Continuum description of solvent dielectrics in molecular-dynamics simulations of proteins

NASA Astrophysics Data System (ADS)

Egwolf, Bernhard; Tavan, Paul

2003-02-01

We present a continuum approach for efficient and accurate calculation of reaction field forces and energies in classical molecular-dynamics (MD) simulations of proteins in water. The derivation proceeds in two steps. First, we reformulate the electrostatics of an arbitrarily shaped molecular system, which contains partially charged atoms and is embedded in a dielectric continuum representing the water. A so-called fuzzy partition is used to exactly decompose the system into partial atomic volumes. The reaction field is expressed by means of dipole densities localized at the atoms. Since these densities cannot be calculated analytically for general systems, we introduce and carefully analyze a set of approximations in a second step. These approximations allow us to represent the dipole densities by simple dipoles localized at the atoms. We derive a system of linear equations for these dipoles, which can be solved numerically by iteration. After determining the two free parameters of our approximate method we check its quality by comparisons (i) with an analytical solution, which is available for a perfectly spherical system, (ii) with forces obtained from a MD simulation of a soluble protein in water, and (iii) with reaction field energies of small molecules calculated by a finite difference method.

Amalgam Electrode-Based Electrochemical Detector for On-Site Direct Determination of Cadmium(II) and Lead(II) from Soils

PubMed Central

Nejdl, Lukas; Kynicky, Jindrich; Brtnicky, Martin; Vaculovicova, Marketa; Adam, Vojtech

2017-01-01

Toxic metal contamination of the environment is a global issue. In this paper, we present a low-cost and rapid production of amalgam electrodes used for determination of Cd(II) and Pb(II) in environmental samples (soils and wastewaters) by on-site analysis using difference pulse voltammetry. Changes in the electrochemical signals were recorded with a miniaturized potentiostat (width: 80 mm, depth: 54 mm, height: 23 mm) and a portable computer. The limit of detection (LOD) was calculated for the geometric surface of the working electrode 15 mm2 that can be varied as required for analysis. The LODs were 80 ng·mL−1 for Cd(II) and 50 ng·mL−1 for Pb(II), relative standard deviation, RSD ≤ 8% (n = 3). The area of interest (Dolni Rozinka, Czech Republic) was selected because there is a deposit of uranium ore and extreme anthropogenic activity. Environmental samples were taken directly on-site and immediately analysed. Duration of a single analysis was approximately two minutes. The average concentrations of Cd(II) and Pb(II) in this area were below the global average. The obtained values were verified (correlated) by standard electrochemical methods based on hanging drop electrodes and were in good agreement. The advantages of this method are its cost and time effectivity (approximately two minutes per one sample) with direct analysis of turbid samples (soil leach) in a 2 M HNO3 environment. This type of sample cannot be analyzed using the classical analytical methods without pretreatment. PMID:28792458

Hypergeometric continuation of divergent perturbation series: II. Comparison with Shanks transformation and Padé approximation

NASA Astrophysics Data System (ADS)

Sanders, Sören; Holthaus, Martin

2017-11-01

We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose-Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions.

An Approximate Analytical Model of Shock Waves from Underground Nuclear Explosions

DTIC Science & Technology

1990-12-01

Explosions, University of California Radiation Laboratory, Rep. UCRL -5675,1 pp. 120 134, 1959. Perret, W. R., and R. C. Bass, Free-field ground motion...Park, PA 16802 Blacksburg, VA 24061 Dr. Ralph Alewine, Ii Dr. Stephen Bratt DARPAJNMRO Center for Seismic Studies 3701 North Fairfax Drive 1300 North...DARP,,NMRO Patrick AFB, FL 3 2925-6001 3701 North Fairfax Drive Arlington, VA 222CN-171a l)r. Richard Sailor Donald L. Springer TASC, Inc. Lawrence

Stability of phases of a square-well fluid within superposition approximation

NASA Astrophysics Data System (ADS)

Piasecki, Jarosław; Szymczak, Piotr; Kozak, John J.

2013-04-01

The analytic and numerical methods introduced previously to study the phase behavior of hard sphere fluids starting from the Yvon-Born-Green (YBG) equation under the Kirkwood superposition approximation (KSA) are adapted to the square-well fluid. We are able to show conclusively that the YBG equation under the KSA closure when applied to the square-well fluid: (i) predicts the existence of an absolute stability limit corresponding to freezing where undamped oscillations appear in the long-distance behavior of correlations, (ii) in accordance with earlier studies reveals the existence of a liquid-vapor transition by the appearance of a "near-critical region" where monotonically decaying correlations acquire very long range, although the system never loses stability.

Analytical Derivation and Experimental Evaluation of Short-Bearing Approximation for Full Journal Bearing

NASA Technical Reports Server (NTRS)

Dubois, George B; Ocvirk, Fred W

1953-01-01

An approximate analytical solution including the effect of end leakage from the oil film of short plain bearings is presented because of the importance of endwise flow in sleeve bearings of the short lengths commonly used. The analytical approximation is supported by experimental data, resulting in charts which facilitate analysis of short plain bearings. The analytical approximation includes the endwise flow and that part of the circumferential flow which is related to surface velocity and film thickness but neglects the effect of film pressure on the circumferential flow. In practical use, this approximation applies best to bearings having a length-diameter ratio up to 1, and the effects of elastic deflection, inlet oil pressure, and changes of clearance with temperature minimize the relative importance of the neglected term. The analytical approximation was found to be an extension of a little-known pressure-distribution function originally proposed by Michell and Cardullo.

Multilayer adsorption of Cu(II) and Cd(II) over Brazilian Orchid Tree (Pata-de-vaca) and its adsorptive properties

NASA Astrophysics Data System (ADS)

Jorgetto, Alexandre de O.; da Silva, Adrielli C. P.; Wondracek, Marcos H. P.; Silva, Rafael I. V.; Velini, Edivaldo D.; Saeki, Margarida J.; Pedrosa, Valber A.; Castro, Gustavo R.

2015-08-01

Through very simple and inexpensive processes, pata-de-vaca leaves were turned into a powder and applied as an adsorbent for the uptake of Cu(II) and Cd(II) from water. The material was characterized through SEM, EDX, FTIR and surface area measurement. The material had its point of zero charge determined (5.24), and its adsorption capacity was evaluated as a function of time, pH and metal concentration. The material presented fast adsorption kinetics, reaching adsorption equilibrium in less than 5 min and it had a good correlation with the pseudo-second order kinetic model. Optimum pH for the adsorption of Cu(II) and Cd(II) were found to be in the range from 4 to 5, approximately. In the experiment as a function of the analyte concentration, analogously to gas adsorption, the material presented a type II isotherm, indicating the formation of multilayers for both species. Such behavior was explained with basis in the alternation between cations and anions over the material's surface, and the maximum adsorption capacity, considering the formation of the multilayers were found to be 0.238 mmol L-1 for Cu(II) and 0.113 mmol L-1 for Cd(II).

Partial Wave Dispersion Relations: Application to Electron-Atom Scattering

NASA Technical Reports Server (NTRS)

Temkin, A.; Drachman, Richard J.

1999-01-01

In this Letter we propose the use of partial wave dispersion relations (DR's) as the way of solving the long-standing problem of correctly incorporating exchange in a valid DR for electron-atom scattering. In particular a method is given for effectively calculating the contribution of the discontinuity and/or poles of the partial wave amplitude which occur in the negative E plane. The method is successfully tested in three cases: (i) the analytically solvable exponential potential, (ii) the Hartree potential, and (iii) the S-wave exchange approximation for electron-hydrogen scattering.

Level 1 environmental assessment performance evaluation. Final report jun 77-oct 78

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

Estes, E.D.; Smith, F.; Wagoner, D.E.

1979-02-01

The report gives results of a two-phased evaluation of Level 1 environmental assessment procedures. Results from Phase I, a field evaluation of the Source Assessment Sampling System (SASS), showed that the SASS train performed well within the desired factor of 3 Level 1 accuracy limit. Three sample runs were made with two SASS trains sampling simultaneously and from approximately the same sampling point in a horizontal duct. A Method-5 train was used to estimate the 'true' particulate loading. The sampling systems were upstream of the control devices to ensure collection of sufficient material for comparison of total particulate, particle sizemore » distribution, organic classes, and trace elements. Phase II consisted of providing each of three organizations with three types of control samples to challenge the spectrum of Level 1 analytical procedures: an artificial sample in methylene chloride, an artificial sample on a flyash matrix, and a real sample composed of the combined XAD-2 resin extracts from all Phase I runs. Phase II results showed that when the Level 1 analytical procedures are carefully applied, data of acceptable accuracy is obtained. Estimates of intralaboratory and interlaboratory precision are made.« less

Radiative recombination data for tungsten ions: II. W{sup 47+}–W{sup 71+}

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

Trzhaskovskaya, M.B., E-mail: Trzhask@MT5605.spb.edu; Nikulin, V.K.

2014-07-15

New radiative recombination and photoionization cross sections, radiative recombination rate coefficients, and radiated power loss rate coefficients are presented for 23 tungsten impurity ions in plasmas. We consider ions from W{sup 47+} to W{sup 71+} that are of importance to fusion studies for ITER and for experiments using electron beam ion traps. The calculations are fully relativistic and all significant multipoles of the radiative field are taken into account. The Dirac–Fock method is used to compute the electron wavefunctions. Radiative recombination rates and radiated power loss rates are found using the relativistic Maxwell–Jüttner distribution of the continuum electron velocity. Themore » total radiative recombination cross sections are given in the electron energy range from 1 eV to ∼80keV. Partial cross sections for ground and excited states are approximated by an analytical expression involving five fit parameters. Radiative recombination rates and radiated power loss rates are calculated in the temperature range from 10{sup 4}K to 10{sup 9}K. The total radiative recombination rates are approximated by another analytical expression with four fit parameters.« less

Analytic Approximation of Carbon Condensation Issues in Type ii Supernovae

NASA Astrophysics Data System (ADS)

Clayton, Donald D.

2013-01-01

I present analytic approximations for some issues related to condensation of graphite, TiC, and silicon carbide in oxygen-rich cores of supernovae of Type II. Increased understanding, which mathematical analysis can support, renders researchers more receptive to condensation in O-rich supernova gases. Taking SN 1987A as typical, my first analysis shows why the abundance of CO molecules reaches an early maximum in which free carbon remains more abundant than CO. This analysis clarifies why O-rich gas cannot oxidize C if 56Co radioactivity is as strong as in SN 1987A. My next analysis shows that the CO abundance could be regarded as being in chemical equilibrium if the CO molecule is given an effective binding energy rather than its laboratory dissociation energy. The effective binding energy makes the thermal dissociation rate of CO equal to its radioactive dissociation rate. This preserves possible relevance for the concept of chemical equilibrium. My next analysis shows that the observed abundances of CO and SiO molecules in SN 1987A rule out frequent suggestions that equilibrium condensation of SUNOCONs has occurred following atomic mixing of the He-burning shell with more central zones in such a way as to reproduce roughly the observed spectrum of isotopes in SUNOCONs while preserving C/O > 1. He atoms admixed along with the excess carbon would destroy CO and SiO molecules, leaving their observed abundances unexplained. The final analysis argues that a chemical quasiequilibrium among grains (but not gas) may exist approximately during condensation, so that its computational use is partially justified as a guide to which mineral phases would be stable against reactions with gas. I illustrate this point with quasiequilibrium calculations by Ebel & Grossman that have shown that graphite is stable even when O/C >1 if prominent molecules are justifiably excluded from the calculation of chemical equilibrium.

Analytical Studies of Boundary Layer Generated Aircraft Interior Noise

NASA Technical Reports Server (NTRS)

Howe, M. S.; Shah, P. L.

1997-01-01

An analysis is made of the "interior noise" produced by high, subsonic turbulent flow over a thin elastic plate partitioned into "panels" by straight edges transverse to the mean flow direction. This configuration models a section of an aircraft fuselage that may be regarded as locally flat. The analytical problem can be solved in closed form to represent the acoustic radiation in terms of prescribed turbulent boundary layer pressure fluctuations. Two cases are considered: (i) the production of sound at an isolated panel edge (i.e., in the approximation in which the correlation between sound and vibrations generated at neighboring edges is neglected), and (ii) the sound generated by a periodic arrangement of identical panels. The latter problem is amenable to exact analytical treatment provided the panel edge conditions are the same for all panels. Detailed predictions of the interior noise depend on a knowledge of the turbulent boundary layer wall pressure spectrum, and are given here in terms of an empirical spectrum proposed by Laganelli and Wolfe. It is expected that these analytical representations of the sound generated by simplified models of fluid-structure interactions can used to validate more general numerical schemes.

Approximate analytical solutions to the double-stance dynamics of the lossy spring-loaded inverted pendulum.

PubMed

Shahbazi, Mohammad; Saranlı, Uluç; Babuška, Robert; Lopes, Gabriel A D

2016-12-05

This paper introduces approximate time-domain solutions to the otherwise non-integrable double-stance dynamics of the 'bipedal' spring-loaded inverted pendulum (B-SLIP) in the presence of non-negligible damping. We first introduce an auxiliary system whose behavior under certain conditions is approximately equivalent to the B-SLIP in double-stance. Then, we derive approximate solutions to the dynamics of the new system following two different methods: (i) updated-momentum approach that can deal with both the lossy and lossless B-SLIP models, and (ii) perturbation-based approach following which we only derive a solution to the lossless case. The prediction performance of each method is characterized via a comprehensive numerical analysis. The derived representations are computationally very efficient compared to numerical integrations, and, hence, are suitable for online planning, increasing the autonomy of walking robots. Two application examples of walking gait control are presented. The proposed solutions can serve as instrumental tools in various fields such as control in legged robotics and human motion understanding in biomechanics.

An iterative analytical technique for the design of interplanetary direct transfer trajectories including perturbations

NASA Astrophysics Data System (ADS)

Parvathi, S. P.; Ramanan, R. V.

2018-06-01

An iterative analytical trajectory design technique that includes perturbations in the departure phase of the interplanetary orbiter missions is proposed. The perturbations such as non-spherical gravity of Earth and the third body perturbations due to Sun and Moon are included in the analytical design process. In the design process, first the design is obtained using the iterative patched conic technique without including the perturbations and then modified to include the perturbations. The modification is based on, (i) backward analytical propagation of the state vector obtained from the iterative patched conic technique at the sphere of influence by including the perturbations, and (ii) quantification of deviations in the orbital elements at periapsis of the departure hyperbolic orbit. The orbital elements at the sphere of influence are changed to nullify the deviations at the periapsis. The analytical backward propagation is carried out using the linear approximation technique. The new analytical design technique, named as biased iterative patched conic technique, does not depend upon numerical integration and all computations are carried out using closed form expressions. The improved design is very close to the numerical design. The design analysis using the proposed technique provides a realistic insight into the mission aspects. Also, the proposed design is an excellent initial guess for numerical refinement and helps arrive at the four distinct design options for a given opportunity.

The classical D-type expansion of spherical H II regions

NASA Astrophysics Data System (ADS)

Williams, Robin J. R.; Bibas, Thomas G.; Haworth, Thomas J.; Mackey, Jonathan

2018-06-01

Recent numerical and analytic work has highlighted some shortcomings in our understanding of the dynamics of H II region expansion, especially at late times, when the H II region approaches pressure equilibrium with the ambient medium. Here we reconsider the idealized case of a constant radiation source in a uniform and spherically symmetric ambient medium, with an isothermal equation of state. A thick-shell solution is developed which captures the stalling of the ionization front and the decay of the leading shock to a weak compression wave as it escapes to large radii. An acoustic approximation is introduced to capture the late-time damped oscillations of the H II region about the stagnation radius. Putting these together, a matched asymptotic equation is derived for the radius of the ionization front which accounts for both the inertia of the expanding shell and the finite temperature of the ambient medium. The solution to this equation is shown to agree very well with the numerical solution at all times, and is superior to all previously published solutions. The matched asymptotic solution can also accurately model the variation of H II region radius for a time-varying radiation source.

Ergodicity of the Stochastic Nosé-Hoover Heat Bath

NASA Astrophysics Data System (ADS)

Wei Chung Lo,; Baowen Li,

2010-07-01

We numerically study the ergodicity of the stochastic Nosé-Hoover heat bath whose formalism is based on the Markovian approximation for the Nosé-Hoover equation [J. Phys. Soc. Jpn. 77 (2008) 103001]. The approximation leads to a Langevin-like equation driven by a fluctuating dissipative force and multiplicative Gaussian white noise. The steady state solution of the associated Fokker-Planck equation is the canonical distribution. We investigate the dynamics of this method for the case of (i) free particle, (ii) nonlinear oscillators and (iii) lattice chains. We derive the Fokker-Planck equation for the free particle and present approximate analytical solution for the stationary distribution in the context of the Markovian approximation. Numerical simulation results for nonlinear oscillators show that this method results in a Gaussian distribution for the particles velocity. We also employ the method as heat baths to study nonequilibrium heat flow in one-dimensional Fermi-Pasta-Ulam (FPU-β) and Frenkel-Kontorova (FK) lattices. The establishment of well-defined temperature profiles are observed only when the lattice size is large. Our results provide numerical justification for such Markovian approximation for classical single- and many-body systems.

Analytic model for the long-term evolution of circular Earth satellite orbits including lunar node regression

NASA Astrophysics Data System (ADS)

Zhu, Ting-Lei; Zhao, Chang-Yin; Zhang, Ming-Jiang

2017-04-01

This paper aims to obtain an analytic approximation to the evolution of circular orbits governed by the Earth's J2 and the luni-solar gravitational perturbations. Assuming that the lunar orbital plane coincides with the ecliptic plane, Allan and Cook (Proc. R. Soc. A, Math. Phys. Eng. Sci. 280(1380):97, 1964) derived an analytic solution to the orbital plane evolution of circular orbits. Using their result as an intermediate solution, we establish an approximate analytic model with lunar orbital inclination and its node regression be taken into account. Finally, an approximate analytic expression is derived, which is accurate compared to the numerical results except for the resonant cases when the period of the reference orbit approximately equals the integer multiples (especially 1 or 2 times) of lunar node regression period.

Consistent Yokoya-Chen Approximation to Beamstrahlung(LCC-0010)

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

Peskin, M

2004-04-22

I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.

Stability and control of the Gossamer human powered aircraft by analysis and flight test

NASA Technical Reports Server (NTRS)

Jex, H. R.; Mitchell, D. G.

1982-01-01

The slow flight speed, very light wing loading, and neutral stability of the Gossamer Condor and the Gossamer Albatross emphasized apparent-mass aerodynamic effects and unusual modes of motion response. These are analyzed, approximated, and discussed, and the resulting transfer functions and dynamic properties are summarized and compared. To verify these analytical models, flight tests were conducted with and electrically powered Gossamer Albatross II. Sensors were installed and their outputs were telemetered to records on the ground. Frequency sweeps of the various controls were made and the data were reduced to frequency domain measures. Results are given for the response of: pitch rate, airspeed and normal acceleration from canard-elevator deflection; roll rate and yaw rate from canard-rudder tilt; and roll rate and yaw rate from wing warp. The reliable data are compared with the analytical predictions.

Approximated analytical solution to an Ebola optimal control problem

NASA Astrophysics Data System (ADS)

Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.

2016-11-01

An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.

Integrating a Smartphone and Molecular Modeling for Determining the Binding Constant and Stoichiometry Ratio of the Iron(II)-Phenanthroline Complex: An Activity for Analytical and Physical Chemistry Laboratories

ERIC Educational Resources Information Center

de Morais, Camilo de L. M.; Silva, Se´rgio R. B.; Vieira, Davi S.; Lima, Ka´ssio M. G.

2016-01-01

The binding constant and stoichiometry ratio for the formation of iron(II)-(1,10-phenanthroline) or iron(II)-o-phenanthroline complexes has been determined by a combination of a low-cost analytical method using a smartphone and a molecular modeling method as a laboratory experiment designed for analytical and physical chemistry courses. Intensity…

Topics in elementary particle physics

NASA Astrophysics Data System (ADS)

Jin, Xiang

The author of this thesis discusses two topics in elementary particle physics: n-ary algebras and their applications to M-theory (Part I), and functional evolution and Renormalization Group flows (Part II). In part I, Lie algebra is extended to four different n-ary algebraic structure: generalized Lie algebra, Filippov algebra, Nambu algebra and Nambu-Poisson tensor; though there are still many other n-ary algebras. A natural property of Generalized Lie algebras — the Bremner identity, is studied, and proved with a totally different method from its original version. We extend Bremner identity to n-bracket cases, where n is an arbitrary odd integer. Filippov algebras do not focus on associativity, and are defined by the Fundamental identity. We add associativity to Filippov algebras, and give examples of how to construct Filippov algebras from su(2), bosonic oscillator, Virasoro algebra. We try to include fermionic charges into the ternary Virasoro-Witt algebra, but the attempt fails because fermionic charges keep generating new charges that make the algebra not closed. We also study the Bremner identity restriction on Nambu algebras and Nambu-Poisson tensors. So far, the only example 3-algebra being used in physics is the BLG model with 3-algebra A4, describing two M2-branes interactions. Its extension with Nambu algebra, BLG-NB model, is believed to describe infinite M2-branes condensation. Also, there is another propose for M2-brane interactions, the ABJM model, which is constructed by ordinary Lie algebra. We compare the symmetry properties between them, and discuss the possible approaches to include these three models into a grand unification theory. In Part II, we give an approximate solution for Schroeder's equations, based on series and conjugation methods. We use the logistic map as an example, and demonstrate that this approximate solution converges to known analytical solutions around the fixed point, around which the approximate solution is constructed. Although the closed-form solutions for Schroeder's equations can not always be approached analytically, by fitting the approximation solutions, one can still obtain closed-form solutions sometimes. Based on Schroeder's theory, approximate solutions for trajectories, velocities and potentials can also be constructed. The approximate solution is significantly useful to calculate the beta function in renormalization group trajectory. By "wrapping" the series solutions with the conjugations from different inverse functions, we generate different branches of the trajectory, and construct a counterexample for a folk theorem about limited cycles.

A non-grey analytical model for irradiated atmospheres. II. Analytical vs. numerical solutions

NASA Astrophysics Data System (ADS)

Parmentier, Vivien; Guillot, Tristan; Fortney, Jonathan J.; Marley, Mark S.

2015-02-01

Context. The recent discovery and characterization of the diversity of the atmospheres of exoplanets and brown dwarfs calls for the development of fast and accurate analytical models. Aims: We wish to assess the goodness of the different approximations used to solve the radiative transfer problem in irradiated atmospheres analytically, and we aim to provide a useful tool for a fast computation of analytical temperature profiles that remains correct over a wide range of atmospheric characteristics. Methods: We quantify the accuracy of the analytical solution derived in paper I for an irradiated, non-grey atmosphere by comparing it to a state-of-the-art radiative transfer model. Then, using a grid of numerical models, we calibrate the different coefficients of our analytical model for irradiated solar-composition atmospheres of giant exoplanets and brown dwarfs. Results: We show that the so-called Eddington approximation used to solve the angular dependency of the radiation field leads to relative errors of up to ~5% on the temperature profile. For grey or semi-grey atmospheres (i.e., when the visible and thermal opacities, respectively, can be considered independent of wavelength), we show that the presence of a convective zone has a limited effect on the radiative atmosphere above it and leads to modifications of the radiative temperature profile of approximately ~2%. However, for realistic non-grey planetary atmospheres, the presence of a convective zone that extends to optical depths smaller than unity can lead to changes in the radiative temperature profile on the order of 20% or more. When the convective zone is located at deeper levels (such as for strongly irradiated hot Jupiters), its effect on the radiative atmosphere is again on the same order (~2%) as in the semi-grey case. We show that the temperature inversion induced by a strong absorber in the optical, such as TiO or VO is mainly due to non-grey thermal effects reducing the ability of the upper atmosphere to cool down rather than an enhanced absorption of the stellar light as previously thought. Finally, we provide a functional form for the coefficients of our analytical model for solar-composition giant exoplanets and brown dwarfs. This leads to fully analytical pressure-temperature profiles for irradiated atmospheres with a relative accuracy better than 10% for gravities between 2.5 m s-2 and 250 m s-2 and effective temperatures between 100 K and 3000 K. This is a great improvement over the commonly used Eddington boundary condition. A FORTRAN implementation of the analytical model is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/574/A35 or at http://www.oca.eu/parmentier/nongrey.Appendix A is available in electronic form at http://www.aanda.org

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.

A spline-based approach for computing spatial impulse responses.

PubMed

Ellis, Michael A; Guenther, Drake; Walker, William F

2007-05-01

Computer simulations are an essential tool for the design of phased-array ultrasonic imaging systems. FIELD II, which determines the two-way temporal response of a transducer at a point in space, is the current de facto standard for ultrasound simulation tools. However, the need often arises to obtain two-way spatial responses at a single point in time, a set of dimensions for which FIELD II is not well optimized. This paper describes an analytical approach for computing the two-way, far-field, spatial impulse response from rectangular transducer elements under arbitrary excitation. The described approach determines the response as the sum of polynomial functions, making computational implementation quite straightforward. The proposed algorithm, named DELFI, was implemented as a C routine under Matlab and results were compared to those obtained under similar conditions from the well-established FIELD II program. Under the specific conditions tested here, the proposed algorithm was approximately 142 times faster than FIELD II for computing spatial sensitivity functions with similar amounts of error. For temporal sensitivity functions with similar amounts of error, the proposed algorithm was about 1.7 times slower than FIELD II using rectangular elements and 19.2 times faster than FIELD II using triangular elements. DELFI is shown to be an attractive complement to FIELD II, especially when spatial responses are needed at a specific point in time.

Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2017-10-01

Over the recent decades, a number of fast approximate solutions of Lippmann-Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

Rapid determination of ions by combined solid-phase extraction--diffuse reflectance spectroscopy

NASA Technical Reports Server (NTRS)

Fritz, James S.; Arena, Matteo P.; Steiner, Steven A.; Porter, Marc D.

2003-01-01

We introduce colorimetric solid-phase extraction (C-SPE) for the rapid determination of selected ions. This new technique links the exhaustive concentration of an analyte by SPE onto a membrane disk surface for quantitative measurement with a hand-held diffuse reflectance spectrometer. The concentration/measurement procedure is complete in approximately 1 min and can be performed almost anywhere. This method has been used to monitor iodine and iodide in spacecraft water in the 0.1-5.0 ppm range and silver(I) in the range of 5.0-1000 microg/l. Applications to the trace analysis of copper(II), nickel(II), iron(III) and chromium(VI) are described. Studies on the mechanism of extraction showed that impregnation of the disk with a surfactant as well as a complexing reagent results in uptake of additional water, which markedly improves the extraction efficiency.

Understanding cooperative behavior in structurally disordered populations

NASA Astrophysics Data System (ADS)

Xu, C.; Zhang, W.; Du, P.; Choi, C. W.; Hui, P. M.

2016-06-01

The effects of an inhomogeneous competing environment on the extent of cooperation are studied within the context of a site-diluted evolutionary snowdrift game on a square lattice, with the occupied sites representing the players, both numerically and analytically. The frequency of cooperation ℱ C generally shows a non-monotonic dependence on the fraction of occupied sites ρ, for different values of the payoff parameter r. Slightly diluting a lattice leads to a lower cooperation for small and high values of r. For a range of r, however, dilution leads to an enhanced cooperation. An analytic treatment is developed for ℱC I + ℱC II, with ℱC I emphasizing the importance of the small clusters of players especially for ℱC II from the other players is shown to be inadequate. A local configuration approximation (LCA) that treats the local competing configurations as the variables and amounts to include spatial correlation up to the neighborhood of a player's neighbors is developed. Results of ℱ C ( ρ) and the number of different local configurations from LCA are in good agreement with simulation results. A transparent physical picture of the dynamics stemming from LCA is also presented. The theoretical approach provides a framework that can be readily applied to competing agent-based models in structurally ordered and disordered populations.

Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

NASA Astrophysics Data System (ADS)

Bervillier, C.; Boisseau, B.; Giacomini, H.

2008-02-01

The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).

Derivation of a closed form analytical expression for fluorescence recovery after photo bleaching in the case of continuous bleaching during read out

NASA Astrophysics Data System (ADS)

Endress, E.; Weigelt, S.; Reents, G.; Bayerl, T. M.

2005-01-01

Measurements of very slow diffusive processes in membranes, like the diffusion of integral membrane proteins, by fluorescence recovery after photo bleaching (FRAP) are hampered by bleaching of the probe during the read out of the fluorescence recovery. In the limit of long observation time (very slow diffusion as in the case of large membrane proteins), this bleaching may cause errors to the recovery function and thus provides error-prone diffusion coefficients. In this work we present a new approach to a two-dimensional closed form analytical solution of the reaction-diffusion equation, based on the addition of a dissipative term to the conventional diffusion equation. The calculation was done assuming (i) a Gaussian laser beam profile for bleaching the spot and (ii) that the fluorescence intensity profile emerging from the spot can be approximated by a two-dimensional Gaussian. The detection scheme derived from the analytical solution allows for diffusion measurements without the constraint of observation bleaching. Recovery curves of experimental FRAP data obtained under non-negligible read-out bleaching for native membranes (rabbit endoplasmic reticulum) on a planar solid support showed excellent agreement with the analytical solution and allowed the calculation of the lipid diffusion coefficient.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

An approximate analytical solution for interlaminar stresses in angle-ply laminates

NASA Technical Reports Server (NTRS)

Rose, Cheryl A.; Herakovich, Carl T.

1991-01-01

An improved approximate analytical solution for interlaminar stresses in finite width, symmetric, angle-ply laminated coupons subjected to axial loading is presented. The solution is based upon statically admissible stress fields which take into consideration local property mismatch effects and global equilibrium requirements. Unknown constants in the admissible stress states are determined through minimization of the complementary energy. Typical results are presented for through-the-thickness and interlaminar stress distributions for angle-ply laminates. It is shown that the results represent an improved approximate analytical solution for interlaminar stresses.

Analytical approximate solutions for a general class of nonlinear delay differential equations.

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

Analytical approximations to seawater optical phase functions of scattering

NASA Astrophysics Data System (ADS)

Haltrin, Vladimir I.

2004-11-01

This paper proposes a number of analytical approximations to the classic and recently measured seawater light scattering phase functions. The three types of analytical phase functions are derived: individual representations for 15 Petzold, 41 Mankovsky, and 91 Gulf of Mexico phase functions; collective fits to Petzold phase functions; and analytical representations that take into account dependencies between inherent optical properties of seawater. The proposed phase functions may be used for problems of radiative transfer, remote sensing, visibility and image propagation in natural waters of various turbidity.

