radiative s-process nucleosynthesis mechanism, the formula is suitable for CEMP stars experiencing recurrent neutron exposures. Combined with the parametric AGB nucleosynthesis model, the formula could be regarded as an effective tool to screen the CEMP stars with a single neutron exposure or a special type. Considering the uncertainty of the (13C) pocket, the role of this formula in understanding the physical conditions necessary to reproduce the observed s-process abundances in CEMP stars needs further study.

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.

"Non-cold" dark matter at small scales: a general approach

NASA Astrophysics Data System (ADS)

Murgia, R.; Merle, A.; Viel, M.; Totzauer, M.; Schneider, A.

2017-11-01

Structure formation at small cosmological scales provides an important frontier for dark matter (DM) research. Scenarios with small DM particle masses, large momenta or hidden interactions tend to suppress the gravitational clustering at small scales. The details of this suppression depend on the DM particle nature, allowing for a direct link between DM models and astrophysical observations. However, most of the astrophysical constraints obtained so far refer to a very specific shape of the power suppression, corresponding to thermal warm dark matter (WDM), i.e., candidates with a Fermi-Dirac or Bose-Einstein momentum distribution. In this work we introduce a new analytical fitting formula for the power spectrum, which is simple yet flexible enough to reproduce the clustering signal of large classes of non-thermal DM models, which are not at all adequately described by the oversimplified notion of WDM . We show that the formula is able to fully cover the parameter space of sterile neutrinos (whether resonantly produced or from particle decay), mixed cold and warm models, fuzzy dark matter, as well as other models suggested by effective theory of structure formation (ETHOS). Based on this fitting formula, we perform a large suite of N-body simulations and we extract important nonlinear statistics, such as the matter power spectrum and the halo mass function. Finally, we present first preliminary astrophysical constraints, based on linear theory, from both the number of Milky Way satellites and the Lyman-α forest. This paper is a first step towards a general and comprehensive modeling of small-scale departures from the standard cold DM model.

Effects of cardiorespiratory fitness and weight status on knowledge of physical activity and fitness, attitude toward physical education, and physical activity.

PubMed

Chen, Senlin; Gu, Xiangli

2018-02-20

The purpose of this study was to examine the effects of cardiorespiratory fitness and weight status on knowledge of physical activity and fitness (PAF knowledge), attitude toward physical education (PE), and physical activity. A total of 343 middle school students participated in the study (Age: M/SD = 12.76/.94, ranging from 11 to 14 years old). PE Metrics™ was used to measure PAF knowledge, and Attitude toward Physical Education Questionnaire and Youth Activity Profile were used to measure attitude, physical activity and sedentary behavior. Fitness and weight status were assessed using FitnessGram and converted to in Healthy Fitness Zone (HFZ) or Not in HFZ. Two-way multivariate analyses of covariance (MANCOVA; gender and grade as covariates) showed a significant group effect for cardiorespiratory fitness (Λ Pilla  = .07, F 4,255  = 5.03, p = .001, [Formula: see text] = .07) but not for weight status (p = .57). PAF knowledge (F 1,258  = 9.49, p < .01, [Formula: see text]= .04), attitude (F 1,258  = 4.45, p < .05, [Formula: see text]= .02) and sedentary behavior (F 1,258  = 6.89, p < .01, [Formula: see text]= .03) all favored the HFZ group. The findings reinforce the importance of promoting cardiorespiratory fitness in middle school PE as students acquire attitude, knowledge, and behaviors needed for active-living.

Zernike expansion coefficients: rescaling and decentring for different pupils and evaluation of corneal aberrations

NASA Astrophysics Data System (ADS)

Comastri, Silvia A.; Perez, Liliana I.; Pérez, Gervasio D.; Martin, Gabriel; Bastida, Karina

2007-03-01

An analytical method to convert the set of Zernike coefficients that fits the wavefront aberration for a pupil into another corresponding to a contracted and horizontally translated pupil is proposed. The underlying selection rules are provided and the resulting conversion formulae for a seventh-order expansion are given. These formulae are applied to calculate corneal aberrations referred to a given pupil centre in terms of those referred to the keratometric vertex supplied by the SN CT1000 topographer. Four typical cases are considered: a sphere and three eyes—normal, keratoconic and post-LASIK. When the pupil centre is fixed and the pupil diameter decreases from 6 mm to the photopic natural one, leaving aside piston, tilt and defocus, the difference between the root mean square wavefront error computed with the formulae and the topographer is less than 0.04 µm. When the pupil diameter is kept equal to the natural one and the pupil centre is displaced, coefficients vary according to the eye. For a 0.3 mm pupil shift, the variation of coma is at most 0.35 µm and that of spherical aberration 0.01 µm.

Self-diffusivity and interdiffusivity of molten aluminum-copper alloys under pressure, derived from molecular dynamics.

PubMed

Rudd, Robert E; Cabot, William H; Caspersen, Kyle J; Greenough, Jeffrey A; Richards, David F; Streitz, Frederick H; Miller, Paul L

2012-03-01

We use molecular dynamics (MD) to simulate diffusion in molten aluminum-copper (AlCu) alloys. The self-diffusivities and Maxwell-Stefan diffusivities are calculated for AlCu mixtures using the Green-Kubo formulas at temperatures from 1000 to 4000 K and pressures from 0 to 25 GPa, along with additional points at higher temperatures and pressures. The diffusivities are corrected for finite-size effects. The Maxwell-Stefan diffusivity is compared to the diffusivity calculated from the self-diffusivities using a generalization of the Darken equation. We find that the effects of cross-correlation are small. Using the calculated self-diffusivities, we have assessed whether dilute hard-sphere and dilute Lennard-Jones models apply to the molten mixture. Neither of the two dilute gas diffusivities describes the diffusivity in molten Al and Cu. We report generalized analytic models for the self-diffusivities and interdiffusivity (mutual diffusivity) that fit the MD results well. The MD-derived transport coefficients are in good agreement with the available experimental data. We also report MD calculations of the viscosity and an analytic fit to those results. The ionic thermal conductivity is discussed briefly.

Self-diffusivity and interdiffusivity of molten aluminum-copper alloys under pressure, derived from molecular dynamics

NASA Astrophysics Data System (ADS)

Rudd, Robert E.; Cabot, William H.; Caspersen, Kyle J.; Greenough, Jeffrey A.; Richards, David F.; Streitz, Frederick H.; Miller, Paul L.

2012-03-01

We use molecular dynamics (MD) to simulate diffusion in molten aluminum-copper (AlCu) alloys. The self-diffusivities and Maxwell-Stefan diffusivities are calculated for AlCu mixtures using the Green-Kubo formulas at temperatures from 1000 to 4000 K and pressures from 0 to 25 GPa, along with additional points at higher temperatures and pressures. The diffusivities are corrected for finite-size effects. The Maxwell-Stefan diffusivity is compared to the diffusivity calculated from the self-diffusivities using a generalization of the Darken equation. We find that the effects of cross-correlation are small. Using the calculated self-diffusivities, we have assessed whether dilute hard-sphere and dilute Lennard-Jones models apply to the molten mixture. Neither of the two dilute gas diffusivities describes the diffusivity in molten Al and Cu. We report generalized analytic models for the self-diffusivities and interdiffusivity (mutual diffusivity) that fit the MD results well. The MD-derived transport coefficients are in good agreement with the available experimental data. We also report MD calculations of the viscosity and an analytic fit to those results. The ionic thermal conductivity is discussed briefly.

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

A determination of the charm content of the proton: The NNPDF Collaboration.

PubMed

Ball, Richard D; Bertone, Valerio; Bonvini, Marco; Carrazza, Stefano; Forte, Stefano; Guffanti, Alberto; Hartland, Nathan P; Rojo, Juan; Rottoli, Luca

2016-01-01

We present an unbiased determination of the charm content of the proton, in which the charm parton distribution function (PDF) is parametrized on the same footing as the light quarks and the gluon in a global PDF analysis. This determination relies on the NLO calculation of deep-inelastic structure functions in the FONLL scheme, generalized to account for massive charm-initiated contributions. When the EMC charm structure function dataset is included, it is well described by the fit, and PDF uncertainties in the fitted charm PDF are significantly reduced. We then find that the fitted charm PDF vanishes within uncertainties at a scale [Formula: see text] GeV for all [Formula: see text], independent of the value of [Formula: see text] used in the coefficient functions. We also find some evidence that the charm PDF at large [Formula: see text] and low scales does not vanish, but rather has an "intrinsic" component, very weakly scale dependent and almost independent of the value of [Formula: see text], carrying less than [Formula: see text] of the total momentum of the proton. The uncertainties in all other PDFs are only slightly increased by the inclusion of fitted charm, while the dependence of these PDFs on [Formula: see text] is reduced. The increased stability with respect to [Formula: see text] persists at high scales and is the main implication of our results for LHC phenomenology. Our results show that if the EMC data are correct, then the usual approach in which charm is perturbatively generated leads to biased results for the charm PDF, though at small x this bias could be reabsorbed if the uncertainty due to the charm mass and missing higher orders were included. We show that LHC data for processes, such as high [Formula: see text] and large rapidity charm pair production and [Formula: see text] production, have the potential to confirm or disprove the implications of the EMC data.

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.

Tunneling of heat: Beyond linear response regime

NASA Astrophysics Data System (ADS)

Walczak, Kamil; Saroka, David

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2011-03-01

We study a 1+1D, stochastic, Burton-Cabrera-Frank (BCF) model of interacting steps fluctuating on a vicinal crystal. The step energy accounts for entropic and nearest-neighbor elastic-dipole interactions. Our goal is to formulate and validate a self-consistent mean-field (MF) formalism to approximately solve the system of coupled, nonlinear stochastic differential equations (SDEs) governing fluctuations in surface motion. We derive formulas for the time-dependent terrace width distribution (TWD) and its steady-state limit. By comparison with kinetic Monte-Carlo simulations, we show that our MF formalism improves upon models in which step interactions are linearized. We also indicate how fitting parameters of our steady state MF TWD may be used to determine the mass transport regime and step interaction energy of certain experimental systems. PP and TLE supported by NSF MRSEC under Grant DMR 05-20471 at U. of Maryland; DM supported by NSF under Grant DMS 08-47587.

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.

Measurement of the top-quark mass in the fully hadronic decay channel from ATLAS data at [Formula: see text].

PubMed

Aad, G; Abbott, B; Abdallah, J; Abdel Khalek, S; Abdinov, O; Aben, R; Abi, B; Abolins, M; AbouZeid, O S; Abramowicz, H; Abreu, H; Abreu, R; Abulaiti, Y; Acharya, B S; Adamczyk, L; Adams, D L; Adelman, J; Adomeit, S; Adye, T; Agatonovic-Jovin, T; Aguilar-Saavedra, J A; Agustoni, M; Ahlen, S P; Ahmadov, F; Aielli, G; Akerstedt, H; Åkesson, T P A; Akimoto, G; Akimov, A V; Alberghi, G L; Albert, J; Albrand, S; Alconada Verzini, M J; Aleksa, M; Aleksandrov, I N; Alexa, C; Alexander, G; Alexandre, G; Alexopoulos, T; Alhroob, M; Alimonti, G; Alio, L; Alison, J; Allbrooke, B M M; Allison, L J; Allport, P P; Almond, J; Aloisio, A; Alonso, A; Alonso, F; Alpigiani, C; Altheimer, A; Alvarez Gonzalez, B; Alviggi, M G; Amako, K; Amaral Coutinho, Y; Amelung, C; Amidei, D; Amor Dos Santos, S P; Amorim, A; Amoroso, S; Amram, N; Amundsen, G; Anastopoulos, C; Ancu, L S; Andari, N; Andeen, T; Anders, C F; Anders, G; Anderson, K J; Andreazza, A; Andrei, V; Anduaga, X S; Angelidakis, S; Angelozzi, I; Anger, P; Angerami, A; Anghinolfi, F; Anisenkov, A V; Anjos, N; Annovi, A; Antonaki, A; Antonelli, M; Antonov, A; Antos, J; Anulli, F; Aoki, M; Aperio Bella, L; Apolle, R; Arabidze, G; Aracena, I; Arai, Y; Araque, J P; Arce, A T H; Arguin, J-F; Argyropoulos, S; Arik, M; Armbruster, A J; Arnaez, O; Arnal, V; Arnold, H; Arratia, M; Arslan, O; Artamonov, A; Artoni, G; Asai, S; Asbah, N; Ashkenazi, A; Åsman, B; Asquith, L; Assamagan, K; Astalos, R; Atkinson, M; Atlay, N B; Auerbach, B; Augsten, K; Aurousseau, M; Avolio, G; Azuelos, G; Azuma, Y; Baak, M A; Baas, A E; Bacci, C; Bachacou, H; Bachas, K; Backes, M; Backhaus, M; Backus Mayes, J; Badescu, E; Bagiacchi, P; Bagnaia, P; Bai, Y; Bain, T; Baines, J T; Baker, O K; Balek, P; Balli, F; Banas, E; Banerjee, Sw; Bannoura, A A E; Bansal, V; Bansil, H S; Barak, L; Baranov, S P; Barberio, E L; Barberis, D; Barbero, M; Barillari, T; Barisonzi, M; Barklow, T; Barlow, N; Barnett, B M; Barnett, R M; Barnovska, Z; Baroncelli, A; Barone, G; Barr, A J; Barreiro, F; 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Crescioli, F; Cribbs, W A; Crispin Ortuzar, M; Cristinziani, M; Croft, V; Crosetti, G; Cuciuc, C-M; Cuhadar Donszelmann, T; Cummings, J; Curatolo, M; Cuthbert, C; Czirr, H; Czodrowski, P; Czyczula, Z; D'Auria, S; D'Onofrio, M; Cunha Sargedas De Sousa, M J Da; Via, C Da; Dabrowski, W; Dafinca, A; Dai, T; Dale, O; Dallaire, F; Dallapiccola, C; Dam, M; Daniells, A C; Dano Hoffmann, M; Dao, V; Darbo, G; Darmora, S; Dassoulas, J A; Dattagupta, A; Davey, W; David, C; Davidek, T; Davies, E; Davies, M; Davignon, O; Davison, A R; Davison, P; Davygora, Y; Dawe, E; Dawson, I; Daya-Ishmukhametova, R K; De, K; de Asmundis, R; De Castro, S; De Cecco, S; De Groot, N; de Jong, P; De la Torre, H; De Lorenzi, F; De Nooij, L; De Pedis, D; De Salvo, A; De Sanctis, U; De Santo, A; De Vivie De Regie, J B; Dearnaley, W J; Debbe, R; Debenedetti, C; Dechenaux, B; Dedovich, D V; Deigaard, I; Del Peso, J; Del Prete, T; Deliot, F; Delitzsch, C M; Deliyergiyev, M; Dell'Acqua, A; Dell'Asta, L; Dell'Orso, M; Della Pietra, M; Della Volpe, D; Delmastro, M; Delsart, P A; Deluca, C; Demers, S; Demichev, M; Demilly, A; Denisov, S P; Derendarz, D; Derkaoui, J E; Derue, F; Dervan, P; Desch, K; Deterre, C; Deviveiros, P O; Dewhurst, A; Dhaliwal, S; Di Ciaccio, A; Di Ciaccio, L; Di Domenico, A; Di Donato, C; Di Girolamo, A; Di Girolamo, B; Di Mattia, A; Di Micco, B; Di Nardo, R; Di Simone, A; Di Sipio, R; Di Valentino, D; Dias, F A; Diaz, M A; Diehl, E B; Dietrich, J; Dietzsch, T A; Diglio, S; Dimitrievska, A; Dingfelder, J; Dionisi, C; Dita, P; Dita, S; Dittus, F; Djama, F; Djobava, T; do Vale, M A B; Do Valle Wemans, A; Doan, T K O; Dobos, D; Doglioni, C; Doherty, T; Dohmae, T; Dolejsi, J; Dolezal, Z; Dolgoshein, B A; Donadelli, M; Donati, S; Dondero, P; Donini, J; Dopke, J; Doria, A; Dova, M T; Doyle, A T; Dris, M; Dubbert, J; Dube, S; Dubreuil, E; Duchovni, E; Duckeck, G; Ducu, O A; Duda, D; Dudarev, A; Dudziak, F; Duflot, L; Duguid, L; Dührssen, M; Dunford, M; Duran Yildiz, H; Düren, M; Durglishvili, A; Dwuznik, M; 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Hamilton, S; Hamity, G N; Hamnett, P G; Han, L; Hanagaki, K; Hanawa, K; Hance, M; Hanke, P; Hanna, R; Hansen, J B; Hansen, J D; Hansen, P H; Hara, K; Hard, A S; Harenberg, T; Hariri, F; Harkusha, S; Harper, D; Harrington, R D; Harris, O M; Harrison, P F; Hartjes, F; Hasegawa, M; Hasegawa, S; Hasegawa, Y; Hasib, A; Hassani, S; Haug, S; Hauschild, M; Hauser, R; Havranek, M; Hawkes, C M; Hawkings, R J; Hawkins, A D; Hayashi, T; Hayden, D; Hays, C P; Hayward, H S; Haywood, S J; Head, S J; Heck, T; Hedberg, V; Heelan, L; Heim, S; Heim, T; Heinemann, B; Heinrich, L; Hejbal, J; Helary, L; Heller, C; Heller, M; Hellman, S; Hellmich, D; Helsens, C; Henderson, J; Henderson, R C W; Heng, Y; Hengler, C; Henrichs, A; Henriques Correia, A M; Henrot-Versille, S; Hensel, C; Herbert, G H; Hernández Jiménez, Y; Herrberg-Schubert, R; Herten, G; Hertenberger, R; Hervas, L; Hesketh, G G; Hessey, N P; Hickling, R; Higón-Rodriguez, E; Hill, E; Hill, J C; Hiller, K H; Hillert, S; Hillier, S J; Hinchliffe, I; 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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; Unal, G; Undrus, A; Unel, G; Ungaro, F C; Unno, Y; Unverdorben, C; Urbaniec, D; Urquijo, P; Usai, G; Usanova, A; Vacavant, L; Vacek, V; Vachon, B; Valencic, N; Valentinetti, S; Valero, A; Valery, L; Valkar, S; Valladolid Gallego, E; Vallecorsa, S; Valls Ferrer, J A; Van Den Wollenberg, W; Van Der Deijl, P C; van der Geer, R; van der Graaf, H; Van Der Leeuw, R; van der Ster, D; 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; Vannucci, F; Vardanyan, G; Vari, R; Varnes, E W; Varol, T; Varouchas, D; Vartapetian, A; Varvell, K E; Vazeille, F; Vazquez Schroeder, T; Veatch, J; Veloso, F; Veneziano, S; Ventura, A; Ventura, D; 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; Vickey Boeriu, O E; Viehhauser, G H A; Viel, S; Vigne, R; Villa, M; Villaplana Perez, M; Vilucchi, E; Vincter, M G; Vinogradov, V B; Virzi, J; Vivarelli, I; Vives Vaque, F; Vlachos, S; Vladoiu, D; Vlasak, M; Vogel, A; Vogel, M; Vokac, P; Volpi, G; Volpi, M; von der Schmitt, H; von Radziewski, H; von Toerne, E; Vorobel, V; Vorobev, K; Vos, M; Voss, R; Vossebeld, J H; Vranjes, N; Vranjes Milosavljevic, M; Vrba, V; Vreeswijk, M; Vu Anh, T; Vuillermet, R; Vukotic, I; Vykydal, Z; Wagner, P; Wagner, W; Wahlberg, H; Wahrmund, S; Wakabayashi, J; Walder, J; Walker, R; Walkowiak, W; Wall, R; Waller, P; Walsh, B; Wang, C; Wang, C; Wang, F; Wang, H; Wang, H; Wang, J; Wang, J; Wang, K; Wang, R; Wang, S M; Wang, T; Wang, X; Wanotayaroj, C; Warburton, A; Ward, C P; Wardrope, D R; Warsinsky, M; Washbrook, A; Wasicki, C; Watkins, P M; Watson, A T; Watson, I J; Watson, M F; Watts, G; Watts, S; Waugh, B M; Webb, S; Weber, M S; Weber, S W; Webster, J S; Weidberg, A R; Weigell, P; Weinert, B; Weingarten, J; Weiser, C; Weits, H; Wells, P S; Wenaus, T; Wendland, D; Weng, Z; Wengler, T; Wenig, S; Wermes, N; Werner, M; Werner, P; Wessels, M; Wetter, J; Whalen, K; White, A; White, M J; White, R; White, S; Whiteson, D; 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; Wilkens, H G; Will, J Z; Williams, H H; Williams, S; Willis, C; Willocq, S; Wilson, A; Wilson, J A; Wingerter-Seez, I; Winklmeier, F; Winter, B T; Wittgen, M; Wittig, T; Wittkowski, J; Wollstadt, S J; Wolter, M W; Wolters, H; Wosiek, B K; Wotschack, J; Woudstra, M J; Wozniak, K W; Wright, M; Wu, M; Wu, S L; Wu, X; Wu, Y; Wulf, E; Wyatt, T R; Wynne, B M; Xella, S; Xiao, M; Xu, D; Xu, L; Yabsley, B; Yacoob, S; Yakabe, R; Yamada, M; Yamaguchi, H; Yamaguchi, Y; Yamamoto, A; Yamamoto, K; Yamamoto, S; Yamamura, T; Yamanaka, T; Yamauchi, K; Yamazaki, Y; Yan, Z; Yang, H; Yang, H; Yang, U K; Yang, Y; Yanush, S; Yao, L; Yao, W-M; Yasu, Y; Yatsenko, E; Yau Wong, K H; Ye, J; Ye, S; Yeletskikh, I; Yen, A L; Yildirim, E; Yilmaz, M; Yoosoofmiya, R; 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; 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

The mass of the top quark is measured in a data set corresponding to 4.6 [Formula: see text] of proton-proton collisions with centre-of-mass energy [Formula: see text] TeV collected by the ATLAS detector at the LHC. Events consistent with hadronic decays of top-antitop quark pairs with at least six jets in the final state are selected. The substantial background from multijet production is modelled with data-driven methods that utilise the number of identified [Formula: see text]-quark jets and the transverse momentum of the sixth leading jet, which have minimal correlation. The top-quark mass is obtained from template fits to the ratio of three-jet to dijet mass. The three-jet mass is calculated from the three jets produced in a top-quark decay. Using these three jets the dijet mass is obtained from the two jets produced in the [Formula: see text] boson decay. The top-quark mass obtained from this fit is thus less sensitive to the uncertainty in the energy measurement of the jets. A binned likelihood fit yields a top-quark mass of [Formula: see text].

Generalized Hill-stability criteria for hierarchical three-body systems at arbitrary inclinations

NASA Astrophysics Data System (ADS)

Grishin, Evgeni; Perets, Hagai B.; Zenati, Yossef; Michaely, Erez

2017-04-01

A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical studies of inclined systems phenomenologically mapped their stability regions, but neither complement it by theoretical framework, nor provided satisfactory fit for their dependence on mutual inclinations. Here we present a novel approach to study the stability of hierarchical three-body systems at arbitrary inclinations, which accounts not only for the instantaneous stability of such systems, but also for the secular stability and evolution through Lidov-Kozai cycles and evection. We generalize the Hill-stability criteria to arbitrarily inclined triple systems, explain the existence of quasi-stable regimes and characterize the inclination dependence of their stability. We complement the analytic treatment with an extensive numerical study, to test our analytic results. We find excellent correspondence up to high inclinations (˜120°), beyond which the agreement is marginal. At such high inclinations, the stability radius is larger, the ratio between the outer and inner periods becomes comparable and our secular averaging approach is no longer strictly valid. We therefore combine our analytic results with polynomial fits to the numerical results to obtain a generalized stability formula for triple systems at arbitrary inclinations. Besides providing a generalized secular-based physical explanation for the stability of non-co-planar systems, our results have direct implications for any triple systems and, in particular, binary planets and moon/satellite systems; we briefly discuss the latter as a test case for our models.

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…

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.

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 mathematical solution for the parameters of three interfering resonances

NASA Astrophysics Data System (ADS)

Han, X.; Shen, C. P.

2018-04-01

The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used. Supported by National Natural Science Foundation of China (NSFC) (11575017, 11761141009), the Ministry of Science and Technology of China (2015CB856701) and the CAS Center for Excellence in Particle Physics (CCEPP)

The asymptotic behaviour of parton distributions at small and large x.

PubMed

Ball, Richard D; Nocera, Emanuele R; Rojo, Juan

2016-01-01

It has been argued from the earliest days of quantum chromodynamics that at asymptotically small values of x the parton distribution functions (PDFs) of the proton behave as [Formula: see text], where the values of [Formula: see text] can be deduced from Regge theory, while at asymptotically large values of x the PDFs behave as [Formula: see text], where the values of [Formula: see text] can be deduced from the Brodsky-Farrar quark counting rules. We critically examine these claims by extracting the exponents [Formula: see text] and [Formula: see text] from various global fits of parton distributions, analysing their scale dependence, and comparing their values to the naive expectations. We find that for valence distributions both Regge theory and counting rules are confirmed, at least within uncertainties, while for sea quarks and gluons the results are less conclusive. We also compare results from various PDF fits for the structure function ratio [Formula: see text] at large x , and caution against unrealistic uncertainty estimates due to overconstrained parametrisations.

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...

A predictive analytic model for the solar modulation of cosmic rays

DOE PAGES

Cholis, Ilias; Hooper, Dan; Linden, Tim

2016-02-23

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

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

PubMed

Poitevin, Eric

2016-01-01

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

Inferring Recent Demography from Isolation by Distance of Long Shared Sequence Blocks

PubMed Central

Ringbauer, Harald; Coop, Graham

2017-01-01

Recently it has become feasible to detect long blocks of nearly identical sequence shared between pairs of genomes. These identity-by-descent (IBD) blocks are direct traces of recent coalescence events and, as such, contain ample signal to infer recent demography. Here, we examine sharing of such blocks in two-dimensional populations with local migration. Using a diffusion approximation to trace genetic ancestry, we derive analytical formulas for patterns of isolation by distance of IBD blocks, which can also incorporate recent population density changes. We introduce an inference scheme that uses a composite-likelihood approach to fit these formulas. We then extensively evaluate our theory and inference method on a range of scenarios using simulated data. We first validate the diffusion approximation by showing that the theoretical results closely match the simulated block-sharing patterns. We then demonstrate that our inference scheme can accurately and robustly infer dispersal rate and effective density, as well as bounds on recent dynamics of population density. To demonstrate an application, we use our estimation scheme to explore the fit of a diffusion model to Eastern European samples in the Population Reference Sample data set. We show that ancestry diffusing with a rate of σ≈50−−100 km/gen during the last centuries, combined with accelerating population growth, can explain the observed exponential decay of block sharing with increasing pairwise sample distance. PMID:28108588

Uncertainties on [Formula: see text] in the MMHT2014 global PDF analysis and implications for SM predictions.

PubMed

Harland-Lang, L A; Martin, A D; Motylinski, P; Thorne, R S

We investigate the uncertainty in the strong coupling [Formula: see text] when allowing it to be a free parameter in the recent MMHT global analyses of deep-inelastic and related hard scattering data that was undertaken to determine the parton distribution functions (PDFs) of the proton. The analysis uses the standard framework of leading twist fixed-order collinear factorisation in the [Formula: see text] scheme. We study the constraints on [Formula: see text] coming from individual data sets by repeating the NNLO and NLO fits spanning the range 0.108 to 0.128 in units of 0.001, making all PDFs sets available. The inclusion of the cross section for inclusive [Formula: see text] production allows us to explore the correlation between the mass [Formula: see text] of the top quark and [Formula: see text]. We find that the best-fit values are [Formula: see text] and [Formula: see text] at NLO and NNLO, respectively, with the central values changing to [Formula: see text] and 0.1178 when the world average of [Formula: see text] is used as a data point. We investigate the interplay between the uncertainties on [Formula: see text] and on the PDFs. In particular we calculate the cross sections for key processes at the LHC and show how the uncertainties from the PDFs and from [Formula: see text] can be provided independently and be combined.

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.

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.

How do physicians become medical experts? A test of three competing theories: distinct domains, independent influence and encapsulation models.

PubMed

Violato, Claudio; Gao, Hong; O'Brien, Mary Claire; Grier, David; Shen, E

2018-05-01

The distinction between basic sciences and clinical knowledge which has led to a theoretical debate on how medical expertise is developed has implications for medical school and lifelong medical education. This longitudinal, population based observational study was conducted to test the fit of three theories-knowledge encapsulation, independent influence, distinct domains-of the development of medical expertise employing structural equation modelling. Data were collected from 548 physicians (292 men-53.3%; 256 women-46.7%; mean age = 24.2 years on admission) who had graduated from medical school 2009-2014. They included (1) Admissions data of undergraduate grade point average and Medical College Admission Test sub-test scores, (2) Course performance data from years 1, 2, and 3 of medical school, and (3) Performance on the NBME exams (i.e., Step 1, Step 2 CK, and Step 3). Statistical fit indices (Goodness of Fit Index-GFI; standardized root mean squared residual-SRMR; root mean squared error of approximation-RSMEA) and comparative fit [Formula: see text] of three theories of cognitive development of medical expertise were used to assess model fit. There is support for the knowledge encapsulation three factor model of clinical competency (GFI = 0.973, SRMR = 0.043, RSMEA = 0.063) which had superior fit indices to both the independent influence and distinct domains theories ([Formula: see text] vs [Formula: see text] [[Formula: see text

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

PubMed

Bauer, P; Attinger, S; Kinzelbach, W

2001-06-01

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

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

PubMed

Wu, Yang; Kelly, Damien P

2014-12-12

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

Non-inverse-square force-distance law for long thin magnets-revisited.

PubMed

Darvell, Brian W; Gilding, Brian H

2012-05-01

It had previously been shown that the inverse-square law does not apply to the force-distance relationship in the case of a long, thin magnet with one end in close proximity to its image in a permeable plane when simple point-like poles are assumed. Treating the system instead as having a 'polar disc', arising from an assumed bundle of dipoles, led to a double integral that could only be evaluated numerically, and a relationship that still did not match observed behavior. Using an elaborate 'stretched' exponential polynomial to represent the position of an 'elastic' polar disc resulted in a fair representation of the physical response, but this was essentially merely the fitting of an arbitrary function. The present purpose was therefore to find an explicit formula for the force-distance relationship in the polar-disc problem and assess its fit to the previously obtained experimental data. Starting from Coulomb's law a corrected integral formula for the force-distance relationship was derived. The integral in this formula was evaluated explicitly using rescaling, changes of order of integration, reduction by symmetry, and change of variables. The resulting formula was then fitted to data that had been obtained for the force exerted by eighty-five rod-shaped magnets (Alnico V, 3 mm diameter, 170 mm long) perpendicular to a large steel plate, as a function of distance, at small separations (<5 mm). Subsequently, the fit of alternative functions was explored. An explicit formula in terms of elliptic integrals was obtained for the polar-disc problem. Despite the greater fidelity, this too was found not to fit the observed physical behavior. Given that failure, nevertheless a simple formula that conforms closely and parsimoniously to the actual magnet data was found. A key feature remains the marked departure from inverse-square behavior. The failure of the explicit formula to fit the data indicates an inadequate model of the physical system. Nonetheless it constitutes a useful tool for quantifying the force-distance relationship on the premise of polar discs. Given these insights, it may now be possible to address the original motivating problem of the behavior of real dental magnets. Copyright © 2012 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Analysis of Hanle-effect signals observed in Si-channel spin accumulation devices

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

Takamura, Yota, E-mail: takamura@spin.pe.titech.ac.jp; Department of Physical Electronics, Tokyo Institute of Technology, 2-12-1, Ookayama, Meguro-ku, Tokyo 152-8552; Akushichi, Taiju

2014-05-07

We reexamined curve-fitting analysis for spin-accumulation signals observed in Si-channel spin-accumulation devices, employing widely-used Lorentz functions and a new formula developed from the spin diffusion equation. A Si-channel spin-accumulation device with a high quality ferromagnetic spin injector was fabricated, and its observed spin-accumulation signals were verified. Experimentally obtained Hanle-effect signals for spin accumulation were not able to be fitted by a single Lorentz function and were reproduced by the newly developed formula. Our developed formula can represent spin-accumulation signals and thus analyze Hanle-effect signals.

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

DTIC Science & Technology

1980-09-01

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

Search for a standard model Higgs boson produced in association with a top-quark pair and decaying to bottom quarks using a matrix element method.

PubMed

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Taylor, D; Vuosalo, C; Woods, N; Collaboration, Authorinst The Cms

A search for a standard model Higgs boson produced in association with a top-quark pair and decaying to bottom quarks is presented. Events with hadronic jets and one or two oppositely charged leptons are selected from a data sample corresponding to an integrated luminosity of 19.5[Formula: see text] collected by the CMS experiment at the LHC in [Formula: see text] collisions at a centre-of-mass energy of 8[Formula: see text]. In order to separate the signal from the larger [Formula: see text]  + jets background, this analysis uses a matrix element method that assigns a probability density value to each reconstructed event under signal or background hypotheses. The ratio between the two values is used in a maximum likelihood fit to extract the signal yield. The results are presented in terms of the measured signal strength modifier, [Formula: see text], relative to the standard model prediction for a Higgs boson mass of 125[Formula: see text]. The observed (expected) exclusion limit at a 95 % confidence level is [Formula: see text] (3.3), corresponding to a best fit value [Formula: see text].

Translucency thresholds for dental materials.

PubMed

Salas, Marianne; Lucena, Cristina; Herrera, Luis Javier; Yebra, Ana; Della Bona, Alvaro; Pérez, María M

2018-05-12

To determine the translucency acceptability and perceptibility thresholds for dental resin composites using CIEDE2000 and CIELAB color difference formulas. A 30-observer panel performed perceptibility and acceptability judgments on 50 pairs of resin composites discs (diameter: 10mm; thickness: 1mm). Disc pair differences for the Translucency Parameter (ΔTP) were calculated using both color difference formulas (ΔTP 00 ranged from 0.11 to 7.98, and ΔTP ab ranged from 0.01 to 12.79). A Takagi-Sugeno-Kang (TSK) Fuzzy Approximation was used as fitting procedure. From the resultant fitting curves, the 95% confidence intervals were estimated and the 50:50% translucency perceptibility and acceptability thresholds (TPT and TAT) were calculated. Differences between thresholds were statistically analyzed using Student t tests (α=0.05). CIEDE2000 50:50% TPT was 0.62 and TAT was 2.62. Corresponding CIELAB values were 1.33 and 4.43, respectively. Translucency perceptibility and acceptability thresholds were significantly different using both color difference formulas (p=0.01 for TPT and p=0.005 for TAT). CIEDE2000 color difference formula provided a better data fit than CIELAB formula. The visual translucency difference thresholds determined with CIEDE2000 color difference formula can serve as reference values in the selection of resin composites and evaluation of its clinical performance. Copyright © 2018 The Academy of Dental Materials. Published by Elsevier Inc. All rights reserved.

The Preferential Tidal Stripping of Dark Matter versus Stars in Galaxies

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Offner stretcher aberrations revisited to compensate material dispersion

NASA Astrophysics Data System (ADS)

Vyhlídka, Štěpán; Kramer, Daniel; Meadows, Alexander; Rus, Bedřich

2018-05-01

We present simple analytical formulae for the calculation of the spectral phase and residual angular dispersion of an ultrashort pulse propagating through the Offner stretcher. Based on these formulae, we show that the radii of curvature of both convex and concave mirrors in the Offner triplet can be adapted to tune the fourth order dispersion term of the spectral phase of the pulse. As an example, a single-grating Offner stretcher design suitable for the suppression of material dispersion in the Ti:Sa PALS laser system is proposed. The results obtained by numerical raytracing well match those calculated from the analytical formulae.

Corrected Four-Sphere Head Model for EEG Signals.

PubMed

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

2017-01-01

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

Corrected Four-Sphere Head Model for EEG Signals

PubMed Central

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

2017-01-01

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

Photoionization of the hydrogen atom in strong magnetic fields

NASA Technical Reports Server (NTRS)

Potekhin, Aleksandr IU.; Pavlov, George G.

1993-01-01

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

On the accuracy of models for predicting sound propagation in fitted rooms.

PubMed

Hodgson, M

1990-08-01

The objective of this article is to make a contribution to the evaluation of the accuracy and applicability of models for predicting the sound propagation in fitted rooms such as factories, classrooms, and offices. The models studied are 1:50 scale models; the method-of-image models of Jovicic, Lindqvist, Hodgson, Kurze, and of Lemire and Nicolas; the emprical formula of Friberg; and Ondet and Barbry's ray-tracing model. Sound propagation predictions by the analytic models are compared with the results of sound propagation measurements in a 1:50 scale model and in a warehouse, both containing various densities of approximately isotropically distributed, rectangular-parallelepipedic fittings. The results indicate that the models of Friberg and of Lemire and Nicolas are fundamentally incorrect. While more generally applicable versions exist, the versions of the models of Jovicic and Kurze studied here are found to be of limited applicability since they ignore vertical-wall reflections. The Hodgson and Lindqvist models appear to be accurate in certain limited cases. This preliminary study found the ray-tracing model of Ondet and Barbry to be the most accurate of all the cases studied. Furthermore, it has the necessary flexibility with respect to room geometry, surface-absorption distribution, and fitting distribution. It appears to be the model with the greatest applicability to fitted-room sound propagation prediction.

