Analytical Ballistic Trajectories with Approximately Linear Drag

Directory of Open Access Journals (Sweden)

Giliam J. P. de Carpentier

2014-01-01

Full Text Available This paper introduces a practical analytical approximation of projectile trajectories in 2D and 3D roughly based on a linear drag model and explores a variety of different planning algorithms for these trajectories. Although the trajectories are only approximate, they still capture many of the characteristics of a real projectile in free fall under the influence of an invariant wind, gravitational pull, and terminal velocity, while the required math for these trajectories and planners is still simple enough to efficiently run on almost all modern hardware devices. Together, these properties make the proposed approach particularly useful for real-time applications where accuracy and performance need to be carefully balanced, such as in computer games.

A Statistical Mechanics Approach to Approximate Analytical Bootstrap Averages

DEFF Research Database (Denmark)

Malzahn, Dorthe; Opper, Manfred

2003-01-01

We apply the replica method of Statistical Physics combined with a variational method to the approximate analytical computation of bootstrap averages for estimating the generalization error. We demonstrate our approach on regression with Gaussian processes and compare our results with averages...

Analytic approximation for the modified Bessel function I -2/3(x)

Science.gov (United States)

Martin, Pablo; Olivares, Jorge; Maass, Fernando

2017-12-01

In the present work an analytic approximation to modified Bessel function of negative fractional order I -2/3(x) is presented. The validity of the approximation is for every positive value of the independent variable. The accuracy is high in spite of the small number (4) of parameters used. The approximation is a combination of elementary functions with rational ones. Power series and assymptotic expansions are simultaneously used to obtain the approximation.

Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

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Xiao-Ying Qin

2014-01-01

Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.

Analytic bounds and approximations for annuities and Asian options

NARCIS (Netherlands)

Vanduffel, S.; Shang, Z.; Henrard, L.; Dhaene, J.; Valdez, E.A.

2008-01-01

Even in case of the Brownian motion as most natural rate of return model it appears too difficult to obtain analytic expressions for most risk measures of constant continuous annuities. In literature the so-called comonotonic approximations have been proposed but these still require the evaluation

Finite Gaussian Mixture Approximations to Analytically Intractable Density Kernels

DEFF Research Database (Denmark)

Khorunzhina, Natalia; Richard, Jean-Francois

The objective of the paper is that of constructing finite Gaussian mixture approximations to analytically intractable density kernels. The proposed method is adaptive in that terms are added one at the time and the mixture is fully re-optimized at each step using a distance measure that approxima...

Approximate analytical modeling of leptospirosis infection

Science.gov (United States)

Ismail, Nur Atikah; Azmi, Amirah; Yusof, Fauzi Mohamed; Ismail, Ahmad Izani

2017-11-01

Leptospirosis is an infectious disease carried by rodents which can cause death in humans. The disease spreads directly through contact with feces, urine or through bites of infected rodents and indirectly via water contaminated with urine and droppings from them. Significant increase in the number of leptospirosis cases in Malaysia caused by the recent severe floods were recorded during heavy rainfall season. Therefore, to understand the dynamics of leptospirosis infection, a mathematical model based on fractional differential equations have been developed and analyzed. In this paper an approximate analytical method, the multi-step Laplace Adomian decomposition method, has been used to conduct numerical simulations so as to gain insight on the spread of leptospirosis infection.

Precise analytic approximations for the Bessel function J1 (x)

Science.gov (United States)

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.

Approximate analytical solutions of Klein-Gordon equation with Hulthen potentials for nonzero angular momentum

International Nuclear Information System (INIS)

Chen Changyuan; Sun Dongsheng; Lu Falin

2007-01-01

Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of bound states are attained for different l. The analytical energy equation and the unnormalized radial wave functions expressed in terms of hypergeometric polynomials are given

Approximate analytic theory of the multijunction grill

International Nuclear Information System (INIS)

Hurtak, O.; Preinhaelter, J.

1991-03-01

An approximate analytic theory of the general multijunction grill is developed. Omitting the evanescent modes in the subsidiary waveguides both at the junction and at the grill mouth and neglecting multiple wave reflection, simple formulae are derived for the reflection coefficient, the amplitudes of the incident and reflected waves and the spectral power density. These quantities are expressed through the basic grill parameters (the electric length of the structure and phase shift between adjacent waveguides) and two sets of reflection coefficients describing wave reflections in the subsidiary waveguides at the junction and at the plasma. Approximate expressions for these coefficients are also given. The results are compared with a numerical solution of two specific examples; they were shown to be useful for the optimization and design of multijunction grills.For the JET structure it is shown that, in the case of a dense plasma,many results can be obtained from the simple formulae for a two-waveguide multijunction grill. (author) 12 figs., 12 refs

Analytic approximations for the elastic moduli of two-phase materials

DEFF Research Database (Denmark)

Zhang, Z. J.; Zhu, Y. K.; Zhang, P.

2017-01-01

Based on the models of series and parallel connections of the two phases in a composite, analytic approximations are derived for the elastic constants (Young's modulus, shear modulus, and Poisson's ratio) of elastically isotropic two-phase composites containing second phases of various volume...

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

Science.gov (United States)

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.

Analytic approximate radiation effects due to Bremsstrahlung

International Nuclear Information System (INIS)

Ben-Zvi, I.

2012-01-01

The purpose of this note is to provide analytic approximate expressions that can provide quick estimates of the various effects of the Bremsstrahlung radiation produced relatively low energy electrons, such as the dumping of the beam into the beam stop at the ERL or field emission in superconducting cavities. The purpose of this work is not to replace a dependable calculation or, better yet, a measurement under real conditions, but to provide a quick but approximate estimate for guidance purposes only. These effects include dose to personnel, ozone generation in the air volume exposed to the radiation, hydrogen generation in the beam dump water cooling system and radiation damage to near-by magnets. These expressions can be used for other purposes, but one should note that the electron beam energy range is limited. In these calculations the good range is from about 0.5 MeV to 10 MeV. To help in the application of this note, calculations are presented as a worked out example for the beam dump of the R and D Energy Recovery Linac.

Analytic approximate radiation effects due to Bremsstrahlung

Energy Technology Data Exchange (ETDEWEB)

Ben-Zvi I.

2012-02-01

The purpose of this note is to provide analytic approximate expressions that can provide quick estimates of the various effects of the Bremsstrahlung radiation produced relatively low energy electrons, such as the dumping of the beam into the beam stop at the ERL or field emission in superconducting cavities. The purpose of this work is not to replace a dependable calculation or, better yet, a measurement under real conditions, but to provide a quick but approximate estimate for guidance purposes only. These effects include dose to personnel, ozone generation in the air volume exposed to the radiation, hydrogen generation in the beam dump water cooling system and radiation damage to near-by magnets. These expressions can be used for other purposes, but one should note that the electron beam energy range is limited. In these calculations the good range is from about 0.5 MeV to 10 MeV. To help in the application of this note, calculations are presented as a worked out example for the beam dump of the R&D Energy Recovery Linac.

An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations

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M. Bishehniasar

2017-01-01

Full Text Available The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs. The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE. Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD method and standard finite difference (SFD technique, which are popular in the literature for solving engineering problems.

Approximation of Analytic Functions by Bessel's Functions of Fractional Order

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Soon-Mo Jung

2011-01-01

Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.

Application of modified analytical function for approximation and computer simulation of diffraction profile

International Nuclear Information System (INIS)

Marrero, S. I.; Turibus, S. N.; Assis, J. T. De; Monin, V. I.

2011-01-01

Data processing of the most of diffraction experiments is based on determination of diffraction line position and measurement of broadening of diffraction profile. High precision and digitalisation of these procedures can be resolved by approximation of experimental diffraction profiles by analytical functions. There are various functions for these purposes both simples, like Gauss function, but no suitable for wild range of experimental profiles and good approximating functions but complicated for practice using, like Vougt or PersonVII functions. Proposed analytical function is modified Cauchy function which uses two variable parameters allowing describing any experimental diffraction profile. In the presented paper modified function was applied for approximation of diffraction lines of steels after various physical and mechanical treatments and simulation of diffraction profiles applied for study of stress gradients and distortions of crystal structure. (Author)

ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. II. RADIATIVE TRANSFER VIA THE TWO-STREAM APPROXIMATION

Energy Technology Data Exchange (ETDEWEB)

Heng, Kevin; Mendonça, João M.; Lee, Jae-Min, E-mail: kevin.heng@csh.unibe.ch, E-mail: joao.mendonca@csh.unibe.ch, E-mail: lee@physik.uzh.ch [University of Bern, Center for Space and Habitability, Sidlerstrasse 5, CH-3012 Bern (Switzerland)

2014-11-01

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior), and solutions for the temperature-pressure profiles. Generally, the problem is mathematically underdetermined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat, and the properties of scattering in both the optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing, and incoming fluxes in the convective regime.

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

Science.gov (United States)

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.

Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.

Directory of Open Access Journals (Sweden)

Giorgos Minas

2017-07-01

Full Text Available In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA overcomes the main limitations of the standard Linear Noise Approximation (LNA to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.

Analytic Approximation to Radiation Fields from Line Source Geometry

International Nuclear Information System (INIS)

Michieli, I.

2000-01-01

Line sources with slab shields represent typical source-shield configuration in gamma-ray attenuation problems. Such shielding problems often lead to the generalized Secant integrals of the specific form. Besides numerical integration approach, various expansions and rational approximations with limited applicability are in use for computing the value of such integral functions. Lately, the author developed rapidly convergent infinite series representation of generalized Secant Integrals involving incomplete Gamma functions. Validity of such representation was established for zero and positive values of integral parameter a (a=0). In this paper recurrence relations for generalized Secant Integrals are derived allowing us simple approximate analytic calculation of the integral for arbitrary a values. It is demonstrated how truncated series representation can be used, as the basis for such calculations, when possibly negative a values are encountered. (author)

Analytical approximation of the erosion rate and electrode wear in micro electrical discharge machining

International Nuclear Information System (INIS)

Kurnia, W; Tan, P C; Yeo, S H; Wong, M

2008-01-01

Theoretical models have been used to predict process performance measures in electrical discharge machining (EDM), namely the material removal rate (MRR), tool wear ratio (TWR) and surface roughness (SR). However, these contributions are mainly applicable to conventional EDM due to limits on the range of energy and pulse-on-time adopted by the models. This paper proposes an analytical approximation of micro-EDM performance measures, based on the crater prediction using a developed theoretical model. The results show that the analytical approximation of the MRR and TWR is able to provide a close approximation with the experimental data. The approximation results for the MRR and TWR are found to have a variation of up to 30% and 24%, respectively, from their associated experimental values. Since the voltage and current input used in the computation are captured in real time, the method can be applied as a reliable online monitoring system for the micro-EDM process

An alternative technique for the implementation of an analytical approximation for transients with temperature feedback

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P. [Instituto Federal do Rio de Janeiro, Nilopolis, RJ (Brazil)], e-mail: dpalmaster@gmail.com; Silva, Adilson C. da; Goncalves, Alessandro C.; Martinez, Aquilino S. [Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear], e-mail: asilva@con.ufrj.br, e-mail: agoncalves@con.ufrj.br, e-mail: aquilino@lmp.ufrj.br

2009-07-01

The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting neutron density variation during the operation of a nuclear reactor. Although different approximate solutions for the system of point kinetics equations with temperature feedback may be found in literature, some of them do not present an explicit dependence in time, which makes the computing implementation difficult and, as a result, its applicability in practical cases. The present paper uses the polynomial adjustment technique to overcome this problem in the analytical approximation as proposed by Nahla. In a systematic comparison with other existing approximations it is concluded that the method is adequate, presenting small deviations in relation to the reference values obtained from the reference numerical method. (author)

An alternative technique for the implementation of an analytical approximation for transients with temperature feedback

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Silva, Adilson C. da; Goncalves, Alessandro C.; Martinez, Aquilino S.

2009-01-01

The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting neutron density variation during the operation of a nuclear reactor. Although different approximate solutions for the system of point kinetics equations with temperature feedback may be found in literature, some of them do not present an explicit dependence in time, which makes the computing implementation difficult and, as a result, its applicability in practical cases. The present paper uses the polynomial adjustment technique to overcome this problem in the analytical approximation as proposed by Nahla. In a systematic comparison with other existing approximations it is concluded that the method is adequate, presenting small deviations in relation to the reference values obtained from the reference numerical method. (author)

Delay in a tandem queueing model with mobile queues: An analytical approximation

NARCIS (Netherlands)

Al Hanbali, Ahmad; de Haan, Roland; Boucherie, Richardus J.; van Ommeren, Jan C.W.

In this paper, we analyze the end-to-end delay performance of a tandem queueing system with mobile queues. Due to state-space explosion, there is no hope for a numerical exact analysis for the joint-queue-length distribution. For this reason, we present an analytical approximation that is based on

An analytic distorted wave approximation for intermediate energy proton scattering

International Nuclear Information System (INIS)

Di Marzio, F.; Amos, K.

1982-01-01

An analytic Distorted Wave approximation has been developed for use in analyses of intermediate energy proton inelastic scattering from nuclei. Applications are made to analyse 402 and 800 MeV data from the isoscalar and isovector 1 + and 2 + states in 12 C and to the 800 MeV data from the excitation of the 2 - (8.88MeV) state in 16 O. Comparisons of predictions made using different model two-nucleon t-matrices and different models of nuclear structure are given

Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

International Nuclear Information System (INIS)

Liu Chunliang; Xie Xi; Chen Yinbao

1991-01-01

The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

Analytical approximations for the amplitude and period of a relaxation oscillator

Directory of Open Access Journals (Sweden)

Golkhou Vahid

2009-01-01

Full Text Available Abstract Background Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters. Results We present, to our knowledge, the first analytical expressions for the period and amplitude of a classic model for the animal circadian clock oscillator. These compact expressions are in good agreement with numerical solutions of corresponding continuous ODEs and for stochastic simulations executed at literature parameter values. The formulas are shown to be useful by permitting quick comparisons relative to a negative-feedback represillator oscillator for noise (10× less sensitive to protein decay rates, efficiency (2× more efficient, and dynamic range (30 to 60 decibel increase. The dynamic range is enhanced at its lower end by a new concentration scale defined by the crossing point of the activator and repressor, rather than from a steady-state expression level. Conclusion Analytical expressions for oscillator dynamics provide a physical understanding for the observations from numerical simulations and suggest additional properties not readily apparent or as yet unexplored. The methods described here may be applied to other nonlinear oscillator designs and biological circuits.

Analytical Evaluation of Beam Deformation Problem Using Approximate Methods

DEFF Research Database (Denmark)

Barari, Amin; Kimiaeifar, A.; Domairry, G.

2010-01-01

The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified......, and this process produces noise in the obtained answers. This paper deals with the solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Perturbation, Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Variational...... Iteration Method (VIM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate for systems of non-linear differential equation....

Analytical approximate solutions of the time-domain diffusion equation in layered slabs.

Science.gov (United States)

Martelli, Fabrizio; Sassaroli, Angelo; Yamada, Yukio; Zaccanti, Giovanni

2002-01-01

Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.

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

Science.gov (United States)

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.

Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions

Science.gov (United States)

Lin, Yezhi; Liu, Yinping; Li, Zhibin

2012-01-01

The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems. Program summaryProgram title: NAPA Catalogue identifier: AEJZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJZ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4060 No. of bytes in distributed program, including test data, etc.: 113 498 Distribution format: tar.gz Programming language: MAPLE R13 Computer: PC Operating system: Windows XP/7 RAM: 2 Gbytes Classification: 4.3 Nature of problem: Solve nonlinear differential equations with initial conditions. Solution method: Adomian decomposition method and Padé technique. Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.

Critical region of a type II superconducting film near Hsub(c2): rational approximants

International Nuclear Information System (INIS)

Ruggeri, G.J.

1979-01-01

The high-temperature perturbative expansions for the thermal quantities of a type II superconducting film are extrapolated to the critical region near Hsub(c2) by means of new rational approximants of the Pade type. The new approximants are forced to reproduce the leading correction to the flux lattice contribution on the low-temperature side of the transition. Compared to those previously considered in the literature: (i) the mutual consistency of the approximants is improved; and (ii) they are nearer to the exact solution of the zero-dimensional Landau-Ginsburg model. (author)

Fatigue crack extension in nozzle junctions; comparison of analytical approximations with experimental data

International Nuclear Information System (INIS)

Broekhoven, M.J.G.; Ruijtenbeek, M.G. van de

1975-01-01

The fracture mechanics based stress intensity factor (K-factor) concept has obtained wide-spread acceptance as a tool for quantitative analysis of both fatigue crack growth and instable fracture. The present study discusses the applicability of various simple analytical approximations by comparing results with experimental data. A semi-analytical procedure has been developed whose main characteristics are: the true stress distribution perpendicular to the crack plane for the uncracked structure is used as input data; an extended version of the Shah and Kobayashi solution for elliptical cracks, loaded on their surfaces by tractions described by fourth order double symmetrical polynomials fit through the data of previous step is used to calculate full K-factor variations along the crack fronts; several corrections, a.o. to correct for free surfaces and for a corner radius are incorporated. The experiments concern careful monitoring crack growth rates (da/dN) under uniaxial fatigue loading of precracked nozzle-on-plate models, a.o. using a closed T.V. circuit. Resulting da/dN versus crack length (a) curves are converted into K versus a curves using da/dN versus ΔK curves for the same material (ASTM A 508 C12) obtained by standard procedures. Comparison of theoretical and experimental data yields the conclusion that: simple analytical approximations as sometimes recommended in literature may largely overestimate or underestimate K-factors for nozzle corner cracks; a computer program based on the semi-analytical procedure yields results within seconds of CPU-time once the input data have been generated. These results compare well with experimental and available finite element data for the range of crack depths of practical concern

Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method

Directory of Open Access Journals (Sweden)

De-Gang Wang

2012-01-01

Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.

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

Science.gov (United States)

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

Analytical approaches for the approximate solution of a nonlinear fractional ordinary differential equation

International Nuclear Information System (INIS)

Basak, K C; Ray, P C; Bera, R K

2009-01-01

The aim of the present analysis is to apply the Adomian decomposition method and He's variational method for the approximate analytical solution of a nonlinear ordinary fractional differential equation. The solutions obtained by the above two methods have been numerically evaluated and presented in the form of tables and also compared with the exact solution. It was found that the results obtained by the above two methods are in excellent agreement with the exact solution. Finally, a surface plot of the approximate solutions of the fractional differential equation by the above two methods is drawn for 0≤t≤2 and 1<α≤2.

Analytical expression for the nonsinglet structure functions at small x in the double logarithmic approximation

International Nuclear Information System (INIS)

Lublinsky, Michael

2004-01-01

A simple analytic expression for the nonsinglet structure function f NS is given. The expression is derived from the result of Ermolaev, Manaenkov, and Ryskin obtained by low x resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD

Analytical approximate equations for the resistivity and its temperature coefficient in thin polycrystalline metallic films

International Nuclear Information System (INIS)

Tellier, C.R.; Tosser, A.J.

1977-01-01

In the usual thickness range of sputtered metallic films, analytical linearized approximate expressions of polycrystalline film resistivity and its t.c.r. are deduced from the Mayadas-Shatzkes theoretical equations. A good experimental fit is observed for Al rf sputtered metal films. (orig.) [de

Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method

International Nuclear Information System (INIS)

Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A

2009-01-01

A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.

Calculation of photon attenuation coefficients of elements and compounds from approximate semi-analytical formulae

International Nuclear Information System (INIS)

Roteta, M.; Baro, J.; Fernandez-Varea, J.M.; Salvat, F.

1994-01-01

The FORTRAN 77 code PHOTAC to compute photon attenuation coefficients of elements and compounds is described. The code is based on the semi-analytical approximate atomic cross sections proposed by Baro et al. (1994). Photoelectric cross sections are calculated directly from a simple analytical expression. Atomic cross sections for coherent and incoherent scattering and for pair production are obtained as integrals of the corresponding differential cross sections. These integrals are evaluated, to a pre-selected accuracy, by using a 20-point Gauss adaptive integration algorithm. Calculated attenuation coefficients agree with recently compiled databases to within equal 1%, in the energy range from 1 KeV to 1 GeV. The complete source listing of the program PHOTAC is included

The auxiliary field method and approximate analytical solutions of the Schroedinger equation with exponential potentials

Energy Technology Data Exchange (ETDEWEB)

Silvestre-Brac, Bernard [LPSC Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France); Semay, Claude; Buisseret, Fabien [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)], E-mail: silvestre@lpsc.in2p3.fr, E-mail: claude.semay@umh.ac.be, E-mail: fabien.buisseret@umh.ac.be

2009-06-19

The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies of the Schroedinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schroedinger equation with exponential potentials of the form -{alpha}r{sup {lambda}}exp(-{beta}r) can also be analytically solved by using the auxiliary field method. Closed formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn to the Yukawa potential and the pure exponential potential.

The auxiliary field method and approximate analytical solutions of the Schroedinger equation with exponential potentials

International Nuclear Information System (INIS)

Silvestre-Brac, Bernard; Semay, Claude; Buisseret, Fabien

2009-01-01

The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies of the Schroedinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schroedinger equation with exponential potentials of the form -αr λ exp(-βr) can also be analytically solved by using the auxiliary field method. Closed formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn to the Yukawa potential and the pure exponential potential

Process-Hardened, Multi-Analyte Sensor for Characterizing Rocket Plum Constituents Under Test Environment, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — The objective of the Phase II STTR project is to develop a prototype multi-analyte sensor system to detect gaseous analytes present in the test stands during...

Technique for approximate analytical calculating the internuclear cascade initiated by medium-energy nucleons in accelerator shields

International Nuclear Information System (INIS)

Kazarnovskij, M.V.; Matushko, G.K.; Matushko, V.L.; Par'ev, Eh.Ya.; Serezhnikov, S.V.

1981-01-01

The problem on propagation of the internuclear cascade initiated by nucleons of 0.1-1 GeV energy in accelerator schielding is solved approximately in the analytical form. Analytical expressions for the function of spatial, angular and energy distribution of the flux density of nucleons with the energy above 20 MeV and some functionals from it are obtained. The results of the calculations obtained by the developed methods are compared with calculations obtained by the method of direct simulation. It is shown that at the atomic mass of shielding material [ru

Approximate analytical solution of diffusion equation with fractional time derivative using optimal homotopy analysis method

Directory of Open Access Journals (Sweden)

S. Das

2013-12-01

Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.

Analytic approximations for inside-outside interferometry

Energy Technology Data Exchange (ETDEWEB)

Padula, S.S.; Gyulassy, M. (Lawrence Berkeley Lab., CA (USA). Nuclear Science Div.)

1990-07-30

Analytical expressions for pion interferometry are derived illustrating the competing effects of various non-ideal aspects of inside-outside cascade dynamics at energies {proportional to}200 AGeV. (orig.).

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

Science.gov (United States)

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.