Coupling photochemical reaction detection based on singlet oxygen sensitization to capillary electrochromatography

PubMed

Dickson; Odom; Ducheneaux; Murray; Milofsky

2000-07-15

Despite the impressive separation efficiency afforded by capillary electrochromatography (CEC), the detection of UV-absorbing compounds following separation in capillary dimensions remains limited by the short path length (5-75 microm) through the column. Moreover, analytes that are poor chromophores present an additional challenge with respect to sensitive detection in CEC. This paper illustrates a new photochemical reaction detection scheme for CEC that takes advantage of the catalytic nature of type II photooxidation reactions. The sensitive detection scheme is selective toward molecules capable of photosensitizing the formation of singlet molecular oxygen (1O2). Following separation by CEC, UV-absorbing analytes promote groundstate 3O2 to an excited state (1O2) which reacts rapidly with tert-butyl-3,4,5-trimethylpyrrolecarboxylate, which is added to the running buffer. Detection is based on the loss of pyrrole. The reaction is catalytic in nature since one analyte molecule may absorb light many times, producing large amounts of 1O2. The detection limit for 9-acetylanthracene, following separation by CEC, is approximately 6 x 10(-9) M (S/N = 3). Optimization of the factors effecting the S/N for four model compounds is discussed.

Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models

NASA Astrophysics Data System (ADS)

Luther, K.; Haitjema, H. M.

2000-04-01

We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.

A comparison of finite element and analytic models of acoustic scattering from rough poroelastic interfaces.

PubMed

Bonomo, Anthony L; Isakson, Marcia J; Chotiros, Nicholas P

2015-04-01

The finite element method is used to model acoustic scattering from rough poroelastic surfaces. Both monostatic and bistatic scattering strengths are calculated and compared with three analytic models: Perturbation theory, the Kirchhoff approximation, and the small-slope approximation. It is found that the small-slope approximation is in very close agreement with the finite element results for all cases studied and that perturbation theory and the Kirchhoff approximation can be considered valid in those instances where their predictions match those given by the small-slope approximation.

Problem-based learning on quantitative analytical chemistry course

NASA Astrophysics Data System (ADS)

Fitri, Noor

2017-12-01

This research applies problem-based learning method on chemical quantitative analytical chemistry, so called as "Analytical Chemistry II" course, especially related to essential oil analysis. The learning outcomes of this course include aspects of understanding of lectures, the skills of applying course materials, and the ability to identify, formulate and solve chemical analysis problems. The role of study groups is quite important in improving students' learning ability and in completing independent tasks and group tasks. Thus, students are not only aware of the basic concepts of Analytical Chemistry II, but also able to understand and apply analytical concepts that have been studied to solve given analytical chemistry problems, and have the attitude and ability to work together to solve the problems. Based on the learning outcome, it can be concluded that the problem-based learning method in Analytical Chemistry II course has been proven to improve students' knowledge, skill, ability and attitude. Students are not only skilled at solving problems in analytical chemistry especially in essential oil analysis in accordance with local genius of Chemistry Department, Universitas Islam Indonesia, but also have skilled work with computer program and able to understand material and problem in English.

Analytical response function for planar Ge detectors

NASA Astrophysics Data System (ADS)

García-Alvarez, Juan A.; Maidana, Nora L.; Vanin, Vito R.; Fernández-Varea, José M.

2016-04-01

We model the response function (RF) of planar HPGe x-ray spectrometers for photon energies between around 10 keV and 100 keV. The RF is based on the proposal of Seltzer [1981. Nucl. Instrum. Methods 188, 133-151] and takes into account the full-energy absorption in the Ge active volume, the escape of Ge Kα and Kβ x-rays and the escape of photons after one Compton interaction. The relativistic impulse approximation is employed instead of the Klein-Nishina formula to describe incoherent photon scattering in the Ge crystal. We also incorporate a simple model for the continuous component of the spectrum produced by the escape of photo-electrons from the active volume. In our calculations we include external interaction contributions to the RF: (i) the incoherent scattering effects caused by the detector's Be window and (ii) the spectrum produced by photo-electrons emitted in the Ge dead layer that reach the active volume. The analytical RF model is compared with pulse-height spectra simulated using the PENELOPE Monte Carlo code.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

General properties and analytical approximations of photorefractive solitons

NASA Astrophysics Data System (ADS)

Geisler, A.; Homann, F.; Schmidt, H.-J.

2004-08-01

We investigate general properties of spatial 1-dimensional bright photorefractive solitons and discuss various analytical approximations for the soliton profile and the half width, both depending on an intensity parameter r. The case of dark solitons is also briefly addressed.

Emission-line studies of young stars. 4: The optical forbidden lines

NASA Astrophysics Data System (ADS)

Hamann, Fred

1994-08-01

Optical forbidden line strengths and profiles are discussed for a sample of 30 T Tauri stars and 12 Herbig Ae-Be stars. Transitions of (C I), (N II), (O I), (O II), (S II), (Ca II), (Cr II), (Fe II), and (Ni II) are detected. Profile variability occurred in DG Tau and probably other sources. The ensemble profiles can be divided into four generic components that may represent distinct emitting regions; (1) narrow rest-velocity lines, (2) 'low'-velocity lines (peaking at less than or approximately +/- 50 km s-1), (3) 'high'-velocity (usually greater than or approximately +/- 100 km s-1) blueshifted peaks or wings, and (4) high-velocity redshifted peaks. Among T Tauri stars, the rest-velocity lines appear most often in sources with weak and narrow permitted lines, such as the Ca II triplet. The low- and high-velocity blueshifted components usually appear together in sources with strong and broad Ca II triplet lines. If the velocity-shifted lines form in jets, the smallest (full) opening angles required by the profiles are less than or approximately 20 deg for the narrow, blueshifted (Ca II) lines of DG Tau and HL Tau. Other lines in DG Tau are much broader, implying larger opening angles or greater velocity dispersions. The variability in DG Tau also implies significant changes in the collimation or velocity coherence on timescales of a few years. RW Aur and AS 353A have blue- and redshifted line peaks that could form in oppositely directed jets. The strong (S II) lambda 6716 and lambda 6731 lines in RW Aur are exclusively redshifted and require opening angles less than or approximately 60 deg. Measurements of different profiles in the same spectrum show that the physical conditions change with the line-of-sight velocities. The most persistent trends are for more (N II) and (O II) and less (O I) lambda 5577 flux at high velocities. Constraints on the physical conditions are derived by modeling the emission lines via multilevel ions in 'coronal ionization equilibrium.' A single temperature and density cannot fully describe the line spectra in any velocity interval. Temperatures in the (O I) region are 9000 less than or approximately Te less than 14,000 K, and the ionization fraction (of H) is less than 35%. The densities derived from (O I) include ne less than or approximately 5 x 105 to approximately 107 cm-3, but ne greater than or approximately 106 cm-3 obtains only at low velocities. In the (S II) regions the densities are lower, 103 less than or approximately ne less than or approximately 7 x 104 cm-3, and the temperatures are probably higher, Te greater than or approximately 13,000 K. At high velocities (only) there is additional hot gas that produces (N II) and (O II), possibly most of the (S II), and little (O I). This region is characterized by Te greater than or approximately 15,000 K, ne less than or approximately 105 cm-3, and an ionization fraction greater than or approximately 50%.

Emission-line studies of young stars. 4: The optical forbidden lines

NASA Technical Reports Server (NTRS)

Hamann, Fred

1994-01-01

Optical forbidden line strengths and profiles are discussed for a sample of 30 T Tauri stars and 12 Herbig Ae-Be stars. Transitions of (C I), (N II), (O I), (O II), (S II), (Ca II), (Cr II), (Fe II), and (Ni II) are detected. Profile variability occurred in DG Tau and probably other sources. The ensemble profiles can be divided into four generic components that may represent distinct emitting regions; (1) narrow rest-velocity lines, (2) 'low'-velocity lines (peaking at less than or approximately +/- 50 km s(exp -1)), (3) 'high'-velocity (usually greater than or approximately +/- 100 km s(exp -1)) blueshifted peaks or wings, and (4) high-velocity redshifted peaks. Among T Tauri stars, the rest-velocity lines appear most often in sources with weak and narrow permitted lines, such as the Ca II triplet. The low- and high-velocity blueshifted components usually appear together in sources with strong and broad Ca II triplet lines. If the velocity-shifted lines form in jets, the smallest (full) opening angles required by the profiles are less than or approximately 20 deg for the narrow, blueshifted (Ca II) lines of DG Tau and HL Tau. Other lines in DG Tau are much broader, implying larger opening angles or greater velocity dispersions. The variability in DG Tau also implies significant changes in the collimation or velocity coherence on timescales of a few years. RW Aur and AS 353A have blue- and redshifted line peaks that could form in oppositely directed jets. The strong (S II) lambda 6716 and lambda 6731 lines in RW Aur are exclusively redshifted and require opening angles less than or approximately 60 deg. Measurements of different profiles in the same spectrum show that the physical conditions change with the line-of-sight velocities. The most persistent trends are for more (N II) and (O II) and less (O I) lambda 5577 flux at high velocities. Constraints on the physical conditions are derived by modeling the emission lines via multilevel ions in 'coronal ionization equilibrium.' A single temperature and density cannot fully describe the line spectra in any velocity interval. Temperatures in the (O I) region are 9000 less than or approximately T(sub e) less than 14,000 K, and the ionization fraction (of H) is less than 35%. The densities derived from (O I) include n(sub e) less than or approximately 5 x 10(exp 5) to approximately 10(exp 7) cm(exp -3), but n(sub e) greater than or approximately 10(exp 6) cm(exp -3) obtains only at low velocities. In the (S II) regions the densities are lower, 10(exp 3) less than or approximately n(sub e) less than or approximately 7 x 10(exp 4) cm(exp -3), and the temperatures are probably higher, T(sub e) greater than or approximately 13,000 K. At high velocities (only) there is additional hot gas that produces (N II) and (O II), possibly most of the (S II), and little (O I). This region is characterized by T(sub e) greater than or approximately 15,000 K, n(sub e) less than or approximately 10(exp 5) cm(exp -3), and an ionization fraction greater than or approximately 50%. When combined with the spatially segregated emitting regions observed by others by spectral imaging, these results suggest decreasing n(sub e) and increasing T(sub e) away from the star in at least the high velocity gas.

Partially Coherent Scattering in Stellar Chromospheres. Part 4; Analytic Wing Approximations

NASA Technical Reports Server (NTRS)

Gayley, K. G.

1993-01-01

Simple analytic expressions are derived to understand resonance-line wings in stellar chromospheres and similar astrophysical plasmas. The results are approximate, but compare well with accurate numerical simulations. The redistribution is modeled using an extension of the partially coherent scattering approximation (PCS) which we term the comoving-frame partially coherent scattering approximation (CPCS). The distinction is made here because Doppler diffusion is included in the coherent/noncoherent decomposition, in a form slightly improved from the earlier papers in this series.

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…

Eikonal Scattering in the sdg Interacting Boson Model:. Analytical Results in the SUsdg(3) Limit and Their Generalizations

NASA Astrophysics Data System (ADS)

Kota, V. K. B.

General expression for the representation matrix elements in the SUsdg(3) limit of the sdg interacting boson model (sdgIBM) is derived that determine the scattering amplitude in the eikonal approximation for medium energy proton-nucleus scattering when the target nucleus is deformed and it is described by the SUsdg(3) limit. The SUsdg(3) result is generalized to two important situations: (i) when the target nucleus ground band states are described as states arising out of angular momentum projection from a general single Kπ = 0+ intrinsic state in sdg space; (ii) for rotational bands built on one-phonon excitations in sdgIBM.

Conservative Analytical Collision Probabilities for Orbital Formation Flying

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

Conservative Analytical Collision Probability for Design of Orbital Formations

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

Problems and solutions of polyethylene glycol co-injection method in multiresidue pesticide analysis by gas chromatography-mass spectrometry: evaluation of instability phenomenon in type II pyrethroids and its suppression by novel analyte protectants.

PubMed

Akutsu, Kazuhiko; Kitagawa, Yoko; Yoshimitsu, Masato; Takatori, Satoshi; Fukui, Naoki; Osakada, Masakazu; Uchida, Kotaro; Azuma, Emiko; Kajimura, Keiji

2018-05-01

Polyethylene glycol 300 is commonly used as a base material for "analyte protection" in multiresidue pesticide analysis via gas chromatography-mass spectrometry. However, the disadvantage of the co-injection method using polyethylene glycol 300 is that it causes peak instability in α-cyano pyrethroids (type II pyrethroids) such as fluvalinate. In this study, we confirmed the instability phenomenon in type II pyrethroids and developed novel analyte protectants for acetone/n-hexane mixture solution to suppress the phenomenon. Our findings revealed that among the examined additive compounds, three lipophilic ascorbic acid derivatives, 3-O-ethyl-L-ascorbic acid, 6-O-palmitoyl-L-ascorbic acid, and 6-O-stearoyl-L-ascorbic acid, could effectively stabilize the type II pyrethroids in the presence of polyethylene glycol 300. A mixture of the three ascorbic acid derivatives and polyethylene glycol 300 proved to be an effective analyte protectant for multiresidue pesticide analysis. Further, we designed and evaluated a new combination of analyte protectant compounds without using polyethylene glycol or the troublesome hydrophilic compounds. Consequently, we obtained a set of 10 medium- and long-chain saturated fatty acids as an effective analyte protectant suitable for acetone/n-hexane solution that did not cause peak instability in type II pyrethroids. These analyte protectants will be useful in multiresidue pesticide analysis by gas chromatography-mass spectrometry in terms of ruggedness and reliable quantitativeness. Graphical abstract Comparison of effectiveness of the addition of lipophilic derivatives of ascorbic acid in controlling the instability phenomenon of fluvalinate with polyethylene glycol 300.

Effects of biases in domain wall network evolution. II. Quantitative analysis

NASA Astrophysics Data System (ADS)

Correia, J. R. C. C. C.; Leite, I. S. C. R.; Martins, C. J. A. P.

2018-04-01

Domain walls form at phase transitions which break discrete symmetries. In a cosmological context, they often overclose the Universe (contrary to observational evidence), although one may prevent this by introducing biases or forcing anisotropic evolution of the walls. In a previous work [Correia et al., Phys. Rev. D 90, 023521 (2014), 10.1103/PhysRevD.90.023521], we numerically studied the evolution of various types of biased domain wall networks in the early Universe, confirming that anisotropic networks ultimately reach scaling while those with a biased potential or biased initial conditions decay. We also found that the analytic decay law obtained by Hindmarsh was in good agreement with simulations of biased potentials, but not of biased initial conditions, and suggested that the difference was related to the Gaussian approximation underlying the analytic law. Here, we extend our previous work in several ways. For the cases of biased potential and biased initial conditions, we study in detail the field distributions in the simulations, confirming that the validity (or not) of the Gaussian approximation is the key difference between the two cases. For anisotropic walls, we carry out a more extensive set of numerical simulations and compare them to the canonical velocity-dependent one-scale model for domain walls, finding that the model accurately predicts the linear scaling regime after isotropization. Overall, our analysis provides a quantitative description of the cosmological evolution of these networks.

The case for visual analytics of arsenic concentrations in foods.

PubMed

Johnson, Matilda O; Cohly, Hari H P; Isokpehi, Raphael D; Awofolu, Omotayo R

2010-05-01

Arsenic is a naturally occurring toxic metal and its presence in food could be a potential risk to the health of both humans and animals. Prolonged ingestion of arsenic contaminated water may result in manifestations of toxicity in all systems of the body. Visual Analytics is a multidisciplinary field that is defined as the science of analytical reasoning facilitated by interactive visual interfaces. The concentrations of arsenic vary in foods making it impractical and impossible to provide regulatory limit for each food. This review article presents a case for the use of visual analytics approaches to provide comparative assessment of arsenic in various foods. The topics covered include (i) metabolism of arsenic in the human body; (ii) arsenic concentrations in various foods; (ii) factors affecting arsenic uptake in plants; (ii) introduction to visual analytics; and (iv) benefits of visual analytics for comparative assessment of arsenic concentration in foods. Visual analytics can provide an information superstructure of arsenic in various foods to permit insightful comparative risk assessment of the diverse and continually expanding data on arsenic in food groups in the context of country of study or origin, year of study, method of analysis and arsenic species.

The Case for Visual Analytics of Arsenic Concentrations in Foods

PubMed Central

Johnson, Matilda O.; Cohly, Hari H.P.; Isokpehi, Raphael D.; Awofolu, Omotayo R.

2010-01-01

Arsenic is a naturally occurring toxic metal and its presence in food could be a potential risk to the health of both humans and animals. Prolonged ingestion of arsenic contaminated water may result in manifestations of toxicity in all systems of the body. Visual Analytics is a multidisciplinary field that is defined as the science of analytical reasoning facilitated by interactive visual interfaces. The concentrations of arsenic vary in foods making it impractical and impossible to provide regulatory limit for each food. This review article presents a case for the use of visual analytics approaches to provide comparative assessment of arsenic in various foods. The topics covered include (i) metabolism of arsenic in the human body; (ii) arsenic concentrations in various foods; (ii) factors affecting arsenic uptake in plants; (ii) introduction to visual analytics; and (iv) benefits of visual analytics for comparative assessment of arsenic concentration in foods. Visual analytics can provide an information superstructure of arsenic in various foods to permit insightful comparative risk assessment of the diverse and continually expanding data on arsenic in food groups in the context of country of study or origin, year of study, method of analysis and arsenic species. PMID:20623005

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

Wu, Baisheng; Liu, Weijia; Lim, C. W.

2017-07-01

A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere

NASA Technical Reports Server (NTRS)

Weinman, J. A.; Twitty, J. T.; Browning, S. R.; Herman, B. M.

1975-01-01

The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few per cent. The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

Substrate mass transfer: analytical approach for immobilized enzyme reactions

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Saibavani, T. N.

2018-04-01

In this paper, the boundary value problem in immobilized enzyme reactions is formulated and approximate expression for substrate concentration without external mass transfer resistance is presented. He’s variational iteration method is used to give approximate and analytical solutions of non-linear differential equation containing a non linear term related to enzymatic reaction. The relevant analytical solution for the dimensionless substrate concentration profile is discussed in terms of dimensionless reaction parameters α and β.

The application of symmetry and centricity to polychordal wedge harmony in "Motherchord"

NASA Astrophysics Data System (ADS)

Cathey, Tully J.

This dissertation is in two volumes. Volume I is an analytical paper in two parts. Part I presents a polychordal harmonic system called the "The Desire Matrix Harmonic System," that was used to compose a work for large orchestra called "Motherchord" (Volume II). The polychords are comprised of two triadic units and of major triads only, built on two pairs of intersecting chromatic scales. The system embraces pitch-centric characteristics as well as symmetry. Scales, or tone sets, are derived from the polychords and used for melodic and contrapuntal purposes. Compositional procedures are developed, and a matrix of polychordal wedges is assembled that serves as a further compositional device. Part II of the paper is an analysis of the formal structure of "Motherchord." "Motherchord" is a one-movement composition of approximately seventeen minutes and forty seconds duration. It is divided into seven parts, but proceeds from beginning to end without a break in sound. The title of the work derives from the central tonic polychord.

Cosmological perturbation theory and the spherical collapse model - II. Non-Gaussian initial conditions

NASA Astrophysics Data System (ADS)

Gaztanaga, Enrique; Fosalba, Pablo

1998-12-01

In Paper I of this series, we introduced the spherical collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants xi_J of density fluctuations in cosmological perturbation theory (PT). Within this approximation, the dynamics is decoupled from the statistics of the initial conditions, so we are able to present here the cumulants for generic non-Gaussian initial conditions, which can be estimated to arbitrary order including the smoothing effects. The SC model turns out to recover the exact leading-order non-linear contributions up to terms involving non-local integrals of the J-point functions. We argue that for the hierarchical ratios S_J, these non-local terms are subdominant and tend to compensate each other. The resulting predictions show a non-trivial time evolution that can be used to discriminate between models of structure formation. We compare these analytic results with non-Gaussian N-body simulations, which turn out to be in very good agreement up to scales where sigma<~1.

Density functional perturbational orbital theory of spin polarization in electronic systems. II. Transition metal dimer complexes.

PubMed

Seo, Dong-Kyun

2007-11-14

We present a theoretical scheme for a semiquantitative analysis of electronic structures of magnetic transition metal dimer complexes within spin density functional theory (DFT). Based on the spin polarization perturbational orbital theory [D.-K. Seo, J. Chem. Phys. 125, 154105 (2006)], explicit spin-dependent expressions of the spin orbital energies and coefficients are derived, which allows to understand how spin orbitals form and change their energies and shapes when two magnetic sites are coupled either ferromagnetically or antiferromagnetically. Upon employment of the concept of magnetic orbitals in the active-electron approximation, a general mathematical formula is obtained for the magnetic coupling constant J from the analytical expression for the electronic energy difference between low-spin broken-symmetry and high-spin states. The origin of the potential exchange and kinetic exchange terms based on the one-electron picture is also elucidated. In addition, we provide a general account of the DFT analysis of the magnetic exchange interactions in compounds for which the active-electron approximation is not appropriate.

APPROXIMATE AND ANALYTICAL SOLUTIONS FOR SOLUTE TRANSPORT FROM AN INJECTION WELL INTO A SINGLE FRACTURE

EPA Science Inventory

In dealing with problems related to land-based nuclear waste management, a number of analytical and approximate solutions were developed to quantify radionuclide transport through fractures contained in the porous formation. t has been reported that by treating the radioactive de...

Analytical treatment of self-phase-modulation beyond the slowly varying envelope approximation

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

Syrchin, M.S.; Zheltikov, A.M.; International Laser Center, M.V. Lomonosov Moscow State University, 119899 Moscow

Analytical treatment of the self-phase-modulation of an ultrashort light pulse is extended beyond the slowly varying envelope approximation. The resulting wave equation is modified to include corrections to self-phase-modulation due to higher-order spatial and temporal derivatives. Analytical solutions are found in the limiting regimes of high nonlinearities and very short pulses. Our results reveal features that can significantly impact both pulse shape and the evolution of the phase.

Comparison between numeric and approximate analytic solutions for the prediction of soil metal uptake by roots. Example of cadmium.

PubMed

Schneider, André; Lin, Zhongbing; Sterckeman, Thibault; Nguyen, Christophe

2018-04-01

The dissociation of metal complexes in the soil solution can increase the availability of metals for root uptake. When it is accounted for in models of bioavailability of soil metals, the number of partial differential equations (PDEs) increases and the computation time to numerically solve these equations may be problematic when a large number of simulations are required, for example for sensitivity analyses or when considering root architecture. This work presents analytical solutions for the set of PDEs describing the bioavailability of soil metals including the kinetics of complexation for three scenarios where the metal complex in solution was fully inert, fully labile, or partially labile. The analytical solutions are only valid i) at steady-state when the PDEs become ordinary differential equations, the transient phase being not covered, ii) when diffusion is the major mechanism of transport and therefore, when convection is negligible, iii) when there is no between-root competition. The formulation of the analytical solutions is for cylindrical geometry but the solutions rely on the spread of the depletion profile around the root, which was modelled assuming a planar geometry. The analytical solutions were evaluated by comparison with the corresponding PDEs for cadmium in the case of the French agricultural soils. Provided that convection was much lower than diffusion (Péclet's number<0.02), the cumulative uptakes calculated from the analytic solutions were in very good agreement with those calculated from the PDEs, even in the case of a partially labile complex. The analytic solutions can be used instead of the PDEs to predict root uptake of metals. The analytic solutions were also used to build an indicator of the contribution of a complex to the uptake of the metal by roots, which can be helpful to predict the effect of soluble organic matter on the bioavailability of soil metals. Copyright © 2017 Elsevier B.V. All rights reserved.

Approximate analytic expression for the Skyrmions crystal

NASA Astrophysics Data System (ADS)

Grandi, Nicolás; Sturla, Mauricio

2018-01-01

We find approximate solutions for the two-dimensional nonlinear Σ-model with Dzyalioshinkii-Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.

Comparison of three methods for wind turbine capacity factor estimation.

PubMed

Ditkovich, Y; Kuperman, A

2014-01-01

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first "quasiexact" approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second "analytic" approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third "approximate" approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation.

Electroanalytical method for determination of lead(II) in orange and apple using kaolin modified platinum electrode.

PubMed

El Mhammedi, M A; Achak, M; Bakasse, M; Chtaini, A

2009-08-01

This paper reports on the use of platinum electrode modified with kaolin (K/Pt) and square wave voltammetry for analytical detection of trace lead(II) in pure water, orange and apple samples. The electroanalytical procedure for determination of the Pb(II) comprises two steps: the chemical accumulation of the analyte under open-circuit conditions followed by the electrochemical detection of the preconcentrated species using square wave voltammetry. The analytical performances of the extraction method has been explored by studying the incubating time, and effect of interferences due to other ions. During the preconcentration step, Pb(II) was accumulated on the surface of the kaolin. The observed detection and quantification limits in pure water were 3.6x10(-9)molL(-1) and 1.2x10(-8)molL(-1), respectively. The precision of the method was also determined; the results was 2.35% (n=5).

Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights

PubMed Central

Nicola, Wilten; Tripp, Bryan; Scott, Matthew

2016-01-01

A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks. PMID:26973503

Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights.

PubMed

Nicola, Wilten; Tripp, Bryan; Scott, Matthew

2016-01-01

A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks.

Circuit transients due to negative bias arcs-II. [on solar cell power systems in low earth orbit

NASA Technical Reports Server (NTRS)

Metz, R. N.

1986-01-01

Two new models of negative-bias arcing on a solar cell power system in Low Earth Orbit are presented. One is an extended, analytical model and the other is a non-linear, numerical model. The models are based on an earlier analytical model in which the interactions between solar cell interconnects and the space plasma as well as the parameters of the power circuit are approximated linearly. Transient voltages due to arcs struck at the negative thermal of the solar panel are calculated in the time domain. The new models treat, respectively, further linear effects within the solar panel load circuit and non-linear effects associated with the plasma interactions. Results of computer calculations with the models show common-mode voltage transients of the electrically floating solar panel struck by an arc comparable to the early model but load transients that differ substantially from the early model. In particular, load transients of the non-linear model can be more than twice as great as those of the early model and more than twenty times as great as the extended, linear model.

Electron Beam Analysis of Micrometeoroids Captured in Aerogel as Stardust Analogues

NASA Technical Reports Server (NTRS)

Graham, G. A.; Sheffield-Parker, J.; Bradley, P.; Kearsley, A. T.; Dai, Z. R.; Mayo, S. C.; Teslich, N.; Snead, C.; Westphal, A. J.; Ishii, H.

2005-01-01

In January 2004, NASA s Stardust spacecraft passed through the tail of Comet 81P/Wild-2. The on-board dust flux monitor instrument indicated that numerous micro- and nano-meter sized cometary dust particles were captured by the dedicated silica aerogel capture cell. The collected cometary particles will be returned to Earth in January 2006. Current Stardust analogues are: (i) Light-gas-gun accelerated individual mineral grains and carbonaceous meteoritic material in aerogels at the Stardust encounter velocity ca.approximately 6 kilometers per second. (ii) Aerogels exposed in low-Earth orbit (LEO) containing preserved cosmic dust grains. Studies of these impacts offer insight into the potential state of the captured cometary dust by Stardust and the suitability of various analytical techniques. A number of papers have discussed the application of sophisticated synchrotron analytical techniques to analyze Stardust particles. Yet much of the understanding gained on the composition and mineralogy of interplanetary dust particles (IDPs) has come from electron microscopy studies. Here we discuss the application of scanning electron microscopy (SEM) for Stardust during the preliminary phase of post-return investigations.

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.

Precise analytic approximations for the Bessel function J1 (x)

NASA Astrophysics Data System (ADS)

Maass, Fernando; Martin, Pablo

2018-03-01

Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.

Copper(II)-rubeanic acid coprecipitation system for separation-preconcentration of trace metal ions in environmental samples for their flame atomic absorption spectrometric determinations.

PubMed

Soylak, Mustafa; Erdogan, Nilgun D

2006-09-21

A simple and facile preconcentration procedure based on the coprecipitation of trace heavy metal ions with copper(II)-rubeanic acid complex has been developed. The analytical parameters including pH, amounts of rubeanic acid, sample volume, etc. was investigated for the quantitative recoveries of Pb(II), Fe(III), Cd(II), Au(III), Pd(II) and Ni(II). No interferic effects were observed from the concomitant ions. The detection limits for analyte ions by 3 sigma were in the range of 0.14 microg/l for iron-3.4 microg/l for lead. The proposed coprecipitation method was successfully applied to water samples from Palas Lake-Kayseri, soil and sediment samples from Kayseri and Yozgat-Turkey.

Correction of Quenching Errors in Analytical Fluorimetry through Use of Time Resolution.

DTIC Science & Technology

1980-05-27

QUENCHING ERRORS IN ANALYTICAL FLUORIMETRY THROUGH USE OF TIME RESOLUTION by Gary M. Hieftje and Gilbert R. Haugen Prepared for Publication in... HIEFTJE , 6 R HAUGEN NOCOIT1-6-0638 UCLASSIFIED TR-25 NL ///I//II IIIII I__I. 111122 Z .. ..12 1.~l8 .2 -4 SECuRITY CLSIIAI1 orTI PAGE MWhno. ee...in Analytical and Clinical Chemistry, vol. 3, D. M. Hercules, G. M. Hieftje , L. R. Snyder, and M4. A. Evenson, eds., Plenum Press, N.Y., 1978, ch. S

Medical Devices; Immunology and Microbiology Devices; Classification of the Device To Detect and Measure Non-Microbial Analyte(s) in Human Clinical Specimens To Aid in Assessment of Patients With Suspected Sepsis. Final order.

PubMed

2017-10-24

The Food and Drug Administration (FDA or we) is classifying the device to detect and measure non-microbial analyte(s) in human clinical specimens to aid in assessment of patients with suspected sepsis into class II (special controls). The special controls that apply to the device type are identified in this order and will be part of the codified language for the device to detect and measure non-microbial analyte(s) in human clinical specimens to aid in assessment of patients with suspected sepsis's classification. We are taking this action because we have determined that classifying the device into class II (special controls) will provide a reasonable assurance of safety and effectiveness of the device. We believe this action will also enhance patients' access to beneficial innovative devices, in part by reducing regulatory burdens.

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.

Numerical modeling and analytical evaluation of light absorption by gold nanostars

NASA Astrophysics Data System (ADS)

Zarkov, Sergey; Akchurin, Georgy; Yakunin, Alexander; Avetisyan, Yuri; Akchurin, Garif; Tuchin, Valery

2018-04-01

In this paper, the regularity of local light absorption by gold nanostars (AuNSts) model is studied by method of numerical simulation. The mutual diffraction influence of individual geometric fragments of AuNSts is analyzed. A comparison is made with an approximate analytical approach for estimating the average bulk density of absorbed power and total absorbed power by individual geometric fragments of AuNSts. It is shown that the results of the approximate analytical estimate are in qualitative agreement with the numerical calculations of the light absorption by AuNSts.