Grouping Minerals by Their Formulas

ERIC Educational Resources Information Center

Mulvey, Bridget

2018-01-01

Minerals are commonly taught in ways that emphasize mineral identification for its own sake or maybe to help identify rocks. But how do minerals fit in with other science content taught? The author uses mineral formulas to help Earth science students wonder about the connection between elements, compounds, mixtures, minerals, and mineral formulas.…

Interpretation of the Coefficients in the Fit y = at + bx + c

ERIC Educational Resources Information Center

Farnsworth, David L.

2006-01-01

The goals of this note are to derive formulas for the coefficients a and b in the least-squares regression plane y = at + bx + c for observations (t[subscript]i,x[subscript]i,y[subscript]i), i = 1, 2, ..., n, and to present meanings for the coefficients a and b. In this note, formulas for the coefficients a and b in the least-squares fit are…

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

NASA Astrophysics Data System (ADS)

Vicsek, Tamas

1997-03-01

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

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

Investigating the Relative Exercise Intensity of Exergames in Prepubertal Children.

PubMed

McNarry, Melitta A; Mackintosh, Kelly A

2016-04-01

The literature remains equivocal as to whether exergames elicit energy expenditure (EE) commensurate with physical activity guidelines. Such discrepancies may be attributable to a reliance on absolute exercise intensities, which fail to account for differences in cardiorespiratory fitness levels. Thirty-four prepubertal children (20 boys, 14 girls; 10.8 ± 1.0 years old) completed a 30-minute exergame (two 15-minute games from "Kinect Adventures! Xbox 360" [Microsoft, Redmond, WA]) and an incremental treadmill test to determine peak oxygen uptake ( [Formula: see text]) throughout which breath-by-breath gas exchange was measured. Both games elicited moderate-intensity physical activity (5.7 ± 1.5 and 5.5 ± 1.4 metabolic equivalents [METs]), with 36 percent demonstrating a mean EE in excess of 6.0 METs, commensurate with vigorous intensity. Furthermore, boys demonstrated higher EE during both games (boys versus girls: Game 1, 6.0 ± 1.7 versus 5.2 ± 1.0 METs; Game 2, 6.0 ± 1.4 versus girls, 4.9 ± 1.2 METs; P < 0.05). Hierarchical linear regression revealed sex, maturity, and fitness to be significant predictors of EE, accounting for 24 percent of the variance: relative exergame [Formula: see text] = 24.53 + (2.12 × Sex) - (0.42 × Maturity offset) - (0.16 × Relative peak [Formula: see text]). There was no correlation between absolute [Formula: see text] during the exergames and peak [Formula: see text], but [Formula: see text] expressed as a percentage of peak [Formula: see text] was correlated with peak [Formula: see text] during both Game 1 (r = -0.62, P < 0.01) and Game 2 (r = -0.59, P < 0.01). The present findings provide further evidence that exergames can elicit EE values commensurate with national physical activity guidelines and extend our understanding of the mediators of EE. Specifically, cardiorespiratory fitness and sex must both be considered in the design and implementation of future interventions seeking to use exergames to enhance physical activity levels and/or cardiorespiratory fitness.

Computer-assisted map projection research

USGS Publications Warehouse

Snyder, John Parr

1985-01-01

Computers have opened up areas of map projection research which were previously too complicated to utilize, for example, using a least-squares fit to a very large number of points. One application has been in the efficient transfer of data between maps on different projections. While the transfer of moderate amounts of data is satisfactorily accomplished using the analytical map projection formulas, polynomials are more efficient for massive transfers. Suitable coefficients for the polynomials may be determined more easily for general cases using least squares instead of Taylor series. A second area of research is in the determination of a map projection fitting an unlabeled map, so that accurate data transfer can take place. The computer can test one projection after another, and include iteration where required. A third area is in the use of least squares to fit a map projection with optimum parameters to the region being mapped, so that distortion is minimized. This can be accomplished for standard conformal, equalarea, or other types of projections. Even less distortion can result if complex transformations of conformal projections are utilized. This bulletin describes several recent applications of these principles, as well as historical usage and background.

A classical regression framework for mediation analysis: fitting one model to estimate mediation effects.

PubMed

Saunders, Christina T; Blume, Jeffrey D

2017-10-26

Mediation analysis explores the degree to which an exposure's effect on an outcome is diverted through a mediating variable. We describe a classical regression framework for conducting mediation analyses in which estimates of causal mediation effects and their variance are obtained from the fit of a single regression model. The vector of changes in exposure pathway coefficients, which we named the essential mediation components (EMCs), is used to estimate standard causal mediation effects. Because these effects are often simple functions of the EMCs, an analytical expression for their model-based variance follows directly. Given this formula, it is instructive to revisit the performance of routinely used variance approximations (e.g., delta method and resampling methods). Requiring the fit of only one model reduces the computation time required for complex mediation analyses and permits the use of a rich suite of regression tools that are not easily implemented on a system of three equations, as would be required in the Baron-Kenny framework. Using data from the BRAIN-ICU study, we provide examples to illustrate the advantages of this framework and compare it with the existing approaches. © The Author 2017. Published by Oxford University Press.

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

PubMed

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

2017-11-10

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

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.

Curve fits of predicted inviscid stagnation-point radiative heating rates, cooling factors, and shock standoff distances for hyperbolic earth entry

NASA Technical Reports Server (NTRS)

Suttles, J. T.; Sullivan, E. M.; Margolis, S. B.

1974-01-01

Curve-fit formulas are presented for the stagnation-point radiative heating rate, cooling factor, and shock standoff distance for inviscid flow over blunt bodies at conditions corresponding to high-speed earth entry. The data which were curve fitted were calculated by using a technique which utilizes a one-strip integral method and a detailed nongray radiation model to generate a radiatively coupled flow-field solution for air in chemical and local thermodynamic equilibrium. The range of free-stream parameters considered were altitudes from about 55 to 70 km and velocities from about 11 to 16 km.sec. Spherical bodies with nose radii from 30 to 450 cm and elliptical bodies with major-to-minor axis ratios of 2, 4, and 6 were treated. Powerlaw formulas are proposed and a least-squares logarithmic fit is used to evaluate the constants. It is shown that the data can be described in this manner with an average deviation of about 3 percent (or less) and a maximum deviation of about 10 percent (or less). The curve-fit formulas provide an effective and economic means for making preliminary design studies for situations involving high-speed earth entry.

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).

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.

Measurement of the [Formula: see text] and [Formula: see text] production cross sections in multilepton final states using 3.2 fb[Formula: see text] of [Formula: see text] collisions at [Formula: see text] = 13 TeV with the ATLAS detector.

PubMed

Aaboud, M; Aad, G; Abbott, B; Abdallah, J; Abdinov, O; Abeloos, B; Aben, R; AbouZeid, O S; Abraham, N L; Abramowicz, H; Abreu, H; Abreu, R; Abulaiti, Y; Acharya, B S; Adamczyk, L; Adams, D L; Adelman, J; Adomeit, S; Adye, T; Affolder, A A; Agatonovic-Jovin, T; Agricola, J; Aguilar-Saavedra, J A; Ahlen, S P; Ahmadov, F; Aielli, G; Akerstedt, H; Åkesson, T P A; Akimov, A V; Alberghi, G L; Albert, J; Albrand, S; Alconada Verzini, M J; Aleksa, M; Aleksandrov, I N; Alexa, C; Alexander, G; Alexopoulos, T; Alhroob, M; Ali, B; Aliev, M; Alimonti, G; Alison, J; Alkire, S P; Allbrooke, B M M; Allen, B W; Allport, P P; Aloisio, A; Alonso, A; Alonso, F; Alpigiani, C; Alstaty, M; Alvarez Gonzalez, B; Álvarez Piqueras, D; Alviggi, M G; Amadio, B T; Amako, K; Amaral Coutinho, Y; Amelung, C; Amidei, D; Amor Dos Santos, S P; Amorim, A; Amoroso, S; Amundsen, G; Anastopoulos, C; Ancu, L S; Andari, N; Andeen, T; Anders, C F; Anders, G; Anders, J K; Anderson, K J; Andreazza, A; Andrei, V; Angelidakis, S; Angelozzi, I; 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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; Zur Nedden, M; Zwalinski, L

2017-01-01

A measurement of the [Formula: see text] and [Formula: see text] production cross sections in final states with either two same-charge muons, or three or four leptons (electrons or muons) is presented. The analysis uses a data sample of proton-proton collisions at [Formula: see text] TeV recorded with the ATLAS detector at the Large Hadron Collider in 2015, corresponding to a total integrated luminosity of 3.2 fb[Formula: see text]. The inclusive cross sections are extracted using likelihood fits to signal and control regions, resulting in [Formula: see text] pb and [Formula: see text] pb, in agreement with the Standard Model predictions.

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)].

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.

Personal Trainers: A Formula for Fitness?

ERIC Educational Resources Information Center

Couzens, Gerald Secor

1992-01-01

As personal fitness trainers move into the mainstream, physicians are increasingly recommending them to patients as part of ongoing health programs. Personal trainers provide personalized fitness programs, including exercise prescriptions and guidelines and nutrition information. The article explains how physicians can find qualified trainers for…

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.

Uncertainty in least-squares fits to the thermal noise spectra of nanomechanical resonators with applications to the atomic force microscope.

PubMed

Sader, John E; Yousefi, Morteza; Friend, James R

2014-02-01

Thermal noise spectra of nanomechanical resonators are used widely to characterize their physical properties. These spectra typically exhibit a Lorentzian response, with additional white noise due to extraneous processes. Least-squares fits of these measurements enable extraction of key parameters of the resonator, including its resonant frequency, quality factor, and stiffness. Here, we present general formulas for the uncertainties in these fit parameters due to sampling noise inherent in all thermal noise spectra. Good agreement with Monte Carlo simulation of synthetic data and measurements of an Atomic Force Microscope (AFM) cantilever is demonstrated. These formulas enable robust interpretation of thermal noise spectra measurements commonly performed in the AFM and adaptive control of fitting procedures with specified tolerances.

Uncertainty in least-squares fits to the thermal noise spectra of nanomechanical resonators with applications to the atomic force microscope

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

Sader, John E., E-mail: jsader@unimelb.edu.au; Yousefi, Morteza; Friend, James R.

2014-02-15

Thermal noise spectra of nanomechanical resonators are used widely to characterize their physical properties. These spectra typically exhibit a Lorentzian response, with additional white noise due to extraneous processes. Least-squares fits of these measurements enable extraction of key parameters of the resonator, including its resonant frequency, quality factor, and stiffness. Here, we present general formulas for the uncertainties in these fit parameters due to sampling noise inherent in all thermal noise spectra. Good agreement with Monte Carlo simulation of synthetic data and measurements of an Atomic Force Microscope (AFM) cantilever is demonstrated. These formulas enable robust interpretation of thermal noisemore » spectra measurements commonly performed in the AFM and adaptive control of fitting procedures with specified tolerances.« less

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].

Vectorlike fermions and Higgs effective field theory revisited

DOE PAGES

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

2017-07-10

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

Physical processes in the strong magnetic fields of accreting neutron stars

NASA Technical Reports Server (NTRS)

Meszaros, P.

1984-01-01

Analytical formulae are fitted to observational data on physical processes occurring in strong magnetic fields surrounding accreting neutron stars. The propagation of normal modes in the presence of a quantizing magnetic field is discussed in terms of a wave equation in Fourier space, quantum electrodynamic effects, polarization and mode ellipticity. The results are applied to calculating the Thomson scattering, bremsstrahlung and Compton scattering cross-sections, which are a function of the frequency, angle and polarization of the magnetic field. Numerical procedures are explored for solving the radiative transfer equations. When applied to modeling X ray pulsars, a problem arises in the necessity to couple the magnetic angle and frequency dependence of the cross-sections with the hydrodynamic equations. The use of time-dependent averaging and approximation techniques is indicated.

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

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

Adachi, Satoshi; Toda, Mikito; Kubotani, Hiroto

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

Analytical modeling of demagnetizing effect in magnetoelectric ferrite/PZT/ferrite trilayers taking into account a mechanical coupling

NASA Astrophysics Data System (ADS)

Loyau, V.; Aubert, A.; LoBue, M.; Mazaleyrat, F.

2017-03-01

In this paper, we investigate the demagnetizing effect in ferrite/PZT/ferrite magnetoelectric (ME) trilayer composites consisting of commercial PZT discs bonded by epoxy layers to Ni-Co-Zn ferrite discs made by a reactive Spark Plasma Sintering (SPS) technique. ME voltage coefficients (transversal mode) were measured on ferrite/PZT/ferrite trilayer ME samples with different thicknesses or phase volume ratio in order to highlight the influence of the magnetic field penetration governed by these geometrical parameters. Experimental ME coefficients and voltages were compared to analytical calculations using a quasi-static model. Theoretical demagnetizing factors of two magnetic discs that interact together in parallel magnetic structures were derived from an analytical calculation based on a superposition method. These factors were introduced in ME voltage calculations which take account of the demagnetizing effect. To fit the experimental results, a mechanical coupling factor was also introduced in the theoretical formula. This reflects the differential strain that exists in the ferrite and PZT layers due to shear effects near the edge of the ME samples and within the bonding epoxy layers. From this study, an optimization in magnitude of the ME voltage is obtained. Lastly, an analytical calculation of demagnetizing effect was conducted for layered ME composites containing higher numbers of alternated layers (n ≥ 5). The advantage of such a structure is then discussed.

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.

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.

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.

MODELING THE NONLINEAR CLUSTERING IN MODIFIED GRAVITY MODELS. I. A FITTING FORMULA FOR THE MATTER POWER SPECTRUM OF f(R) GRAVITY

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

Zhao, Gong-Bo, E-mail: gongbo@icosmology.info; Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX

2014-04-01

Based on a suite of N-body simulations of the Hu-Sawicki model of f(R) gravity with different sets of model and cosmological parameters, we develop a new fitting formula with a numeric code, MGHalofit, to calculate the nonlinear matter power spectrum P(k) for the Hu-Sawicki model. We compare the MGHalofit predictions at various redshifts (z ≤ 1) to the f(R) simulations and find that the relative error of the MGHalofit fitting formula of P(k) is no larger than 6% at k ≤ 1 h Mpc{sup –1} and 12% at k in (1, 10] h Mpc{sup –1}, respectively. Based on a sensitivitymore » study of an ongoing and a future spectroscopic survey, we estimate the detectability of a signal of modified gravity described by the Hu-Sawicki model using the power spectrum up to quasi-nonlinear scales.« less

Quasi-analytical treatment of spatially averaged radiation transfer in complex terrain

NASA Astrophysics Data System (ADS)

Löwe, H.; Helbig, N.

2012-04-01

We provide a new quasi-analytical method to compute the topographic influence on the effective albedo of complex topography as required for meteorological, land-surface or climate models. We investigate radiative transfer in complex terrain via the radiosity equation on isotropic Gaussian random fields. Under controlled approximations we derive expressions for domain averages of direct, diffuse and terrain radiation and the sky view factor. Domain averaged quantities are related to a type of level-crossing probability of the random field which is approximated by longstanding results developed for acoustic scattering at ocean boundaries. This allows us to express all non-local horizon effects in terms of a local terrain parameter, namely the mean squared slope. Emerging integrals are computed numerically and fit formulas are given for practical purposes. As an implication of our approach we provide an expression for the effective albedo of complex terrain in terms of the sun elevation angle, mean squared slope, the area averaged surface albedo, and the direct-to-diffuse ratio of solar radiation. As an application, we compute the effective albedo for the Swiss Alps and discuss possible generalizations of the method.

A quality control method for intensity-modulated radiation therapy planning based on generalized equivalent uniform dose.

PubMed

Pang, Haowen; Sun, Xiaoyang; Yang, Bo; Wu, Jingbo

2018-05-01

To ensure good quality intensity-modulated radiation therapy (IMRT) planning, we proposed the use of a quality control method based on generalized equivalent uniform dose (gEUD) that predicts absorbed radiation doses in organs at risk (OAR). We conducted a retrospective analysis of patients who underwent IMRT for the treatment of cervical carcinoma, nasopharyngeal carcinoma (NPC), or non-small cell lung cancer (NSCLC). IMRT plans were randomly divided into data acquisition and data verification groups. OAR in the data acquisition group for cervical carcinoma and NPC were further classified as sub-organs at risk (sOAR). The normalized volume of sOAR and normalized gEUD (a = 1) were analyzed using multiple linear regression to establish a fitting formula. For NSCLC, the normalized intersection volume of the planning target volume (PTV) and lung, the maximum diameter of the PTV (left-right, anterior-posterior, and superior-inferior), and the normalized gEUD (a = 1) were analyzed using multiple linear regression to establish a fitting formula for the lung gEUD (a = 1). The r-squared and P values indicated that the fitting formula was a good fit. In the data verification group, IMRT plans verified the accuracy of the fitting formula, and compared the gEUD (a = 1) for each OAR between the subjective method and the gEUD-based method. In conclusion, the gEUD-based method can be used effectively for quality control and can reduce the influence of subjective factors on IMRT planning optimization. © 2018 The Authors. Journal of Applied Clinical Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.

Measurement of the top-quark mass in all-jets [Formula: see text] events in pp collisions at [Formula: see text] TeV.

PubMed

Chatrchyan, S; Khachatryan, V; Sirunyan, A M; Tumasyan, A; Adam, W; Bergauer, T; Dragicevic, M; Erö, J; Fabjan, C; Friedl, M; Frühwirth, R; Ghete, V M; Hörmann, N; Hrubec, J; Jeitler, M; Kiesenhofer, W; Knünz, V; Krammer, M; Krätschmer, I; Liko, D; Mikulec, I; Rabady, D; Rahbaran, B; Rohringer, C; Rohringer, H; Schöfbeck, R; Strauss, J; Taurok, A; Treberer-Treberspurg, W; Waltenberger, W; Wulz, C-E; Mossolov, V; Shumeiko, N; Suarez Gonzalez, J; Alderweireldt, S; Bansal, M; Bansal, S; Cornelis, T; De Wolf, E A; Janssen, X; Knutsson, A; Luyckx, S; Mucibello, L; Ochesanu, S; Roland, B; Rougny, R; Van Haevermaet, H; Van Mechelen, P; Van Remortel, N; Van Spilbeeck, A; Blekman, F; Blyweert, S; D'Hondt, J; Kalogeropoulos, A; Keaveney, J; Maes, M; Olbrechts, A; Tavernier, S; Van Doninck, W; Van Mulders, P; Van Onsem, G P; Villella, I; Clerbaux, B; De Lentdecker, G; Favart, L; Gay, A P R; Hreus, T; Léonard, A; Marage, P E; Mohammadi, A; Perniè, L; Reis, T; Seva, T; Thomas, L; Vander Velde, C; Vanlaer, P; Wang, J; Adler, V; Beernaert, K; Benucci, L; Cimmino, A; Costantini, S; Dildick, S; Garcia, G; Klein, B; Lellouch, J; Marinov, A; Mccartin, J; Ocampo Rios, A A; Ryckbosch, D; Sigamani, M; Strobbe, N; Thyssen, F; Tytgat, M; Walsh, S; Yazgan, E; Zaganidis, N; Basegmez, S; Beluffi, C; Bruno, G; Castello, R; Caudron, A; Ceard, L; Delaere, C; du Pree, T; Favart, D; Forthomme, L; Giammanco, A; Hollar, J; Jez, P; Lemaitre, V; Liao, J; Militaru, O; Nuttens, C; Pagano, D; Pin, A; Piotrzkowski, K; Popov, A; Selvaggi, M; Vizan Garcia, J M; Beliy, N; Caebergs, T; Daubie, E; Hammad, G H; Alves, G A; Correa Martins Junior, M; Martins, T; Pol, M E; Souza, M H G; Aldá Júnior, W L; Carvalho, W; Chinellato, J; Custódio, A; Da Costa, E M; De Jesus Damiao, D; De Oliveira Martins, C; Fonseca De Souza, S; Malbouisson, H; Malek, M; Matos Figueiredo, D; Mundim, L; Nogima, H; Prado Da Silva, W L; Santoro, A; Sznajder, A; Tonelli Manganote, E J; Vilela Pereira, A; Bernardes, C A; Dias, F A; Fernandez Perez Tomei, T R; Gregores, E M; Lagana, C; Marinho, F; Mercadante, P G; Novaes, S F; Padula, Sandra S; Genchev, V; Iaydjiev, P; Piperov, S; Rodozov, M; Sultanov, G; Vutova, M; Dimitrov, A; Hadjiiska, R; Kozhuharov, V; Litov, L; Pavlov, B; Petkov, P; Bian, J G; Chen, G M; Chen, H S; Jiang, C H; Liang, D; Liang, S; Meng, X; Tao, J; Wang, J; Wang, X; Wang, Z; Xiao, H; Xu, M; Asawatangtrakuldee, C; Ban, Y; Guo, Y; Li, Q; Li, W; Liu, S; Mao, Y; Qian, S J; Wang, D; Zhang, L; Zou, W; Avila, C; Carrillo Montoya, C A; Gomez, J P; Gomez Moreno, B; Sanabria, J C; Godinovic, N; Lelas, D; Plestina, R; Polic, D; Puljak, I; Antunovic, Z; Kovac, M; Brigljevic, V; Duric, S; Kadija, K; Luetic, J; Mekterovic, D; Morovic, S; Tikvica, L; Attikis, A; Mavromanolakis, G; Mousa, J; Nicolaou, C; Ptochos, F; Razis, P A; Finger, M; Finger, M; Abdelalim, A A; Assran, Y; Ellithi Kamel, A; Mahmoud, M A; Radi, A; Kadastik, M; Müntel, M; Murumaa, M; Raidal, M; Rebane, L; Tiko, A; Eerola, P; Fedi, G; Voutilainen, M; Härkönen, J; Karimäki, V; 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The mass of the top quark is measured using a sample of [Formula: see text] candidate events with at least six jets in the final state. The sample is selected from data collected with the CMS detector in pp collisions at [Formula: see text] TeV in 2011 and corresponds to an integrated luminosity of 3.54 [Formula: see text]. The mass is reconstructed for each event employing a kinematic fit of the jets to a [Formula: see text] hypothesis. The top-quark mass is measured to be [Formula: see text] GeV. A combination with previously published measurements in other decay modes by CMS yields a mass of [Formula: see text] GeV.

Empirical investigation of a field theory formula and Black's formula for the price of an interest-rate caplet

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.; Liang, Cui

2007-01-01

The industry standard for pricing an interest-rate caplet is Black's formula. Another distinct price of the same caplet can be derived using a quantum field theory model of the forward interest rates. An empirical study is carried out to compare the two caplet pricing formulae. Historical volatility and correlation of forward interest rates are used to generate the field theory caplet price; another approach is to fit a parametric formula for the effective volatility using market caplet price. The study shows that the field theory model generates the price of a caplet and cap fairly accurately. Black's formula for a caplet is compared with field theory pricing formula. It is seen that the field theory formula for caplet price has many advantages over Black's formula.

Measurement of the charge asymmetry in top-quark pair production in the lepton-plus-jets final state in pp collision data at [Formula: see text] with the ATLAS detector.

PubMed

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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; Zur Nedden, M; Zurzolo, G; Zwalinski, L

This paper reports inclusive and differential measurements of the [Formula: see text] charge asymmetry [Formula: see text] in [Formula: see text] of [Formula: see text][Formula: see text] collisions recorded by the ATLAS experiment at the Large Hadron Collider at CERN. Three differential measurements are performed as a function of the invariant mass, transverse momentum and longitudinal boost of the [Formula: see text] system. The [Formula: see text] pairs are selected in the single-lepton channels ( e or [Formula: see text]) with at least four jets, and a likelihood fit is used to reconstruct the [Formula: see text] event kinematics. A Bayesian unfolding procedure is performed to infer the asymmetry at parton level from the observed data distribution. The inclusive [Formula: see text] charge asymmetry is measured to be [Formula: see text] (stat. [Formula: see text] syst.). The inclusive and differential measurements are compatible with the values predicted by the Standard Model.

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

PubMed

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

2018-03-21

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

Fitting Item Response Theory Models to Two Personality Inventories: Issues and Insights.

PubMed

Chernyshenko, O S; Stark, S; Chan, K Y; Drasgow, F; Williams, B

2001-10-01

The present study compared the fit of several IRT models to two personality assessment instruments. Data from 13,059 individuals responding to the US-English version of the Fifth Edition of the Sixteen Personality Factor Questionnaire (16PF) and 1,770 individuals responding to Goldberg's 50 item Big Five Personality measure were analyzed. Various issues pertaining to the fit of the IRT models to personality data were considered. We examined two of the most popular parametric models designed for dichotomously scored items (i.e., the two- and three-parameter logistic models) and a parametric model for polytomous items (Samejima's graded response model). Also examined were Levine's nonparametric maximum likelihood formula scoring models for dichotomous and polytomous data, which were previously found to provide good fits to several cognitive ability tests (Drasgow, Levine, Tsien, Williams, & Mead, 1995). The two- and three-parameter logistic models fit some scales reasonably well but not others; the graded response model generally did not fit well. The nonparametric formula scoring models provided the best fit of the models considered. Several implications of these findings for personality measurement and personnel selection were described.

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.

Dynamic characteristics of oxygen consumption.

PubMed

Ye, Lin; Argha, Ahmadreza; Yu, Hairong; Celler, Branko G; Nguyen, Hung T; Su, Steven

2018-04-23

Previous studies have indicated that oxygen uptake ([Formula: see text]) is one of the most accurate indices for assessing the cardiorespiratory response to exercise. In most existing studies, the response of [Formula: see text] is often roughly modelled as a first-order system due to the inadequate stimulation and low signal to noise ratio. To overcome this difficulty, this paper proposes a novel nonparametric kernel-based method for the dynamic modelling of [Formula: see text] response to provide a more robust estimation. Twenty healthy non-athlete participants conducted treadmill exercises with monotonous stimulation (e.g., single step function as input). During the exercise, [Formula: see text] was measured and recorded by a popular portable gas analyser ([Formula: see text], COSMED). Based on the recorded data, a kernel-based estimation method was proposed to perform the nonparametric modelling of [Formula: see text]. For the proposed method, a properly selected kernel can represent the prior modelling information to reduce the dependence of comprehensive stimulations. Furthermore, due to the special elastic net formed by [Formula: see text] norm and kernelised [Formula: see text] norm, the estimations are smooth and concise. Additionally, the finite impulse response based nonparametric model which estimated by the proposed method can optimally select the order and fit better in terms of goodness-of-fit comparing to classical methods. Several kernels were introduced for the kernel-based [Formula: see text] modelling method. The results clearly indicated that the stable spline (SS) kernel has the best performance for [Formula: see text] modelling. Particularly, based on the experimental data from 20 participants, the estimated response from the proposed method with SS kernel was significantly better than the results from the benchmark method [i.e., prediction error method (PEM)] ([Formula: see text] vs [Formula: see text]). The proposed nonparametric modelling method is an effective method for the estimation of the impulse response of VO 2 -Speed system. Furthermore, the identified average nonparametric model method can dynamically predict [Formula: see text] response with acceptable accuracy during treadmill exercise.

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

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus and their use in data fitting.

PubMed

Field, Timothy R; Bain, Alex D

2014-01-01

Even for large quadrupolar interactions, the powder spectrum of the central transition for a half-integral spin is relatively narrow, because it is unperturbed to first order. However, the second-order perturbation is still orientation dependent, so it generates a characteristic lineshape. This lineshape has both finite step discontinuities and singularities where the spectrum is infinite, in theory. The relative positions of these features are well-known and they play an important role in fitting experimental data. However, there has been relatively little discussion of how high the steps are, so we present explicit formulae for these heights. This gives a full characterization of the features in this lineshape which can lead to an analysis of the spectrum without the usual laborious powder average. The transition frequency, as a function of the orientation angles, shows critical points: maxima, minima and saddle points. The maxima and minima correspond to the step discontinuities and the saddle points generate the singularities. Near a maximum, the contours are ellipses, whose dimensions are determined by the second derivatives of the frequency with respect to the polar and azimuthal angles. The density of points is smooth as the contour levels move up and down, but then drops to zero when a maximum is passed, giving a step. The height of the step is determined by the Hessian matrix-the matrix of all partial second derivatives. The points near the poles and the saddle points require a more detailed analysis, but this can still be done analytically. The resulting formulae are then compared to numerical simulations of the lineshape. We expand this calculation to include a relatively simple case where there is chemical shielding anisotropy and use this to fit experimental (139)La spectra of La2O3. Copyright © 2014 Elsevier Inc. All rights reserved.

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.

SU-E-T-120: Analytic Dose Verification for Patient-Specific Proton Pencil Beam Scanning Plans

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

Chang, C; Mah, D

2015-06-15

Purpose: To independently verify the QA dose of proton pencil beam scanning (PBS) plans using an analytic dose calculation model. Methods: An independent proton dose calculation engine is created using the same commissioning measurements as those employed to build our commercially available treatment planning system (TPS). Each proton PBS plan is exported from the TPS in DICOM format and calculated by this independent dose engine in a standard 40 x 40 x 40 cm water tank. This three-dimensional dose grid is then compared with the QA dose calculated by the commercial TPS, using standard Gamma criterion. A total of 18more » measured pristine Bragg peaks, ranging from 100 to 226 MeV, are used in the model. Intermediate proton energies are interpolated. Similarly, optical properties of the spots are measured in air over 15 cm upstream and downstream, and fitted to a second-order polynomial. Multiple Coulomb scattering in water is approximated analytically using Preston and Kohler formula for faster calculation. The effect of range shifters on spot size is modeled with generalized Highland formula. Note that the above formulation approximates multiple Coulomb scattering in water and we therefore chose not use the full Moliere/Hanson form. Results: Initial examination of 3 patient-specific prostate PBS plans shows that agreement exists between 3D dose distributions calculated by the TPS and the independent proton PBS dose calculation engine. Both calculated dose distributions are compared with actual measurements at three different depths per beam and good agreements are again observed. Conclusion: Results here showed that 3D dose distributions calculated by this independent proton PBS dose engine are in good agreement with both TPS calculations and actual measurements. This tool can potentially be used to reduce the amount of different measurement depths required for patient-specific proton PBS QA.« less

Corrigendum to "A semi-empirical airfoil stall noise model based on surface pressure measurements" [J. Sound Vib. 387 (2017) 127-162

NASA Astrophysics Data System (ADS)

Bertagnolio, Franck; Madsen, Helge Aa.; Fischer, Andreas; Bak, Christian

2018-06-01

In the above-mentioned paper, two model formulae were tuned to fit experimental data of surface pressure spectra measured in various wind tunnels. They correspond to high and low Reynolds number flow scalings, respectively. It turns out that there exist typographical errors in both formulae numbered (9) and (10) in the original paper. There, these formulae read:

A Statistical Guide to the Design of Deep Mutational Scanning Experiments

PubMed Central

Matuszewski, Sebastian; Hildebrandt, Marcel E.; Ghenu, Ana-Hermina; Jensen, Jeffrey D.; Bank, Claudia

2016-01-01

The characterization of the distribution of mutational effects is a key goal in evolutionary biology. Recently developed deep-sequencing approaches allow for accurate and simultaneous estimation of the fitness effects of hundreds of engineered mutations by monitoring their relative abundance across time points in a single bulk competition. Naturally, the achievable resolution of the estimated fitness effects depends on the specific experimental setup, the organism and type of mutations studied, and the sequencing technology utilized, among other factors. By means of analytical approximations and simulations, we provide guidelines for optimizing time-sampled deep-sequencing bulk competition experiments, focusing on the number of mutants, the sequencing depth, and the number of sampled time points. Our analytical results show that sampling more time points together with extending the duration of the experiment improves the achievable precision disproportionately compared with increasing the sequencing depth or reducing the number of competing mutants. Even if the duration of the experiment is fixed, sampling more time points and clustering these at the beginning and the end of the experiment increase experimental power and allow for efficient and precise assessment of the entire range of selection coefficients. Finally, we provide a formula for calculating the 95%-confidence interval for the measurement error estimate, which we implement as an interactive web tool. This allows for quantification of the maximum expected a priori precision of the experimental setup, as well as for a statistical threshold for determining deviations from neutrality for specific selection coefficient estimates. PMID:27412710

Measurement of quarkonium production at forward rapidity in [Formula: see text] collisions at [Formula: see text]TeV.

PubMed

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The inclusive production cross sections at forward rapidity of [Formula: see text], [Formula: see text], [Formula: see text](1S) and [Formula: see text](2S) are measured in [Formula: see text] collisions at [Formula: see text] with the ALICE detector at the LHC. The analysis is based on a data sample corresponding to an integrated luminosity of 1.35 pb[Formula: see text]. Quarkonia are reconstructed in the dimuon-decay channel and the signal yields are evaluated by fitting the [Formula: see text] invariant mass distributions. The differential production cross sections are measured as a function of the transverse momentum [Formula: see text] and rapidity [Formula: see text], over the ranges [Formula: see text] GeV/c for [Formula: see text], [Formula: see text] GeV/c for all other resonances and for [Formula: see text]. The measured cross sections integrated over [Formula: see text] and [Formula: see text], and assuming unpolarized quarkonia, are: [Formula: see text] [Formula: see text]b, [Formula: see text] [Formula: see text]b, [Formula: see text] nb and [Formula: see text] nb, where the first uncertainty is statistical and the second one is systematic. The results are compared to measurements performed by other LHC experiments and to theoretical models.

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.

Observation of the diphoton decay of the Higgs boson and measurement of its properties.

PubMed

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Observation of the diphoton decay mode of the recently discovered Higgs boson and measurement of some of its properties are reported. The analysis uses the entire dataset collected by the CMS experiment in proton-proton collisions during the 2011 and 2012 LHC running periods. The data samples correspond to integrated luminosities of 5.1[Formula: see text]at [Formula: see text] and 19.7[Formula: see text]at 8[Formula: see text] . A clear signal is observed in the diphoton channel at a mass close to 125[Formula: see text] with a local significance of [Formula: see text], where a significance of [Formula: see text] is expected for the standard model Higgs boson. The mass is measured to be [Formula: see text] , and the best-fit signal strength relative to the standard model prediction is [Formula: see text][Formula: see text][Formula: see text]. Additional measurements include the signal strength modifiers associated with different production mechanisms, and hypothesis tests between spin-0 and spin-2 models.

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.

Mathematical Storage-Battery Models

NASA Technical Reports Server (NTRS)

Chapman, C. P.; Aston, M.

1985-01-01

Empirical formula represents performance of electrical storage batteries. Formula covers many battery types and includes numerous coefficients adjusted to fit peculiarities of each type. Battery and load parameters taken into account include power density in battery, discharge time, and electrolyte temperature. Applications include electric-vehicle "fuel" gages and powerline load leveling.

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

PubMed Central

Zhou, Chenming

2017-01-01

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

Bulk diffusion in a kinetically constrained lattice gas

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Analysis of sustainable pest control using a pesticide and a screened refuge.

PubMed

Ringland, John; George, Prasanth

2011-05-01

We describe and analyze a 'screened refuge' technique for indefinitely sustaining control of insect pests using transgenic pesticidal crops or an applied pesticide, even when resistance is not recessive. The screen is a physical barrier that restricts pest movement. In a deterministic discrete-time model of the use of this technique, we obtain asymptotic analytical formulas for the two important equilibria of the system in terms of the refuge size and the pest fitnesses, mutation rates, and mobility out of and into the refuge. One of the equilibria is stable and is the point at which the pest population is controlled. The other is a saddle whose stable manifold bounds the basin of attraction of the former: its location provides a measure of the tolerance of the control mechanism to perturbations in the resistant allele density.

Barrier modification in sub-barrier fusion reaction 64Ni+100Mo using Wong formula with Skyrme forces in semiclassical formalism

NASA Astrophysics Data System (ADS)

Kumar, Raj; Gupta, Raj K.