On the validity of the equivalent-photon approximation for virtual photon-photon collisions

International Nuclear Information System (INIS)

Carimalo, C.; Kessler, P.; Parisi, J.

1979-05-01

For virtual photon-photon collisions in electron storage rings, one derive the equivalent-photon approximation from a helicity treatment, and present it in two forms, involving respectively (i) polarized transverse photons ('transverse-photon approximation') and (ii) unpolarized ones ('Williams-Weizsaecker approximation'). One first postulates the conditions of validity of the approximation on the basis of analytic considerations, and then check them numerically in the case of the process e e → e e μ + μ - . For this check, we consider the completely differentiated cross section as far as approximation (i) is concerned; and in the case of approximation (ii), the cross section differentiated with respect to all variables except the azimuthal angles. The results are given in the form of Tables showing the lower and higher limit of the error involved in the approximation for a large variety of kinematic configurations (i. e., energy losses and scattering angles of both electrons). Those Tables are discussed in detail, and conclusions are drawn as to the applicability of the equivalent-photon approximation to future experiments to be performed with high-energy electron storage rings

Fast and Analytical EAP Approximation from a 4th-Order Tensor.

Science.gov (United States)

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

Approximate analytical solution to the Boussinesq equation with a sloping water-land boundary

Science.gov (United States)

Tang, Yuehao; Jiang, Qinghui; Zhou, Chuangbing

2016-04-01

An approximate solution is presented to the 1-D Boussinesq equation (BEQ) characterizing transient groundwater flow in an unconfined aquifer subject to a constant water variation at the sloping water-land boundary. The flow equation is decomposed to a linearized BEQ and a head correction equation. The linearized BEQ is solved using a Laplace transform. By means of the frozen-coefficient technique and Gauss function method, the approximate solution for the head correction equation can be obtained, which is further simplified to a closed-form expression under the condition of local energy equilibrium. The solutions of the linearized and head correction equations are discussed from physical concepts. Especially for the head correction equation, the well posedness of the approximate solution obtained by the frozen-coefficient method is verified to demonstrate its boundedness, which can be further embodied as the upper and lower error bounds to the exact solution of the head correction by statistical analysis. The advantage of this approximate solution is in its simplicity while preserving the inherent nonlinearity of the physical phenomenon. Comparisons between the analytical and numerical solutions of the BEQ validate that the approximation method can achieve desirable precisions, even in the cases with strong nonlinearity. The proposed approximate solution is applied to various hydrological problems, in which the algebraic expressions that quantify the water flow processes are derived from its basic solutions. The results are useful for the quantification of stream-aquifer exchange flow rates, aquifer response due to the sudden reservoir release, bank storage and depletion, and front position and propagation speed.

Analytic evaluation of LAMPF II Booster Cavity design

International Nuclear Information System (INIS)

Friedrichs, C.C.

1985-01-01

Through the past few decades, a great deal of sophistication has evolved in the numeric codes used to evaluate electromagnetically resonant structures. The numeric methods are extremely precise, even for complicated geometries, whereas analytic methods require a simple uniform geometry and a simple, known mode configuration if the same precision is to be obtained. The code SUPERFISH, which is near the present state-of-the-art of numeric methods, does have the following limitations: No circumferential geometry variations are permissible; there are no provisions for magnetic or dielectric losses; and finally, it is impractical (because of the complexity of the code) to modify it to extract particular bits of data one might want that are not provided by the code as written. This paper describes how SUPERFISH was used as an aid in derivating an analytic model of the LAMPF II Booster Cavity. Once a satisfactory model was derived, simple FORTRAN codes were generated to provide whatever data was required. The analytic model is made up of TEM- and radial-mode transmission-line sections, as well as lumped elements where appropriate. Radial transmission-line equations, which include losses, were not found in any literature, and the extension of the lossless equations to include magnetic and dielectric losses are included in this paper

Approximative analytic eigenvalues for orbital excitations in the case of a coulomb potential plus linear and quadratic radial terms

International Nuclear Information System (INIS)

Rekab, S.; Zenine, N.

2006-01-01

We consider the three dimensional non relativistic eigenvalue problem in the case of a Coulomb potential plus linear and quadratic radial terms. In the framework of the Rayleigh-Schrodinger Perturbation Theory, using a specific choice of the unperturbed Hamiltonian, we obtain approximate analytic expressions for the eigenvalues of orbital excitations. The implications and the range of validity of the obtained analytic expression are discussed

Analytic number theory, approximation theory, and special functions in honor of Hari M. Srivastava

CERN Document Server

Rassias, Michael

2014-01-01

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality, and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics, and other computational and applied sciences.

Fast and Analytical EAP Approximation from a 4th-Order Tensor

Directory of Open Access Journals (Sweden)

Aurobrata Ghosh

2012-01-01

Full Text Available Generalized diffusion tensor imaging (GDTI was developed to model complex apparent diffusivity coefficient (ADC using higher-order tensors (HOTs and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP. Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF, since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

An analytical approximation scheme to two-point boundary value problems of ordinary differential equations

International Nuclear Information System (INIS)

Boisseau, Bruno; Forgacs, Peter; Giacomini, Hector

2007-01-01

A new (algebraic) approximation scheme to find global solutions of two-point boundary value problems of ordinary differential equations (ODEs) is presented. The method is applicable for both linear and nonlinear (coupled) ODEs whose solutions are analytic near one of the boundary points. It is based on replacing the original ODEs by a sequence of auxiliary first-order polynomial ODEs with constant coefficients. The coefficients in the auxiliary ODEs are uniquely determined from the local behaviour of the solution in the neighbourhood of one of the boundary points. The problem of obtaining the parameters of the global (connecting) solutions, analytic at one of the boundary points, reduces to find the appropriate zeros of algebraic equations. The power of the method is illustrated by computing the approximate values of the 'connecting parameters' for a number of nonlinear ODEs arising in various problems in field theory. We treat in particular the static and rotationally symmetric global vortex, the skyrmion, the Abrikosov-Nielsen-Olesen vortex, as well as the 't Hooft-Polyakov magnetic monopole. The total energy of the skyrmion and of the monopole is also computed by the new method. We also consider some ODEs coming from the exact renormalization group. The ground-state energy level of the anharmonic oscillator is also computed for arbitrary coupling strengths with good precision. (fast track communication)

An analytical expression for the non-singlet structure functions at small χ in the double logarithmic approximation

International Nuclear Information System (INIS)

Lublinsky, M.

2004-01-01

A simple analytic expression for the non-singlet structure function fns is given. The expression is derived from the result of B. I. Ermolaev et al. (1996) obtained by low x resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD. (orig.)

Uniform analytic approximation of Wigner rotation matrices

Science.gov (United States)

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.

Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations

KAUST Repository

Castrillon, Julio

2016-03-02

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remapped onto a corresponding PDE with a fixed deterministic domain. We show that the solution can be analytically extended to a well defined region in CN with respect to the random variables. A sparse grid stochastic collocation method is then used to compute the mean and variance of the QoI. Finally, convergence rates for the mean and variance of the QoI are derived and compared to those obtained in numerical experiments.

Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry

International Nuclear Information System (INIS)

Wei Gaofeng; Dong Shihai

2008-01-01

In this Letter the approximately analytical bound state solutions of the Dirac equation with the Manning-Rosen potential for arbitrary spin-orbit coupling quantum number k are carried out by taking a properly approximate expansion for the spin-orbit coupling term. In the case of exact spin symmetry, the associated two-component spinor wave functions of the Dirac equation for arbitrary spin-orbit quantum number k are presented and the corresponding bound state energy equation is derived. We study briefly two special cases; the general s-wave problem and the equal scalar and vector Manning-Rosen potential

Analytical approximations for the long-term decay behavior of spent fuel and high-level waste

International Nuclear Information System (INIS)

Malbrain, C.M.; Deutch, J.M.; Lester, R.K.

1982-01-01

Simple analytical approximations are presented that describe the radioactivity and radiogenic decay heat behavior of high-level wastes (HLWs) from various nuclear fuel cycles during the first 100,000 years of waste life. The correlations are based on detailed computations of HLW properties carried out with the isotope generation and depletion code ORIGEN 2. The ambiguities encountered in using simple comparisons of the hazards posed by HLWs and naturally occurring mineral deposits to establish the longevity requirements for geologic waste disposal schemes are discussed

Analytical models approximating individual processes: a validation method.

Science.gov (United States)

Favier, C; Degallier, N; Menkès, C E

2010-12-01

Upscaling population models from fine to coarse resolutions, in space, time and/or level of description, allows the derivation of fast and tractable models based on a thorough knowledge of individual processes. The validity of such approximations is generally tested only on a limited range of parameter sets. A more general validation test, over a range of parameters, is proposed; this would estimate the error induced by the approximation, using the original model's stochastic variability as a reference. This method is illustrated by three examples taken from the field of epidemics transmitted by vectors that bite in a temporally cyclical pattern, that illustrate the use of the method: to estimate if an approximation over- or under-fits the original model; to invalidate an approximation; to rank possible approximations for their qualities. As a result, the application of the validation method to this field emphasizes the need to account for the vectors' biology in epidemic prediction models and to validate these against finer scale models. Copyright © 2010 Elsevier Inc. All rights reserved.

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

Science.gov (United States)

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.

Calculation of photon attenuation coefficients of elements and compounds from approximate semi-analytical formulae

Energy Technology Data Exchange (ETDEWEB)

Roteta, M; Baro, J; Fernandez-Varea, J M; Salvat, F

1994-07-01

The FORTRAN 77 code PHOTAC to compute photon attenuation coefficients of elements and compounds is described. The code is based on the semi analytical approximate atomic cross sections proposed by Baro et al. (1994). Photoelectric cross sections for coherent and incoherent scattering and for pair production are obtained as integrals of the corresponding differential cross sections. These integrals are evaluated, to a pre-selected accuracy, by using a 20-point Gauss adaptive integration algorithm. Calculated attenuation coefficients agree with recently compiled databases to within - 1%, in the energy range from 1 keV to 1 GeV. The complete source listing of the program PHOTAC is included. (Author) 14 refs.

Calculation of photon attenuation coefficients of elements and compounds from approximate semi-analytical formulae

International Nuclear Information System (INIS)

Roteta, M.; Baro, J.; Fernandez-Varea, J. M.; Salvat, F.

1994-01-01

The FORTRAN 77 code PHOTAC to compute photon attenuation coefficients of elements and compounds is described. The code is based on the semi analytical approximate atomic cross sections proposed by Baro et al. (1994). Photoelectric cross sections for coherent and incoherent scattering and for pair production are obtained as integrals of the corresponding differential cross sections. These integrals are evaluated, to a pre-selected accuracy, by using a 20-point Gauss adaptive integration algorithm. Calculated attenuation coefficients agree with recently compiled databases to within - 1%, in the energy range from 1 keV to 1 GeV. The complete source listing of the program PHOTAC is included. (Author) 14 refs

Intertemporal Asset Allocation with Habit Formation in Preferences: An Approximate Analytical Solution

DEFF Research Database (Denmark)

Pedersen, Thomas Quistgaard

In this paper we derive an approximate analytical solution to the optimal con- sumption and portfolio choice problem of an infinitely-lived investor with power utility defined over the difference between consumption and an external habit. The investor is assumed to have access to two tradable......-linearized surplus consumption ratio. The "difference habit model" implies that the relative risk aversion is time-varying which is in line with recent ev- idence from the asset pricing literature. We show that accounting for habit a¤ects both the myopic and intertemporal hedge component of optimal asset demand......, and introduces an additional component that works as a hedge against changes in the investor's habit level. In an empirical application, we calibrate the model to U.S. data and show that habit formation has significant effects on both the optimal consumption and portfolio choice compared to a standard CRRA...

Rayleigh approximation to ground state of the Bose and Coulomb glasses

Science.gov (United States)

Ryan, S. D.; Mityushev, V.; Vinokur, V. M.; Berlyand, L.

2015-01-01

Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties. PMID:25592417

Analytical approximation of the nanoscale dose distribution in an irradiated medium with an embedded nanoparticle

International Nuclear Information System (INIS)

Chernov, V; Barboza-Flores, M; Chernov, G

2012-01-01

In this work we propose an analytical approach describing the dose distribution around a NP embedded in a medium. The approach describes the following sequence of events: The homogenous and isotropic creation of secondary electrons under incident photon fluence; travel of the created electrons toward the NP surface and their escaping from the NP with different energies and angles; deposition of energy in surrounding medium. The radial dose distribution around the NP was found as the average energy deposited by the escaped electrons in a spherical shell at a distance r from the NP center normalized to its mass. The continuous slowing down approximation and the assumption that created electrons travel in a straight-line path were used. As result, a set of analytical expressions describing the dose distribution was derived. The expressions were applied to the calculation of the dose distribution around spherical gold NPs of different size embedded in water. It was shown that the dose distribution is close to the 1/r 2 dependence and practically independent of the NP radius.

Approximated and User Steerable tSNE for Progressive Visual Analytics

NARCIS (Netherlands)

Pezzotti, N.; Lelieveldt, B.P.F.; van der Maaten, L.J.P.; Hollt, T.; Eisemann, E.; Vilanova Bartroli, A.

2016-01-01

Progressive Visual Analytics aims at improving the interactivity in existing analytics techniques by means of visualization as well as interaction with intermediate results. One key method for data analysis is dimensionality reduction, for example, to produce 2D embeddings that can be visualized and

Algorithms and analytical solutions for rapidly approximating long-term dispersion from line and area sources

Science.gov (United States)

Barrett, Steven R. H.; Britter, Rex E.

Predicting long-term mean pollutant concentrations in the vicinity of airports, roads and other industrial sources are frequently of concern in regulatory and public health contexts. Many emissions are represented geometrically as ground-level line or area sources. Well developed modelling tools such as AERMOD and ADMS are able to model dispersion from finite (i.e. non-point) sources with considerable accuracy, drawing upon an up-to-date understanding of boundary layer behaviour. Due to mathematical difficulties associated with line and area sources, computationally expensive numerical integration schemes have been developed. For example, some models decompose area sources into a large number of line sources orthogonal to the mean wind direction, for which an analytical (Gaussian) solution exists. Models also employ a time-series approach, which involves computing mean pollutant concentrations for every hour over one or more years of meteorological data. This can give rise to computer runtimes of several days for assessment of a site. While this may be acceptable for assessment of a single industrial complex, airport, etc., this level of computational cost precludes national or international policy assessments at the level of detail available with dispersion modelling. In this paper, we extend previous work [S.R.H. Barrett, R.E. Britter, 2008. Development of algorithms and approximations for rapid operational air quality modelling. Atmospheric Environment 42 (2008) 8105-8111] to line and area sources. We introduce approximations which allow for the development of new analytical solutions for long-term mean dispersion from line and area sources, based on hypergeometric functions. We describe how these solutions can be parameterized from a single point source run from an existing advanced dispersion model, thereby accounting for all processes modelled in the more costly algorithms. The parameterization method combined with the analytical solutions for long-term mean

Approximation for the adjoint neutron spectrum

International Nuclear Information System (INIS)

Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

2002-01-01

The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)

Analytical approximations of diving-wave imaging in constant-gradient medium

KAUST Repository

Stovas, Alexey

2014-06-24

Full-waveform inversion (FWI) in practical applications is currently used to invert the direct arrivals (diving waves, no reflections) using relatively long offsets. This is driven mainly by the high nonlinearity introduced to the inversion problem when reflection data are included, which in some cases require extremely low frequency for convergence. However, analytical insights into diving waves have lagged behind this sudden interest. We use analytical formulas that describe the diving wave’s behavior and traveltime in a constant-gradient medium to develop insights into the traveltime moveout of diving waves and the image (model) point dispersal (residual) when the wrong velocity is used. The explicit formulations that describe these phenomena reveal the high dependence of diving-wave imaging on the gradient and the initial velocity. The analytical image point residual equation can be further used to scan for the best-fit linear velocity model, which is now becoming a common sight as an initial velocity model for FWI. We determined the accuracy and versatility of these analytical formulas through numerical tests.

A study of density effects in plasmas using analytical approximations for the self-consistent potential

Science.gov (United States)

Poirier, M.

2015-06-01

Density effects in ionized matter require particular attention since they modify energies, wavefunctions and transition rates with respect to the isolated-ion situation. The approach chosen in this paper is based on the ion-sphere model involving a Thomas-Fermi-like description for free electrons, the bound electrons being described by a full quantum mechanical formalism. This permits to deal with plasmas out of thermal local equilibrium, assuming only a Maxwell distribution for free electrons. For H-like ions, such a theory provides simple and rather accurate analytical approximations for the potential created by free electrons. Emphasis is put on the plasma potential rather than on the electron density, since the energies and wavefunctions depend directly on this potential. Beyond the uniform electron gas model, temperature effects may be analyzed. In the case of H-like ions, this formalism provides analytical perturbative expressions for the energies, wavefunctions and transition rates. Explicit expressions are given in the case of maximum orbital quantum number, and compare satisfactorily with results from a direct integration of the radial Schrödinger equation. Some formulas for lower orbital quantum numbers are also proposed.

The generalized gradient approximation in solids and molecules

International Nuclear Information System (INIS)

Haas, P.

2010-01-01

Today, most methods are based on theoretical calculations of the electronic structure of molecules, surfaces and solids on density functional theory (DFT) and the resulting Kohn-Sham equations. Unfortunately, the exact analytical expression for the exchange-correlation functional is not known and has to be approximated. The reliability of such a Kohn-Sham calculation depends i) from the numerical accuracy and ii) from the used approximation for the exchange-correlation energy. To solve the Kohn-Sham equations, the WIEN2k code, which is one of the most accurate methods for solid-state calculations, is used. The search for better approximations for the exchange-correlation energy is an intense field of research in chemistry and physics. The main objectives of the dissertation is the development, implementation and testing of advanced exchange-correlation functionals and the analysis of existing functionals. The focus of this work are GGA - functionals. Such GGA functionals are still the most widely used functionals, in particular because they are easy to implement and require little computational effort. Several recent studies have shown that an improvement of the GGA should be possible. A detailed analysis of the results will allow us to understand why a particular GGA approximation for a class of elements (compounds) works better than for another. (Kancsar) [de

Approximation by planar elastic curves

DEFF Research Database (Denmark)

Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge

2016-01-01

We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....

Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods

Directory of Open Access Journals (Sweden)

Norhasimah Mahiddin

2014-01-01

Full Text Available The modified decomposition method (MDM and homotopy perturbation method (HPM are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.

An analytic, approximate method for modeling steady, three-dimensional flow to partially penetrating wells

Science.gov (United States)

Bakker, Mark

2001-05-01

An analytic, approximate solution is derived for the modeling of three-dimensional flow to partially penetrating wells. The solution is written in terms of a correction on the solution for a fully penetrating well and is obtained by dividing the aquifer up, locally, in a number of aquifer layers. The resulting system of differential equations is solved by application of the theory for multiaquifer flow. The presented approach has three major benefits. First, the solution may be applied to any groundwater model that can simulate flow to a fully penetrating well; the solution may be superimposed onto the solution for the fully penetrating well to simulate the local three-dimensional drawdown and flow field. Second, the approach is applicable to isotropic, anisotropic, and stratified aquifers and to both confined and unconfined flow. Third, the solution extends over a small area around the well only; outside this area the three-dimensional effect of the partially penetrating well is negligible, and no correction to the fully penetrating well is needed. A number of comparisons are made to existing three-dimensional, analytic solutions, including radial confined and unconfined flow and a well in a uniform flow field. It is shown that a subdivision in three layers is accurate for many practical cases; very accurate solutions are obtained with more layers.

Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation

Directory of Open Access Journals (Sweden)

G. H. Gudmundsson

2008-07-01

Full Text Available New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses.

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

Science.gov (United States)

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.

Approximate analytical solution of the Dirac equation for pseudospin symmetry with modified Po schl-Teller potential and trigonometric Scarf II non-central potential using asymptotic iteration method

International Nuclear Information System (INIS)

Pratiwi, B N; Suparmi, A; Cari, C; Yunianto, M; Husein, A S

2016-01-01

We apllied asymptotic iteration method (AIM) to obtain the analytical solution of the Dirac equation in case exact pseudospin symmetry in the presence of modified Pcischl- Teller potential and trigonometric Scarf II non-central potential. The Dirac equation was solved by variables separation into one dimensional Dirac equation, the radial part and angular part equation. The radial and angular part equation can be reduced into hypergeometric type equation by variable substitution and wavefunction substitution and then transform it into AIM type equation to obtain relativistic energy eigenvalue and wavefunctions. Relativistic energy was calculated numerically by Matlab software. And then relativistic energy spectrum and wavefunctions were visualized by Matlab software. The results show that the increase in the radial quantum number n_r causes decrease in the relativistic energy spectrum. The negative value of energy is taken due to the pseudospin symmetry limit. Several quantum wavefunctions were presented in terms of the hypergeometric functions. (paper)

Mutual capture of dipolar molecules at low and very low energies. I. Approximate analytical treatment.

Science.gov (United States)

Nikitin, E E; Troe, J

2010-09-16

Approximate analytical expressions are derived for the low-energy rate coefficients of capture of two identical dipolar polarizable rigid rotors in their lowest nonresonant (j(1) = 0 and j(2) = 0) and resonant (j(1) = 0,1 and j(2) = 1,0) states. The considered range extends from the quantum, ultralow energy regime, characterized by s-wave capture, to the classical regime described within fly wheel and adiabatic channel approaches, respectively. This is illustrated by the table of contents graphic (available on the Web) that shows the scaled rate coefficients for the mutual capture of rotors in the resonant state versus the reduced wave vector between the Bethe zero-energy (left arrows) and classical high-energy (right arrow) limits for different ratios δ of the dipole-dipole to dispersion interaction.

Solution of the point kinetics equations in the presence of Newtonian temperature feedback by Pade approximations via the analytical inversion method

International Nuclear Information System (INIS)

Aboanber, A E; Nahla, A A

2002-01-01

A method based on the Pade approximations is applied to the solution of the point kinetics equations with a time varying reactivity. The technique consists of treating explicitly the roots of the inhour formula. A significant improvement has been observed by treating explicitly the most dominant roots of the inhour equation, which usually would make the Pade approximation inaccurate. Also the analytical inversion method which permits a fast inversion of polynomials of the point kinetics matrix is applied to the Pade approximations. Results are presented for several cases of Pade approximations using various options of the method with different types of reactivity. The formalism is applicable equally well to non-linear problems, where the reactivity depends on the neutron density through temperature feedback. It was evident that the presented method is particularly good for cases in which the reactivity can be represented by a series of steps and performed quite well for more general cases

Approximate analytical relationships for linear optimal aeroelastic flight control laws

Science.gov (United States)

Kassem, Ayman Hamdy

1998-09-01

This dissertation introduces new methods to uncover functional relationships between design parameters of a contemporary control design technique and the resulting closed-loop properties. Three new methods are developed for generating such relationships through analytical expressions: the Direct Eigen-Based Technique, the Order of Magnitude Technique, and the Cost Function Imbedding Technique. Efforts concentrated on the linear-quadratic state-feedback control-design technique applied to an aeroelastic flight control task. For this specific application, simple and accurate analytical expressions for the closed-loop eigenvalues and zeros in terms of basic parameters such as stability and control derivatives, structural vibration damping and natural frequency, and cost function weights are generated. These expressions explicitly indicate how the weights augment the short period and aeroelastic modes, as well as the closed-loop zeros, and by what physical mechanism. The analytical expressions are used to address topics such as damping, nonminimum phase behavior, stability, and performance with robustness considerations, and design modifications. This type of knowledge is invaluable to the flight control designer and would be more difficult to formulate when obtained from numerical-based sensitivity analysis.