Photoionization of the diffuse interstellar medium and galactic halo by OB associtations

NASA Technical Reports Server (NTRS)

Dove, James B.; Shull, J. Michael

1994-01-01

Assuming smoothly varying H I distributions in te Galactic disk, we have calculated the geometry of diffuse II regions due to OB associations in the Galactic plane. Near the solar circle, OB associations with a Lyman continuum (Lyc) photon luminosity Psi(sub Lyc) = 3.3 x 10(exp 7) cm(exp -2) s(exp -1), produce H II regions that are density bounded in the vertical direction (H II chimneys) allowing Lyc to escape the gaseous disk and penetrate into the Galactic halo. We provide analytic formulae for the Lyc escape fraction as functions of S(sub 0) O-star catalog of Garmany and a new Lyc stellar stellar Lyc stellar flux calibration, we find a production rate of Lyc photons by OB associations within 2.5 kpc of Psi(sub Lyc) = 3.3 x 10(exp 7) cm(exp -2) s(exp -1). Integrating the fraction of Lyc photons that escape the disk over our adopted luminosity function of OB associations, we estimate that approximately 7% of the ionizing photons, or Phi(sub Lyc) = 2.3 x 10(exp 6) cm(exp -2) s(exp -1), escape each side of the H I disk layer and penetrate the diffuse ionized medium ('Reynolds layer'). This flux is sufficient to explain the potoionization of this, although we have not constructed a model for the observed H-alpha emission and pulsar dispersion measures that is fully consistent with the absorption rate of Lyc in the H II layer. Since our quiescent model does not account for the effects of dynamic chimneys and superbubbles, which should enhance Lyc escape, we conclude the O stars are the probable source of ionizing radiation for the Reynolds layer. For a random distribution of OB associations throughout the disk, the Lyc flux is nearly uniform for heights Z is greater than approximately 0.8 kpc above the midplane.

Synthesis, characterization and application of a new chelating resin for solid phase extraction, preconcentration and determination of trace metals in some dairy samples by flame atomic absorption spectrometry.

PubMed

Daşbaşı, Teslima; Saçmacı, Şerife; Çankaya, Nevin; Soykan, Cengiz

2016-11-15

In this study, a simple and rapid solid phase extraction/preconcentration procedure was developed for determination of Cd(II), Co(II), Cr(III), Cu(II), Fe(III), Mn(II), Pb(II), and Zn(II) trace metals by flame atomic absorption spectrometry (FAAS). A new chelating resin, poly(N-cyclohexylacrylamide-co-divinylbenzene-co-2-acrylamido-2-methyl-1-propanesulfonic acid) (NCA-co-DVB-co-AMPS) (hereafter CDAP) was synthesized and characterized. The influences of the analytical parameters such as pH of the sample solution, type and concentration of eluent, flow rates of the sample and eluent, volume of the sample and eluent, amount of chelating resin, and interference of ions were examined. The limit of detection (LOD) of analytes were found (3s) to be in the range of 0.65-1.90μgL(-1). Preconcentration factor (PF) of 200 and the relative standard deviation (RSD) of ⩽2% were achieved (n=11). The developed method was applied for determination of analytes in some dairy samples and certified reference materials. Copyright © 2016 Elsevier Ltd. All rights reserved.

Analytic approximations to the modon dispersion relation. [in oceanography

NASA Technical Reports Server (NTRS)

Boyd, J. P.

1981-01-01

Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

Analytical solutions of the Klein-Gordon equation for Manning-Rosen potential with centrifugal term through Nikiforov-Uvarov method

NASA Astrophysics Data System (ADS)

Hatami, N.; Setare, M. R.

2017-10-01

We present approximate analytical solutions of the Klein-Gordon equation with arbitrary l state for the Manning-Rosen potential using the Nikiforov-Uvarov method and adopting the approximation scheme for the centrifugal term. We provide the bound state energy spectrum and the wave function in terms of the hypergeometric functions.

Nonlinear core deflection in injection molding

NASA Astrophysics Data System (ADS)

Poungthong, P.; Giacomin, A. J.; Saengow, C.; Kolitawong, C.; Liao, H.-C.; Tseng, S.-C.

2018-05-01

Injection molding of thin slender parts is often complicated by core deflection. This deflection is caused by molten plastics race tracking through the slit between the core and the rigid cavity wall. The pressure of this liquid exerts a lateral force of the slender core causing the core to bend, and this bending is governed by a nonlinear fifth order ordinary differential equation for the deflection that is not directly in the position along the core. Here we subject this differential equation to 6 sets of boundary conditions, corresponding to 6 commercial core constraints. For each such set of boundary conditions, we develop an explicit approximate analytical solution, including both a linear term and a nonlinear term. By comparison with finite difference solutions, we find our new analytical solutions to be accurate. We then use these solutions to derive explicit analytical approximations for maximum deflections and for the core position of these maximum deflections. Our experiments on the base-gated free-tip boundary condition agree closely with our new explicit approximate analytical solution.

Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Alal Hosen, Md.; Chowdhury, M. S. H.; Yeakub Ali, Mohammad; Faris Ismail, Ahmad

2017-12-01

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

Modeling of phonon scattering in n-type nanowire transistors using one-shot analytic continuation technique

NASA Astrophysics Data System (ADS)

Bescond, Marc; Li, Changsheng; Mera, Hector; Cavassilas, Nicolas; Lannoo, Michel

2013-10-01

We present a one-shot current-conserving approach to model the influence of electron-phonon scattering in nano-transistors using the non-equilibrium Green's function formalism. The approach is based on the lowest order approximation (LOA) to the current and its simplest analytic continuation (LOA+AC). By means of a scaling argument, we show how both LOA and LOA+AC can be easily obtained from the first iteration of the usual self-consistent Born approximation (SCBA) algorithm. Both LOA and LOA+AC are then applied to model n-type silicon nanowire field-effect-transistors and are compared to SCBA current characteristics. In this system, the LOA fails to describe electron-phonon scattering, mainly because of the interactions with acoustic phonons at the band edges. In contrast, the LOA+AC still well approximates the SCBA current characteristics, thus demonstrating the power of analytic continuation techniques. The limits of validity of LOA+AC are also discussed, and more sophisticated and general analytic continuation techniques are suggested for more demanding cases.

Multiplexed analysis combining distinctly-sized CdTe-MPA quantum dots and chemometrics for multiple mutually interfering analyte determination.

PubMed

Bittar, Dayana B; Ribeiro, David S M; Páscoa, Ricardo N M J; Soares, José X; Rodrigues, S Sofia M; Castro, Rafael C; Pezza, Leonardo; Pezza, Helena R; Santos, João L M

2017-11-01

Semiconductor quantum dots (QDs) have demonstrated a great potential as fluorescent probes for heavy metals monitoring. However, their great reactivity, whose tunability could be difficult to attain, could impair selectivity yielding analytical results with poor accuracy. In this work, the combination in the same analysis of multiple QDs, each with a particular ability to interact with the analyte, assured a multi-point detection that was not only exploited for a more precise analyte discrimination but also for the simultaneous discrimination of multiple mutually interfering species, in the same sample. Three different MPA-CdTe QDs (2.5, 3.0 and 3.8nm) with a good size distribution, confirmed by the FWHM values of 48.6, 55.4 and 80.8nm, respectively, were used. Principal component analysis (PCA) and partial least squares regression (PLS) were used for fluorescence data analysis. Mixtures of two MPA-CdTe QDs, emitting at different wavelength namely 549/566, 549/634 and 566/634nm were assayed. The 549/634nm emitting QDs mixture provided the best results for the discrimination of distinct ions on binary and ternary mixtures. The obtained RMSECV and R 2 CV values for the binary mixture were good, namely, from 0.01 to 0.08mgL -1 and from 0.74 to 0.89, respectively. Regarding the ternary mixture the RMSECV and R 2 CV values were good for Hg(II) (0.06 and 0.73mgL -1 , respectively) and Pb(II) (0.08 and 0.87mg L -1 , respectively) and acceptable for Cu(II) (0.02 and 0.51mgL -1 , respectively). In conclusion, the obtained results showed that the developed approach is capable of resolve binary and ternary mixtures of Pb (II), Hg (II) and Cu (II), providing accurate information about lead (II) and mercury (II) concentration and signaling the occurrence of Cu (II). Copyright © 2017 Elsevier B.V. All rights reserved.

1996 PAMS hydrocarbon QA studies in EPA Region II: Part II. Trends and insights

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

Teitz, A.; Kantz, M.

1997-12-31

Comparison of ambient air samples between EPA Region II and the PAMS monitoring organizations within the Region, and comparisons among EPA Regions I, II, and III, revealed the following analytical trends: (1) Agreement between laboratories was typically between 10-20% for many of the PAMS analytes found at higher concentrations, i.e., butane, isopentane, benzene, toluene, and m/p-xylene; (2) Nafion dryer systems tended to underestimate the amount of acetylene by 35-50%; (3) Isobutylene co-elution with 1-butene proved difficult to resolve unless a 100 meter DB-1 or a regular length PLOT GC column was used; (4) Organizations that monitor for polar compounds foundmore » that co-elution of ethanol/acetone can interfere with the analysis of 1-pentene; (5) Analytical systems capable of polar analyses can have co-elution and/or misidentification of these aldehydes, typically in the styrene/heptanal/o-xylene regions of the chromatogram; and (6) Tetrachloroethylene was found to interfere with octane quantitation in some analyses.« less

Nonlinear identification using a B-spline neural network and chaotic immune approaches

NASA Astrophysics Data System (ADS)

dos Santos Coelho, Leandro; Pessôa, Marcelo Wicthoff

2009-11-01

One of the important applications of B-spline neural network (BSNN) is to approximate nonlinear functions defined on a compact subset of a Euclidean space in a highly parallel manner. Recently, BSNN, a type of basis function neural network, has received increasing attention and has been applied in the field of nonlinear identification. BSNNs have the potential to "learn" the process model from input-output data or "learn" fault knowledge from past experience. BSNN can be used as function approximators to construct the analytical model for residual generation too. However, BSNN is trained by gradient-based methods that may fall into local minima during the learning procedure. When using feed-forward BSNNs, the quality of approximation depends on the control points (knots) placement of spline functions. This paper describes the application of a modified artificial immune network inspired optimization method - the opt-aiNet - combined with sequences generate by Hénon map to provide a stochastic search to adjust the control points of a BSNN. The numerical results presented here indicate that artificial immune network optimization methods are useful for building good BSNN model for the nonlinear identification of two case studies: (i) the benchmark of Box and Jenkins gas furnace, and (ii) an experimental ball-and-tube system.

An analytical technique for approximating unsteady aerodynamics in the time domain

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1980-01-01

An analytical technique is presented for approximating unsteady aerodynamic forces in the time domain. The order of elements of a matrix Pade approximation was postulated, and the resulting polynomial coefficients were determined through a combination of least squares estimates for the numerator coefficients and a constrained gradient search for the denominator coefficients which insures stable approximating functions. The number of differential equations required to represent the aerodynamic forces to a given accuracy tends to be smaller than that employed in certain existing techniques where the denominator coefficients are chosen a priori. Results are shown for an aeroelastic, cantilevered, semispan wing which indicate a good fit to the aerodynamic forces for oscillatory motion can be achieved with a matrix Pade approximation having fourth order numerator and second order denominator polynomials.

Analytical approximations to the Hotelling trace for digital x-ray detectors

NASA Astrophysics Data System (ADS)

Clarkson, Eric; Pineda, Angel R.; Barrett, Harrison H.

2001-06-01

The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

SP70-alpha-benzoin oxime chelating resin for preconcentration-separation of Pb(II), Cd(II), Co(II) and Cr(III) in environmental samples.

PubMed

Narin, Ibrahim; Surme, Yavuz; Bercin, Erdogan; Soylak, Mustafa

2007-06-25

In the presented work, alpha-benzoin oxime immobilized SP70 chelating resin was synthesized for separation and preconcentration of Pb(II), Cd(II), Co(II) and Cr(III). The optimization procedure for analytical parameters including pH, eluent type, flow rate, etc. was examined in order to gain quantitative recoveries of analyte ions. The effects of foreign ions on the recoveries of studied metal ions were also investigated. The detection limits (3sigma) were found to be 16.0, 4.2, 1.3, 2.4microgL(-1) for Pb, Cd, Co and Cr, respectively. The preconcentration factor was 75 for Pb, 100 for Cd, Co and Cr. The optimized method was validated with certified reference materials and successfully applied to the waters, crops and pharmaceutical samples with good results (recoveries greater than 95%, R.S.D. lower than 10%).

Flow over Canopies with Complex Morphologies

NASA Astrophysics Data System (ADS)

Rubol, S.; Ling, B.; Battiato, I.

2017-12-01

Quantifying and predicting how submerged vegetation affects the velocity profile of riverine systems is crucial in ecohydraulics to properly assess the water quality and ecological functions or rivers. The state of the art includes a plethora of models to study the flow and transport over submerged canopies. However, most of them are validated against data collected in flume experiments with rigid cylinders. With the objective of investigating the capability of a simple analytical solution for vegetated flow to reproduce and predict the velocity profile of complex shaped flexible canopies, we use the flow model proposed by Battiato and Rubol [WRR 2013] as the analytical approximation of the mean velocity profile above and within the canopy layer. This model has the advantages (i) to threat the canopy layer as a porous medium, whose geometrical properties are associated with macroscopic effective permeability and (ii) to use input parameters that can be estimated by remote sensing techniques, such us the heights of the water level and the canopy. The analytical expressions for the average velocity profile and the discharge are tested against data collected across a wide range of canopy morphologies commonly encountered in riverine systems, such as grasses, woody vegetation and bushes. Results indicate good agreement between the analytical expressions and the data for both simple and complex plant geometry shapes. The rescaled low submergence velocities in the canopy layer followed the same scaling found in arrays of rigid cylinders. In addition, for the dataset analyzed, the Darcy friction factor scaled with the inverse of the bulk Reynolds number multiplied by the ratio of the fluid to turbulent viscosity.

Nonlinear electroelastic deformations of dielectric elastomer composites: II - Non-Gaussian elastic dielectrics

NASA Astrophysics Data System (ADS)

Lefèvre, Victor; Lopez-Pamies, Oscar

2017-02-01

This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi-)conducting/high-permittivity particles to dielectric elastomers does not lead to the extreme electrostriction enhancements observed in experiments. It is posited that such extreme enhancements are the manifestation of interphasial phenomena.

An analytic performance model of disk arrays and its application

NASA Technical Reports Server (NTRS)

Lee, Edward K.; Katz, Randy H.

1991-01-01

As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.

On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1994-01-01

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

MASS SPECTROMETRY FOR RISK MANAGEMENT OF DRINKING WATER TREATMENT; II. DISINFECTION BY-PRODUCTS: HALOACETIC ACIDS

EPA Science Inventory

Risk management of drinking water relies on quality analytical data. Analytical methodology can often be adapted from environmental monitoring sources. However, risk management sometimes presents special analytical challenges because data may be needed from a source for which n...

The interstellar medium in the starburst regions of NGC 253 and NGC 3256

NASA Astrophysics Data System (ADS)

Carral, P.; Hollenbach, D. J.; Lord, S. D.; Colgan, S. W. J.; Haas, Michael R.; Rubin, R. H.; Erickson, E. F.

1994-03-01

We discuss observations of the (C II) 158 micrometers, (O I) 63 micrometers, (Si II) 35 micrometers, (O III) 52,88 micrometers, and (S III) 33 micrometers fine-structure transitions toward the central 45 seconds of the starburst galaxies NGC 253 and NGC 3256. The (C II) and (O I) emission probably originates in photodissociated gas at the surfaces of molecular clouds, although a small (less than or approximately 30%) contribution to the (C II) flux from H II regions cannot be ruled out. The (O III) and (S III) lines originate in H II regions and the (Si II) flux is best explained as originating in H II regions with some contribution from photodissociation regions (PDRs). The gas phase silicon abundance is nearly solar in NGC 253, which we interpret as evidence for grain destruction in the starburst region. We find that the photodissociated atomic gas has densities approximately 104/cu cm and temperature 200-300 K. About 2% of the gas is in this phase. The thermal gas pressure in the PDRs, P(PDR)/k approximately 1-3 x 106 K/cu cm, might represent the 'typical' interstellar gas pressure in starburst systems. The Far Ultraviolet (FUV) radiation fields illuminating the clouds are 103-104 stronger than the local Galactic FUV field and come from the contribution of many closely packed O and B stars. For the central 250 pc of NGC 253, we find that the H II gas has an average density ne is approximately 400/cu cm. This corresponds to a thermal pressure P(H II)/k approximately 7 x 106 K/cu cm which is approximately P(PDR)/k, suggesting that the ionized gas is in pressure equilibrium with the photodissociated gas at the surfaces of molecular clouds. The H II gas fills a significant fraction, approximately 0.01-0.3, of the volume between the clouds. The effective temperature of the ionizing stars in NGC 253 is greater than or approximately 34,500 K; 2 x 105 O7.5 stars would produce the observed Lyman continuum photon luminosity. The average separation between the stars is approximately 3 pc. Applying the simple model for the interstellar medium in galactic nuclei of Wolfire, Tielens, & Hollenbach (1990), we find the molecular gas in the central regions of NGC 253 and NGC 3256 to be distributed in a large number (5 x 103 to 5 x 105) of small (0.5-2 pc), dense (approximately 104/cu cm) clouds (or alternatively 'thin-flattened' structures) with volume filling factors 10-3 to 10-2, very different from the local Interstellar Medium (ISM) of the Galaxy. We suggest a self-consistent scenario for the ISM in NGC 253 in which clouds and H II gas are in pressure balance with a supernova-shocked, hot 1-3 x 106 K, low-density (approximately 104/cu cm), all pervasive medium. A feedback mechanism may be indicated in which the pressure generated by the supernovae compresses the molecular clouds and triggers further massive star formation. The similarity of ISM parameters deduced for NGC 253, NGC 3256, and M82 (Lord et al. 1993) suggests that the ISM properties are independent of the luminosity of the starburst or the triggering mechanism, but are rather endemic to starburst systems. The starburst in NGC 3256 appears to be a scaled-up version of the NGC 253 and M82 starbursts.

A semi-analytical study of positive corona discharge in wire-plane electrode configuration

NASA Astrophysics Data System (ADS)

Yanallah, K.; Pontiga, F.; Chen, J. H.

2013-08-01

Wire-to-plane positive corona discharge in air has been studied using an analytical model of two species (electrons and positive ions). The spatial distributions of electric field and charged species are obtained by integrating Gauss's law and the continuity equations of species along the Laplacian field lines. The experimental values of corona current intensity and applied voltage, together with Warburg's law, have been used to formulate the boundary condition for the electron density on the corona wire. To test the accuracy of the model, the approximate electric field distribution has been compared with the exact numerical solution obtained from a finite element analysis. A parametrical study of wire-to-plane corona discharge has then been undertaken using the approximate semi-analytical solutions. Thus, the spatial distributions of electric field and charged particles have been computed for different values of the gas pressure, wire radius and electrode separation. Also, the two dimensional distribution of ozone density has been obtained using a simplified plasma chemistry model. The approximate semi-analytical solutions can be evaluated in a negligible computational time, yet provide precise estimates of corona discharge variables.

Paired emitter-detector diode detection with dual wavelength monitoring for enhanced sensitivity to transition metals in ion chromatography with post-column reaction.

PubMed

O' Toole, Martina; Barron, Leon; Shepherd, Roderick; Paull, Brett; Nesterenko, Pavel; Diamond, Dermot

2009-01-01

The combination of post-column derivatisation and visible detection are regularly employed in ion chromatography (IC) to detect poorly absorbing species. Although this mode is often highly sensitive, one disadvantage is the increase in repeating baseline artifacts associated with out-of-sync pumping systems. The work presented here will demonstrate the use of a second generation design paired emitter-detector diode (PEDD-II) detection mode offering enhanced sensitivity to transition metals in IC by markedly reducing this problem and also by improving signal noise. First generation designs demonstrated the use of a single integrated PEDD detector cell as a simple, small (15 x 5 mm), highly sensitive, low cost photometric detector for the detection of metals in IC. The basic principle of this detection mode lies in the employment of two linear light emitting diodes (LEDs), one operating in normal mode as a light source and the other in reverse bias serving as a light detector. The second generation PEDD-II design showed increased sensitivity for Mn(II)- and Co(II)-2-(pyridylazo)resorcinol (PAR) complexes as a result of two simultaneously acquiring detection cells--one analytical PEDD cell and one reference PEDD cell. Therefore, the PEDD-II employs two wavelengths whereby one monitors the analyte reaction product and the second monitors a wavelength close to the isosbestic point. The optimum LED wavelength to be used for the analytical cell was investigated to maximise peak response. The fabrication process for both the analytical and reference PEDD cells was validated by determining the reproducibility of detectors within a batch. The reproducibility and sensitivity of the PEDD-II detector was then investigated using signals obtained from both intra- and inter-day chromatograms.

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

PubMed

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

Improvement of LOD in Fluorescence Detection with Spectrally Nonuniform Background by Optimization of Emission Filtering.

PubMed

Galievsky, Victor A; Stasheuski, Alexander S; Krylov, Sergey N

2017-10-17

The limit-of-detection (LOD) in analytical instruments with fluorescence detection can be improved by reducing noise of optical background. Efficiently reducing optical background noise in systems with spectrally nonuniform background requires complex optimization of an emission filter-the main element of spectral filtration. Here, we introduce a filter-optimization method, which utilizes an expression for the signal-to-noise ratio (SNR) as a function of (i) all noise components (dark, shot, and flicker), (ii) emission spectrum of the analyte, (iii) emission spectrum of the optical background, and (iv) transmittance spectrum of the emission filter. In essence, the noise components and the emission spectra are determined experimentally and substituted into the expression. This leaves a single variable-the transmittance spectrum of the filter-which is optimized numerically by maximizing SNR. Maximizing SNR provides an accurate way of filter optimization, while a previously used approach based on maximizing a signal-to-background ratio (SBR) is the approximation that can lead to much poorer LOD specifically in detection of fluorescently labeled biomolecules. The proposed filter-optimization method will be an indispensable tool for developing new and improving existing fluorescence-detection systems aiming at ultimately low LOD.

Analytical Ferrography Standardization.

DTIC Science & Technology

1982-01-01

AD-AII6 508 MECHANICAL TECHNOLOGY INC LATHAM NY RESEARCH AND 0EV--ETC F/6 7/4 ANALYTICAL FERROGRAPHY STANDARDIZATION. (U) JAN 82 P A SENHOLZI, A S...ii Mwl jutio7 Unimte SMechanical Technology Incorporated Research and Development Division ReerhadDvlpetDvso I FINAL REPORT ANALYTICAL FERROGRAPHY ...Final Report MTI Technical Report No. 82TRS6 ANALYTICAL FERROGRAPHY STANDARDIZATION P. B. Senholzi A. S. Maciejewski Applications Engineering Mechanical

Analytical approximations to the dynamics of an array of coupled DC SQUIDs

NASA Astrophysics Data System (ADS)

Berggren, Susan; Palacios, Antonio

2014-04-01

Coupled dynamical systems that operate near the onset of a bifurcation can lead, under certain conditions, to strong signal amplification effects. Over the past years we have studied this generic feature on a wide range of systems, including: magnetic and electric fields sensors, gyroscopic devices, and arrays of loops of superconducting quantum interference devices, also known as SQUIDs. In this work, we consider an array of SQUID loops connected in series as a case study to derive asymptotic analytical approximations to the exact solutions through perturbation analysis. Two approaches are considered. First, a straightforward expansion in which the non-linear parameter related to the inductance of the DC SQUID is treated as the small perturbation parameter. Second, a more accurate procedure that considers the SQUID phase dynamics as non-uniform motion on a circle. This second procedure is readily extended to the series array and it could serve as a mathematical framework to find approximate solutions to related complex systems with high-dimensionality. To the best of our knowledge, an approximate analytical solutions to an array of SQUIDs has not been reported yet in the literature.

Nuclear magnetic resonance signal dynamics of liquids in the presence of distant dipolar fields, revisited

PubMed Central

Barros, Wilson; Gochberg, Daniel F.; Gore, John C.

2009-01-01

The description of the nuclear magnetic resonance magnetization dynamics in the presence of long-range dipolar interactions, which is based upon approximate solutions of Bloch–Torrey equations including the effect of a distant dipolar field, has been revisited. New experiments show that approximate analytic solutions have a broader regime of validity as well as dependencies on pulse-sequence parameters that seem to have been overlooked. In order to explain these experimental results, we developed a new method consisting of calculating the magnetization via an iterative formalism where both diffusion and distant dipolar field contributions are treated as integral operators incorporated into the Bloch–Torrey equations. The solution can be organized as a perturbative series, whereby access to higher order terms allows one to set better boundaries on validity regimes for analytic first-order approximations. Finally, the method legitimizes the use of simple analytic first-order approximations under less demanding experimental conditions, it predicts new pulse-sequence parameter dependencies for the range of validity, and clarifies weak points in previous calculations. PMID:19425789

Spacing of bending-induced fractures at saturation: Numerical models and approximate analytical solution

NASA Astrophysics Data System (ADS)

Schöpfer, Martin; Lehner, Florian; Grasemann, Bernhard; Kaserer, Klemens; Hinsch, Ralph

2017-04-01

John G. Ramsay's sketch of structures developed in a layer progressively folded and deformed by tangential longitudinal strain (Figure 7-65 in Folding and Fracturing of Rocks) and the associated strain pattern analysis have been reproduced in many monographs on Structural Geology and are referred to in numerous publications. Although the origin of outer-arc extension fractures is well-understood and documented in many natural examples, geomechanical factors controlling their (finite or saturation) spacing are hitherto unexplored. This study investigates the formation of bending-induced fractures during constant-curvature forced folding using Distinct Element Method (DEM) numerical modelling. The DEM model comprises a central brittle layer embedded within weaker (low modulus) elastic layers; the layer interfaces are frictionless (free slip). Folding of this three-layer system is enforced by a velocity boundary condition at the model base, while a constant overburden pressure is maintained at the model top. The models illustrate several key stages of fracture array development: (i) Prior to the onset of fracture, the neutral surface is located midway between the layer boundaries; (ii) A first set of regularly spaced fractures develops once the tensile stress in the outer-arc equals the tensile strength of the layer. Since the layer boundaries are frictionless, these bending-induced fractures propagate through the entire layer; (iii) After the appearance of the first fracture set, the rate of fracture formation decreases rapidly and so-called infill fractures develop approximately midway between two existing fractures (sequential infilling); (iv) Eventually no new fractures form, irrespective of any further increase in fold curvature (fracture saturation). Analysis of the interfacial normal stress distributions suggests that at saturation the fracture-bound blocks are subjected to a loading condition similar to three-point bending. Using classical beam theory an analytical solution is derived for the critical fracture spacing, i.e. the spacing below which the maximum tensile stress cannot reach the layer strength. The model results are consistent with an approximate analytical solution, and illustrate that the spacing of bending-induced fractures is proportional to layer thickness and a square root function of the ratio of layer tensile strength to confining pressure. Although highly idealised, models and analysis presented in this study offer an explanation for fracture saturation during folding and point towards certain key factors that may control fracture spacing in natural systems.

A reagent-free tubular biofilm reactor for on-line determination of biochemical oxygen demand.

PubMed

Liu, Changyu; Zhao, Huijun; Gao, Shan; Jia, Jianbo; Zhao, Limin; Yong, Daming; Dong, Shaojun

2013-07-15

We reported a reagent-free tubular biofilm reactor (BFR) based analytical system for rapid online biochemical oxygen demand (BOD) determination. The BFR was cultivated using microbial seeds from activated sludge. It only needs tap water to operate and does not require any chemical reagent. The analytical performance of this reagent-free BFR system was found to be equal to or better than the BFR system operated using phosphate buffer saline (PBS) and high purity deionized water. The system can readily achieve a limit of detection of 0.25 mg O2 L(-1), possessing superior reproducibility, and long-term operational and storage stability. More importantly, we confirmed for the first time that the BFR system is capable of tolerating common toxicants found in wastewaters, such as 3,5-dichlorophenol and Zn(II), Cr(VI), Cd(II), Cu(II), Pb(II), Mn(II) and Ni(II), enabling the method to be applied to a wide range of wastewaters. The sloughing and clogging are the important attributes affecting the operational stability, hence, the reliability of most online wastewater monitoring systems, which can be effectively avoided, benefiting from the tubular geometry of the reactor and high flow rate conditions. These advantages, coupled with simplicity in device, convenience in operation and minimal maintenance, make such a reagent-free BFR analytical system promising for practical BOD online determination. Copyright © 2013 Elsevier B.V. All rights reserved.

Wave transience in a compressible atmosphere. I - Transient internal wave, mean-flow interaction. II - Transient equatorial waves in the quasi-biennial oscillation

NASA Technical Reports Server (NTRS)

Dunkerton, T. J.

1981-01-01

Analytical and numerical solutions are obtained in an approximate quasi-linear model, to describe the way in which vertically propagating waves give rise to mean flow accelerations in an atmosphere due to the effects of wave transience. These effects in turn result from compressibility and vertical group velocity feedback, and culminate in the spontaneous formation and descent of regions of strong mean wind shear. The numerical solutions display mean flow accelerations due to Kelvin waves in the equatorial stratosphere, with wave absorption altering the transience mechanism in such significant respects as causing the upper atmospheric mean flow acceleration to be very sensitive to the precise magnitude and distribution of the damping mechanisms. The numerical simulations of transient equatorial waves in the quasi-biennial oscillation are also considered.

On the widespread use of the Corrsin hypothesis in diffusion theories

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

Tautz, R. C.; Shalchi, A.

2010-12-15

In the past four decades, several nonlinear theories have been developed to describe (i) the motion of charged test particles through a turbulent magnetized plasma and (ii) the random walk of magnetic field lines. In many such theories, the so-called Corrsin independence hypothesis has been applied to enforce analytical tractability. In this note, it is shown that the Corrsin hypothesis is part of most nonlinear diffusion theories. In some cases, the Corrsin approximation is somewhat hidden, while in other cases a different name is used for the same approach. It is shown that even the researchers who criticized the applicationmore » of this hypothesis have used it in their nonlinear diffusion theories. It is hoped that the present article will eliminate the recently caused confusion about the applicability and validity of the Corrsin hypothesis.« less

Gas dynamics of a supersonic radial jet. Part II

NASA Astrophysics Data System (ADS)

Kosarev, V. F.; Klinkov, S. V.; Zaikovskii, V. N.

2016-05-01

The paper presents the radial distributions of the pressure measured with a Pitot tube for the case of a radial jet with/without swirling of the input flow in the pre-chamber; the length of the supersonic part of the jet, dependency of the jet thickness as a function of the distance from the nozzle outlet, and approximating analytical formula for the jet thickness that generalizes the experimental data. Experimental data demonstrated that at the deposition distances lower than 4-6 gauges from the nozzle outlet, the solid particle velocity and temperature are almost uniform over the jet cross section. This means that the target surface can be allocated here without loss in coating quality and deposition coefficient. The maximal recommended distance where the deposition is still possible is the length of l s0 ~ 16 gauges.

The environmental effect on the radial breathing mode of carbon nanotubes. II. Shell model approximation for internally and externally adsorbed fluids

NASA Astrophysics Data System (ADS)

Longhurst, M. J.; Quirke, N.