2011-09-01

We obtain the nuclear proximity potential by using semiclassical extended Thomas Fermi (ETF) approach in Skyrme energy density formalism (SEDF), and use it in the extended l-summed Wong formula under frozen density approximation. This method has the advantage of allowing the use of different Skyrme forces, giving different barriers. Thus, for a given reaction, we could choose a Skyrme force with proper barrier characteristics, not-requiring extra "barrier lowering" or "barrier narrowing" for a best fit to data. For the 64Ni+100Mo reaction, the l-summed Wong formula, with effects of deformations and orientations of nuclei included, fits the fusion-evaporation cross section data exactly for the force GSkI, requiring additional barrier modifications for forces SIII and SV. However, the same for other similar reactions, like 58,64Ni+58,64Ni, fit the data best for SIII force. Hence, the barrier modification effects in l-summed Wong expression depend on the choice of Skyrme force in semiclassical ETF method.

Study of the [Formula: see text] and [Formula: see text] decays with the ATLAS detector.

PubMed

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The decays [Formula: see text] and [Formula: see text] are studied with the ATLAS detector at the LHC using a dataset corresponding to integrated luminosities of 4.9 and 20.6 fb[Formula: see text] of pp collisions collected at centre-of-mass energies [Formula: see text] TeV and 8 TeV, respectively. Signal candidates are identified through [Formula: see text] and [Formula: see text] decays. With a two-dimensional likelihood fit involving the [Formula: see text] reconstructed invariant mass and an angle between the [Formula: see text] and [Formula: see text] candidate momenta in the muon pair rest frame, the yields of [Formula: see text] and [Formula: see text], and the transverse polarisation fraction in [Formula: see text] decay are measured. The transverse polarisation fraction is determined to be [Formula: see text], and the derived ratio of the branching fractions of the two modes is [Formula: see text], where the first error is statistical and the second is systematic. Finally, a sample of [Formula: see text] decays is used to derive the ratios of branching fractions [Formula: see text] and [Formula: see text], where the third error corresponds to the uncertainty of the branching fraction of [Formula: see text] decay. The available theoretical predictions are generally consistent with the measurement.

Creating a non-linear total sediment load formula using polynomial best subset regression model

NASA Astrophysics Data System (ADS)

Okcu, Davut; Pektas, Ali Osman; Uyumaz, Ali

2016-08-01

The aim of this study is to derive a new total sediment load formula which is more accurate and which has less application constraints than the well-known formulae of the literature. 5 most known stream power concept sediment formulae which are approved by ASCE are used for benchmarking on a wide range of datasets that includes both field and flume (lab) observations. The dimensionless parameters of these widely used formulae are used as inputs in a new regression approach. The new approach is called Polynomial Best subset regression (PBSR) analysis. The aim of the PBRS analysis is fitting and testing all possible combinations of the input variables and selecting the best subset. Whole the input variables with their second and third powers are included in the regression to test the possible relation between the explanatory variables and the dependent variable. While selecting the best subset a multistep approach is used that depends on significance values and also the multicollinearity degrees of inputs. The new formula is compared to others in a holdout dataset and detailed performance investigations are conducted for field and lab datasets within this holdout data. Different goodness of fit statistics are used as they represent different perspectives of the model accuracy. After the detailed comparisons are carried out we figured out the most accurate equation that is also applicable on both flume and river data. Especially, on field dataset the prediction performance of the proposed formula outperformed the benchmark formulations.

Band head spin assignment of superdeformed bands in 133Pr using two-parameter formulae

NASA Astrophysics Data System (ADS)

Sharma, Honey; Mittal, H. M.

2018-03-01

The two-parameter formulae viz. the power index formula, the nuclear softness formula and the VMI model are adopted to accredit the band head spin (I0) of four superdeformed rotational bands in 133Pr. The technique of least square fitting is used to accredit the band head spin for four superdeformed rotational bands in 133Pr. The root mean deviation among the computed transition energies and well-known experimental transition energies are attained by extracting the model parameters from the two-parameter formulae. The determined transition energies are in excellent agreement with the experimental transition energies, whenever exact spins are accredited. The power index formula coincides well with the experimental data and provides minimum root mean deviation. So, the power index formula is more efficient tool than the nuclear softness formula and the VMI model. The deviation of dynamic moment of inertia J(2) against the rotational frequency is also examined.

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

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

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

A three-time-point method for assessing kinetic parameters of 64Cu-labeled Ramucirumab trapping in VEGFR-2 positive lung tumors.

PubMed

Laffon, Eric; Marthan, Roger

2017-11-01

To describe a three-time-point method for estimating kinetic parameters involved in 64 Cu-labeled Ramucirumab ( 64 Cu-NOTA-RamAb) trapping of VEGFR-2 positive lung tumors. Positron emission tomography (microPET) data of tumor-bearing mice for 64 Cu-NOTA-RamAb trapping in VEGFR-2 positive HCC4006 tumor were used, involving tissue activity measurements acquired at 3, 24 and 48 h post-injection, without and with administration of RamAb blocking dose. A kinetic model provided an analytical formula describing the tissue time-activity-curve, involving 64 Cu-NOTA-RamAb uptake (Ki), release rate constant (k R ) and fraction of free tracer in blood and interstitial volume (F). Fitting analytical formula outcomes on mean microPET data yielded values of the kinetic parameters: Ki = 0.0314/0.0123 gram of blood per hour per gram of tissue, k R  = 0.0387/0.0313 h -1 and F = 0.2075/0.2007 gram of blood per gram of tissue, without/with RamAb blocking dose, respectively (R = 0.99999 for the graph displaying microPET versus theoretical data; P < .01). Three independent kinetic parameters (Ki, k R and F) can be assessed from three data points acquired at early, mid and late imaging, i.e., at 3, 24 and 48 h post-injection, for further characterization of 64 Cu-NOTA-RamAb trapping in VEGFR-2 positive lung tumors. Copyright © 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

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

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

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

PubMed

Godfrey, A Ruth; Brenton, A Gareth

2012-09-01

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

Theory and Circuit Model for Lossy Coaxial Transmission Line

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

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

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

Xu, Yonggen

2014-11-01

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

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.

Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems.

PubMed

Guérin, T; Dean, D S

2015-12-01

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

Dispersive analysis of the pion transition form factor.

PubMed

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

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Derivation of a formula for the resonance integral for a nonorthogonal basis set

PubMed Central

Yim, Yung-Chang; Eyring, Henry

1981-01-01

In a self-consistent field calculation, a formula for the off-diagonal matrix elements of the core Hamiltonian is derived for a nonorthogonal basis set by a polyatomic approach. A set of parameters is then introduced for the repulsion integral formula of Mataga-Nishimoto to fit the experimental data. The matrix elements computed for the nonorthogonal basis set in the π-electron approximation are transformed to those for an orthogonal basis set by the Löwdin symmetrical orthogonalization. PMID:16593009

Simple Physics-Based Analytical Formulas for the Potentials of Mean Force of the Interaction of Amino Acid Side Chains in Water. VII. Charged-Hydrophobic/Polar and Polar-Hydrophobic/Polar Side Chains.

PubMed

Makowski, Mariusz; Liwo, Adam; Scheraga, Harold A

2017-01-19

The physics-based potentials of side-chain-side-chain interactions corresponding to pairs composed of charged and polar, polar and polar, charged and hydrophobic, and hydrophobic and hydrophobic side chains have been determined. A total of 144 four-dimensional potentials of mean force (PMFs) of all possible pairs of molecules modeling these pairs were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation, and the analytical expressions were then fitted to the PMFs. Depending on the type of interacting sites, the analytical approximation to the PMF is a sum of terms corresponding to van der Waals interactions and cavity-creation involving the nonpolar sections of the side chains and van der Waals, cavity-creation, and electrostatic (charge-dipole or dipole-dipole) interaction energies and polarization energies involving the charged or polar sections of the side chains. The model used in this work reproduces all features of the interacting pairs. The UNited RESidue force field with the new side-chain-side-chain interaction potentials was preliminarily tested with the N-terminal part of the B-domain of staphylococcal protein A (PDBL 1BDD ; a three-α-helix bundle) and UPF0291 protein YnzC from Bacillus subtilis (PDB: 2HEP ; an α-helical hairpin).

Who gets how much: funding formulas in federal public health programs.

PubMed

Buehler, James W; Holtgrave, David R

2007-01-01

Federal public health programs use a mix of formula-based and competitive methods to allocate funds among states and other constituent jurisdictions. Characteristics of formula-based allocations used by a convenience sample of four programs, three from the Centers for Disease Control and Prevention and one from the Health Resources and Services Administration, are described to illustrate formula-based allocation methods in public health. Data sources in these public health formulas include population counts and funding proportions based on historical precedent. None include factors that adjust allocations based on variations in the availability of local resources or the cost of delivering services. Formula-funded activities are supplemented by programs that target specific prevention needs or encourage development of innovative methods to address emerging problems, using set-aside funds. A public health finance research agenda should address ways to improve the fit between funding allocation formulas and program objectives.

A Survey of Xenon Ion Sputter Yield Data and Fits Relevant to Electric Propulsion Spacecraft Integration

NASA Technical Reports Server (NTRS)

Yim, John T.

2017-01-01

A survey of low energy xenon ion impact sputter yields was conducted to provide a more coherent baseline set of sputter yield data and accompanying fits for electric propulsion integration. Data uncertainties are discussed and different available curve fit formulas are assessed for their general suitability. A Bayesian parameter fitting approach is used with a Markov chain Monte Carlo method to provide estimates for the fitting parameters while characterizing the uncertainties for the resulting yield curves.

The mathematical formula of the intravaginal ejaculation latency time (IELT) distribution of lifelong premature ejaculation differs from the IELT distribution formula of men in the general male population

PubMed Central

Janssen, Paddy K.C.

2016-01-01

Purpose To find the most accurate mathematical description of the intravaginal ejaculation latency time (IELT) distribution in the general male population. Materials and Methods We compared the fitness of various well-known mathematical distributions with the IELT distribution of two previously published stopwatch studies of the Caucasian general male population and a stopwatch study of Dutch Caucasian men with lifelong premature ejaculation (PE). The accuracy of fitness is expressed by the Goodness of Fit (GOF). The smaller the GOF, the more accurate is the fitness. Results The 3 IELT distributions are gamma distributions, but the IELT distribution of lifelong PE is another gamma distribution than the IELT distribution of men in the general male population. The Lognormal distribution of the gamma distributions most accurately fits the IELT distribution of 965 men in the general population, with a GOF of 0.057. The Gumbel Max distribution most accurately fits the IELT distribution of 110 men with lifelong PE with a GOF of 0.179. There are more men with lifelong PE ejaculating within 30 and 60 seconds than can be extrapolated from the probability density curve of the Lognormal IELT distribution of men in the general population. Conclusions Men with lifelong PE have a distinct IELT distribution, e.g., a Gumbel Max IELT distribution, that can only be retrieved from the general male population Lognormal IELT distribution when thousands of men would participate in a IELT stopwatch study. The mathematical formula of the Lognormal IELT distribution is useful for epidemiological research of the IELT. PMID:26981594

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

PubMed

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

2013-12-15

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

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

NASA Astrophysics Data System (ADS)

Vaeth, H. M.; Chanmugam, G.

1995-05-01

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

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

PubMed

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

2017-01-01

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

A Statistical Guide to the Design of Deep Mutational Scanning Experiments.

PubMed

Matuszewski, Sebastian; Hildebrandt, Marcel E; Ghenu, Ana-Hermina; Jensen, Jeffrey D; Bank, Claudia

2016-09-01

The characterization of the distribution of mutational effects is a key goal in evolutionary biology. Recently developed deep-sequencing approaches allow for accurate and simultaneous estimation of the fitness effects of hundreds of engineered mutations by monitoring their relative abundance across time points in a single bulk competition. Naturally, the achievable resolution of the estimated fitness effects depends on the specific experimental setup, the organism and type of mutations studied, and the sequencing technology utilized, among other factors. By means of analytical approximations and simulations, we provide guidelines for optimizing time-sampled deep-sequencing bulk competition experiments, focusing on the number of mutants, the sequencing depth, and the number of sampled time points. Our analytical results show that sampling more time points together with extending the duration of the experiment improves the achievable precision disproportionately compared with increasing the sequencing depth or reducing the number of competing mutants. Even if the duration of the experiment is fixed, sampling more time points and clustering these at the beginning and the end of the experiment increase experimental power and allow for efficient and precise assessment of the entire range of selection coefficients. Finally, we provide a formula for calculating the 95%-confidence interval for the measurement error estimate, which we implement as an interactive web tool. This allows for quantification of the maximum expected a priori precision of the experimental setup, as well as for a statistical threshold for determining deviations from neutrality for specific selection coefficient estimates. Copyright © 2016 by the Genetics Society of America.

Queues with Dropping Functions and General Arrival Processes

PubMed Central

Chydzinski, Andrzej; Mrozowski, Pawel

2016-01-01

In a queueing system with the dropping function the arriving customer can be denied service (dropped) with the probability that is a function of the queue length at the time of arrival of this customer. The potential applicability of such mechanism is very wide due to the fact that by choosing the shape of this function one can easily manipulate several performance characteristics of the queueing system. In this paper we carry out analysis of the queueing system with the dropping function and a very general model of arrival process—the model which includes batch arrivals and the interarrival time autocorrelation, and allows for fitting the actual shape of the interarrival time distribution and its moments. For such a system we obtain formulas for the distribution of the queue length and the overall customer loss ratio. The analytical results are accompanied with numerical examples computed for several dropping functions. PMID:26943171

The entrainment matrix of a superfluid nucleon mixture at finite temperatures

NASA Astrophysics Data System (ADS)

Leinson, Lev B.

2018-06-01

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

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.

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

NASA Astrophysics Data System (ADS)

Cai, Yangjian; Zhang, Lei

2006-07-01

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

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

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

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

1980-09-01

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

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.

Running coupling constant from lattice studies of gluon and ghost propagators

NASA Astrophysics Data System (ADS)

Cucchieri, A.; Mendes, T.

2004-12-01

We present a numerical study of the running coupling constant in four-dimensional pure-SU(2) lattice gauge theory. The running coupling is evaluated by fitting data for the gluon and ghost propagators in minimal Landau gauge. Following Refs. [1, 2], the fitting formulae are obtained by a simultaneous integration of the β function and of a function coinciding with the anomalous dimension of the propagator in the momentum subtraction scheme. We consider these formulae at three and four loops. The fitting method works well, especially for the ghost case, for which statistical error and hyper-cubic effects are very small. Our present result for ΛMS is 200-40+60 MeV, where the error is purely systematic. We are currently extending this analysis to five loops in order to reduce this systematic error.

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.

AN EMPIRICAL FORMULA FOR THE DISTRIBUTION FUNCTION OF A THIN EXPONENTIAL DISC

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

Sharma, Sanjib; Bland-Hawthorn, Joss

2013-08-20

An empirical formula for a Shu distribution function that reproduces a thin disc with exponential surface density to good accuracy is presented. The formula has two free parameters that specify the functional form of the velocity dispersion. Conventionally, this requires the use of an iterative algorithm to produce the correct solution, which is computationally taxing for applications like Markov Chain Monte Carlo model fitting. The formula has been shown to work for flat, rising, and falling rotation curves. Application of this methodology to one of the Dehnen distribution functions is also shown. Finally, an extension of this formula to reproducemore » velocity dispersion profiles that are an exponential function of radius is also presented. Our empirical formula should greatly aid the efficient comparison of disc models with large stellar surveys or N-body simulations.« less

Parameterization of fission barrier heights of medium, heavy and super heavy nuclei

NASA Astrophysics Data System (ADS)

Manjunatha, H. C.

2017-12-01

A new semi empirical formula is proposed for fission barrier heights of medium, heavy and super heavy nuclei in the atomic number region 50 ≤ Z ≤ 130. The fitting parameters for the proposed formula are obtained by making a polynomial fit to the available theoretical and experimental data. The calculated fission barrier heights are compared with that of experiments and other theoretical models such as SHF(SLy6) (Burvenich et al. in Phys Rev C 69:014307, 2004), SHFB(SkM) (Baran et al. in Nucl Phys A 944:442, 2015), FRLDM (Möller et al. in Phys Rev C 79:064304, 2009), ETFSI (SkSC4) with Skyrme SkSC4 force (Mamdouh et al. in Nucl Phys A 679:337, 2001), WS (Kowal et al. in Phys Rev C 82:014303, 2010) and CDFT(DD-ME2) (Abusara et al. in Phys Rev C 85:024314, 2012). The standard deviation for fission barrier heights produced by present formula is evaluated. The good agreement of present formula with the experiments and other models suggests that the present formula could be used to evaluate the fission barrier heights of medium, heavy and super heavy nuclei in the region 50 ≤ Z ≤ 130. This formula is a first of its kind that produces fission barrier heights of 2858 nuclei with the only simple inputs of only neutron number (N), proton number (Z) and mass number (A).

Parameterization of fission barrier heights of medium, heavy and super heavy nuclei

NASA Astrophysics Data System (ADS)

Manjunatha, H. C.

2018-04-01

A new semi empirical formula is proposed for fission barrier heights of medium, heavy and super heavy nuclei in the atomic number region 50 ≤ Z ≤ 130. The fitting parameters for the proposed formula are obtained by making a polynomial fit to the available theoretical and experimental data. The calculated fission barrier heights are compared with that of experiments and other theoretical models such as SHF(SLy6) (Burvenich et al. in Phys Rev C 69:014307, 2004), SHFB(SkM) (Baran et al. in Nucl Phys A 944:442, 2015), FRLDM (Möller et al. in Phys Rev C 79:064304, 2009), ETFSI (SkSC4) with Skyrme SkSC4 force (Mamdouh et al. in Nucl Phys A 679:337, 2001), WS (Kowal et al. in Phys Rev C 82:014303, 2010) and CDFT(DD-ME2) (Abusara et al. in Phys Rev C 85:024314, 2012). The standard deviation for fission barrier heights produced by present formula is evaluated. The good agreement of present formula with the experiments and other models suggests that the present formula could be used to evaluate the fission barrier heights of medium, heavy and super heavy nuclei in the region 50 ≤ Z ≤ 130. This formula is a first of its kind that produces fission barrier heights of 2858 nuclei with the only simple inputs of only neutron number (N), proton number (Z) and mass number (A).

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

Anxiety symptom interpretation: A potential mechanism explaining the cardiorespiratory fitness-anxiety relationship.

PubMed

Williams, Sarah E; Carroll, Douglas; Veldhuijzen van Zanten, Jet J C S; Ginty, Annie T

2016-03-15

Higher cardiorespiratory fitness is associated with lower trait anxiety, but research has not examined whether fitness is associated with state anxiety levels and the interpretation of these symptoms. The aim of this paper was to (1) reexamine the association between cardiorespiratory fitness and general anxiety and (2) examine anxiety intensity and perceptions of these symptoms prior to an acute psychological stress task. Participants (N=185; 81% female; Mage=18.04, SD=0.43 years) completed a 10-minute Paced Serial Addition Test. General anxiety was assessed using the anxiety subscale of the Hospital Anxiety Depression Scale. Cognitive and somatic anxiety intensity and perceptions of symptoms was assessed immediately prior to the acute psychological stress task using the Immediate Anxiety Measures Scale. Cardiorespiratory fitness was calculated using a validated standardized formula. Higher levels of cardiorespiratory fitness were associated with lower levels of general anxiety. Path analysis supported a model whereby perceptions of anxiety symptoms mediated the relationship between cardiorespiratory fitness and levels of anxiety experienced during the stress task; results remained significant after adjusting for general anxiety levels. Specifically, higher levels of cardiorespiratory fitness were positively associated with more positive perceptions of anxiety symptoms and lower levels of state anxiety. A standard formula rather than maximal testing was used to assess cardiorespiratory fitness, self-report questionnaires were used to assess anxiety, and the study was cross-sectional in design. Results suggest a potential mechanism explaining how cardiorespiratory fitness can reduce anxiety levels. Copyright © 2016 Elsevier B.V. All rights reserved.

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.

Using weighted power mean for equivalent square estimation.

PubMed

Zhou, Sumin; Wu, Qiuwen; Li, Xiaobo; Ma, Rongtao; Zheng, Dandan; Wang, Shuo; Zhang, Mutian; Li, Sicong; Lei, Yu; Fan, Qiyong; Hyun, Megan; Diener, Tyler; Enke, Charles

2017-11-01

Equivalent Square (ES) enables the calculation of many radiation quantities for rectangular treatment fields, based only on measurements from square fields. While it is widely applied in radiotherapy, its accuracy, especially for extremely elongated fields, still leaves room for improvement. In this study, we introduce a novel explicit ES formula based on Weighted Power Mean (WPM) function and compare its performance with the Sterling formula and Vadash/Bjärngard's formula. The proposed WPM formula is ESWPMa,b=waα+1-wbα1/α for a rectangular photon field with sides a and b. The formula performance was evaluated by three methods: standard deviation of model fitting residual error, maximum relative model prediction error, and model's Akaike Information Criterion (AIC). Testing datasets included the ES table from British Journal of Radiology (BJR), photon output factors (S cp ) from the Varian TrueBeam Representative Beam Data (Med Phys. 2012;39:6981-7018), and published S cp data for Varian TrueBeam Edge (J Appl Clin Med Phys. 2015;16:125-148). For the BJR dataset, the best-fit parameter value α = -1.25 achieved a 20% reduction in standard deviation in ES estimation residual error compared with the two established formulae. For the two Varian datasets, employing WPM reduced the maximum relative error from 3.5% (Sterling) or 2% (Vadash/Bjärngard) to 0.7% for open field sizes ranging from 3 cm to 40 cm, and the reduction was even more prominent for 1 cm field sizes on Edge (J Appl Clin Med Phys. 2015;16:125-148). The AIC value of the WPM formula was consistently lower than its counterparts from the traditional formulae on photon output factors, most prominent on very elongated small fields. The WPM formula outperformed the traditional formulae on three testing datasets. With increasing utilization of very elongated, small rectangular fields in modern radiotherapy, improved photon output factor estimation is expected by adopting the WPM formula in treatment planning and secondary MU check. © 2017 The Authors. Journal of Applied Clinical Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.

Arbitrarily accurate twin composite π -pulse sequences

NASA Astrophysics Data System (ADS)

Torosov, Boyan T.; Vitanov, Nikolay V.

2018-04-01

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

Analytical pricing formulas for hybrid variance swaps with regime-switching

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

PubMed

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

2013-06-01

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

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

PubMed

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

2015-11-01

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

Two-photon microscopy measurement of cerebral metabolic rate of oxygen using periarteriolar oxygen concentration gradients.

PubMed

Sakadžić, Sava; Yaseen, Mohammad A; Jaswal, Rajeshwer; Roussakis, Emmanuel; Dale, Anders M; Buxton, Richard B; Vinogradov, Sergei A; Boas, David A; Devor, Anna

2016-10-01

The cerebral metabolic rate of oxygen ([Formula: see text]) is an essential parameter for evaluating brain function and pathophysiology. However, the currently available approaches for quantifying [Formula: see text] rely on complex multimodal imaging and mathematical modeling. Here, we introduce a method that allows estimation of [Formula: see text] based on a single measurement modality-two-photon imaging of the partial pressure of oxygen ([Formula: see text]) in cortical tissue. We employed two-photon phosphorescence lifetime microscopy (2PLM) and the oxygen-sensitive nanoprobe PtP-C343 to map the tissue [Formula: see text] distribution around cortical penetrating arterioles. [Formula: see text] is subsequently estimated by fitting the changes of tissue [Formula: see text] around arterioles with the Krogh cylinder model of oxygen diffusion. We measured the baseline [Formula: see text] in anesthetized rats and modulated tissue [Formula: see text] levels by manipulating the depth of anesthesia. This method provides [Formula: see text] measurements localized within [Formula: see text] and it may provide oxygen consumption measurements in individual cortical layers or within confined cortical regions, such as in ischemic penumbra and the foci of functional activation.

Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8[Formula: see text].

PubMed

Khachatryan, V; Sirunyan, A M; Tumasyan, A; Adam, W; Bergauer, T; Dragicevic, M; Erö, J; Friedl, M; Frühwirth, R; Ghete, V M; Hartl, C; Hörmann, N; Hrubec, J; Jeitler, M; Kiesenhofer, W; Knünz, V; Krammer, M; Krätschmer, I; Liko, D; Mikulec, I; Rabady, D; Rahbaran, B; Rohringer, H; Schöfbeck, R; Strauss, J; Treberer-Treberspurg, W; Waltenberger, W; Wulz, C-E; Mossolov, V; Shumeiko, N; Suarez Gonzalez, J; Alderweireldt, S; Bansal, S; Cornelis, T; De Wolf, E A; Janssen, X; Knutsson, A; Lauwers, J; Luyckx, S; Ochesanu, S; Rougny, R; Van De Klundert, M; Van Haevermaet, H; Van Mechelen, P; Van Remortel, N; Van Spilbeeck, A; Blekman, F; Blyweert, S; D'Hondt, J; Daci, N; Heracleous, N; Keaveney, J; Lowette, S; Maes, M; Olbrechts, A; Python, Q; Strom, D; Tavernier, S; Van Doninck, W; Van Mulders, P; Van Onsem, G P; Villella, I; Caillol, C; Clerbaux, B; De Lentdecker, G; Dobur, D; Favart, L; Gay, A P R; Grebenyuk, A; Léonard, A; Mohammadi, A; Perniè, L; Randle-Conde, A; Reis, T; Seva, T; Thomas, L; Vander Velde, C; Vanlaer, P; Wang, J; Zenoni, F; Adler, V; Beernaert, K; Benucci, L; Cimmino, A; Costantini, S; Crucy, S; Fagot, A; Garcia, G; Mccartin, J; Ocampo Rios, A A; Poyraz, D; Ryckbosch, D; Salva Diblen, S; Sigamani, M; Strobbe, N; Thyssen, F; Tytgat, M; Yazgan, E; Zaganidis, N; Basegmez, S; Beluffi, C; Bruno, G; Castello, R; Caudron, A; Ceard, L; Da Silveira, G G; Delaere, C; du Pree, T; Favart, D; Forthomme, L; Giammanco, A; Hollar, J; Jafari, A; Jez, P; Komm, M; Lemaitre, V; Nuttens, C; Pagano, D; Perrini, L; Pin, A; Piotrzkowski, K; Popov, A; Quertenmont, L; Selvaggi, M; Vidal Marono, M; Vizan Garcia, J M; Beliy, N; Caebergs, T; Daubie, E; Hammad, G H; Júnior, W L Aldá; Alves, G A; Brito, L; Correa Martins Junior, M; Martins, T Dos Reis; Molina, J; Mora Herrera, C; Pol, M E; Teles, P Rebello; Carvalho, W; Chinellato, J; Custódio, A; Da Costa, E M; De Jesus Damiao, D; De Oliveira Martins, C; Fonseca De Souza, S; Malbouisson, H; Matos Figueiredo, D; Mundim, L; Nogima, H; Prado Da Silva, W L; Santaolalla, J; Santoro, A; Sznajder, A; Tonelli Manganote, E J; Vilela Pereira, A; Bernardes, C A; Dogra, S; Fernandez Perez Tomei, T R; Gregores, E M; Mercadante, P G; Novaes, S F; Padula, Sandra S; Aleksandrov, A; Genchev, V; Hadjiiska, R; Iaydjiev, P; Marinov, A; Piperov, S; Rodozov, M; Stoykova, S; Sultanov, G; Vutova, M; Dimitrov, A; Glushkov, I; Litov, L; Pavlov, B; Petkov, P; Bian, J G; Chen, G M; Chen, H S; Chen, M; Cheng, T; Du, R; Jiang, C H; Plestina, R; Romeo, F; Tao, J; Wang, Z; Asawatangtrakuldee, C; Ban, Y; Liu, S; Mao, Y; Qian, S J; Wang, D; Xu, Z; Zhang, F; Zhang, L; Zou, W; Avila, C; Cabrera, A; Chaparro Sierra, L F; Florez, C; Gomez, J P; Gomez Moreno, B; Sanabria, J C; Godinovic, N; Lelas, D; Polic, D; Puljak, I; Antunovic, Z; Kovac, M; Brigljevic, V; Kadija, K; Luetic, J; Mekterovic, D; Sudic, L; Attikis, A; Mavromanolakis, G; Mousa, J; Nicolaou, C; Ptochos, F; Razis, P A; Rykaczewski, H; Bodlak, M; Finger, M; Finger, M; Assran, Y; Ellithi Kame, A; Mahmoud, M A; Radi, A; Kadastik, M; Murumaa, M; Raidal, M; Tiko, A; Eerola, P; Voutilainen, M; Härkönen, J; Heikkilä, J K; Karimäki, V; Kinnunen, R; Kortelainen, M J; Lampén, T; Lassila-Perini, K; Lehti, S; Lindén, T; Luukka, P; Mäenpää, T; Peltola, T; Tuominen, E; Tuominiemi, J; Tuovinen, E; Wendland, L; Talvitie, J; Tuuva, T; Besancon, M; Couderc, F; Dejardin, M; Denegri, D; Fabbro, B; Faure, J L; Favaro, C; Ferri, F; Ganjour, S; Givernaud, A; Gras, P; Hamel de Monchenault, G; Jarry, P; Locci, E; Malcles, J; Rander, J; Rosowsky, A; Titov, M; Baffioni, S; Beaudette, F; Busson, P; Chapon, E; Charlot, C; Dahms, T; Dobrzynski, L; Filipovic, N; Florent, A; Granier de Cassagnac, R; Mastrolorenzo, L; Miné, P; Naranjo, I N; Nguyen, M; Ochando, C; Ortona, G; Paganini, P; Regnard, S; Salerno, R; Sauvan, J B; Sirois, Y; Veelken, C; Yilmaz, Y; Zabi, A; Agram, J-L; Andrea, J; Aubin, A; Bloch, D; Brom, J-M; Chabert, E C; Collard, C; Conte, E; Fontaine, J-C; Gelé, D; Goerlach, U; Goetzmann, C; Le Bihan, A-C; Skovpen, K; Van Hove, P; Gadrat, S; Beauceron, S; Beaupere, N; Bernet, C; Boudoul, G; Bouvier, E; Brochet, S; Carrillo Montoya, C A; Chasserat, J; Chierici, R; Contardo, D; Courbon, B; Depasse, P; El Mamouni, H; Fan, J; Fay, J; Gascon, S; Gouzevitch, M; Ille, B; Kurca, T; Lethuillier, M; Mirabito, L; Pequegnot, A L; Perries, S; Ruiz Alvarez, J D; Sabes, D; Sgandurra, L; Sordini, V; Vander Donckt, M; Verdier, P; Viret, S; Xiao, H; Tsamalaidze, Z; Autermann, C; Beranek, S; Bontenackels, M; Edelhoff, M; Feld, L; Heister, A; Klein, K; Lipinski, M; Ostapchuk, A; Preuten, M; Raupach, F; Sammet, J; Schael, S; Schulte, J F; Weber, H; Wittmer, B; Zhukov, V; Ata, M; Brodski, M; Dietz-Laursonn, E; Duchardt, D; Erdmann, M; Fischer, R; Güth, A; Hebbeker, T; Heidemann, C; Hoepfner, K; Klingebiel, D; Knutzen, S; Kreuzer, P; Merschmeyer, M; Meyer, A; Millet, P; Olschewski, M; Padeken, K; Papacz, P; Reithler, H; Schmitz, S A; Sonnenschein, L; Teyssier, D; Thüer, S; Cherepanov, V; Erdogan, Y; Flügge, G; Geenen, H; Geisler, M; Haj Ahmad, W; Hoehle, F; Kargoll, B; Kress, T; Kuessel, Y; Künsken, A; Lingemann, J; Nowack, A; Nugent, I M; Pistone, C; Pooth, O; Stahl, A; Aldaya Martin, M; Asin, I; Bartosik, N; Behr, J; Behrens, U; Bell, A J; Bethani, A; Borras, K; Burgmeier, A; Cakir, A; Calligaris, L; Campbell, A; Choudhury, S; Costanza, F; Diez Pardos, C; Dolinska, G; Dooling, S; Dorland, T; Eckerlin, G; Eckstein, D; Eichhorn, T; Flucke, G; Garcia, J Garay; Geiser, A; Gizhko, A; Gunnellini, P; Hauk, J; Hempel, M; Jung, H; Kalogeropoulos, A; Karacheban, O; Kasemann, M; Katsas, P; Kieseler, J; Kleinwort, C; Korol, I; Krücker, D; Lange, W; Leonard, J; Lipka, K; Lobanov, A; Lohmann, W; Lutz, B; Mankel, R; Marfin, I; Melzer-Pellmann, I-A; Meyer, A B; Mittag, G; Mnich, J; Mussgiller, A; Naumann-Emme, S; Nayak, A; Ntomari, E; Perrey, H; Pitzl, D; Placakyte, R; Raspereza, A; Ribeiro Cipriano, P M; Roland, B; Ron, E; Sahin, M Ö; Salfeld-Nebgen, J; Saxena, P; Schoerner-Sadenius, T; Schröder, M; Seitz, C; Spannagel, S; Vargas Trevino, A D R; Walsh, R; Wissing, C; Blobel, V; Centis Vignali, M; Draeger, A R; Erfle, J; Garutti, E; Goebel, K; Görner, M; Haller, J; Hoffmann, M; Höing, R S; Junkes, A; Kirschenmann, H; Klanner, R; Kogler, R; Lapsien, T; Lenz, T; Marchesini, I; Marconi, D; Ott, J; Peiffer, T; Perieanu, A; Pietsch, N; Poehlsen, J; Poehlsen, T; Rathjens, D; Sander, C; Schettler, H; Schleper, P; Schlieckau, E; Schmidt, A; Seidel, M; Sola, V; Stadie, H; Steinbrück, G; Troendle, D; Usai, E; Vanelderen, L; Vanhoefer, A; Barth, C; Baus, C; Berger, J; Böser, C; Butz, E; Chwalek, T; De Boer, W; Descroix, A; Dierlamm, A; Feindt, M; Frensch, F; Giffels, M; Gilbert, A; Hartmann, F; Hauth, T; Husemann, U; Katkov, I; Kornmayer, A; Lobelle Pardo, P; Mozer, M U; Müller, T; Müller, Th; Nürnberg, A; Quast, G; Rabbertz, K; Röcker, S; Simonis, H J; Stober, F M; Ulrich, R; Wagner-Kuhr, J; Wayand, S; Weiler, T; Wolf, R; Anagnostou, G; Daskalakis, G; Geralis, T; Giakoumopoulou, V A; Kyriakis, A; Loukas, D; Markou, A; 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Kolberg, T; Lu, Y; Mignerey, A C; Pedro, K; Skuja, A; Tonjes, M B; Tonwar, S C; Apyan, A; Barbieri, R; Bierwagen, K; Busza, W; Cali, I A; Di Matteo, L; Gomez Ceballos, G; Goncharov, M; Gulhan, D; Klute, M; Lai, Y S; Lee, Y-J; Levin, A; Luckey, P D; Paus, C; Ralph, D; Roland, C; Roland, G; Stephans, G S F; Sumorok, K; Velicanu, D; Veverka, J; Wyslouch, B; Yang, M; Zanetti, M; Zhukova, V; Dahmes, B; Gude, A; Kao, S C; Klapoetke, K; Kubota, Y; Mans, J; Nourbakhsh, S; Rusack, R; Singovsky, A; Tambe, N; Turkewitz, J; Acosta, J G; Oliveros, S; Avdeeva, E; Bloom, K; Bose, S; Claes, D R; Dominguez, A; Gonzalez Suarez, R; Keller, J; Knowlton, D; Kravchenko, I; Lazo-Flores, J; Meier, F; Ratnikov, F; Snow, G R; Zvada, M; Dolen, J; Godshalk, A; Iashvili, I; Kharchilava, A; Kumar, A; Rappoccio, S; Alverson, G; Barberis, E; Baumgartel, D; Chasco, M; Massironi, A; Morse, D M; Nash, D; Orimoto, T; Trocino, D; Wang, R J; Wood, D; Zhang, J; Hahn, K A; Kubik, A; Mucia, N; Odell, N; Pollack, B; Pozdnyakov, A; Schmitt, M; Stoynev, S; Sung, K; Velasco, M; Won, S; Brinkerhoff, A; Chan, K M; Drozdetskiy, A; Hildreth, M; Jessop, C; Karmgard, D J; Kellams, N; Lannon, K; Lynch, S; Marinelli, N; Musienko, Y; Pearson, T; Planer, M; Ruchti, R; Smith, G; Valls, N; Wayne, M; Wolf, M; Woodard, A; Antonelli, L; Brinson, J; Bylsma, B; Durkin, L S; Flowers, S; Hart, A; Hill, C; Hughes, R; Kotov, K; Ling, T Y; Luo, W; Puigh, D; Rodenburg, M; Winer, B L; Wolfe, H; Wulsin, H W; Driga, O; Elmer, P; Hardenbrook, J; Hebda, P; Koay, S A; Lujan, P; Marlow, D; Medvedeva, T; Mooney, M; Olsen, J; Piroué, P; Quan, X; Saka, H; Stickland, D; Tully, C; Werner, J S; Zuranski, A; Brownson, E; Malik, S; Mendez, H; Ramirez Vargas, J E; Barnes, V E; Benedetti, D; Bortoletto, D; Gutay, L; Hu, Z; Jha, M K; Jones, M; Jung, K; Kress, M; Leonardo, N; Miller, D H; Neumeister, N; Primavera, F; Radburn-Smith, B C; Shi, X; Shipsey, I; Silvers, D; Svyatkovskiy, A; Wang, F; Xie, W; Xu, L; Zablocki, J; Parashar, N; Stupak, J; Adair, A; Akgun, B; Ecklund, K M; Geurts, F J M; Li, W; Michlin, B; Padley, B P; Redjimi, R; Roberts, J; Zabel, J; Betchart, B; Bodek, A; de Barbaro, P; Demina, R; Eshaq, Y; Ferbel, T; Galanti, M; Garcia-Bellido, A; Goldenzweig, P; Han, J; Harel, A; Hindrichs, O; Khukhunaishvili, A; Korjenevski, S; Petrillo, G; Verzetti, M; Vishnevskiy, D; Ciesielski, R; Demortier, L; Goulianos, K; Mesropian, C; Arora, S; Barker, A; Chou, J P; Contreras-Campana, C; Contreras-Campana, E; Duggan, D; Ferencek, D; Gershtein, Y; Gray, R; Halkiadakis, E; Hidas, D; Kaplan, S; Lath, A; Panwalkar, S; Park, M; Salur, S; Schnetzer, S; Sheffield, D; Somalwar, S; Stone, R; Thomas, S; Thomassen, P; Walker, M; Rose, K; Spanier, S; York, A; Bouhali, O; Castaneda Hernandez, A; Dalchenko, M; De Mattia, M; Dildick, S; Eusebi, R; Flanagan, W; Gilmore, J; Kamon, T; Khotilovich, V; Krutelyov, V; Montalvo, R; Osipenkov, I; Pakhotin, Y; Patel, R; Perloff, A; Roe, J; Rose, A; Safonov, A; Suarez, I; Tatarinov, A; Ulmer, K A; Akchurin, N; Cowden, C; Damgov, J; Dragoiu, C; Dudero, P R; Faulkner, J; Kovitanggoon, K; Kunori, S; Lee, S W; Libeiro, T; Volobouev, I; Appelt, E; Delannoy, A G; Greene, S; Gurrola, A; Johns, W; Maguire, C; Mao, Y; Melo, A; Sharma, M; Sheldon, P; Snook, B; Tuo, S; Velkovska, J; Arenton, M W; Boutle, S; Cox, B; Francis, B; Goodell, J; Hirosky, R; Ledovskoy, A; Li, H; Lin, C; Neu, C; Wolfe, E; Wood, J; Clarke, C; Harr, R; Karchin, P E; Kottachchi Kankanamge Don, C; Lamichhane, P; Sturdy, J; Belknap, D A; Carlsmith, D; Cepeda, M; Dasu, S; Dodd, L; Duric, S; Friis, E; Hall-Wilton, R; Herndon, M; Hervé, A; Klabbers, P; Lanaro, A; Lazaridis, C; Levine, A; Loveless, R; Mohapatra, A; Ojalvo, I; Perry, T; Pierro, G A; Polese, G; Ross, I; Sarangi, T; Savin, A; Smith, W H; Taylor, D; Vuosalo, C; Woods, N; Roinishvili, V

Properties of the Higgs boson with mass near 125[Formula: see text] are measured in proton-proton collisions with the CMS experiment at the LHC. Comprehensive sets of production and decay measurements are combined. The decay channels include [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] pairs. The data samples were collected in 2011 and 2012 and correspond to integrated luminosities of up to 5.1[Formula: see text] at 7[Formula: see text] and up to 19.7[Formula: see text] at 8[Formula: see text]. From the high-resolution [Formula: see text] and [Formula: see text] channels, the mass of the Higgs boson is determined to be [Formula: see text]. For this mass value, the event yields obtained in the different analyses tagging specific decay channels and production mechanisms are consistent with those expected for the standard model Higgs boson. The combined best-fit signal relative to the standard model expectation is [Formula: see text] at the measured mass. The couplings of the Higgs boson are probed for deviations in magnitude from the standard model predictions in multiple ways, including searches for invisible and undetected decays. No significant deviations are found.