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

Science.gov (United States)

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.

PEP-II vacuum system pressure profile modeling using EXCEL

International Nuclear Information System (INIS)

Nordby, M.; Perkins, C.

1994-06-01

A generic, adaptable Microsoft EXCEL program to simulate molecular flow in beam line vacuum systems is introduced. Modeling using finite-element approximation of the governing differential equation is discussed, as well as error estimation and program capabilities. The ease of use and flexibility of the spreadsheet-based program is demonstrated. PEP-II vacuum system models are reviewed and compared with analytical models

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

Science.gov (United States)

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.

Analytical Predictions of Fatigue Crack Growth in the Lower Plate of the F-111 Wing Pivot Fitting Fuel Flow Hole Number 58

National Research Council Canada - National Science Library

MUrtagh, B

1998-01-01

... (then General Dynamics), predicted a fatigue life of approximately 57,000 flight hours. An equivalent analysis was conducted using the analytical crack closure code, FASTRAN II, and this resulted in a life prediction of about 25,000 flight hours...

Chemical evolution of two-component galaxies. II

International Nuclear Information System (INIS)

Caimmi, R.

1978-01-01

In order to confirm and refine the results obtained in a previous paper the chemical evolution of two-component (spheroid + disk) galaxies is derived rejecting the instantaneous recycling approximation, by means of numerical computations, accounting for (i) the collapse phase of the gas, assumed to be uniform in density and composition, and (ii) a birth-rate stellar function. Computations are performed relatively to the solar neighbourhood and to model galaxies which closely resemble the real morphological sequence: in both cases, numerical results are compared with analytical ones. The numerical models of this paper constitute a first-order approximation, while higher order approximations could be made by rejecting the hypothesis of uniform density and composition, and making use of detailed dynamical models. (Auth.)

Approximating the physical inner product of loop quantum cosmology

International Nuclear Information System (INIS)

Bahr, Benjamin; Thiemann, Thomas

2007-01-01

In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity

Analytical approximations for matter effects on CP violation in the accelerator-based neutrino oscillations with E≲1 GeV

Energy Technology Data Exchange (ETDEWEB)

Xing, Zhi-zhong [Institute of High Energy Physics, Chinese Academy of Sciences,Beijing 100049 (China); School of Physical Sciences, University of Chinese Academy of Sciences,Beijing 100049 (China); Center for High Energy Physics, Peking University,Beijing 100080 (China); Zhu, Jing-yu [Institute of High Energy Physics, Chinese Academy of Sciences,Beijing 100049 (China)

2016-07-04

Given an accelerator-based neutrino experiment with the beam energy E≲1 GeV, we expand the probabilities of ν{sub μ}→ν{sub e} and ν̄{sub μ}→ν̄{sub e} oscillations in matter in terms of two small quantities Δ{sub 21}/Δ{sub 31} and A/Δ{sub 31}, where Δ{sub 21}≡m{sub 2}{sup 2}−m{sub 1}{sup 2} and Δ{sub 31}≡m{sub 3}{sup 2}−m{sub 1}{sup 2} are the neutrino mass-squared differences, and A measures the strength of terrestrial matter effects. Our analytical approximations are numerically more accurate than those made by Freund in this energy region, and thus they are particularly applicable for the study of leptonic CP violation in the low-energy MOMENT, ESSνSM and T2K oscillation experiments. As a by-product, the new analytical approximations help us to easily understand why the matter-corrected Jarlskog parameter J̃ peaks at the resonance energy E{sub ∗}≃0.14 GeV (or 0.12 GeV) for the normal (or inverted) neutrino mass hierarchy, and how the three Dirac unitarity triangles are deformed due to the terrestrial matter contamination. We also affirm that a medium-baseline neutrino oscillation experiment with the beam energy E lying in the E{sub ∗}≲E≲2E{sub ∗} range is capable of exploring leptonic CP violation with little matter-induced suppression.

An approximation to the interference term using Frobenius Method

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear; E-mail: aquilino@lmp.ufrj.br

2007-07-01

An analytical approximation of the interference term {chi}(x,{xi}) is proposed. The approximation is based on the differential equation to {chi}(x,{xi}) using the Frobenius method and the parameter variation. The analytical expression of the {chi}(x,{xi}) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U{sup 238} isotope for different energies and temperature ranges. (author)

An approximation to the interference term using Frobenius Method

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da

2007-01-01

An analytical approximation of the interference term χ(x,ξ) is proposed. The approximation is based on the differential equation to χ(x,ξ) using the Frobenius method and the parameter variation. The analytical expression of the χ(x,ξ) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U 238 isotope for different energies and temperature ranges. (author)

Role of dust in H II regions

International Nuclear Information System (INIS)

Sarazin, C.L.

1975-01-01

The purpose of this dissertation is to determine quantitatively the effects of U.V. absorbing dust on H II regions, and compare these effects with observations. Many observations indicate that dust grains are present within H II regions. An analytic theory is presented which describes all three of the effects of dust in H II regions. Although this model is relatively crude, it is useful in determining the approximate size of the modifications due to dust. In order to explore this problem more carefully, detailed numerical models of H II regions with dust were constructed. The ionization and thermal structure of these model H II regions is discussed. The observational consequences of the presence of dust are explored; the optical line intensities, radio continuum and line fluxes, and infrared emission of model H II regions with dust are given. These numerical models are compared with observations of diffuse nebulae. The optical line ratios are compared to several nearby bright H II regions, and it is found that the dust models may explain several anomalies in their spectrum

Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation

International Nuclear Information System (INIS)

Bozkaya, Uğur; Sherrill, C. David

2016-01-01

An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the “gradient terms”: computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C 10 H 22 ), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.

An analytic Pade-motivated QCD coupling

International Nuclear Information System (INIS)

Martinez, H. E.; Cvetic, G.

2010-01-01

We consider a modification of the Minimal Analytic (MA) coupling of Shirkov and Solovtsov. This modified MA (mMA) coupling reflects the desired analytic properties of the space-like observables. We show that an approximation by Dirac deltas of its discontinuity function ρ is equivalent to a Pade(rational) approximation of the mMA coupling that keeps its analytic structure. We propose a modification to mMA that, as preliminary results indicate, could be an improvement in the evaluation of low-energy observables compared with other analytic couplings.

Solid-phase extraction of Mn(II), Co(II), Ni(II), Cu(II), Cd(II) and Pb(II) ions from environmental samples by flame atomic absorption spectrometry (FAAS)

Energy Technology Data Exchange (ETDEWEB)

Duran, Celal [Department of Chemistry, Faculty of Art and Science, Karadeniz Technical University, 61080 Trabzon (Turkey); Gundogdu, Ali [Department of Chemistry, Faculty of Art and Science, Karadeniz Technical University, 61080 Trabzon (Turkey); Bulut, Volkan Numan [Department of Chemistry, Giresun Faculty of Art and Science, Karadeniz Technical University, 28049 Giresun (Turkey); Soylak, Mustafa [Department of Chemistry, Faculty of Art and Science, Erciyes University, 38039 Kayseri (Turkey)]. E-mail: soylak@erciyes.edu.tr; Elci, Latif [Department of Chemistry, Faculty of Art and Science, Pamukkale University, 20020 Denizli (Turkey); Sentuerk, Hasan Basri [Department of Chemistry, Faculty of Art and Science, Karadeniz Technical University, 61080 Trabzon (Turkey); Tuefekci, Mehmet [Department of Chemistry, Faculty of Art and Science, Karadeniz Technical University, 61080 Trabzon (Turkey)

2007-07-19

A new method using a column packed with Amberlite XAD-2010 resin as a solid-phase extractant has been developed for the multi-element preconcentration of Mn(II), Co(II), Ni(II), Cu(II), Cd(II), and Pb(II) ions based on their complex formation with the sodium diethyldithiocarbamate (Na-DDTC) prior to flame atomic absorption spectrometric (FAAS) determinations. Metal complexes sorbed on the resin were eluted by 1 mol L{sup -1} HNO{sub 3} in acetone. Effects of the analytical conditions over the preconcentration yields of the metal ions, such as pH, quantity of Na-DDTC, eluent type, sample volume and flow rate, foreign ions etc. have been investigated. The limits of detection (LOD) of the analytes were found in the range 0.08-0.26 {mu}g L{sup -1}. The method was validated by analyzing three certified reference materials. The method has been applied for the determination of trace elements in some environmental samples.

Bent approximations to synchrotron radiation optics

International Nuclear Information System (INIS)

Heald, S.

1981-01-01

Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors

Approximating Markov Chains: What and why

International Nuclear Information System (INIS)

Pincus, S.

1996-01-01

Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to open-quote open-quote solve,close-quote close-quote or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the attractor, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. copyright 1996 American Institute of Physics

Approximating the Analytic Fourier Transform with the Discrete Fourier Transform

OpenAIRE

Axelrod, Jeremy

2015-01-01

The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.

Approximating distributions from moments

Science.gov (United States)

Pawula, R. F.

1987-11-01

A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.

Self-consistent approximations beyond the CPA: Part II

International Nuclear Information System (INIS)

Kaplan, T.; Gray, L.J.

1982-01-01

This paper concentrates on a self-consistent approximation for random alloys developed by Kaplan, Leath, Gray, and Diehl. The construction of the augmented space formalism for a binary alloy is sketched, and the notation to be used derived. Using the operator methods of the augmented space, the self-consistent approximation is derived for the average Green's function, and for evaluating the self-energy, taking into account the scattering by clusters of excitations. The particular cluster approximation desired is derived by treating the scattering by the excitations with S /SUB T/ exactly. Fourier transforms on the disorder-space clustersite labels solve the self-consistent set of equations. Expansion to short range order in the alloy is also discussed. A method to reduce the problem to a computationally tractable form is described

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

International Nuclear Information System (INIS)

Sanders, Sören; Holthaus, Martin

2017-01-01

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. (paper)

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

Science.gov (United States)

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.

Pion-nucleus cross sections approximation

International Nuclear Information System (INIS)

Barashenkov, V.S.; Polanski, A.; Sosnin, A.N.

1990-01-01

Analytical approximation of pion-nucleus elastic and inelastic interaction cross-section is suggested, with could be applied in the energy range exceeding several dozens of MeV for nuclei heavier than beryllium. 3 refs.; 4 tabs

Analytic structure of the wave function for a hydrogen atom in an analytic potential

International Nuclear Information System (INIS)

Hill, R.N.

1984-01-01

The rate of convergence of an approximate method for solving Schroedinger's equation depends on the ability of the approximating sequence to mimic the analytic structure of the unknown exact wave function. Thus a knowledge of the analytic structure of the wave function can be of great value when approximation schemes are designed. Consider the Schroedinger equation [- 1/2 del 2 -r -1 +V(r)]Psi(r) = EPsi(r) for a hydrogen atom in a potential V(r). The general theory of elliptic partial differential equations implies that Psi is analytic at regular points, but no general theory is available at singular points. The present paper investigates the Coulomb singular point at r = 0 and shows that, if V(r) = V 1 (x, y, z)+rV 2 (x, y, z) where V 1 and V 2 are analytic functions of x, y, z at x = y = z = 0, then the wave function has the form Psi(r) = Psi 1 (x, y, z)+rPsi 2 (x, y, z) where Psi 1 and Psi 2 are analytic functions of x, y, z at x = y = z = 0

Approximate Bayesian computation.

Directory of Open Access Journals (Sweden)

Mikael Sunnåker

Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.

Approximation of the Thomas-Fermi-Dirac potential for neutral atoms

International Nuclear Information System (INIS)

Jablonski, A.

1992-01-01

The frequently used analytical expression of Bonham and Strand approximating the Thomas-Fermi-Dirac (TFD) potential is closely analyzed. This expression does not satisfy the boundary conditions of the TFD differential equation, in particular, does not comprise the finite radius of the TFD potential. A modification of the analytical expression is proposed to adjust it to the boundary conditions. A new fit is made on the basis of the variational formulation of the TFD problem. An attempt is also made in the present work to develop a new numerical procedure providing very accurate solutions of this problem. Such solutions form a reference to check the quality of analytical approximations. Exemplary calculations of the elastic scattering cross sections are made for different expressions approximating the TFD potential to visualize the influence of the inaccuracies of the fit. It seems that the elastic scattering calculations should be based on extensive tables with the accurate values of the TFD screening function rather than on fitted analytical expressions. (orig.)

Comment on 'Approximation for a large-angle simple pendulum period'

International Nuclear Information System (INIS)

Yuan Qingxin; Ding Pei

2009-01-01

In a recent letter, Belendez et al (2009 Eur. J. Phys. 30 L25-8) proposed an alternative of approximation for the period of a simple pendulum suggested earlier by Hite (2005 Phys. Teach. 43 290-2) who set out to improve on the Kidd and Fogg formula (2002 Phys. Teach. 40 81-3). As a response to the approximation scheme, we obtain another analytical approximation for the large-angle pendulum period, which owns the simplicity and accuracy in evaluating the exact period, and moreover, for amplitudes less than 144 deg. the analytical approximate expression is more accurate than others in the literature. (letters and comments)

Coulomb couplings in solubilised light harvesting complex II (LHCII): challenging the ideal dipole approximation from TDDFT calculations.

Science.gov (United States)

López-Tarifa, P; Liguori, Nicoletta; van den Heuvel, Naudin; Croce, Roberta; Visscher, Lucas

2017-07-19

The light harvesting complex II (LHCII), is a pigment-protein complex responsible for most of the light harvesting in plants. LHCII harvests sunlight and transfers excitation energy to the reaction centre of the photo-system, where the water oxidation process takes place. The energetics of LHCII can be modulated by means of conformational changes allowing a switch from a harvesting to a quenched state. In this state, the excitation energy is no longer transferred but converted into thermal energy to prevent photooxidation. Based on molecular dynamics simulations at the microsecond time scale, we have recently proposed that the switch between different fluorescent states can be probed by correlating shifts in the chromophore-chromophore Coulomb interactions to particular protein movements. However, these findings are based upon calculations in the ideal point dipole approximation (IDA) where the Coulomb couplings are simplified as first order dipole-dipole interactions, also assuming that the chromophore transition dipole moments lay in particular directions of space with constant moduli (FIX-IDA). In this work, we challenge this approximation using the time-dependent density functional theory (TDDFT) combined with the frozen density embedding (FDE) approach. Our aim is to establish up to which limit FIX-IDA can be applied and which chromophore types are better described under this approximation. For that purpose, we use the classical trajectories of solubilised light harvesting complex II (LHCII) we have recently reported [Liguori et al., Sci. Rep., 2015, 5, 15661] and selected three pairs of chromophores containing chlorophyll and carotenoids (Chl and Car): Chla611-Chla612, Chlb606-Chlb607 and Chla612-Lut620. Using the FDE in the Tamm-Dancoff approximation (FDEc-TDA), we show that IDA is accurate enough for predicting Chl-Chl Coulomb couplings. However, the FIX-IDA largely overestimates Chl-Car interactions mainly because the transition dipole for the Cars is not

Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation

Science.gov (United States)

Salajegheh, Maral; Nejad, S. Mohammad Moosavi; Khanpour, Hamzeh; Tehrani, S. Atashbar

2018-05-01

In this paper, we present SMKA18 analysis, which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton g1p(x ,Q2) , neutron g1n(x ,Q2) , and deuteron g1d(x ,Q2) spin-dependent structure functions data set including the most recent high-precision measurements from COMPASS16 experiments at CERN, which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard Hessian error propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering data set and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of x .

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

Directory of Open Access Journals (Sweden)

Lukas Nejdl

2017-08-01

Full Text Available 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.

Analytic nuclear scattering theories

International Nuclear Information System (INIS)

Di Marzio, F.; University of Melbourne, Parkville, VIC

1999-01-01

A wide range of nuclear reactions are examined in an analytical version of the usual distorted wave Born approximation. This new approach provides either semi analytic or fully analytic descriptions of the nuclear scattering processes. The resulting computational simplifications, when used within the limits of validity, allow very detailed tests of both nuclear interaction models as well as large basis models of nuclear structure to be performed

Analytic Approximations for Soliton Solutions of Short-Wave Models for Camassa-Holm and Degasperis-Procesi Equations

International Nuclear Information System (INIS)

Yang Pei; Li Zhibin; Chen Yong

2010-01-01

In this paper, the short-wave model equations are investigated, which are associated with the Camassa-Holm (CH) and Degasperis-Procesi (DP) shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformations back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems. (general)

Biosorption of copper(II), lead(II), iron(III) and cobalt(II) on Bacillus sphaericus-loaded Diaion SP-850 resin

International Nuclear Information System (INIS)

Tuzen, Mustafa; Uluozlu, Ozgur Dogan; Usta, Canan; Soylak, Mustafa

2007-01-01

The biosorption of copper(II), lead(II), iron(III) and cobalt(II) on Bacillus sphaericus-loaded Diaion SP-850 resin for preconcentration-separation of them have been investigated. The sorbed analytes on biosorbent were eluted by using 1 mol L -1 HCl and analytes were determined by flame atomic absorption spectrometry. The influences of analytical parameters including amounts of pH, B. sphaericus, sample volume etc. on the quantitative recoveries of analytes were investigated. The effects of alkaline, earth alkaline ions and some metal ions on the retentions of the analytes on the biosorbent were also examined. Separation and preconcentration of Cu, Pb, Fe and Co ions from real samples was achieved quantitatively. The detection limits by 3 sigma for analyte ions were in the range of 0.20-0.75 μg L -1 for aqueous samples and in the range of 2.5-9.4 ng g -1 for solid samples. The validation of the procedure was performed by the analysis of the certified standard reference materials (NRCC-SLRS 4 Riverine Water, SRM 2711 Montana soil and GBW 07605 Tea). The presented method was applied to the determination of analyte ions in green tea, black tea, cultivated mushroom, boiled wheat, rice and soil samples with successfully results

Problem-based learning on quantitative analytical chemistry course

Science.gov (United States)

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.

Interpretation of plasma impurity deposition probes. Analytic approximation

Science.gov (United States)

Stangeby, P. C.

1987-10-01

Insertion of a probe into the plasma induces a high speed flow of the hydrogenic plasma to the probe which, by friction, accelerates the impurity ions to velocities approaching the hydrogenic ion acoustic speed, i.e., higher than the impurity ion thermal speed. A simple analytic theory based on this effect provides a relation between impurity fluxes to the probe Γimp and the undisturbed impurity ion density nimp, with the hydrogenic temperature and density as input parameters. Probe size also influences the collection process and large probes are found to attract a higher flux density than small probes in the same plasma. The quantity actually measured, cimp, the impurity atom surface density (m-2) net-deposited on the probe, is related to Γimp and thus to nimp by taking into account the partial removal of deposited material caused by sputtering and the redeposition process.

Inertial parameters in the interacting boson fermion approximation

International Nuclear Information System (INIS)

Dukelsky, J.; Lima, C.

1986-06-01

The Hartree-Bose-Fermi and the adiabatic approximations are used to derive analytic formulas for the moment of inertia and the decoupling parameter of the interacting boson fermion approximation for deformed systems. These formulas are applied to the SU(3) dynamical symmetry, obtaining perfect agreement with the exact results. (Authors) [pt

Cosmological applications of Padé approximant

International Nuclear Information System (INIS)

Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

2014-01-01

As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation

Cosmological applications of Padé approximant

Science.gov (United States)

Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

2014-01-01

As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.

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

Science.gov (United States)

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.

PWL approximation of nonlinear dynamical systems, part II: identification issues

International Nuclear Information System (INIS)

De Feo, O; Storace, M

2005-01-01

This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes a black-box identification method based on state space reconstruction and PWL approximation, and applies it to some particularly significant dynamical systems (two topological normal forms and the Colpitts oscillator)

The approximate analytical solution of the internal problem of conductive and laminar free convection

Directory of Open Access Journals (Sweden)

M. I. Popov

2016-01-01

Full Text Available The approximate analytical solution of a problem about nonstationary free convection in the conductive and laminar mode of the Newtonian liquid in square area at the instantaneous change of temperature of a sidewall and lack of heat fluxes is submitted on top and bottom the bases. The equations of free convection in an approximation of Oberbeka-Bussinesk are linearized due to neglect by convective items. For reduction of number of hydrothermal parameters the system is given to the dimensionless look by introduction of scales for effect and explanatory variables. Transition from classical variables to the variables "whirlwind-a flow function" allowed to reduce system to a nonstationary heat conduction equation and a nonstationary nonuniform biharmonic equation, and the first is not dependent on the second. The decision in the form of a flow function is received by application integral a sine - Fourier transforms with terminating limits to a biharmonic equation at first on a variable x, and then on a variable y. The flow function has an appearance of a double series of Fourier on sine with coefficients in an integral form. Coefficients of a row represent integrals from unknown functions. On the basis of a hypothesis of an express type of integrals coefficients are calculated from the linear equation system received from boundary conditions on partial derivatives of function. Dependence of structure of a current on Prandtl's number is investigated. The cards of streamlines and isolines of components of speed describing development of a current from the moment of emergence before transition to a stationary state are received. The schedules of a field of vectors of speeds in various time illustrating dynamics of a current are provided. Reliability of a hypothesis of an express type of integral coefficients is confirmed by adequacy to physical sense and coherence of the received results with the numerical solution of a problem.

Approximate analytical solutions in the analysis of elastic structures of complex geometry

Science.gov (United States)

Goloskokov, Dmitriy P.; Matrosov, Alexander V.

2018-05-01

A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.

Approximate and analytical solutions for solute transport from an injection well into a single fracture

International Nuclear Information System (INIS)

Chen, C.S.; Yates, S.R.

1989-01-01

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. It has been reported that by treating the radioactive decay constant as the appropriate first-order rate constant, these solutions can also be used to study injection problems of a similar nature subject to first-order chemical or biological reactions. The fracture is idealized by a pair of parallel, smooth plates separated by an aperture of constant thickness. Groundwater was assumed to be immobile in the underlying and overlying porous formations due to their low permeabilities. However, the injected radionuclides were able to move from the fracture into the porous matrix by molecular diffusion (the matrix diffusion) due to possible concentration gradients across the interface between the fracture and the porous matrix. Calculation of the transient solutions is not straightforward, and the paper documents a contained Fortran program, which computes the Stehfest inversion, the Airy functions, and gives the concentration distributions in the fracture as well as in the porous matrix for both transient and steady-state cases

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

Science.gov (United States)

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

2010-12-01

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

Approximation of the Doppler broadening function by Frobenius method

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C.