2006-11-01

We have previously shown that the upshift in the radial breathing mode (RBM) of closed (or infinite) carbon nanotubes in solution is almost entirely due to coupling of the RBM with an adsorbed layer of fluid on the nanotube surface. The upshift can be modeled analytically by considering the adsorbed fluid as an infinitesimally thin shell, which interacts with the nanotube via a continuum Lennard-Jones potential. Here we extend the model to include internally as well as externally adsorbed waterlike molecules, and find that filling the nanotubes leads to an additional upshift of two to six wave numbers. We show that using molecular dynamics, the RBM can be accurately reproduced by replacing the fluid molecules with a mean field harmonic shell potential, greatly reducing simulation times.

The entorhinal cortex of the Megachiroptera: a comparative study of Wahlberg's epauletted fruit bat and the straw-coloured fruit bat.

PubMed

Gatome, Catherine W; Slomianka, Lutz; Mwangi, Dieter K; Lipp, Hans-Peter; Amrein, Irmgard

2010-05-01

This study describes the organisation of the entorhinal cortex of the Megachiroptera, straw-coloured fruit bat and Wahlberg's epauletted fruit bat. Using Nissl and Timm stains, parvalbumin and SMI-32 immunohistochemistry, we identified five fields within the medial (MEA) and lateral (LEA) entorhinal areas. MEA fields E(CL) and E(C) are characterised by a poor differentiation between layers II and III, a distinct layer IV and broad, stratified layers V and VI. LEA fields E(I), E(R) and E(L) are distinguished by cell clusters in layer II, a clear differentiation between layers II and III, a wide columnar layer III and a broad sublayer Va. Clustering in LEA layer II was more typical of the straw-coloured fruit bat. Timm-staining was most intense in layers Ib and II across all fields and layer III of field E(R). Parvalbumin-like staining varied along a medio-lateral gradient with highest immunoreactivity in layers II and III of MEA and more lateral fields of LEA. Sparse SMI-32-like immunoreactivity was seen only in Wahlberg's epauletted fruit bat. Of the neurons in MEA layer II, ovoid stellate cells account for approximately 38%, polygonal stellate cells for approximately 8%, pyramidal cells for approximately 18%, oblique pyramidal cells for approximately 6% and other neurons of variable morphology for approximately 29%. Differences between bats and other species in cellular make-up and cytoarchitecture of layer II may relate to their three-dimensional habitat. Cytoarchitecture of layer V in conjunction with high encephalisation and structural changes in the hippocampus suggest similarities in efferent hippocampal --> entorhinal --> cortical interactions between fruit bats and primates.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was built using the OpenMDAO framework. Pycycle provides analytic derivatives allowing for an efficient use of gradient-based optimization methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Solid-phase extraction of some heavy metal ions on a double-walled carbon nanotube disk and determination by flame atomic absorption spectrometry.

PubMed

Karatepe, Aslihan; Soylak, Mustafa; Elçi, Latif

2011-01-01

A new preconcentration method was developed for the determination of trace amounts of Cu(II), Fe(III), Pb(II), Ni(II), and Cd(II) on a double-walled carbon nanotube disk. 4-(2-Thiazolylazo) resorcinol was used as a complexing reagent. The effects of parameters, including pH of the solutions, amounts of complexing reagent, eluent type, sample volume, flow rates of solutions, and matrix ions were examined for quantitative recoveries of the studied analyte ions. The retained metal ions were eluted by 2 M HNO3. The LOD values for the analytes were in the range of 0.7-4.4 microg/mL. Natural water samples and standard reference materials were analyzed by the presented method.

Trace level voltammetric determination of heavy metals and total mercury in tea matrices (Camellia sinensis).

PubMed

Melucci, Dora; Locatelli, Marcello; Locatelli, Clinio

2013-12-01

An analytical procedure regarding the voltammetric determination of mercury(II), copper(II), lead(II), cadmium(II) and zinc(II) by square wave anodic stripping voltammetry (SWASV) in matrices involved in food chain is proposed. In particular, tea leaves were analyzed as real samples. The digestion of each matrix was carried out using a concentrated HCl-HNO3-H2SO4 acidic attack mixture; 0.01 mol L(-1) EDTA-Na2+ 0.15 mol L(-1) NaCl + 0.5 mol L(-1) HCl was employed as the supporting electrolyte. The voltammetric measurements were carried out using a conventional three electrode cell, employing, as working electrodes, a gold electrode (GE) and a stationary hanging mercury drop electrode (HMDE). The analytical procedure has been verified on the standard reference materials Spinach Leaves NIST-SRM 1570a, Tomato Leaves NIST-SRM 1573a and Apple Leaves NIST-SRM 1515. For all the elements, the precision as repeatability, expressed as relative standard deviation (sr) was of the order of 3-5%, while the trueness, expressed as relative error (e) was of the order of 3-7%. Once set up on the standard reference materials, the analytical procedure was applied to commercial tea leaves samples. A critical comparison with spectroscopic measurements is also discussed.

Convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks

NASA Astrophysics Data System (ADS)

Long, Yin; Zhang, Xiao-Jun; Wang, Kui

2018-05-01

In this paper, convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks (RBDNs) are studied. First, we find and demonstrate that the average degree is convergent in the form of power law. Meanwhile, we discover that the ratios of the back items to front items of convergent reminder are independent of network link number for large network size, and we theoretically prove that the limit of the ratio is a constant. Moreover, since it is difficult to calculate the analytical solution of the average degree for large network sizes, we adopt numerical method to obtain approximate expression of the average degree to approximate its analytical solution. Finally, simulations are presented to verify our theoretical results.

The Beck Depression Inventory-II: Testing for Measurement Equivalence and Factor Mean Differences across Hong Kong and American Adolescents

ERIC Educational Resources Information Center

Byrne, Barbara M.; Stewart, Sunita M.; Kennard, Betsy D.; Lee, Peter W. H.

2007-01-01

Working within the framework of a confirmatory factor analytic (CFA) model, this study adds another dimension to construct validation of both the Beck Depression Inventory-II (BDI-II; Beck, Steer, & Brown, 1996) and a Chinese version of the BDI-II (C-BDI-II; Chinese Behavioral Sciences Society, 2000). Specifically, we tested for measurement…

An Analytical Chemistry Experiment in Simultaneous Spectrophotometric Determination of Fe(III) and Cu(II) with Hexacyanoruthenate(II) Reagent.

ERIC Educational Resources Information Center

Mehra, M. C.; Rioux, J.

1982-01-01

Experimental procedures, typical observations, and results for the simultaneous analysis of Fe(III) and Cu(II) in a solution are discussed. The method is based on selective interaction between the two ions and potassium hexacyanoruthenate(II) in acid solution involving no preliminary sample preparations. (Author/JN)

Padé Approximant and Minimax Rational Approximation in Standard Cosmology

NASA Astrophysics Data System (ADS)

Zaninetti, Lorenzo

2016-02-01

The luminosity distance in the standard cosmology as given by $\\Lambda$CDM and consequently the distance modulus for supernovae can be defined by the Pad\\'e approximant. A comparison with a known analytical solution shows that the Pad\\'e approximant for the luminosity distance has an error of $4\\%$ at redshift $= 10$. A similar procedure for the Taylor expansion of the luminosity distance gives an error of $4\\%$ at redshift $=0.7 $; this means that for the luminosity distance, the Pad\\'e approximation is superior to the Taylor series. The availability of an analytical expression for the distance modulus allows applying the Levenberg--Marquardt method to derive the fundamental parameters from the available compilations for supernovae. A new luminosity function for galaxies derived from the truncated gamma probability density function models the observed luminosity function for galaxies when the observed range in absolute magnitude is modeled by the Pad\\'e approximant. A comparison of $\\Lambda$CDM with other cosmologies is done adopting a statistical point of view.

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

NASA Astrophysics Data System (ADS)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

2016-08-01

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

Analytic studies of the hard dumbell fluid

NASA Astrophysics Data System (ADS)

Morriss, G. P.; Cummings, P. T.

A closed form analytic theory for the structure of the hard dumbell fluid is introduced and evaluated. It is found to be comparable in accuracy to the reference interaction site approximation (RISA) of Chandler and Andersen.

Digital hologram transformations for RGB color holographic display with independent image magnification and translation in 3D.

PubMed

Makowski, Piotr L; Zaperty, Weronika; Kozacki, Tomasz

2018-01-01

A new framework for in-plane transformations of digital holograms (DHs) is proposed, which provides improved control over basic geometrical features of holographic images reconstructed optically in full color. The method is based on a Fourier hologram equivalent of the adaptive affine transformation technique [Opt. Express18, 8806 (2010)OPEXFF1094-408710.1364/OE.18.008806]. The solution includes four elementary geometrical transformations that can be performed independently on a full-color 3D image reconstructed from an RGB hologram: (i) transverse magnification; (ii) axial translation with minimized distortion; (iii) transverse translation; and (iv) viewing angle rotation. The independent character of transformations (i) and (ii) constitutes the main result of the work and plays a double role: (1) it simplifies synchronization of color components of the RGB image in the presence of mismatch between capture and display parameters; (2) provides improved control over position and size of the projected image, particularly the axial position, which opens new possibilities for efficient animation of holographic content. The approximate character of the operations (i) and (ii) is examined both analytically and experimentally using an RGB circular holographic display system. Additionally, a complex animation built from a single wide-aperture RGB Fourier hologram is presented to demonstrate full capabilities of the developed toolset.

A solid phase extraction procedure for the determination of Cd(II) and Pb(II) ions in food and water samples by flame atomic absorption spectrometry.

PubMed

Daşbaşı, Teslima; Saçmacı, Şerife; Ülgen, Ahmet; Kartal, Şenol

2015-05-01

A relatively rapid, accurate and precise solid phase extraction method is presented for the determination of cadmium(II) and lead(II) in various food and water samples. Quantitation is carried out by flame atomic absorption spectrometry (FAAS). The method is based on the retention of the trace metal ions on Dowex Marathon C, a strong acid cation exchange resin. Some important parameters affecting the analytical performance of the method such as pH, flow rate and volume of the sample solution; type, concentration, volume, flow rate of the eluent; and matrix effects on the retention of the metal ions were investigated. Common coexisting ions did not interfere on the separation and determination of the analytes. The detection limits (3 σb) for Cd(II) and Pb(II) were found as 0.13 and 0.18 μg L(-1), respectively, while the limit of quantification values (10 σb) were computed as 0.43 and 0.60 μg L(-1) for the same sequence of the analytes. The precision (as relative standard deviation was lower than 4% at 5 μg L(-1) Cd(II) and 10 μg L(-1) Pb(II) levels, and the preconcentration factor was found to be 250. The accuracy of the proposed procedure was verified by analysing the certified reference materials, SPS-WW2 Batch 108 wastewater level 2 and INCT-TL-1 tea leaves, with the satisfactory results. In addition, for the accuracy of the method the recovery studies (⩾ 95%) were carried out. The method was applied to the determination of the analytes in the various natural waters (lake water, tap water, waste water with boric acid, waste water with H2SO4) and food samples (pomegranate flower, organic pear, radish leaf, lamb meat, etc.), and good results were obtained. While the food samples almost do not contain cadmium, they have included lead at low levels of 0.13-1.12 μg g(-1). Copyright © 2014 Elsevier Ltd. All rights reserved.

Horizon-absorbed energy flux in circularized, nonspinning black-hole binaries, and its effective-one-body representation

NASA Astrophysics Data System (ADS)

Nagar, Alessandro; Akcay, Sarp

2012-02-01

We propose, within the effective-one-body approach, a new, resummed analytical representation of the gravitational-wave energy flux absorbed by a system of two circularized (nonspinning) black holes. This expression is such that it is well-behaved in the strong-field, fast-motion regime, notably up to the effective-one-body-defined last unstable orbit. Building conceptually upon the procedure adopted to resum the multipolar asymptotic energy flux, we introduce a multiplicative decomposition of the multipolar absorbed flux made by three factors: (i) the leading-order contribution, (ii) an “effective source” and (iii) a new residual amplitude correction (ρ˜ℓmH)2ℓ. In the test-mass limit, we use a frequency-domain perturbative approach to accurately compute numerically the horizon-absorbed fluxes along a sequence of stable and unstable circular orbits, and we extract from them the functions ρ˜ℓmH. These quantities are then fitted via rational functions. The resulting analytically represented test-mass knowledge is then suitably hybridized with lower-order analytical information that is valid for any mass ratio. This yields a resummed representation of the absorbed flux for a generic, circularized, nonspinning black-hole binary. Our result adds new information to the state-of-the-art calculation of the absorbed flux at fractional 5 post-Newtonian order [S. Taylor and E. Poisson, Phys. Rev. D 78, 084016 (2008)], which is recovered in the weak-field limit approximation by construction.

Analytical steady-state solutions for water-limited cropping systems using saline irrigation water

NASA Astrophysics Data System (ADS)

Skaggs, T. H.; Anderson, R. G.; Corwin, D. L.; Suarez, D. L.

2014-12-01

Due to the diminishing availability of good quality water for irrigation, it is increasingly important that irrigation and salinity management tools be able to target submaximal crop yields and support the use of marginal quality waters. In this work, we present a steady-state irrigated systems modeling framework that accounts for reduced plant water uptake due to root zone salinity. Two explicit, closed-form analytical solutions for the root zone solute concentration profile are obtained, corresponding to two alternative functional forms of the uptake reduction function. The solutions express a general relationship between irrigation water salinity, irrigation rate, crop salt tolerance, crop transpiration, and (using standard approximations) crop yield. Example applications are illustrated, including the calculation of irrigation requirements for obtaining targeted submaximal yields, and the generation of crop-water production functions for varying irrigation waters, irrigation rates, and crops. Model predictions are shown to be mostly consistent with existing models and available experimental data. Yet the new solutions possess advantages over available alternatives, including: (i) the solutions were derived from a complete physical-mathematical description of the system, rather than based on an ad hoc formulation; (ii) the analytical solutions are explicit and can be evaluated without iterative techniques; (iii) the solutions permit consideration of two common functional forms of salinity induced reductions in crop water uptake, rather than being tied to one particular representation; and (iv) the utilized modeling framework is compatible with leading transient-state numerical models.

Improving the analytical performance and versatility of paper spray mass spectrometry via paper microfluidics.

PubMed

Murray, Ian; Walker, Glenn; Bereman, Michael S

2016-06-20

Two paper-based microfluidic techniques, photolithography and wax patterning, were investigated for their potential to improve upon the sensitivity, reproducibility, and versatility of paper spray mass spectrometry. The main limitation of photolithography was the significant signal (approximately three orders of magnitude) above background which was attributed to the chemicals used in the photoresist process. Hydrophobic barriers created via wax patterning were discovered to have approximately 2 orders of magnitude less background signal compared to analogous barriers created using photolithography. A minimum printed wax barrier thickness of approximately 0.3 mm was necessary to consistently retain commonly used paper spray solvents (1 : 1 water : acetonitrile/methanol) and avoid leakage. Constricting capillary flow via wax-printed channels yielded both a significant increase in signal and detection time for detection of model analytes. This signal increase, which was attributed to restricting the radial flow of analyte/solvent on paper (i.e., a concentrating effect), afforded a significant increase in sensitivity (p ≪ 0.05) for the detection of pesticides spiked into residential tap water using a five-point calibration curve. Finally, unique mixing designs using wax patterning can be envisioned to perform on-paper analyte derivatization.

Automated facial recognition and candidate list rank change of computer generated facial approximations generated with multiple eye orb positions.

PubMed

Parks, Connie L; Monson, Keith L

2016-09-01

Expanding on research previously reported by the authors, this study further examines the recognizability of ReFace facial approximations generated with the following eye orb positions: (i) centrally within the bony eye socket, (ii) 1.0mm superior and 2.0mm lateral relative to center, and (iii) 1.0mm superior and 2.5mm lateral relative to center. Overall, 81% of the test subjects' approximation ranks improved with the use of either of the two supero-lateral eye orbs. Highly significant performance differences (p<0.01) were observed between the approximations with centrally positioned eye orbs (i) and approximations with the eye orbs placed in the supero-laterally positions (ii and iii). Noteworthy was the observation that in all cases when the best rank for an approximation was obtained with the eye orbs in position (iii), the second best rank was achieved with the eye orbs in position (ii). A similar pattern was also observed when the best rank was obtained with the eye orbs in position (ii), with 60% of the second best ranks observed in position (iii). It is argued, therefore, that an approximation constructed with the eye orbs placed in either of the two supero-lateral positions may be more effective and operationally informative than centrally positioned orbs. Copyright © 2016. Published by Elsevier Ireland Ltd.

Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies

NASA Technical Reports Server (NTRS)

Mirels, Harold

1959-01-01

Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.

On accelerated flow of MHD powell-eyring fluid via homotopy analysis method

NASA Astrophysics Data System (ADS)

Salah, Faisal; Viswanathan, K. K.; Aziz, Zainal Abdul

2017-09-01

The aim of this article is to obtain the approximate analytical solution for incompressible magnetohydrodynamic (MHD) flow for Powell-Eyring fluid induced by an accelerated plate. Both constant and variable accelerated cases are investigated. Approximate analytical solution in each case is obtained by using the Homotopy Analysis Method (HAM). The resulting nonlinear analysis is carried out to generate the series solution. Finally, Graphical outcomes of different values of the material constants parameters on the velocity flow field are discussed and analyzed.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

PubMed

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

Siewert solutions of transcendental equations, generalized Lambert functions and physical applications

NASA Astrophysics Data System (ADS)

Barsan, Victor

2018-05-01

Several classes of transcendental equations, mainly eigenvalue equations associated to non-relativistic quantum mechanical problems, are analyzed. Siewert's systematic approach of such equations is discussed from the perspective of the new results recently obtained in the theory of generalized Lambert functions and of algebraic approximations of various special or elementary functions. Combining exact and approximate analytical methods, quite precise analytical outputs are obtained for apparently untractable problems. The results can be applied in quantum and classical mechanics, magnetism, elasticity, solar energy conversion, etc.

Solutions of the Dirac Equation with the Shifted DENG-FAN Potential Including Yukawa-Like Tensor Interaction

NASA Astrophysics Data System (ADS)

Yahya, W. A.; Falaye, B. J.; Oluwadare, O. J.; Oyewumi, K. J.

2013-08-01

By using the Nikiforov-Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng-Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schr\\"{o}dinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary

PubMed Central

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations. PMID:27031232

Probing the galactic disk and halo. 2: Hot interstellar gas toward the inner galaxy star HD 156359

NASA Technical Reports Server (NTRS)

Sembach, Kenneth R.; Savage, Blair D.; Lu, Limin

1995-01-01

We present Goddard High Resolution Spectrograph intermediate-resolution measurements of the 1233-1256 A spectral region of HD 156396, a halo star at l = 328.7 deg, b = -14.5 deg in the inner Galaxy with a line-of sight distance of 11.1 kpc and a z-distance of -2.8 kpc. The data have a resolution of 18 km/s Full Width at Half Maximum (FWHM) and a signal-to-noise ratio of approximately 50:1. We detect interstellar lines of Mg II, S II, S II, Ge II, and N V and determine log N/(Mg II) = 15.78 +0.25, -0.27, log N(Si II) greater than 13.70, log N(S II) greater than 15.76, log N(Ge II) = 12.20 +0.09,-0.11, and log N(N v) = 14.06 +/- 0.02. Assuming solar reference abundances, the diffuse clouds containing Mg, S, and Ge along the sight line have average logarithmic depletions D(Mg) = -0.6 +/- 0.3 dex, D(S) greater than -0.2 dex, and D(Ge) = -0.2 +/- 0.2 dex. The Mg and Ge depletions are approximately 2 times smaller than is typical of diffuse clouds in the solar vicinity. Galactic rotational modeling of the N v profiles indicates that the highly ionized gas traced by this ion has a scale height of approximately 1 kpc if gas at large z-distances corotates with the underlying disk gas. Rotational modeling of the Si iv and C iv profiles measured by the IUE satellite yields similar scale height estimates. The scale height results contrast with previous studies of highly ionized gas in the outer Milky Way that reveal a more extended gas distribtion with h approximately equals 3-4 kpc. We detect a high-velocity feature in N v and Si II v(sub LSR) approximately equals + 125 km/s) that is probably created in an interface between warm and hot gas.

Physical Conditions of the Interstellar Medium in Star-forming Galaxies at z1.5

NASA Technical Reports Server (NTRS)

Hayashi, Masao; Ly, Chun; Shimasaku, Kazuhiro; Motohara, Kentaro; Malkan, Matthew A.; Nagao, Tohru; Kashikawa, Nobunari; Goto, Ryosuke; Naito, Yoshiaki

2015-01-01

We present results from Subaru/FMOS near-infrared (NIR) spectroscopy of 118 star-forming galaxies at z approximately equal to 1.5 in the Subaru Deep Field. These galaxies are selected as [O II] lambda 3727 emitters at z approximately equal to 1.47 and 1.62 from narrow-band imaging. We detect H alpha emission line in 115 galaxies, [O III] lambda 5007 emission line in 45 galaxies, and H Beta, [N II] lambda 6584, and [S II]lambda lambda 6716, 6731 in 13, 16, and 6 galaxies, respectively. Including the [O II] emission line, we use the six strong nebular emission lines in the individual and composite rest-frame optical spectra to investigate physical conditions of the interstellar medium in star-forming galaxies at z approximately equal to 1.5. We find a tight correlation between H alpha and [O II], which suggests that [O II] can be a good star formation rate (SFR) indicator for galaxies at z approximately equal to 1.5. The line ratios of H alpha / [O II] are consistent with those of local galaxies. We also find that [O II] emitters have strong [O III] emission lines. The [O III]/[O II] ratios are larger than normal star-forming galaxies in the local Universe, suggesting a higher ionization parameter. Less massive galaxies have larger [O III]/[O II] ratios. With evidence that the electron density is consistent with local galaxies, the high ionization of galaxies at high redshifts may be attributed to a harder radiation field by a young stellar population and/or an increase in the number of ionizing photons from each massive star.

Approximation methods in relativistic eigenvalue perturbation theory

NASA Astrophysics Data System (ADS)

Noble, Jonathan Howard

In this dissertation, three questions, concerning approximation methods for the eigenvalues of quantum mechanical systems, are investigated: (i) What is a pseudo--Hermitian Hamiltonian, and how can its eigenvalues be approximated via numerical calculations? This is a fairly broad topic, and the scope of the investigation is narrowed by focusing on a subgroup of pseudo--Hermitian operators, namely, PT--symmetric operators. Within a numerical approach, one projects a PT--symmetric Hamiltonian onto an appropriate basis, and uses a straightforward two--step algorithm to diagonalize the resulting matrix, leading to numerically approximated eigenvalues. (ii) Within an analytic ansatz, how can a relativistic Dirac Hamiltonian be decoupled into particle and antiparticle degrees of freedom, in appropriate kinematic limits? One possible answer is the Foldy--Wouthuysen transform; however, there are alter- native methods which seem to have some advantages over the time--tested approach. One such method is investigated by applying both the traditional Foldy--Wouthuysen transform and the "chiral" Foldy--Wouthuysen transform to a number of Dirac Hamiltonians, including the central-field Hamiltonian for a gravitationally bound system; namely, the Dirac-(Einstein-)Schwarzschild Hamiltonian, which requires the formal- ism of general relativity. (iii) Are there are pseudo--Hermitian variants of Dirac Hamiltonians that can be approximated using a decoupling transformation? The tachyonic Dirac Hamiltonian, which describes faster-than-light spin-1/2 particles, is gamma5--Hermitian, i.e., pseudo-Hermitian. Superluminal particles remain faster than light upon a Lorentz transformation, and hence, the Foldy--Wouthuysen program is unsuited for this case. Thus, inspired by the Foldy--Wouthuysen program, a decoupling transform in the ultrarelativistic limit is proposed, which is applicable to both sub- and superluminal particles.

Quantum noise spectra for periodically driven cavity optomechanics

NASA Astrophysics Data System (ADS)

Aranas, E. B.; Akram, M. Javed; Malz, Daniel; Monteiro, T. S.

2017-12-01

A growing number of experimental setups in cavity optomechanics exploit periodically driven fields. However, such setups are not amenable to analysis by using simple, yet powerful, closed-form expressions of linearized optomechanics, which have provided so much of our present understanding of experimental optomechanics. In the present paper, we formulate a method to calculate quantum noise spectra in modulated optomechanical systems, which we analyze, compare, and discuss with two other recently proposed solutions: we term these (i) frequency-shifted operators, (ii) Floquet [Phys. Rev. A 94, 023803 (2016), 10.1103/PhysRevA.94.023803], and (iii) iterative analysis [New J. Phys. 18, 113021 (2016), 10.1088/1367-2630/18/11/113021]. We prove that (i) and (ii) yield equivalent noise spectra and find that (iii) is an analytical approximation to (i) for weak modulations. We calculate the noise spectra of a doubly modulated system describing experiments of levitated particles in hybrid electro-optical traps. We show excellent agreement with Langevin stochastic simulations in the thermal regime and predict squeezing in the quantum regime. Finally, we reveal how otherwise-inaccessible spectral components of a modulated system can be measured in heterodyne detection through an appropriate choice of modulation frequencies.

Comparison with CLPX II airborne data using DMRT model

USGS Publications Warehouse

Xu, X.; Liang, D.; Andreadis, K.M.; Tsang, L.; Josberger, E.G.

2009-01-01

In this paper, we considered a physical-based model which use numerical solution of Maxwell Equations in three-dimensional simulations and apply into Dense Media Radiative Theory (DMRT). The model is validated in two specific dataset from the second Cold Land Processes Experiment (CLPX II) at Alaska and Colorado. The data were all obtain by the Ku-band (13.95GHz) observations using airborne imaging polarimetric scatterometer (POLSCAT). Snow is a densely packed media. To take into account the collective scattering and incoherent scattering, analytical Quasi-Crystalline Approximation (QCA) and Numerical Maxwell Equation Method of 3-D simulation (NMM3D) are used to calculate the extinction coefficient and phase matrix. DMRT equations were solved by iterative solution up to 2nd order for the case of small optical thickness and full multiple scattering solution by decomposing the diffuse intensities into Fourier series was used when optical thickness exceed unity. It was shown that the model predictions agree with the field experiment not only co-polarization but also cross-polarization. For Alaska region, the input snow structure data was obtain by the in situ ground observations, while for Colorado region, we combined the VIC model to get the snow profile. ??2009 IEEE.

Resonant Hall effect under generation of a self-sustaining mode of spin current in nonmagnetic bipolar conductors with identical characters between holes and electrons

NASA Astrophysics Data System (ADS)

Sakai, Masamichi; Takao, Hiraku; Matsunaga, Tomoyoshi; Nishimagi, Makoto; Iizasa, Keitaro; Sakuraba, Takahito; Higuchi, Koji; Kitajima, Akira; Hasegawa, Shigehiko; Nakamura, Osamu; Kurokawa, Yuichiro; Awano, Hiroyuki

2018-03-01

We have proposed an enhancement mechanism of the Hall effect, the signal of which is amplified due to the generation of a sustaining mode of spin current. Our analytic derivations of the Hall resistivity revealed the conditions indispensable for the observation of the effect: (i) the presence of the transverse component of an effective electric field due to spin splitting in chemical potential in addition to the longitudinal component; (ii) the simultaneous presence of holes and electrons each having approximately the same characteristics; (iii) spin-polarized current injection from magnetized electrodes; (iv) the boundary condition for the transverse current (J c, y = 0). The model proposed in this study was experimentally verified by using van der Pauw-type Hall devices consisting of the nonmagnetic bipolar conductor YH x (x ≃ 2) and TbFeCo electrodes. Replacing Au electrodes with TbFeCo electrodes alters the Hall resistivity from the ordinary Hall effect to the anomalous Hall-like effect with an enhancement factor of approximately 50 at 4 T. We interpreted the enhancement phenomenon in terms of the present model.

An Analytical Solution for Transient Thermal Response of an Insulated Structure

NASA Technical Reports Server (NTRS)

Blosser, Max L.

2012-01-01

An analytical solution was derived for the transient response of an insulated aerospace vehicle structure subjected to a simplified heat pulse. This simplified problem approximates the thermal response of a thermal protection system of an atmospheric entry vehicle. The exact analytical solution is solely a function of two non-dimensional parameters. A simpler function of these two parameters was developed to approximate the maximum structural temperature over a wide range of parameter values. Techniques were developed to choose constant, effective properties to represent the relevant temperature and pressure-dependent properties for the insulator and structure. A technique was also developed to map a time-varying surface temperature history to an equivalent square heat pulse. Using these techniques, the maximum structural temperature rise was calculated using the analytical solutions and shown to typically agree with finite element simulations within 10 to 20 percent over the relevant range of parameters studied.

Analytical approximations for spiral waves

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

Löber, Jakob, E-mail: jakob@physik.tu-berlin.de; Engel, Harald

2013-12-15

We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +}more » with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.« less

On the Factor Structure of the Beck Depression Inventory-II: G Is the Key

ERIC Educational Resources Information Center

Brouwer, Danny; Meijer, Rob R.; Zevalkink, Jolien

2013-01-01

The Beck Depression Inventory-II (BDI-II; Beck, Steer, & Brown, 1996) is intended to measure severity of depression, and because items represent a broad range of depressive symptoms, some multidimensionality exists. In recent factor-analytic studies, there has been a debate about whether the BDI-II can be considered as one scale or whether…

The influence of anisotropy on the core structure of Shockley partial dislocations within FCC materials

NASA Astrophysics Data System (ADS)

Szajewski, B. A.; Hunter, A.; Luscher, D. J.; Beyerlein, I. J.

2018-01-01

Both theoretical and numerical models of dislocations often necessitate the assumption of elastic isotropy to retain analytical tractability in addition to reducing computational load. As dislocation based models evolve towards physically realistic material descriptions, the assumption of elastic isotropy becomes increasingly worthy of examination. We present an analytical dislocation model for calculating the full dissociated core structure of dislocations within anisotropic face centered cubic (FCC) crystals as a function of the degree of material elastic anisotropy, two misfit energy densities on the γ-surface ({γ }{{isf}}, {γ }{{usf}}) and the remaining elastic constants. Our solution is independent of any additional features of the γ-surface. Towards this pursuit, we first demonstrate that the dependence of the anisotropic elasticity tensor on the orientation of the dislocation line within the FCC crystalline lattice is small and may be reasonably neglected for typical materials. With this approximation, explicit analytic solutions for the anisotropic elasticity tensor {B} for both nominally edge and screw dislocations within an FCC crystalline lattice are devised, and employed towards defining a set of effective isotropic elastic constants which reproduce fully anisotropic results, however do not retain the bulk modulus. Conversely, Hill averaged elastic constants which both retain the bulk modulus and reasonably approximate the dislocation core structure are employed within subsequent numerical calculations. We examine a wide range of materials within this study, and the features of each partial dislocation core are sufficiently localized that application of discrete linear elasticity accurately describes the separation of each partial dislocation core. In addition, the local features (the partial dislocation core distribution) are well described by a Peierls-Nabarro dislocation model. We develop a model for the displacement profile which depends upon two disparate dislocation length scales which describe the core structure; (i) the equilibrium stacking fault width between two Shockley partial dislocations, R eq and (ii) the maximum slip gradient, χ, of each Shockley partial dislocation. We demonstrate excellent agreement between our own analytic predictions, numerical calculations, and R eq computed directly by both ab-initio and molecular statics methods found elsewhere within the literature. The results suggest that understanding of various plastic mechanisms, e.g., cross-slip and nucleation may be augmented with the inclusion of elastic anisotropy.