A comparison of small-field tissue phantom ratio data generation methods for an Elekta Agility 6 MV photon beam

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

Richmond, Neil, E-mail: neil.richmond@stees.nhs.uk; Brackenridge, Robert

2014-04-01

Tissue-phantom ratios (TPRs) are a common dosimetric quantity used to describe the change in dose with depth in tissue. These can be challenging and time consuming to measure. The conversion of percentage depth dose (PDD) data using standard formulae is widely employed as an alternative method in generating TPR. However, the applicability of these formulae for small fields has been questioned in the literature. Functional representation has also been proposed for small-field TPR production. This article compares measured TPR data for small 6 MV photon fields against that generated by conversion of PDD using standard formulae to assess the efficacymore » of the conversion data. By functionally fitting the measured TPR data for square fields greater than 4 cm in length, the TPR curves for smaller fields are generated and compared with measurements. TPRs and PDDs were measured in a water tank for a range of square field sizes. The PDDs were converted to TPRs using standard formulae. TPRs for fields of 4 × 4 cm{sup 2} and larger were used to create functional fits. The parameterization coefficients were used to construct extrapolated TPR curves for 1 × 1 cm{sup 2}, 2 × 2-cm{sup 2}, and 3 × 3-cm{sup 2} fields. The TPR data generated using standard formulae were in excellent agreement with direct TPR measurements. The TPR data for 1 × 1-cm{sup 2}, 2 × 2-cm{sup 2}, and 3 × 3-cm{sup 2} fields created by extrapolation of the larger field functional fits gave inaccurate initial results. The corresponding mean differences for the 3 fields were 4.0%, 2.0%, and 0.9%. Generation of TPR data using a standard PDD-conversion methodology has been shown to give good agreement with our directly measured data for small fields. However, extrapolation of TPR data using the functional fit to fields of 4 × 4 cm{sup 2} or larger resulted in generation of TPR curves that did not compare well with the measured data.« less

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

NASA Astrophysics Data System (ADS)

Zinoviev, A. N.

2017-09-01

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

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.

Log-periodic crashes revisited

NASA Astrophysics Data System (ADS)

Matsushita, Raul; da Silva, Sergio; Figueiredo, Annibal; Gleria, Iram

2006-05-01

We revisit the finding that crashes can be deterministic and governed by log-periodic formulas [D. Sornette, A. Johansen, Significance of log-periodic precursors to financial crashes, Quant. Finance 1 (2001) 452-471; D. Sornette, W.X. Zhou, The US 2000-2002 market descent: how much longer and deeper?, Quant. Finance 2 (2002) 468-481]. One- and two-harmonic equations are usually employed to fit daily data during bubble episodes. But a three-harmonics has been shown to fit anti-bubbles [A. Johansen, D. Sornette, Financial “anti-bubbles”: log-periodicity in gold and Nikkei collapses, Int. J. Mod. Phys. C 10 (1999) 563-575]. Here we show that the three-harmonic formula can work for bubble episodes as well as anti-bubbles. This is illustrated with daily data from the Brazilian real-US dollar exchange rate. And we also show that the three-harmonics can fit an intraday data set from that foreign exchange rate.

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.

Nuclear Matter Properties with the Re-evaluated Coefficients of Liquid Drop Model

NASA Astrophysics Data System (ADS)

Chowdhury, P. Roy; Basu, D. N.

2006-06-01

The coefficients of the volume, surface, Coulomb, asymmetry and pairing energy terms of the semiempirical liquid drop model mass formula have been determined by furnishing best fit to the observed mass excesses. Slightly different sets of the weighting parameters for liquid drop model mass formula have been obtained from minimizations of \\chi 2 and mean square deviation. The most recent experimental and estimated mass excesses from Audi-Wapstra-Thibault atomic mass table have been used for the least square fitting procedure. Equation of state, nuclear incompressibility, nuclear mean free path and the most stable nuclei for corresponding atomic numbers, all are in good agreement with the experimental results.

Interference fits and stress-corrosion failure. [aircraft parts fatigue life analysis

NASA Technical Reports Server (NTRS)

Hanagud, S.; Carter, A. E.

1976-01-01

It is pointed out that any proper design of interference fit fastener, interference fit bushings, or stress coining processes should consider both the stress-corrosion susceptibility and fatigue-life improvement together. Investigations leading to such a methodology are discussed. A service failure analysis of actual aircraft parts is considered along with the stress-corrosion susceptibility of cold-working interference fit bushings. The optimum design of the amount of interference is considered, giving attention to stress formulas and aspects of design methodology.

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.

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.

A Performance Comparison on the Probability Plot Correlation Coefficient Test using Several Plotting Positions for GEV Distribution.

NASA Astrophysics Data System (ADS)

Ahn, Hyunjun; Jung, Younghun; Om, Ju-Seong; Heo, Jun-Haeng

2014-05-01

It is very important to select the probability distribution in Statistical hydrology. Goodness of fit test is a statistical method that selects an appropriate probability model for a given data. The probability plot correlation coefficient (PPCC) test as one of the goodness of fit tests was originally developed for normal distribution. Since then, this test has been widely applied to other probability models. The PPCC test is known as one of the best goodness of fit test because it shows higher rejection powers among them. In this study, we focus on the PPCC tests for the GEV distribution which is widely used in the world. For the GEV model, several plotting position formulas are suggested. However, the PPCC statistics are derived only for the plotting position formulas (Goel and De, In-na and Nguyen, and Kim et al.) in which the skewness coefficient (or shape parameter) are included. And then the regression equations are derived as a function of the shape parameter and sample size for a given significance level. In addition, the rejection powers of these formulas are compared using Monte-Carlo simulation. Keywords: Goodness-of-fit test, Probability plot correlation coefficient test, Plotting position, Monte-Carlo Simulation ACKNOWLEDGEMENTS This research was supported by a grant 'Establishing Active Disaster Management System of Flood Control Structures by using 3D BIM Technique' [NEMA-12-NH-57] from the Natural Hazard Mitigation Research Group, National Emergency Management Agency of Korea.

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

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

Saez-Beltran, M; Fernandez Gonzalez, F

2014-06-15

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

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

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

Jiang, X; Baad, M; Reiser, I

2014-06-15

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

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.

Fitting a function to time-dependent ensemble averaged data.

PubMed

Fogelmark, Karl; Lomholt, Michael A; Irbäck, Anders; Ambjörnsson, Tobias

2018-05-03

Time-dependent ensemble averages, i.e., trajectory-based averages of some observable, are of importance in many fields of science. A crucial objective when interpreting such data is to fit these averages (for instance, squared displacements) with a function and extract parameters (such as diffusion constants). A commonly overlooked challenge in such function fitting procedures is that fluctuations around mean values, by construction, exhibit temporal correlations. We show that the only available general purpose function fitting methods, correlated chi-square method and the weighted least squares method (which neglects correlation), fail at either robust parameter estimation or accurate error estimation. We remedy this by deriving a new closed-form error estimation formula for weighted least square fitting. The new formula uses the full covariance matrix, i.e., rigorously includes temporal correlations, but is free of the robustness issues, inherent to the correlated chi-square method. We demonstrate its accuracy in four examples of importance in many fields: Brownian motion, damped harmonic oscillation, fractional Brownian motion and continuous time random walks. We also successfully apply our method, weighted least squares including correlation in error estimation (WLS-ICE), to particle tracking data. The WLS-ICE method is applicable to arbitrary fit functions, and we provide a publically available WLS-ICE software.

Use of the HR index to predict maximal oxygen uptake during different exercise protocols.

PubMed

Haller, Jeannie M; Fehling, Patricia C; Barr, David A; Storer, Thomas W; Cooper, Christopher B; Smith, Denise L

2013-10-01

This study examined the ability of the HRindex model to accurately predict maximal oxygen uptake ([Formula: see text]O2max) across a variety of incremental exercise protocols. Ten men completed five incremental protocols to volitional exhaustion. Protocols included three treadmill (Bruce, UCLA running, Wellness Fitness Initiative [WFI]), one cycle, and one field (shuttle) test. The HRindex prediction equation (METs = 6 × HRindex - 5, where HRindex = HRmax/HRrest) was used to generate estimates of energy expenditure, which were converted to body mass-specific estimates of [Formula: see text]O2max. Estimated [Formula: see text]O2max was compared with measured [Formula: see text]O2max. Across all protocols, the HRindex model significantly underestimated [Formula: see text]O2max by 5.1 mL·kg(-1)·min(-1) (95% CI: -7.4, -2.7) and the standard error of the estimate (SEE) was 6.7 mL·kg(-1)·min(-1). Accuracy of the model was protocol-dependent, with [Formula: see text]O2max significantly underestimated for the Bruce and WFI protocols but not the UCLA, Cycle, or Shuttle protocols. Although no significant differences in [Formula: see text]O2max estimates were identified for these three protocols, predictive accuracy among them was not high, with root mean squared errors and SEEs ranging from 7.6 to 10.3 mL·kg(-1)·min(-1) and from 4.5 to 8.0 mL·kg(-1)·min(-1), respectively. Correlations between measured and predicted [Formula: see text]O2max were between 0.27 and 0.53. Individual prediction errors indicated that prediction accuracy varied considerably within protocols and among participants. In conclusion, across various protocols the HRindex model significantly underestimated [Formula: see text]O2max in a group of aerobically fit young men. Estimates generated using the model did not differ from measured [Formula: see text]O2max for three of the five protocols studied; nevertheless, some individual prediction errors were large. The lack of precision among estimates may limit the utility of the HRindex model; however, further investigation to establish the model's predictive accuracy is warranted.

Approximate Formula for the Vertical Asymptote of Projectile Motion in Midair

ERIC Educational Resources Information Center

Chudinov, Peter Sergey

2010-01-01

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

Design sensitivity analysis of nonlinear structural response

NASA Technical Reports Server (NTRS)

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

1987-01-01

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

Computation of HORRAT values.

PubMed

McClure, Foster D; Lee, Jung-Keun

2003-01-01

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

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.

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

Discussion on fresh air volume in Temperature and Humidity Independent Control of Air-conditioning System

NASA Astrophysics Data System (ADS)

Cheng, Xiaolong; Liu, Jinxiang; Wang, Yu; Yuan, Xiaolei; Jin, Hui

2018-05-01

The fresh air volume in Temperature and Humidity Independent Control of Air-conditioning System(THIC) of a typical office was comfirmed, under the premise of adopting the refrigeration dehumidifying fresh air unit(7°C/12°C). By detailed calculating the space moisture load and the fresh air volume required for dehumidification in 120 selected major cities in China, it can be inferred that the minimum fresh air volume required for dehumidification in THIC is mainly determined by the local outdoor air moisture and the outdoor wind speed; Then the mathematical fitting software Matlab was used to fit the three parameters, and a simplified formula for calculating the minimum per capita fresh air volume required for dehumidification was obtained; And the indoor relative humidity was simulated by the numerical software Airpak and the results by using the formula data and the data for hygiene were compared to verify the relibility of the simplified formula.

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

NASA Astrophysics Data System (ADS)

Sakhr, Jamal; Nieminen, John M.

2018-03-01

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

Lyapunov dimension formula for the global attractor of the Lorenz system

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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

PubMed

Guérin, T

2017-08-01

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

Analytic halo approach to the bispectrum of galaxies in redshift space

NASA Astrophysics Data System (ADS)

Yamamoto, Kazuhiro; Nan, Yue; Hikage, Chiaki

2017-02-01

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

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

PubMed Central

Homentcovschi, Dorel; Miles, Ronald N.

2010-01-01

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

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.

Developing an assessment based on physical fitness age to evaluate motor function in frail and healthy elderly women

PubMed Central

Nakagaichi, Masaki; Anan, Yuya; Hikiji, Yuto; Uratani, Sou

2018-01-01

Objectives The purpose of this study was to identify a method for assessing physical fitness age that is easy to use with both frail and healthy elderly women and to examine its validity. Methods Principal component analysis was used to develop a formula of physical fitness age from four motor function variables. The subjects comprised 688 (75.7±6.0 years) elderly women, in order to develop a physical fitness scale. The formula for calculating physical fitness age was expressed as physical fitness age =−0.419× grip strength −0.096× balancing on one leg with eyes open −0.737×30 s chair stand +0.503× figure-of-8 walking test +0.47× chronological age +52.68. Results Measures obtained from subjects in the frail elderly (n=11, 73.0±2.3 years) and exercise (n=10, 70.8±3.1 years) groups were used to examine the validity of the assessment. The mean physical fitness age of the frail elderly group (79.0±3.7 years) was significantly higher than its mean chronological age (73.0±2.3 years, p<0.05). The mean physical fitness age of the exercise group (65.6±3.1 years) was significantly lower than the chronological age (70.8±3.1 years, p<0.05). Conclusion These findings confirm that physical fitness age scores are applicable to frail and healthy elderly women. Physical fitness age is a valid measure of motor function in elderly women. PMID:29416326

Developing an assessment based on physical fitness age to evaluate motor function in frail and healthy elderly women.

PubMed

Nakagaichi, Masaki; Anan, Yuya; Hikiji, Yuto; Uratani, Sou

2018-01-01

The purpose of this study was to identify a method for assessing physical fitness age that is easy to use with both frail and healthy elderly women and to examine its validity. Principal component analysis was used to develop a formula of physical fitness age from four motor function variables. The subjects comprised 688 (75.7±6.0 years) elderly women, in order to develop a physical fitness scale. The formula for calculating physical fitness age was expressed as physical fitness age =-0.419× grip strength -0.096× balancing on one leg with eyes open -0.737×30 s chair stand +0.503× figure-of-8 walking test +0.47× chronological age +52.68. Measures obtained from subjects in the frail elderly (n=11, 73.0±2.3 years) and exercise (n=10, 70.8±3.1 years) groups were used to examine the validity of the assessment. The mean physical fitness age of the frail elderly group (79.0±3.7 years) was significantly higher than its mean chronological age (73.0±2.3 years, p <0.05). The mean physical fitness age of the exercise group (65.6±3.1 years) was significantly lower than the chronological age (70.8±3.1 years, p <0.05). These findings confirm that physical fitness age scores are applicable to frail and healthy elderly women. Physical fitness age is a valid measure of motor function in elderly women.

Bicubic uniform B-spline wavefront fitting technology applied in computer-generated holograms

NASA Astrophysics Data System (ADS)

Cao, Hui; Sun, Jun-qiang; Chen, Guo-jie

2006-02-01

This paper presented a bicubic uniform B-spline wavefront fitting technology to figure out the analytical expression for object wavefront used in Computer-Generated Holograms (CGHs). In many cases, to decrease the difficulty of optical processing, off-axis CGHs rather than complex aspherical surface elements are used in modern advanced military optical systems. In order to design and fabricate off-axis CGH, we have to fit out the analytical expression for object wavefront. Zernike Polynomial is competent for fitting wavefront of centrosymmetric optical systems, but not for axisymmetrical optical systems. Although adopting high-degree polynomials fitting method would achieve higher fitting precision in all fitting nodes, the greatest shortcoming of this method is that any departure from the fitting nodes would result in great fitting error, which is so-called pulsation phenomenon. Furthermore, high-degree polynomials fitting method would increase the calculation time in coding computer-generated hologram and solving basic equation. Basing on the basis function of cubic uniform B-spline and the character mesh of bicubic uniform B-spline wavefront, bicubic uniform B-spline wavefront are described as the product of a series of matrices. Employing standard MATLAB routines, four kinds of different analytical expressions for object wavefront are fitted out by bicubic uniform B-spline as well as high-degree polynomials. Calculation results indicate that, compared with high-degree polynomials, bicubic uniform B-spline is a more competitive method to fit out the analytical expression for object wavefront used in off-axis CGH, for its higher fitting precision and C2 continuity.

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.

Loss tangent and complex modulus estimated by acoustic radiation force creep and shear wave dispersion

PubMed Central

Amador, Carolina; Urban, Matthew W; Chen, Shigao; Greenleaf, James F

2012-01-01

Elasticity imaging methods have been used to study tissue mechanical properties and have demonstrated that tissue elasticity changes with disease state. In current shear wave elasticity imaging methods typically only shear wave speed is measured and rheological models, e.g., Kelvin-Voigt, Maxwell and Standard Linear Solid, are used to solve for tissue mechanical properties such as the shear viscoelastic complex modulus. This paper presents a method to quantify viscoelastic material properties in a model-independent way by estimating the complex shear elastic modulus over a wide frequency range using time-dependent creep response induced by acoustic radiation force. This radiation force induced creep (RFIC) method uses a conversion formula that is the analytic solution of a constitutive equation. The proposed method in combination with Shearwave Dispersion Ultrasound Vibrometry (SDUV) is used to measure the complex modulus so that knowledge of the applied radiation force magnitude is not necessary. The conversion formula is shown to be sensitive to sampling frequency and the first reliable measure in time according to numerical simulations using the Kelvin-Voigt model creep strain and compliance. Representative model-free shear complex moduli from homogeneous tissue mimicking phantoms and one excised swine kidney were obtained. This work proposes a novel model-free ultrasound-based elasticity method that does not require a rheological model with associated fitting requirements. PMID:22345425

Loss tangent and complex modulus estimated by acoustic radiation force creep and shear wave dispersion.

PubMed

Amador, Carolina; Urban, Matthew W; Chen, Shigao; Greenleaf, James F

2012-03-07

Elasticity imaging methods have been used to study tissue mechanical properties and have demonstrated that tissue elasticity changes with disease state. In current shear wave elasticity imaging methods typically only shear wave speed is measured and rheological models, e.g. Kelvin-Voigt, Maxwell and Standard Linear Solid, are used to solve for tissue mechanical properties such as the shear viscoelastic complex modulus. This paper presents a method to quantify viscoelastic material properties in a model-independent way by estimating the complex shear elastic modulus over a wide frequency range using time-dependent creep response induced by acoustic radiation force. This radiation force induced creep method uses a conversion formula that is the analytic solution of a constitutive equation. The proposed method in combination with shearwave dispersion ultrasound vibrometry is used to measure the complex modulus so that knowledge of the applied radiation force magnitude is not necessary. The conversion formula is shown to be sensitive to sampling frequency and the first reliable measure in time according to numerical simulations using the Kelvin-Voigt model creep strain and compliance. Representative model-free shear complex moduli from homogeneous tissue mimicking phantoms and one excised swine kidney were obtained. This work proposes a novel model-free ultrasound-based elasticity method that does not require a rheological model with associated fitting requirements.

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.

Brillouin Frequency Shift of Fiber Distributed Sensors Extracted from Noisy Signals by Quadratic Fitting.

PubMed

Zheng, Hanrong; Fang, Zujie; Wang, Zhaoyong; Lu, Bin; Cao, Yulong; Ye, Qing; Qu, Ronghui; Cai, Haiwen

2018-01-31

It is a basic task in Brillouin distributed fiber sensors to extract the peak frequency of the scattering spectrum, since the peak frequency shift gives information on the fiber temperature and strain changes. Because of high-level noise, quadratic fitting is often used in the data processing. Formulas of the dependence of the minimum detectable Brillouin frequency shift (BFS) on the signal-to-noise ratio (SNR) and frequency step have been presented in publications, but in different expressions. A detailed deduction of new formulas of BFS variance and its average is given in this paper, showing especially their dependences on the data range used in fitting, including its length and its center respective to the real spectral peak. The theoretical analyses are experimentally verified. It is shown that the center of the data range has a direct impact on the accuracy of the extracted BFS. We propose and demonstrate an iterative fitting method to mitigate such effects and improve the accuracy of BFS measurement. The different expressions of BFS variances presented in previous papers are explained and discussed.

Topological and statistical properties of nonlinear force-free fields

NASA Astrophysics Data System (ADS)

Mangalam, A.; Prasad, A.

2018-01-01

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

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

Hirano, Teruyuki; Suto, Yasushi; Taruya, Atsushi

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

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.

A fast method to compute Three-Dimensional Infrared Radiative Transfer in non scattering medium

NASA Astrophysics Data System (ADS)

Makke, Laurent; Musson-Genon, Luc; Carissimo, Bertrand

2014-05-01

The Atmospheric Radiation field has seen the development of more accurate and faster methods to take into account absoprtion in participating media. Radiative fog appears with clear sky condition due to a significant cooling during the night, so scattering is left out. Fog formation modelling requires accurate enough method to compute cooling rates. Thanks to High Performance Computing, multi-spectral approach of Radiative Transfer Equation resolution is most often used. Nevertheless, the coupling of three-dimensionnal radiative transfer with fluid dynamics is very detrimental to the computational cost. To reduce the time spent in radiation calculations, the following method uses analytical absorption functions fitted by Sasamori (1968) on Yamamoto's charts (Yamamoto,1956) to compute a local linear absorption coefficient. By averaging radiative properties, this method eliminates the spectral integration. For an isothermal atmosphere, analytical calculations lead to an explicit formula between emissivities functions and linear absorption coefficient. In the case of cooling to space approximation, this analytical expression gives very accurate results compared to correlated k-distribution. For non homogeneous paths, we propose a two steps algorithm. One-dimensional radiative quantities and linear absorption coefficient are computed by a two-flux method. Then, three-dimensional RTE under the grey medium assumption is solved with the DOM. Comparisons with measurements of radiative quantities during ParisFOG field (2006) shows the cability of this method to handle strong vertical variations of pressure/temperature and gases concentrations.

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.

Measurement of double-differential cross sections for top quark pair production in pp collisions at [Formula: see text][Formula: see text] and impact on parton distribution functions.

PubMed

Sirunyan, A M; Tumasyan, A; Adam, W; Asilar, E; Bergauer, T; Brandstetter, J; Brondolin, E; Dragicevic, M; Erö, J; Flechl, M; Friedl, M; Frühwirth, R; Ghete, V M; Hartl, C; Hörmann, N; Hrubec, J; Jeitler, M; König, A; Krätschmer, I; Liko, D; Matsushita, T; Mikulec, I; Rabady, D; Rad, N; Rahbaran, B; Rohringer, H; Schieck, J; Strauss, J; Waltenberger, W; Wulz, C-E; Dvornikov, O; Makarenko, V; Mossolov, V; Suarez Gonzalez, J; Zykunov, V; Shumeiko, N; Alderweireldt, S; De Wolf, E A; Janssen, X; Lauwers, J; Van De Klundert, M; Van Haevermaet, H; Van Mechelen, P; Van Remortel, N; Van Spilbeeck, A; Abu Zeid, S; Blekman, F; D'Hondt, J; Daci, N; De Bruyn, I; Deroover, K; Lowette, S; Moortgat, S; Moreels, L; Olbrechts, A; Python, Q; Skovpen, K; Tavernier, S; Van Doninck, W; Van Mulders, P; Van Parijs, I; Brun, H; Clerbaux, B; De Lentdecker, G; Delannoy, H; Fasanella, G; Favart, L; Goldouzian, R; Grebenyuk, A; Karapostoli, G; Lenzi, T; Léonard, A; Luetic, J; Maerschalk, T; Marinov, A; Randle-Conde, A; Seva, T; Vander Velde, C; Vanlaer, P; Vannerom, D; Yonamine, R; Zenoni, F; Zhang, F; Cornelis, T; Dobur, D; Fagot, A; Gul, M; Khvastunov, I; Poyraz, D; Salva, S; Schöfbeck, R; Tytgat, M; Van Driessche, W; Yazgan, E; Zaganidis, N; Bakhshiansohi, H; Bondu, O; Brochet, S; Bruno, G; Caudron, A; De Visscher, S; Delaere, C; Delcourt, M; Francois, B; Giammanco, A; Jafari, A; Komm, M; Krintiras, G; Lemaitre, V; Magitteri, A; Mertens, A; Musich, M; Piotrzkowski, K; Quertenmont, L; Selvaggi, M; Vidal Marono, M; Wertz, S; Beliy, N; Aldá Júnior, W L; Alves, F L; Alves, G A; Brito, L; Hensel, C; Moraes, A; Pol, M E; Rebello Teles, P; Chagas, E Belchior Batista Das; Carvalho, W; Chinellato, J; Custódio, A; Da Costa, E M; Da Silveira, G G; De Jesus Damiao, D; De Oliveira Martins, C; De Souza, S Fonseca; Guativa, L M Huertas; Malbouisson, H; Matos Figueiredo, D; Mora Herrera, C; Mundim, L; Nogima, H; Prado Da Silva, W L; Santoro, A; Sznajder, A; Tonelli Manganote, E J; Torres Da Silva De Araujo, F; Vilela Pereira, A; 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Khan, A; Kyberd, P; Reid, I D; Symonds, P; Teodorescu, L; Turner, M; Borzou, A; Call, K; Dittmann, J; Hatakeyama, K; Liu, H; Pastika, N; Bartek, R; Dominguez, A; Buccilli, A; Cooper, S I; Henderson, C; Rumerio, P; West, C; Arcaro, D; Avetisyan, A; Bose, T; Gastler, D; Rankin, D; Richardson, C; Rohlf, J; Sulak, L; Zou, D; Benelli, G; Cutts, D; Garabedian, A; Hakala, J; Heintz, U; Hogan, J M; Jesus, O; Kwok, K H M; Laird, E; Landsberg, G; Mao, Z; Narain, M; Piperov, S; Sagir, S; Spencer, E; Syarif, R; Breedon, R; Burns, D; Calderon De La Barca Sanchez, M; Chauhan, S; Chertok, M; Conway, J; Conway, R; Cox, P T; Erbacher, R; Flores, C; Funk, G; Gardner, M; Ko, W; Lander, R; Mclean, C; Mulhearn, M; Pellett, D; Pilot, J; Shalhout, S; Shi, M; Smith, J; Squires, M; Stolp, D; Tos, K; Tripathi, M; Bachtis, M; Bravo, C; Cousins, R; Dasgupta, A; Florent, A; Hauser, J; Ignatenko, M; Mccoll, N; Saltzberg, D; Schnaible, C; Valuev, V; Weber, M; Bouvier, E; Burt, K; Clare, R; Ellison, J; Gary, J W; Ghiasi Shirazi, S M A; Hanson, G; Heilman, J; Jandir, P; Kennedy, E; Lacroix, F; Long, O R; Olmedo Negrete, M; Paneva, M I; Shrinivas, A; Si, W; Wei, H; Wimpenny, S; Yates, B R; Branson, J G; Cerati, G B; Cittolin, S; Derdzinski, M; Gerosa, R; Holzner, A; Klein, D; Krutelyov, V; Letts, J; Macneill, I; Olivito, D; Padhi, S; Pieri, M; Sani, M; Sharma, V; Simon, S; Tadel, M; Vartak, A; Wasserbaech, S; Welke, C; Wood, J; Würthwein, F; Yagil, A; Zevi Della Porta, G; Amin, N; Bhandari, R; Bradmiller-Feld, J; Campagnari, C; Dishaw, A; Dutta, V; Franco Sevilla, M; George, C; Golf, F; Gouskos, L; Gran, J; Heller, R; Incandela, J; Mullin, S D; Ovcharova, A; Qu, H; Richman, J; Stuart, D; Suarez, I; Yoo, J; Anderson, D; Bendavid, J; Bornheim, A; Bunn, J; Duarte, J; Lawhorn, J M; Mott, A; Newman, H B; Pena, C; Spiropulu, M; Vlimant, J R; Xie, S; Zhu, R Y; Andrews, M B; Ferguson, T; Paulini, M; Russ, J; Sun, M; Vogel, H; Vorobiev, I; Weinberg, M; Cumalat, J P; Ford, W T; Jensen, F; Johnson, A; Krohn, M; Leontsinis, S; Mulholland, T; Stenson, K; Wagner, S R; Alexander, J; Chaves, J; Chu, J; Dittmer, S; Mcdermott, K; Mirman, N; Patterson, J R; Rinkevicius, A; Ryd, A; Skinnari, L; Soffi, L; Tan, S M; Tao, Z; Thom, J; Tucker, J; Wittich, P; Zientek, M; Winn, D; Abdullin, S; Albrow, M; Apollinari, G; Apresyan, A; Banerjee, S; Bauerdick, L A T; Beretvas, A; Berryhill, J; Bhat, P C; Bolla, G; Burkett, K; Butler, J N; Cheung, H W K; Chlebana, F; Cihangir, S; Cremonesi, M; Elvira, V D; Fisk, I; Freeman, J; Gottschalk, E; Gray, L; Green, D; Grünendahl, S; Gutsche, O; Hare, D; Harris, R M; Hasegawa, S; Hirschauer, J; Hu, Z; Jayatilaka, B; Jindariani, S; Johnson, M; Joshi, U; Klima, B; Kreis, B; Lammel, S; Linacre, J; Lincoln, D; Lipton, R; Liu, M; Liu, T; Lopes De Sá, R; Lykken, J; Maeshima, K; Magini, N; Marraffino, J M; Maruyama, S; Mason, D; McBride, P; Merkel, P; Mrenna, S; Nahn, S; O'Dell, V; Pedro, K; Prokofyev, O; Rakness, G; Ristori, L; Sexton-Kennedy, E; Soha, A; Spalding, W J; Spiegel, L; Stoynev, S; Strait, J; Strobbe, N; Taylor, L; Tkaczyk, S; Tran, N V; Uplegger, L; Vaandering, E W; Vernieri, C; Verzocchi, M; Vidal, R; Wang, M; Weber, H A; Whitbeck, A; Wu, Y; Acosta, D; Avery, P; Bortignon, P; Bourilkov, D; Brinkerhoff, A; Carnes, A; Carver, M; Curry, D; Das, S; Field, R D; Furic, I K; Konigsberg, J; Korytov, A; Low, J F; Ma, P; Matchev, K; Mei, H; Mitselmakher, G; Rank, D; Shchutska, L; Sperka, D; Thomas, L; Wang, J; Wang, S; Yelton, J; Linn, S; Markowitz, P; Martinez, G; Rodriguez, J L; Ackert, A; Adams, T; Askew, A; Bein, S; Hagopian, S; Hagopian, V; Johnson, K F; Kolberg, T; Perry, T; Prosper, H; Santra, A; Yohay, R; Baarmand, M M; Bhopatkar, V; Colafranceschi, S; Hohlmann, M; Noonan, D; Roy, T; Yumiceva, F; Adams, M R; Apanasevich, L; Berry, D; Betts, R R; Cavanaugh, R; Chen, X; Evdokimov, O; Gerber, C E; Hangal, D A; Hofman, D J; Jung, K; Kamin, J; Sandoval Gonzalez, I D; Trauger, H; Varelas, N; Wang, H; Wu, Z; Zhang, J; Bilki, B; Clarida, W; Dilsiz, K; Durgut, S; Gandrajula, R P; Haytmyradov, M; Khristenko, V; Merlo, J-P; Mermerkaya, H; Mestvirishvili, A; Moeller, A; Nachtman, J; Ogul, H; Onel, Y; Ozok, F; Penzo, A; Snyder, C; Tiras, E; Wetzel, J; Yi, K; Blumenfeld, B; Cocoros, A; Eminizer, N; Fehling, D; Feng, L; Gritsan, A V; Maksimovic, P; Roskes, J; Sarica, U; Swartz, M; Xiao, M; You, C; Al-Bataineh, A; Baringer, P; Bean, A; Boren, S; Bowen, J; Castle, J; Forthomme, L; Khalil, S; Kropivnitskaya, A; Majumder, D; Mcbrayer, W; Murray, M; Sanders, S; Stringer, R; Tapia Takaki, J D; Wang, Q; Ivanov, A; Kaadze, K; Maravin, Y; Mohammadi, A; Saini, L K; Skhirtladze, N; Toda, S; Rebassoo, F; Wright, D; Anelli, C; Baden, A; Baron, O; Belloni, A; Calvert, B; Eno, S C; Ferraioli, C; Gomez, J A; Hadley, N J; Jabeen, S; Jeng, G Y; Kellogg, R G; Kunkle, J; Mignerey, A C; Ricci-Tam, F; Shin, Y H; Skuja, A; Tonjes, M B; Tonwar, S C; Abercrombie, D; Allen, B; Apyan, A; Azzolini, V; Barbieri, R; Baty, A; Bi, R; Bierwagen, K; Brandt, S; Busza, W; Cali, I A; D'Alfonso, M; Demiragli, Z; Gomez Ceballos, G; Goncharov, M; Hsu, D; Iiyama, Y; Innocenti, G M; Klute, M; Kovalskyi, D; Krajczar, K; Lai, Y S; Lee, Y-J; Levin, A; Luckey, P D; Maier, B; Marini, A C; Mcginn, C; Mironov, C; Narayanan, S; Niu, X; Paus, C; Roland, C; Roland, G; Salfeld-Nebgen, J; Stephans, G S F; Tatar, K; Velicanu, D; Wang, J; Wang, T W; Wyslouch, B; Benvenuti, A C; Chatterjee, R M; Evans, A; Hansen, P; Kalafut, S; Kao, S C; Kubota, Y; Lesko, Z; Mans, J; Nourbakhsh, S; Ruckstuhl, N; Rusack, R; Tambe, N; Turkewitz, J; Acosta, J G; Oliveros, S; Avdeeva, E; Bloom, K; Claes, D R; Fangmeier, C; Gonzalez Suarez, R; Kamalieddin, R; Kravchenko, I; Malta Rodrigues, A; Monroy, J; Siado, J E; Snow, G R; Stieger, B; Alyari, M; Dolen, J; Godshalk, A; Harrington, C; Iashvili, I; Kaisen, J; Nguyen, D; Parker, A; Rappoccio, S; Roozbahani, B; Alverson, G; Barberis, E; Hortiangtham, A; Massironi, A; Morse, D M; Nash, D; Orimoto, T; Teixeira De Lima, R; Trocino, D; Wang, R-J; Wood, D; Bhattacharya, S; Charaf, O; Hahn, K A; Mucia, N; Odell, N; Pollack, B; Schmitt, M H; Sung, K; Trovato, M; Velasco, M; Dev, N; Hildreth, M; Hurtado Anampa, K; Jessop, C; Karmgard, D J; Kellams, N; Lannon, K; Marinelli, N; Meng, F; Mueller, C; Musienko, Y; Planer, M; Reinsvold, A; Ruchti, R; Rupprecht, N; Smith, G; Taroni, S; Wayne, M; Wolf, M; Woodard, A; Alimena, J; Antonelli, L; Bylsma, B; Durkin, L S; Flowers, S; Francis, B; Hart, A; Hill, C; Ji, W; Liu, B; Luo, W; Puigh, D; Winer, B L; Wulsin, H W; Cooperstein, S; Driga, O; Elmer, P; Hardenbrook, J; Hebda, P; Lange, D; Luo, J; Marlow, D; Medvedeva, T; Mei, K; Ojalvo, I; Olsen, J; Palmer, C; Piroué, P; Stickland, D; Svyatkovskiy, A; Tully, C; Malik, S; Barker, A; Barnes, V E; Folgueras, S; Gutay, L; Jha, M K; Jones, M; Jung, A W; Khatiwada, A; Miller, D H; Neumeister, N; Schulte, J F; Shi, X; Sun, J; Wang, F; Xie, W; Parashar, N; Stupak, J; Adair, A; Akgun, B; Chen, Z; Ecklund, K M; Geurts, F J M; Guilbaud, M; Li, W; Michlin, B; Northup, M; Padley, B P; Roberts, J; Rorie, J; Tu, Z; Zabel, J; Betchart, B; Bodek, A; de Barbaro, P; Demina, R; Duh, Y T; Ferbel, T; Galanti, M; Garcia-Bellido, A; Han, J; Hindrichs, O; Khukhunaishvili, A; Lo, K H; Tan, P; Verzetti, M; Agapitos, A; Chou, J P; Gershtein, Y; Gómez Espinosa, T A; Halkiadakis, E; Heindl, M; Hughes, E; Kaplan, S; Kunnawalkam Elayavalli, R; Kyriacou, S; Lath, A; Montalvo, R; Nash, K; Osherson, M; Saka, H; Salur, S; Schnetzer, S; Sheffield, D; Somalwar, S; Stone, R; Thomas, S; Thomassen, P; Walker, M; Delannoy, A G; Foerster, M; Heideman, J; Riley, G; Rose, K; Spanier, S; Thapa, K; Bouhali, O; Celik, A; Dalchenko, M; De Mattia, M; Delgado, A; Dildick, S; Eusebi, R; Gilmore, J; Huang, T; Juska, E; Kamon, T; Mueller, R; Pakhotin, Y; Patel, R; Perloff, A; Perniè, L; Rathjens, D; Safonov, A; Tatarinov, A; Ulmer, K A; Akchurin, N; Damgov, J; De Guio, F; Dragoiu, C; Dudero, P R; Faulkner, J; Gurpinar, E; Kunori, S; Lamichhane, K; Lee, S W; Libeiro, T; Peltola, T; Undleeb, S; Volobouev, I; Wang, Z; Greene, S; Gurrola, A; Janjam, R; Johns, W; Maguire, C; Melo, A; Ni, H; Sheldon, P; Tuo, S; Velkovska, J; Xu, Q; Arenton, M W; Barria, P; Cox, B; Hirosky, R; Ledovskoy, A; Li, H; Neu, C; Sinthuprasith, T; Sun, X; Wang, Y; Wolfe, E; Xia, F; Clarke, C; Harr, R; Karchin, P E; Sturdy, J; Zaleski, S; Belknap, D A; Buchanan, J; Caillol, C; Dasu, S; Dodd, L; Duric, S; Gomber, B; Grothe, M; Herndon, M; Hervé, A; Hussain, U; Klabbers, P; Lanaro, A; Levine, A; Long, K; Loveless, R; Pierro, G A; Polese, G; Ruggles, T; Savin, A; Smith, N; Smith, W H; Taylor, D; Woods, N