2005-01-01

An analytical approximation of the Doppler broadening function ψ(x,ξ) is proposed. This approximation is based on the solution of the differential equation for ψ(x,ξ) using the methods of Frobenius and the parameters variation. The analytical form derived for ψ(x,ξ) in terms of elementary functions is very simple and precise. It can be useful for applications related to the treatment of nuclear resonances mainly for the calculations of multigroup parameters and self-protection factors of the resonances, being the last used to correct microscopic cross-sections measurements by the activation technique. (author)

Integral approximants for functions of higher monodromic dimension

Energy Technology Data Exchange (ETDEWEB)

Baker, G.A. Jr.

1987-01-01

In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.

An Approximate Method for the Acoustic Attenuating VTI Eikonal Equation

KAUST Repository

Hao, Q.

2017-05-26

We present an approximate method to solve the acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis (VTI). A perturbation method is used to derive the perturbation formula for complex-valued traveltimes. The application of Shanks transform further enhances the accuracy of approximation. We derive both analytical and numerical solutions to the acoustic eikonal equation. The analytic solution is valid for homogeneous VTI media with moderate anellipticity and strong attenuation and attenuation-anisotropy. The numerical solution is applicable for inhomogeneous attenuating VTI media.

An Approximate Method for the Acoustic Attenuating VTI Eikonal Equation

KAUST Repository

Hao, Q.; Alkhalifah, Tariq Ali

2017-01-01

We present an approximate method to solve the acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis (VTI). A perturbation method is used to derive the perturbation formula for complex-valued traveltimes. The application of Shanks transform further enhances the accuracy of approximation. We derive both analytical and numerical solutions to the acoustic eikonal equation. The analytic solution is valid for homogeneous VTI media with moderate anellipticity and strong attenuation and attenuation-anisotropy. The numerical solution is applicable for inhomogeneous attenuating VTI media.

Cr(III,Mn(II,Fe(III,Co(II,Ni(II,Cu(II and Zn(II Complexes with Diisobutyldithiocarbamato Ligand

Directory of Open Access Journals (Sweden)

Mohammad Tarique

2011-01-01

Full Text Available The synthesis of sulphur and nitrogen containing dithiocarbamato ligand derived from diisobutylamine as well as its coordination compounds with 3d series transition metals is presented. These synthesized compounds were characterized on the basis of elemental analysis, conductometric measurements and IR spectral studies. The analytical data showed the stoichiometry 1:2 and 1:3 for the compounds of the types ML2 {M=Mn(II, Co(II, Ni(II, Cu(II and Zn(II} and M'L3{M'=Cr(III and Fe(III} respectively. The conductometric measurements proved the non-electrolytic behaviour of all the compounds. The bidentate nature of dithiocarbamato moiety was confirmed on the basis of IR spectral data.

Traveltime approximations for inhomogeneous HTI media

KAUST Repository

Alkhalifah, Tariq Ali

2011-01-01

Traveltimes information is convenient for parameter estimation especially if the medium is described by an anisotropic set of parameters. This is especially true if we could relate traveltimes analytically to these medium parameters, which is generally hard to do in inhomogeneous media. As a result, I develop traveltimes approximations for horizontaly transversely isotropic (HTI) media as simplified and even linear functions of the anisotropic parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to η and the azimuthal symmetry direction (usually used to describe the fracture direction) from a generally inhomogeneous elliptically anisotropic background medium. The resulting approximations can provide accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations out there. These equations will allow us to readily extend the inhomogenous background elliptical anisotropic model to an HTI with a variable, but smoothly varying, η and horizontal symmetry direction values. © 2011 Society of Exploration Geophysicists.

2> for a scalar field in 2D black holes: A new uniform approximation

International Nuclear Information System (INIS)

Frolov, V.; Sushkov, S.V.; Zelnikov, A.

2003-01-01

We study nonconformal quantum scalar fields and averages of their local observables (such as 2 > ren and μν > ren ) in the spacetime of a two-dimensional black hole. In order to get an analytical approximation for these expressions the WKB approximation is often used. We demonstrate that at the horizon the WKB approximation is violated for a nonconformal field, that is, when the field mass or/and the parameter of nonminimal coupling does not vanish. We propose a new 'uniform approximation' which solves this problem. We use this approximation to obtain an improved analytical approximation for 2 > ren in the two-dimensional black hole geometry. We compare the results obtained with numerical calculations

Distribution of Steps with Finite-Range Interactions: Analytic Approximations and Numerical Results

Science.gov (United States)

GonzáLez, Diego Luis; Jaramillo, Diego Felipe; TéLlez, Gabriel; Einstein, T. L.

2013-03-01

While most Monte Carlo simulations assume only nearest-neighbor steps interact elastically, most analytic frameworks (especially the generalized Wigner distribution) posit that each step elastically repels all others. In addition to the elastic repulsions, we allow for possible surface-state-mediated interactions. We investigate analytically and numerically how next-nearest neighbor (NNN) interactions and, more generally, interactions out to q'th nearest neighbor alter the form of the terrace-width distribution and of pair correlation functions (i.e. the sum over n'th neighbor distribution functions, which we investigated recently.[2] For physically plausible interactions, we find modest changes when NNN interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

Science.gov (United States)

Bodin, Jacques

2015-03-01

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

Approximation for the adjoint neutron spectrum; Aproximacao para o espectro adjunto de neutrons

Energy Technology Data Exchange (ETDEWEB)

Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear

2002-07-01

The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)

An analytical approximation for the prediction of transients with temperature feedback

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P. [Instituto Federal do Rio de Janeiro (IFRJ), RJ (Brazil); Martinez, Aquilino S. [COPPE/UFRJ, RJ (Brazil). Programa de Engenharia Nuclear

2010-05-15

In the present paper a new analytical solution for the point kinetics equation system with temperature feedback is presented. This solution is based on the expansion of the neutron density in terms of the generation time of prompt neutrons (Nahla, 2009) and presents the advantage of being explicit in time and having a simple functional form in comparison with other existing formulations in supercritical transients. (orig.)

An analytical approximation for the prediction of transients with temperature feedback

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Martinez, Aquilino S.

2010-01-01

In the present paper a new analytical solution for the point kinetics equation system with temperature feedback is presented. This solution is based on the expansion of the neutron density in terms of the generation time of prompt neutrons (Nahla, 2009) and presents the advantage of being explicit in time and having a simple functional form in comparison with other existing formulations in supercritical transients. (orig.)

An approximate and an analytical solution to the carousel-pendulum problem

Energy Technology Data Exchange (ETDEWEB)

Vial, Alexandre [Pole Physique, Mecanique, Materiaux et Nanotechnologies, Universite de technologie de Troyes, 12, rue Marie Curie BP-2060, F-10010 Troyes Cedex (France)], E-mail: alexandre.vial@utt.fr

2009-09-15

We show that an improved solution to the carousel-pendulum problem can be easily obtained through a first-order Taylor expansion, and its accuracy is determined after the obtention of an unusable analytical exact solution, advantageously replaced by a numerical one. It is shown that the accuracy is unexpectedly high, even when the ratio length of the pendulum to carousel radius approaches unity. (letters and comments)

Establishment of Approximate Analytical Model of Oil Film Force for Finite Length Tilting Pad Journal Bearings

Directory of Open Access Journals (Sweden)

Yongliang Wang

2015-01-01

Full Text Available Tilting pad bearings offer unique dynamic stability enabling successful deployment of high-speed rotating machinery. The model of dynamic stiffness, damping, and added mass coefficients is often used for rotordynamic analyses, and this method does not suffice to describe the dynamic behaviour due to the nonlinear effects of oil film force under larger shaft vibration or vertical rotor conditions. The objective of this paper is to present a nonlinear oil force model for finite length tilting pad journal bearings. An approximate analytic oil film force model was established by analysing the dynamic characteristic of oil film of a single pad journal bearing using variable separation method under the dynamic π oil film boundary condition. And an oil film force model of a four-tilting-pad journal bearing was established by using the pad assembly technique and considering pad tilting angle. The validity of the model established was proved by analyzing the distribution of oil film pressure and the locus of journal centre for tilting pad journal bearings and by comparing the model established in this paper with the model established using finite difference method.

Nuclear legislation analytical study. Regulatory and institutional framework for nuclear activities in OECD member countries. Volume II

International Nuclear Information System (INIS)

1984-01-01

This study is part of a series of analytical studies of the major aspects of nuclear legislation in OECD Member countries and is published in two volumes. This volume II of the study is a revision and an expansion of a 1969 study concerning the organisation and general regime governing nuclear activities. The national studies were prepared, to the extent possible, following a standard plan for all countries to facilitate information retrieval and comparison. This volume also contains tables of international conventions of relevance to the nuclear field. (NEA) [fr

Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

Directory of Open Access Journals (Sweden)

Yaobing Zhao

2014-01-01

Full Text Available This paper presents approximate series solutions for nonlinear free vibration of suspended cables via the Lindstedt-Poincare method and homotopy analysis method, respectively. Firstly, taking into account the geometric nonlinearity of the suspended cable as well as the quasi-static assumption, a mathematical model is presented. Secondly, two analytical methods are introduced to obtain the approximate series solutions in the case of nonlinear free vibration. Moreover, small and large sag-to-span ratios and initial conditions are chosen to study the nonlinear dynamic responses by these two analytical methods. The numerical results indicate that frequency amplitude relationships obtained with different analytical approaches exhibit some quantitative and qualitative differences in the cases of motions, mode shapes, and particular sag-to-span ratios. Finally, a detailed comparison of the differences in the displacement fields and cable axial total tensions is made.

Approximate solutions of the Wei Hua oscillator using the Pekeris ...

Indian Academy of Sciences (India)

The approximate analytical bound-state solutions of the Schrödinger equation for the. Wei Hua oscillator are carried out in N-dimensional space by taking Pekeris approximation scheme to the orbital centrifugal term. Solutions of the corresponding hyper-radial equation are obtained using the conventional Nikiforov–Uvarov ...

 Higher Order Improvements for Approximate Estimators

DEFF Research Database (Denmark)

Kristensen, Dennis; Salanié, Bernard

Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties of such appr......Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties...... of such approximate estimators at a low computational cost. The first two methods correct the objective function so as to remove the leading term of the bias due to the approximation. One variant provides an analytical bias adjustment, but it only works for estimators based on stochastic approximators......, such as simulation-based estimators. Our second bias correction is based on ideas from the resampling literature; it eliminates the leading bias term for non-stochastic as well as stochastic approximators. Finally, we propose an iterative procedure where we use Newton-Raphson (NR) iterations based on a much finer...

Cosmological models in globally geodesic coordinates. II. Near-field approximation

International Nuclear Information System (INIS)

Liu Hongya

1987-01-01

A near-field approximation dealing with the cosmological field near a typical freely falling observer is developed within the framework established in the preceding paper [J. Math. Phys. 28, xxxx(1987)]. It is found that for the matter-dominated era the standard cosmological model of general relativity contains the Newtonian cosmological model, proposed by Zel'dovich, as its near-field approximation in the observer's globally geodesic coordinate system

Analytical Evaluation to Determine Selected PAHs in a Contaminated Soil With Type II Fuel

International Nuclear Information System (INIS)

Garcia Alonso, S.; Perez Pastor, R. M.; Sevillano Castano, M. L.; Garcia Frutos, F. J.

2010-01-01

A study on the optimization of an ultrasonic extraction method for selected PAHs determination in soil contaminated by type II fuel and by using HPLC with fluorescence detector is presented. The main objective was optimize the analytical procedure, minimizing the volume of solvent and analysis time and avoiding possible loss by evaporation. This work was carried out as part of a project that investigated a remediation process of agricultural land affected by an accidental spillage of fuel (Plan Nacional I + D + i, CTM2007-64 537). The paper is structured as: Optimization of wavelengths in the chromatographic conditions to improve resolution in the analysis of fuel samples. Optimization of the main parameters affecting in the extraction process by sonication. Comparison of results with those obtained by accelerated solvent extraction. (Author) 3 refs.

On the analytic continuation of functions defined by Legendre series

International Nuclear Information System (INIS)

Grinstein, F.F.

1981-07-01

An infinite diagonal sequence of Punctual Pade Approximants is considered for the approximate analytical continuation of a function defined by a formal Legendre series. The technique is tested in the case of two series with exactly known analytical sum: the generating function for Legendre polynomials and the Coulombian scattering amplitude. (author)

Analytic approaches to atomic response properties

International Nuclear Information System (INIS)

Lamm, E.E.

1980-01-01

Many important response properties, e.g., multipole polarizabilites and sum rules, photodetachment cross sections, and closely-related long-range dispersion force coefficients, are insensitive to details of electronic structure. In this investigation, analytic asymptotic theories of atomic response properties are constructed that yield results as accurate as those obtained by more elaborate numerical methods. In the first chapter, a novel and simple method is used to determined the multipole sum rules S/sub l/(-k), for positive and negative values of k, of the hydrogen atom and the hydrogen negative ion in the asymptotic approximation. In the second chapter, an analytically-tractable extended asymptotic model for the response properites of weakly-bound anions is proposed and the multipole polarizability, multipole sum rules, and photodetachment cross section determined by the model are computed analytically. Dipole polarizabilities and photodetachment cross sections determined from the model for Li-, Na-, and K- are compared with the numercal results of Moores and Norcross. Agreement is typically within 15% if the pseudopotential is included. In the third chapter a comprehensive and unified treatment of atomic multipole oscillator strengths, dynamic multipole polarizabilites, and dispersion force constants in a variety of Coulomb-like approximations is presented. A theoretically and computationally superior modification of the original Bates-Damgaard (BD) procedure, referred to here as simply the Coulomb approximation (CA), is introduced. An analytic expression for the dynamic multipole polarizability is found which contains as special cases this quantity within the CA, the extended Coulomb approximation (ECA) of Adelman and Szabo, and the quantum defect orbital (QDO) method of Simons

Analytic solutions of a class of nonlinearly dynamic systems

International Nuclear Information System (INIS)

Wang, M-C; Zhao, X-S; Liu, X

2008-01-01

In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently

The Case for Visual Analytics of Arsenic Concentrations in Foods

Directory of Open Access Journals (Sweden)

Omotayo R. Awofolu

2010-04-01

Full Text Available 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.

Approximation methods for the partition functions of anharmonic systems

International Nuclear Information System (INIS)

Lew, P.; Ishida, T.

1979-07-01

The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations

Quantal density functional theory II. Approximation methods and applications

International Nuclear Information System (INIS)

Sahni, Viraht

2010-01-01

This book is on approximation methods and applications of Quantal Density Functional Theory (QDFT), a new local effective-potential-energy theory of electronic structure. What distinguishes the theory from traditional density functional theory is that the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and the correlation contribution to the kinetic energy -- the Correlation-Kinetic effects -- are separately and explicitly defined. As such it is possible to study each property of interest as a function of the different electron correlations. Approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT, are developed. The applications are to the few-electron inhomogeneous electron gas systems in atoms and molecules, as well as to the many-electron inhomogeneity at metallic surfaces. (orig.)

Analysis of the dynamical cluster approximation for the Hubbard model

OpenAIRE

Aryanpour, K.; Hettler, M. H.; Jarrell, M.

2002-01-01

We examine a central approximation of the recently introduced Dynamical Cluster Approximation (DCA) by example of the Hubbard model. By both analytical and numerical means we study non-compact and compact contributions to the thermodynamic potential. We show that approximating non-compact diagrams by their cluster analogs results in a larger systematic error as compared to the compact diagrams. Consequently, only the compact contributions should be taken from the cluster, whereas non-compact ...

Nuclear data processing, analysis, transformation and storage with Pade-approximants

International Nuclear Information System (INIS)

Badikov, S.A.; Gay, E.V.; Guseynov, M.A.; Rabotnov, N.S.

1992-01-01

A method is described to generate rational approximants of high order with applications to neutron data handling. The problems considered are: The approximations of neutron cross-sections in resonance region producing the parameters for Adler-Adler type formulae; calculations of resulting rational approximants' errors given in analytical form allowing to compute the error at any energy point inside the interval of approximation; calculations of the correlation coefficient of error values in two arbitrary points provided that experimental errors are independent and normally distributed; a method of simultaneous generation of a few rational approximants with identical set of poles; functionals other than LSM; two-dimensional approximation. (orig.)

Low-energy approximation of K-N-T formula

International Nuclear Information System (INIS)

Markovic, S.; Simovic, R.; Markovic, S.)

2007-01-01

A simplified version of the K-N-T formula is derived in this paper by using some well justified approximations in low (diagnostic) range of photon energies. This formula is suitable mostly for analytical purposes and practical calculations [sr

Analytic energy gradients for orbital-optimized MP3 and MP2.5 with the density-fitting approximation: An efficient implementation.

Science.gov (United States)

Bozkaya, Uğur

2018-03-15

Efficient implementations of analytic gradients for the orbital-optimized MP3 and MP2.5 and their standard versions with the density-fitting approximation, which are denoted as DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5, are presented. The DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5 methods are applied to a set of alkanes and noncovalent interaction complexes to compare the computational cost with the conventional MP3, MP2.5, OMP3, and OMP2.5. Our results demonstrate that density-fitted perturbation theory (DF-MP) methods considered substantially reduce the computational cost compared to conventional MP methods. The efficiency of our DF-MP methods arise from the reduced input/output (I/O) time and the acceleration of gradient related terms, such as computations of particle density and generalized Fock matrices (PDMs and GFM), solution of the Z-vector equation, back-transformations of PDMs and GFM, and evaluation of analytic gradients in the atomic orbital basis. Further, application results show that errors introduced by the DF approach are negligible. Mean absolute errors for bond lengths of a molecular set, with the cc-pCVQZ basis set, is 0.0001-0.0002 Å. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Diophantine approximation and Dirichlet series

CERN Document Server

Queffélec, Hervé

2013-01-01

This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...

Oblique incidence effects in direct x-ray detectors: A first-order approximation using a physics-based analytical model

International Nuclear Information System (INIS)

Badano, Aldo; Freed, Melanie; Fang Yuan

2011-01-01

Purpose: The authors describe the modifications to a previously developed analytical model of indirect CsI:Tl-based detector response required for studying oblique x-ray incidence effects in direct semiconductor-based detectors. This first-order approximation analysis allows the authors to describe the associated degradation in resolution in direct detectors and compare the predictions to the published data for indirect detectors. Methods: The proposed model is based on a physics-based analytical description developed by Freed et al. [''A fast, angle-dependent, analytical model of CsI detector response for optimization of 3D x-ray breast imaging systems,'' Med. Phys. 37(6), 2593-2605 (2010)] that describes detector response functions for indirect detectors and oblique incident x rays. The model, modified in this work to address direct detector response, describes the dependence of the response with x-ray energy, thickness of the transducer layer, and the depth-dependent blur and collection efficiency. Results: The authors report the detector response functions for indirect and direct detector models for typical thicknesses utilized in clinical systems for full-field digital mammography (150 μm for indirect CsI:Tl and 200 μm for a-Se direct detectors). The results suggest that the oblique incidence effect in a semiconductor detector differs from that in indirect detectors in two ways: The direct detector model produces a sharper overall PRF compared to the response corresponding to the indirect detector model for normal x-ray incidence and a larger relative increase in blur along the x-ray incidence direction compared to that found in indirect detectors with respect to the response at normal incidence angles. Conclusions: Compared to the effect seen in indirect detectors, the direct detector model exhibits a sharper response at normal x-ray incidence and a larger relative increase in blur along the x-ray incidence direction with respect to the blur in the

Spherical anharmonic oscillator in self-similar approximation

International Nuclear Information System (INIS)

Yukalova, E.P.; Yukalov, V.I.

1992-01-01

The method of self-similar approximation is applied here for calculating the eigenvalues of the three-dimensional spherical anharmonic oscillator. The advantage of this method is in its simplicity and high accuracy. The comparison with other known analytical methods proves that this method is more simple and accurate. 25 refs

Approximate Computing Techniques for Iterative Graph Algorithms

Energy Technology Data Exchange (ETDEWEB)

Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram

2017-12-18

Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.

Unsaturated b-ketoesters and their Ni(II, Cu(II and Zn(II complexes

Directory of Open Access Journals (Sweden)

MUHAMMED BASHEER UMMATHUR

2009-03-01

Full Text Available A new series of b-ketoesters in which the keto group is attached to the olefinic linkage were synthesized by the reaction of methyl acetoacetate and aromatic aldehydes under specified conditions. The existence of these compounds predominantly in the intramolecularly hydrogen bonded enol form was well demonstrated from their IR, 1H-NMR and mass spectral data. Details on the formation of their [ML2] complexes with Ni(II, Cu(II and Zn(II and the nature of the bonding are discussed on the basis of analytical and spectral data.

Light scattering by cubical particle in the WKB approximation

Directory of Open Access Journals (Sweden)

redouane lamsoudi

2017-11-01

Full Text Available In this work, we determined the analytical expressions of the form factor of a cubical particle in the WKB approximation. We adapted some variables (size parameter, refractive index, the scattering angle and found the form factor in the approximation of Rayleigh-Gans-Debye (RGD, Anomalous Diffraction (AD, and determined the efficiency factor of the extinction. Finally, to illustrate our formalism, we analyzed some numerical examples

Dataset concerning the analytical approximation of the Ae3 temperature

Directory of Open Access Journals (Sweden)

B.L. Ennis

2017-02-01

The dataset includes the terms of the function and the values for the polynomial coefficients for major alloying elements in steel. A short description of the approximation method used to derive and validate the coefficients has also been included. For discussion and application of this model, please refer to the full length article entitled “The role of aluminium in chemical and phase segregation in a TRIP-assisted dual phase steel” 10.1016/j.actamat.2016.05.046 (Ennis et al., 2016 [1].

A simple analytic approximation to the Rayleigh-Bénard stability threshold

NARCIS (Netherlands)

Prosperetti, Andrea

2011-01-01

The Rayleigh-Bénard linear stability problem is solved by means of a Fourier series expansion. It is found that truncating the series to just the first term gives an excellent explicit approximation to the marginal stability relation between the Rayleigh number and the wave number of the

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

Science.gov (United States)

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.

HPTA: High-Performance Text Analytics

OpenAIRE

Vandierendonck, Hans; Murphy, Karen; Arif, Mahwish; Nikolopoulos, Dimitrios S.

2017-01-01

One of the main targets of data analytics is unstructured data, which primarily involves textual data. High-performance processing of textual data is non-trivial. We present the HPTA library for high-performance text analytics. The library helps programmers to map textual data to a dense numeric representation, which can be handled more efficiently. HPTA encapsulates three performance optimizations: (i) efficient memory management for textual data, (ii) parallel computation on associative dat...

Analytically solvable models of reaction-diffusion systems

Energy Technology Data Exchange (ETDEWEB)

Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)

2004-05-01

We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.