Evaluation of Analytical Modeling Functions for the Phonation Onset Process.

PubMed

Petermann, Simon; Kniesburges, Stefan; Ziethe, Anke; Schützenberger, Anne; Döllinger, Michael

2016-01-01

The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO), called the voice onset time (VOT), is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps) was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW) during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1) reliability of the fit function for a correct approximation of VO; (2) consistency represented by the standard deviation of VOT; and (3) accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW.

Development and application of accurate analytical models for single active electron potentials

NASA Astrophysics Data System (ADS)

Miller, Michelle; Jaron-Becker, Agnieszka; Becker, Andreas

2015-05-01

The single active electron (SAE) approximation is a theoretical model frequently employed to study scenarios in which inner-shell electrons may productively be treated as frozen spectators to a physical process of interest, and accurate analytical approximations for these potentials are sought as a useful simulation tool. Density function theory is often used to construct a SAE potential, requiring that a further approximation for the exchange correlation functional be enacted. In this study, we employ the Krieger, Li, and Iafrate (KLI) modification to the optimized-effective-potential (OEP) method to reduce the complexity of the problem to the straightforward solution of a system of linear equations through simple arguments regarding the behavior of the exchange-correlation potential in regions where a single orbital dominates. We employ this method for the solution of atomic and molecular potentials, and use the resultant curve to devise a systematic construction for highly accurate and useful analytical approximations for several systems. Supported by the U.S. Department of Energy (Grant No. DE-FG02-09ER16103), and the U.S. National Science Foundation (Graduate Research Fellowship, Grants No. PHY-1125844 and No. PHY-1068706).

Fibrillar Chromospheric Spicule-Like Counterparts to an EUV and Soft X-Ray Blowout Coronal Jet

NASA Technical Reports Server (NTRS)

Sterling, Alphonse C.; Harra, Louise K.; Moore, Ronald L.

2010-01-01

We observe an erupting jet feature in a solar polar coronal hole, using data from Hinode/SOT, EIS, and XRT, with supplemental data from STEREO/EUVI. From EUV and soft X-ray (SXR) images we identify the erupting feature as a blowout coronal jet: in SXRs it is a jet with bright base, and in EUV it appears as an eruption of relatively cool (approximately 50,000 K) material of horizontal size scale approximately 30" originating from the base of the SXR jet. In SOT Ca II H images the most pronounced analog is a pair of thin (approximately 1") ejections, at the locations of either of the two legs of the erupting EUV jet. These Ca II features eventually rise beyond 45", leaving the SOT field of view, and have an appearance similar to standard spicules except that they are much taller. They have velocities similar to that of "type II" spicules, approximately 100 kilometers per second, and they appear to have spicule-like substructures splitting off from them with horizontal velocity approximately 50 kilometers per second, similar to the velocities of splitting spicules measured by Sterling et al. (2010). Motions of splitting features and of other substructures suggest that the macroscopic EUV jet is spinning or unwinding as it is ejected. This and earlier work suggests that a sub-population of Ca II type II spicules are the Ca II manifestation of portions of larger-scale erupting magnetic jets. A different sub-population of type II spicules could be blowout jets occurring on a much smaller horizontal size scale than the event we observe here.

Proxy-SU(3) symmetry in heavy deformed nuclei

NASA Astrophysics Data System (ADS)

Bonatsos, Dennis; Assimakis, I. E.; Minkov, N.; Martinou, Andriana; Cakirli, R. B.; Casten, R. F.; Blaum, K.

2017-06-01

Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions. Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calculation with the original shell model orbits and with the new proxy set. Method: We invoke an approximate, analytic, treatment of the Nilsson model, that allows the above vetting and yet is also transparent in understanding the approximations involved in the new proxy-SU(3). Results: It is found that the new scheme yields a Nilsson diagram for well-deformed nuclei that is very close to the original Nilsson diagram. The specific levels of approximation in the new scheme are also shown, for each major shell. Conclusions: The new proxy-SU(3) scheme is a good approximation to the full set of orbits in a major shell. Being able to replace a complex shell model calculation with a symmetry-based description now opens up the possibility to predict many properties of nuclei analytically and often in a parameter-free way. The new scheme works best for heavier nuclei, precisely where full microscopic calculations are most challenged. Some cases in which the new scheme can be used, often analytically, to make specific predictions, are shown in a subsequent paper.

Geometries in Soft Matter From Geometric Frustration, Liquid Droplets to Electrostatics in Solution

NASA Astrophysics Data System (ADS)

Yao, Zhenwei

This thesis explores geometric aspects of soft matter systems. The topics covered fall into three categories: (i) geometric frustrations, including the interplay of geometry and topological defects in two dimensional systems, and the frustration of a planar sheet attached to a curved surface; (ii) geometries of liquid droplets, including the curvature driven instabilities of toroidal liquid droplets and the self-propulsion of droplets on a spatially varying surface topography; (iii) the study of the electric double layer structure around charged spherical interfaces by a geometric method. In (i), we study the crystalline order on capillary bridges with varying Gaussian curvature. Energy requires the appearance of topological defects on the surface, which are natural spots for biological activity and chemical functionalization. We further study how liquid crystalline order deforms flexible structured vesicles. In particular we find faceted tetrahedral vesicle as the ground state, which may lead to the design of supra-molecular structures with tetrahedral symmetry and new classes of nano-carriers. Furthermore, by a simple paper model we explore the geometric frustration on a planar sheet when brought to a negative curvature surface in a designed elasto-capillary system. In (ii), motivated by the idea of realizing crystalline order on a stable toroidal droplet and a beautiful experiment on toroidal droplets, we study the Rayleigh instability and the shrinking instability of thin and fat toroidal droplets, where the toroidal geometry plays an essential role. In (iii), by a geometric mapping we construct an approximate analytic spherical solution to the nonlinear Poisson-Boltzmann equation, and identify the applicability regime of the solution. The derived geometric solution enables further analytical study of spherical electrostatic systems such as colloidal suspensions.

Two charges on plane in a magnetic field I. “Quasi-equal” charges and neutral quantum system at rest cases

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

Escobar-Ruiz, M.A., E-mail: mauricio.escobar@nucleares.unam.mx; Turbiner, A.V., E-mail: turbiner@nucleares.unam.mx

Low-lying bound states for the problem of two Coulomb charges of finite masses on a plane subject to a constant magnetic field B perpendicular to the plane are considered. Major emphasis is given to two systems: two charges with the equal charge-to-mass ratio (quasi-equal charges) and neutral systems with concrete results for the hydrogen atom and two electrons (quantum dot). It is shown that for these two cases, when a neutral system is at rest (the center-of-mass momentum is zero), some outstanding properties occur: in double polar coordinates in CMS (R,ϕ) and relative (ρ,φ) coordinate systems (i) the eigenfunctions aremore » factorizable, all factors except for ρ-dependent are found analytically, they have definite relative angular momentum, (ii) dynamics in ρ-direction is the same for both systems being described by a funnel-type potential; (iii) at some discrete values of dimensionless magnetic fields b≤1 the system becomes quasi-exactly-solvable and a finite number of eigenfunctions in ρ are polynomials. The variational method is employed. Trial functions are based on combining for the phase of a wavefunction (a) the WKB expansion at large distances, (b) the perturbation theory at small distances (c) with a form of the known analytically (quasi-exactly-solvable) eigenfunctions. Such a form of trial function appears as a compact uniform approximation for lowest eigenfunctions. For the lowest states with relative magnetic quantum numbers s=0,1,2 this approximation gives not less than 7 s.d., 8 s.d., 9 s.d., respectively, for the total energy E(B) for magnetic fields 0.049a.u.« less

Analytical ground state for the Jaynes-Cummings model with ultrastrong coupling

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

Zhang Yuanwei; Institute of Theoretical Physics, Shanxi University, Taiyuan 030006; Chen Gang

2011-06-15

We present a generalized variational method to analytically obtain the ground-state properties of the Jaynes-Cummings model with the ultrastrong coupling. An explicit expression for the ground-state energy, which agrees well with the numerical simulation in a wide range of the experimental parameters, is given. In particular, the introduced method can successfully solve this Jaynes-Cummings model with the positive detuning (the atomic resonant level is larger than the photon frequency), which cannot be treated in the adiabatical approximation and the generalized rotating-wave approximation. Finally, we also demonstrate analytically how to control the mean photon number by means of the current experimentalmore » parameters including the photon frequency, the coupling strength, and especially the atomic resonant level.« less

Similarity solution of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Lockington, D. A.; Parlange, J.-Y.; Parlange, M. B.; Selker, J.

Similarity transforms of the Boussinesq equation in a semi-infinite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial differential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15-36] use a hodograph method to derive an integral equation formulation of the new differential equation which they solve by numerical iteration. In the present paper, the convergence of their scheme is improved such that numerical iteration can be avoided for all practical purposes. However, a simpler analytical approach is also presented which is based on Shampine's transformation of the boundary value problem to an initial value problem. This analytical approximation is remarkably simple and yet more accurate than the analytical hodograph approximations.

Multivariate test power approximations for balanced linear mixed models in studies with missing data.

PubMed

Ringham, Brandy M; Kreidler, Sarah M; Muller, Keith E; Glueck, Deborah H

2016-07-30

Multilevel and longitudinal studies are frequently subject to missing data. For example, biomarker studies for oral cancer may involve multiple assays for each participant. Assays may fail, resulting in missing data values that can be assumed to be missing completely at random. Catellier and Muller proposed a data analytic technique to account for data missing at random in multilevel and longitudinal studies. They suggested modifying the degrees of freedom for both the Hotelling-Lawley trace F statistic and its null case reference distribution. We propose parallel adjustments to approximate power for this multivariate test in studies with missing data. The power approximations use a modified non-central F statistic, which is a function of (i) the expected number of complete cases, (ii) the expected number of non-missing pairs of responses, or (iii) the trimmed sample size, which is the planned sample size reduced by the anticipated proportion of missing data. The accuracy of the method is assessed by comparing the theoretical results to the Monte Carlo simulated power for the Catellier and Muller multivariate test. Over all experimental conditions, the closest approximation to the empirical power of the Catellier and Muller multivariate test is obtained by adjusting power calculations with the expected number of complete cases. The utility of the method is demonstrated with a multivariate power analysis for a hypothetical oral cancer biomarkers study. We describe how to implement the method using standard, commercially available software products and give example code. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Quantitative Characterization of the Microstructure and Transport Properties of Biopolymer Networks

PubMed Central

Jiao, Yang; Torquato, Salvatore

2012-01-01

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient De and mean survival time τ) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function P(δ) for the networks and present a variety of analytical estimates of the effective diffusion coefficient De for finite-sized diffusing particles, including the low-density approximation, the Ogston approximation, and the Torquato approximation. The Hashin-Strikman upper bound on the effective diffusion coefficient De and the pore-size lower bound on the mean survival time τ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient De as well as the mean survival time τ, which is related to nuclear magnetic resonance (NMR) relaxation times. Our numerical results for De are in excellent agreement with analytical results for simple network microstructures, such as periodic arrays of parallel cylinders. Specifically, the Torquato approximation provides the most accurate estimates of De for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for τ for the networks at different collagen concentrations, extending the work of Yeong and Torquato [J. Chem. Phys. 106, 8814 (1997)]. We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here. The use of cross-property relations to link other physical properties to the transport properties of collagen networks is also discussed. PMID:22683739

Recent Developments in the Speciation and Determination of Mercury Using Various Analytical Techniques

PubMed Central

Suvarapu, Lakshmi Narayana; Baek, Sung-Ok

2015-01-01

This paper reviews the speciation and determination of mercury by various analytical techniques such as atomic absorption spectrometry, voltammetry, inductively coupled plasma techniques, spectrophotometry, spectrofluorometry, high performance liquid chromatography, and gas chromatography. Approximately 126 research papers on the speciation and determination of mercury by various analytical techniques published in international journals since 2013 are reviewed. PMID:26236539

Applications of organo-silica nanocomposites for SPNE of Hg(II)

NASA Astrophysics Data System (ADS)

Kaur, Anupreet

2016-02-01

An analytical method using modified SiO2 nanoparticles as solid-phase extractant has been developed for the preconcentration of trace amounts of Hg(II) in different water samples. Conditions of the analysis such as preconcentration factor, effect of pH, sample volume, shaking time, elution conditions and effects of interfering ions for the recovery of analyte were investigated. The adsorption capacity of nanometer SiO2-APTMS was found to be 181.42 µmol g-1 at optimum pH and the detection limit (3σ) was 0.45 µg L-1. The extractant showed rapid kinetic sorption. The adsorption equilibrium of Hg(II) on nanometer SiO2-APTMS was achieved just in 15 min. Adsorbed Hg(II) was easily eluted with 4 mL of 2.0 M hydrochloric acid. The maximum preconcentration factor was 75. The method was applied for the determination of trace amounts of Hg(II) in various synthetic samples and water samples.

Evolutionary Games of Multiplayer Cooperation on Graphs

PubMed Central

Arranz, Jordi; Traulsen, Arne

2016-01-01

There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering. PMID:27513946

Speciation of Mn(II), Mn(VII) and total manganese in water and food samples by coprecipitation-atomic absorption spectrometry combination.

PubMed

Citak, Demirhan; Tuzen, Mustafa; Soylak, Mustafa

2010-01-15

A speciation procedure based on the coprecipitation of manganese(II) with zirconium(IV) hydroxide has been developed for the investigation of levels of manganese species. The determination of manganese levels was performed by flame atomic absorption spectrometry (FAAS). Total manganese was determined after the reduction of Mn(VII) to Mn(II) by ascorbic acid. The analytical parameters including pH, amount of zirconium(IV), sample volume, etc., were investigated for the quantitative recoveries of manganese(II). The effects of matrix ions were also examined. The recoveries for manganese(II) were in the range of 95-98%. Preconcentration factor was calculated as 50. The detection limit for the analyte ions based on 3 sigma (n=21) was 0.75 microg L(-1) for Mn(II). The relative standard deviation was found to be lower than 7%. The validation of the presented procedure was performed by analysis of certified reference material having different matrices, NIST SRM 1515 (Apple Leaves) and NIST SRM 1568a (Rice Flour). The procedure was successfully applied to natural waters and food samples.

Mercury(II) and methyl mercury determinations in water and fish samples by using solid phase extraction and cold vapour atomic absorption spectrometry combination.

PubMed

Tuzen, Mustafa; Karaman, Isa; Citak, Demirhan; Soylak, Mustafa

2009-07-01

A method has been developed for mercury(II) and methyl mercury speciation on Staphylococcus aureus loaded Dowex Optipore V-493 micro-column in the presented work, by using cold vapour atomic absorption spectrometry. Selective and sequential elution with 0.1 molL(-1) HCl for methyl mercury and 2 molL(-1) HCl for mercury(II) were performed at the pH range of 2-6. Optimal analytical conditions including pH, amounts of biosorbent, sample volumes were investigated. The detection limits of the analytes were 2.5 ngL(-1) for Hg(II) and 1.7 ngL(-1) for methyl mercury. The capacity of biosorbent for mercury(II) and methyl mercury was 6.5 and 5.4 mgg(-1), respectively. The validation of the presented procedure is performed by the analysis of standard reference material. The speciation procedure established was successfully applied to the speciation of mercury(II) and methyl mercury in natural water and microwave digested fish samples.

Analytical Chemistry of Surfaces: Part II. Electron Spectroscopy.

ERIC Educational Resources Information Center

Hercules, David M.; Hercules, Shirley H.

1984-01-01

Discusses two surface techniques: X-ray photoelectron spectroscopy (ESCA) and Auger electron spectroscopy (AES). Focuses on fundamental aspects of each technique, important features of instrumentation, and some examples of how ESCA and AES have been applied to analytical surface problems. (JN)

The existence and abundance of ghost ancestors in biparental populations.

PubMed

Gravel, Simon; Steel, Mike

2015-05-01

In a randomly-mating biparental population of size N there are, with high probability, individuals who are genealogical ancestors of every extant individual within approximately log2(N) generations into the past. We use this result of J. Chang to prove a curious corollary under standard models of recombination: there exist, with high probability, individuals within a constant multiple of log2(N) generations into the past who are simultaneously (i) genealogical ancestors of each of the individuals at the present, and (ii) genetic ancestors to none of the individuals at the present. Such ancestral individuals-ancestors of everyone today that left no genetic trace-represent 'ghost' ancestors in a strong sense. In this short note, we use simple analytical argument and simulations to estimate how many such individuals exist in finite Wright-Fisher populations. Copyright © 2015 Elsevier Inc. All rights reserved.

Positron production in heavy-ion collisions. II. Application of the formalism to the case of the U+U collision

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

Tomoda, T.

1982-07-01

The method developed in the preceding paper is applied to the calculation of the spectra of positrons produced in the U + U collision. Matrix elements of the radial derivative operator between adiabatic basis states are calculated in the monopole approximation, with the finite nuclear size taken into account. These matrix elements are then modified for the supercritical case with the use of the analytical method presented in paper I of this series. The coupled differential equations for the occupation amplitudes of the basis states are solved and the positron spectra are obtained for the U + U collision. Itmore » is shown that the decomposition of the production probability into a spontaneous and an induced part depends on the definition of the resonance state and cannot be given unambiguously. The results are compared with those obtained by Reinhardt et al.« less

Predictive data modeling of human type II diabetes related statistics

NASA Astrophysics Data System (ADS)

Jaenisch, Kristina L.; Jaenisch, Holger M.; Handley, James W.; Albritton, Nathaniel G.

2009-04-01

During the course of routine Type II treatment of one of the authors, it was decided to derive predictive analytical Data Models of the daily sampled vital statistics: namely weight, blood pressure, and blood sugar, to determine if the covariance among the observed variables could yield a descriptive equation based model, or better still, a predictive analytical model that could forecast the expected future trend of the variables and possibly eliminate the number of finger stickings required to montior blood sugar levels. The personal history and analysis with resulting models are presented.

Formic Acid: Development of an Analytical Method and Use as Process Indicator in Anaerobic Systems

DTIC Science & Technology

1992-03-01

distilled to remove compounds such as cinnamic , glycolic and levulinic acids which can be oxidized to formic acid by ceric sulfate, thus interfering...I AD-A250 668 D0 ,I I I 111 Wl’i ill EDT|CS ELECTE MAY 27 1992 I C I FORMIC ACID : DEVELCPMENT OF AN ANALYTICAL METHOD AND USE AS A PROCESS INDICATOR...OF TECHNOLOGY A UNIT OF THE UNIVERSITY SYSTEM OF GEORGIA SCHOOL OF CIVIL ENGINEERING ATLANTA, GEORGIA 30332 iIi ii FORMIC ACID : DEVELOPMENT OF AN

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1988-01-01

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

On the first crossing distributions in fractional Brownian motion and the mass function of dark matter haloes

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

Hiotelis, Nicos; Popolo, Antonino Del, E-mail: adelpopolo@oact.inaf.it, E-mail: hiotelis@ipta.demokritos.gr

We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions derived by simulating paths from fractional Brownian motion. We compare the results of the analytical solutions with both those of simulations and those of some approximated solutions which have been used in the literature. Finally, we present multiplicity functions for dark matter structures resulting from our analytical approach and we compare with those resulting from N-body simulations. We show that the results of analytical solutions aremore » in good agreement with those of path simulations but differ significantly from those derived from approximated solutions. Additionally, multiplicity functions derived from fractional Brownian motion are poor fits of the those which result from N-body simulations. We also present comparisons with other models which are exist in the literature and we discuss different ways of improving the agreement between analytical results and N-body simulations.« less

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was recently built using the OpenMDAO framework. This tool uses equilibrium chemistry based thermodynamics, and provides analytic derivatives. This allows for stable and efficient use of gradient-based optimization and sensitivity analysis methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a multi-point turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Fractional Fourier transform of truncated elliptical Gaussian beams.

PubMed

Du, Xinyue; Zhao, Daomu

2006-12-20

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

Periodized Daubechies wavelets

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

Restrepo, J.M.; Leaf, G.K.; Schlossnagle, G.

1996-03-01

The properties of periodized Daubechies wavelets on [0,1] are detailed and counterparts which form a basis for L{sup 2}(R). Numerical examples illustrate the analytical estimates for convergence and demonstrated by comparison with Fourier spectral methods the superiority of wavelet projection methods for approximations. The analytical solution to inner products of periodized wavelets and their derivatives, which are known as connection coefficients, is presented, and their use ius illustrated in the approximation of two commonly used differential operators. The periodization of the connection coefficients in Galerkin schemes is presented in detail.

2D/3D image charge for modeling field emission

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

Jensen, Kevin L.; Shiffler, Donald A.; Harris, John R.

Analytic image charge approximations exist for planar and spherical metal surfaces but approximations for more complex geometries, such as the conical and wirelike structures characteristic of field emitters, are lacking. Such models are the basis for the evaluation of Schottky lowering factors in equations for current density. The development of a multidimensional image charge approximation, useful for a general thermal-field emission equation used in space charge studies, is given and based on an analytical model using a prolate spheroidal geometry. A description of how the model may be adapted to be used with a line charge model appropriate for carbonmore » nanotube and carbon fiber field emitters is discussed. [http://dx.doi.org/10.1116/1.4968007]« less

2D/3D image charge for modeling field emission

DOE PAGES

Jensen, Kevin L.; Shiffler, Donald A.; Harris, John R.; ...

2017-03-01

Analytic image charge approximations exist for planar and spherical metal surfaces but approximations for more complex geometries, such as the conical and wirelike structures characteristic of field emitters, are lacking. Such models are the basis for the evaluation of Schottky lowering factors in equations for current density. The development of a multidimensional image charge approximation, useful for a general thermal-field emission equation used in space charge studies, is given and based on an analytical model using a prolate spheroidal geometry. A description of how the model may be adapted to be used with a line charge model appropriate for carbonmore » nanotube and carbon fiber field emitters is discussed. [http://dx.doi.org/10.1116/1.4968007]« less

Hybrid perturbation methods based on statistical time series models

NASA Astrophysics Data System (ADS)

San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario

2016-04-01

In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.

Analysis of the impacts of horizontal translation and scaling on wavefront approximation coefficients with rectangular pupils for Chebyshev and Legendre polynomials.

PubMed

Sun, Wenqing; Chen, Lei; Tuya, Wulan; He, Yong; Zhu, Rihong

2013-12-01

Chebyshev and Legendre polynomials are frequently used in rectangular pupils for wavefront approximation. Ideally, the dataset completely fits with the polynomial basis, which provides the full-pupil approximation coefficients and the corresponding geometric aberrations. However, if there are horizontal translation and scaling, the terms in the original polynomials will become the linear combinations of the coefficients of the other terms. This paper introduces analytical expressions for two typical situations after translation and scaling. With a small translation, first-order Taylor expansion could be used to simplify the computation. Several representative terms could be selected as inputs to compute the coefficient changes before and after translation and scaling. Results show that the outcomes of the analytical solutions and the approximated values under discrete sampling are consistent. With the computation of a group of randomly generated coefficients, we contrasted the changes under different translation and scaling conditions. The larger ratios correlate the larger deviation from the approximated values to the original ones. Finally, we analyzed the peak-to-valley (PV) and root mean square (RMS) deviations from the uses of the first-order approximation and the direct expansion under different translation values. The results show that when the translation is less than 4%, the most deviated 5th term in the first-order 1D-Legendre expansion has a PV deviation less than 7% and an RMS deviation less than 2%. The analytical expressions and the computed results under discrete sampling given in this paper for the multiple typical function basis during translation and scaling in the rectangular areas could be applied in wavefront approximation and analysis.

Controlling false-negative errors in microarray differential expression analysis: a PRIM approach.

PubMed

Cole, Steve W; Galic, Zoran; Zack, Jerome A

2003-09-22

Theoretical considerations suggest that current microarray screening algorithms may fail to detect many true differences in gene expression (Type II analytic errors). We assessed 'false negative' error rates in differential expression analyses by conventional linear statistical models (e.g. t-test), microarray-adapted variants (e.g. SAM, Cyber-T), and a novel strategy based on hold-out cross-validation. The latter approach employs the machine-learning algorithm Patient Rule Induction Method (PRIM) to infer minimum thresholds for reliable change in gene expression from Boolean conjunctions of fold-induction and raw fluorescence measurements. Monte Carlo analyses based on four empirical data sets show that conventional statistical models and their microarray-adapted variants overlook more than 50% of genes showing significant up-regulation. Conjoint PRIM prediction rules recover approximately twice as many differentially expressed transcripts while maintaining strong control over false-positive (Type I) errors. As a result, experimental replication rates increase and total analytic error rates decline. RT-PCR studies confirm that gene inductions detected by PRIM but overlooked by other methods represent true changes in mRNA levels. PRIM-based conjoint inference rules thus represent an improved strategy for high-sensitivity screening of DNA microarrays. Freestanding JAVA application at http://microarray.crump.ucla.edu/focus

ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. II. LAMB, SURFACE, AND CENTRIFUGAL WAVES

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

Peralta, J.; López-Valverde, M. A.; Imamura, T.

2014-07-01

This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the backgroundmore » wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.« less

The Transient Dermal Exposure II: Post-Exposure Absorption and Evaporation of Volatile Compounds

PubMed Central

FRASCH, H. FREDERICK; BUNGE, ANNETTE L.

2016-01-01

The transient dermal exposure is one where the skin is exposed to chemical for a finite duration, after which the chemical is removed and no residue remains on the skin’s surface. Chemical within the skin at the end of the exposure period can still enter the systemic circulation. If it has some volatility, a portion of it will evaporate from the surface before it has a chance to be absorbed by the body. The fate of this post-exposure “skin depot” is the focus of this theoretical study. Laplace domain solutions for concentration distribution, flux, and cumulative mass absorption and evaporation are presented, and time domain results are obtained through numerical inversion. The Final Value Theorem is applied to obtain the analytical solutions for the total fractional absorption by the body and evaporation from skin at infinite time following a transient exposure. The solutions depend on two dimensionless variables: χ, the ratio of evaporation rate to steady-state dermal permeation rate; and the ratio of exposure time to membrane lag time. Simple closed form algebraic equations are presented that closely approximate the complete analytical solutions. Applications of the theory to the dermal risk assessment of pharmaceutical, occupational, and environmental exposures are presented for four example chemicals. PMID:25611182

Protein C and protein S deficiencies: similarities and differences between two brothers playing in the same game.

PubMed

Bereczky, Zsuzsanna; Kovács, Kitti B; Muszbek, László

2010-12-01

Protein C (PC) and protein S (PS) are vitamin K-dependent glycoproteins that play an important role in the regulation of blood coagulation as natural anticoagulants. PC is activated by thrombin and the resulting activated PC (APC) inactivates membrane-bound activated factor VIII and factor V. The free form of PS is an important cofactor of APC. Deficiencies in these proteins lead to an increased risk of venous thromboembolism; a few reports have also associated these deficiencies with arterial diseases. The degree of risk and the prevalence of PC and PS deficiency among patients with thrombosis and in those in the general population have been examined by several population studies with conflicting results, primarily due to methodological variability. The molecular genetic background of PC and PS deficiencies is heterogeneous. Most of the mutations cause type I deficiency (quantitative disorder). Type II deficiency (dysfunctional molecule) is diagnosed in approximately 5%-15% of cases. The diagnosis of PC and PS deficiencies is challenging; functional tests are influenced by several pre-analytical and analytical factors, and the diagnosis using molecular genetics also has special difficulties. Large gene segment deletions often remain undetected by DNA sequencing methods. The presence of the PS pseudogene makes genetic diagnosis even more complicated.

Soliton polarization rotation in fiber lasers

NASA Astrophysics Data System (ADS)

Afanasjev, V. V.

1995-02-01

I have found the approximate analytical solution in explicit form for a vector soliton with an arbitrary component ratio. My solution describes the dependence of soliton intensity on polarization angle and also nonlinear polarization rotation. The analytical results agree well with the numerical simulations.

Goal-Oriented Probability Density Function Methods for Uncertainty Quantification

DTIC Science & Technology

2015-12-11

approximations or data-driven approaches. We investigated the accuracy of analytical tech- niques based Kubo -Van Kampen operator cumulant expansions for...analytical techniques based Kubo -Van Kampen operator cumulant expansions for Langevin equations driven by fractional Brownian motion and other noises

Experimental and Analytical Studies of Shielding Concepts for Point Sources and Jet Noises.

NASA Astrophysics Data System (ADS)

Wong, Raymond Lee Man

This analytical and experimental study explores concepts for jet noise shielding. Model experiments centre on solid planar shields, simulating engine-over-wing installations, and 'sugar scoop' shields. Tradeoff on effective shielding length is set by interference 'edge noise' as the shield trailing edge approaches the spreading jet. Edge noise is minimized by (i) hyperbolic cutouts which trim off the portions of most intense interference between the jet flow and the barrier and (ii) hybrid shields--a thermal refractive extension (a flame); for (ii) the tradeoff is combustion noise. In general, shielding attenuation increases steadily with frequency, following low frequency enhancement by edge noise. Although broadband attenuation is typically only several dB, the reduction of the subjectively weighted perceived noise levels is higher. In addition, calculated ground contours of peak PN dB show a substantial contraction due to shielding: this reaches 66% for one of the 'sugar scoop' shields for the 90 PN dB contour. The experiments are complemented by analytical predictions. They are divided into an engineering scheme for jet noise shielding and more rigorous analysis for point source shielding. The former approach combines point source shielding with a suitable jet source distribution. The results are synthesized into a predictive algorithm for jet noise shielding: the jet is modelled as a line distribution of incoherent sources with narrow band frequency (TURN)(axial distance)('-1). The predictive version agrees well with experiment (1 to 1.5 dB) up to moderate frequencies. The insertion loss deduced from the point source measurements for semi-infinite as well as finite rectangular shields agrees rather well with theoretical calculation based on the exact half plane solution and the superposition of asymptotic closed-form solutions. An approximate theory, the Maggi-Rubinowicz line integral, is found to yield reasonable predictions for thin barriers including cutouts if a certain correction is applied. The more exact integral equation approach (solved numerically) is applied to a more demanding geometry: a half round sugar scoop shield. It is found that the solutions of integral equation derived from Helmholtz formula in normal derivative form show satisfactory agreement with measurements.

Basic physical processes and reduced models for plasma detachment

NASA Astrophysics Data System (ADS)

Stangeby, P. C.