2017-01-01

Normalized double-differential cross sections for top quark pair ([Formula: see text]) production are measured in pp collisions at a centre-of-mass energy of 8[Formula: see text] with the CMS experiment at the LHC. The analyzed data correspond to an integrated luminosity of 19.7[Formula: see text]. The measurement is performed in the dilepton [Formula: see text] final state. The [Formula: see text] cross section is determined as a function of various pairs of observables characterizing the kinematics of the top quark and [Formula: see text] system. The data are compared to calculations using perturbative quantum chromodynamics at next-to-leading and approximate next-to-next-to-leading orders. They are also compared to predictions of Monte Carlo event generators that complement fixed-order computations with parton showers, hadronization, and multiple-parton interactions. Overall agreement is observed with the predictions, which is improved when the latest global sets of proton parton distribution functions are used. The inclusion of the measured [Formula: see text] cross sections in a fit of parametrized parton distribution functions is shown to have significant impact on the gluon distribution.

Global stability for epidemic models on multiplex networks.

PubMed

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

2018-05-01

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

Simple 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…

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.

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.

Superconducting properties and μSR study of the noncentrosymmetric superconductor Nb0.5Os0.5.

PubMed

Singh, D; Barker, J A T; Thamizhavel, A; Hillier, A D; Paul, D McK; Singh, R P

2018-01-22

The properties of the noncentrosymmetric superconductor (α-[Formula: see text] structure) Nb 0.5 Os 0.5 have been investigated using resistivity, magnetization, specific heat, and muon spin relaxation and rotation (μSR) measurements. These measurements suggest that Nb 0.5 Os 0.5 is a weakly coupled ([Formula: see text]) type-II superconductor ([Formula: see text]), having a bulk superconducting transition temperature T c   =  3.07 K. The specific heat data fits well with the single-gap BCS model indicating nodeless s-wave superconductivity in Nb 0.5 Os 0.5 . The μSR measurements also confirm [Formula: see text]-wave superconductivity with the preserved time-reversal symmetry.

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".

NOTE ON TRAVEL TIME SHIFTS DUE TO AMPLITUDE MODULATION IN TIME-DISTANCE HELIOSEISMOLOGY MEASUREMENTS

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

Nigam, R.; Kosovichev, A. G., E-mail: rakesh@quake.stanford.ed, E-mail: sasha@quake.stanford.ed

Correct interpretation of acoustic travel times measured by time-distance helioseismology is essential to get an accurate understanding of the solar properties that are inferred from them. It has long been observed that sunspots suppress p-mode amplitude, but its implications on travel times have not been fully investigated so far. It has been found in test measurements using a 'masking' procedure, in which the solar Doppler signal in a localized quiet region of the Sun is artificially suppressed by a spatial function, and using numerical simulations that the amplitude modulations in combination with the phase-speed filtering may cause systematic shifts ofmore » acoustic travel times. To understand the properties of this procedure, we derive an analytical expression for the cross-covariance of a signal that has been modulated locally by a spatial function that has azimuthal symmetry and then filtered by a phase-speed filter typically used in time-distance helioseismology. Comparing this expression to the Gabor wavelet fitting formula without this effect, we find that there is a shift in the travel times that is introduced by the amplitude modulation. The analytical model presented in this paper can be useful also for interpretation of travel time measurements for the non-uniform distribution of oscillation amplitude due to observational effects.« less

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.

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.

Velocity of a freely rising gas bubble in a soda-lime silicate glass melt

NASA Technical Reports Server (NTRS)

Hornyak, E. J.; Weinberg, M. C.

1984-01-01

A comparison is conducted between measured velocities for the buoyant rise of single bubbles of varying size and composition, in a soda-lime silicate glass melt, with the steady state velocities predicted by the Stokes and Hadamard-Rybczynski formulas. In all cases, the data are noted to fit the Hadamard-Rybczynski expression for steady state rise speed considerably better than the Stokes formula.

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.

Band head spin assignment of superdeformed bands in Hg isotopes through power index formula

NASA Astrophysics Data System (ADS)

Sharma, Honey; Mittal, H. M.

2018-05-01

The power index formula has been used to obtain the band head spin (I 0) of all the superdeformed (SD) bands in Hg isotopes. A least squares fitting approach is used. The root mean square deviations between the determined and the observed transition energies are calculated by extracting the model parameters using the power index formula. Whenever definite spins are available, the determined and the observed transition energies are in accordance with each other. The computed values of dynamic moment of inertia J (2) obtained by using the power index formula and its deviation with the rotational frequency is also studied. Excellent agreement is shown between the calculated and the experimental results for J (2) versus the rotational frequency. Hence, the power index formula works very well for all the SD bands in Hg isotopes expect for 195Hg(2, 3, 4).

Rapid evaluation for dielectronic recombination rate coefficients of the H-like isoelectronic sequence.

NASA Astrophysics Data System (ADS)

Teng, H.; Xu, Z.

1996-09-01

The authors present a set of accurate formulae for the rapid calculation of dielectronic recombination rate coefficients of H-like ions from Ne (Z = 10) to Ni (Z = 29) with an electron temperature range from 0.6 to 10 keV. This set of formulae are obtained by fitting directly the dielectronic recombination rate coefficients calculated on the basis of the intermediate - coupling multi - configuration Hartree-Fock model made by Karim and Bhalla (1988). The dielectronic recombination rate coefficients from these formulae are in close agreement with the original results of Karim et al. The errors are generally less than 0.1%. The results are also compared with the ones obtained by a set of new rate formulae developed by Hahn. These formulae can be used for generating dielectronic recombination rate coefficients of some H-like ions where the explicit calculations are unavailable. The detailed results are tabulated and discussed.

Comparison of formula and number-right scoring in undergraduate medical training: a Rasch model analysis.

PubMed

Cecilio-Fernandes, Dario; Medema, Harro; Collares, Carlos Fernando; Schuwirth, Lambert; Cohen-Schotanus, Janke; Tio, René A

2017-11-09

Progress testing is an assessment tool used to periodically assess all students at the end-of-curriculum level. Because students cannot know everything, it is important that they recognize their lack of knowledge. For that reason, the formula-scoring method has usually been used. However, where partial knowledge needs to be taken into account, the number-right scoring method is used. Research comparing both methods has yielded conflicting results. As far as we know, in all these studies, Classical Test Theory or Generalizability Theory was used to analyze the data. In contrast to these studies, we will explore the use of the Rasch model to compare both methods. A 2 × 2 crossover design was used in a study where 298 students from four medical schools participated. A sample of 200 previously used questions from the progress tests was selected. The data were analyzed using the Rasch model, which provides fit parameters, reliability coefficients, and response option analysis. The fit parameters were in the optimal interval ranging from 0.50 to 1.50, and the means were around 1.00. The person and item reliability coefficients were higher in the number-right condition than in the formula-scoring condition. The response option analysis showed that the majority of dysfunctional items emerged in the formula-scoring condition. The findings of this study support the use of number-right scoring over formula scoring. Rasch model analyses showed that tests with number-right scoring have better psychometric properties than formula scoring. However, choosing the appropriate scoring method should depend not only on psychometric properties but also on self-directed test-taking strategies and metacognitive skills.

A study of coherence of soft gluons in hadron jets

NASA Astrophysics Data System (ADS)

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

1990-09-01

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

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

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

Naito, O.

2015-08-15

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

Retrospective Analysis of NIST Standard Reference Material 1450, Fibrous Glass Board, for Thermal Insulation Measurements.

PubMed

Zarr, Robert R; Heckert, N Alan; Leigh, Stefan D

2014-01-01

Thermal conductivity data acquired previously for the establishment of Standard Reference Material (SRM) 1450, Fibrous Glass Board, as well as subsequent renewals 1450a, 1450b, 1450c, and 1450d, are re-analyzed collectively and as individual data sets. Additional data sets for proto-1450 material lots are also included in the analysis. The data cover 36 years of activity by the National Institute of Standards and Technology (NIST) in developing and providing thermal insulation SRMs, specifically high-density molded fibrous-glass board, to the public. Collectively, the data sets cover two nominal thicknesses of 13 mm and 25 mm, bulk densities from 60 kg·m(-3) to 180 kg·m(-3), and mean temperatures from 100 K to 340 K. The analysis repetitively fits six models to the individual data sets. The most general form of the nested set of multilinear models used is given in the following equation: [Formula: see text]where λ(ρ,T) is the predicted thermal conductivity (W·m(-1)·K(-1)), ρ is the bulk density (kg·m(-3)), T is the mean temperature (K) and ai (for i = 1, 2, … 6) are the regression coefficients. The least squares fit results for each model across all data sets are analyzed using both graphical and analytic techniques. The prevailing generic model for the majority of data sets is the bilinear model in ρ and T. [Formula: see text] One data set supports the inclusion of a cubic temperature term and two data sets with low-temperature data support the inclusion of an exponential term in T to improve the model predictions. Physical interpretations of the model function terms are described. Recommendations for future renewals of SRM 1450 are provided. An Addendum provides historical background on the origin of this SRM and the influence of the SRM on external measurement programs.

TTVFaster: First order eccentricity transit timing variations (TTVs)

NASA Astrophysics Data System (ADS)

Agol, Eric; Deck, Katherine

2016-04-01

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

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

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

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

PubMed

Wu, Wen; Wu, Zhouhu; Song, Zhiwen

2017-07-01

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

Measurement of the W boson polarisation in [Formula: see text] events from pp collisions at [Formula: see text] = 8 TeV in the lepton + jets channel with ATLAS.

PubMed

Aaboud, M; Aad, G; Abbott, B; Abdallah, J; Abdinov, O; Abeloos, B; AbouZeid, O S; Abraham, N L; Abramowicz, H; Abreu, H; Abreu, R; Abulaiti, Y; Acharya, B S; Adachi, S; Adamczyk, L; Adams, D L; Adelman, J; Adomeit, S; Adye, T; Affolder, A A; Agatonovic-Jovin, T; Aguilar-Saavedra, J A; Ahlen, S P; Ahmadov, F; Aielli, G; Akerstedt, H; Åkesson, T P A; Akimov, A V; Alberghi, G L; Albert, J; Albrand, S; Alconada Verzini, M J; Aleksa, M; Aleksandrov, I N; Alexa, C; Alexander, G; Alexopoulos, T; Alhroob, M; Ali, B; Aliev, M; Alimonti, G; Alison, J; Alkire, S P; Allbrooke, B M M; Allen, B W; Allport, P P; Aloisio, A; Alonso, A; Alonso, F; Alpigiani, C; Alshehri, A A; Alstaty, M; Alvarez Gonzalez, B; Álvarez Piqueras, D; Alviggi, M G; Amadio, B T; Amaral Coutinho, Y; Amelung, C; Amidei, D; Amor Dos Santos, S P; Amorim, A; Amoroso, S; Amundsen, G; Anastopoulos, C; Ancu, L S; Andari, N; Andeen, T; Anders, C F; Anders, J K; Anderson, K J; Andreazza, A; Andrei, V; Angelidakis, S; Angelozzi, I; Angerami, A; Anghinolfi, F; Anisenkov, A V; Anjos, N; Annovi, A; Antel, C; Antonelli, M; Antonov, A; Antrim, D J; Anulli, F; Aoki, M; Aperio Bella, L; Arabidze, G; Arai, Y; Araque, J P; Araujo Ferraz, V; Arce, A T H; Arduh, F A; Arguin, J-F; Argyropoulos, S; Arik, M; Armbruster, A J; Armitage, L J; Arnaez, O; Arnold, H; Arratia, M; Arslan, O; Artamonov, A; Artoni, G; Artz, S; Asai, S; Asbah, N; Ashkenazi, A; Åsman, B; Asquith, L; Assamagan, K; Astalos, R; Atkinson, M; Atlay, N B; Augsten, K; Avolio, G; Axen, B; Ayoub, M K; Azuelos, G; Baak, M A; Baas, A E; Baca, M J; Bachacou, H; Bachas, K; Backes, M; Backhaus, M; Bagiacchi, P; Bagnaia, P; Bai, Y; Baines, J T; Bajic, M; Baker, O K; Baldin, E M; Balek, P; Balestri, T; Balli, F; Balunas, W K; Banas, E; Banerjee, Sw; Bannoura, A A E; Barak, L; Barberio, E L; Barberis, D; Barbero, M; Barillari, T; Barisits, M-S; Barklow, T; Barlow, N; Barnes, S L; Barnett, B M; Barnett, R M; Barnovska-Blenessy, Z; Baroncelli, A; Barone, G; Barr, A J; Barranco Navarro, L; Barreiro, F; Barreiro Guimarães da Costa, J; Bartoldus, R; Barton, A E; Bartos, P; Basalaev, A; Bassalat, A; Bates, R L; Batista, S J; Batley, J R; Battaglia, M; Bauce, M; Bauer, F; Bawa, H S; Beacham, J B; Beattie, M D; Beau, T; Beauchemin, P H; Bechtle, P; Beck, H P; Becker, K; Becker, M; Beckingham, M; Becot, C; Beddall, A J; Beddall, A; Bednyakov, V A; Bedognetti, M; Bee, C P; Beemster, L J; Beermann, T A; Begel, M; Behr, J K; Bell, A S; Bella, G; Bellagamba, L; Bellerive, A; Bellomo, M; Belotskiy, K; Beltramello, O; Belyaev, N L; Benary, O; Benchekroun, D; Bender, M; Bendtz, K; Benekos, N; Benhammou, Y; Benhar Noccioli, E; Benitez, J; Benjamin, D P; Bensinger, J R; Bentvelsen, S; Beresford, L; Beretta, M; Berge, D; Bergeaas Kuutmann, E; Berger, N; Beringer, J; Berlendis, S; Bernard, N R; Bernius, C; Bernlochner, F U; Berry, T; Berta, P; Bertella, C; Bertoli, G; Bertolucci, F; Bertram, I A; Bertsche, C; Bertsche, D; Besjes, G J; Bessidskaia Bylund, O; Bessner, M; Besson, N; Betancourt, C; Bethani, A; Bethke, S; Bevan, A J; Bianchi, R M; Bianco, M; Biebel, O; Biedermann, D; Bielski, R; Biesuz, N V; Biglietti, M; Bilbao De Mendizabal, J; Billoud, T R V; Bilokon, H; Bindi, M; Bingul, A; Bini, C; Biondi, S; Bisanz, T; Bjergaard, D M; Black, C W; Black, J E; Black, K M; Blackburn, D; Blair, R E; Blazek, T; Bloch, I; Blocker, C; Blue, A; Blum, W; Blumenschein, U; Blunier, S; Bobbink, G J; Bobrovnikov, V S; Bocchetta, S S; Bocci, A; Bock, C; Boehler, M; Boerner, D; Bogaerts, J A; Bogavac, D; Bogdanchikov, A G; Bohm, C; Boisvert, V; Bokan, P; Bold, T; Boldyrev, A S; Bomben, M; Bona, M; Boonekamp, M; Borisov, A; Borissov, G; Bortfeldt, J; Bortoletto, D; Bortolotto, V; Bos, K; Boscherini, D; Bosman, M; Bossio Sola, J D; Boudreau, J; Bouffard, J; Bouhova-Thacker, E V; Boumediene, D; Bourdarios, C; Boutle, S K; Boveia, A; Boyd, J; Boyko, I R; Bracinik, J; Brandt, A; Brandt, G; Brandt, O; Bratzler, U; Brau, B; Brau, J E; Breaden Madden, W D; Brendlinger, K; Brennan, A J; Brenner, L; 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Zimmermann, S; Zinonos, Z; Zinser, M; Ziolkowski, M; Živković, L; Zobernig, G; Zoccoli, A; Zur Nedden, M; Zwalinski, L

2017-01-01

This paper presents a measurement of the polarisation of W bosons from [Formula: see text] decays, reconstructed in events with one high-[Formula: see text] lepton and at least four jets. Data from pp collisions at the LHC were collected at [Formula: see text] = 8 TeV and correspond to an integrated luminosity of 20.2 fb[Formula: see text]. The angle [Formula: see text] between the b -quark from the top quark decay and a direct W boson decay product in the W boson rest frame is sensitive to the W boson polarisation. Two different W decay products are used as polarisation analysers: the charged lepton and the down-type quark for the leptonically and hadronically decaying W boson, respectively. The most precise measurement of the W boson polarisation via the distribution of [Formula: see text] is obtained using the leptonic analyser and events in which at least two of the jets are tagged as b -quark jets. The fitted fractions of longitudinal, left- and right-handed polarisation states are [Formula: see text], [Formula: see text] and [Formula: see text], and are the most precisely measured W boson polarisation fractions to date. Limits on anomalous couplings of the Wtb vertex are set.

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG).

PubMed

Aoki, S; Aoki, Y; Bečirević, D; Bernard, C; Blum, T; Colangelo, G; Della Morte, M; Dimopoulos, P; Dürr, S; Fukaya, H; Golterman, M; Gottlieb, Steven; Hashimoto, S; Heller, U M; Horsley, R; Jüttner, A; Kaneko, T; Lellouch, L; Leutwyler, H; Lin, C-J D; Lubicz, V; Lunghi, E; Mawhinney, R; Onogi, T; Pena, C; Sachrajda, C T; Sharpe, S R; Simula, S; Sommer, R; Vladikas, A; Wenger, U; Wittig, H

2017-01-01

We review lattice results related to pion, kaon, D - and B -meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor [Formula: see text], arising in the semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay constant ratio [Formula: see text] and its consequences for the CKM matrix elements [Formula: see text] and [Formula: see text]. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of [Formula: see text] and [Formula: see text] Chiral Perturbation Theory. We review the determination of the [Formula: see text] parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for [Formula: see text] and [Formula: see text] (also new compared to the previous review), as well as those for D - and B -meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant [Formula: see text].

Multisite concordance of apparent diffusion coefficient measurements across the NCI Quantitative Imaging Network.

PubMed

Newitt, David C; Malyarenko, Dariya; Chenevert, Thomas L; Quarles, C Chad; Bell, Laura; Fedorov, Andriy; Fennessy, Fiona; Jacobs, Michael A; Solaiyappan, Meiyappan; Hectors, Stefanie; Taouli, Bachir; Muzi, Mark; Kinahan, Paul E; Schmainda, Kathleen M; Prah, Melissa A; Taber, Erin N; Kroenke, Christopher; Huang, Wei; Arlinghaus, Lori R; Yankeelov, Thomas E; Cao, Yue; Aryal, Madhava; Yen, Yi-Fen; Kalpathy-Cramer, Jayashree; Shukla-Dave, Amita; Fung, Maggie; Liang, Jiachao; Boss, Michael; Hylton, Nola

2018-01-01

Diffusion weighted MRI has become ubiquitous in many areas of medicine, including cancer diagnosis and treatment response monitoring. Reproducibility of diffusion metrics is essential for their acceptance as quantitative biomarkers in these areas. We examined the variability in the apparent diffusion coefficient (ADC) obtained from both postprocessing software implementations utilized by the NCI Quantitative Imaging Network and online scan time-generated ADC maps. Phantom and in vivo breast studies were evaluated for two ([Formula: see text]) and four ([Formula: see text]) [Formula: see text]-value diffusion metrics. Concordance of the majority of implementations was excellent for both phantom ADC measures and in vivo [Formula: see text], with relative biases [Formula: see text] ([Formula: see text]) and [Formula: see text] (phantom [Formula: see text]) but with higher deviations in ADC at the lowest phantom ADC values. In vivo [Formula: see text] concordance was good, with typical biases of [Formula: see text] to 3% but higher for online maps. Multiple b -value ADC implementations were separated into two groups determined by the fitting algorithm. Intergroup mean ADC differences ranged from negligible for phantom data to 2.8% for [Formula: see text] in vivo data. Some higher deviations were found for individual implementations and online parametric maps. Despite generally good concordance, implementation biases in ADC measures are sometimes significant and may be large enough to be of concern in multisite studies.

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.

Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures.

PubMed

Heyes, David M; Santos, Andrés

2018-06-07

A detailed comparison between the Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state of hard-sphere mixtures is made with Molecular Dynamics (MD) simulations of the same compositions. The Labík and Smith simulation technique [S. Labík and W. R. Smith, Mol. Simul. 12, 23-31 (1994)] was used to implement the Widom particle insertion method to calculate the excess chemical potential, βμ 0 ex , of a test particle of variable diameter, σ 0 , immersed in a hard-sphere fluid mixture with different compositions and values of the packing fraction, η. Use is made of the fact that the only polynomial representation of βμ 0 ex which is consistent with the limits σ 0 → 0 and σ 0 → ∞ has to be of the cubic form, i.e., c 0 (η)+c¯ 1 (η)σ 0 /M 1 +c¯ 2 (η)(σ 0 /M 1 ) 2 +c¯ 3 (η)(σ 0 /M 1 ) 3 , where M 1 is the first moment of the distribution. The first two coefficients, c 0 (η) and c¯ 1 (η), are known analytically, while c¯ 2 (η) and c¯ 3 (η) were obtained by fitting the MD data to this expression. This in turn provides a method to determine the excess free energy per particle, βa ex , in terms of c¯ 2 , c¯ 3 , and the compressibility factor, Z. Very good agreement between the BMCSL formulas and the MD data is found for βμ 0 ex , Z, and βa ex for binary mixtures and continuous particle size distributions with the top-hat analytic form. However, the BMCSL theory typically slightly underestimates the simulation values, especially for Z, differences which the Boublík-Carnahan-Starling-Kolafa formulas and an interpolation between two Percus-Yevick routes capture well in different ranges of the system parameter space.

Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures

NASA Astrophysics Data System (ADS)

Heyes, David M.; Santos, Andrés

2018-06-01

A detailed comparison between the Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state of hard-sphere mixtures is made with Molecular Dynamics (MD) simulations of the same compositions. The Labík and Smith simulation technique [S. Labík and W. R. Smith, Mol. Simul. 12, 23-31 (1994)] was used to implement the Widom particle insertion method to calculate the excess chemical potential, β μ0ex, of a test particle of variable diameter, σ0, immersed in a hard-sphere fluid mixture with different compositions and values of the packing fraction, η. Use is made of the fact that the only polynomial representation of β μ0ex which is consistent with the limits σ0 → 0 and σ0 → ∞ has to be of the cubic form, i.e., c0(η ) +c¯ 1(η ) σ0/M1+c¯ 2(η ) (σ0/M1 ) 2+c¯ 3(η ) (σ0/M1 ) 3, where M1 is the first moment of the distribution. The first two coefficients, c0(η) and c¯ 1(η ) , are known analytically, while c¯ 2(η ) and c¯ 3(η ) were obtained by fitting the MD data to this expression. This in turn provides a method to determine the excess free energy per particle, βaex, in terms of c¯ 2, c¯ 3, and the compressibility factor, Z. Very good agreement between the BMCSL formulas and the MD data is found for β μ0ex, Z, and βaex for binary mixtures and continuous particle size distributions with the top-hat analytic form. However, the BMCSL theory typically slightly underestimates the simulation values, especially for Z, differences which the Boublík-Carnahan-Starling-Kolafa formulas and an interpolation between two Percus-Yevick routes capture well in different ranges of the system parameter space.

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.

A high precision semi-analytic mass function

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

Del Popolo, Antonino; Pace, Francesco; Le Delliou, Morgan, E-mail: adelpopolo@oact.inaf.it, E-mail: francesco.pace@manchester.ac.uk, E-mail: delliou@ift.unesp.br

In this paper, extending past works of Del Popolo, we show how a high precision mass function (MF) can be obtained using the excursion set approach and an improved barrier taking implicitly into account a non-zero cosmological constant, the angular momentum acquired by tidal interaction of proto-structures and dynamical friction. In the case of the ΛCDM paradigm, we find that our MF is in agreement at the 3% level to Klypin's Bolshoi simulation, in the mass range M {sub vir} = 5 × 10{sup 9} h {sup −1} M {sub ⊙}–−5 × 10{sup 14} h {sup −1} M {sub ⊙}more » and redshift range 0 ∼< z ∼< 10. For z = 0 we also compared our MF to several fitting formulae, and found in particular agreement with Bhattacharya's within 3% in the mass range 10{sup 12}–10{sup 16} h {sup −1} M {sub ⊙}. Moreover, we discuss our MF validity for different cosmologies.« less

Self-consistent approach for neutral community models with speciation

NASA Astrophysics Data System (ADS)

Haegeman, Bart; Etienne, Rampal S.

2010-03-01

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

Option pricing for stochastic volatility model with infinite activity Lévy jumps

NASA Astrophysics Data System (ADS)

Gong, Xiaoli; Zhuang, Xintian

2016-08-01

The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.

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

ERIC Educational Resources Information Center

Beau, Mathieu

2012-01-01

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

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

ERIC Educational Resources Information Center

Wang, Tianyou

2009-01-01

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

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

Golyatina, R. I.; Maiorov, S. A., E-mail: mayorov-sa@mail.ru

The drift velocities of noble-gas and mercury ions in a constant homogeneous electric field are calculated using Monte Carlo simulations. The ion mobility is analyzed as a function of the field strength and gas temperature. The fitting parameters for calculating the drift velocity by the Frost formula at gas temperatures of 4.2, 77, 300, 1000, and 2000 K are obtained. A general approximate formula for the drift velocity as a function of the reduced field and gas temperature is derived.

Study of a generalized birks formula for the scintillation response of a CaMoO4 crystal

NASA Astrophysics Data System (ADS)

Lee, J. Y.; Kim, H. J.; Kang, Sang Jun; Lee, M. H.

2017-12-01

We have investigated the scintillation characteristics of CaMoO4 (CMO) crystals by using a gamma source and various internal alpha sources. A 137Cs source with 662-keV gamma-rays was used for the gamma-quanta light yield calibration. Internal radioactive contaminations provided alpha particles with different energies from 5.41 to 7.88 MeV. We developed a C++ program based on the ROOT package for the fitting of parameters in a generalized Birks semi-empirical formula by combining the experimental and the simulation data. Results for the fitted Birks parameters are k b1 = 3.3 × 10 -3 (g/MeVcm2) for the 1st parameter and k b2 = 7.9 × 10 -5 (g/MeVcm2)2 for the 2nd parameter. The χ2/n.d.f. (Number of Degree of Freedom) is calculated as 0.1/4. We were able to estimate the 238U and 234U contaminations in a CMO crystal by using the generalized Birks semi-empirical formula.

Attenuation of thermal neutrons by an imperfect single crystal

NASA Astrophysics Data System (ADS)

Naguib, K.; Adib, M.

1996-06-01

A semi-empirical formula is given which allows one to calculate the total thermal cross section of an imperfect single crystal as a function of crystal constants, temperature and neutron energy E, in the energy range between 3 meV and 10 eV. The formula also includes the contribution of the parasitic Bragg scattering to the total cross section that takes into account the crystal mosaic spread value and its orientation with respect to the neutron beam direction. A computer program (ISCANF) was developed to calculate the total attenuation of neutrons using the proposed formula. The ISCANF program was applied to investigate the neutron attenuation through a copper single crystal. The calculated values of the neutron transmission through the imperfect copper single crystal were fitted to the measured ones in the energy range 3 - 40 meV at different crystal orientations. The result of fitting shows that use of the computer program ISCANF allows one to predict the behaviour of the total cross section of an imperfect copper single crystal for the whole energy range.

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.

betaFIT: A computer program to fit pointwise potentials to selected analytic functions

NASA Astrophysics Data System (ADS)

Le Roy, Robert J.; Pashov, Asen

2017-01-01

This paper describes program betaFIT, which performs least-squares fits of sets of one-dimensional (or radial) potential function values to four different types of sophisticated analytic potential energy functional forms. These families of potential energy functions are: the Expanded Morse Oscillator (EMO) potential [J Mol Spectrosc 1999;194:197], the Morse/Long-Range (MLR) potential [Mol Phys 2007;105:663], the Double Exponential/Long-Range (DELR) potential [J Chem Phys 2003;119:7398], and the "Generalized Potential Energy Function (GPEF)" form introduced by Šurkus et al. [Chem Phys Lett 1984;105:291], which includes a wide variety of polynomial potentials, such as the Dunham [Phys Rev 1932;41:713], Simons-Parr-Finlan [J Chem Phys 1973;59:3229], and Ogilvie-Tipping [Proc R Soc A 1991;378:287] polynomials, as special cases. This code will be useful for providing the realistic sets of potential function shape parameters that are required to initiate direct fits of selected analytic potential functions to experimental data, and for providing better analytical representations of sets of ab initio results.

Highly accurate analytic formulae for projectile motion subjected to quadratic drag

NASA Astrophysics Data System (ADS)

Turkyilmazoglu, Mustafa

2016-05-01

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

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

PubMed

Ansorge, Martin; Dubský, Pavel; Ušelová, Kateřina

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2010-12-01

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

The Extended Erlang-Truncated Exponential distribution: Properties and application to rainfall data.

PubMed

Okorie, I E; Akpanta, A C; Ohakwe, J; Chikezie, D C

2017-06-01

The Erlang-Truncated Exponential ETE distribution is modified and the new lifetime distribution is called the Extended Erlang-Truncated Exponential EETE distribution. Some statistical and reliability properties of the new distribution are given and the method of maximum likelihood estimate was proposed for estimating the model parameters. The usefulness and flexibility of the EETE distribution was illustrated with an uncensored data set and its fit was compared with that of the ETE and three other three-parameter distributions. Results based on the minimized log-likelihood ([Formula: see text]), Akaike information criterion (AIC), Bayesian information criterion (BIC) and the generalized Cramér-von Mises [Formula: see text] statistics shows that the EETE distribution provides a more reasonable fit than the one based on the other competing distributions.

Test of a General Formula for Black Hole Gravitational Wave Kicks

NASA Technical Reports Server (NTRS)

van Meter, James R.; Miller, M. Coleman; Baker, John G.; Boggs, William D.; Kelly, Bernard J.

2010-01-01

Although the gravitational wave kick velocity in the orbital plane of coalescing black holes has been understood for some time, apparently conflicting formulae have been proposed for the dominant outof- plane kick, each a good fit to different data sets. This is important to resolve because it is only the out-of-plane kicks that can reach more than 500 km s-l and can thus eject merged remnants from galaxies. Using a different ansatz for the out-of-plane kick, we show that we can fit almost all existing data to better than 5%. This is good enough for any astrophysical calculation and shows that the previous apparent conflict was only because the two data sets explored different aspects of the kick parameter space.

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.

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.

Search for an additional, heavy Higgs boson in the [Formula: see text] decay channel at [Formula: see text] in [Formula: see text] collision data with the ATLAS detector.