Scaling in situ cosmogenic nuclide production rates using analytical approximations to atmospheric cosmic-ray fluxes

Science.gov (United States)

Lifton, Nathaniel; Sato, Tatsuhiko; Dunai, Tibor J.

2014-01-01

Several models have been proposed for scaling in situ cosmogenic nuclide production rates from the relatively few sites where they have been measured to other sites of interest. Two main types of models are recognized: (1) those based on data from nuclear disintegrations in photographic emulsions combined with various neutron detectors, and (2) those based largely on neutron monitor data. However, stubborn discrepancies between these model types have led to frequent confusion when calculating surface exposure ages from production rates derived from the models. To help resolve these discrepancies and identify the sources of potential biases in each model, we have developed a new scaling model based on analytical approximations to modeled fluxes of the main atmospheric cosmic-ray particles responsible for in situ cosmogenic nuclide production. Both the analytical formulations and the Monte Carlo model fluxes on which they are based agree well with measured atmospheric fluxes of neutrons, protons, and muons, indicating they can serve as a robust estimate of the atmospheric cosmic-ray flux based on first principles. We are also using updated records for quantifying temporal and spatial variability in geomagnetic and solar modulation effects on the fluxes. A key advantage of this new model (herein termed LSD) over previous Monte Carlo models of cosmogenic nuclide production is that it allows for faster estimation of scaling factors based on time-varying geomagnetic and solar inputs. Comparing scaling predictions derived from the LSD model with those of previously published models suggest potential sources of bias in the latter can be largely attributed to two factors: different energy responses of the secondary neutron detectors used in developing the models, and different geomagnetic parameterizations. Given that the LSD model generates flux spectra for each cosmic-ray particle of interest, it is also relatively straightforward to generate nuclide-specific scaling

Spectral, thermal, electrochemical and analytical studies on Cd(II) and Hg(II) thiosemicarbazone complexes

Science.gov (United States)

El-Asmy, A. A.; El-Gammal, O. A.; Saleh, H. S.

2008-11-01

The coordination characteristic of the investigated thiosemicarbazones towards hazard pollutants, Cd(II) and Hg(II), becomes the first goal. Their complexes have been studied by microanalysis, thermal, electrochemical and spectral (electronic, IR and MS) studies. The substitutent (salicylaldehyde, acetophenone, benzophenone, o-hydroxy- p-methoxybenzophenone or diacetylmonoxime) plays an important role in the complex formation. The coordination sites were the S for thiosemicarbazide (HTS); NN for benzophenone thiosemicarbazone (HBTS); NS for acetophenone thiosemicarbazone (HATS) and salicylaldehyde thiosemicarbazone (H 2STS); NNS or NSO for diacetylmonoxime thiosemicarbazone (H 2DMTS). The stability constants of Hg(II) complexes were higher than Cd(II). The kinetic and thermodynamic parameters for the different thermal decomposition steps in the complexes have been evaluated. The activation energy values of the first step ordered the complexes as: [Cd(H 2STS)Cl 2]H 2O > [Cd(H 2DAMTS)Cl 2] > [Cd(HBTS) 2Cl 2]2H 2O > [Cd(HATS) 2Cl 2]. The CV of [Cd(H 2STS)Cl 2]H 2O and [Hg(HBTS)Cl 2] were recorded. The use of H 2DMTS as a new reagent for the separation and determination of Cd(II) ions from water and some synthetic samples using flotation technique is aimed to be discussed.

Pade approximants for the ground-state energy of closed-shell quantum dots

International Nuclear Information System (INIS)

Gonzalez, A.; Partoens, B.; Peeters, F.M.

1997-08-01

Analytic approximations to the ground-state energy of closed-shell quantum dots (number of electrons from 2 to 210) are presented in the form of two-point Pade approximants. These Pade approximants are constructed from the small- and large-density limits of the energy. We estimated that the maximum error, reached for intermediate densities, is less than ≤ 3%. Within that present approximation the ground-state is found to be unpolarized. (author). 21 refs, 3 figs, 2 tabs

Analytical modeling of worldwide medical radiation use

International Nuclear Information System (INIS)

Mettler, F.A. Jr.; Davis, M.; Kelsey, C.A.; Rosenberg, R.; Williams, A.

1987-01-01

An analytical model was developed to estimate the availability and frequency of medical radiation use on a worldwide basis. This model includes medical and dental x-ray, nuclear medicine, and radiation therapy. The development of an analytical model is necessary as the first step in estimating the radiation dose to the world's population from this source. Since there is no data about the frequency of medical radiation use in more than half the countries in the world and only fragmentary data in an additional one-fourth of the world's countries, such a model can be used to predict the uses of medical radiation in these countries. The model indicates that there are approximately 400,000 medical x-ray machines worldwide and that approximately 1.2 billion diagnostic medical x-ray examinations are performed annually. Dental x-ray examinations are estimated at 315 million annually and approximately 22 million in-vivo diagnostic nuclear medicine examinations. Approximately 4 million radiation therapy procedures or courses of treatment are undertaken annually

Improved WKB approximation for quantum tunneling: Application to heavy-ion fusion

Energy Technology Data Exchange (ETDEWEB)

Toubiana, A.J. [Universidade Federal do Rio de Janeiro, Departamento de Engenharia Nuclear, Escola Politecnica, C.P. 68529, Rio de Janeiro, RJ (Brazil); Ecole CentraleSupelec, Gif-sur-Yvette (France); Paris Saclay, Saint-Aubin (France); Canto, L.F. [Universidade Federal do Rio de Janeiro, Instituto de Fisica, C.P. 68528, Rio de Janeiro (Brazil); Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil); Hussein, M.S. [Universidade de Sao Paulo, Instituto de Estudos Avancados, C.P. 72012, Sao Paulo, SP (Brazil); Universidade de Sao Paulo, Instituto de Fisica, C.P. 66318, Sao Paulo, SP (Brazil); Instituto Tecnologico de Aeronautica, CTA, Departamento de Fisica, Sao Jose dos Campos, Sao Paulo, SP (Brazil)

2017-02-15

In this paper we revisit the one-dimensional tunnelling problem. We consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical continuation of the radial coordinate to the complex plane. We investigate the validity of this approximation by comparing their predictions for the cross section and for the barrier distribution with the corresponding quantum-mechanical results. We find that the extended Kemble's approximation reproduces the results of quantum mechanics with great accuracy. (orig.)

Global sensitivity analysis using low-rank tensor approximations

International Nuclear Information System (INIS)

Konakli, Katerina; Sudret, Bruno

2016-01-01

In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these indices at low computational cost, by post-processing the coefficients of polynomial meta-models belonging to the class of low-rank tensor approximations. Meta-models of this class can be particularly efficient in representing responses of high-dimensional models, because the number of unknowns in their general functional form grows only linearly with the input dimension. The proposed approach is validated in example applications, where the Sobol' indices derived from the meta-model coefficients are compared to reference indices, the latter obtained by exact analytical solutions or Monte-Carlo simulation with extremely large samples. Moreover, low-rank tensor approximations are confronted to the popular polynomial chaos expansion meta-models in case studies that involve analytical rank-one functions and finite-element models pertinent to structural mechanics and heat conduction. In the examined applications, indices based on the novel approach tend to converge faster to the reference solution with increasing size of the experimental design used to build the meta-model. - Highlights: • A new method is proposed for global sensitivity analysis of high-dimensional models. • Low-rank tensor approximations (LRA) are used as a meta-modeling technique. • Analytical formulas for the Sobol' indices in terms of LRA coefficients are derived. • The accuracy and efficiency of the approach is illustrated in application examples. • LRA-based indices are compared to indices based on polynomial chaos expansions.

Effective Summation and Interpolation of Series by Self-Similar Root Approximants

Directory of Open Access Journals (Sweden)

Simon Gluzman

2015-06-01

Full Text Available We describe a simple analytical method for effective summation of series, including divergent series. The method is based on self-similar approximation theory resulting in self-similar root approximants. The method is shown to be general and applicable to different problems, as is illustrated by a number of examples. The accuracy of the method is not worse, and in many cases better, than that of Padé approximants, when the latter can be defined.

Analytical inversions in remote sensing of particle size distributions. IV - Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation

Science.gov (United States)

Fymat, A. L.; Smith, C. B.

1979-01-01

It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.

An analytical approach to the positive reactivity void coefficient of TRIGA Mark-II reactor

International Nuclear Information System (INIS)

Edgue, Erdinc; Yarman, Tolga

1988-01-01

Previous calculations of reactivity void coefficient of I.T.U. TRIGA Mark-II Reactor was done by the second author et al. The theoretical predictions were afterwards, checked in this reactor experimentally. In this work an analytical approach is developed to evaluate rather quickly the reactivity void coefficient of I.T.U. TRIGA Mark-II, versus the size of the void inserted into the reactor. It is thus assumed that the reactor is a cylindrical, bare nuclear system. Next a belt of water of 2πrΔrH is introduced axially at a distance r from the center line of the system. r here, is the thickness of the belt, and H is the height of the reactor. The void is described by decreasing the water density in the belt region. A two group diffusion theory is adopted to determine the criticality of our configuration. The space dependency of the group fluxes are, thereby, assumed to be J 0 (2.405 r / R) cos (π Z / H), the same as that associated with the original bare reactor uniformly loaded prior to the change. A perturbation type of approach, thence, furnishes the effect of introducing a void in the belt region. The reactivity void coefficient can, rather surprisingly, be indeed positive. To our knowledge, this fact had not been established, by the supplier. The agreement of our predictions with the experimental results is good. (author)

The phase transition lines in pair approximation for the basic reinfection model SIRI

International Nuclear Information System (INIS)

Stollenwerk, Nico; Martins, Jose; Pinto, Alberto

2007-01-01

For a spatial stochastic epidemic model we investigate in the pair approximation scheme the differential equations for the moments. The basic reinfection model of susceptible-infected-recovered-reinfected or SIRI type is analysed, its phase transition lines calculated analytically in this pair approximation

Synthesis, characterization and biological studies of 2-(4-nitro phenylaminocarbonyl)benzoic acid and its complexes with Cr(III), Co(II), Ni(II), Cu(II) and Zn(II)

International Nuclear Information System (INIS)

Aqeel Ashraf, M.; Jamil Maah, M.; Yusuf, I.

2012-01-01

Cr(III), Co(II), Ni(II), Cu(II) and Zn(II) salts of 2-(4-nitro phenylaminocarbonyl)benzoic acid were characterized by physical, analytical and spectroscopic studies and checked for their in-vitro antimicrobial activity against three bacterial strains, Mycobacterium smegmatis (Gram +ve), Escherichia coli (Gram -ve), Pseudomonas aeuroginosa (Gram -ve) and three fungal strains, Nigrospora oryzae, Aspergillus niger and Candida albicans. The antimicrobial activities of the metal complexes - were found to be greater than those of 2-(4-nitro phenylaminocarbonyl)benzoic acid alone.

Orbits in a Stäckel approximation.

Science.gov (United States)

de Bruyne, V.; Leeuwin, F.; Dejonghe, H.

One family of potentials frequently used for dynamical models for galaxies are the Stackel potentials (e.g. de Zeeuw et al., 1986, MNRAS 221, 1001, Dejonghe et al., 1996, A&A 306, 363) because of their unique analytical tractability. An axisymmetric model is determined by a potential psi(R,z) and a distribution function F(E,Lz,I3), generally depending on 3 integrals of motion. It has indeed been known for a long time that the integration of orbits in many realistic potentials reveals the presence of an effective third integral I3. Unfortunately, no general analytic expression exists for such an integral, and this has put a limitation on designing anisotropic axisymmetric models. However, I3 can be computed analytically if a Stackel potential is used. This could be used as a local analytic approximation for the third integral in general potentials. One long-standing concern though, is that SPs form only a very small subspace in the family of all potentials, and may not capture the essential of the dynamics for a general potential. One way to address this issue is to compare orbits in both potentials. We therefore fit a Stackel potential (like in Mathieu et al., A&A 314, 25), for different radial ranges, to a spheroidal (MN-)potential (Miyamoto-Nagai, 1975, PASJ 27, 533), and compare orbits for an appropriate sampling of integral space. As a result, we find that the orbit shapes are very similar (as exhibited on surfaces of section, or by the orbital densities). The Stackel I3 is found to be a good approximation to a third integral of the MN-potential. The variation of I3 along an orbit in the MN-potential is of the same order as the difference between the two potentials.

Application of Carrier Element-Free Co-precipitation Method for Ni(II), Cu(II) and Zn(II) Ions Determination in Water Samples Using Chrysin

International Nuclear Information System (INIS)

Layth Imad Abd Ali; Wan Aini Wan Ibrahim; Azli Sulaiman; Mohd Marsin Sanagi

2015-01-01

A co-precipitation method was developed to separate and pre-concentrate Ni(II), Cu(II) and Zn(II) ions using an organic co precipitant, chrysin without adding any carrier element termed as carrier element-free co-precipitation (CEFC). Analytes were determined using flame atomic absorption spectrometry (FAAS). The influence of analytical conditions, such as pH of the solution, quantity of co-precipitant, standing time, centrifugation rate and time, sample volume, and interference of concomitant ions were investigated over the recovery yields of the trace metals. The limit of detection, the limit of quantification and linearity range obtained from the FAAS measurements were found to be in the range of 0.64 to 0.86 μg L -1 , 2.13 to 2.86 μg L -1 and 0.9972 to 0.9989 for Ni(II), Cu(III) and Zn(II) ions, respectively. The precision of the method, evaluated as the relative standard deviation (RSD) obtained after analyzing a series of 10 replicates, was between 2.6 % to 3.9 % for the trace metal ions. The proposed procedure was applied and validated by analyzing river water reference material for trace metals (SLRS-5) and spiking trace metal ions in some water samples. The recoveries of the analyte metal ions were between 94.7-101.2 %. (author)

Modified method of perturbed stationary states. II. Semiclassical and low-velocity quantal approximations

International Nuclear Information System (INIS)

Green, T.A.

1978-10-01

For one-electron heteropolar systems, the wave-theoretic Lagrangian of Paper I 2 is simplified in two distinct approximations. The first is semiclassical; the second is quantal, for velocities below those for which the semiclassical treatment is reliable. For each approximation, unitarity and detailed balancing are discussed. Then, the variational method as described by Demkov is used to determine the coupled equations for the radial functions and the Euler-Lagrange equations for the translational factors which are part of the theory. Specific semiclassical formulae for the translational factors are given in a many-state approximation. Low-velocity quantal formulae are obtained in a one-state approximation. The one-state results of both approximations agree with an earlier determination by Riley. 14 references

Approximate Controllability of Semilinear Neutral Stochastic Integrodifferential Inclusions with Infinite Delay

Directory of Open Access Journals (Sweden)

Meili Li

2015-01-01

Full Text Available The approximate controllability of semilinear neutral stochastic integrodifferential inclusions with infinite delay in an abstract space is studied. Sufficient conditions are established for the approximate controllability. The results are obtained by using the theory of analytic resolvent operator, the fractional power theory, and the theorem of nonlinear alternative for Kakutani maps. Finally, an example is provided to illustrate the theory.

Analytic approximation to the largest eigenvalue distribution of a white Wishart matrix

CSIR Research Space (South Africa)

Vlok, JD

2012-08-14

Full Text Available offers largely simplified computation and provides statistics such as the mean value and region of support of the largest eigenvalue distribution. Numeric results from the literature are compared with the approximation and Monte Carlo simulation results...

Semi-analytic techniques for calculating bubble wall profiles

International Nuclear Information System (INIS)

Akula, Sujeet; Balazs, Csaba; White, Graham A.

2016-01-01

We present semi-analytic techniques for finding bubble wall profiles during first order phase transitions with multiple scalar fields. Our method involves reducing the problem to an equation with a single field, finding an approximate analytic solution and perturbing around it. The perturbations can be written in a semi-analytic form. We assert that our technique lacks convergence problems and demonstrate the speed of convergence on an example potential. (orig.)

Ni(II

African Journals Online (AJOL)

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analytical chemistry, catalysis, electrochemistry, ring-opening metathesis ... Ethanol was dried over anhydrous copper(II) sulfate and distilled over metallic sodium. ... All bacteria were inoculated into Nutrient Broth (Difco) and incubated for 24 h ...

Analytic solutions of hydrodynamics equations

International Nuclear Information System (INIS)

Coggeshall, S.V.

1991-01-01

Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1-D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions

Analytical and numerical studies of approximate phase velocity matching based nonlinear S0 mode Lamb waves for the detection of evenly distributed microstructural changes

International Nuclear Information System (INIS)

Wan, X; Xu, G H; Tao, T F; Zhang, Q; Tse, P W

2016-01-01

Most previous studies on nonlinear Lamb waves are conducted using mode pairs that satisfying strict phase velocity matching and non-zero power flux criteria. However, there are some limitations in existence. First, strict phase velocity matching is not existed in the whole frequency bandwidth; Second, excited center frequency is not always exactly equal to the true phase-velocity-matching frequency; Third, mode pairs are isolated and quite limited in number; Fourth, exciting a single desired primary mode is extremely difficult in practice and the received signal is quite difficult to process and interpret. And few attention has been paid to solving these shortcomings. In this paper, nonlinear S0 mode Lamb waves at low-frequency range satisfying approximate phase velocity matching is proposed for the purpose of overcoming these limitations. In analytical studies, the secondary amplitudes with the propagation distance considering the fundamental frequency, the maximum cumulative propagation distance (MCPD) with the fundamental frequency and the maximum linear cumulative propagation distance (MLCPD) using linear regression analysis are investigated. Based on analytical results, approximate phase velocity matching is quantitatively characterized as the relative phase velocity deviation less than a threshold value of 1%. Numerical studies are also conducted using tone burst as the excitation signal. The influences of center frequency and frequency bandwidth on the secondary amplitudes and MCPD are investigated. S1–S2 mode with the fundamental frequency at 1.8 MHz, the primary S0 mode at the center frequencies of 100 and 200 kHz are used respectively to calculate the ratios of nonlinear parameter of Al 6061-T6 to Al 7075-T651. The close agreement of the computed ratios to the actual value verifies the effectiveness of nonlinear S0 mode Lamb waves satisfying approximate phase velocity matching for characterizing the material nonlinearity. Moreover, the ratios derived

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

Science.gov (United States)

Ito, Kazufumi; Teglas, Russell

1987-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations

KAUST Repository

Castrillon, Julio; Nobile, Fabio; Tempone, Raul

2016-01-01

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem

The fluctuation Hall conductivity and the Hall angle in type-II superconductor under magnetic field

Energy Technology Data Exchange (ETDEWEB)

Tinh, Bui Duc, E-mail: tinhbd@hnue.edu.vn [Institute of Research and Development, Duy Tan University, K7/25 Quang Trung, Danang (Viet Nam); Department of Physics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi (Viet Nam); Hoc, Nguyen Quang; Thu, Le Minh [Department of Physics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi (Viet Nam)

2016-02-15

Highlights: • The time-dependent Ginzburg–Landau was used to calculate fluctuation Hall conductivity and Hall angle in type-II superconductor in 2D and 3D. • We obtain analytical expressions for the fluctuation Hall conductivity and the Hall angle summing all Landau levels without need to cutoff higher Landau levels to treat arbitrary magnetic field. • The results were compared to the experimental data on YBCO. - Abstract: The fluctuation Hall conductivity and the Hall angle, describing the Hall effect, are calculated for arbitrary value of the imaginary part of the relaxation time in the frame of the time-dependent Ginzburg–Landau theory in type II-superconductor with thermal noise describing strong thermal fluctuations. The self-consistent Gaussian approximation is used to treat the nonlinear interaction term in dynamics. We obtain analytical expressions for the fluctuation Hall conductivity and the Hall angle summing all Landau levels without need to cutoff higher Landau levels to treat arbitrary magnetic field. The results are compared with experimental data on high-T{sub c} superconductor.

Approximate solutions to Mathieu's equation

Science.gov (United States)

Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

2018-06-01

Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

Multi-compartment linear noise approximation

International Nuclear Information System (INIS)

Challenger, Joseph D; McKane, Alan J; Pahle, Jürgen

2012-01-01

The ability to quantify the stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally expensive. Building on previous work, a linear noise approximation is developed for biochemical models with many compartments, for example cells. The procedure is then implemented in the software package COPASI. This technique is illustrated with two simple examples and is then applied to a more realistic biochemical model. Expressions for the noise, given in the form of covariance matrices, are presented. (paper)

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

Science.gov (United States)

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.

Interacting steps with finite-range interactions: Analytical approximation and numerical results

Science.gov (United States)

Jaramillo, Diego Felipe; Téllez, Gabriel; González, Diego Luis; Einstein, T. L.

2013-05-01

We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions q on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

Approximations to the non-adiabatic particle response in toroidal geometry

International Nuclear Information System (INIS)

Schep, T.J.; Braams, B.J.

1981-08-01

The non-adiabatic part of the particle response to low-frequency electromagnetic modes with long parallel wavelengths is discussed. Analytic approximations to the kernels of the integrals that relate the amplitudes of the perturbed potentials to the non-adiabatic part of the perturbed density in an axisymmetric toroidal configuration are presented and the results are compared with numerical calculations. It is shown that both in the plane slab and in toroidal geometry the kernel contains a logarithmic singularity. This singularity is associated with particles with vanishing parallel velocity so that, in toroidal geometry, it is related with the behaviour of trapped particles near their turning points. In contrast to the plane slab, in toroidal geometry this logarithmic singularity is mainly real and associated with non-resonant particles. Apart from this logarithmic term, the kernel contains a complex regular part arising from resonant as well as from non-resonant particles. The analytic approximations that will be presented make the dispersion relation of drift-type modes in toroidal geometry amenable to analytic as well as to simpler numerical calculation of the growth rate and of the spatial mode structure

Calibration of the Accuscan II In Vivo System for I-131 Thyroid Counting

Energy Technology Data Exchange (ETDEWEB)

Orval R. Perry; David L. Georgeson

2011-07-01

This report describes the March 2011 calibration of the Accuscan II HpGe In Vivo system for I-131 thyroid counting. The source used for the calibration was an Analytics mixed gamma source 82834-121 distributed in an epoxy matrix in a Wheaton Liquid Scintillation Vial with energies from 88.0 keV to 1836.1 keV. The center of the detectors was position 64-feet from the vault floor. This position places the approximate center line of the detectors at the center line of the source in the thyroid tube. The calibration was performed using an RMC II phantom (Appendix J). Validation testing was performed using a Ba-133 source and an ANSI N44.3 Phantom (Appendix I). This report includes an overview introduction and records for the energy/FWHM and efficiency calibrations including verification counting. The Accuscan II system was successfully calibrated for counting the thyroid for I-131 and verified in accordance with ANSI/HPS N13.30-1996 criteria.

Delta-function Approximation SSC Model in 3C 273 S. J. Kang1 ...