2018-04-01

The divertor of a tokamak reactor will have to satisfy a number of critical constraints, the first of which is that the divertor targets not fail due to excessive heating or sputter-erosion. This paramount constraint of target survival defines the operating window for the principal plasma properties at the divertor target, the density n t and temperature, T t. In particular T et < 10 eV is shown to be required. Code and experimental studies show that the pressure–momentum loss by the plasma that occurs along flux tubes in the edge, between the divertor entrance and target, (i) correlates strongly with T et, and (ii) begins to increase as T et falls below 10 eV, becoming very strong by 1 eV. The transition between the high-recycling regime and the detached divertor regime has therefore been defined here to occur when T et < 10 eV. Simple analytic models are developed (i) to relate (T t, n t) to the controlling conditions ‘upstream’ e.g. at the divertor entrance, and (ii) in turn to relate (T t, n t) to other important divertor quantities including (a) the required level of radiative cooling in the divertor, and (b) the ion flux to the target in the presence of volumetric loss of particles, momentum and power in the divertor. The 2 Point Model, 2PM, is a widely used analytic model for relating (T t, n t) to the controlling upstream conditions. The 2PM is derived here for various levels of complexity regarding the effects included. Analytic models of divertor detachment provide valuable insight and useful approximations, but more complete modeling requires the use of edge codes such as EDGE2D, SOLPS, SONIC, UEDGE, etc. Edge codes have grown to become quite sophisticated and now constitute, in effect, ‘code-experiments’ that—just as for actual experiments—can benefit from interpretation in terms of simple conceptual frameworks. 2 Point Model Formatting, 2PMF, of edge code output can provide such a conceptual framework. Methods of applying 2PMF are illustrated here with some examples.

Demonstration/Validation of the Snap Sampler Passive Ground Water Sampling Device for Sampling Inorganic Analytes at the Former Pease Air Force Base

DTIC Science & Technology

2009-07-01

viii Unit Conversion Factors...sampler is also an economic alternative for sampling for inorganic analytes. ERDC/CRREL TR-09-12 xii Unit Conversion Factors Multiply By To Obtain...head- space and then covered with two layers of tightly fitting aluminum foil. To dissolve the analytes, the solutions were stirred for approximately

Sampling of illicit drugs for quantitative analysis--part II. Study of particle size and its influence on mass reduction.

PubMed

Bovens, M; Csesztregi, T; Franc, A; Nagy, J; Dujourdy, L

2014-01-01

The basic goal in sampling for the quantitative analysis of illicit drugs is to maintain the average concentration of the drug in the material from its original seized state (the primary sample) all the way through to the analytical sample, where the effect of particle size is most critical. The size of the largest particles of different authentic illicit drug materials, in their original state and after homogenisation, using manual or mechanical procedures, was measured using a microscope with a camera attachment. The comminution methods employed included pestle and mortar (manual) and various ball and knife mills (mechanical). The drugs investigated were amphetamine, heroin, cocaine and herbal cannabis. It was shown that comminution of illicit drug materials using these techniques reduces the nominal particle size from approximately 600 μm down to between 200 and 300 μm. It was demonstrated that the choice of 1 g increments for the primary samples of powdered drugs and cannabis resin, which were used in the heterogeneity part of our study (Part I) was correct for the routine quantitative analysis of illicit seized drugs. For herbal cannabis we found that the appropriate increment size was larger. Based on the results of this study we can generally state that: An analytical sample weight of between 20 and 35 mg of an illicit powdered drug, with an assumed purity of 5% or higher, would be considered appropriate and would generate an RSDsampling in the same region as the RSDanalysis for a typical quantitative method of analysis for the most common, powdered, illicit drugs. For herbal cannabis, with an assumed purity of 1% THC (tetrahydrocannabinol) or higher, an analytical sample weight of approximately 200 mg would be appropriate. In Part III we will pull together our homogeneity studies and particle size investigations and use them to devise sampling plans and sample preparations suitable for the quantitative instrumental analysis of the most common illicit drugs. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Synthesis, characterisation and analytical application of Fe₃O₄@SiO₂@polyaminoquinoline magnetic nanocomposite for the extraction and pre-concentration of Cd(II) and Pb(II) in food samples.

PubMed

Manoochehri, Mahboobeh; Asgharinezhad, Ali Akbar; Shekari, Nafiseh

2015-01-01

This work describes a novel Fe₃O₄@SiO₂@polyaminoquinoline magnetic nanocomposite and its application in the pre-concentration of Cd(II) and Pb(II) ions. The parameters affecting the pre-concentration procedure were optimised by a Box-Behnken design through response surface methodology. Three variables (extraction time, magnetic sorbent amount and pH) were selected as the main factors affecting the sorption step, while four variables (type, volume and concentration of the eluent, and elution time) were selected as main factors in the optimisation study of the elution step. Following the sorption and elution of analytes, the ions were quantified by flame atomic absorption spectrometry (FASS). The limits of detection were 0.1 and 0.7 ng ml(-1) for Cd(II) and Pb(II) ions, respectively. All the relative standard deviations were less than 7.6%. The sorption capacities of this new sorbent were 57 mg g(-)(1) for Cd(II) and 73 mg g(-1) for Pb(II). Ultimately, this nanocomposite was successfully applied to the rapid extraction of trace quantities of these heavy metal ions from seafood and agricultural samples and satisfactory results were obtained.

Stochastic dynamics and mechanosensitivity of myosin II minifilaments

NASA Astrophysics Data System (ADS)

Albert, Philipp J.; Erdmann, Thorsten; Schwarz, Ulrich S.

2014-09-01

Tissue cells are in a state of permanent mechanical tension that is maintained mainly by myosin II minifilaments, which are bipolar assemblies of tens of myosin II molecular motors contracting actin networks and bundles. Here we introduce a stochastic model for myosin II minifilaments as two small myosin II motor ensembles engaging in a stochastic tug-of-war. Each of the two ensembles is described by the parallel cluster model that allows us to use exact stochastic simulations and at the same time to keep important molecular details of the myosin II cross-bridge cycle. Our simulation and analytical results reveal a strong dependence of myosin II minifilament dynamics on environmental stiffness that is reminiscent of the cellular response to substrate stiffness. For small stiffness, minifilaments form transient crosslinks exerting short spikes of force with negligible mean. For large stiffness, minifilaments form near permanent crosslinks exerting a mean force which hardly depends on environmental elasticity. This functional switch arises because dissociation after the power stroke is suppressed by force (catch bonding) and because ensembles can no longer perform the power stroke at large forces. Symmetric myosin II minifilaments perform a random walk with an effective diffusion constant which decreases with increasing ensemble size, as demonstrated for rigid substrates with an analytical treatment.

Physics of cosmological cascades and observable properties

NASA Astrophysics Data System (ADS)

Fitoussi, T.; Belmont, R.; Malzac, J.; Marcowith, A.; Cohen-Tanugi, J.; Jean, P.

2017-04-01

TeV photons from extragalactic sources are absorbed in the intergalactic medium and initiate electromagnetic cascades. These cascades offer a unique tool to probe the properties of the universe at cosmological scales. We present a new Monte Carlo code dedicated to the physics of such cascades. This code has been tested against both published results and analytical approximations, and is made publicly available. Using this numerical tool, we investigate the main cascade properties (spectrum, halo extension and time delays), and study in detail their dependence on the physical parameters (extragalactic magnetic field, extragalactic background light, source redshift, source spectrum and beaming emission). The limitations of analytical solutions are emphasized. In particular, analytical approximations account only for the first generation of photons and higher branches of the cascade tree are neglected.

User's Guide To CHEAP0 II-Economic Analysis of Stand Prognosis Model Outputs

Treesearch

Joseph E. Horn; E. Lee Medema; Ervin G. Schuster

1986-01-01

CHEAP0 II provides supplemental economic analysis capability for users of version 5.1 of the Stand Prognosis Model, including recent regeneration and insect outbreak extensions. Although patterned after the old CHEAP0 model, CHEAP0 II has more features and analytic capabilities, especially for analysis of existing and uneven-aged stands....

THEORETICAL METHODS FOR COMPUTING ELECTRICAL CONDITIONS IN WIRE-PLATE ELECTROSTATIC PRECIPITATORS

EPA Science Inventory

The paper describes a new semi-empirical, approximate theory for predicting electrical conditions. In the approximate theory, analytical expressions are derived for calculating voltage-current characteristics and electric potential, electric field, and space charge density distri...

10 CFR 431.445 - Determination of small electric motor efficiency.

Code of Federal Regulations, 2012 CFR

2012-01-01

... statistical analysis, computer simulation or modeling, or other analytic evaluation of performance data. (3... statistical analysis, computer simulation or modeling, and other analytic evaluation of performance data on.... (ii) If requested by the Department, the manufacturer shall conduct simulations to predict the...

The Genetic Basis of Phenotypic Adaptation II: The Distribution of Adaptive Substitutions in the Moving Optimum Model

PubMed Central

Kopp, Michael; Hermisson, Joachim

2009-01-01

We consider a population that adapts to a gradually changing environment. Our aim is to describe how ecological and genetic factors combine to determine the genetic basis of adaptation. Specifically, we consider the evolution of a polygenic trait that is under stabilizing selection with a moving optimum. The ecological dynamics are defined by the strength of selection, \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\usepackage[Euler]{upgreek} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{\\tilde {{\\sigma}}}}\\end{equation*}\\end{document}, and the speed of the optimum, \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\usepackage[Euler]{upgreek} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}\\tilde {{\\upsilon}}\\end{equation*}\\end{document}; the key genetic parameters are the mutation rate Θ and the variance of the effects of new mutations, ω. We develop analytical approximations within an “adaptive-walk” framework and describe how selection acts as a sieve that transforms a given distribution of new mutations into the distribution of adaptive substitutions. Our analytical results are complemented by individual-based simulations. We find that (i) the ecological dynamics have a strong effect on the distribution of adaptive substitutions and their impact depends largely on a single composite measure \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\usepackage[Euler]{upgreek} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}{\\mathrm{{\\gamma}}}=\\tilde {{\\upsilon}}/({\\mathrm{\\tilde {{\\sigma}}}}{\\Theta}{\\mathrm{{\\omega}}}^{3})\\end{equation*}\\end{document}, which combines the ecological and genetic parameters; (ii) depending on γ, we can distinguish two distinct adaptive regimes: for large γ the adaptive process is mutation limited and dominated by genetic constraints, whereas for small γ it is environmentally limited and dominated by the external ecological dynamics; (iii) deviations from the adaptive-walk approximation occur for large mutation rates, when different mutant alleles interact via linkage or epistasis; and (iv) in contrast to predictions from previous models assuming constant selection, the distribution of adaptive substitutions is generally not exponential. PMID:19805820

Investigating the two-moment characterisation of subcellular biochemical networks.

PubMed

Ullah, Mukhtar; Wolkenhauer, Olaf

2009-10-07

While ordinary differential equations (ODEs) form the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise. The most common formulation of stochastic models for biochemical networks is the chemical master equation (CME). While stochastic simulations are a practical way to realise the CME, analytical approximations offer more insight into the influence of noise. Towards that end, the two-moment approximation (2MA) is a promising addition to the established analytical approaches including the chemical Langevin equation (CLE) and the related linear noise approximation (LNA). The 2MA approach directly tracks the mean and (co)variance which are coupled in general. This coupling is not obvious in CME and CLE and ignored by LNA and conventional ODE models. We extend previous derivations of 2MA by allowing (a) non-elementary reactions and (b) relative concentrations. Often, several elementary reactions are approximated by a single step. Furthermore, practical situations often require the use of relative concentrations. We investigate the applicability of the 2MA approach to the well-established fission yeast cell cycle model. Our analytical model reproduces the clustering of cycle times observed in experiments. This is explained through multiple resettings of M-phase promoting factor (MPF), caused by the coupling between mean and (co)variance, near the G2/M transition.

Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter

NASA Astrophysics Data System (ADS)

Bisnovatyi-Kogan, G. S.; Glushikhina, M. V.

2018-04-01

The solution of Boltzmann equation for plasma in magnetic field with arbitrarily degenerate electrons and nondegenerate nuclei is obtained by Chapman-Enskog method. Functions generalizing Sonine polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in nonquantized magnetic field is calculated. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained and compared with results of previous authors. The Lorentz approximation with neglecting of electron-electron encounters is asymptotically exact for strongly degenerate plasma. For the first time, analytical expressions for the heat conductivity tensor for nondegenerate electrons in the presence of a magnetic field are obtained in the three-polynomial approximation with account of electron-electron collisions. Account of the third polynomial improved substantially the precision of results. In the two-polynomial approximation, the obtained solution coincides with the published results. For strongly degenerate electrons, an asymptotically exact analytical solution for the heat conductivity tensor in the presence of a magnetic field is obtained for the first time. This solution has a considerably more complicated dependence on the magnetic field than those in previous publications and gives a several times smaller relative value of the thermal conductivity across the magnetic field at ωτ * 0.8.

Coordinate downregulation of CaM kinase II and phospholamban accompanies contractile phenotype transition in the hyperthyroid rabbit soleus.

PubMed

Jiang, M; Xu, A; Jones, D L; Narayanan, N

2004-09-01

This study investigated the effects of l-thyroxine-induced hyperthyroidism on Ca(2+)/calmodulin (CaM)-dependent protein kinase (CaM kinase II)-mediated sarcoplasmic reticulum (SR) protein phosphorylation, SR Ca(2+) pump (Ca(2+)-ATPase) activity, and contraction duration in slow-twitch soleus muscle of the rabbit. Phosphorylation of Ca(2+)-ATPase and phospholamban (PLN) by endogenous CaM kinase II was found to be significantly lower (30-50%) in soleus of the hyperthyroid compared with euthyroid rabbit. Western blotting analysis revealed higher levels of sarco(endo)plasmic reticulum Ca(2+)-ATPase (SERCA) 1 ( approximately 150%) Ca(2+) pump isoform, unaltered levels of SERCA2 Ca(2+) pump isoform, and lower levels of PLN ( approximately 50%) and delta-, beta-, and gamma-CaM kinase II (40 approximately 70%) in soleus of the hyperthyroid rabbit. SR vesicles from hyperthyroid rabbit soleus displayed approximately twofold higher ATP-energized Ca(2+) uptake and Ca(2+)-stimulated ATPase activities compared with that from euthyroid control. The V(max) of Ca(2+) uptake (in nmol Ca(2+).mg SR protein(-1).min(-1): euthyroid, 818 +/- 73; hyperthyroid, 1,649 +/- 90) but not the apparent affinity of the Ca(2+)-ATPase for Ca(2+) (euthyroid, 0.97 +/- 0.02 microM, hyperthyroid, 1.09 +/- 0.04 microM) differed significantly between the two groups. CaM kinase II-mediated stimulation of Ca(2+) uptake by soleus muscle SR was approximately 60% lower in the hyperthyroid compared with euthyroid. Isometric twitch force of soleus measured in situ was significantly greater ( approximately 36%), and the time to peak force and relaxation time were significantly lower ( approximately 30-40%), in the hyperthyroid. These results demonstrate that thyroid hormone-induced transition in contractile properties of the rabbit soleus is associated with coordinate downregulation of the expression and function of PLN and CaM kinase II and selective upregulation of the expression and function of SERCA1, but not SERCA2, isoform of the SR Ca(2+) pump.

Noise Certification Predictions for FJX-2-Powered Aircraft Using Analytic Methods

NASA Technical Reports Server (NTRS)

Berton, Jeffrey J.

1999-01-01

Williams International Co. is currently developing the 700-pound thrust class FJX-2 turbofan engine for the general Aviation Propulsion Program's Turbine Engine Element. As part of the 1996 NASA-Williams cooperative working agreement, NASA agreed to analytically calculate the noise certification levels of the FJX-2-powered V-Jet II test bed aircraft. Although the V-Jet II is a demonstration aircraft that is unlikely to be produced and certified, the noise results presented here may be considered to be representative of the noise levels of small, general aviation jet aircraft that the FJX-2 would power. A single engine variant of the V-Jet II, the V-Jet I concept airplane, is also considered. Reported in this paper are the analytically predicted FJX-2/V-Jet noise levels appropriate for Federal Aviation Regulation certification. Also reported are FJX-2/V-Jet noise levels using noise metrics appropriate for the propeller-driven aircraft that will be its major market competition, as well as a sensitivity analysis of the certification noise levels to major system uncertainties.

Effect of coulomb spline on rotor dynamic response

NASA Technical Reports Server (NTRS)

Nataraj, C.; Nelson, H. D.; Arakere, N.

1985-01-01

A rigid rotor system coupled by a coulomb spline is modelled and analyzed by approximate analytical and numerical analytical methods. Expressions are derived for the variables of the resulting limit cycle and are shown to be quite accurate for a small departure from isotropy.

An outer approximation method for the road network design problem

PubMed Central

2018-01-01

Best investment in the road infrastructure or the network design is perceived as a fundamental and benchmark problem in transportation. Given a set of candidate road projects with associated costs, finding the best subset with respect to a limited budget is known as a bilevel Discrete Network Design Problem (DNDP) of NP-hard computationally complexity. We engage with the complexity with a hybrid exact-heuristic methodology based on a two-stage relaxation as follows: (i) the bilevel feature is relaxed to a single-level problem by taking the network performance function of the upper level into the user equilibrium traffic assignment problem (UE-TAP) in the lower level as a constraint. It results in a mixed-integer nonlinear programming (MINLP) problem which is then solved using the Outer Approximation (OA) algorithm (ii) we further relax the multi-commodity UE-TAP to a single-commodity MILP problem, that is, the multiple OD pairs are aggregated to a single OD pair. This methodology has two main advantages: (i) the method is proven to be highly efficient to solve the DNDP for a large-sized network of Winnipeg, Canada. The results suggest that within a limited number of iterations (as termination criterion), global optimum solutions are quickly reached in most of the cases; otherwise, good solutions (close to global optimum solutions) are found in early iterations. Comparative analysis of the networks of Gao and Sioux-Falls shows that for such a non-exact method the global optimum solutions are found in fewer iterations than those found in some analytically exact algorithms in the literature. (ii) Integration of the objective function among the constraints provides a commensurate capability to tackle the multi-objective (or multi-criteria) DNDP as well. PMID:29590111

Generalized approximate spin projection calculations of effective exchange integrals of the CaMn4O5 cluster in the S1 and S3 states of the oxygen evolving complex of photosystem II.

PubMed

Isobe, H; Shoji, M; Yamanaka, S; Mino, H; Umena, Y; Kawakami, K; Kamiya, N; Shen, J-R; Yamaguchi, K

2014-06-28

Full geometry optimizations followed by the vibrational analysis were performed for eight spin configurations of the CaMn4O4X(H2O)3Y (X = O, OH; Y = H2O, OH) cluster in the S1 and S3 states of the oxygen evolution complex (OEC) of photosystem II (PSII). The energy gaps among these configurations obtained by vertical, adiabatic and adiabatic plus zero-point-energy (ZPE) correction procedures have been used for computation of the effective exchange integrals (J) in the spin Hamiltonian model. The J values are calculated by the (1) analytical method and the (2) generalized approximate spin projection (AP) method that eliminates the spin contamination errors of UB3LYP solutions. Using J values derived from these methods, exact diagonalization of the spin Hamiltonian matrix was carried out, yielding excitation energies and spin densities of the ground and lower-excited states of the cluster. The obtained results for the right (R)- and left (L)-opened structures in the S1 and S3 states are found to be consistent with available optical and magnetic experimental results. Implications of the computational results are discussed in relation to (a) the necessity of the exact diagonalization for computations of reliable energy levels, (b) magneto-structural correlations in the CaMn4O5 cluster of the OEC of PSII, (c) structural symmetry breaking in the S1 and S3 states, and (d) the right- and left-handed scenarios for the O-O bond formation for water oxidation.

An outer approximation method for the road network design problem.

PubMed

Asadi Bagloee, Saeed; Sarvi, Majid

2018-01-01

Best investment in the road infrastructure or the network design is perceived as a fundamental and benchmark problem in transportation. Given a set of candidate road projects with associated costs, finding the best subset with respect to a limited budget is known as a bilevel Discrete Network Design Problem (DNDP) of NP-hard computationally complexity. We engage with the complexity with a hybrid exact-heuristic methodology based on a two-stage relaxation as follows: (i) the bilevel feature is relaxed to a single-level problem by taking the network performance function of the upper level into the user equilibrium traffic assignment problem (UE-TAP) in the lower level as a constraint. It results in a mixed-integer nonlinear programming (MINLP) problem which is then solved using the Outer Approximation (OA) algorithm (ii) we further relax the multi-commodity UE-TAP to a single-commodity MILP problem, that is, the multiple OD pairs are aggregated to a single OD pair. This methodology has two main advantages: (i) the method is proven to be highly efficient to solve the DNDP for a large-sized network of Winnipeg, Canada. The results suggest that within a limited number of iterations (as termination criterion), global optimum solutions are quickly reached in most of the cases; otherwise, good solutions (close to global optimum solutions) are found in early iterations. Comparative analysis of the networks of Gao and Sioux-Falls shows that for such a non-exact method the global optimum solutions are found in fewer iterations than those found in some analytically exact algorithms in the literature. (ii) Integration of the objective function among the constraints provides a commensurate capability to tackle the multi-objective (or multi-criteria) DNDP as well.

Analytical Solution for the Anisotropic Rabi Model: Effects of Counter-Rotating Terms

NASA Astrophysics Data System (ADS)

Zhang, Guofeng; Zhu, Hanjie

2015-03-01

The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.

Analytical solution for the anisotropic Rabi model: effects of counter-rotating terms.

PubMed

Zhang, Guofeng; Zhu, Hanjie

2015-03-04

The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.

Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: Analytical approximation

NASA Astrophysics Data System (ADS)

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

2017-09-01

Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. Lü, A. Perkins, C. Pope, and K. Stelle [Phys. Rev. Lett. 114, 171601 (2015), 10.1103/PhysRevLett.114.171601] found a numerical solution describing a spherically symmetric non-Schwarzschild asymptotically flat black hole in Einstein gravity with added higher derivative terms. Using the general and quickly convergent parametrization in terms of the continued fractions, we represent this numerical solution in the analytical form, which is accurate not only near the event horizon or far from the black hole, but in the whole space. Thereby, the obtained analytical form of the metric allows one to study easily all the further properties of the black hole, such as thermodynamics, Hawking radiation, particle motion, accretion, perturbations, stability, quasinormal spectrum, etc. Thus, the found analytical approximate representation can serve in the same way as an exact solution.

Analytical Solution for the Anisotropic Rabi Model: Effects of Counter-Rotating Terms

PubMed Central

Zhang, Guofeng; Zhu, Hanjie

2015-01-01

The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model. PMID:25736827

Effect of Cu(II), Cd(II) and Zn(II) on Pb(II) biosorption by algae Gelidium-derived materials.

PubMed

Vilar, Vítor J P; Botelho, Cidália M S; Boaventura, Rui A R

2008-06-15

Biosorption of Pb(II), Cu(II), Cd(II) and Zn(II) from binary metal solutions onto the algae Gelidium sesquipedale, an algal industrial waste and a waste-based composite material was investigated at pH 5.3, in a batch system. Binary Pb(II)/Cu(II), Pb(II)/Cd(II) and Pb(II)/Zn(II) solutions have been tested. For the same equilibrium concentrations of both metal ions (1 mmol l(-1)), approximately 66, 85 and 86% of the total uptake capacity of the biosorbents is taken by lead ions in the systems Pb(II)/Cu(II), Pb(II)/Cd(II) and Pb(II)/Zn(II), respectively. Two-metal results were fitted to a discrete and a continuous model, showing the inhibition of the primary metal biosorption by the co-cation. The model parameters suggest that Cd(II) and Zn(II) have the same decreasing effect on the Pb(II) uptake capacity. The uptake of Pb(II) was highly sensitive to the presence of Cu(II). From the discrete model it was possible to obtain the Langmuir affinity constant for Pb(II) biosorption. The presence of the co-cations decreases the apparent affinity of Pb(II). The experimental results were successfully fitted by the continuous model, at different pH values, for each biosorbent. The following sequence for the equilibrium affinity constants was found: Pb>Cu>Cd approximately Zn.

Interpretation of sucrose gradient sedimentation pattern of deoxyribonucleic acid fragments resulting from random breaks.

PubMed

Litwin, S; Shahn, E; Kozinski, A W

1969-07-01

Mass distribution in a sucrose gradient of deoxyribonucleic acid (DNA) fragments arising as a result of random breaks is predicted by analytical means from which computer evaluations are plotted. The analytical results are compared with the results of verifying experiments: (i) a Monte Carlo computer experiment in which simulated molecules of DNA were individuals of unit length subjected to random "breaks" applied by a random number generator, and (ii) an in vitro experiment in which molecules of T4 DNA, highly labeled with (32)P, were stored in liquid nitrogen for variable periods of time during which a precisely known number of (32)P atoms decayed, causing single-stranded breaks. The distribution of sizes of the resulting fragments was measured in an alkaline sucrose gradient. The profiles obtained in this fashion were compared with the mathematical predictions. Both experiments agree with the analytical approach and thus permit the use of the graphs obtained from the latter as a means of determining the average number of random breaks in DNA from distributions obtained experimentally in a sucrose gradient. An example of the application of this procedure to a previously unresolved problem is provided in the case of DNA from ultraviolet-irradiated phage which undergoes a dose-dependent intracellular breakdown. The relationship between the number of lethal hits and the number of single-stranded breaks was not previously established. A comparison of the calculated number of nicks per strand of DNA with the known dose in phage-lethal hits reveals a relationship closely approximating one lethal hit to one single-stranded break.

Analytical approximation of a distorted reflector surface defined by a discrete set of points

NASA Technical Reports Server (NTRS)

Acosta, Roberto J.; Zaman, Afroz A.

1988-01-01

Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern.

Energy analysis in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-07-01

The gravity assist or flyby is investigated by analysing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. First, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighbourhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the Solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

Analysis of THG modes for femtosecond laser pulse

NASA Astrophysics Data System (ADS)

Trofimov, Vyacheslav A.; Sidorov, Pavel S.

2017-05-01

THG is used nowadays in many practical applications such as a substance diagnostics, and biological objects imaging, and etc. With developing of new materials and technology (for example, photonic crystal) an attention to THG process analysis grow. Therefore, THG features understanding are a modern problem. Early we have developed new analytical approach based on using the problem invariant for analytical solution construction of the THG process. It should be stressed that we did not use a basic wave non-depletion approximation. Nevertheless, a long pulse duration approximation and plane wave approximation has applied. The analytical solution demonstrates, in particular, an optical bistability property (and may other regimes of frequency tripling) for the third harmonic generation process. But, obviously, this approach does not reflect an influence of a medium dispersion on the frequency tripling. Therefore, in this paper we analyze THG efficiency of a femtosecond laser pulse taking into account a second order dispersion affect as well as self- and crossmodulation of the interacting waves affect on the frequency conversion process. Analysis is made using a computer simulation on the base of Schrödinger equations describing the process under consideration.

Energy Analysis in the Elliptic Restricted Three-body Problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-05-01

The gravity assist or flyby is investigated by analyzing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. Firstly, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighborhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

HART-II: Prediction of Blade-Vortex Interaction Loading

DTIC Science & Technology

2003-09-01

14:30 (2) Improvement of DLR Rotor Aero- acoustic Code ( APSIM ) and its Valida- tion with Analytic Solution J. Yin, J. Delfs (5...of DLR Rotor Aero- acoustic Code ( APSIM ) and its Valida- tion with Analytic Solution J. Yin, J. Delfs (5) Aeroelastic Stability Analysis of...of DLR Rotor Aero- acoustic Code ( APSIM ) and its Valida- tion with Analytic Solution J. Yin, J. Delfs (5) Aeroelastic Stability Analysis of

Change of subunit composition of mitochondrial complex II (succinate-ubiquinone reductase/quinol-fumarate reductase) in Ascaris suum during the migration in the experimental host.

PubMed

Iwata, Fumiko; Shinjyo, Noriko; Amino, Hisako; Sakamoto, Kimitoshi; Islam, M Khyrul; Tsuji, Naotoshi; Kita, Kiyoshi

2008-03-01

The mitochondrial metabolic pathway of the parasitic nematode Ascaris suum changes dramatically during its life cycle, to adapt to changes in the environmental oxygen concentration. We previously showed that A. suum mitochondria express stage-specific isoforms of complex II (succinate-ubiquinone reductase: SQR/quinol-fumarate reductase: QFR). The flavoprotein (Fp) and small subunit of cytochrome b (CybS) in adult complex II differ from those of infective third stage larval (L3) complex II. However, there is no difference in the iron-sulfur cluster (Ip) or the large subunit of cytochrome b (CybL) between adult and L3 isoforms of complex II. In the present study, to clarify the changes that occur in the respiratory chain of A. suum larvae during their migration in the host, we examined enzymatic activity, quinone content and complex II subunit composition in mitochondria of lung stage L3 (LL3) A. suum larvae. LL3 mitochondria showed higher QFR activity ( approximately 160 nmol/min/mg) than mitochondria of A. suum at other stages (L3: approximately 80 nmol/min/mg; adult: approximately 70 nmol/min/mg). Ubiquinone content in LL3 mitochondria was more abundant than rhodoquinone ( approximately 1.8 nmol/mg versus approximately 0.9 nmol/mg). Interestingly, the results of two-dimensional bule-native/sodium dodecyl sulfate polyacrylamide gel electrophoresis analyses showed that LL3 mitochondria contained larval Fp (Fp(L)) and adult Fp (Fp(A)) at a ratio of 1:0.56, and that most LL3 CybS subunits were of the adult form (CybS(A)). This clearly indicates that the rearrangement of complex II begins with a change in the isoform of the anchor CybS subunit, followed by a similar change in the Fp subunit.

Small-x asymptotics of the quark helicity distribution: Analytic results

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2017-06-15

In this Letter, we analytically solve the evolution equations for the small-x asymptotic behavior of the (flavor singlet) quark helicity distribution in the large- N c limit. Here, these evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerically. This approximate numerical solution, however, revealed simplifying properties of the small-x asymptotics, which we exploit here to obtain an analytic solution.

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.

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

PubMed

Pipe, James G; Zwart, Nicholas R

2014-01-01

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

Padé approximant for normal stress differences in large-amplitude oscillatory shear flow

NASA Astrophysics Data System (ADS)

Poungthong, P.; Saengow, C.; Giacomin, A. J.; Kolitawong, C.; Merger, D.; Wilhelm, M.

2018-04-01

Analytical solutions for the normal stress differences in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the inexact form of the first few terms of a series expansion in the shear rate amplitude. Here, we improve the accuracy of these truncated expansions by replacing them with rational functions called Padé approximants. The recent advent of exact solutions in LAOS presents an opportunity to identify accurate and useful Padé approximants. For this identification, we replace the truncated expansion for the corotational Jeffreys fluid with its Padé approximants for the normal stress differences. We uncover the most accurate and useful approximant, the [3,4] approximant, and then test its accuracy against the exact solution [C. Saengow and A. J. Giacomin, "Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow," Phys. Fluids 29, 121601 (2017)]. We use Ewoldt grids to show the stunning accuracy of our [3,4] approximant in LAOS. We quantify this accuracy with an objective function and then map it onto the Pipkin space. Our two applications illustrate how to use our new approximant reliably. For this, we use the Spriggs relations to generalize our best approximant to multimode, and then, we compare with measurements on molten high-density polyethylene and on dissolved polyisobutylene in isobutylene oligomer.

Rapid and sensitive insulated isothermal PCR for point-of-need feline leukaemia virus detection.