PubMed

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Schmitt, S; Schmitt, S; Schneider, B; Schnellbach, Y J; Schnoor, U; Schoeffel, L; Schoening, A; Schoenrock, B D; Schopf, E; Schorlemmer, A L S; Schott, M; Schouten, D; Schovancova, J; Schramm, S; Schreyer, M; Schroeder, C; Schuh, N; Schultens, M J; Schultz-Coulon, H-C; Schulz, H; Schumacher, M; Schumm, B A; Schune, Ph; Schwanenberger, C; Schwartzman, A; Schwarz, T A; Schwegler, Ph; Schweiger, H; Schwemling, Ph; Schwienhorst, R; Schwindling, J; Schwindt, T; Sciacca, F G; Scifo, E; Sciolla, G; Scuri, F; Scutti, F; Searcy, J; Sedov, G; Sedykh, E; Seema, P; Seidel, S C; Seiden, A; Seifert, F; Seixas, J M; Sekhniaidze, G; Sekhon, K; Sekula, S J; Seliverstov, D M; Semprini-Cesari, N; Serfon, C; Serin, L; Serkin, L; Serre, T; Sessa, M; Seuster, R; Severini, H; Sfiligoj, T; Sforza, F; Sfyrla, A; Shabalina, E; Shamim, M; Shan, L Y; Shang, R; Shank, J T; Shapiro, M; Shatalov, P B; Shaw, K; Shaw, S M; Shcherbakova, A; Shehu, C Y; Sherwood, P; Shi, L; Shimizu, S; Shimmin, C O; Shimojima, M; Shiyakova, M; Shmeleva, A; Shoaleh Saadi, D; Shochet, M J; Shojaii, S; Shrestha, S; Shulga, E; Shupe, M A; Shushkevich, S; Sicho, P; Sidebo, P E; Sidiropoulou, O; Sidorov, D; Sidoti, A; Siegert, F; Sijacki, Dj; Silva, J; Silver, Y; Silverstein, S B; Simak, V; Simard, O; Simic, Lj; Simion, S; Simioni, E; Simmons, B; Simon, D; Sinervo, P; Sinev, N B; Sioli, M; Siragusa, G; Sisakyan, A N; Sivoklokov, S Yu; Sjölin, J; Sjursen, T B; Skinner, M B; Skottowe, H P; Skubic, P; Slater, M; Slavicek, T; Slawinska, M; Sliwa, K; Smakhtin, V; Smart, B H; Smestad, L; Smirnov, S Yu; Smirnov, Y; Smirnova, L N; Smirnova, O; Smith, M N K; Smith, R W; Smizanska, M; Smolek, K; Snesarev, A A; Snidero, G; Snyder, S; Sobie, R; Socher, F; Soffer, A; Soh, D A; Sokhrannyi, G; Solans, C A; Solar, M; Solc, J; Soldatov, E Yu; Soldevila, U; Solodkov, A A; Soloshenko, A; Solovyanov, O V; Solovyev, V; Sommer, P; Song, H Y; Soni, N; Sood, A; Sopczak, A; Sopko, B; Sopko, V; Sorin, V; Sosa, D; Sosebee, M; Sotiropoulou, C L; Soualah, R; 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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; 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; Temple, D; Ten Kate, H; 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, R J; Thompson, A S; Thomsen, L A; Thomson, E; Thomson, M; Thun, R P; Tibbetts, M J; Ticse Torres, R E; Tikhomirov, V O; Tikhonov, Yu A; Timoshenko, S; Tiouchichine, E; Tipton, P; Tisserant, S; Todome, K; Todorov, T; Todorova-Nova, S; Tojo, J; Tokár, S; Tokushuku, K; Tollefson, K; Tolley, E; Tomlinson, L; Tomoto, M; Tompkins, L; Toms, K; 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; Trischuk, W; Trocmé, B; Troncon, C; Trottier-McDonald, M; Trovatelli, M; True, P; Truong, L; 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; Turra, R; Turvey, A J; Tuts, P M; Tykhonov, A; Tylmad, M; Tyndel, M; Ueda, I; Ueno, R; Ughetto, M; Ugland, 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; Valencic, N; Valentinetti, S; Valero, A; Valery, L; Valkar, S; Valladolid Gallego, E; Vallecorsa, S; Valls Ferrer, J A; 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; Vannucci, F; Vardanyan, G; Vari, R; Varnes, E W; Varol, T; Varouchas, D; Vartapetian, A; Varvell, K E; Vazeille, F; Vazquez Schroeder, T; Veatch, J; Veloce, L M; Veloso, F; Velz, T; Veneziano, S; Ventura, A; Ventura, D; 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; Vickey Boeriu, O E; Viehhauser, G H A; Viel, S; Vigne, R; Villa, M; Villaplana Perez, M; Vilucchi, E; Vincter, M G; Vinogradov, V B; Vivarelli, I; Vives Vaque, F; Vlachos, S; Vladoiu, D; Vlasak, M; Vogel, M; Vokac, P; Volpi, G; Volpi, M; von der Schmitt, H; von Radziewski, H; von Toerne, E; Vorobel, V; Vorobev, K; Vos, M; Voss, R; Vossebeld, J H; Vranjes, N; Vranjes Milosavljevic, M; 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Zibell, A; Zieminska, D; Zimine, N I; Zimmermann, C; Zimmermann, S; Zinonos, Z; Zinser, M; Ziolkowski, M; Živković, L; Zobernig, G; Zoccoli, A; Zur Nedden, M; Zurzolo, G; Zwalinski, L

A search is presented for a high-mass Higgs boson in the [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] decay modes using the ATLAS detector at the CERN Large Hadron Collider. The search uses proton-proton collision data at a centre-of-mass energy of 8 TeV corresponding to an integrated luminosity of 20.3 fb[Formula: see text]. The results of the search are interpreted in the scenario of a heavy Higgs boson with a width that is small compared with the experimental mass resolution. The Higgs boson mass range considered extends up to [Formula: see text] for all four decay modes and down to as low as 140 [Formula: see text], depending on the decay mode. No significant excess of events over the Standard Model prediction is found. A simultaneous fit to the four decay modes yields upper limits on the production cross-section of a heavy Higgs boson times the branching ratio to [Formula: see text] boson pairs. 95 % confidence level upper limits range from 0.53 pb at [Formula: see text] GeV to 0.008 pb at [Formula: see text] GeV for the gluon-fusion production mode and from 0.31 pb at [Formula: see text] GeV to 0.009 pb at [Formula: see text] GeV for the vector-boson-fusion production mode. The results are also interpreted in the context of Type-I and Type-II two-Higgs-doublet models.

Size separation of analytes using monomeric surfactants

DOEpatents

Yeung, Edward S.; Wei, Wei

2005-04-12

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

General monogamy of Tsallis q -entropy entanglement in multiqubit systems

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Determination of calcium, copper, iron, magnesium, manganese, potassium, phosphorus, sodium, and zinc in fortified food products by microwave digestion and inductively coupled plasma-optical emission spectrometry: single-laboratory validation and ring trial.

PubMed

Poitevin, Eric

2012-01-01

A single-laboratory validation (SLV) and a ring trial (RT) were undertaken to determine nine nutritional elements in food products by inductively coupled plasma-optical emission spectrometry in order to modernize AOAC Official Method 984.27. The improvements involved extension of the scope to all food matrixes (including infant formula), optimized microwave digestion, selected analytical lines, internal standardization, and ion buffering. Simultaneous determination of nine elements (calcium, copper, iron, potassium, magnesium, manganese, sodium, phosphorus, and zinc) was made in food products. Sample digestion was performed through wet digestion of food samples by microwave technology with either closed- or open-vessel systems. Validation was performed to characterize the method for selectivity, sensitivity, linearity, accuracy, precision, recovery, ruggedness, and uncertainty. The robustness and efficiency of this method was proven through a successful RT using experienced independent food industry laboratories. Performance characteristics are reported for 13 certified and in-house reference materials, populating the AOAC triangle food sectors, which fulfilled AOAC criteria and recommendations for accuracy (trueness, recovery, and z-scores) and precision (repeatability and reproducibility RSD, and HorRat values) regarding SLVs and RTs. This multielemental method is cost-efficient, time-saving, accurate, and fit-for-purpose according to ISO 17025 Norm and AOAC acceptability criteria, and is proposed as an extended updated version of AOAC Official Method 984.27 for fortified food products, including infant formula.

Measuring strain and rotation fields at the dislocation core in graphene

NASA Astrophysics Data System (ADS)

Bonilla, L. L.; Carpio, A.; Gong, C.; Warner, J. H.

2015-10-01

Strain fields, dislocations, and defects may be used to control electronic properties of graphene. By using advanced imaging techniques with high-resolution transmission electron microscopes, we have measured the strain and rotation fields about dislocations in monolayer graphene with single-atom sensitivity. These fields differ qualitatively from those given by conventional linear elasticity. However, atom positions calculated from two-dimensional (2D) discrete elasticity and three-dimensional discrete periodized Föppl-von Kármán equations (dpFvKEs) yield fields close to experiments when determined by geometric phase analysis. 2D theories produce symmetric fields whereas those from experiments exhibit asymmetries. Numerical solutions of dpFvKEs provide strain and rotation fields of dislocation dipoles and pairs that also exhibit asymmetries and, compared with experiments, may yield information on out-of-plane displacements of atoms. While discrete theories need to be solved numerically, analytical formulas for strains and rotation about dislocations can be obtained from 2D Mindlin's hyperstress theory. These formulas are very useful for fitting experimental data and provide a template to ascertain the importance of nonlinear and nonplanar effects. Measuring the parameters of this theory, we find two characteristic lengths between three and four times the lattice spacings that control dilatation and rotation about a dislocation. At larger distances from the dislocation core, the elastic fields decay to those of conventional elasticity. Our results may be relevant for strain engineering in graphene and other 2D materials of current interest.

Short-Term High-Intensity Interval Training on Body Composition and Blood Glucose in Overweight and Obese Young Women.

PubMed

Kong, Zhaowei; Sun, Shengyan; Liu, Min; Shi, Qingde

2016-01-01

This study was to determine the effects of five-week high-intensity interval training (HIIT) on cardiorespiratory fitness, body composition, blood glucose, and relevant systemic hormones when compared to moderate-intensity continuous training (MICT) in overweight and obese young women. Methods . Eighteen subjects completed 20 sessions of HIIT or MICT for five weeks. HIIT involved 60 × 8 s cycling at ~90% of peak oxygen consumption ([Formula: see text]) interspersed with 12 s recovery, whereas MICT involved 40-minute continuous cycling at 65% of [Formula: see text]. [Formula: see text], body composition, blood glucose, and fasting serum hormones, including leptin, growth hormone, testosterone, cortisol, and fibroblast growth factor 21, were measured before and after training. Results . Both exercise groups achieved significant improvements in [Formula: see text] (+7.9% in HIIT versus +11.7% in MICT) and peak power output (+13.8% in HIIT versus +21.9% in MICT) despite no training effects on body composition or the relevant systemic hormones. Blood glucose tended to be decreased after the intervention ( p = 0.062). The rating of perceived exertion in MICT was higher than that in HIIT ( p = 0.042). Conclusion . Compared with MICT, short-term HIIT is more time-efficient and is perceived as being easier for improving cardiorespiratory fitness and fasting blood glucose for overweight and obese young women.

Analytic representation of FK/Fπ in two loop chiral perturbation theory

NASA Astrophysics Data System (ADS)

Ananthanarayan, B.; Bijnens, Johan; Friot, Samuel; Ghosh, Shayan

2018-05-01

We present an analytic representation of FK/Fπ as calculated in three-flavor two-loop chiral perturbation theory, which involves expressing three mass scale sunsets in terms of Kampé de Fériet series. We demonstrate how approximations may be made to obtain relatively compact analytic representations. An illustrative set of fits using lattice data is also presented, which shows good agreement with existing fits.

The importance of excluded solvent volume effects in computing hydration free energies.

PubMed

Yang, Pei-Kun; Lim, Carmay

2008-11-27

Continuum dielectric methods such as the Born equation have been widely used to compute the electrostatic component of the solvation free energy, DeltaG(solv)(elec), because they do not need to include solvent molecules explicitly and are thus far less costly compared to molecular simulations. All of these methods can be derived from Gauss Law of Maxwell's equations, which yields an analytical solution for the solvation free energy, DeltaG(Born), when the solute is spherical. However, in Maxwell's equations, the solvent is assumed to be a structureless continuum, whereas in reality, the near-solute solvent molecules are highly structured unlike far-solute bulk solvent. Since we have recently reformulated Gauss Law of Maxwell's equations to incorporate the near-solute solvent structure by considering excluded solvent volume effects, we have used it in this work to derive an analytical solution for the hydration free energy of an ion. In contrast to continuum solvent models, which assume that the normalized induced solvent electric dipole density P(n) is constant, P(n) mimics that observed from simulations. The analytical formula for the ionic hydration free energy shows that the Born radius, which has been used as an adjustable parameter to fit experimental hydration free energies, is no longer ill defined but is related to the radius and polarizability of the water molecule, the hydration number, and the first peak position of the solute-solvent radial distribution function. The resulting DeltaG(solv)(elec) values are shown to be close to the respective experimental numbers.

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.

Evaluation of dose-response relationship between smoking load and cardiopulmonary fitness in adult smokers: A cross-sectional study.

PubMed

Lauria, V T; Sperandio, E F; de Sousa, T L W; de Oliveira Vieira, W; Romiti, M; de Toledo Gagliardi, A R; Arantes, R L; Dourado, V Z

To evaluate the dose-response relationship between smoking load and cardiopulmonary fitness, as measured with cardiopulmonary exercise testing (CPET), in adult smokers free of respiratory diseases. After a complete clinical evaluation and spirometry, 95 adult smokers (35 men and 60 women) underwent CPET on a treadmill. The physiological responses during CPET showed lower cardiorespiratory fitness levels, regardless of smoking load, with a peak [Formula: see text] lower than 100% of the expected value and a lower maximum heart rate. We observed a significant moderate negative correlation between smoking load and peak [Formula: see text] . The smoking load also presented a significant negative correlation with maximum heart rate(r=-0.36; p<0.05), lactate threshold(r=-0.45; p<0.05), and peak ventilation(r=-0.43; p<0.05). However, a dose-response relationship between smoking load quartiles and cardiopulmonary fitness was not found comparing quartiles of smoking loads after adjustment for age, sex and cardiovascular risk. There appears to be no dose-response relationship between SL and cardiopulmonary fitness in adult smokers with preserved pulmonary function, after adjusting the analysis for age and cardiovascular risk. Our results suggest that smoking cessation might be useful as the primary strategy to prevent cardiopulmonary fitness decline in smokers, regardless of smoking load. Thus, even a very low dose of tobacco use must be avoided in preventive strategies focusing on becoming people more physically active and fit. Copyright © 2016 Sociedade Portuguesa de Pneumologia. Published by Elsevier España, S.L.U. All rights reserved.

A Festival Formula that Forestalls Flops.

ERIC Educational Resources Information Center

Vinje, Faye

1980-01-01

A successful community festival will be unique, will fit the character and interests of the community, and should be headed by a versatile coordinator who can administer fund raising, publicity, and recordkeeping. (RJG)

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.

Revisit submergence of ice blocks in front of ice cover—an experimental study

NASA Astrophysics Data System (ADS)

Wang, Jun; Wu, Yi-fan; Sui, Jueyi

2018-04-01

The present paper studies the stabilities of ice blocks in front of an ice cover based on experiments carried out in laboratory by using four types of ice blocks with different dimensions. The forces acting on the ice blocks in front of the ice cover are analyzed. The critical criteria for the entrainment of ice blocks in front of the ice cover are established by considering the drag force caused by the flowing water, the collision force, and the hydraulic pressure force. Formula for determining whether or not an ice block will be entrained under the ice cover is derived. All three dimensions of the ice block are considered in the proposed formula. The velocities calculated by using the developed formula are compared with those of calculated by other formulas proposed by other researchers, as well as the measured flow velocities for the entrainment of ice blocks in laboratory. The fitting values obtained by using the derived formula agree well with the experimental results.

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

PubMed

Sullivan, Darryl

2016-01-01

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

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

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

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

Mixed-order phase transition in a colloidal crystal.

PubMed

Alert, Ricard; Tierno, Pietro; Casademunt, Jaume

2017-12-05

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

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.

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

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.

Analytic modeling of aerosol size distributions

NASA Technical Reports Server (NTRS)

Deepack, A.; Box, G. P.

1979-01-01

Mathematical functions commonly used for representing aerosol size distributions are studied parametrically. Methods for obtaining best fit estimates of the parameters are described. A catalog of graphical plots depicting the parametric behavior of the functions is presented along with procedures for obtaining analytical representations of size distribution data by visual matching of the data with one of the plots. Examples of fitting the same data with equal accuracy by more than one analytic model are also given.

A Review of Discrete Element Method (DEM) Particle Shapes and Size Distributions for Lunar Soil

NASA Technical Reports Server (NTRS)

Lane, John E.; Metzger, Philip T.; Wilkinson, R. Allen

2010-01-01

As part of ongoing efforts to develop models of lunar soil mechanics, this report reviews two topics that are important to discrete element method (DEM) modeling the behavior of soils (such as lunar soils): (1) methods of modeling particle shapes and (2) analytical representations of particle size distribution. The choice of particle shape complexity is driven primarily by opposing tradeoffs with total number of particles, computer memory, and total simulation computer processing time. The choice is also dependent on available DEM software capabilities. For example, PFC2D/PFC3D and EDEM support clustering of spheres; MIMES incorporates superquadric particle shapes; and BLOKS3D provides polyhedra shapes. Most commercial and custom DEM software supports some type of complex particle shape beyond the standard sphere. Convex polyhedra, clusters of spheres and single parametric particle shapes such as the ellipsoid, polyellipsoid, and superquadric, are all motivated by the desire to introduce asymmetry into the particle shape, as well as edges and corners, in order to better simulate actual granular particle shapes and behavior. An empirical particle size distribution (PSD) formula is shown to fit desert sand data from Bagnold. Particle size data of JSC-1a obtained from a fine particle analyzer at the NASA Kennedy Space Center is also fitted to a similar empirical PSD function.

Parametrizing growth in dark energy and modified gravity models

NASA Astrophysics Data System (ADS)

Resco, Miguel Aparicio; Maroto, Antonio L.

2018-02-01

It is well known that an extremely accurate parametrization of the growth function of matter density perturbations in Λ CDM cosmology, with errors below 0.25%, is given by f (a )=Ωmγ(a ) with γ ≃0.55 . In this work, we show that a simple modification of this expression also provides a good description of growth in modified gravity theories. We consider the model-independent approach to modified gravity in terms of an effective Newton constant written as μ (a ,k )=Geff/G and show that f (a )=β (a )Ωmγ(a ) provides fits to the numerical solutions with similar accuracy to that of Λ CDM . In the time-independent case with μ =μ (k ), simple analytic expressions for β (μ ) and γ (μ ) are presented. In the time-dependent (but scale-independent) case μ =μ (a ), we show that β (a ) has the same time dependence as μ (a ). As an example, explicit formulas are provided in the Dvali-Gabadadze-Porrati (DGP) model. In the general case, for theories with μ (a ,k ), we obtain a perturbative expansion for β (μ ) around the general relativity case μ =1 which, for f (R ) theories, reaches an accuracy below 1%. Finally, as an example we apply the obtained fitting functions in order to forecast the precision with which future galaxy surveys will be able to measure the μ parameter.

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

PubMed

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

2017-11-01

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

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.

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.

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…

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.

Correction for isotopic interferences between analyte and internal standard in quantitative mass spectrometry by a nonlinear calibration function.

PubMed

Rule, Geoffrey S; Clark, Zlatuse D; Yue, Bingfang; Rockwood, Alan L

2013-04-16

Stable isotope-labeled internal standards are of great utility in providing accurate quantitation in mass spectrometry (MS). An implicit assumption has been that there is no "cross talk" between signals of the internal standard and the target analyte. In some cases, however, naturally occurring isotopes of the analyte do contribute to the signal of the internal standard. This phenomenon becomes more pronounced for isotopically rich compounds, such as those containing sulfur, chlorine, or bromine, higher molecular weight compounds, and those at high analyte/internal standard concentration ratio. This can create nonlinear calibration behavior that may bias quantitative results. Here, we propose the use of a nonlinear but more accurate fitting of data for these situations that incorporates one or two constants determined experimentally for each analyte/internal standard combination and an adjustable calibration parameter. This fitting provides more accurate quantitation in MS-based assays where contributions from analyte to stable labeled internal standard signal exist. It can also correct for the reverse situation where an analyte is present in the internal standard as an impurity. The practical utility of this approach is described, and by using experimental data, the approach is compared to alternative fits.

Standardization and validation of the body weight adjustment regression equations in Olympic weightlifting.

PubMed

Kauhanen, Heikki; Komi, Paavo V; Häkkinen, Keijo

2002-02-01

The problems in comparing the performances of Olympic weightlifters arise from the fact that the relationship between body weight and weightlifting results is not linear. In the present study, this relationship was examined by using a nonparametric curve fitting technique of robust locally weighted regression (LOWESS) on relatively large data sets of the weightlifting results made in top international competitions. Power function formulas were derived from the fitted LOWESS values to represent the relationship between the 2 variables in a way that directly compares the snatch, clean-and-jerk, and total weightlifting results of a given athlete with those of the world-class weightlifters (golden standards). A residual analysis of several other parametric models derived from the initial results showed that they all experience inconsistencies, yielding either underestimation or overestimation of certain body weights. In addition, the existing handicapping formulas commonly used in normalizing the performances of Olympic weightlifters did not yield satisfactory results when applied to the present data. It was concluded that the devised formulas may provide objective means for the evaluation of the performances of male weightlifters, regardless of their body weights, ages, or performance levels.

Reliability measurement for mixed mode failures of 33/11 kilovolt electric power distribution stations.

PubMed

Alwan, Faris M; Baharum, Adam; Hassan, Geehan S

2013-01-01

The reliability of the electrical distribution system is a contemporary research field due to diverse applications of electricity in everyday life and diverse industries. However a few research papers exist in literature. This paper proposes a methodology for assessing the reliability of 33/11 Kilovolt high-power stations based on average time between failures. The objective of this paper is to find the optimal fit for the failure data via time between failures. We determine the parameter estimation for all components of the station. We also estimate the reliability value of each component and the reliability value of the system as a whole. The best fitting distribution for the time between failures is a three parameter Dagum distribution with a scale parameter [Formula: see text] and shape parameters [Formula: see text] and [Formula: see text]. Our analysis reveals that the reliability value decreased by 38.2% in each 30 days. We believe that the current paper is the first to address this issue and its analysis. Thus, the results obtained in this research reflect its originality. We also suggest the practicality of using these results for power systems for both the maintenance of power systems models and preventive maintenance models.

Computer modeling of lung cancer diagnosis-to-treatment process

PubMed Central

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

2015-01-01

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

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.

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.

Integrating virtual screening and biochemical experimental approach to identify potential anti-cancer agents from drug databank.

PubMed

Deka, Suman Jyoti; Roy, Ashalata; Manna, Debasis; Trivedi, Vishal

2018-06-01

Chemical libraries constitute a reservoir of pharmacophoric molecules to identify potent anti-cancer agents. Virtual screening of heterocyclic compound library in conjugation with the agonist-competition assay, toxicity-carcinogenicity analysis, and string-based structural searches enabled us to identify several drugs as potential anti-cancer agents targeting protein kinase C (PKC) as a target. Molecular modeling study indicates that Cinnarizine fits well within the PKC C2 domain and exhibits extensive interaction with the protein residues. Molecular dynamics simulation of PKC-Cinnarizine complex at different temperatures (300, 325, 350, 375, and 400[Formula: see text]K) confirms that Cinnarizine fits nicely into the C2 domain and forms a stable complex. The drug Cinnarizine was found to bind PKC with a dissociation constant Kd of [Formula: see text]M. The breast cancer cells stimulated with Cinnarizine causes translocation of PKC-[Formula: see text] to the plasma membrane as revealed by immunoblotting and immunofluorescence studies. Cinnarizine also dose dependently reduced the viability of MDAMB-231 and MCF-7 breast cancer cells with an IC[Formula: see text] of [Formula: see text] and [Formula: see text]g/mL, respectively. It is due to the disturbance of cell cycle of breast cancer cells with reduction of S-phase and accumulation of cells in G1-phase. It disturbs mitochondrial membrane potentials to release cytochrome C into the cytosol and activates caspase-3 to induce apoptosis in cancer cells. The cell death was due to induction of apoptosis involving mitochondrial pathway. Hence, the current study has assigned an additional role to Cinnarizine as an activator of PKC and potentials of the approach to identify new molecules for anti-cancer therapy. Thus, in silico screening along with biochemical experimentation is a robust approach to assign additional roles to the drugs present in the databank for anti-cancer therapy.

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.

Analytical fitting model for rough-surface BRDF.

PubMed

Renhorn, Ingmar G E; Boreman, Glenn D

2008-08-18

A physics-based model is developed for rough surface BRDF, taking into account angles of incidence and scattering, effective index, surface autocovariance, and correlation length. Shadowing is introduced on surface correlation length and reflectance. Separate terms are included for surface scatter, bulk scatter and retroreflection. Using the FindFit function in Mathematica, the functional form is fitted to BRDF measurements over a wide range of incident angles. The model has fourteen fitting parameters; once these are fixed, the model accurately describes scattering data over two orders of magnitude in BRDF without further adjustment. The resulting analytical model is convenient for numerical computations.

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

NASA Astrophysics Data System (ADS)

Cai, Yangjian; Ge, Di

2006-08-01

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

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

NASA Astrophysics Data System (ADS)

Bhattacharya, Kolahal

2016-03-01

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

Predictability in cellular automata.

PubMed

Agapie, Alexandru; Andreica, Anca; Chira, Camelia; Giuclea, Marius

2014-01-01

Modelled as finite homogeneous Markov chains, probabilistic cellular automata with local transition probabilities in (0, 1) always posses a stationary distribution. This result alone is not very helpful when it comes to predicting the final configuration; one needs also a formula connecting the probabilities in the stationary distribution to some intrinsic feature of the lattice configuration. Previous results on the asynchronous cellular automata have showed that such feature really exists. It is the number of zero-one borders within the automaton's binary configuration. An exponential formula in the number of zero-one borders has been proved for the 1-D, 2-D and 3-D asynchronous automata with neighborhood three, five and seven, respectively. We perform computer experiments on a synchronous cellular automaton to check whether the empirical distribution obeys also that theoretical formula. The numerical results indicate a perfect fit for neighbourhood three and five, which opens the way for a rigorous proof of the formula in this new, synchronous case.

Modeling a Material's Instantaneous Velocity during Acceleration Driven by a Detonation's Gas-Push Process

NASA Astrophysics Data System (ADS)

Backofen, Joseph E.

2005-07-01

This paper will describe both the scientific findings and the model developed in order to quantfy a material's instantaneous velocity versus position, time, or the expansion ratio of an explosive's gaseous products while its gas pressure is accelerating the material. The formula derived to represent this gas-push process for the 2nd stage of the BRIGS Two-Step Detonation Propulsion Model was found to fit very well the published experimental data available for twenty explosives. When the formula's two key parameters (the ratio Vinitial / Vfinal and ExpansionRatioFinal) were adjusted slightly from the average values describing closely many explosives to values representing measured data for a particular explosive, the formula's representation of that explosive's gas-push process was improved. The time derivative of the velocity formula representing acceleration and/or pressure compares favorably to Jones-Wilkins-Lee equation-of-state model calculations performed using published JWL parameters.

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Non-Gaussian limit fluctuations in active swimmer suspensions

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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

Neither short-term sprint nor endurance training enhances thermal response to exercise in a hot environment.

PubMed

McGarr, Gregory W; Hartley, Geoffrey L; Cheung, Stephen S

2014-01-01

Improvements in fitness from a brief period of physical training may elicit sufficient physiological adaptations to decrease thermal strain during exercise in the heat. This study tested heat adaptation from short-term endurance (ET) and sprint-interval (SIT) training in moderately fit individuals. The ET group (n = 8) cycled at 65% [Formula: see text] for 8 sessions (4 sessions each at 60 and 90 min, respectively) over two weeks, while the SIT group (n = 8) performed repeated 30-s Wingate sprints (resistance 7.5% body mass; 4 sessions each of 4 and 5 sprints, respectively). [Formula: see text] and heat stress testing (HST; 60 min cycling at 65% [Formula: see text] at 35ºC, 40% relative humidity) were performed pre- and post-training. [Formula: see text]increased by 11% (p = 0.025) and 14% (p = 0.020) for the ET and SIT groups post-training, respectively. Thermal stress was similar pre- and post-training, with no significant difference in the rate of whole-body metabolic heat production (p = 0.106) for either group post-training. Cardiovascular improvement was evident with both ET and SIT, with a significant mean decrease (p = 0.014) in HR for both groups (ET: 146 ± 15 beats·min(-1)pre vs. 142 ± 12 beats·min(-1)post; SIT: 149 ± 15 beats·min(-1)pre vs. 146 ± 12 beats·min(-1)post) during the HST post-training. However, mean sweat loss (p = 0.248) and the rise in core temperature (p = 0. 260) did not change significantly comparing pre- and post-training HST. While short-term ET and SIT both induced significant improvements in aerobic fitness and decreased cardiovascular strain, neither elicited improved thermal responses during exercise in the heat and do not replace heat acclimatization.

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.

Measured maximal heart rates compared to commonly used age-based prediction equations in the Heritage Family Study.

PubMed

Sarzynski, M A; Rankinen, T; Earnest, C P; Leon, A S; Rao, D C; Skinner, J S; Bouchard, C

2013-01-01

The purpose of this study was to examine how well two commonly used age-based prediction equations for maximal heart rate (HRmax ) estimate the actual HRmax measured in Black and White adults from the HERITAGE Family Study. A total of 762 sedentary subjects (39% Black, 57% Females) from HERITAGE were included. HRmax was measured during maximal exercise tests using cycle ergometers. Age-based HRmax was predicted using the Fox (220-age) and Tanaka (208 - 0.7 × age) formulas. The standard error of estimate (SEE) of predicted HRmax was 12.4 and 11.4 bpm for the Fox and Tanaka formulas, respectively, indicating a wide-spread of measured-HRmax values are compared to their age-predicted values. The SEE (shown as Fox/Tanaka) was higher in Blacks (14.4/13.1 bpm) and Males (12.6/11.7 bpm) compared to Whites (11.0/10.2 bpm) and Females (12.3/11.2 bpm) for both formulas. The SEE was higher in subjects above the BMI median (12.8/11.9 bpm) and below the fitness median (13.4/12.4 bpm) when compared to those below the BMI median (12.2/11.0 bpm) and above the fitness median (11.4/10.3) for both formulas. Our findings show that based on the SEE, the prevailing age-based estimated HRmax equations do not precisely predict an individual's measured-HRmax . Copyright © 2013 Wiley Periodicals, Inc.

Mean Normalized Gain: A New Method for the Assessment of the Aerobic System Temporal Dynamics during Randomly Varying Exercise in Humans.

PubMed

Beltrame, Thomas; Hughson, Richard L

2017-01-01

The temporal dynamics of the oxygen uptake ([Formula: see text]) during moderate exercise has classically been related to physical fitness and a slower [Formula: see text] dynamics was associated with deterioration of physical health. However, methods that better characterize the aerobic system temporal dynamics remain challenging. The purpose of this study was to develop a new method (named mean normalized gain, MNG ) to systematically characterize the [Formula: see text] temporal dynamics. Eight healthy, young adults (28 ± 6 years old, 175 ± 7 cm and 79 ± 13 kg) performed multiple pseudorandom binary sequence cycling protocols on different days and time of the day. The MNG was calculated as the normalized amplitude of the [Formula: see text] signal in frequency-domain. The MNG was validated considering the time constant τ obtained from time-domain analysis as reference. The intra-subject consistency of the MNG was checked by testing the same participant on different days and times of the day. The MNG and τ were strongly negatively correlated ( r = -0.86 and p = 0.005). The MNG measured on different days and periods of the day was similar between conditions. Calculations for the MNG have inherent filtering characteristics enhancing reliability for the evaluation of the aerobic system temporal dynamics. In conclusion, the present study successfully validated the use of the MNG for aerobic system analysis and as a potential complementary tool to assess changes in physical fitness.

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.

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

Breast milk - pumping and storing

MedlinePlus

... sure they have been washed in hot, soapy water and rinsed well. Heavy duty bags that fit into a bottle. DO NOT use everyday plastic bags or formula bottle bags. They leak. Store your breast milk. Date the milk before ...

78 FR 59415 - Formula Grants for Rural Areas: Guidance and Application Instructions

Federal Register 2010, 2011, 2012, 2013, 2014

2013-09-26

... project identified that fits in either Category A or B, FTA recommends the funds remain unobligated until... receive Tribal Transit funds, they must comply with certain cross-cutting requirements as listed in...

Random Evolutionary Dynamics Driven by Fitness and House-of-Cards Mutations: Sampling Formulae

NASA Astrophysics Data System (ADS)

Huillet, Thierry E.

2017-07-01

We first revisit the multi-allelic mutation-fitness balance problem, especially when mutations obey a house of cards condition, where the discrete-time deterministic evolutionary dynamics of the allelic frequencies derives from a Shahshahani potential. We then consider multi-allelic Wright-Fisher stochastic models whose deviation to neutrality is from the Shahshahani mutation/selection potential. We next focus on the weak selection, weak mutation cases and, making use of a Gamma calculus, we compute the normalizing partition functions of the invariant probability densities appearing in their Wright-Fisher diffusive approximations. Using these results, generalized Ewens sampling formulae (ESF) from the equilibrium distributions are derived. We start treating the ESF in the mixed mutation/selection potential case and then we restrict ourselves to the ESF in the simpler house-of-cards mutations only situation. We also address some issues concerning sampling problems from infinitely-many alleles weak limits.

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.

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

PubMed

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Kirk, Toby L.

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

Alexandrov, A.; Zhdanov, V.

2016-12-01

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

Unified semiclassical approach to electronic transport from diffusive to ballistic regimes

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Analysis of Thermal Track Buckling in the Lateral Plane

DOT National Transportation Integrated Search

1976-09-01

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

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

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

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

1958-05-14

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

Cavity mode enhancement of terahertz emission from equilateral triangular microstrip antennas of the high-T c superconductor Bi2Sr2CaCu2O8 + δ.

PubMed

Cerkoney, Daniel P; Reid, Candy; Doty, Constance M; Gramajo, Ashley; Campbell, Tyler D; Morales, Manuel A; Delfanazari, Kaveh; Tsujimoto, Manabu; Kashiwagi, Takanari; Yamamoto, Takashi; Watanabe, Chiharu; Minami, Hidetoshi; Kadowaki, Kazuo; Klemm, Richard A

2017-01-11

We study the transverse magnetic (TM) electromagnetic cavity mode wave functions for an ideal equilateral triangular microstrip antenna (MSA) exhibiting C 3v point group symmetry. When the C 3v operations are imposed upon the antenna, the TM(m,n) modes with wave vectors [Formula: see text] are much less dense than commonly thought. The R 3 operations restrict the integral n and m to satisfy [Formula: see text], where [Formula: see text] and [Formula: see text] for the modes even and odd under reflections about the three mirror planes, respectively. We calculate the forms of representative wave functions and the angular dependence of the output power when these modes are excited by the uniform and non-uniform ac Josephson current sources in thin, ideally equilateral triangular MSAs employing the intrinsic Josephson junctions in the high transition temperature T c superconductor Bi 2 Sr 2 CaCu 2 [Formula: see text], and fit the emissions data from an earlier sample for which the C 3v symmetry was apparently broken.

Analysis on ventilation pressure of fire area in longitudinal ventilation of underground tunnel

NASA Astrophysics Data System (ADS)

Li, Jiaxin; Li, Yanfeng; Feng, Xiao; Li, Junmei

2018-03-01

In order to solve the problem of ventilation pressure loss in the fire area under the fire condition, the wind pressure loss model of the fire area is established based on the thermodynamic equilibrium relation. The semi-empirical calculation formula is obtained by using the model experiment and CFD simulation. The validity of the formula is verified. The results show that the ventilation pressure loss in the fire zone is proportional to the convective heat release rate at the critical velocity, which is inversely proportional to the upstream ventilation velocity and the tunnel cross-sectional area. The proposed formula is consistent with the law of the tunnel fire test fitting formula that results are close, in contrast, the advantage lies in a clear theoretical basis and ventilation velocity values. The resistance of road tunnel ventilation system is calculated accurately and reliably, and then an effective emergency ventilation operation program is developed. It is necessary to consider the fire zone ventilation pressure loss. The proposed ventilation pressure loss formula can be used for design calculation after thorough verification.

Absorption coefficients of silicon: A theoretical treatment

NASA Astrophysics Data System (ADS)

Tsai, Chin-Yi

2018-05-01

A theoretical model with explicit formulas for calculating the optical absorption and gain coefficients of silicon is presented. It incorporates direct and indirect interband transitions and considers the effects of occupied/unoccupied carrier states. The indirect interband transition is calculated from the second-order time-independent perturbation theory of quantum mechanics by incorporating all eight possible routes of absorption or emission of photons and phonons. Absorption coefficients of silicon are calculated from these formulas. The agreements and discrepancies among the calculated results, the Rajkanan-Singh-Shewchun (RSS) formula, and Green's data are investigated and discussed. For example, the RSS formula tends to overestimate the contributions of indirect transitions for cases with high photon energy. The results show that the state occupied/unoccupied effect is almost negligible for silicon absorption coefficients up to the onset of the optical gain condition where the energy separation of Quasi-Femi levels between electrons and holes is larger than the band-gap energy. The usefulness of using the physics-based formulas, rather than semi-empirical fitting ones, for absorption coefficients in theoretical studies of photovoltaic devices is also discussed.

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

NASA Astrophysics Data System (ADS)

Bieniek, Ronald

2008-05-01

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

Simple physics-based analytical formulas for the potentials of mean force of the interaction of amino-acid side chains in water. V. Like-charged side chains.