Indian Academy of Sciences (India)

Abstract. We obtain an approximate analytical solution using δ approximate calculation on the traditional one-zone synchrotron self-. Compton (SSC) model. In this model, we describe the electron energy distribution by a broken power-law function with a sharp cut-off, and non- thermal photons are produced by both ...

Efficient approximations of dispersion relations in optical waveguides with varying refractive-index profiles.

Science.gov (United States)

Li, Yutian; Zhu, Jianxin

2015-05-04

In this paper we consider the problem of computing the eigen-modes for the varying refractive-index profile in an open waveguide. We first approximate the refractive-index by a piecewise polynomial of degree two, and the corresponding Sturm-Liouville problem (eigenvalue problem) of the Helmholtz operator in each layer can be solved analytically by the Kummer functions. Then, analytical approximate dispersion equations are established for both TE and TM cases. Furthermore, the approximate dispersion equations converge fast to the exact ones for the continuous refractive-index function as the maximum value of the subinterval sizes tends to zero. Suitable numerical methods, such as Müller's method or the chord secant method, may be applied to the dispersion relations to compute the eigenmodes. Numerical simulations show that our method is very practical and efficient for computing eigenmodes.

Analysis of expansion phase experiments with improved approximation schemes

International Nuclear Information System (INIS)

Foit, J.J.

1987-05-01

A steady-state flow of a single-phase and incompressible fluid across a singularity is studied. Based on these theoretical considerations new approximation methods for the pressure gradient term in the SIMMER-II momentum equations are proposed which give a satisfactory pressure change in flows across singularities. The expansion phase experiments with a dipplate performed by SRI-International are evaluated to examine the quality of the proposed approximation schemes. (orig.) [de

EPICOR-II resin characterization and proposed methods for degradation analysis. Rev. 1

International Nuclear Information System (INIS)

Doyle, J.D.; McConnell, J.W. Jr.; Sanders, R.D. Sr.

1984-06-01

One goal of the EPICOR-II Research and Disposition Program is the examination of the EPICOR-II organic ion-exchange resins for physical and chemical degradation. This report summarizes preliminary information necessary for the evaluation of the resins for degradation. Degradation of the synthetic organic ion-exchange resins should be efficiently and accurately measurable by using the baseline data provided by the nonirradiated resin characterization. The degradation threshold is about 10 8 rads, approximately the same dose rate the resins will have received by the examination date. If degradation has not occurred at the first examination point, later examinations will detect resin degradation using the same analytical methods. The results from the characterization tests will yield practical and useful data on the actual effects of radiation on commercial synthetic organic ion-exchange resins. 10 references, 12 figures

Approximate Bayesian evaluations of measurement uncertainty

Science.gov (United States)

Possolo, Antonio; Bodnar, Olha

2018-04-01

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

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

Science.gov (United States)

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.

Higher accuracy analytical approximations to a nonlinear oscillator with discontinuity by He's homotopy perturbation method

International Nuclear Information System (INIS)

Belendez, A.; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A.

2008-01-01

He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient

Statistical trajectory of an approximate EM algorithm for probabilistic image processing

International Nuclear Information System (INIS)

Tanaka, Kazuyuki; Titterington, D M

2007-01-01

We calculate analytically a statistical average of trajectories of an approximate expectation-maximization (EM) algorithm with generalized belief propagation (GBP) and a Gaussian graphical model for the estimation of hyperparameters from observable data in probabilistic image processing. A statistical average with respect to observed data corresponds to a configuration average for the random-field Ising model in spin glass theory. In the present paper, hyperparameters which correspond to interactions and external fields of spin systems are estimated by an approximate EM algorithm. A practical algorithm is described for gray-level image restoration based on a Gaussian graphical model and GBP. The GBP approach corresponds to the cluster variation method in statistical mechanics. Our main result in the present paper is to obtain the statistical average of the trajectory in the approximate EM algorithm by using loopy belief propagation and GBP with respect to degraded images generated from a probability density function with true values of hyperparameters. The statistical average of the trajectory can be expressed in terms of recursion formulas derived from some analytical calculations

Communication: Analytic continuation of the virial series through the critical point using parametric approximants

Energy Technology Data Exchange (ETDEWEB)

Barlow, Nathaniel S., E-mail: nsbsma@rit.edu [School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623 (United States); Schultz, Andrew J., E-mail: ajs42@buffalo.edu; Kofke, David A., E-mail: kofke@buffalo.edu [Department of Chemical and Biological Engineering, University at Buffalo, State University of New York, Buffalo, New York 14260 (United States); Weinstein, Steven J., E-mail: sjweme@rit.edu [Department of Chemical Engineering, Rochester Institute of Technology, Rochester, New York 14623 (United States)

2015-08-21

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.

Communication: Analytic continuation of the virial series through the critical point using parametric approximants.

Science.gov (United States)

Barlow, Nathaniel S; Schultz, Andrew J; Weinstein, Steven J; Kofke, David A

2015-08-21

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

Science.gov (United States)

Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

2018-03-01

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

Chiral analysis of alpha-diimine Ru(II) and Fe(II) complexes by capillary electrophoresis using sulfated cyclodextrins as stereoselectors

Czech Academy of Sciences Publication Activity Database

Sázelová, Petra; Koval, Dušan; Severa, Lukáš; Teplý, Filip; Kašička, Václav

2017-01-01

Roč. 38, č. 15 (2017), s. 1913-1921 ISSN 0173-0835 R&D Projects: GA ČR(CZ) GA15-01948S; GA ČR GA13-32974S; GA ČR GA13-19213S Institutional support: RVO:61388963 Keywords : binding constant * capillary electrophoresis * chiral separation * polypyridyl Fe(II) complex * polypyridyl Ru(II) complex Subject RIV: CB - Analytical Chemistry, Separation OBOR OECD: Analytical chemistry Impact factor: 2.744, year: 2016

Variational Gaussian approximation for Poisson data

Science.gov (United States)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Analytical Electron Diffraction from Iii-V and II-Vi Semiconductors

Science.gov (United States)

Spellward, Paul

Available from UMI in association with The British Library. This thesis describes the development and evaluation of a number of new TEM-based techniques for the measurement of composition in ternary III-V and II-VI semiconductors. New methods of polarity determination in binary and ternary compounds are also presented. The theory of high energy electron diffraction is outlined, with particular emphasis on zone axis diffraction from well-defined strings. An account of TEM microstructural studies of Cd_{rm x}Hg _{rm 1-x}Te and CdTe epitaxial layers, which provided the impetus for developing the diffraction-based analytical techniques, is given. The wide range of TEM-based compositional determination techniques is described. The use of HOLZ deficiency lines to infer composition from a lattice parameter measurement is evaluated. In the case of Cd_{ rm x}Hg_{rm 1-x}Te, it is found to be inferior to other techniques developed. Studies of dynamical aspects of HOLZ diffraction can yield information about the dispersion surface from which a measure of composition may be obtained. This technique is evaluated for Al_{rm x}Ga_{rm 1-x} As, in which it is found to be of some use, and for Cd_{rm x}Hg _{rm 1-x}Te, in which the large Debye-Waller factor associated with mercury in discovered to render the method of little value. A number of critical voltages may be measured in medium voltage TEMs. The (111) zone axis critical voltage of Cd_{rm x}Hg _{rm 1-x}Te is found to vary significantly with x and forms the basis of an accurate technique for composition measurement in that ternary compound. Other critical voltage phenomena are investigated. In Al _{rm x}Ga_ {rm 1-x}As and other light ternaries, a non-systematic critical voltage is found to vary with x, providing a good indicator of composition. Critical voltage measurements may be made by conventional CBED or by various other techniques, which may also simultaneously yield information on the spatial variation of composition. The

Evaluation of the highly sensitive Roche thyroglobulin II assay and establishment of a reference limit for thyroglobulin-negative patient samples

Directory of Open Access Journals (Sweden)

Dorien M. Rotteveel-de Groot

2016-08-01

Full Text Available Objectives: Thyroglobulin (Tg measurements are used to monitor for residual thyroid tissue in patients with differentiated thyroid cancer (DTC after thyroidectomy and radioiodine ablative therapy. In recent years highly sensitive Tg assays have been developed. In this study the analytical performance of the new Roche Elecsys Tg II assay was evaluated and compared with the well documented Access2 Tg assay (Beckman–Coulter. Design and methods: Analytical performance was examined using various Clinical and Laboratory Standards Institute (CLSI evaluation protocols. Tg negative patient sera were used to establish an upper reference limit (URL for the Elecsys Tg II assay. Results: Non-linearity, drift and carry-over according to CLSI EP10 and EP6 in a measuring range of 0.04–500 ng/mL were non-significant. Total precision according to CLSI EP5 was 10% at a Tg concentration of 0.08 ng/mL. A patient serum comparison performed according to a modified CLSI EP9 protocol showed a significant difference of a factor of approximately 1.4, despite using an identical CRM calibrator. The Elecsys Tg II assay measured Tg with a two-fold higher sensitivity than the Access2 assay. Finally, using human sera without Tg, an URL of 0.05 ng/mL was determined. Conclusions: In our hands the highly sensitive Elecsys Tg II assay shows a good analytical performance and a higher sensitivity compared to the Access2 Tg assay. An URL of 0.05 ng/mL for the Elecsys Tg II assay was determined which may improve the clinical utility of the assay for the detection of residual DTC or disease recurrence. Keywords: Thyroglobulin, Roche Elecsys Tg II assay, validation, reporting limit

Evaluation of the highly sensitive Roche thyroglobulin II assay and establishment of a reference limit for thyroglobulin-negative patient samples.

Science.gov (United States)

Rotteveel-de Groot, Dorien M; Ross, H Alec; Janssen, Marcel J R; Netea-Maier, Romana T; Oosting, Janine D; Sweep, Fred C G J; van Herwaarden, Antonius E

2016-08-01

Thyroglobulin (Tg) measurements are used to monitor for residual thyroid tissue in patients with differentiated thyroid cancer (DTC) after thyroidectomy and radioiodine ablative therapy. In recent years highly sensitive Tg assays have been developed. In this study the analytical performance of the new Roche Elecsys Tg II assay was evaluated and compared with the well documented Access2 Tg assay (Beckman-Coulter). Analytical performance was examined using various Clinical and Laboratory Standards Institute (CLSI) evaluation protocols. Tg negative patient sera were used to establish an upper reference limit (URL) for the Elecsys Tg II assay. Non-linearity, drift and carry-over according to CLSI EP10 and EP6 in a measuring range of 0.04-500 ng/mL were non-significant. Total precision according to CLSI EP5 was 10% at a Tg concentration of 0.08 ng/mL. A patient serum comparison performed according to a modified CLSI EP9 protocol showed a significant difference of a factor of approximately 1.4, despite using an identical CRM calibrator. The Elecsys Tg II assay measured Tg with a two-fold higher sensitivity than the Access2 assay. Finally, using human sera without Tg, an URL of 0.05 ng/mL was determined. In our hands the highly sensitive Elecsys Tg II assay shows a good analytical performance and a higher sensitivity compared to the Access2 Tg assay. An URL of 0.05 ng/mL for the Elecsys Tg II assay was determined which may improve the clinical utility of the assay for the detection of residual DTC or disease recurrence.

The binary collision approximation: Background and introduction

International Nuclear Information System (INIS)

Robinson, M.T.

1992-08-01

The binary collision approximation (BCA) has long been used in computer simulations of the interactions of energetic atoms with solid targets, as well as being the basis of most analytical theory in this area. While mainly a high-energy approximation, the BCA retains qualitative significance at low energies and, with proper formulation, gives useful quantitative information as well. Moreover, computer simulations based on the BCA can achieve good statistics in many situations where those based on full classical dynamical models require the most advanced computer hardware or are even impracticable. The foundations of the BCA in classical scattering are reviewed, including methods of evaluating the scattering integrals, interaction potentials, and electron excitation effects. The explicit evaluation of time at significant points on particle trajectories is discussed, as are scheduling algorithms for ordering the collisions in a developing cascade. An approximate treatment of nearly simultaneous collisions is outlined and the searching algorithms used in MARLOWE are presented

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

Science.gov (United States)

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-15

diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries

Science.gov (United States)

Asgharzadeh, Hafez; Borazjani, Iman

2016-01-01

diagonal of the Jacobian further improves the performance by 42 – 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80–90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future. PMID:28042172

An approximation method for diffusion based leaching models

International Nuclear Information System (INIS)

Shukla, B.S.; Dignam, M.J.

1987-01-01

In connection with the fixation of nuclear waste in a glassy matrix equations have been derived for leaching models based on a uniform concentration gradient approximation, and hence a uniform flux, therefore requiring the use of only Fick's first law. In this paper we improve on the uniform flux approximation, developing and justifying the approach. The resulting set of equations are solved to a satisfactory approximation for a matrix dissolving at a constant rate in a finite volume of leachant to give analytical expressions for the time dependence of the thickness of the leached layer, the diffusional and dissolutional contribution to the flux, and the leachant composition. Families of curves are presented which cover the full range of all the physical parameters for this system. The same procedure can be readily extended to more complex systems. (author)

A meromorphic extension of Oka-Weil approximation in a Stein manifold

International Nuclear Information System (INIS)

Lutterodt, C.H.

1988-06-01

The results concerning the generalization of the Oka-Weil approximation theorem over a polynomial polyhedron using as a basic tool a Montessus-type theorem are extended to an analytic polyhedral subset in some Stein manifold X. 9 refs

Analytical Approach to Polarization Mode Dispersion in Linearly Spun Fiber with Birefringence

Directory of Open Access Journals (Sweden)

Vinod K. Mishra

2016-01-01

Full Text Available The behavior of Polarization Mode Dispersion (PMD in spun optical fiber is a topic of great interest in optical networking. Earlier work in this area has focused more on approximate or numerical solutions. In this paper we present analytical results for PMD in spun fibers with triangular spin profile function. It is found that in some parameter ranges the analytical results differ from the approximations.

Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

International Nuclear Information System (INIS)

Kushner, Harold J.

2012-01-01

This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.

A multi scale approximation solution for the time dependent Boltzmann-transport equation

International Nuclear Information System (INIS)

Merk, B.

2004-03-01

The basis of all transient simulations for nuclear reactor cores is the reliable calculation of the power production. The local power distribution is generally calculated by solving the space, time, energy and angle dependent neutron transport equation known as Boltzmann equation. The computation of exact solutions of the Boltzmann equation is very time consuming. For practical numerical simulations approximated solutions are usually unavoidable. The objective of this work is development of an effective multi scale approximation solution for the Boltzmann equation. Most of the existing methods are based on separation of space and time. The new suggested method is performed without space-time separation. This effective approximation solution is developed on the basis of an expansion for the time derivative of different approximations to the Boltzmann equation. The method of multiple scale expansion is used for the expansion of the time derivative, because the problem of the stiff time behaviour can't be expressed by standard expansion methods. This multiple scale expansion is used in this work to develop approximation solutions for different approximations of the Boltzmann equation, starting from the expansion of the point kinetics equations. The resulting analytic functions are used for testing the applicability and accuracy of the multiple scale expansion method for an approximation solution with 2 delayed neutron groups. The results are tested versus the exact analytical results for the point kinetics equations. Very good agreement between both solutions is obtained. The validity of the solution with 2 delayed neutron groups to approximate the behaviour of the system with 6 delayed neutron groups is demonstrated in an additional analysis. A strategy for a solution with 4 delayed neutron groups is described. A multiple scale expansion is performed for the space-time dependent diffusion equation for one homogenized cell with 2 delayed neutron groups. The result is

Analyticity and the Global Information Field

Directory of Open Access Journals (Sweden)

Evgeni A. Solov'ev

2015-03-01

Full Text Available The relation between analyticity in mathematics and the concept of a global information field in physics is reviewed. Mathematics is complete in the complex plane only. In the complex plane, a very powerful tool appears—analyticity. According to this property, if an analytic function is known on the countable set of points having an accumulation point, then it is known everywhere. This mysterious property has profound consequences in quantum physics. Analyticity allows one to obtain asymptotic (approximate results in terms of some singular points in the complex plane which accumulate all necessary data on a given process. As an example, slow atomic collisions are presented, where the cross-sections of inelastic transitions are determined by branch-points of the adiabatic energy surface at a complex internuclear distance. Common aspects of the non-local nature of analyticity and a recently introduced interpretation of classical electrodynamics and quantum physics as theories of a global information field are discussed.

Studies of heat transport to forced-flow He II

International Nuclear Information System (INIS)

Dresner, L.; Kashani, A.; Van Sciver, S.W.

1985-01-01

Analytical and experimental studies of heat transport to forced-flow He II are reported. The work is pertinent to the transfer of He II in space. An analytical model has been developed that establishes a condition for two-phase flow to occur in the transfer line. This condition sets an allowable limit to the heat leak into the transfer line. Experimental measurements of pressure drop and flow meter performances indicate that turbulent He II can be analyzed in terms of classical pressure drop correlations

Nodal approximations in space and time for neutron kinetics

International Nuclear Information System (INIS)

Grossman, L.M.; Hennart, J.P.

2005-01-01

A general formalism is described of the nodal type in time and space for the neutron kinetics equations. In space, several nodal methods are given of the Raviart-Thomas type (RT0 and RT1), of the Brezzi-Douglas-Marini type (BDM0 and BDM1) and of the Brezzi-Douglas-Fortin-Marini type (BDFM 1). In time, polynomial and analytical approximations are derived. In the analytical case, they are based on the inclusion of an exponential term in the basis function. They can be continuous or discontinuous in time, leading in particular to the well-known Crank-Nicolson, Backward Euler and θ schemes

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

Science.gov (United States)

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.…

Minimum Analytical Chemistry Requirements for Pit Manufacturing at Los Alamos National Laboratory; TOPICAL

International Nuclear Information System (INIS)

Moy, Ming M.; Leasure, Craig S.

1998-01-01

Analytical chemistry is one of several capabilities necessary for executing the Stockpile Stewardship and Management Program at Los Alamos National Laboratory (LANL). Analytical chemistry capabilities reside in the Chemistry Metallurgy Research (CMR) Facility and Plutonium Facility (TA-55). These analytical capabilities support plutonium recovery operations, plutonium metallurgy, and waste management. Analytical chemistry capabilities at both nuclear facilities are currently being configured to support pit manufacturing. This document summarizes the minimum analytical chemistry capabilities required to sustain pit manufacturing at LANL. By the year 2004, approximately$16 million will be required to procure analytical instrumentation to support pit manufacturing. In addition,$8.5 million will be required to procure glovebox enclosures. An estimated 50% increase in costs has been included for installation of analytical instruments and glovebox enclosures. However, no general and administrative (G and A) taxes have been included. If an additional 42.5/0 G and A tax were to be incurred, approximately$35 million would be required over the next five years to prepare analytical chemistry to support a 50-pit-per-year manufacturing capability by the year 2004

Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem

KAUST Repository

Younis, Mohammad I.

2014-01-01

We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions

Direct application of Padé approximant for solving nonlinear differential equations.

Science.gov (United States)

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

2014-01-01

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

Analytic solution of integral equations for molecular fluids

International Nuclear Information System (INIS)

Cummings, P.T.

1984-01-01

We review some recent progress in the analytic solution of integral equations for molecular fluids. The site-site Ornstein-Zernike (SSOZ) equation with approximate closures appropriate to homonuclear diatomic fluids both with and without attractive dispersion-like interactions has recently been solved in closed form analytically. In this paper, the close relationship between the SSOZ equation for homonuclear dumbells and the usual Ornstein-Zernike (OZ) equation for atomic fluids is carefully elucidated. This relationship is a key motivation for the analytic solutions of the SSOZ equation that have been obtained to date. (author)

Analytical Thermal Field Theory Applicable to Oil Hydraulic Fluid Film Lubrication

DEFF Research Database (Denmark)

Johansen, Per; Roemer, Daniel Beck; Pedersen, Henrik C.

2014-01-01

the analytical approach provides an alternative to existing computationally expensive numerical methods. The paper presents the dimensional analysis, which provides the foundation for the derivation of the analytical approximation. Subsequently, the perturbation method is applied in order to find an asymptotic...

Commissioning of the laboratory of Atucha II NPP. Implementation and optimization of analytical techniques, quality aspects

International Nuclear Information System (INIS)

Schoenbrod, Betina; Quispe, Benjamin; Cattaneo, Alberto; Rodriguez, Ivanna; Chocron, Mauricio; Farias, Silvia

2012-09-01

Atucha II NPP is a Pressurized Vessel Heavy Water Reactor (PVHWR) of 740 MWe designed by SIEMENSKWU. After some years of delay, this NPP is in advanced construction state, being the beginning of commercial operation expected for 2013. Nucleoelectrica Argentina (N.A.S.A.) is the company in charge of the finalization of this project and the future operation of the plant. The Comision Nacional de Energia Atomica (C.N.E.A.) is the R and D nuclear institution in the country that, among many other topics, provides technical support to the stations. The Commissioning Chemistry Division of CNAII is in charge of the commissioning of the demineralization water plant and the organization of the chemical laboratory. The water plant started operating successfully in July 2010 and is providing the plant with nuclear grade purity water. Currently, in the conventional ('cold') laboratory several activities are taking place. On one hand, analytical techniques for the future operation of the plant are being tested and optimized. On the other hand, the laboratory is participating in the cleaning and conservation of the different components of the plant, providing technical support and the necessary analysis. To define the analytical techniques for the normal operation of the plant, the parameters to be measured and their range were established in the Chemistry Manual. The necessary equipment and reagents were bought. In this work, a summary of the analytical techniques that are being implemented and optimized is presented. Common anions (chloride, sulfate, fluoride, bromide and nitrate) are analyzed by ion chromatography. Cations, mainly sodium, are determined by absorption spectrometry. A UV-Vis spectrometer is used to determine silicates, iron, ammonia, DQO, total solids, true color and turbidity. TOC measurements are performed with a TOC analyzer. To optimize the methods, several parameters are evaluated: linearity, detection and quantification limits, precision and

Analytical theory of frequency-multiplying gyro-traveling-wave-tubes

International Nuclear Information System (INIS)

Nusinovich, G.S.; Chen, W.; Granatstein, V.L.

2001-01-01

The theory is developed which describes analytically the gain and bandwidth in frequency-multiplying gyro-traveling-wave-tubes. In this theory the input waveguide is considered in the small-signal approximation. Then, in the drift region separating the input and output waveguides, the electron ballistic bunching evolves which causes the appearance in the electron current density of the harmonics of the signal frequency. The excitation of the output waveguide by one of these harmonics is considered in a specified current approximation. This makes the analytical study of a large-signal operation possible. The theory is illustrated by using it to analyze the performance of an existing experimental tube

Nonstandard approximation schemes for lower dimensional quantum field theories

International Nuclear Information System (INIS)

Fitzpatrick, D.A.