PubMed

Wilkes, Rebecca P; Anis, Eman; Dunbar, Dawn; Lee, Pei-Yu A; Tsai, Yun-Long; Lee, Fu-Chun; Chang, Hsiao-Fen G; Wang, Hwa-Tang T; Graham, Elizabeth M

2018-04-01

Objectives Feline leukaemia virus (FeLV), a gamma retrovirus, causes diseases of the feline haematopoietic system that are invariably fatal. Rapid and accurate testing at the point-of-need (PON) supports prevention of virus spread and management of clinical disease. This study evaluated the performance of an insulated isothermal PCR (iiPCR) that detects proviral DNA, and a reverse transcription (RT)-iiPCR that detects both viral RNA and proviral DNA, for FeLV detection at the PON. Methods Mycoplasma haemofelis, feline coronavirus, feline herpesvirus, feline calicivirus and feline immunodeficiency virus were used to test analytical specificity. In vitro transcribed RNA, artificial plasmid, FeLV strain American Type Culture Collection VR-719 and a clinical FeLV isolate were used in the analytical sensitivity assays. A retrospective study including 116 clinical plasma and serum samples that had been tested with virus isolation, real-time PCR and ELISA, and a prospective study including 150 clinical plasma and serum samples were implemented to evaluate the clinical performances of the iiPCR-based methods for FeLV detection. Results Ninety-five percent assay limit of detection was calculated to be 16 RNA and five DNA copies for the RT-iiPCR, and six DNA copies for the iiPCR. Both reactions had analytical sensitivity comparable to a reference real-time PCR (qPCR) and did not detect five non-target feline pathogens. The clinical performance of the RT-iiPCR and iiPCR had 98.82% agreement (kappa[κ] = 0.97) and 100% agreement (κ = 1.0), respectively, with the qPCR (n = 85). The agreement between an automatic nucleic extraction/RT-iiPCR system and virus isolation to detect FeLV in plasma or serum was 95.69% (κ = 0.95) and 98.67% (κ = 0.85) in a retrospective (n = 116) and a prospective (n = 150) study, respectively. Conclusions and relevance These results suggested that both RT-iiPCR and iiPCR assays can serve as reliable tools for PON FeLV detection.

On the effect of the degeneracy among dark energy parameters

NASA Astrophysics Data System (ADS)

Gong, Yungui; Gao, Qing

2014-01-01

The dynamics of scalar fields as dark energy is well approximated by some general relations between the equation of state parameter and the fractional energy density . Based on the approximation, for slowly rolling scalar fields, we derived the analytical expressions of which reduce to the popular Chevallier-Polarski-Linder parametrization with an explicit degeneracy relation between and . The models approximate the dynamics of scalar fields well and help eliminate the degeneracies among , , and . With the explicit degeneracy relations, we test their effects on the constraints of the cosmological parameters. We find that: (1) The analytical relations between and for the two models are consistent with observational data. (2) The degeneracies have little effect on . (3) The error of was reduced about 30 % with the degeneracy relations.

Local CC2 response method based on the Laplace transform: analytic energy gradients for ground and excited states.

PubMed

Ledermüller, Katrin; Schütz, Martin

2014-04-28

A multistate local CC2 response method for the calculation of analytic energy gradients with respect to nuclear displacements is presented for ground and electronically excited states. The gradient enables the search for equilibrium geometries of extended molecular systems. Laplace transform is used to partition the eigenvalue problem in order to obtain an effective singles eigenvalue problem and adaptive, state-specific local approximations. This leads to an approximation in the energy Lagrangian, which however is shown (by comparison with the corresponding gradient method without Laplace transform) to be of no concern for geometry optimizations. The accuracy of the local approximation is tested and the efficiency of the new code is demonstrated by application calculations devoted to a photocatalytic decarboxylation process of present interest.

Second derivatives for approximate spin projection methods

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

Thompson, Lee M.; Hratchian, Hrant P., E-mail: hhratchian@ucmerced.edu

2015-02-07

The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical secondmore » derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.« less

Synthesis and characterization of an organic reagent 4-(6-bromo-2-benzothiazolylazo) pyrogallol and its analytical application.

PubMed

Naser, N A; Kahdim, K H; Taha, D N

2012-01-01

Organic reagent, 4-(6-Bromo-2-Benzothiazolylazo) pyrogallol (4-Br-BTAP), was synthesized by coupling reaction of diazotized 2-amino-6-bromobenzothiazole with pyrogallol and purified using ethanol recrystallization method. Analysis and characterization of synthesized product were carried out using melting point, elementary analysis, IR and H¹-NMR. Dissociation constants of the organic reagent were calculated by spectrophotometric method. Absorption spectra of the 4-Br-BTAP in solvents of different polarities were investigated. Analytical application of 4-Br-BTAP was established with Cu (II) and Pd (II).

Dynamics of the surveying gyrocompass

NASA Astrophysics Data System (ADS)

Petrenko, V. E.; Zakharenko, S. A.; Ponomarenko, A. E.

The dynamics of the surveying gyrocompass is investigated analytically for the case of perturbations due to ball bearing imperfections. Approximate analytical expressions are obtained for calculating the natural frequencies of the compass in the presence of parametric perturbations of this kind. An example of natural frequency calculations is presented.

Unimolecular diffusion-mediated reactions with a nonrandom time-modulated absorbing barrier

NASA Technical Reports Server (NTRS)

Bashford, D.; Weaver, D. L.

1986-01-01

A diffusion-reaction model with time-dependent reactivity is formulated and applied to unimolecular reactions. The model is solved exactly numerically and approximately analytically for the unreacted fraction as a function of time. It is shown that the approximate analytical solution is valid even when the system is far from equilibrium, and when the reactivity probability is more complicated than a square-wave function of time. A discussion is also given of an approach to problems of this type using a stochastically fluctuating reactivity, and the first-passage time for a particular example is derived.

Spline methods for approximating quantile functions and generating random samples

NASA Technical Reports Server (NTRS)

Schiess, J. R.; Matthews, C. G.

1985-01-01

Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.

Analytical Method of Approximating the Motion of a Spinning Vehicle with Variable Mass and Inertia Properties Acted Upon by Several Disturbing Parameters

NASA Technical Reports Server (NTRS)

Buglia, James J.; Young, George R.; Timmons, Jesse D.; Brinkworth, Helen S.

1961-01-01

An analytical method has been developed which approximates the dispersion of a spinning symmetrical body in a vacuum, with time-varying mass and inertia characteristics, under the action of several external disturbances-initial pitching rate, thrust misalignment, and dynamic unbalance. The ratio of the roll inertia to the pitch or yaw inertia is assumed constant. Spin was found to be very effective in reducing the dispersion due to an initial pitch rate or thrust misalignment, but was completely Ineffective in reducing the dispersion of a dynamically unbalanced body.

Theoretical Assessment of Compressibility Factor of Gases by Using Second Virial Coefficient

NASA Astrophysics Data System (ADS)

Mamedov, Bahtiyar A.; Somuncu, Elif; Askerov, Iskender M.

2018-01-01

We present a new analytical approximation for determining the compressibility factor of real gases at various temperature values. This algorithm is suitable for the accurate evaluation of the compressibility factor using the second virial coefficient with a Lennard-Jones (12-6) potential. Numerical examples are presented for the gases H2, N2, He, CO2, CH4 and air, and the results are compared with other studies in the literature. Our results showed good agreement with the data in the literature. The consistency of the results demonstrates the effectiveness of our analytical approximation for real gases.

Wheel/Rail Force Measurement at the Washington Metropolitan Area Transit Authority - Phase II. Volume II. Test Report.

DOT National Transportation Integrated Search

1983-06-01

In support of the Office of Rail and Construction Technology of the Urban Mass Transportation Administration, the Transportation Systems Center (TSC) is conducting analytical and experimental studies to relate transit truck design characteristics, wh...

Approximate Solutions for Ideal Dam-Break Sediment-Laden Flows on Uniform Slopes

NASA Astrophysics Data System (ADS)

Ni, Yufang; Cao, Zhixian; Borthwick, Alistair; Liu, Qingquan

2018-04-01

Shallow water hydro-sediment-morphodynamic (SHSM) models have been applied increasingly widely in hydraulic engineering and geomorphological studies over the past few decades. Analytical and approximate solutions are usually sought to verify such models and therefore confirm their credibility. Dam-break flows are often evoked because such flows normally feature shock waves and contact discontinuities that warrant refined numerical schemes to solve. While analytical and approximate solutions to clear-water dam-break flows have been available for some time, such solutions are rare for sediment transport in dam-break flows. Here we aim to derive approximate solutions for ideal dam-break sediment-laden flows resulting from the sudden release of a finite volume of frictionless, incompressible water-sediment mixture on a uniform slope. The approximate solutions are presented for three typical sediment transport scenarios, i.e., pure advection, pure sedimentation, and concurrent entrainment and deposition. Although the cases considered in this paper are not real, the approximate solutions derived facilitate suitable benchmark tests for evaluating SHSM models, especially presently when shock waves can be numerically resolved accurately with a suite of finite volume methods, while the accuracy of the numerical solutions of contact discontinuities in sediment transport remains generally poorer.

ANALYTICAL METHOD FOR THE DETERMINATION OF PHENYLGLUCURONIDE IN RAINBOW TROUT GILL WATER

EPA Science Inventory

Phenylglucuronide (PG), a primary phase II metabolite of phenol, can be excreted by fish through urine and feces, similar to mammals. In addition, it may also be possible to eliminate it through a fish's gills. In order to assess the significance of gill water elimination, analyt...

Instrumentation: Photodiode Array Detectors in UV-VIS Spectroscopy. Part II.

ERIC Educational Resources Information Center

Jones, Dianna G.

1985-01-01

A previous part (Analytical Chemistry; v57 n9 p1057A) discussed the theoretical aspects of diode ultraviolet-visual (UV-VIS) spectroscopy. This part describes the applications of diode arrays in analytical chemistry, also considering spectroelectrochemistry, high performance liquid chromatography (HPLC), HPLC data processing, stopped flow, and…

Error analysis of analytic solutions for self-excited near-symmetric rigid bodies - A numerical study

NASA Technical Reports Server (NTRS)

Kia, T.; Longuski, J. M.

1984-01-01

Analytic error bounds are presented for the solutions of approximate models for self-excited near-symmetric rigid bodies. The error bounds are developed for analytic solutions to Euler's equations of motion. The results are applied to obtain a simplified analytic solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.

Two-dimensional analytic weighting functions for limb scattering

NASA Astrophysics Data System (ADS)

Zawada, D. J.; Bourassa, A. E.; Degenstein, D. A.

2017-10-01

Through the inversion of limb scatter measurements it is possible to obtain vertical profiles of trace species in the atmosphere. Many of these inversion methods require what is often referred to as weighting functions, or derivatives of the radiance with respect to concentrations of trace species in the atmosphere. Several radiative transfer models have implemented analytic methods to calculate weighting functions, alleviating the computational burden of traditional numerical perturbation methods. Here we describe the implementation of analytic two-dimensional weighting functions, where derivatives are calculated relative to atmospheric constituents in a two-dimensional grid of altitude and angle along the line of sight direction, in the SASKTRAN-HR radiative transfer model. Two-dimensional weighting functions are required for two-dimensional inversions of limb scatter measurements. Examples are presented where the analytic two-dimensional weighting functions are calculated with an underlying one-dimensional atmosphere. It is shown that the analytic weighting functions are more accurate than ones calculated with a single scatter approximation, and are orders of magnitude faster than a typical perturbation method. Evidence is presented that weighting functions for stratospheric aerosols calculated under a single scatter approximation may not be suitable for use in retrieval algorithms under solar backscatter conditions.

An improved 3D MoF method based on analytical partial derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2016-12-01

MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.

Testing approximations for non-linear gravitational clustering

NASA Technical Reports Server (NTRS)

Coles, Peter; Melott, Adrian L.; Shandarin, Sergei F.

1993-01-01

The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

Nanoporous gold film based SPR sensors for trace chemical detection

NASA Astrophysics Data System (ADS)

Wang, Li; Gong, Xiaoqing; Wan, Xiumei; Lu, Dan-feng; Qi, Zhi-mei

2017-02-01

Thin films of nanoporous gold (NPG) have both localized and propagating surface plasmon resonance (SPR) effects. The propagating SPR effect of NPG film combined with its huge internal surface area makes it applicable as an evanescent wave sensor with high sensitivity. In this work, NPG films with controlled thicknesses were fabricated on glass substrates by sputtering deposition of AuAg films followed by dealloying in nitric acid. By using of the NPG films as the sensing layer, a broadband wavelength-interrogated SPR sensor was prepared for chemical and biological detection. The propagating SPR absorption band in the visible-near infrared region was clearly observed upon exposure of the NPG film to air, and this band was detected to move to longer wavelengths in response to adsorption of molecules within the NPG film. Simulations based on Fresnel equations combined with Bruggeman approximation were carried out for optimizing the propagating SPR property of NPG film. The sensor's performance was investigated using both bisphenol A (BPA) and lead (II) ions as analytes. According to the experimental results, the detection limits of the sensor are 5 nmol·L-1 for BPA and 1 nmol·L-1 for lead (II) ions. The work demonstrated the outstanding applicability of the NPG film based SPR sensor for sensitive environmental monitoring.

Further aspects of ochratoxin A-cation interactions: complex formation with zinc ions and a novel analytical application of ochratoxin A-magnesium interaction in the HPLC-FLD system.

PubMed

Poór, Miklós; Kuzma, Mónika; Matisz, Gergely; Li, Yin; Perjési, Pál; Kunsági-Máté, Sándor; Kőszegi, Tamás

2014-04-10

Ochratoxin A (OTA) is a mycotoxin produced by different Aspergillus and Penicillium species. Since its mechanism of action is not fully understood yet, it is important to gain further insight into different interactions of OTA at the molecular level. OTA is found worldwide in many foods and drinks. Moreover, it can also be detected in human and animal tissues and body fluids, as well. Therefore, the development of highly sensitive quantitative methods for the determination of OTA is of utmost importance. OTA most likely forms complexes with divalent cations, both in cells and body fluids. In the present study, the OTA-zinc interaction was investigated and compared to OTA-magnesium complex formation using fluorescence spectroscopy and molecular modeling. Our results show that zinc(II) ion forms a two-fold higher stable complex with OTA than magnesium(II) ion. In addition, based on the enhanced fluorescence emission of OTA in its magnesium-bound form, a novel RP-HPLC-fluorescence detector (FLD) method was also established. Our results highlight that the application of magnesium chloride in alkaline eluents results in an approximately two-fold increase in sensitivity using the HPLC-FLD technique.

A predator-prey model with a holling type I functional response including a predator mutual interference

USGS Publications Warehouse

Seo, G.; DeAngelis, D.L.

2011-01-01

The most widely used functional response in describing predator-prey relationships is the Holling type II functional response, where per capita predation is a smooth, increasing, and saturating function of prey density. Beddington and DeAngelis modified the Holling type II response to include interference of predators that increases with predator density. Here we introduce a predator-interference term into a Holling type I functional response. We explain the ecological rationale for the response and note that the phase plane configuration of the predator and prey isoclines differs greatly from that of the Beddington-DeAngelis response; for example, in having three possible interior equilibria rather than one. In fact, this new functional response seems to be quite unique. We used analytical and numerical methods to show that the resulting system shows a much richer dynamical behavior than the Beddington-DeAngelis response, or other typically used functional responses. For example, cyclic-fold, saddle-fold, homoclinic saddle connection, and multiple crossing bifurcations can all occur. We then use a smooth approximation to the Holling type I functional response with predator mutual interference to show that these dynamical properties do not result from the lack of smoothness, but rather from subtle differences in the functional responses. ?? 2011 Springer Science+Business Media, LLC.

High-Lift Flight Tunnel - Phase II Report. Phase 2 Report

NASA Technical Reports Server (NTRS)

Lofftus, David; Lund, Thomas; Rote, Donald; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

The High-Lift Flight Tunnel (HiLiFT) concept is a revolutionary approach to aerodynamic ground testing. This concept utilizes magnetic levitation and linear motors to propel an aerodynamic model through a tube containing a quiescent test medium. This medium (nitrogen) is cryogenic and pressurized to achieve full flight Reynolds numbers higher than any existing ground test facility world-wide for the range of 0.05 to 0.50 Mach. The results of the Phase II study provide excellent assurance that the HiLiFT concept will provide a valuable low-speed, high Reynolds number ground test facility. The design studies concluded that the HiLiFT facility is feasible to build and operate and the analytical studies revealed no insurmountable difficulties to realizing a practical high Reynolds number ground test facility. It was determined that a national HiLiFT facility, including development, would cost approximately $400M and could be operational by 2013 if fully funded. Study participants included National Aeronautics and Space Administration Langley Research Center as the Program Manager and MSE Technology Applications, Inc., (MSE) of Butte, Montana as the prime contractor and study integrator. MSE#s subcontractors included the University of Texas at Arlington for aerodynamic analyses and the Argonne National Laboratory for magnetic levitation and linear motor technology support.

Analytical Solutions for Radiative Transfer: Implications for Giant Planet Formation by Disk Instability

NASA Astrophysics Data System (ADS)

Boss, Alan P.

2009-03-01

The disk instability mechanism for giant planet formation is based on the formation of clumps in a marginally gravitationally unstable protoplanetary disk, which must lose thermal energy through a combination of convection and radiative cooling if they are to survive and contract to become giant protoplanets. While there is good observational support for forming at least some giant planets by disk instability, the mechanism has become theoretically contentious, with different three-dimensional radiative hydrodynamics codes often yielding different results. Rigorous code testing is required to make further progress. Here we present two new analytical solutions for radiative transfer in spherical coordinates, suitable for testing the code employed in all of the Boss disk instability calculations. The testing shows that the Boss code radiative transfer routines do an excellent job of relaxing to and maintaining the analytical results for the radial temperature and radiative flux profiles for a spherical cloud with high or moderate optical depths, including the transition from optically thick to optically thin regions. These radial test results are independent of whether the Eddington approximation, diffusion approximation, or flux-limited diffusion approximation routines are employed. The Boss code does an equally excellent job of relaxing to and maintaining the analytical results for the vertical (θ) temperature and radiative flux profiles for a disk with a height proportional to the radial distance. These tests strongly support the disk instability mechanism for forming giant planets.

A New Equivalence Theory Method for Treating Doubly Heterogeneous Fuel - II. Verifications

DOE PAGES

Choi, Sooyoung; Kong, Chidong; Lee, Deokjung; ...

2015-03-09

A new methodology has been developed recently to treat resonance self-shielding in systems for which the fuel compact region of a reactor lattice consists of small fuel grains dispersed in a graphite matrix. The theoretical development adopts equivalence theory in both micro- and macro-level heterogeneities to provide approximate analytical expressions for the shielded cross sections, which may be interpolated from a table of resonance integrals or Bondarenko factors using a modified background cross section as the interpolation parameter. This paper describes the first implementation of the theoretical equations in a reactor analysis code. In order to reduce discrepancies caused bymore » use of the rational approximation for collision probabilities in the original derivation, a new formulation for a doubly heterogeneous Bell factor is developed in this paper to improve the accuracy of doubly heterogeneous expressions. This methodology is applied to a wide range of pin cell and assembly test problems with varying geometry parameters, material compositions, and temperatures, and the results are compared with continuous-energy Monte Carlo simulations to establish the accuracy and range of applicability of the new approach. It is shown that the new doubly heterogeneous self-shielding method including the Bell factor correction gives good agreement with reference Monte Carlo results.« less

Integrated miniature fluorescent probe to leverage the sensing potential of ZnO quantum dots for the detection of copper (II) ions.

PubMed

Ng, Sing Muk; Wong, Derrick Sing Nguong; Phung, Jane Hui Chiun; Chin, Suk Fun; Chua, Hong Siang

2013-11-15

Quantum dots are fluorescent semiconductor nanoparticles that can be utilised for sensing applications. This paper evaluates the ability to leverage their analytical potential using an integrated fluorescent sensing probe that is portable, cost effective and simple to handle. ZnO quantum dots were prepared using the simple sol-gel hydrolysis method at ambient conditions and found to be significantly and specifically quenched by copper (II) ions. This ZnO quantum dots system has been incorporated into an in-house developed miniature fluorescent probe for the detection of copper (II) ions in aqueous medium. The probe was developed using a low power handheld black light as excitation source and three photo-detectors as sensor. The sensing chamber placed between the light source and detectors was made of 4-sided clear quartz windows. The chamber was housed within a dark compartment to avoid stray light interference. The probe was operated using a microcontroller (Arduino Uno Revision 3) that has been programmed with the analytical response and the working algorithm of the electronics. The probe was sourced with a 12 V rechargeable battery pack and the analytical readouts were given directly using a LCD display panel. Analytical optimisations of the ZnO quantum dots system and the probe have been performed and further described. The probe was found to have a linear response range up to 0.45 mM (R(2)=0.9930) towards copper (II) ion with a limit of detection of 7.68×10(-7) M. The probe has high repeatable and reliable performance. Copyright © 2013 Elsevier B.V. All rights reserved.

Detection of the 158 Micrometers[CII] Transition at z=1.3: Evidence for a Galaxy-Wide Starburst

NASA Technical Reports Server (NTRS)

Hailey-Dunsheath, S.; Nikola, T.; Oberst, T. E.; Parshley, S. C.; Benford, D. J.; Staguhn, J. G.; Tucker, C. E.

2010-01-01

We report the detection of 158 micron [C II] fine-structure line emission from MIPS J142824.0+352619, a hyperluminous ( L(sub IR) approximates 10(exp 13) L (sub solar)) starburst galaxy at z = 1.3. The line is bright, corresponding to a fraction L(sub [Cu II] L(sub Fir) approximates 2 x 10(exp -3) of the far-IR (FIR) continuum. The [C II], CO, and FIR continuum emission may be modeled as arising from photodissociation regions (PDRs) that have a characteristic gas density of n approximates 10(exp 4.2) /cm(exp 3) , and that are illuminated by a far-UV radiation field approximately 10(exp 3.2) times more intense than the local interstellar radiation field. The mass in these PDRs accounts for approximately half of the molecular gas mass in this galaxy. The L(sub [CII])/L(sub FIR) ratio is higher than observed in local ultralummous infrared galaxies or in the few high-redshift QSOs detected in [C II], but the L(sub [CII])/L(sub FIR) and L(sub CO)/L(sub FIR) ratios are similar to the values seen in nearby starburst galaxies. This suggests that MIPS J142824.0+352619 is a scaled-up version of a starburst nucleus, with the burst extended over several kiloparsecs.

Uniform analytic approximation of Wigner rotation matrices

NASA Astrophysics Data System (ADS)

Hoffmann, Scott E.

2018-02-01

We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

An approximate analytical solution for describing surface runoff and sediment transport over hillslope

NASA Astrophysics Data System (ADS)

Tao, Wanghai; Wang, Quanjiu; Lin, Henry

2018-03-01

Soil and water loss from farmland causes land degradation and water pollution, thus continued efforts are needed to establish mathematical model for quantitative analysis of relevant processes and mechanisms. In this study, an approximate analytical solution has been developed for overland flow model and sediment transport model, offering a simple and effective means to predict overland flow and erosion under natural rainfall conditions. In the overland flow model, the flow regime was considered to be transitional with the value of parameter β (in the kinematic wave model) approximately two. The change rate of unit discharge with distance was assumed to be constant and equal to the runoff rate at the outlet of the plane. The excess rainfall was considered to be constant under uniform rainfall conditions. The overland flow model developed can be further applied to natural rainfall conditions by treating excess rainfall intensity as constant over a small time interval. For the sediment model, the recommended values of the runoff erosion calibration constant (cr) and the splash erosion calibration constant (cf) have been given in this study so that it is easier to use the model. These recommended values are 0.15 and 0.12, respectively. Comparisons with observed results were carried out to validate the proposed analytical solution. The results showed that the approximate analytical solution developed in this paper closely matches the observed data, thus providing an alternative method of predicting runoff generation and sediment yield, and offering a more convenient method of analyzing the quantitative relationships between variables. Furthermore, the model developed in this study can be used as a theoretical basis for developing runoff and erosion control methods.

Nanometric depth resolution from multi-focal images in microscopy.

PubMed

Dalgarno, Heather I C; Dalgarno, Paul A; Dada, Adetunmise C; Towers, Catherine E; Gibson, Gavin J; Parton, Richard M; Davis, Ilan; Warburton, Richard J; Greenaway, Alan H

2011-07-06

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels.

Nanometric depth resolution from multi-focal images in microscopy

PubMed Central

Dalgarno, Heather I. C.; Dalgarno, Paul A.; Dada, Adetunmise C.; Towers, Catherine E.; Gibson, Gavin J.; Parton, Richard M.; Davis, Ilan; Warburton, Richard J.; Greenaway, Alan H.

2011-01-01

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels. PMID:21247948

Studies on Some Biologically Cobalt(II), Copper(II) and Zinc(II) Complexes With ONO, NNO and SNO Donor Pyrazinoylhydrazine-Derived Ligands

PubMed Central

Praveen, Marapaka; Sherazi, Syed K. A.

1998-01-01

Biologically active complexes of Co(II), Ni(II), Cu(II) and Zn(II) with novel ONO, NNO and SNO donor pyrazinoylhydrazine-derived compounds have been prepared and characterized on the basis of analytical data and various physicochemical studies. Distorted octahedral structures for all the complexes have been proposed. The synthesized ligands and their complexes have been screened for their antibacterial activity against bacterial species Escherichia coli, Pseudomonas aeruginosa, Staphylococcus aureus and Klebsiella pneumonae. The activity data show the metal complexes to be more active than the parent free ligands against one or more bacterial species. PMID:18475857

An overview of city analytics

PubMed Central

Higham, Desmond J.; Batty, Michael; Bettencourt, Luís M. A.; Greetham, Danica Vukadinović; Grindrod, Peter

2017-01-01

We introduce the 14 articles in the Royal Society Open Science themed issue on City Analytics. To provide a high-level, strategic, overview, we summarize the topics addressed and the analytical tools deployed. We then give a more detailed account of the individual contributions. Our overall aims are (i) to highlight exciting advances in this emerging, interdisciplinary field, (ii) to encourage further activity and (iii) to emphasize the variety of new, public-domain, datasets that are available to researchers. PMID:28386454

Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

Changes in photochemically significant solar UV spectral irradiance as estimated by the composite Mg II index and scale factors

NASA Technical Reports Server (NTRS)

Deland, Matthew T.; Cebula, Richard P.

1994-01-01

Quantitative assessment of the impact of solar ultraviolet irradiance variations on stratospheric ozone abundances currently requires the use of proxy indicators. The Mg II core-to-wing index has been developed as an indicator of solar UV activity between 175-400 nm that is independent of most instrument artifacts, and measures solar variability on both rotational and solar cycle time scales. Linear regression fits have been used to merge the individual Mg II index data sets from the Nimbus-7, NOAA-9, and NOAA-11 instruments onto a single reference scale. The change in 27-dayrunning average of the composite Mg II index from solar maximum to solar minimum is approximately 8 percent for solar cycle 21, and approximately 9 percent for solar cycle 22 through January 1992. Scaling factors based on the short-term variations in the Mg II index and solar irradiance data sets have been developed to estimate solar variability at mid-UV and near-UV wavelengths. Near 205 nm, where solar irradiance variations are important for stratospheric photo-chemistry and dynamics, the estimated change in irradiance during solar cycle 22 is approximately 10 percent using the composite Mg II index and scale factors.

A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-II beam

NASA Astrophysics Data System (ADS)

F, Khannous; A, A. A. Ebrahim; A, Belafhal

2016-04-01

Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric-Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre-Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

NBD-labelled phospholipid accelerates apolipoprotein C-II amyloid fibril formation but is not incorporated into mature fibrils

PubMed Central

Ryan, Timothy M.; Griffin, Michael D. W.; Bailey, Michael F.; Schuck, Peter; Howlett, Geoffrey J.

2014-01-01

Human apolipoprotein (apo) C-II is one of several lipid-binding proteins that self-assemble into fibrils and accumulate in disease-related amyloid deposits. A general characteristic of these amyloid deposits is the presence of lipids, known to modulate individual steps in amyloid fibril formation. ApoC-II fibril formation is activated by sub-micellar phospholipids but inhibited by micellar lipids. We examined the mechanism for the activation by sub-micellar lipids using the fluorescently-labelled, short-chain phospholipid, 1-dodecyl-[(7-nitro-2-1,3-benzoxadiazol-4-yl)amino]-2-hydroxy-glycero-3-phosphocholine (NBD-lyso-12-PC). Addition of submicellar NBD-lyso-12-PC increased the rate of fibril formation by apoC-II approximately two-fold. Stopped flow kinetic analysis using fluorescence detection and low, non-fibril forming concentrations of apoC-II indicated NBD-Lyso-12-PC binds rapidly, in the millisecond timescale, followed by the slower formation of discrete apoC-II tetramers. Sedimentation velocity analysis showed NBD-Lyso-12-PC binds to both apoC-II monomers and tetramers at approximately 5 sites per monomer with an average dissociation constant of approximately 10 μM. Mature apoC-II fibrils formed in the presence of NBD-Lyso-12-PC were devoid of lipid indicating a purely catalytic role for sub-micellar lipids in the activation of apoC-II fibril formation. These studies demonstrate the catalytic potential of small amphiphilic molecules to control protein folding and fibril assembly pathways. PMID:21985034

Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in a conductor

NASA Astrophysics Data System (ADS)

Grants, Ilmārs; Bojarevičs, Andris; Gerbeth, Gunter

2016-06-01

Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.

Interaction and charge transfer between dielectric spheres: Exact and approximate analytical solutions.

PubMed

Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning

2016-11-21

We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.

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

PubMed

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

2000-08-20

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

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

Spectrum Evolution of Accelerating or Slowing down Soliton at its Propagation in a Medium with Gold Nanorods

NASA Astrophysics Data System (ADS)

Trofimov, Vyacheslav A.; Lysak, Tatiana M.

2018-04-01

We investigate both numerically and analytically the spectrum evolution of a novel type soliton - nonlinear chirped accelerating or decelerating soliton - at a femtosecond pulse propagation in a medium containing noble nanoparticles. In our consideration, we take into account one- or two-photon absorption of laser radiation by nanorods, and time-dependent nanorod aspect ratio changing due to their melting or reshaping because of laser energy absorption. The chirped solitons are formed due to the trapping of laser radiation by the nanorods reshaping fronts, if a positive or negative phase-amplitude grating is induced by laser radiation. Accelerating or slowing down chirped soliton formation is accompanied by the soliton spectrum blue or red shift. To prove our numerical results, we derived the approximate analytical law for the spectrum maximum intensity evolution along the propagation coordinate, based on earlier developed approximate analytical solutions for accelerating and decelerating solitons.

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...

Evaluation of an Approximate Method for Synthesizing Covariance Matrices for Use in Meta-Analytic SEM

ERIC Educational Resources Information Center

Beretvas, S. Natasha; Furlow, Carolyn F.

2006-01-01

Meta-analytic structural equation modeling (MA-SEM) is increasingly being used to assess model-fit for variables' interrelations synthesized across studies. MA-SEM researchers have analyzed synthesized correlation matrices using structural equation modeling (SEM) estimation that is designed for covariance matrices. This can produce incorrect…

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.