PubMed

Makowski, Mariusz; Liwo, Adam; Sobolewski, Emil; Scheraga, Harold A

2011-05-19

A new model of side-chain-side-chain interactions for charged side-chains of amino acids, to be used in the UNRES force-field, has been developed, in which a side chain consists of a nonpolar and a charged site. The interaction energy between the nonpolar sites is composed of a Gay-Berne and a cavity term; the interaction energy between the charged sites consists of a Lennard-Jones term, a Coulombic term, a generalized-Born term, and a cavity term, while the interaction energy between the nonpolar and charged sites is composed of a Gay-Berne and a polarization term. We parametrized the energy function for the models of all six pairs of natural like-charged amino-acid side chains, namely propionate-propionate (for the aspartic acid-aspartic acid pair), butyrate-butyrate (for the glutamic acid-glutamic acid pair), propionate-butyrate (for the aspartic acid-glutamic acid pair), pentylamine cation-pentylamine cation (for the lysine-lysine pair), 1-butylguanidine cation-1-butylguanidine cation (for the arginine-arginine pair), and pentylamine cation-1-butylguanidine cation (for the lysine-arginine pair). By using umbrella-sampling molecular dynamics simulations in explicit TIP3P water, we determined the potentials of mean force of the above-mentioned pairs as functions of distance and orientation and fitted analytical expressions to them. The positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the orientation of the molecules were well represented by analytical expressions for all systems. The values of the parameters of all the energy components are physically reasonable, which justifies use of such potentials in coarse-grain protein-folding simulations. © 2011 American Chemical Society

Exponential asymptotics of homoclinic snaking

NASA Astrophysics Data System (ADS)

Dean, A. D.; Matthews, P. C.; Cox, S. M.; King, J. R.

2011-12-01

We study homoclinic snaking in the cubic-quintic Swift-Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319-54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement.

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

PubMed

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

2014-02-01

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

A 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

On the neutralization in low energy ion scattering spectroscopy (leiss): He + ions on clean and oxygen covered Ni(001) surfaces

NASA Astrophysics Data System (ADS)

Preuss, E.

1981-10-01

A formula for the He + ion survival probability against neutralization is presented, which was derived from the fit of the azimuthal angular dependence of the Ni peak heights on clean and O covered Ni(001) surfaces observed in LEISS experiments and computer simulations. The formula contains a collision- and two Auger-type neutralization terms for the ion trajectories prolonged by multiple collisions above the "neutralization surface plane", which was assumed to be corrugated and shaped like muffin-tins.

Study on friction coefficient of soft soil based on particle flow code

NASA Astrophysics Data System (ADS)

Lei, Xiaohong; Zhang, Zhongwei

2017-04-01

There has no uniform method for determining the micro parameters in particle flow code, and the corresponding formulas obtained by each scholar can only be applied to similar situations. In this paper, the relationship between the micro parameters friction coefficient and macro parameters friction angle is established by using the two axis servo compression as the calibration experiment, and the corresponding formula is fitted to solve the difficulties of determining the PFC micro parameters which provide a reference for determination of the micro parameters of soft soil.

Default risk modeling beyond the first-passage approximation: extended Black-Cox model.

PubMed

Katz, Yuri A; Shokhirev, Nikolai V

2010-07-01

We develop a generalization of the Black-Cox structural model of default risk. The extended model captures uncertainty related to firm's ability to avoid default even if company's liabilities momentarily exceeding its assets. Diffusion in a linear potential with the radiation boundary condition is used to mimic a company's default process. The exact solution of the corresponding Fokker-Planck equation allows for derivation of analytical expressions for the cumulative probability of default and the relevant hazard rate. Obtained closed formulas fit well the historical data on global corporate defaults and demonstrate the split behavior of credit spreads for bonds of companies in different categories of speculative-grade ratings with varying time to maturity. Introduction of the finite rate of default at the boundary improves valuation of credit risk for short time horizons, which is the key advantage of the proposed model. We also consider the influence of uncertainty in the initial distance to the default barrier on the outcome of the model and demonstrate that this additional source of incomplete information may be responsible for nonzero credit spreads for bonds with very short time to maturity.

Densities and eccentricities of 139 Kepler planets from transit time variations

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

Hadden, Sam; Lithwick, Yoram

2014-05-20

We extract densities and eccentricities of 139 sub-Jovian planets by analyzing transit time variations (TTVs) obtained by the Kepler mission through Quarter 12. We partially circumvent the degeneracies that plague TTV inversion with the help of an analytical formula for the TTV. From the observed TTV phases, we find that most of these planets have eccentricities of the order of a few percent. More precisely, the rms eccentricity is 0.018{sub −0.004}{sup +0.005}, and planets smaller than 2.5 R {sub ⊕} are around twice as eccentric as those bigger than 2.5 R {sub ⊕}. We also find a best-fit density-radius relationshipmore » ρ ≈ 3 g cm{sup –3} × (R/3 R {sub ⊕}){sup –2.3} for the 56 planets that likely have small eccentricity and hence small statistical correction to their masses. Many planets larger than 2.5 R {sub ⊕} are less dense than water, implying that their radii are largely set by a massive hydrogen atmosphere.« less

A Comprehensive X-Ray Absorption Model for Atomic Oxygen

NASA Technical Reports Server (NTRS)

Gorczyca, T. W.; Bautista, M. A.; Hasoglu, M. F.; Garcia, J.; Gatuzz, E.; Kaastra, J. S.; Kallman, T. R.; Manson, S. T.; Mendoza, C.; Raassen, A. J. J.;

A method to align a bent crystal for channeling experiments by using quasichanneling oscillations

NASA Astrophysics Data System (ADS)

Sytov, A. I.; Guidi, V.; Tikhomirov, V. V.; Bandiera, L.; Bagli, E.; Germogli, G.; Mazzolari, A.; Romagnoni, M.

2018-04-01

A method to calculate both the bent crystal angle of alignment and radius of curvature by using only one distribution of deflection angles has been developed. The method is based on measuring of the angular position of recently predicted and observed quasichanneling oscillations in the deflection angle distribution and consequent fitting of both the radius and angular alignment by analytic formulae. In this paper this method is applied on the example of simulated angular distributions over a wide range of values of both radius and alignment for electrons. It is carried out through the example of (111) nonequidistant planes though this technique is general and could be applied to any kind of planes. In addition, the method application constraints are also discussed. It is shown by simulations that this method, being in fact a sort of beam diagnostics, allows one in a certain case to increase the crystal alignment accuracy as well as to control precisely the radius of curvature inside an accelerator tube without vacuum breaking. In addition, it speeds up the procedure of crystal alignment in channeling experiments, reducing beamtime consuming.

Distortion in the thermal noise spectrum and quality factor of nanomechanical devices due to finite frequency resolution with applications to the atomic force microscope.

PubMed

Sader, John E; Sanelli, Julian; Hughes, Barry D; Monty, Jason P; Bieske, Evan J

2011-09-01

The thermal noise spectrum of nanomechanical devices is commonly used to characterize their mechanical properties and energy dissipation. This spectrum is measured from finite time series of Brownian motion of the device, which is windowed and Fourier transformed. Here, we present a theoretical and experimental investigation of the effect of such finite sampling on the measured device quality factor. We prove that if no spectral window is used, the thermal noise spectrum retains its original Lorentzian distribution but with a reduced quality factor, indicating an apparent enhancement in energy dissipation. A simple analytical formula is derived connecting the true and measured quality factors - this enables extraction of the true device quality factor from measured data. Common windows used to reduce spectral leakage are found to distort the (true) Lorentzian shape, potentially making fitting problematic. These findings are expected to be of particular importance for devices with high quality factors, where spectral resolution can be limited in practice. Comparison and validation using measurements on atomic force microscope cantilevers are presented. © 2011 American Institute of Physics

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

Xia, T. Y.; Zhang, Y.

We present an analytical calculation of the spectra of CMB anisotropies and polarizations generated by relic gravitational waves (RGWs). As a substantial extension to the previous studies, three new ingredients are included in this work. First, the analytic C{sub l}{sup TT} and C{sub l}{sup TE} are given; especially the latter can be useful to extract signal of RGWs from the observed data in the zero-multipole method. Second, a fitting formula of the decaying factor on small scales is given, coming from the visibility function around the photon decoupling. Third, the impacts by the neutrino free-streaming (NFS) is examined, a processmore » that occurred in the early universe and leaves observable imprints on CMB via RGWs. It is found that the analytic C{sub l}{sup TT} and C{sub l}{sup TE} have profiles agreeing with the numeric ones, except that C{sub l}{sup TT} in a range l{<=}10 and the first trough of C{sub l}{sup TE} around l{approx}75 have some deviations. With the new damping factor, the analytic C{sub l}{sup EE} and C{sub l}{sup BB} match with the numeric ones with the maximum errors only {approx}3% up to the first three peaks for l{<=}600, improving the previous studies substantially. The correspondence of the positions of peaks of C{sub l}{sup XX} and those of RGWs are also demonstrated explicitly. We also find that NFS reduces the amplitudes of C{sub l}{sup XX} by (20%{approx}35%) for l{approx_equal}(100{approx}600) and shifts slightly their peaks to smaller angles. Detailed analyses show that the zero multipoles l{sub 0}, where C{sub l}{sup TE} crosses 0, are shifted to larger values by NFS. This shifting effect is as important as those caused by different inflation models and different baryon fractions.« less

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

Cardiorespiratory Fitness Is Associated with Selective Attention in Healthy Male High-School Students.

PubMed

Wengaard, Eivind; Kristoffersen, Morten; Harris, Anette; Gundersen, Hilde

2017-01-01

Background : Previous studies have shown associations of physical fitness and cognition in children and in younger and older adults. However, knowledge about associations in high-school adolescents and young adults is sparse. Thus, the aim of this study was to evaluate the association of physical fitness, measured as maximal oxygen uptake ([Formula: see text]), muscle mass, weekly training, and cognitive function in the executive domains of selective attention and inhibitory control, in healthy male high-school students. Methods : Fifty-four males (17.9 ± 0.9 years, 72 ± 11 kg and 182 ± 7 cm) completed a [Formula: see text] test, a body composition test and a visual cognitive task based on the Posner cue paradigm with three types of stimuli with different attentional demands (i.e., stimuli presentation following no cue, valid cue or invalid cue presentations). The task consisted of 336 target stimuli, where 56 (17%) of the target stimuli appeared without a cue (no cue), 224 (67%) appeared in the same rectangle as the cue (valid cue) and 56 (17%) appeared in the rectangle opposite to the cue (invalid cue). Mean reaction time (RT) and corresponding errors was calculated for each stimuli type. Total task duration was 9 min and 20 s In addition, relevant background information was obtained in a questionnaire. Results : Linear mixed model analyses showed that higher [Formula: see text] was associated with faster RT for stimuli following invalid cue (Estimate = -2.69, SE = 1.03, p = 0.011), and for stimuli following valid cue (Estimate = -2.08, SE = 1.03, p = 0.048). There was no association of muscle mass and stimuli ( F = 1.01, p = 0.397) or of weekly training and stimuli ( F = 0.99, p = 0.405). Conclusion : The results suggest that cardiorespiratory fitness is associated with cognitive performance in healthy male high-school students in the executive domains of selective attention.

Genetic parameters and expected responses to selection for components of feed efficiency in a Duroc pig line.

PubMed

Sánchez, Juan P; Ragab, Mohamed; Quintanilla, Raquel; Rothschild, Max F; Piles, Miriam

2017-12-01

Improving feed efficiency ([Formula: see text]) is a key factor for any pig breeding company. Although this can be achieved by selection on an index of multi-trait best linear unbiased prediction of breeding values with optimal economic weights, considering deviations of feed intake from actual needs ([Formula: see text]) should be of value for further research on biological aspects of [Formula: see text]. Here, we present a random regression model that extends the classical definition of [Formula: see text] by including animal-specific needs in the model. Using this model, we explore the genetic determinism of several [Formula: see text] components: use of feed for growth ([Formula: see text]), use of feed for backfat deposition ([Formula: see text]), use of feed for maintenance ([Formula: see text]), and unspecific efficiency in the use of feed ([Formula: see text]). Expected response to alternative selection indexes involving different components is also studied. Based on goodness-of-fit to the available feed intake ([Formula: see text]) data, the model that assumes individual (genetic and permanent) variation in the use of feed for maintenance, [Formula: see text] and [Formula: see text] showed the best performance. Joint individual variation in feed allocation to maintenance, growth and backfat deposition comprised 37% of the individual variation of [Formula: see text]. The estimated heritabilities of [Formula: see text] using the model that accounts for animal-specific needs and the traditional [Formula: see text] model were 0.12 and 0.18, respectively. The estimated heritabilities for the regression coefficients were 0.44, 0.39 and 0.55 for [Formula: see text], [Formula: see text] and [Formula: see text], respectively. Estimates of genetic correlations of [Formula: see text] were positive with amount of feed used for [Formula: see text] and [Formula: see text] but negative for [Formula: see text]. Expected response in overall efficiency, reducing [Formula: see text] without altering performance, was 2.5% higher when the model assumed animal-specific needs than when the traditional definition of [Formula: see text] was considered. Expected response in overall efficiency, by reducing [Formula: see text] without altering performance, is slightly better with a model that assumes animal-specific needs instead of batch-specific needs to correct [Formula: see text]. The relatively small difference between the traditional [Formula: see text] model and our model is due to random intercepts (unspecific use of feed) accounting for the majority of variability in [Formula: see text]. Overall, a model that accounts for animal-specific needs for [Formula: see text], [Formula: see text] and [Formula: see text] is statistically superior and allows for the possibility to act differentially on [Formula: see text] components.

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.

New Objective Refraction Metric Based on Sphere Fitting to the Wavefront

PubMed Central

Martínez-Finkelshtein, Andreí

2017-01-01

Purpose To develop an objective refraction formula based on the ocular wavefront error (WFE) expressed in terms of Zernike coefficients and pupil radius, which would be an accurate predictor of subjective spherical equivalent (SE) for different pupil sizes. Methods A sphere is fitted to the ocular wavefront at the center and at a variable distance, t. The optimal fitting distance, topt, is obtained empirically from a dataset of 308 eyes as a function of objective refraction pupil radius, r0, and used to define the formula of a new wavefront refraction metric (MTR). The metric is tested in another, independent dataset of 200 eyes. Results For pupil radii r0 ≤ 2 mm, the new metric predicts the equivalent sphere with similar accuracy (<0.1D), however, for r0 > 2 mm, the mean error of traditional metrics can increase beyond 0.25D, and the MTR remains accurate. The proposed metric allows clinicians to obtain an accurate clinical spherical equivalent value without rescaling/refitting of the wavefront coefficients. It has the potential to be developed into a metric which will be able to predict full spherocylindrical refraction for the desired illumination conditions and corresponding pupil size. PMID:29104804

New Objective Refraction Metric Based on Sphere Fitting to the Wavefront.

PubMed

Jaskulski, Mateusz; Martínez-Finkelshtein, Andreí; López-Gil, Norberto

2017-01-01

To develop an objective refraction formula based on the ocular wavefront error (WFE) expressed in terms of Zernike coefficients and pupil radius, which would be an accurate predictor of subjective spherical equivalent (SE) for different pupil sizes. A sphere is fitted to the ocular wavefront at the center and at a variable distance, t . The optimal fitting distance, t opt , is obtained empirically from a dataset of 308 eyes as a function of objective refraction pupil radius, r 0 , and used to define the formula of a new wavefront refraction metric (MTR). The metric is tested in another, independent dataset of 200 eyes. For pupil radii r 0 ≤ 2 mm, the new metric predicts the equivalent sphere with similar accuracy (<0.1D), however, for r 0 > 2 mm, the mean error of traditional metrics can increase beyond 0.25D, and the MTR remains accurate. The proposed metric allows clinicians to obtain an accurate clinical spherical equivalent value without rescaling/refitting of the wavefront coefficients. It has the potential to be developed into a metric which will be able to predict full spherocylindrical refraction for the desired illumination conditions and corresponding pupil size.

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

Macro-microscopic mass formulae and nuclear mass predictions

NASA Astrophysics Data System (ADS)

Royer, G.; Guilbaud, M.; Onillon, A.

2010-12-01

Different mass formulae derived from the liquid drop model and the pairing and shell energies of the Thomas-Fermi model have been studied and compared. They include or not the diffuseness correction to the Coulomb energy, the charge exchange correction term, the curvature energy, different forms of the Wigner term and powers of the relative neutron excess I=(N-Z)/A. Their coefficients have been determined by a least square fitting procedure to 2027 experimental atomic masses (G. Audi et al. (2003) [1]). The Coulomb diffuseness correction Z/A term or the charge exchange correction Z/A term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately but their coefficients are very unstable. The different fits lead to a surface energy coefficient of around 17-18 MeV. A large equivalent rms radius ( r=1.22-1.24 fm) or a shorter central radius may be used. An rms deviation of 0.54 MeV can be reached between the experimental and theoretical masses. The remaining differences come probably mainly from the determination of the shell and pairing energies. Mass predictions of selected expressions have been compared to 161 new experimental masses and the correct agreement allows to provide extrapolations to masses of 656 selected exotic nuclei.

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.

Lane-Emden equation with inertial force and general polytropic dynamic model for molecular cloud cores

NASA Astrophysics Data System (ADS)

Li, DaLei; Lou, Yu-Qing; Esimbek, Jarken

2018-01-01

We study self-similar hydrodynamics of spherical symmetry using a general polytropic (GP) equation of state and derive the GP dynamic Lane-Emden equation (LEE) with a radial inertial force. In reference to Lou & Cao, we solve the GP dynamic LEE for both polytropic index γ = 1 + 1/n and the isothermal case n → +∞; our formalism is more general than the conventional polytropic model with n = 3 or γ = 4/3 of Goldreich & Weber. For proper boundary conditions, we obtain an exact constant solution for arbitrary n and analytic variable solutions for n = 0 and n = 1, respectively. Series expansion solutions are derived near the origin with the explicit recursion formulae for the series coefficients for both the GP and isothermal cases. By extensive numerical explorations, we find that there is no zero density at a finite radius for n ≥ 5. For 0 ≤ n < 5, we adjust the inertial force parameter c and find the range of c > 0 for monotonically decreasing density from the origin and vanishing at a finite radius for c being less than a critical value Ccr. As astrophysical applications, we invoke our solutions of the GP dynamic LEE with central finite boundary conditions to fit the molecular cloud core Barnard 68 in contrast to the static isothermal Bonnor-Ebert sphere by Alves et al. Our GP dynamic model fits appear to be sensibly consistent with several more observations and diagnostics for density, temperature and gas pressure profiles.

Predictability in Cellular Automata

PubMed Central

Agapie, Alexandru; Andreica, Anca; Chira, Camelia; Giuclea, Marius

2014-01-01

Modelled as finite homogeneous Markov chains, probabilistic cellular automata with local transition probabilities in (0, 1) always posses a stationary distribution. This result alone is not very helpful when it comes to predicting the final configuration; one needs also a formula connecting the probabilities in the stationary distribution to some intrinsic feature of the lattice configuration. Previous results on the asynchronous cellular automata have showed that such feature really exists. It is the number of zero-one borders within the automaton's binary configuration. An exponential formula in the number of zero-one borders has been proved for the 1-D, 2-D and 3-D asynchronous automata with neighborhood three, five and seven, respectively. We perform computer experiments on a synchronous cellular automaton to check whether the empirical distribution obeys also that theoretical formula. The numerical results indicate a perfect fit for neighbourhood three and five, which opens the way for a rigorous proof of the formula in this new, synchronous case. PMID:25271778

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.

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

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

A self-consistent first-principle based approach to model carrier mobility in organic materials

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

Meded, Velimir; Friederich, Pascal; Symalla, Franz

2015-12-31

Transport through thin organic amorphous films, utilized in OLEDs and OPVs, has been a challenge to model by using ab-initio methods. Charge carrier mobility depends strongly on the disorder strength and reorganization energy, both of which are significantly affected by the details in environment of each molecule. Here we present a multi-scale approach to describe carrier mobility in which the materials morphology is generated using DEPOSIT, a Monte Carlo based atomistic simulation approach, or, alternatively by molecular dynamics calculations performed with GROMACS. From this morphology we extract the material specific hopping rates, as well as the on-site energies using amore » fully self-consistent embedding approach to compute the electronic structure parameters, which are then used in an analytic expression for the carrier mobility. We apply this strategy to compute the carrier mobility for a set of widely studied molecules and obtain good agreement between experiment and theory varying over several orders of magnitude in the mobility without any freely adjustable parameters. The work focuses on the quantum mechanical step of the multi-scale workflow, explains the concept along with the recently published workflow optimization, which combines density functional with semi-empirical tight binding approaches. This is followed by discussion on the analytic formula and its agreement with established percolation fits as well as kinetic Monte Carlo numerical approaches. Finally, we skatch an unified multi-disciplinary approach that integrates materials science simulation and high performance computing, developed within EU project MMM@HPC.« less

Quasi-analytical treatment of spatially averaged radiation transfer in complex terrain

NASA Astrophysics Data System (ADS)

LöWe, H.; Helbig, N.

2012-10-01

We provide a new quasi-analytical method to compute the subgrid topographic influences on the shortwave radiation fluxes and the effective albedo in complex terrain as required for large-scale meteorological, land surface, or climate models. We investigate radiative transfer in complex terrain via the radiosity equation on isotropic Gaussian random fields. Under controlled approximations we derive expressions for domain-averaged fluxes of direct, diffuse, and terrain radiation and the sky view factor. Domain-averaged quantities can be related to a type of level-crossing probability of the random field, which is approximated by long-standing results developed for acoustic scattering at ocean boundaries. This allows us to express all nonlocal horizon effects in terms of a local terrain parameter, namely, the mean-square slope. Emerging integrals are computed numerically, and fit formulas are given for practical purposes. As an implication of our approach, we provide an expression for the effective albedo of complex terrain in terms of the Sun elevation angle, mean-square slope, the area-averaged surface albedo, and the ratio of atmospheric direct beam to diffuse radiation. For demonstration we compute the decrease of the effective albedo relative to the area-averaged albedo in Switzerland for idealized snow-covered and clear-sky conditions at noon in winter. We find an average decrease of 5.8% and spatial patterns which originate from characteristics of the underlying relief. Limitations and possible generalizations of the method are discussed.

Cumulative radiation exposure and associated cancer risk estimates for scoliosis patients: Impact of repetitive full spine radiography.

PubMed

Law, Martin; Ma, Wang-Kei; Lau, Damian; Chan, Eva; Yip, Lawrance; Lam, Wendy

2016-03-01

To quantitatively evaluate the cumulative effective dose and associated cancer risk for scoliotic patients undergoing repetitive full spine radiography during their diagnosis and follow up periods. Organ absorbed doses of full spine exposed scoliotic patients at different age were computer simulated with the use of PCXMC software. Gender specific effective dose was then calculated with the ICRP-103 approach. Values of lifetime attributable cancer risk for patients exposed at different age were calculated for both patient genders and for Asian and Western population. Mathematical fitting for effective dose and for lifetime attributable cancer risk, as function of exposed age, was analytically obtained to quantitatively estimate patient cumulated effective dose and cancer risk. The cumulative effective dose of full spine radiography with posteroanterior and lateral projection for patients exposed annually at age between 5 and 30 years using digital radiography system was calculated as 15mSv. The corresponding cumulative lifetime attributable cancer risk for Asian and Western population was calculated as 0.08-0.17%. Female scoliotic patients would be at a statistically significant higher cumulated cancer risk than male patients under the same full spine radiography protocol. We demonstrate the use of computer simulation and analytic formula to quantitatively obtain the cumulated effective dose and cancer risk at any age of exposure, both of which are valuable information to medical personnel and patients' parents concern about radiation safety in repetitive full spine radiography. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

THREE-POINT PHASE CORRELATIONS: A NEW MEASURE OF NONLINEAR LARGE-SCALE STRUCTURE

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

Wolstenhulme, Richard; Bonvin, Camille; Obreschkow, Danail

2015-05-10

We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field, is a robust statistical measure allowing the extraction of information in the nonlinear and non-Gaussian regime. We show that, in perturbation theory, the line correlation is sensitive to the coupling kernel F{sub 2}, which governs the nonlinear gravitational evolution of the density field. We compare our analytical expression with results from numerical simulations and find a 1σ agreement for separations r ≳ 30 h{sup −1} Mpc.more » Fitting formulae for the power spectrum and the nonlinear coupling kernel at small scales allow us to extend our prediction into the strongly nonlinear regime, where we find a 1σ agreement with the simulations for r ≳ 2 h{sup −1} Mpc. We discuss the advantages of the line correlation relative to standard statistical measures like the bispectrum. Unlike the latter, the line correlation is independent of the bias, in the regime where the bias is local and linear. Furthermore, the variance of the line correlation is independent of the Gaussian variance on the modulus of the density field. This suggests that the line correlation can probe more precisely the nonlinear regime of gravity, with less contamination from the power spectrum variance.« less

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

PubMed

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

2008-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1981-01-01

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

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.

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.

Mathematical beta function formulation for maxillary arch form prediction in normal occlusion population.

PubMed

Mina, Morteza; Borzabadi-Farahani, Ali; Tehranchi, Azita; Nouri, Mahtab; Younessian, Farnaz

2017-04-01

The aim of this study was to assess the dental arch curvature in subjects with normal occlusion in an Iranian population and propose a beta function formula to predict maxillary arch form using the mandibular intermolar widths (IMW) and intermolar depths (IMD). The materials used were study casts of 54 adolescents with normal occlusion and mean age of 14.1 years (25 males, 29 females, age range 12-16 years). Curve-fitting analyses were carried out and the curves passing through the facial-axis point of the canines, premolars, first molars, and the incisal edges of the anterior teeth were studied using a 3D laser scanner. Using the measured IMW and IMD of the dental arches at the maxillary and mandibular first molar region, a beta function formula proposed for predicting maxillary arch form. The accuracy of the proposed formula was assessed on 10 randomly selected dental casts. The mean (SD) of the maxillary and mandibular IMW and IMD were 57.92 (4.75), 54.19 (5.31), and 31.59 (2.90) and 28.10 (2.59) mm, respectively. There was no gender dimorphism (P > 0.05) for both variables (IMW, IMD). There was a strong positive association (n = 10, Pearson r = 0.98, P < 0.05) between the measured (actual) maxillary arch length and proposed arch length derived from generated formula. The goodness of fit (whole arch) for the proposed beta function formula, using adjusted r square measure and root mean square in 10 patients averaged 0.97 and 1.49 mm, respectively. The corresponding figures for the maxillary anterior arch (canine to canine) were 0.90 and 0.92 mm, respectively. The proposed beta function formula used for predicting maxillary arch form based on two mandibular measures (IMW, IMD) was found to have a high accuracy for maxillary arch prediction in the Iranian population and may be used as a guide to fabricate customized arch wires or as an aid in maxillary reconstructive surgery.

Mass Distribution and Gravitational Potential of the Milky Way

NASA Astrophysics Data System (ADS)

Ninković, Slobodan

2017-04-01

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

A Malaria Transmission Model with Temperature-Dependent Incubation Period.

PubMed

Wang, Xiunan; Zhao, Xiao-Qiang

2017-05-01

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

Power spectrum for the small-scale Universe

NASA Astrophysics Data System (ADS)

Widrow, Lawrence M.; Elahi, Pascal J.; Thacker, Robert J.; Richardson, Mark; Scannapieco, Evan

2009-08-01

The first objects to arise in a cold dark matter (CDM) universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution (N = 7203-15843) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) ~ kn, with -2.5 <= n <= - 1. Self-similar scaling is established for n = -1 and -2 more convincingly than in previous, lower resolution simulations and for the first time, self-similar scaling is established for an n = -2.25 simulation. However, finite box-size effects induce departures from self-similar scaling in our n = -2.5 simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theory's ability to predict the power spectrum in the quasi-linear regime. In the non-linear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis versus halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high-k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.

The anatomy of floating shock fitting. [shock waves computation for flow field

NASA Technical Reports Server (NTRS)

Salas, M. D.

1975-01-01

The floating shock fitting technique is examined. Second-order difference formulas are developed for the computation of discontinuities. A procedure is developed to compute mesh points that are crossed by discontinuities. The technique is applied to the calculation of internal two-dimensional flows with arbitrary number of shock waves and contact surfaces. A new procedure, based on the coalescence of characteristics, is developed to detect the formation of shock waves. Results are presented to validate and demonstrate the versatility of the technique.

Cubic scaling algorithms for RPA correlation using interpolative separable density fitting

NASA Astrophysics Data System (ADS)

Lu, Jianfeng; Thicke, Kyle

2017-12-01

We present a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in χ0 by use of Cauchy's integral formula. This introduces an additional integral to be carried out, for which we provide a geometrically convergent quadrature rule. Our scheme also uses the newly developed Interpolative Separable Density Fitting algorithm to further reduce the computational cost in a way analogous to that of the Resolution of Identity method.

Fitting Photometry of Blended Microlensing Events

NASA Astrophysics Data System (ADS)

Thomas, Christian L.; Griest, Kim

2006-03-01

We reexamine the usefulness of fitting blended light-curve models to microlensing photometric data. We find agreement with previous workers (e.g., Woźniak & Paczyński) that this is a difficult proposition because of the degeneracy of blend fraction with other fit parameters. We show that follow-up observations at specific point along the light curve (peak region and wings) of high-magnification events are the most helpful in removing degeneracies. We also show that very small errors in the baseline magnitude can result in problems in measuring the blend fraction and study the importance of non-Gaussian errors in the fit results. The biases and skewness in the distribution of the recovered blend fraction is discussed. We also find a new approximation formula relating the blend fraction and the unblended fit parameters to the underlying event duration needed to estimate microlensing optical depth.

Analysis of Environmental Contamination resulting from ...

EPA Pesticide Factsheets

Catastrophic incidents can generate a large number of samples with analytically diverse types including forensic, clinical, environmental, food, and others. Environmental samples include water, wastewater, soil, air, urban building and infrastructure materials, and surface residue. Such samples may arise not only from contamination from the incident but also from the multitude of activities surrounding the response to the incident, including decontamination. This document summarizes a range of activities to help build laboratory capability in preparation for analysis following a catastrophic incident, including selection and development of fit-for-purpose analytical methods for chemical, biological, and radiological contaminants. Fit-for-purpose methods are those which have been selected to meet project specific data quality objectives. For example, methods could be fit for screening contamination in the early phases of investigation of contamination incidents because they are rapid and easily implemented, but those same methods may not be fit for the purpose of remediating the environment to safe levels when a more sensitive method is required. While the exact data quality objectives defining fitness-for-purpose can vary with each incident, a governing principle of the method selection and development process for environmental remediation and recovery is based on achieving high throughput while maintaining high quality analytical results. This paper illu

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.

ESTIMATING THE RADIUS OF THE CONVECTIVE CORE OF MAIN-SEQUENCE STARS FROM OBSERVED OSCILLATION FREQUENCIES

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

Yang, Wuming, E-mail: yangwuming@bnu.edu.cn, E-mail: yangwuming@ynao.ac.cn

The determination of the size of the convective core of main-sequence stars is usually dependent on the construction of models of stars. Here we introduce a method to estimate the radius of the convective core of main-sequence stars with masses between about 1.1 and 1.5 M {sub ⊙} from observed frequencies of low-degree p -modes. A formula is proposed to achieve the estimation. The values of the radius of the convective core of four known stars are successfully estimated by the formula. The radius of the convective core of KIC 9812850 estimated by the formula is 0.140 ± 0.028 Rmore » {sub ⊙}. In order to confirm this prediction, a grid of evolutionary models was computed. The value of the convective-core radius of the best-fit model of KIC 9812850 is 0.149 R {sub ⊙}, which is in good agreement with that estimated by the formula from observed frequencies. The formula aids in understanding the interior structure of stars directly from observed frequencies. The understanding is not dependent on the construction of models.« less

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

PubMed

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

2014-09-01

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

Using Genetic Programming with Prior Formula Knowledge to Solve Symbolic Regression Problem.

PubMed

Lu, Qiang; Ren, Jun; Wang, Zhiguang

2016-01-01

A researcher can infer mathematical expressions of functions quickly by using his professional knowledge (called Prior Knowledge). But the results he finds may be biased and restricted to his research field due to limitation of his knowledge. In contrast, Genetic Programming method can discover fitted mathematical expressions from the huge search space through running evolutionary algorithms. And its results can be generalized to accommodate different fields of knowledge. However, since GP has to search a huge space, its speed of finding the results is rather slow. Therefore, in this paper, a framework of connection between Prior Formula Knowledge and GP (PFK-GP) is proposed to reduce the space of GP searching. The PFK is built based on the Deep Belief Network (DBN) which can identify candidate formulas that are consistent with the features of experimental data. By using these candidate formulas as the seed of a randomly generated population, PFK-GP finds the right formulas quickly by exploring the search space of data features. We have compared PFK-GP with Pareto GP on regression of eight benchmark problems. The experimental results confirm that the PFK-GP can reduce the search space and obtain the significant improvement in the quality of SR.

Analysis of the numerical differentiation formulas of functions with large gradients

NASA Astrophysics Data System (ADS)

Tikhovskaya, S. V.

2017-10-01

The solution of a singularly perturbed problem corresponds to a function with large gradients. Therefore the question of interpolation and numerical differentiation of such functions is relevant. The interpolation based on Lagrange polynomials on uniform mesh is widely applied. However, it is known that the use of such interpolation for the function with large gradients leads to estimates that are not uniform with respect to the perturbation parameter and therefore leads to errors of order O(1). To obtain the estimates that are uniform with respect to the perturbation parameter, we can use the polynomial interpolation on a fitted mesh like the piecewise-uniform Shishkin mesh or we can construct on uniform mesh the interpolation formula that is exact on the boundary layer components. In this paper the numerical differentiation formulas for functions with large gradients based on the interpolation formulas on the uniform mesh, which were proposed by A.I. Zadorin, are investigated. The formulas for the first and the second derivatives of the function with two or three interpolation nodes are considered. Error estimates that are uniform with respect to the perturbation parameter are obtained in the particular cases. The numerical results validating the theoretical estimates are discussed.

The photon PDF from high-mass Drell-Yan data at the LHC.

PubMed

Giuli, F

2017-01-01

Achieving the highest precision for theoretical predictions at the LHC requires the calculation of hard-scattering cross sections that include perturbative QCD corrections up to (N)NNLO and electroweak (EW) corrections up to NLO. Parton distribution functions (PDFs) need to be provided with matching accuracy, which in the case of QED effects involves introducing the photon parton distribution of the proton, [Formula: see text]. In this work a determination of the photon PDF from fits to recent ATLAS measurements of high-mass Drell-Yan dilepton production at [Formula: see text] TeV is presented. This analysis is based on the xFitter framework, and has required improvements both in the APFEL program, to account for NLO QED effects, and in the aMCfast interface to account for the photon-initiated contributions in the EW calculations within MadGraph5_aMC@NLO. The results are compared with other recent QED fits and determinations of the photon PDF, consistent results are found.

Ultra-heavy cosmic rays: Theoretical implications of recent observations

NASA Technical Reports Server (NTRS)

Blake, J. B.; Hainebach, K. L.; Schramm, D. N.; Anglin, J. D.

1977-01-01

Extreme ultraheavy cosmic ray observations (Z greater or equal 70) are compared with r-process models. A detailed cosmic ray propagation calculation is used to transform the calculated source distributions to those observed at the earth. The r-process production abundances are calculated using different mass formulae and beta-rate formulae; an empirical estimate based on the observed solar system abundances is used also. There is the continued strong indication of an r-process dominance in the extreme ultra-heavy cosmic rays. However it is shown that the observed high actinide/Pt ratio in the cosmic rays cannot be fit with the same r-process calculation which also fits the solar system material. This result suggests that the cosmic rays probably undergo some preferential acceleration in addition to the apparent general enrichment in heavy (r-process) material. As estimate also is made of the expected relative abundance of superheavy elements in the cosmic rays if the anomalous heavy xenon in carbonaceous chondrites is due to a fissioning superheavy element.

Fitting Formulae and Constraints for the Existence of S-type and P-type Habitable Zones in Binary Systems

NASA Astrophysics Data System (ADS)

Wang, Zhaopeng; Cuntz, Manfred

2017-10-01

We derive fitting formulae for the quick determination of the existence of S-type and P-type habitable zones (HZs) in binary systems. Based on previous work, we consider the limits of the climatological HZ in binary systems (which sensitively depend on the system parameters) based on a joint constraint encompassing planetary orbital stability and a habitable region for a possible system planet. Additionally, we employ updated results on planetary climate models obtained by Kopparapu and collaborators. Our results are applied to four P-type systems (Kepler-34, Kepler-35, Kepler-413, and Kepler-1647) and two S-type systems (TrES-2 and KOI-1257). Our method allows us to gauge the existence of climatological HZs for these systems in a straightforward manner with detailed consideration of the observational uncertainties. Further applications may include studies of other existing systems as well as systems to be identified through future observational campaigns.