1981-01-01

The purpose of this thesis has been to apply two different nonstandard approximation schemes to a variety of lower-dimensional schemes. In doing this, we show their applicability where (e.g., Feynman or Rayleigh-Schroedinger) approximation schemes are inapplicable. We have applied the well-known mean-field approximation scheme by Guralnik et al. to general lower dimensional theories - the phi 4 field theory in one dimension, and the massive and massless Thirring models in two dimensions. In each case, we derive a bound-state propagator and then expand the theory in terms of the original and bound-state propagators. The results obtained can be compared with previously known results thereby show, in general, reasonably good convergence. In the second half of the thesis, we develop a self-consistent quantum mechanical approximation scheme. This can be applied to any monotonic polynomial potential. It has been applied in detail to the anharmonic oscillator, and the results in several analytical domains are very good, including extensive tables of numerical results

Synthesis, characterization and biological studies of 2-(4-nitrophenylamino-carbonyl)benzoic acid and its complexes with Cr(III), Co(II), Ni(II), Cu(II) and Zn(II)

International Nuclear Information System (INIS)

Imran, M; Nazir, S.; Latif, S.; Mahmood, Z.

2010-01-01

Cr(III), Co(II), Ni(II), Cu(II) and Zn(II) complexes of 2-(4-Nitrophenyl aminocarbonyl)benzoic acid were synthesized and characterized on the basis of physical, analytical and spectroscopic data. The ligands, as well as its metal complexes were checked for their in-vitro antimicrobial activity against three bacterial strains, Mycobacterium smegmatis, Escherichia coli, Pseudomonas aeuroginosa, and three fungal strains, Nigrospora oryzae, Aspergillus niger and Candida albicans. Disc diffusion method and Tube diffusion test were used for antibacterial and antifungal activities, respectively. The synthesized complexes only show significant antifungal activity but inactive for antibacterial, however, in general, the metal complexes were found to be more active against antimicrobial activities as compared to their un complexed ligand. (author)

Analytic Solutions of Special Functional Equations

Directory of Open Access Journals (Sweden)

Octav Olteanu

2013-07-01

Full Text Available We recall some of our earlier results on the construction of a mapping defined implicitly, without using the implicit function theorem. All these considerations work in the real case, for functions and operators. Then we consider the complex case, proving the analyticity of the function defined implicitly, under certain hypothesis. Some consequences are given. An approximating formula for the analytic form of the solution is also given. Finally, one illustrates the preceding results by an application to a concrete functional and operatorial equation. Some related examples are given.

39 (APPROXIMATE ANALYTICAL SOLUTION)

African Journals Online (AJOL)

Rotating machines like motors, turbines, compressors etc. are generally subjected to periodic forces and the system parameters remain more or less constant. ... parameters change and, consequently, the natural frequencies too, due to reasons of changing gyroscopic moments, centrifugal forces, bearing characteristics,.

A variational approach to operator and matrix Pade approximation. Applications to potential scattering and field theory

International Nuclear Information System (INIS)

Mery, P.

1977-01-01

The operator and matrix Pade approximation are defined. The fact that these approximants can be derived from the Schwinger variational principle is emphasized. In potential theory, using this variational aspect it is shown that the matrix Pade approximation allow to reproduce the exact solution of the Lippman-Schwinger equation with any required accuracy taking only into account the knowledge of the first two coefficients in the Born expansion. The deep analytic structure of this variational matrix Pade approximation (hyper Pade approximation) is discussed

Analytic approximations to nonlinear boundary value problems modeling beam-type nano-electromechanical systems

Energy Technology Data Exchange (ETDEWEB)

Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics

2017-06-01

Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.

Comparison of approximate methods for multiple scattering in high-energy collisions. II

International Nuclear Information System (INIS)

Nolan, A.M.; Tobocman, W.; Werby, M.F.

1976-01-01

The scattering in one dimension of a particle by a target of N like particles in a bound state has been studied. The exact result for the transmission probability has been compared with the predictions of the Glauber theory, the Watson optical potential model, and the adiabatic (or fixed scatterer) approximation. The approximate methods optical potential model is second best. The Watson method is found to work better when the kinematics suggested by Foldy and Walecka are used rather than that suggested by Watson, that is to say, when the two-body of the nucleon-nucleon reduced mass

Scattering Light by а Cylindrical Capsule with Arbitrary End Caps in the Rayleigh-Gans-Debye Approximation

Directory of Open Access Journals (Sweden)

K. A. Shapovalov

2015-01-01

Full Text Available The paper concerns the light scattering problem of biological objects of complicated structure.It considers optically “soft” (having a refractive index close to that of a surrounding medium homogeneous cylindrical capsules, composed of three parts: central one that is cylindrical and two symmetrical rounding end caps. Such capsules can model more broad class of biological objects than the ordinary shapes of a spheroid or sphere. But, unfortunately, if a particle has other than a regular geometrical shape, then it is very difficult or impossible to solve the scattering problem analytically in its most general form that oblige us to use numerical and approximate analytical methods. The one of such approximate analytical method is the Rayleigh-Gans-Debye approximation (or the first Born approximation.So, the Rayleigh-Gans-Debye approximation is valid for different objects having size from nanometer to millimeter and depending on wave length and refractive index of an object under small phase shift of central ray.The formulas for light scattering amplitude of cylindrical capsule with arbitrary end caps in the Rayleigh-Gans-Debye approximation in scalar form are obtained. Then the light scattering phase function [or element of scattering matrix f11] for natural incident light (unpolarized or arbitrary polarized light is calculated.Numerical results for light scattering phase functions of cylindrical capsule with conical, spheroidal, paraboloidal ends in the Rayleigh-Gans-Debye approximation are compared. Also numerical results for light scattering phase function of cylindrical capsule with conical ends in the Rayleigh-Gans-Debye approximation and in the method of Purcell-Pennypacker (or Discrete Dipole method are compared. The good agreement within an application range of the RayleighGans-Debye approximation is obtained.Further continuation of the work, perhaps, is a consideration of multilayer cylindrical capsule in the Rayleigh

Calculating Resonance Positions and Widths Using the Siegert Approximation Method

Science.gov (United States)

Rapedius, Kevin

2011-01-01

Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…

Analytical method for predicting plastic flow in notched fiber composite materials

International Nuclear Information System (INIS)

Flynn, P.L.; Ebert, L.J.

1977-01-01

An analytical system was developed for prediction of the onset and progress of plastic flow of oriented fiber composite materials in which both externally applied complex stress states and stress raisers were present. The predictive system was a unique combination of two numerical systems, the ''SAAS II'' finite element analysis system and a micromechanics finite element program. The SAAS II system was used to generate the three-dimensional stress distributions, which were used as the input into the finite element micromechanics program. Appropriate yielding criteria were then applied to this latter program. The accuracy of the analytical system was demonstrated by the agreement between the analytically predicted and the experimentally measured flow values of externally notched tungsten wire reinforced copper oriented fiber composites, in which the fiber fraction was 50 vol pct

Development of the relativistic impulse approximation

International Nuclear Information System (INIS)

Wallace, S.J.

1985-01-01

This talk contains three parts. Part I reviews the developments which led to the relativistic impulse approximation for proton-nucleus scattering. In Part II, problems with the impulse approximation in its original form - principally the low energy problem - are discussed and traced to pionic contributions. Use of pseudovector covariants in place of pseudoscalar ones in the NN amplitude provides more satisfactory low energy results, however, the difference between pseudovector and pseudoscalar results is ambiguous in the sense that it is not controlled by NN data. Only with further theoretical input can the ambiguity be removed. Part III of the talk presents a new development of the relativistic impulse approximation which is the result of work done in the past year and a half in collaboration with J.A. Tjon. A complete NN amplitude representation is developed and a complete set of Lorentz invariant amplitudes are calculated based on a one-meson exchange model and appropriate integral equations. A meson theoretical basis for the important pair contributions to proton-nucleus scattering is established by the new developments. 28 references

Two-dimensional analytic weighting functions for limb scattering

Science.gov (United States)

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.

Analytical solutions of the electrostatically actuated curled beam problem

KAUST Repository

Younis, Mohammad I.

2014-07-24

This works presents analytical expressions of the electrostatically actuated initially deformed cantilever beam problem. The formulation is based on the continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximation. In such cases, multi-mode reduced order models are shown to yield accurate results. © 2014 Springer-Verlag Berlin Heidelberg.

Solution of the Chew-Low equations in the quadratic approximation

International Nuclear Information System (INIS)

Gerdt, V.P.; Zharkov, A.Yu.

1982-01-01

Within the framework of the iteration scheme for constructing the general solution of the Chew-Low equations as suggested earlier the second order power contributions are found. In contrast to the linear approximation obtained before the quadratic approximation includes an infinite number of poles on the complex plane of the uniformizing variable w. It is shown that taking into account the second order corrections in the general solution allows us to select the class of solutions possessing the Born pole at w=0. The most cumbersome part of analytical computations has been carried out by computer using the algebraic system REDUCE-2

Approximate deconvolution models of turbulence analysis, phenomenology and numerical analysis

CERN Document Server

Layton, William J

2012-01-01

This volume presents a mathematical development of a recent approach to the modeling and simulation of turbulent flows based on methods for the approximate solution of inverse problems. The resulting Approximate Deconvolution Models or ADMs have some advantages over more commonly used turbulence models – as well as some disadvantages. Our goal in this book is to provide a clear and complete mathematical development of ADMs, while pointing out the difficulties that remain. In order to do so, we present the analytical theory of ADMs, along with its connections, motivations and complements in the phenomenology of and algorithms for ADMs.

Sulfite induced autoxidation of Cu(II/tetra/ penta and hexaglycine complexes: spectrophotometric and rotating-ring-disk glassy carbon electrode studies and analytical potentialities

Directory of Open Access Journals (Sweden)

Alipázaga Maria V.

2003-01-01

Full Text Available The oxidation of Cu(II complexes with tetra, penta and hexaglycine in borate buffer aqueous solution, by dissolved oxygen is strongly accelerated by sulfite. The formation of Cu(III complexes with maximum absorbances at 250 nm (e = 9000 mol-1 L cm-1 and 365 nm (e = 7120 mol-1 L cm-1 was also characterized by using rotating ring-disk voltammetry, whose anodic and cathodic components were observed in voltammograms recorded in solutions containing Cu(II. Voltammograms, obtained at various rotation speeds, showed that the Cu(III species electrochemically generated is not stable over the entire time window of the experiment and in solutions containing tetraglycine the overall limiting current is controlled by the kinetics of an equilibrium involving Cu(II species.The calculated first order rate constant of the decomposition was 4.37x10-3 s-1. Electrochemical experiments carried out in Cu(II solutions after the addition of relatively small amounts of sulfite demonstrated that the Cu(III species formed in the chemical reaction is the same as the one collected at the ring electrode when Cu(II is oxidized at the disk electrode in ring-disk voltammetry. The concentration of Cu(III complexes is proportional to the amount of added sulfite and the results indicated that indirect analytical methods for sulfite may be developed by means of spectrophotometric or amperometric detection of the chemically generated product.

A new look at the statistical assessment of approximate and rigorous methods for the estimation of stabilized formation temperatures in geothermal and petroleum wells

International Nuclear Information System (INIS)

Espinoza-Ojeda, O M; Santoyo, E; Andaverde, J

2011-01-01

Approximate and rigorous solutions of seven heat transfer models were statistically examined, for the first time, to estimate stabilized formation temperatures (SFT) of geothermal and petroleum boreholes. Constant linear and cylindrical heat source models were used to describe the heat flow (either conductive or conductive/convective) involved during a borehole drilling. A comprehensive statistical assessment of the major error sources associated with the use of these models was carried out. The mathematical methods (based on approximate and rigorous solutions of heat transfer models) were thoroughly examined by using four statistical analyses: (i) the use of linear and quadratic regression models to infer the SFT; (ii) the application of statistical tests of linearity to evaluate the actual relationship between bottom-hole temperatures and time function data for each selected method; (iii) the comparative analysis of SFT estimates between the approximate and rigorous predictions of each analytical method using a β ratio parameter to evaluate the similarity of both solutions, and (iv) the evaluation of accuracy in each method using statistical tests of significance, and deviation percentages between 'true' formation temperatures and SFT estimates (predicted from approximate and rigorous solutions). The present study also enabled us to determine the sensitivity parameters that should be considered for a reliable calculation of SFT, as well as to define the main physical and mathematical constraints where the approximate and rigorous methods could provide consistent SFT estimates

Diophantine approximation and badly approximable sets

DEFF Research Database (Denmark)

Kristensen, S.; Thorn, R.; Velani, S.

2006-01-01

. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

Validity of the Born approximation for beyond Gaussian weak lensing observables

Science.gov (United States)

Petri, Andrea; Haiman, Zoltán; May, Morgan

2017-06-01

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N -body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O (Φ3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O (Φ4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5 σ . Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.

Analytical expression for the bit error rate of cascaded all-optical regenerators

DEFF Research Database (Denmark)

Mørk, Jesper; Öhman, Filip; Bischoff, S.

2003-01-01

We derive an approximate analytical expression for the bit error rate of cascaded fiber links containing all-optical 2R-regenerators. A general analysis of the interplay between noise due to amplification and the degree of reshaping (nonlinearity) of the regenerator is performed.......We derive an approximate analytical expression for the bit error rate of cascaded fiber links containing all-optical 2R-regenerators. A general analysis of the interplay between noise due to amplification and the degree of reshaping (nonlinearity) of the regenerator is performed....

Sample Exchange Evaluation (SEE) Report - Phase II

Energy Technology Data Exchange (ETDEWEB)

Winters, W.I.

1994-09-28

This report describes the results from Phase II of the Sample Exchange Evaluation (SEE) Program, a joint effort to compare analytical laboratory performance on samples from the Hanford Site`s high-level waste tanks. In Phase II, the program has been expanded to include inorganic constituents in addition to radionuclides. Results from Phase II that exceeded 20% relative percent difference criteria are identified.

Sample Exchange Evaluation (SEE) Report - Phase II

International Nuclear Information System (INIS)

Winters, W.I.

1994-01-01

This report describes the results from Phase II of the Sample Exchange Evaluation (SEE) Program, a joint effort to compare analytical laboratory performance on samples from the Hanford Site's high-level waste tanks. In Phase II, the program has been expanded to include inorganic constituents in addition to radionuclides. Results from Phase II that exceeded 20% relative percent difference criteria are identified

Microwave magnetoelectric fields: An analytical study of topological characteristics

Energy Technology Data Exchange (ETDEWEB)

Joffe, R., E-mail: ioffr1@gmail.com [Microwave Magnetic Laboratory, Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Beer Sheva (Israel); Department of Electrical and Electronics Engineering, Shamoon College of Engineering, Beer Sheva (Israel); Shavit, R.; Kamenetskii, E.O. [Microwave Magnetic Laboratory, Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Beer Sheva (Israel)

2015-10-15

The near fields originated from a small quasi-two-dimensional ferrite disk with magnetic-dipolar-mode (MDM) oscillations are the fields with broken dual (electric-magnetic) symmetry. Numerical studies show that such fields – called the magnetoelectric (ME) fields – are distinguished by the power-flow vortices and helicity parameters (E.O. Kamenetskii, R. Joffe, R. Shavit, Phys. Rev. E 87 (2013) 023201). These numerical studies can well explain recent experimental results with MDM ferrite disks. In the present paper, we obtain analytically topological characteristics of the ME-field modes. For this purpose, we used a method of successive approximations. In the second approximation we take into account the influence of the edge regions of an open ferrite disk, which are excluded in the first-approximation solving of the magnetostatic (MS) spectral problem. Based on the analytical method, we obtain a “pure” structure of the electric and magnetic fields outside the MDM ferrite disk. The analytical studies can display some fundamental features that are non-observable in the numerical results. While in numerical investigations, one cannot separate the ME fields from the external electromagnetic (EM) radiation, the present theoretical analysis allows clearly distinguish the eigen topological structure of the ME fields. Importantly, this ME-field structure gives evidence for certain phenomena that can be related to the Tellegen and bianisotropic coupling effects. We discuss the question whether the MDM ferrite disk can exhibit properties of the cross magnetoelectric polarizabilities. - Highlights: • We obtain analytically topological characteristics of the ME-field modes. • We take into account the influence of the edge regions of an open ferrite disk. • We obtain a “pure” structure of the electromagnetic fields outside the ferrite disk. • Analytical studies show features that are non-observable in the numerical results. • ME-field gives evidence for

Microwave magnetoelectric fields: An analytical study of topological characteristics

International Nuclear Information System (INIS)

Joffe, R.; Shavit, R.; Kamenetskii, E.O.

2015-01-01

The near fields originated from a small quasi-two-dimensional ferrite disk with magnetic-dipolar-mode (MDM) oscillations are the fields with broken dual (electric-magnetic) symmetry. Numerical studies show that such fields – called the magnetoelectric (ME) fields – are distinguished by the power-flow vortices and helicity parameters (E.O. Kamenetskii, R. Joffe, R. Shavit, Phys. Rev. E 87 (2013) 023201). These numerical studies can well explain recent experimental results with MDM ferrite disks. In the present paper, we obtain analytically topological characteristics of the ME-field modes. For this purpose, we used a method of successive approximations. In the second approximation we take into account the influence of the edge regions of an open ferrite disk, which are excluded in the first-approximation solving of the magnetostatic (MS) spectral problem. Based on the analytical method, we obtain a “pure” structure of the electric and magnetic fields outside the MDM ferrite disk. The analytical studies can display some fundamental features that are non-observable in the numerical results. While in numerical investigations, one cannot separate the ME fields from the external electromagnetic (EM) radiation, the present theoretical analysis allows clearly distinguish the eigen topological structure of the ME fields. Importantly, this ME-field structure gives evidence for certain phenomena that can be related to the Tellegen and bianisotropic coupling effects. We discuss the question whether the MDM ferrite disk can exhibit properties of the cross magnetoelectric polarizabilities. - Highlights: • We obtain analytically topological characteristics of the ME-field modes. • We take into account the influence of the edge regions of an open ferrite disk. • We obtain a “pure” structure of the electromagnetic fields outside the ferrite disk. • Analytical studies show features that are non-observable in the numerical results. • ME-field gives evidence for

Analytic description of four-wave mixing in silicon-on-insulator waveguides

DEFF Research Database (Denmark)

Friis, Søren Michael Mørk; Koefoed, Jacob Gade; Guo, Kai

2018-01-01

and becomes a nonlinear differential equation that we solve analytically without further approximations. The signal and idler equations have no known solutions for arbitrary pump power evolution, but we calculate approximate field expressions based on a Magnus expansion, which has been used to study time...

Inference Under a Wright-Fisher Model Using an Accurate Beta Approximation

DEFF Research Database (Denmark)

Tataru, Paula; Bataillon, Thomas; Hobolth, Asger

2015-01-01

frequencies and the influence of evolutionary pressures, such as mutation and selection. Despite its simple mathematical formulation, exact results for the distribution of allele frequency (DAF) as a function of time are not available in closed analytic form. Existing approximations build......, the probability of being on the boundary can be positive, corresponding to the allele being either lost or fixed. Here, we introduce the beta with spikes, an extension of the beta approximation, which explicitly models the loss and fixation probabilities as two spikes at the boundaries. We show that the addition...

DNA binding and biological activity of mixed ligand complexes of Cu(II, Ni(II and Co(II with quinolones and N donor ligand

Directory of Open Access Journals (Sweden)

S.M M Akram

2015-10-01

Full Text Available  AbstractMixed ligand complexes of  Cu(II, Ni(II and Co(II have been synthesized by using levofloxacin and bipyridyl and characterized using spectral and analytical techniques. The binding behavior of the Ni(II and Cu(II complexes with herring sperm DNA(Hs-DNA were determined using electronic absorption titration, viscometric measurements and cyclic voltammetry measurements. The binding constant calculated  for Cu(II and Ni(II complexes are 2.0 x 104 and 4.0 x 104 M-1 respectively. Detailed analysis reveals that these metal complexes interact with DNA through intercalative binding mode. The nuclease activity of  Cu(II and Ni(II complexes with ct-DNA was carried out using agarose gel electrophoresis technique. The antioxidant activities for the synthesized complexes have been tested and the antibacterial activity for Ni(II complex was also checked.Key words: Intercalation, hypochromism, red shift and  peak potential.

Fowler's approximation for the surface tension and surface energy of Lennard-Jones fluids revisited

International Nuclear Information System (INIS)

Mulero, A; Galan, C; Cuadros, F

2003-01-01

We present a detailed study of the validity of Fowler's approximation for calculating the surface tension and the surface energy of Lennard-Jones fluids. To do so, we consider three different explicit analytical expressions for the radial distribution function (RDF), including one proposed by our research group, together with very accurate expressions for the liquid and vapour densities, also proposed by our group. The calculation of the surface tension from the direct correlation function using both the Percus-Yevick and the hypernetted-chain approximations is also considered. Finally, our results are compared with those obtained by other authors by computer simulations or through relevant theoretical approximations. In particular, we consider the analytical expression proposed by Kalikmanov and Hofmans (1994 J. Phys.: Condens. Matter 6 2207-14) for the surface tension. Our results indicate that the values for the surface energy in Fowler's approximation obtained by other authors are adequate, and can be calculated from the RDF models. For the surface tension, however, the values considered as valid in previous works seem to be incorrect. The correct values can be obtained from our model for the RDF or from the Kalikmanov and Hofmans expression with suitable inputs

Separation and preconcentration of lead(II), cobalt(II), and nickel(II) on EDTA immobilized activated carbon cloth prior to flame atomic absorption spectrometric determination in environmental samples

OpenAIRE

ALOTHMAN, ZEID ABDULLAH; YILMAZ, ERKAN; HABİLA, MOHAMED; SOYLAK, MUSTAFA

2015-01-01

The synthesis and characterization of ethylenediaminetetraacetic acid immobilized activated carbon cloth was performed in the present work. It was used for preconcentration-separation of lead(II), cobalt(II), and nickel(II) at trace levels as an adsorbent. Factors including pH, concentration and volume of eluent, sample and eluent flow rates, sample volume, and effect of coexisting ions on the solid phase extraction of analytes were examined. The preconcentration factor was 50. The detection ...

Problems with the quenched approximation in the chiral limit

International Nuclear Information System (INIS)

Sharpe, S.R.

1992-01-01

In the quenched approximation, loops of the light singlet meson (the η') give rise to a type of chiral logarithm absent in full QCD. These logarithms are singular in the chiral limit, throwing doubt upon the utility of the quenched approximation. In previous work, I summed a class of diagrams, leading to non-analytic power dependencies such as left-angle anti ψψ right-angle ∝ m q -δ /(1+δ) I suggested, however, that these peculiar results could be redefined away. Here I give an alternative derivation of the results, based on the renormalization group, and argue that they cannot be redefined away. I discuss the evidence (or lack thereof) for such effects in numerical data

Pade approximants and the calculation of effective interactions

International Nuclear Information System (INIS)

Schucan, T.H.

1975-01-01

The analytic properties of the effective interaction in nuclei have become increasingly well understood in the last few years. It has been found that the corresponding series expansion diverges in most practical applications due to the occurrence of low lying collective states. It is the purpose of this paper to review and discuss an approximation scheme that has been used to rearrange this series with the aim to overcome the difficulties connected with its divergence. (orig./WL) [de

Study of some approximation schemes in the spin-boson problem

International Nuclear Information System (INIS)

Kenkre, V.M.; Giuggioli, L.