Serum ARCHITECT PIVKA-II reference interval in healthy Chinese adults: Sub-analysis from a prospective multicenter study.

PubMed

Yan, Cunling; Hu, Jian; Yang, Jia; Chen, Zhaoyun; Li, Huijun; Wei, Lianhua; Zhang, Wei; Xing, Hao; Sang, Guoyao; Wang, Xiaoqin; Han, Ruilin; Liu, Ping; Li, Zhihui; Li, Zhiyan; Huang, Ying; Jiang, Li; Li, Shunjun; Dai, Shuyang; Wang, Nianyue; Yang, Yongfeng; Ma, Li; Soh, Andrew; Beshiri, Agim; Shen, Feng; Yang, Tian; Fan, Zhuping; Zheng, Yijie; Chen, Wei

2018-04-01

Protein induced by vitamin K absence or antagonist-II (PIVKA-II) has been widely used as a biomarker for liver cancer diagnosis in Japan for decades. However, the reference intervals for serum ARCHITECT PIVKA-II have not been established in the Chinese population. Thus, this study aimed to measure serum PIVKA-II levels in healthy Chinese subjects. This is a sub-analysis from the prospective, cross-sectional and multicenter study (ClinicalTrials.gov Identifier: NCT03047603). A total of 892 healthy participants (777 Han and 115 Uygur) with complete health checkup results were recruited from 7 regional centers in China. Serum PIVKA-II level was measured by ARCHITECT immunoassay. All 95% reference ranges were estimated by nonparametric method. The distribution of PIVKA-II values showed significant difference with ethnicity and sex, but not age. The 95% reference range of PIVKA-II was 13.62-40.38 mAU/ml in Han Chinese subjects and 15.16-53.74 mAU/ml in Uygur subjects. PIVKA-II level was significantly higher in males than in females (P < 0.001). The 95% reference range of PIVKA-II was 15.39-42.01 mAU/ml in Han males while 11.96-39.13 mAU/ml in Han females. The reference interval of serum PIVKA-II on the Architect platform was established in healthy Chinese adults. This will be valuable for future clinical and laboratory studies performed using the Architect analyzer. Different ethnic backgrounds and analytical methods underline the need for redefining the reference interval of analytes such as PIVKA-II, in central laboratories in different countries. Copyright © 2018 The Canadian Society of Clinical Chemists. Published by Elsevier Inc. All rights reserved.

Evaluation of Laser Stabilization and Imaging Systems for LCLS-II - Final Paper

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

Barry, Matthew

2015-08-20

By combining the top performing commercial laser beam stabilization system with the most ideal optical imaging configuration, the beamline for the Linear Accelerator Coherent Light Source II (LCLS-II) will deliver the highest quality and most stable beam to the cathode. To determine the optimal combination, LCLS-II beamline conditions were replicated and the systems tested with a He-Ne laser. The Guidestar-II and MRC active laser beam stabilization systems were evaluated for their ideal positioning and stability. Both a two and four lens optical imaging configuration was then evaluated for beam imaging quality, magnification properties, and natural stability. In their best performancesmore » when tested over fifteen hours, Guidestar-II kept the beam stable over approximately 70-110um while the MRC system kept it stable over approximately 90-100um. During short periods of time, Guidestar-II kept the beam stable between 10-20um, but was more susceptible to drift over time, while the MRC system maintained the beam between 30-50um with less overall drift. The best optical imaging configuration proved to be a four lens system that images to the iris located in the cathode room and from there, imaged to the cathode. The magnification from the iris to the cathode was 2:1, within an acceptable tolerance to the expected 2.1:1 magnification. The two lens configuration was slightly more stable in small periods of time (less than 10 minutes) without the assistance of a stability system, approximately 55um compared to approximately 70um, but the four lens configurations beam image had a significantly flatter intensity distribution compared to the two lens configuration which had a Gaussian distribution. A final test still needs to be run with both stability systems running at the same time through the four lens system. With this data, the optimal laser beam stabilization system can be determined for the beamline of LCLS-II.« less

A generalized analytical model for radiative transfer in vacuum thermal insulation of space vehicles

NASA Astrophysics Data System (ADS)

Krainova, Irina V.; Dombrovsky, Leonid A.; Nenarokomov, Aleksey V.; Budnik, Sergey A.; Titov, Dmitry M.; Alifanov, Oleg M.

2017-08-01

The previously developed spectral model for radiative transfer in vacuum thermal insulation of space vehicles is generalized to take into account possible thermal contact between a fibrous spacer and one of the neighboring aluminum foil layers. An approximate analytical solution based on slightly modified two-flux approximation for radiative transfer in a semi-transparent fibrous spacer is derived. It was shown that thermal contact between the spacer and adjacent foil may decrease significantly the quality of thermal insulation because of an increase in radiative flux to/from the opposite aluminum foil. Theoretical predictions are confirmed by comparison with new results of laboratory experiments.

Monitoring by forward scatter radar techniques: an improved second-order analytical model

NASA Astrophysics Data System (ADS)

Falconi, Marta Tecla; Comite, Davide; Galli, Alessandro; Marzano, Frank S.; Pastina, Debora; Lombardo, Pierfrancesco

2017-10-01

In this work, a second-order phase approximation is introduced to provide an improved analytical model of the signal received in forward scatter radar systems. A typical configuration with a rectangular metallic object illuminated while crossing the baseline, in far- or near-field conditions, is considered. An improved second-order model is compared with a simplified one already proposed by the authors and based on a paraxial approximation. A phase error analysis is carried out to investigate benefits and limitations of the second-order modeling. The results are validated by developing full-wave numerical simulations implementing the relevant scattering problem on a commercial tool.

Stress generation in thermally grown oxide films. [oxide scale spalling from superalloy substrates

NASA Technical Reports Server (NTRS)

Kumnick, A. J.; Ebert, L. J.

1981-01-01

A three dimensional finite element analysis was conducted, using the ANSYS computer program, of the stress state in a thin oxide film thermally formed on a rectangular piece of NiCrAl alloy. The analytical results indicate a very high compressive stress in the lateral directions of the film (approximately 6200 MPa), and tensile stresses in the metal substrate that ranged from essentially zero to about 55 MPa. It was found further that the intensity of the analytically determined average stresses could be approximated reasonably well by the modification of an equation developed previously by Oxx for stresses induced into bodies by thermal gradients.

Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

DOE PAGES

Jia, Shaoyang; Pennington, M. R.

2017-08-01

With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

Brownian systems with spatially inhomogeneous activity

NASA Astrophysics Data System (ADS)

Sharma, A.; Brader, J. M.

2017-09-01

We generalize the Green-Kubo approach, previously applied to bulk systems of spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016), 10.1063/1.4966153], to include spatially inhomogeneous activity. The method is applied to predict the spatial dependence of the average orientation per particle and the density. The average orientation is given by an integral over the self part of the Van Hove function and a simple Gaussian approximation to this quantity yields an accurate analytical expression. Taking this analytical result as input to a dynamic density functional theory approximates the spatial dependence of the density in good agreement with simulation data. All theoretical predictions are validated using Brownian dynamics simulations.

The Potential-Well Distortion Effect and Coherent Instabilities of Electron Bunches in Storage Rings

NASA Astrophysics Data System (ADS)

Korchuganov, V. N.; Smygacheva, A. S.; Fomin, E. A.

2018-05-01

The effect of electromagnetic interaction between electron bunches and the vacuum chamber of a storage ring on the longitudinal motion of bunches is studied. Specifically, the potential-well distortion effect and the so-called coherent instabilities of coupled bunches are considered. An approximate analytical solution for the frequencies of incoherent oscillations of bunches distributed arbitrarily within the ring is obtained for a distorted potential well. A new approach to determining frequencies of coherent oscillations and an approximate analytical relation for estimating the stability of a system of bunches as a function of their distribution in the accelerator orbit are presented.

Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

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

Jia, Shaoyang; Pennington, M. R.

With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

Solar neutrino masses and mixing from bilinear R-parity broken supersymmetry: Analytical versus numerical results

NASA Astrophysics Data System (ADS)

Díaz, M.; Hirsch, M.; Porod, W.; Romão, J.; Valle, J.

2003-07-01

We give an analytical calculation of solar neutrino masses and mixing at one-loop order within bilinear R-parity breaking supersymmetry, and compare our results to the exact numerical calculation. Our method is based on a systematic perturbative expansion of R-parity violating vertices to leading order. We find in general quite good agreement between the approximate and full numerical calculations, but the approximate expressions are much simpler to implement. Our formalism works especially well for the case of the large mixing angle Mikheyev-Smirnov-Wolfenstein solution, now strongly favored by the recent KamLAND reactor neutrino data.

Evolution of Hyperbolic-Secant Pulses Towards Cross-Phase Modulation Induced Optical Wave Breaking and Soliton or Soliton Trains Generation in Quintic Nonlinear Fibers

NASA Astrophysics Data System (ADS)

Zhong, Xian-Qiong; Zhang, Xiao-Xia; Du, Xian-Tong; Liu, Yong; Cheng, Ke

2015-10-01

The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking (OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity (QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses. Supported by the Postdoctoral Fund of China under Grant No. 2011M501402, the Key Project of Chinese Ministry of Education under Grant No. 210186, the Major Project of Natural Science Supported by the Educational Department of Sichuan Province under Grant No. 13ZA0081, the Key Project of National Natural Science Foundation of China under Grant No 61435010, and the National Natural Science Foundation of China under Grant No. 61275039

Comparison of Three Methods for Wind Turbine Capacity Factor Estimation

PubMed Central

Ditkovich, Y.; Kuperman, A.

2014-01-01

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first “quasiexact” approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second “analytic” approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third “approximate” approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation. PMID:24587755

Approximate analytical solution for induction heating of solid cylinders

DOE PAGES

Jankowski, Todd Andrew; Pawley, Norma Helen; Gonzales, Lindsey Michal; ...

2015-10-20

An approximate solution to the mathematical model for induction heating of a solid cylinder in a cylindrical induction coil is presented here. The coupled multiphysics model includes equations describing the electromagnetic field in the heated object, a heat transfer simulation to determine temperature of the heated object, and an AC circuit simulation of the induction heating power supply. A multiple-scale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closed-form expressions for the electromagnetic field and heat generation rate in the solid cylinder, for the equivalent impedance of the associated tank circuit, and formore » the frequency response of a variable frequency power supply driving the tank circuit. The solution developed here is validated by comparing predicted power supply frequency to both experimental measurements and calculated values from finite element analysis for heating of graphite cylinders in an induction furnace. The simple expressions from the analytical solution clearly show the functional dependence of the power supply frequency on the material properties of the load and the geometrical characteristics of the furnace installation. In conclusion, the expressions developed here provide physical insight into observations made during load signature analysis of induction heating.« less

Rapid perfusion quantification using Welch-Satterthwaite approximation and analytical spectral filtering

NASA Astrophysics Data System (ADS)

Krishnan, Karthik; Reddy, Kasireddy V.; Ajani, Bhavya; Yalavarthy, Phaneendra K.

2017-02-01

CT and MR perfusion weighted imaging (PWI) enable quantification of perfusion parameters in stroke studies. These parameters are calculated from the residual impulse response function (IRF) based on a physiological model for tissue perfusion. The standard approach for estimating the IRF is deconvolution using oscillatory-limited singular value decomposition (oSVD) or Frequency Domain Deconvolution (FDD). FDD is widely recognized as the fastest approach currently available for deconvolution of CT Perfusion/MR PWI. In this work, three faster methods are proposed. The first is a direct (model based) crude approximation to the final perfusion quantities (Blood flow, Blood volume, Mean Transit Time and Delay) using the Welch-Satterthwaite approximation for gamma fitted concentration time curves (CTC). The second method is a fast accurate deconvolution method, we call Analytical Fourier Filtering (AFF). The third is another fast accurate deconvolution technique using Showalter's method, we call Analytical Showalter's Spectral Filtering (ASSF). Through systematic evaluation on phantom and clinical data, the proposed methods are shown to be computationally more than twice as fast as FDD. The two deconvolution based methods, AFF and ASSF, are also shown to be quantitatively accurate compared to FDD and oSVD.

S-curve networks and an approximate method for estimating degree distributions of complex networks

NASA Astrophysics Data System (ADS)

Guo, Jin-Li

2010-12-01

In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 (Internet Protocol version 4) addresses, this paper proposes a forecasting model by using S curve (logistic curve). The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions (i.e., Barabási-Albert method) is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabási-Albert method commonly used in current network research.

Efficient method for the calculation of mean extinction. II. Analyticity of the complex extinction efficiency of homogeneous spheroids and finite cylinders.

PubMed

Xing, Z F; Greenberg, J M

1994-08-20

The analyticity of the complex extinction efficiency is examined numerically in the size-parameter domain for homogeneous prolate and oblate spheroids and finite cylinders. The T-matrix code, which is the most efficient program available to date, is employed to calculate the individual particle-extinction efficiencies. Because of its computational limitations in the size-parameter range, a slightly modified Hilbert-transform algorithm is required to establish the analyticity numerically. The findings concerning analyticity that we reported for spheres (Astrophys. J. 399, 164-175, 1992) apply equally to these nonspherical particles.

76 FR 69653 - Abamectin (avermectin); Pesticide Tolerances

Federal Register 2010, 2011, 2012, 2013, 2014

2011-11-09

... are available in Pesticide Analytical Manual II (PAM II) for citrus and processed fractions (Method I... (ID) number EPA-HQ-OPP-2010-0619. All documents in the docket are listed in the docket index available... available, e.g., Confidential Business Information (CBI) or other information whose disclosure is restricted...

Increased Rail Transit Vehicle Crashworthiness in Head-On Collisions. Volume II. Primary Collision.

DOT National Transportation Integrated Search

1980-06-01

A specific goal of safety is to reduce the number of injuries that may result from the collision of two trains. In Volume II, an analytical model in two dimensions, longitudinal and vertical, of the primary collision of two impacting urban railcar co...

30 CFR 57.22227 - Approved testing devices (I-A, I-B, I-C, II-A, II-B, III, IV, V-A, and V-B mines).

Code of Federal Regulations, 2010 CFR

2010-07-01

... be used in Subcategory I-C mines. (c)(1) If electrically powered, remote sensing devices are used.... (2) If air samples are delivered to remote analytical devices through sampling tubes, such tubes...

Approximating Smooth Step Functions Using Partial Fourier Series Sums

DTIC Science & Technology

2012-09-01

interp1(xt(ii), smoothstepbez( t(ii), min(t(ii)), max(t(ii)), ’y’), t(ii), ’linear’, ’ extrap ’); ii = find( abs(t - tau/2) <= epi ); iii = t(ii...interp1( xt(ii), smoothstepbez( rt, min(rt), max(rt), ’y’), t(ii), ’linear’, ’ extrap ’ ); % stepm(ii) = 1 - interp1(xt(ii), smoothstepbez( t(ii...min(t(ii)), max(t(ii)), ’y’), t(ii), ’linear’, ’ extrap ’); In this case, because x is also defined as a function of the independent parameter

Proposed Modifications to the Conceptual Model of Coaching Efficacy and Additional Validity Evidence for the Coaching Efficacy Scale II-High School Teams

ERIC Educational Resources Information Center

Myers, Nicholas; Feltz, Deborah; Chase, Melissa

2011-01-01

The purpose of this study was to determine whether theoretically relevant sources of coaching efficacy could predict the measures derived from the Coaching Efficacy Scale II-High School Teams (CES II-HST). Data were collected from head coaches of high school teams in the United States (N = 799). The analytic framework was a multiple-group…

40 CFR Appendix A to Subpart E of... - Interim Transmission Electron Microscopy Analytical Methods-Mandatory and Nonmandatory-and...

Code of Federal Regulations, 2011 CFR

2011-07-01

... representative of the air entering the abatement site. c. Two field blanks are to be taken by removing the cap... of Sample Data Quality Objectives is shown in the following Table II: EC01AP92.003 C. Sample Shipment... or the Burdette procedure (Ref. 7 of Unit II.J.) ii. Plasma etching of the collapsed filter is...

40 CFR Appendix A to Subpart E of... - Interim Transmission Electron Microscopy Analytical Methods-Mandatory and Nonmandatory-and...

Code of Federal Regulations, 2010 CFR

2010-07-01

... representative of the air entering the abatement site. c. Two field blanks are to be taken by removing the cap... of Sample Data Quality Objectives is shown in the following Table II: EC01AP92.003 C. Sample Shipment... or the Burdette procedure (Ref. 7 of Unit II.J.) ii. Plasma etching of the collapsed filter is...

An analytical theory of a scattering of radio waves on meteoric ionization - II. Solution of the integro-differential equation in case of backscatter

NASA Astrophysics Data System (ADS)

Pecina, P.

2016-12-01

The integro-differential equation for the polarization vector P inside the meteor trail, representing the analytical solution of the set of Maxwell equations, is solved for the case of backscattering of radio waves on meteoric ionization. The transversal and longitudinal dimensions of a typical meteor trail are small in comparison to the distances to both transmitter and receiver and so the phase factor appearing in the kernel of the integral equation is large and rapidly changing. This allows us to use the method of stationary phase to obtain an approximate solution of the integral equation for the scattered field and for the corresponding generalized radar equation. The final solution is obtained by expanding it into the complete set of Bessel functions, which results in solving a system of linear algebraic equations for the coefficients of the expansion. The time behaviour of the meteor echoes is then obtained using the generalized radar equation. Examples are given for values of the electron density spanning a range from underdense meteor echoes to overdense meteor echoes. We show that the time behaviour of overdense meteor echoes using this method is very different from the one obtained using purely numerical solutions of the Maxwell equations. Our results are in much better agreement with the observations performed e.g. by the Ondřejov radar.

Postperovskite phase equilibria in the MgSiO3-Al2O3 system.

PubMed

Tsuchiya, Jun; Tsuchiya, Taku

2008-12-09

We investigate high-P,T phase equilibria of the MgSiO(3)-Al(2)O(3) system by means of the density functional ab initio computation methods with multiconfiguration sampling. Being different from earlier studies based on the static substitution properties with no consideration of Rh(2)O(3)(II) phase, present calculations demonstrate that (i) dissolving Al(2)O(3) tends to decrease the postperovskite transition pressure of MgSiO(3) but the effect is not significant ( approximately -0.2 GPa/mol% Al(2)O(3)); (ii) Al(2)O(3) produces the narrow perovskite+postperovskite coexisting P,T area (approximately 1 GPa) for the pyrolitic concentration (x(Al2O3) approximately 6 mol%), which is sufficiently responsible to the deep-mantle D'' seismic discontinuity; (iii) the transition would be smeared (approximately 4 GPa) for the basaltic Al-rich composition (x(Al2O3) approximately 20 mol%), which is still seismically visible unless iron has significant effects; and last (iv) the perovskite structure spontaneously changes to the Rh(2)O(3)(II) with increasing the Al concentration involving small displacements of the Mg-site cations.

Loglinear Approximate Solutions to Real-Business-Cycle Models: Some Observations

ERIC Educational Resources Information Center

Lau, Sau-Him Paul; Ng, Philip Hoi-Tak

2007-01-01

Following the analytical approach suggested in Campbell, the authors consider a baseline real-business-cycle (RBC) model with endogenous labor supply. They observe that the coefficients in the loglinear approximation of the dynamic equations characterizing the equilibrium are related to the fundamental parameters in a relatively simple manner.…

Evaluation of calcium alginate beads for Ce, La and Nd preconcentration from groundwater prior to ICP OES analysis.

PubMed

Arantes de Carvalho, Gabriel G; Kondaveeti, Stalin; Petri, Denise F S; Fioroto, Alexandre M; Albuquerque, Luiza G R; Oliveira, Pedro V

2016-12-01

Analytical methods for the determination of rare earth elements (REE) in natural waters by plasma spectrochemical techniques often require sample preparation procedures for analytes preconcentration as well as for removing matrix constituents, that may interfere on the analytical measurements. In the present work, calcium alginate (CA) beads were used for the first time aiming at Ce, La and Nd preconcentration from groundwater samples for further determination by inductively coupled plasma optical emission spectrometry (ICP OES). Test samples were analyzed in batch mode by transferring a 40mL test portion (pH=5±0.2) into a 50mL polyethylene flask containing 125mg CA beads. After 15min contact, the analytes were quantitatively extracted from the loaded CA beads with 2.0mL of 1.0molL -1 HCl solution for further determination by ICP OES, using Ce (II) 456.236, La (II) 379.478 and Nd (II) 430.358nm emission lines. The proposed approach is a reliable alternative for REE single-stage preconcentration from aqueous samples, as it provided accurate results based on the addition and recovery analysis of groundwater. The results obtained by the proposed method were also compared with those from reference method based on inductively coupled plasma mass spectrometry (ICP-MS) and no significant differences were observed after applying the Student's t-test at 95% confidence level. Copyright © 2016 Elsevier B.V. All rights reserved.

Double power series method for approximating cosmological perturbations

NASA Astrophysics Data System (ADS)

Wren, Andrew J.; Malik, Karim A.

2017-04-01

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.

Synthesis, structural characterization, fluorescence, antimicrobial, antioxidant and DNA cleavage studies of Cu(II) complexes of formyl chromone Schiff bases.

PubMed

Kavitha, P; Saritha, M; Laxma Reddy, K

2013-02-01

Cu(II) complexes have been synthesized from different Schiff bases, such as 3-((2-hydroxy phenylimino)methyl)-4H-chromen-4-one (HL(1)), 2-((4-oxo-4H-chromen-3-yl)methylneamino) benzoicacid (HL(2)), 3-((3-hydroxypyridin-2-ylimino)methyl)-4H-chromen-4-one (HL(3)) and 3-((2-mercaptophenylimino)methyl)-4H-chromen-4-one (HL(4)). The complexes were characterized by analytical, molar conductance, IR, electronic, magnetic, ESR, thermal, powder XRD and SEM studies. The analytical data reveal that metal to ligand molar ratio is 1:2 in all the complexes. Molar conductivity data indicates that all the Cu(II) complexes are neutral. On the basis of magnetic and electronic spectral data, distorted octahedral geometry is proposed for all the Cu(II) complexes. Thermal behaviour of the synthesized complexes illustrates the presence of lattice water molecules in the complexes. X-ray diffraction studies reveal that all the ligands and their Cu(II) complexes have triclinic system with different unit cell parameters. Antimicrobial, antioxidant and DNA cleavage activities indicate that metal complexes exhibited greater activity as compared with ligands. Copyright © 2012 Elsevier B.V. All rights reserved.

Analytical phase diagrams for colloids and non-adsorbing polymer.

PubMed

Fleer, Gerard J; Tuinier, Remco

2008-11-04

We review the free-volume theory (FVT) of Lekkerkerker et al. [Europhys. Lett. 20 (1992) 559] for the phase behavior of colloids in the presence of non-adsorbing polymer and we extend this theory in several aspects: (i) We take the solvent into account as a separate component and show that the natural thermodynamic parameter for the polymer properties is the insertion work Pi(v), where Pi is the osmotic pressure of the (external) polymer solution and v the volume of a colloid particle. (ii) Curvature effects are included along the lines of Aarts et al. [J. Phys.: Condens. Matt. 14 (2002) 7551] but we find accurate simple power laws which simplify the mathematical procedure considerably. (iii) We find analytical forms for the first, second, and third derivatives of the grand potential, needed for the calculation of the colloid chemical potential, the pressure, gas-liquid critical points and the critical endpoint (cep), where the (stable) critical line ends and then coincides with the triple point. This cep determines the boundary condition for a stable liquid. We first apply these modifications to the so-called colloid limit, where the size ratio q(R)=R/a between the radius of gyration R of the polymer and the particle radius a is small. In this limit the binodal polymer concentrations are below overlap: the depletion thickness delta is nearly equal to R, and Pi can be approximated by the ideal (van't Hoff) law Pi=Pi(0)=phi/N, where phi is the polymer volume fraction and N the number of segments per chain. The results are close to those of the original Lekkerkerker theory. However, our analysis enables very simple analytical expressions for the polymer and colloid concentrations in the critical and triple points and along the binodals as a function of q(R). Also the position of the cep is found analytically. In order to make the model applicable to higher size ratio's q(R) (including the so-called protein limit where q(R)>1) further extensions are needed. We introduce the size ratio q=delta/a, where the depletion thickness delta is no longer of order R. In the protein limit the binodal concentrations are above overlap. In such semidilute solutions delta approximately xi, where the De Gennes blob size (correlation length) xi scales as xi approximately phi(-gamma), with gamma=0.77 for good solvents and gamma=1 for a theta solvent. In this limit Pi=Pi(sd) approximately phi(3gamma). We now apply the following additional modifications: With these latter two modifications we obtain again a fully analytical model with simple equations for critical and triple points as a function of q(R). In the protein limit the binodal polymer concentrations scale as q(R)(1/gamma), and phase diagrams phiq(R)(-1/gamma) versus the colloid concentration eta become universal (i.e., independent of the size ratio q(R)). The predictions of this generalized free-volume theory (GFVT) are in excellent agreement with experiment and with computer simulations, not only for the colloid limit but also for the protein limit (and the crossover between these limits). The q(R)(1/gamma) scaling is accurately reproduced by both simulations and other theoretical models. The liquid window is the region between phi(c) (critical point) and phi(t) (triple point). In terms of the ratio phi(t)/phi(c) the liquid window extends from 1 in the cep (here phi(t)-phi(c)=0) to 2.2 in the protein limit. Hence, the liquid window is narrow: it covers at most a factor 2.2 in (external) polymer concentration.

FAST MAGNETIC FIELD AMPLIFICATION IN THE EARLY UNIVERSE: GROWTH OF COLLISIONLESS PLASMA INSTABILITIES IN TURBULENT MEDIA

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

Falceta-Gonçalves, D.; Kowal, G.

2015-07-20

In this work we report on a numerical study of the cosmic magnetic field amplification due to collisionless plasma instabilities. The collisionless magnetohydrodynamic equations derived account for the pressure anisotropy that leads, in specific conditions, to the firehose and mirror instabilities. We study the time evolution of seed fields in turbulence under the influence of such instabilities. An approximate analytical time evolution of the magnetic field is provided. The numerical simulations and the analytical predictions are compared. We found that (i) amplification of the magnetic field was efficient in firehose-unstable turbulent regimes, but not in the mirror-unstable models; (ii) the growthmore » rate of the magnetic energy density is much faster than the turbulent dynamo; and (iii) the efficient amplification occurs at small scales. The analytical prediction for the correlation between the growth timescales and pressure anisotropy is confirmed by the numerical simulations. These results reinforce the idea that pressure anisotropies—driven naturally in a turbulent collisionless medium, e.g., the intergalactic medium, could efficiently amplify the magnetic field in the early universe (post-recombination era), previous to the collapse of the first large-scale gravitational structures. This mechanism, though fast for the small-scale fields (∼kpc scales), is unable to provide relatively strong magnetic fields at large scales. Other mechanisms that were not accounted for here (e.g., collisional turbulence once instabilities are quenched, velocity shear, or gravitationally induced inflows of gas into galaxies and clusters) could operate afterward to build up large-scale coherent field structures in the long time evolution.« less

Some elements of a theory of multidimensional complex variables. I - General theory. II - Expansions of analytic functions and application to fluid flows

NASA Technical Reports Server (NTRS)

Martin, E. Dale

1989-01-01

The paper introduces a new theory of N-dimensional complex variables and analytic functions which, for N greater than 2, is both a direct generalization and a close analog of the theory of ordinary complex variables. The algebra in the present theory is a commutative ring, not a field. Functions of a three-dimensional variable were defined and the definition of the derivative then led to analytic functions.

Evaluation of a reconfigurable portable instrument for copper determination based on luminescent carbon dots.

PubMed

Salinas-Castillo, Alfonso; Morales, Diego P; Lapresta-Fernández, Alejandro; Ariza-Avidad, María; Castillo, Encarnación; Martínez-Olmos, Antonio; Palma, Alberto J; Capitan-Vallvey, Luis Fermin

2016-04-01

A portable reconfigurable platform for copper (Cu(II)) determination based on luminescent carbon dot (Cdots) quenching is described. The electronic setup consists of a light-emitting diode (LED) as the carbon dot optical exciter and a photodiode as a light-to-current converter integrated in the same instrument. Moreover, the overall analog conditioning is simply performed with one integrated solution, a field-programmable analog array (FPAA), which makes it possible to reconfigure the filter and gain stages in real time. This feature provides adaptability to use the platform as an analytical probe for carbon dots coming from different batches with some variations in luminescence characteristics. The calibration functions obtained that fit a modified Stern-Volmer equation were obtained using luminescence signals from Cdots quenching by Cu(II). The analytical applicability of the reconfigurable portable instrument for Cu(II) using Cdots has been successfully demonstrated in tap water analysis.

Dimensional transitions in thermodynamic properties of ideal Maxwell-Boltzmann gases

NASA Astrophysics Data System (ADS)

Aydin, Alhun; Sisman, Altug

2015-04-01

An ideal Maxwell-Boltzmann gas confined in various rectangular nanodomains is considered under quantum size effects. Thermodynamic quantities are calculated from their relations with the partition function, which consists of triple infinite summations over momentum states in each direction. To obtain analytical expressions, summations are converted to integrals for macrosystems by a continuum approximation, which fails at the nanoscale. To avoid both the numerical calculation of summations and the failure of their integral approximations at the nanoscale, a method which gives an analytical expression for a single particle partition function (SPPF) is proposed. It is shown that a dimensional transition in momentum space occurs at a certain magnitude of confinement. Therefore, to represent the SPPF by lower-dimensional analytical expressions becomes possible, rather than numerical calculation of summations. Considering rectangular domains with different aspect ratios, a comparison of the results of derived expressions with those of summation forms of the SPPF is made. It is shown that analytical expressions for the SPPF give very precise results with maximum relative errors of around 1%, 2% and 3% at exactly the transition point for single, double and triple transitions, respectively. Based on dimensional transitions, expressions for free energy, entropy, internal energy, chemical potential, heat capacity and pressure are given analytically valid for any scale.

An analytical approach to the CMB polarization in a spatially closed background

NASA Astrophysics Data System (ADS)

Niazy, Pedram; Abbassi, Amir H.

2018-03-01

The scalar mode polarization of the cosmic microwave background is derived in a spatially closed universe from the Boltzmann equation using the line of sight integral method. The EE and TE multipole coefficients have been extracted analytically by considering some tolerable approximations such as considering the evolution of perturbation hydrodynamically and sudden transition from opacity to transparency at the time of last scattering. As the major advantage of analytic expressions, CEE,ℓS and CTE,ℓ explicitly show the dependencies on baryon density ΩB, matter density ΩM, curvature ΩK, primordial spectral index ns, primordial power spectrum amplitude As, Optical depth τreion, recombination width σt and recombination time tL. Using a realistic set of cosmological parameters taken from a fit to data from Planck, the closed universe EE and TE power spectrums in the scalar mode are compared with numerical results from the CAMB code and also latest observational data. The analytic results agree with the numerical ones on the big and moderate scales. The peak positions are in good agreement with the numerical result on these scales while the peak heights agree with that to within 20% due to the approximations have been considered for these derivations. Also, several interesting properties of CMB polarization are revealed by the analytic spectra.