Fitting Formulae and Constraints for the Existence of S-type and P-type Habitable Zones in Binary Systems

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

Wang Zhaopeng; Cuntz, Manfred, E-mail: zhaopeng.wang@mavs.uta.edu, E-mail: cuntz@uta.edu

We derive fitting formulae for the quick determination of the existence of S-type and P-type habitable zones (HZs) in binary systems. Based on previous work, we consider the limits of the climatological HZ in binary systems (which sensitively depend on the system parameters) based on a joint constraint encompassing planetary orbital stability and a habitable region for a possible system planet. Additionally, we employ updated results on planetary climate models obtained by Kopparapu and collaborators. Our results are applied to four P-type systems (Kepler-34, Kepler-35, Kepler-413, and Kepler-1647) and two S-type systems (TrES-2 and KOI-1257). Our method allows us tomore » gauge the existence of climatological HZs for these systems in a straightforward manner with detailed consideration of the observational uncertainties. Further applications may include studies of other existing systems as well as systems to be identified through future observational campaigns.« less

Development of formula varsity race car chassis

NASA Astrophysics Data System (ADS)

Abdullah, M. A.; Mansur, M. R.; Tamaldin, N.; Thanaraj, K.

2013-12-01

Three chassis designs have been developed using commercial computer aided design (CAD) software. The design is based on the specifications of UTeM Formula VarsityTM 2012 (FV2012). The selection of the design is derived from weighted matrix which consists of reliability, cost, time consumption and weight. The score of the matrix is formulated based on relative weighted factor among the selections. All three designs are then fabricated using selected materials available. The actual cost, time consumption and weight of the chassis's are compared with the theoretical weighted scores. Standard processes of cuttings, fittings and welding are performed in chassis mock up and fabrication. The chassis is later assembled together with suspension systems, steering linkages, brake systems, engine system, and drive shaft systems. Once the chassis is assembled, the studies of driver's ergonomic and part accessibility are performed. The completion in final fittings and assembly of the race car and its reliability demonstrate an outstanding design for manufacturing (DFM) practices of the chassis.

Optimization of blade motion of vertical axis turbine

NASA Astrophysics Data System (ADS)

Ma, Yong; Zhang, Liang; Zhang, Zhi-yang; Han, Duan-feng

2016-04-01

In this paper, a method is proposed to improve the energy efficiency of the vertical axis turbine. First of all, a single disk multiple stream-tube model is used to calculate individual fitness. Genetic algorithm is adopted to optimize blade pitch motion of vertical axis turbine with the maximum energy efficiency being selected as the optimization objective. Then, a particular data processing method is proposed, fitting the result data into a cosine-like curve. After that, a general formula calculating the blade motion is developed. Finally, CFD simulation is used to validate the blade pitch motion formula. The results show that the turbine's energy efficiency becomes higher after the optimization of blade pitch motion; compared with the fixed pitch turbine, the efficiency of variable-pitch turbine is significantly improved by the active blade pitch control; the energy efficiency declines gradually with the growth of speed ratio; besides, compactness has lager effect on the blade motion while the number of blades has little effect on it.

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

Generalized Keller-Simmons formula for nonisothermal plasma-assisted sputtering depositions

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

Palmero, A.; Rudolph, H.; Habraken, F. H. P. M.

2006-11-20

A general description of the relation between the sputtering rate and the deposition rate in plasma-assisted sputtering deposition has been developed. The equation derived yields the so-called Keller-Simmons [IBM J. Res. Dev. 23, 24 (1979)] formula in the limit of zero thermal gradients in the deposition system. It is shown that the Keller-Simmons formula can still be applied to fit the experimental results if the characteristic pressure-distance product, p{sub 0}L{sub 0}, is related to the temperature of the sputter cathode and the growing film. Using this relation, it is found that the variations in the values for p{sub 0}L{sub 0}more » for different experimental conditions agree with the thus far not well understood experimental trends reported in the literature.« less

Investigation of non-hydroxamate scaffolds against HDAC6 inhibition: A pharmacophore modeling, molecular docking, and molecular dynamics simulation approach.

PubMed

Zeb, Amir; Park, Chanin; Son, Minky; Rampogu, Shailima; Alam, Syed Ibrar; Park, Seok Ju; Lee, Keun Woo

2018-06-01

Proteins deacetylation by Histone deacetylase 6 (HDAC6) has been shown in various human chronic diseases like neurodegenerative diseases and cancer, and hence is an important therapeutic target. Since, the existing inhibitors have hydroxamate group, and are not HDAC6-selective, therefore, this study has designed to investigate non-hydroxamate HDAC6 inhibitors. Ligand-based pharmacophore was generated from 26 training set compounds of HDAC6 inhibitors. The statistical parameters of pharmacophore (Hypo1) included lowest total cost of 115.63, highest cost difference of 135.00, lowest RMSD of 0.70 and the highest correlation of 0.98. The pharmacophore was validated by Fischer's Randomization and Test Set validation, and used as screening tool for chemical databases. The screened compounds were filtered by fit value ([Formula: see text]), estimated Inhibitory Concentration (IC[Formula: see text]) ([Formula: see text]), Lipinski's Rule of Five and Absorption, Distribution, Metabolism, Excretion, and Toxicity (ADMET) Descriptors to identify drug-like compounds. Furthermore, the drug-like compounds were docked into the active site of HDAC6. The best docked compounds were selected having goldfitness score [Formula: see text] and [Formula: see text], and hydrogen bond interaction with catalytic active residues. Finally, three inhibitors having sulfamoyl group were selected by Molecular Dynamic (MD) simulation, which showed stable root mean square deviation (RMSD) (1.6-1.9[Formula: see text]Å), lowest potential energy ([Formula: see text][Formula: see text]kJ/mol), and hydrogen bonding with catalytic active residues of HDAC6.

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.

dPotFit: A computer program to fit diatomic molecule spectral data to potential energy functions

NASA Astrophysics Data System (ADS)

Le Roy, Robert J.

2017-01-01

This paper describes program dPotFit, which performs least-squares fits of diatomic molecule spectroscopic data consisting of any combination of microwave, infrared or electronic vibrational bands, fluorescence series, and tunneling predissociation level widths, involving one or more electronic states and one or more isotopologs, and for appropriate systems, second virial coefficient data, to determine analytic potential energy functions defining the observed levels and other properties of each state. Four families of analytical potential functions are available for fitting in the current version of dPotFit: the Expanded Morse Oscillator (EMO) function, the Morse/Long-Range (MLR) function, the Double-Exponential/Long-Range (DELR) function, and the 'Generalized Potential Energy Function' (GPEF) of Šurkus, which incorporates a variety of polynomial functional forms. In addition, dPotFit allows sets of experimental data to be tested against predictions generated from three other families of analytic functions, namely, the 'Hannover Polynomial' (or "X-expansion") function, and the 'Tang-Toennies' and Scoles-Aziz 'HFD', exponential-plus-van der Waals functions, and from interpolation-smoothed pointwise potential energies, such as those obtained from ab initio or RKR calculations. dPotFit also allows the fits to determine atomic-mass-dependent Born-Oppenheimer breakdown functions, and singlet-state Λ-doubling, or 2Σ splitting radial strength functions for one or more electronic states. dPotFit always reports both the 95% confidence limit uncertainty and the "sensitivity" of each fitted parameter; the latter indicates the number of significant digits that must be retained when rounding fitted parameters, in order to ensure that predictions remain in full agreement with experiment. It will also, if requested, apply a "sequential rounding and refitting" procedure to yield a final parameter set defined by a minimum number of significant digits, while ensuring no significant loss of accuracy in the predictions yielded by those parameters.

Hollow Gaussian Schell-model beam and its propagation

NASA Astrophysics Data System (ADS)

Wang, Li-Gang; Wang, Li-Qin

2008-03-01

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

A 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.

Lattice QCD and the timelike pion form factor.

PubMed

Meyer, Harvey B

2011-08-12

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

Minimum-Cost Aircraft Descent Trajectories with a Constrained Altitude Profile

NASA Technical Reports Server (NTRS)

Wu, Minghong G.; Sadovsky, Alexander V.

2015-01-01

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

Spatial derivatives of flow quantities behind curved shocks of all strengths

NASA Technical Reports Server (NTRS)

Darden, C. M.

1984-01-01

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

Sound velocity in five-component air mixtures of various densities

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

Stupakov, Gennady; Zhou, Demin

2016-04-01

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

Analytical effective tensor for flow-through composites

DOEpatents

Sviercoski, Rosangela De Fatima [Los Alamos, NM

2012-06-19

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

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

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

Stupakov, Gennady; Zhou, Demin

2016-04-21

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

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

PubMed

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

2016-01-01

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

29 CFR 1910.103 - Hydrogen.

Code of Federal Regulations, 2013 CFR

2013-07-01

..., threaded, socket, or compression fittings. Gaskets and thread sealants shall be suitable for hydrogen... closures. (v) Piping, tubing, and fittings. (a) Piping, tubing, and fittings and gasket and thread sealants... including process or analytical equipment. (c) Be located 25 feet from concentrations of people. (d) Be...

SU-G-BRC-17: Using Generalized Mean for Equivalent Square Estimation

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

Zhou, S; Fan, Q; Lei, Y

Purpose: Equivalent Square (ES) is a widely used concept in radiotherapy. It enables us to determine many important quantities for a rectangular treatment field, without measurement, based on the corresponding values from its ES field. In this study, we propose a Generalized Mean (GM) type ES formula and compare it with other established formulae using benchmark datasets. Methods: Our GM approach is expressed as ES=(w•fx^α+(1-w)•fy^α)^(1/α), where fx, fy, α, and w represent field sizes, power index, and a weighting factor, respectively. When α=−1 it reduces to well-known Sterling type ES formulae. In our study, α and w are determined throughmore » least-square-fitting. Akaike Information Criterion (AIC) was used to benchmark the performance of each formula. BJR (Supplement 17) ES field table for X-ray PDDs and open field output factor tables in Varian TrueBeam representative dataset were used for validation. Results: Switching from α=−1 to α=−1.25, a 20% reduction in standard deviation of residual error in ES estimation was achieved for the BJR dataset. The maximum relative residual error was reduced from ∼3% (in Sterling formula) or ∼2% (in Vadash/Bjarngard formula) down to ∼1% in GM formula for open fields of all energies and at rectangular field sizes from 3cm to 40cm in the Varian dataset. The improvement of the GM over the Sterling type ES formulae is particularly noticeable for very elongated rectangular fields with short width. AIC analysis confirmed the superior performance of the GM formula after taking into account the expanded parameter space. Conclusion: The GM significantly outperforms Sterling type formulae at slightly increased computational cost. The GM calculation may nullify the requirement of data measurement for many rectangular fields and hence shorten the Linac commissioning process. Improved dose calculation accuracy is also expected by adopting the GM formula into treatment planning and secondary MU check systems.« 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…

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.

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.

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

A Hartree-Fock-Bogoliubov mass formula

NASA Astrophysics Data System (ADS)

Samyn, M.; Goriely, S.; Heenen, P.-H.; Pearson, J. M.; Tondeur, F.

2002-03-01

In order to have more reliable predictions of nuclear masses at the neutron drip line, we here go beyond the recent mass formula HFBCS-1 and present a new mass formula, HFB-1, based on the Hartree-Fock-Bogoliubov method. As with the HFBCS-1 mass formula, we use a 10-parameter Skyrme force along with a 4-parameter δ-function pairing force and a 2-parameter phenomenological Wigner term. However, with the original HFBCS-1 Skyrme force (MSk7), the rms error becomes unacceptably large and a new force fit is required. With the isoscalar and isovector effective masses constrained to be equal, the remaining 15 degrees of freedom are fitted to the masses of all the 1754 measured nuclei with A⩾16, | N- Z|>2 given in the 1995 Audi-Wapstra compilation. The rms error with respect to the masses of all the 1888 measured nuclei with Z, N⩾8 is 0.764 MeV. A complete mass table, HFB-1 (available on the Web), has been constructed, giving all nuclei lying between the two drip lines over the range Z, N⩾8 and Z⩽120. A comparison between HFB-1 and HFBCS-1 mass tables shows that the HFBCS model is a very good approximation of the HFB theory, in particular for masses, the extrapolated masses never differing by more than 2 MeV below Z⩽110. We also find that the behaviour of shell gaps far away from the region of beta stability does not depend on whether the HFBCS or HFB methods are used, in particular, no quenching of astrophysical interest arises from replacing the BCS method by the Bogoliubov method.

Inference and analysis of xenon outflow curves under multi-pulse injection in two-dimensional chromatography.

PubMed

Shu-Jiang, Liu; Zhan-Ying, Chen; Yin-Zhong, Chang; Shi-Lian, Wang; Qi, Li; Yuan-Qing, Fan

2013-10-11

Multidimensional gas chromatography is widely applied to atmospheric xenon monitoring for the Comprehensive Nuclear-Test-Ban Treaty (CTBT). To improve the capability for xenon sampling from the atmosphere, sampling techniques have been investigated in detail. The sampling techniques are designed by xenon outflow curves which are influenced by many factors, and the injecting condition is one of the key factors that could influence the xenon outflow curves. In this paper, the xenon outflow curves of single-pulse injection in two-dimensional gas chromatography has been tested and fitted as a function of exponential modified Gaussian distribution. An inference formula of the xenon outflow curve for six-pulse injection is derived, and the inference formula is also tested to compare with its fitting formula of the xenon outflow curve. As a result, the curves of both the one-pulse and six-pulse injections obey the exponential modified Gaussian distribution when the temperature of the activated carbon column's temperature is 26°C and the flow rate of the carrier gas is 35.6mLmin(-1). The retention time of the xenon peak for one-pulse injection is 215min, and the peak width is 138min. For the six-pulse injection, however, the retention time is delayed to 255min, and the peak width broadens to 222min. According to the inferred formula of the xenon outflow curve for the six-pulse injection, the inferred retention time is 243min, the relative deviation of the retention time is 4.7%, and the inferred peak width is 225min, with a relative deviation of 1.3%. Copyright © 2013 Elsevier B.V. All rights reserved.

The effect of wall thickness distribution on mechanical reliability and strength in unidirectional porous ceramics.

PubMed

Seuba, Jordi; Deville, Sylvain; Guizard, Christian; Stevenson, Adam J

2016-01-01

Macroporous ceramics exhibit an intrinsic strength variability caused by the random distribution of defects in their structure. However, the precise role of microstructural features, other than pore volume, on reliability is still unknown. Here, we analyze the applicability of the Weibull analysis to unidirectional macroporous yttria-stabilized-zirconia (YSZ) prepared by ice-templating. First, we performed crush tests on samples with controlled microstructural features with the loading direction parallel to the porosity. The compressive strength data were fitted using two different fitting techniques, ordinary least squares and Bayesian Markov Chain Monte Carlo, to evaluate whether Weibull statistics are an adequate descriptor of the strength distribution. The statistical descriptors indicated that the strength data are well described by the Weibull statistical approach, for both fitting methods used. Furthermore, we assess the effect of different microstructural features (volume, size, densification of the walls, and morphology) on Weibull modulus and strength. We found that the key microstructural parameter controlling reliability is wall thickness. In contrast, pore volume is the main parameter controlling the strength. The highest Weibull modulus ([Formula: see text]) and mean strength (198.2 MPa) were obtained for the samples with the smallest and narrowest wall thickness distribution (3.1 [Formula: see text]m) and lower pore volume (54.5%).

Hartree-Fock mass formulas and extrapolation to new mass data

NASA Astrophysics Data System (ADS)

Goriely, S.; Samyn, M.; Heenen, P.-H.; Pearson, J. M.; Tondeur, F.

2002-08-01

The two previously published Hartree-Fock (HF) mass formulas, HFBCS-1 and HFB-1 (HF-Bogoliubov), are shown to be in poor agreement with new Audi-Wapstra mass data. The problem lies first with the prescription adopted for the cutoff of the single-particle spectrum used with the δ-function pairing force, and second with the Wigner term. We find an optimal mass fit if the spectrum is cut off both above EF+15 MeV and below EF-15 MeV, EF being the Fermi energy of the nucleus in question. In addition to the Wigner term of the form VW exp(-λ|N-Z|/A) already included in the two earlier HF mass formulas, we find that a second Wigner term linear in |N-Z| leads to a significant improvement in lighter nuclei. These two features are incorporated into our new Hartree-Fock-Bogoliubov model, which leads to much improved extrapolations. The 18 parameters of the model are fitted to the 2135 measured masses for N,Z>=8 with an rms error of 0.674 MeV. With this parameter set a complete mass table, labeled HFB-2, has been constructed, going from one drip line to the other, up to Z=120. The new pairing-cutoff prescription favored by the new mass data leads to weaker neutron-shell gaps in neutron-rich nuclei.

On the Role of Imitation on Adolescence Methamphetamine Abuse Dynamics.

PubMed

Mushanyu, J; Nyabadza, F; Muchatibaya, G; Stewart, A G R

2017-03-01

Adolescence methamphetamine use is an issue of considerable concern due to its correlation with later delinquency, divorce, unemployment and health problems. Understanding how adolescents initiate methamphetamine abuse is important in developing effective prevention programs. We formulate a mathematical model for the spread of methamphetamine abuse using nonlinear ordinary differential equations. It is assumed that susceptibles are recruited into methamphetamine use through imitation. An epidemic threshold value, [Formula: see text], termed the abuse reproduction number, is proposed and defined herein in the drug-using context. The model is shown to exhibit the phenomenon of backward bifurcation. This means that methamphetamine problems may persist in the population even if [Formula: see text] is less than one. Sensitivity analysis of [Formula: see text] was performed to determine the relative importance of different parameters in methamphetamine abuse initiation. The model is then fitted to data on methamphetamine users less than 20 years old reporting methamphetamine as their primary substance of abuse in the treatment centres of Cape Town and parameter values that give the best fit are chosen. Results show that the proportion of methamphetamine users less than 20 years old reporting methamphetamine as their primary substance of abuse will continue to decrease in Cape Town of South Africa. The results suggest that intervention programs targeted at reducing adolescence methamphetamine abuse, are positively impacting methamphetamine abuse.

Physical characteristics of experienced and junior open-wheel car drivers.

PubMed

Raschner, Christian; Platzer, Hans-Peter; Patterson, Carson

2013-01-01

Despite the popularity of open-wheel car racing, scientific literature about the physical characteristics of competitive race car drivers is scarce. The purpose of this study was to compare selected fitness parameters of experienced and junior open-wheel race car drivers. The experienced drivers consisted of five Formula One, two GP2 and two Formula 3 drivers, and the nine junior drivers drove in the Formula Master, Koenig, BMW and Renault series. The following fitness parameters were tested: multiple reactions, multiple anticipation, postural stability, isometric upper body strength, isometric leg extension strength, isometric grip strength, cyclic foot speed and jump height. The group differences were calculated using the Mann-Whitney U-test. Because of the multiple testing strategy used, the statistical significance was Bonferroni corrected and set at P < 0.004. Significant differences between the experienced and junior drivers were found only for the jump height parameter (P = 0.002). The experienced drivers tended to perform better in leg strength (P = 0.009), cyclic foot speed (P = 0.024) and grip strength (P = 0.058). None of the other variables differed between the groups. The results suggested that the experienced drivers were significantly more powerful than the junior drivers: they tended to be quicker and stronger (18% to 25%) but without statistical significance. The experienced drivers demonstrated excellent strength and power compared with other high-performance athletes.

A Quantitative Review of the Relationship between Person-Organization Fit and Behavioral Outcomes

ERIC Educational Resources Information Center

Hoffman, Brian J.; Woehr, David J.

2006-01-01

This paper extends the meta-analysis of Verquer, Beehr, and Wagner by providing a meta-analytic review of the relationship between person-organization fit (PO fit) and behavioral criteria (job performance, organizational citizenship behaviors, and turnover). Results indicate that PO fit is weakly to moderately related to each of these outcome…

Fuzzy Analytic Hierarchy Process-based Chinese Resident Best Fitness Behavior Method Research.

PubMed

Wang, Dapeng; Zhang, Lan

2015-01-01

With explosive development in Chinese economy and science and technology, people's pursuit of health becomes more and more intense, therefore Chinese resident sports fitness activities have been rapidly developed. However, different fitness events popularity degrees and effects on body energy consumption are different, so bases on this, the paper researches on fitness behaviors and gets Chinese residents sports fitness behaviors exercise guide, which provides guidance for propelling to national fitness plan's implementation and improving Chinese resident fitness scientization. The paper starts from the perspective of energy consumption, it mainly adopts experience method, determines Chinese resident favorite sports fitness event energy consumption through observing all kinds of fitness behaviors energy consumption, and applies fuzzy analytic hierarchy process to make evaluation on bicycle riding, shadowboxing practicing, swimming, rope skipping, jogging, running, aerobics these seven fitness events. By calculating fuzzy rate model's membership and comparing their sizes, it gets fitness behaviors that are more helpful for resident health, more effective and popular. Finally, it gets conclusions that swimming is a best exercise mode and its membership is the highest. Besides, the memberships of running, rope skipping and shadowboxing practicing are also relative higher. It should go in for bodybuilding by synthesizing above several kinds of fitness events according to different physical conditions; different living conditions so that can better achieve the purpose of fitness exercises.

Analytical study of the effects of soft tissue artefacts on functional techniques to define axes of rotation.

PubMed

De Rosario, Helios; Page, Álvaro; Besa, Antonio

2017-09-06

The accurate location of the main axes of rotation (AoR) is a crucial step in many applications of human movement analysis. There are different formal methods to determine the direction and position of the AoR, whose performance varies across studies, depending on the pose and the source of errors. Most methods are based on minimizing squared differences between observed and modelled marker positions or rigid motion parameters, implicitly assuming independent and uncorrelated errors, but the largest error usually results from soft tissue artefacts (STA), which do not have such statistical properties and are not effectively cancelled out by such methods. However, with adequate methods it is possible to assume that STA only account for a small fraction of the observed motion and to obtain explicit formulas through differential analysis that relate STA components to the resulting errors in AoR parameters. In this paper such formulas are derived for three different functional calibration techniques (Geometric Fitting, mean Finite Helical Axis, and SARA), to explain why each technique behaves differently from the others, and to propose strategies to compensate for those errors. These techniques were tested with published data from a sit-to-stand activity, where the true axis was defined using bi-planar fluoroscopy. All the methods were able to estimate the direction of the AoR with an error of less than 5°, whereas there were errors in the location of the axis of 30-40mm. Such location errors could be reduced to less than 17mm by the methods based on equations that use rigid motion parameters (mean Finite Helical Axis, SARA) when the translation component was calculated using the three markers nearest to the axis. Copyright © 2017 Elsevier Ltd. All rights reserved.

Electrostatic roles in electron transfer from [NiFe] hydrogenase to cytochrome c3 from Desulfovibrio vulgaris Miyazaki F.

PubMed

Sugimoto, Yu; Kitazumi, Yuki; Shirai, Osamu; Nishikawa, Koji; Higuchi, Yoshiki; Yamamoto, Masahiro; Kano, Kenji

2017-05-01

Electrostatic interactions between proteins are key factors that govern the association and reaction rate. We spectroscopically determine the second-order reaction rate constant (k) of electron transfer from [NiFe] hydrogenase (H 2 ase) to cytochrome (cyt) c 3 at various ionic strengths (I). The k value decreases with I. To analyze the results, we develop a semi-analytical formula for I dependence of k based on the assumptions that molecules are spherical and the reaction proceeds via a transition state. Fitting of the formula to the experimental data reveals that the interaction occurs in limited regions with opposite charges and with radii much smaller than those estimated from crystal structures. This suggests that local charges in H 2 ase and cyt c 3 play important roles in the reaction. Although the crystallographic data indicate a positive electrostatic potential over almost the entire surface of the proteins, there exists a small region with negative potential on H 2 ase at which the electron transfer from H 2 ase to cyt c 3 may occur. This local negative potential region is identical to the hypothetical interaction sphere predicted by the analysis. Furthermore, I dependence of k is predicted by the Adaptive Poisson-Boltzmann Solver considering all charges of the amino acids in the proteins and the configuration of H 2 ase/cyt c 3 complex. The calculation reproduces the experimental results except at extremely low I. These results indicate that the stabilization derived from the local electrostatic interaction in the H 2 ase/cyt c 3 complex overcomes the destabilization derived from the electrostatic repulsion of the overall positive charge of both proteins. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

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.

Analytical functions for beta and gamma absorbed fractions of iodine-131 in spherical and ellipsoidal volumes.

PubMed

Mowlavi, Ali Asghar; Fornasier, Maria Rossa; Mirzaei, Mohammd; Bregant, Paola; de Denaro, Mario

2014-10-01

The beta and gamma absorbed fractions in organs and tissues are the important key factors of radionuclide internal dosimetry based on Medical Internal Radiation Dose (MIRD) approach. The aim of this study is to find suitable analytical functions for beta and gamma absorbed fractions in spherical and ellipsoidal volumes with a uniform distribution of iodine-131 radionuclide. MCNPX code has been used to calculate the energy absorption from beta and gamma rays of iodine-131 uniformly distributed inside different ellipsoids and spheres, and then the absorbed fractions have been evaluated. We have found the fit parameters of a suitable analytical function for the beta absorbed fraction, depending on a generalized radius for ellipsoid based on the radius of sphere, and a linear fit function for the gamma absorbed fraction. The analytical functions that we obtained from fitting process in Monte Carlo data can be used for obtaining the absorbed fractions of iodine-131 beta and gamma rays for any volume of the thyroid lobe. Moreover, our results for the spheres are in good agreement with the results of MIRD and other scientific literatures.

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.

Full-scale tank car rollover tests - survivability of top fittings and top fittings protective structures : final report.

DOT National Transportation Integrated Search

2016-05-01

Full-scale rollover crash tests were performed on three non-pressure tank carbodies to validate previous analytical work and : determine the effectiveness of two different types of protective structures in protecting the top fittings. The tests were ...

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.

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.

Identical superdeformed bands in yrast 152Dy: a systematic description

NASA Astrophysics Data System (ADS)

Dadwal, Anshul; Mittal, H. M.

2018-06-01

The nuclear softness (NS) formula, semiclassical particle rotor model (PRM) and modified exponential model with pairing attenuation are used for the systematic study of the identical superdeformed bands in the A ∼ 150 mass region. These formulae/models are employed to study the identical superdeformed bands relative to the yrast SD band 152Dy(1), {152Dy(1), 151Tb(2)}, {152Dy(1), 151Dy(4)} (midpoint), {152Dy(1), 153Dy(2)} (quarter point), {152Dy(1), 153Dy(3)} (three-quarter point). The parameters, baseline moment of inertia ({{I}}0), alignment (i) and effective pairing parameter (Δ0) are calculated using the least-squares fitting of the γ-ray transitions energies in the NS formula, semiclassical-PRM and modified exponential model with pairing attenuation, respectively. The calculated parameters are found to depend sensitively on the proposed baseline spin (I 0).

Age estimation in northern Chinese children by measurement of open apices in tooth roots.

PubMed

Guo, Yu-Cheng; Yan, Chun-Xia; Lin, Xing-Wei; Zhou, Hong; Li, Ju-Ping; Pan, Feng; Zhang, Zhi-Yong; Wei, Lai; Tang, Zheng; Chen, Teng

2015-01-01

The aim of this study was to assess the accuracy of Cameriere's methods on dental age estimation in the northern Chinese population. A sample of orthopantomographs of 785 healthy children (397 girls and 388 boys) aged between 5 and 15 years was collected. The seven left permanent mandibular teeth were evaluated with Cameriere's method. The sample was split into a training set to develop a Chinese-specific prediction formula and a test set to validate this novel developed formula. Following the training dataset study, the variables gender (g), x 3 (canine teeth), x 4 (first premolar), x 7 (second molar), N 0, and the first-order interaction between s and N 0 contributed significantly to the fit, yielding the following linear regression formula: Age = 10.202 + 0.826 g - 4.068x 3 - 1.536x 4 - 1.959x 7 + 0.536 N 0 - 0.219 s [Symbol: see text] N 0, where g is a variable, 1 for boys and 0 for girls. The equation explained 91.2 % (R (2) = 0.912) of the total deviance. By analyzing the test dataset, the accuracy of the European formula and Chinese formula was determined by the difference between the estimated dental age (DA) and chronological age (CA). The European formula verified on the collected Chinese children underestimated chronological age with a mean difference of around -0.23 year, while the Chinese formula underestimated the chronological age with a mean difference of -0.04 year. Significant differences in mean differences in years (DA - CA) and absolute difference (AD) between the Chinese-specific prediction formula and Cameriere's European formula were observed. In conclusion, a Chinese-specific prediction formula based on a large Chinese reference sample could ameliorate the age prediction accuracy in the age group of children.

Restoration of longitudinal images.

PubMed

Hu, Y; Frieden, B R

1988-01-15

In this paper, a method of restoring longitudinal images is developed. By using the transfer function for longitudinal objects, and inverse filtering, a longitudinal image may be restored. The Fourier theory and sampling theorems for transverse images cannot be used directly in the longitudinal case. A modification and reasonable approximation are introduced. We have numerically established a necessary relationship between just-resolved longitudinal separation (after inverse filtering), noise level, and the taking conditions of object distance and lens diameter. An empirical formula is also found to well-fit the computed results. This formula may be of use for designing optical systems which are to image longitudinal details, such as in robotics or microscopy.

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements.

PubMed

Daszkiewicz, Karol; Maquer, Ghislain; Zysset, Philippe K

2017-06-01

Boundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from [Formula: see text] scans of femoral heads and vertebral bodies. They were converted into [Formula: see text] models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs- and KUBCs-based tensors were determined for each sample. "In situ" stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset-Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors, and model parameters [Formula: see text] (Poisson's ratio) [Formula: see text] and [Formula: see text] (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on [Formula: see text]. However, KUBCs- and PMUBCs-based [Formula: see text] and [Formula: see text], respectively, decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.

Electron beam energy chirp control with a rectangular corrugated structure at the Linac Coherent Light Source

DOE PAGES

Zhang, Zhen; Bane, Karl; Ding, Yuantao; ...

2015-01-30

In this study, electron beam energy chirp is an important parameter that affects the bandwidth and performance of a linac-based, free-electron laser. In this paper we study the wakefields generated by a beam passing between at metallic plates with small corrugations, and then apply such a device as a passive dechirper for the Linac Coherent Light Source (LCLS) energy chirp control with a multi-GeV and femtosecond electron beam. Similar devices have been tested in several places at relatively low energies (~100 MeV) and with relatively long bunches (> 1ps). In the parameter regime of the LCLS dechirper, with the corrugationmore » size similar to the gap between the plates, the analytical solutions of the wakefields are no longer applicable, and we resort to a field matching program to obtain the wakes. Based on the numerical calculations, we fit the short-range, longitudinal wakes to simple formulas, valid over a large, useful parameter range. Finally, since the transverse wakefields - both dipole and quadrupole-are strong, we compute and include them in beam dynamics simulations to investigate the error tolerances when this device is introduced in the LCLS.« less

On the buckling of hexagonal boron nitride nanoribbons via structural mechanics

NASA Astrophysics Data System (ADS)

Giannopoulos, Georgios I.

2018-03-01

Monolayer hexagonal boron nitride nanoribbons have similar crystal structure as graphene nanoribbons, have excellent mechanical, thermal insulating and dielectric properties and additionally present chemical stability. These allotropes of boron nitride can be used in novel applications, in which graphene is not compatible, to achieve remarkable performance. The purpose of the present work is to provide theoretical estimations regarding the buckling response of hexagonal boron nitride monolayer under compressive axial loadings. For this reason, a structural mechanics method is formulated which employs the exact equilibrium atomistic structure of the specific two-dimensional nanomaterial. In order to represent the interatomic interactions appearing between boron and nitrogen atoms, the Dreiding potential model is adopted which is realized by the use of three-dimensional, two-noded, spring-like finite elements of appropriate stiffness matrices. The critical compressive loads that cause the buckling of hexagonal boron nitride nanoribbons are computed with respect to their size and chirality while some indicative buckled shapes of them are illustrated. Important conclusions arise regarding the effect of the size and chirality on the structural stability of the hexagonal boron nitride monolayers. An analytical buckling formula, which provides good fitting of the numerical outcome, is proposed.

Default risk modeling beyond the first-passage approximation: Extended Black-Cox model

NASA Astrophysics Data System (ADS)

Katz, Yuri A.; Shokhirev, Nikolai V.

2010-07-01

We develop a generalization of the Black-Cox structural model of default risk. The extended model captures uncertainty related to firm’s ability to avoid default even if company’s liabilities momentarily exceeding its assets. Diffusion in a linear potential with the radiation boundary condition is used to mimic a company’s default process. The exact solution of the corresponding Fokker-Planck equation allows for derivation of analytical expressions for the cumulative probability of default and the relevant hazard rate. Obtained closed formulas fit well the historical data on global corporate defaults and demonstrate the split behavior of credit spreads for bonds of companies in different categories of speculative-grade ratings with varying time to maturity. Introduction of the finite rate of default at the boundary improves valuation of credit risk for short time horizons, which is the key advantage of the proposed model. We also consider the influence of uncertainty in the initial distance to the default barrier on the outcome of the model and demonstrate that this additional source of incomplete information may be responsible for nonzero credit spreads for bonds with very short time to maturity.

Normalized inverse characterization of sound absorbing rigid porous media.

PubMed

Zieliński, Tomasz G

2015-06-01

This paper presents a methodology for the inverse characterization of sound absorbing rigid porous media, based on standard measurements of the surface acoustic impedance of a porous sample. The model parameters need to be normalized to have a robust identification procedure which fits the model-predicted impedance curves with the measured ones. Such a normalization provides a substitute set of dimensionless (normalized) parameters unambiguously related to the original model parameters. Moreover, two scaling frequencies are introduced, however, they are not additional parameters and for different, yet reasonable, assumptions of their values, the identification procedure should eventually lead to the same solution. The proposed identification technique uses measured and computed impedance curves for a porous sample not only in the standard configuration, that is, set to the rigid termination piston in an impedance tube, but also with air gaps of known thicknesses between the sample and the piston. Therefore, all necessary analytical formulas for sound propagation in double-layered media are provided. The methodology is illustrated by one numerical test and by two examples based on the experimental measurements of the acoustic impedance and absorption of porous ceramic samples of different thicknesses and a sample of polyurethane foam.

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.

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.

Analysis of environmental contamination resulting from catastrophic incidents: part 2. Building laboratory capability by selecting and developing analytical methodologies.

PubMed

Magnuson, Matthew; Campisano, Romy; Griggs, John; Fitz-James, Schatzi; Hall, Kathy; Mapp, Latisha; Mullins, Marissa; Nichols, Tonya; Shah, Sanjiv; Silvestri, Erin; Smith, Terry; Willison, Stuart; Ernst, Hiba

2014-11-01

Catastrophic incidents can generate a large number of samples of analytically diverse types, including forensic, clinical, environmental, food, and others. Environmental samples include water, wastewater, soil, air, urban building and infrastructure materials, and surface residue. Such samples may arise not only from contamination from the incident but also from the multitude of activities surrounding the response to the incident, including decontamination. This document summarizes a range of activities to help build laboratory capability in preparation for sample analysis following a catastrophic incident, including selection and development of fit-for-purpose analytical methods for chemical, biological, and radiological contaminants. Fit-for-purpose methods are those which have been selected to meet project specific data quality objectives. For example, methods could be fit for screening contamination in the early phases of investigation of contamination incidents because they are rapid and easily implemented, but those same methods may not be fit for the purpose of remediating the environment to acceptable levels when a more sensitive method is required. While the exact data quality objectives defining fitness-for-purpose can vary with each incident, a governing principle of the method selection and development process for environmental remediation and recovery is based on achieving high throughput while maintaining high quality analytical results. This paper illustrates the result of applying this principle, in the form of a compendium of analytical methods for contaminants of interest. The compendium is based on experience with actual incidents, where appropriate and available. This paper also discusses efforts aimed at adaptation of existing methods to increase fitness-for-purpose and development of innovative methods when necessary. The contaminants of interest are primarily those potentially released through catastrophes resulting from malicious activity. However, the same techniques discussed could also have application to catastrophes resulting from other incidents, such as natural disasters or industrial accidents. Further, the high sample throughput enabled by the techniques discussed could be employed for conventional environmental studies and compliance monitoring, potentially decreasing costs and/or increasing the quantity of data available to decision-makers. Published by Elsevier Ltd.

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.

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

NASA Technical Reports Server (NTRS)

King, H. F.; Komornicki, A.

1986-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2011-04-01

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

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.

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.

High-Contrast Gratings based Spoof Surface Plasmons

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

On the superposition principle in interference experiments.

PubMed

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

2015-05-14

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