2004-01-01

Some approximation schemes used in the description of the evolution of the spin-boson system are studied through numerical and analytic methods. Among the procedures investigated are semiclassical approximations and the memory function approach. An infinitely large number of semiclassical approximations are discussed. Their two extreme limits are shown to be characterized, respectively, by effective energy mismatch and effective intersite transfer. The validity of the two limits is explored by explicit numerical calculations for important regions in parameter space, and it is shown that they can provide good descriptions in the so-called adiabatic and anti-adiabatic regimes, respectively. The memory function approach, which provides an excellent approximation scheme for a certain range of parameters, is shown to be connected to other approaches such as the non-interacting blip approximation. New results are derived from the memory approach in semiclassical contexts. Comments are made on thermal effects in the spin-boson problem, the discrete non-linear Schroedinger equation, and connections to the areas of dynamic localization, and quantum control

Balancing Exchange Mixing in Density-Functional Approximations for Iron Porphyrin.

Science.gov (United States)

Berryman, Victoria E J; Boyd, Russell J; Johnson, Erin R

2015-07-14

Predicting the correct ground-state multiplicity for iron(II) porphyrin, a high-spin quintet, remains a significant challenge for electronic-structure methods, including commonly employed density functionals. An even greater challenge for these methods is correctly predicting favorable binding of O2 to iron(II) porphyrin, due to the open-shell singlet character of the adduct. In this work, the performance of a modest set of contemporary density-functional approximations is assessed and the results interpreted using Bader delocalization indices. It is found that inclusion of greater proportions of Hartree-Fock exchange, in hybrid or range-separated hybrid functionals, has opposing effects; it improves the ability of the functional to identify the ground state but is detrimental to predicting favorable dioxygen binding. Because of the uncomplementary nature of these properties, accurate prediction of both the relative spin-state energies and the O2 binding enthalpy eludes conventional density-functional approximations.

Removal of nickel(II and palladium(II from surface waters

Directory of Open Access Journals (Sweden)

V. Sharifzade

2013-04-01

Full Text Available A new sorbent was prepared using alumina and 5-Br-PADAP, and its adsorption ability for the removal of Ni(II and Pd(II from different waters was investigated. The procedure is based on retention of the analytes on the alumina load with 5-Br-PADAP at pH ~ 6. The separation/preconcentration conditions for the quantitative recoveries were investigated. The limit of detections (LOD based on three times the standard deviations of the blank, were 0.187 and 0.253 ng mL-1 for Ni(II and Pd(II, respectively. Obtained sorption capacities for 1 g sorbent were 6.0 mg Ni(II and 11.0 mg Pd(II. The linearity was maintained in the concentration range of 0.625 to 6.0 ng mL-1 for Ni(II and 0.416 to 7.0 ng mL-1 for Pd(II in the original solution. Eight replicate determinations of a mixture containing 2.0 µg mL-1 each of the elements in the final solution gave relative standard deviation of ±0.82 and ±1.12% for Ni(II and Pd(II, respectively. The proposed method was successfully applied to the determination trace amounts of Ni(II and Pd(II in the surface water samples.DOI: http://dx.doi.org/10.4314/bcse.v27i1.2

An outer approximation method for the road network design problem.

Science.gov (United States)

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.

Swiss-cheese models and the Dyer-Roeder approximation

Energy Technology Data Exchange (ETDEWEB)

Fleury, Pierre, E-mail: fleury@iap.fr [Institut d' Astrophysique de Paris, UMR-7095 du CNRS, Université Pierre et Marie Curie, 98 bis, boulevard Arago, 75014 Paris (France)

2014-06-01

In view of interpreting the cosmological observations precisely, especially when they involve narrow light beams, it is crucial to understand how light propagates in our statistically homogeneous, clumpy, Universe. Among the various approaches to tackle this issue, Swiss-cheese models propose an inhomogeneous spacetime geometry which is an exact solution of Einstein's equation, while the Dyer-Roeder approximation deals with inhomogeneity in an effective way. In this article, we demonstrate that the distance-redshift relation of a certain class of Swiss-cheese models is the same as the one predicted by the Dyer-Roeder approach, at a well-controlled level of approximation. Both methods are therefore equivalent when applied to the interpretation of, e.g., supernova obervations. The proof relies on completely analytical arguments, and is illustrated by numerical results.

Plasma Physics Approximations in Ares

International Nuclear Information System (INIS)

Managan, R. A.

2015-01-01

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

Analytical applications of some macro-schiff's bases for spectrophotometric determination of some metal ions

International Nuclear Information System (INIS)

Ahmed, N. A. M.

2005-06-01

In this research three schiff's bases PAD, N, NBPAD and N, NBHPAD were synthesized by condensation of o-phenylenediamine with p-aminoacetophenone, to give an intermediate which then further condensed with benzil, and 2,5 hexanedione, respectively, in ethanol to give macro schiff's bases. These schiff's bases were identified using I.R spectra, UV/VIS spectrophotometer, elemental analyzer, and melting point. Their applications as analytical reagents were studied using UV/VIS spectrophotometer with Pb(II), Cr(VI), Cu(II), Cd(II), V(V), Ni(II), Hg(II), Zn(II), Co(II), Fe(II) and Fe(III). Various parameters were investigated in order to find their optimum conditions for the analytical application of these schiff's bases. These include the effect of solvent, the effect of micelle as well as the presence of foreign metal ions. Good results were obtained for determination of Cr(VI), and V(V) with N, NBPAD in terms of linearity detection limit, and interference, and for the determination of Fe(II) with N, NBHPAD. The stoichiometry of some these complexes was determined. The study also showed a good results for the determination of Hg(II), and Pb(II) (two serious environmental pollutants) if interference is removed.(Author)

Super-sample covariance approximations and partial sky coverage

Science.gov (United States)

Lacasa, Fabien; Lima, Marcos; Aguena, Michel

2018-04-01

Super-sample covariance (SSC) is the dominant source of statistical error on large scale structure (LSS) observables for both current and future galaxy surveys. In this work, we concentrate on the SSC of cluster counts, also known as sample variance, which is particularly useful for the self-calibration of the cluster observable-mass relation; our approach can similarly be applied to other observables, such as galaxy clustering and lensing shear. We first examined the accuracy of two analytical approximations proposed in the literature for the flat sky limit, finding that they are accurate at the 15% and 30-35% level, respectively, for covariances of counts in the same redshift bin. We then developed a harmonic expansion formalism that allows for the prediction of SSC in an arbitrary survey mask geometry, such as large sky areas of current and future surveys. We show analytically and numerically that this formalism recovers the full sky and flat sky limits present in the literature. We then present an efficient numerical implementation of the formalism, which allows fast and easy runs of covariance predictions when the survey mask is modified. We applied our method to a mask that is broadly similar to the Dark Energy Survey footprint, finding a non-negligible negative cross-z covariance, i.e. redshift bins are anti-correlated. We also examined the case of data removal from holes due to, for example bright stars, quality cuts, or systematic removals, and find that this does not have noticeable effects on the structure of the SSC matrix, only rescaling its amplitude by the effective survey area. These advances enable analytical covariances of LSS observables to be computed for current and future galaxy surveys, which cover large areas of the sky where the flat sky approximation fails.

Structural characterization and antioxidant properties of Cu(II) and Ni(II) complexes derived from dicyandiamide

Science.gov (United States)

Kertmen, Seda Nur; Gonul, Ilyas; Kose, Muhammet

2018-01-01

New Cu(II) and Ni(II) complexes derived from dicyandiamide were synthesized and characterised by spectroscopic and analytical methods. Molecular structures of the complexes were determined by single crystal X-ray diffraction studies. In the complexes, the Cu(II) or Ni(II) ions are four-coordinate with a slight distorted square planar geometry. The ligands (L-nPen and L-iPen) derived from dicyandiamide formed via nucleophilic addition of alcohol solvent molecule in the presence Cu(II) or Ni(II) ions. Complexes were stabilised by intricate array of hydrogen bonding interactions. Antioxidant activity of the complexes was evaluated by DPPH radical scavenging and CUPRAC methods. The complexes exhibit antioxidant activity, however, their activities were much lower than standard antioxidants (Vitamin C and trolox).

MASCOTTE: analytical model of eddy current signals

International Nuclear Information System (INIS)

Delsarte, G.; Levy, R.

1992-01-01

Tube examination is a major application of the eddy current technique in the nuclear and petrochemical industries. Such examination configurations being specially adapted to analytical modes, a physical model is developed on portable computers. It includes simple approximations made possible by the effective conditions of the examinations. The eddy current signal is described by an analytical formulation that takes into account the tube dimensions, the sensor conception, the physical characteristics of the defect and the examination parameters. Moreover, the model makes it possible to associate real signals and simulated signals

Traveling-cluster approximation for uncorrelated amorphous systems

International Nuclear Information System (INIS)

Sen, A.K.; Mills, R.; Kaplan, T.; Gray, L.J.

1984-01-01

We have developed a formalism for including cluster effects in the one-electron Green's function for a positionally disordered (liquid or amorphous) system without any correlation among the scattering sites. This method is an extension of the technique known as the traveling-cluster approximation (TCA) originally obtained and applied to a substitutional alloy by Mills and Ratanavararaksa. We have also proved the appropriate fixed-point theorem, which guarantees, for a bounded local potential, that the self-consistent equations always converge upon iteration to a unique, Herglotz solution. To our knowledge, this is the only analytic theory for considering cluster effects. Furthermore, we have performed some computer calculations in the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results have been compared with ''exact calculations'' (which, in principle, take into account all cluster effects) and with the coherent-potential approximation (CPA), which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA and yet, apparently, the pair approximation distorts some of the features of the exact results

Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates

Directory of Open Access Journals (Sweden)

Mohammad Mehdi Rashidi

2008-01-01

Full Text Available The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

Synthesis and characterization of nickel(II), cobalt(II), copper(II), manganese(II), zinc(II), zirconium(IV), dioxouranium(VI) and dioxomolybdenum(VI) complexes of a new Schiff base derived from salicylaldehyde and 5-methylpyrazole-3-carbohydrazide

International Nuclear Information System (INIS)

Syamal, A.; Maurya, M.R.

1986-01-01

Synthesis of a new Schiff base derived from salicylaldehyde and 5-methylpyrazole-3-carbohydrazide, and its coordination compounds with nickel(II), cobalt(II), copper(II), manganese(II), zinc(II), zirconium(IV), dioxouranium(VI) and dioxomolybdenum(VI) are described. The ligand and the complexes have been characterized on the basis of analytical, conductance, molecular weight, i.r., electronic and n.m.r. spectra and magnetic susceptibility measurements. The stoichiometries of the complexes are represented as NiL . 3H 2 O, CoL . 2H 2 O, CuL, MnL . 2H 2 O, ZnL . H 2 O, Zr(OH) 2 (LH) 2 , Zr(OH) 2 L . 2MeOH, UO 2 L . MeOH and MoO 2 L . MeOH (where LH 2 =Schiff base). The copper(II) complex shows a subnormal magnetic moment due to antiferromagnetic exchange interaction while the nickel(II), cobalt(II) and manganese(II) complexes show normal magnetic moments at room temperature. The i.r. and n.m.r. spectral studies show that the Schiff base behaves as a dibasic and tridentate ligand coordinating through the deprotonated phenolic oxygen, enolic oxygen and azomethine nitrogen. (orig.)

Saha and temperature relaxation approximations for the study of ionization instability in partially ionized plasma

International Nuclear Information System (INIS)

Numano, M.

1976-01-01

The growth rates for the ionization instability obtained using the Saha and temperature relaxation approximations are compared with those obtained from an exact treatment, and the requirements for validity of these two approximations are obtained analytically. For the range of plasma parameters pertinent to MHD power generation it is found that the Saha approximation is valid for relatively high electron temperature, which it becomes inapplicable as the electron temperature is decreased. On the other hand, the temperature relaxation approximation is accurate over a wide range of electron temperature. It is found also that the marginal condition for the ionization instability is correctly obtained from both approximations. (author)

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

Science.gov (United States)

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.

Essential partial differential equations analytical and computational aspects

CERN Document Server

Griffiths, David F; Silvester, David J

2015-01-01

This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods.   Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems.   The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test unde...

MRS2016: Rigid Moon Rotation Series in the Relativistic Approximation

Science.gov (United States)

Pashkevich, V. V.

2017-03-01

The rigid Moon rotation problem is studied for the relativistic (kinematical) case, in which the geodetic perturbations in the Moon rotation are taken into account. As the result of this research the high-precision Moon Rotation Series MRS2016 in the relativistic approximation was constructed for the first time and the discrepancies between the high-precision numerical and the semi-analytical solutions of the rigid Moon rotation were investigated with respect to the fixed ecliptic of epoch J2000, by the numerical and analytical methods. The residuals between the numerical solution and MRS2016 in the perturbing terms of the physical librations do not exceed 80 mas and 10 arc seconds over 2000 and 6000 years, respectively.

Understanding operational risk capital approximations: First and second orders

Directory of Open Access Journals (Sweden)

Gareth W. Peters

2013-07-01

Full Text Available We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord, highlighting along the way the significant loss events that have been attributed to the Operational Risk class that was introduced in the Basel II and III accords. Then we provide a semi-tutorial discussion on the modelling aspects of capital estimation under a Loss Distributional Approach (LDA. Our emphasis is to focuss on the important loss processes with regard to those that contribute most to capital, the so called “high consequence, low frequency" loss processes. This leads us to provide a tutorial overview of heavy tailed loss process modelling in OpRisk under Basel III, with discussion on the implications of such tail assumptions for the severity model in an LDA structure. This provides practitioners with a clear understanding of the features that they may wish to consider when developing OpRisk severity models in practice. From this discussion on heavy tailed severity models, we then develop an understanding of the impact such models have on the right tail asymptotics of the compound loss process and we provide detailed presentation of what are known as first and second order tail approximations for the resulting heavy tailed loss process. From this we develop a tutorial on three key families of risk measures and their equivalent second order asymptotic approximations: Value-at-Risk (Basel III industry standard; Expected Shortfall (ES and the Spectral Risk Measure. These then form the capital approximations. We then provide a few example case studies to illustrate the accuracy of these asymptotic captial approximations, the rate of the convergence of the assymptotic result as a function of the LDA frequency and severity model parameters, the sensitivity

Estimating the approximation error when fixing unessential factors in global sensitivity analysis

Energy Technology Data Exchange (ETDEWEB)

Sobol' , I.M. [Institute for Mathematical Modelling of the Russian Academy of Sciences, Moscow (Russian Federation); Tarantola, S. [Joint Research Centre of the European Commission, TP361, Institute of the Protection and Security of the Citizen, Via E. Fermi 1, 21020 Ispra (Italy)]. E-mail: stefano.tarantola@jrc.it; Gatelli, D. [Joint Research Centre of the European Commission, TP361, Institute of the Protection and Security of the Citizen, Via E. Fermi 1, 21020 Ispra (Italy)]. E-mail: debora.gatelli@jrc.it; Kucherenko, S.S. [Imperial College London (United Kingdom); Mauntz, W. [Department of Biochemical and Chemical Engineering, Dortmund University (Germany)

2007-07-15

One of the major settings of global sensitivity analysis is that of fixing non-influential factors, in order to reduce the dimensionality of a model. However, this is often done without knowing the magnitude of the approximation error being produced. This paper presents a new theorem for the estimation of the average approximation error generated when fixing a group of non-influential factors. A simple function where analytical solutions are available is used to illustrate the theorem. The numerical estimation of small sensitivity indices is discussed.

Clinical and radiographic assessment of approximal carious lesions

International Nuclear Information System (INIS)

Espelid, I.; Tveit, A.B.

1986-01-01

The aim of the study was to compare the radiographic diagnosis of approximal carious lesions with visual observations of the approximal surfaces and within drilled Class II cavities (made into the pulp). Sound (n=28) and carious (n=123) approximal surfaces of extracted premolars and molars were radiographed. The radiographs were studied by seven observers to diagnose caries. Lesions without cavitation were most often classified as sound (61.3%). When lesions had cavities, the rate of detection increased to 89.1%. Sound surfaces were erroneously classified as carious in 15.7% of cases. Statistically, about 6 our of every 10 qualitative assessments of lesion depth on the basis of radiographs, correctly recorded lesions as being in enamel or extending into dentin. The interexaminer variation in radiographic caries diagnosis were mostly due to difference in diagnostic criteria, whereas differences in diagnostic capability were less important

Algebraically approximate and noisy realization of discrete-time systems and digital images

CERN Document Server

Hasegawa, Yasumichi

2009-01-01

This monograph deals with approximation and noise cancellation of dynamical systems which include linear and nonlinear input/output relationships. It also deal with approximation and noise cancellation of two dimensional arrays. It will be of special interest to researchers, engineers and graduate students who have specialized in filtering theory and system theory and digital images. This monograph is composed of two parts. Part I and Part II will deal with approximation and noise cancellation of dynamical systems or digital images respectively. From noiseless or noisy data, reduction will be

Argon analytical procedures for potassium-argon dating

International Nuclear Information System (INIS)

Gabites, J.E.; Adams, C.J.

1981-01-01

A manual for the argon analytical methods involved in potassium-argon geochronology, including: i) operating procedures for the ultra-high vacuum argon extraction/purification equipment for the analysis of nanolitre quantities of radiogenic argon in rocks, minerals and gases; ii) operating procedures for the AEI-MS10 gas source mass spectrometer

Defense Waste Processing Facility prototypic analytical laboratory

International Nuclear Information System (INIS)

Policke, T.A.; Bryant, M.F.; Spencer, R.B.

1991-01-01

The Defense Waste Processing Technology (DWPT) Analytical Laboratory is a relatively new laboratory facility at the Savannah River Site (SRS). It is a non-regulated, non-radioactive laboratory whose mission is to support research and development (R ampersand D) and waste treatment operations by providing analytical and experimental services in a way that is safe, efficient, and produces quality results in a timely manner so that R ampersand D personnel can provide quality technical data and operations personnel can efficiently operate waste treatment facilities. The modules are sample receiving, chromatography I, chromatography II, wet chemistry and carbon, sample preparation, and spectroscopy

Analytical solutions of the electrostatically actuated curled beam problem

KAUST Repository

Younis, Mohammad I.

2014-01-01

This works presents analytical expressions of the electrostatically actuated initially deformed cantilever beam problem. The formulation is based on the continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We

Slow Growth and Optimal Approximation of Pseudoanalytic Functions on the Disk

Directory of Open Access Journals (Sweden)

Devendra Kumar

2013-07-01

Full Text Available Pseudoanalytic functions (PAF are constructed as complex combination of real-valued analytic solutions to the Stokes-Betrami System. These solutions include the generalized biaxisymmetric potentials. McCoy [10] considered the approximation of pseudoanalytic functions on the disk. Kumar et al. [9] studied the generalized order and generalized type of PAF in terms of the Fourier coefficients occurring in its local expansion and optimal approximation errors in Bernstein sense on the disk. The aim of this paper is to improve the results of McCoy [10] and Kumar et al. [9]. Our results apply satisfactorily for slow growth.

A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices

Science.gov (United States)

AlQurashi, Ahmed; Selvakumar, C. R.

2018-06-01

There had been tremendous growth in the field of Integrated circuits (ICs) in the past fifty years. Scaling laws mandated both lateral and vertical dimensions to be reduced and a steady increase in doping densities. Most of the modern semiconductor devices have invariably heavily doped regions where Fermi-Dirac Integrals are required. Several attempts have been devoted to developing analytical approximations for Fermi-Dirac Integrals since numerical computations of Fermi-Dirac Integrals are difficult to use in semiconductor devices, although there are several highly accurate tabulated functions available. Most of these analytical expressions are not sufficiently suitable to be employed in semiconductor device applications due to their poor accuracy, the requirement of complicated calculations, and difficulties in differentiating and integrating. A new approximation has been developed for the Fermi-Dirac integrals of the order 1/2 by using Prony's method and discussed in this paper. The approximation is accurate enough (Mean Absolute Error (MAE) = 0.38%) and easy enough to be used in semiconductor device equations. The new approximation of Fermi-Dirac Integrals is applied to a more generalized Einstein Relation which is an important relation in semiconductor devices.

Diversity comparison of Pareto front approximations in many-objective optimization.

Science.gov (United States)

Li, Miqing; Yang, Shengxiang; Liu, Xiaohui

2014-12-01

Diversity assessment of Pareto front approximations is an important issue in the stochastic multiobjective optimization community. Most of the diversity indicators in the literature were designed to work for any number of objectives of Pareto front approximations in principle, but in practice many of these indicators are infeasible or not workable when the number of objectives is large. In this paper, we propose a diversity comparison indicator (DCI) to assess the diversity of Pareto front approximations in many-objective optimization. DCI evaluates relative quality of different Pareto front approximations rather than provides an absolute measure of distribution for a single approximation. In DCI, all the concerned approximations are put into a grid environment so that there are some hyperboxes containing one or more solutions. The proposed indicator only considers the contribution of different approximations to nonempty hyperboxes. Therefore, the computational cost does not increase exponentially with the number of objectives. In fact, the implementation of DCI is of quadratic time complexity, which is fully independent of the number of divisions used in grid. Systematic experiments are conducted using three groups of artificial Pareto front approximations and seven groups of real Pareto front approximations with different numbers of objectives to verify the effectiveness of DCI. Moreover, a comparison with two diversity indicators used widely in many-objective optimization is made analytically and empirically. Finally, a parametric investigation reveals interesting insights of the division number in grid and also offers some suggested settings to the users with different preferences.

Approximate effective nonlinear coefficient of second-harmonic generation in KTiOPO(4).

Science.gov (United States)

Asaumi, K

1993-10-20

A simplified approximate expression for the effective nonlinear coefficient of type-II second-harmonicgeneration in KTiOPO(4) was obtained by observing that the difference between the refractive indices n(x) and n(y) is 1 order of magnitude smaller than the difference between n(z) and n(y) (or n(x)). The agreement of this approximate equation with the true definition is good, with a maximum discrepancy of 4%.

Hybrid diffusion and two-flux approximation for multilayered tissue light propagation modeling

Science.gov (United States)

Yudovsky, Dmitry; Durkin, Anthony J.

2011-07-01

Accurate and rapid estimation of fluence, reflectance, and absorbance in multilayered biological media has been essential in many biophotonics applications that aim to diagnose, cure, or model in vivo tissue. The radiative transfer equation (RTE) rigorously models light transfer in absorbing and scattering media. However, analytical solutions to the RTE are limited even in simple homogeneous or plane media. Monte Carlo simulation has been used extensively to solve the RTE. However, Monte Carlo simulation is computationally intensive and may not be practical for applications that demand real-time results. Instead, the diffusion approximation has been shown to provide accurate estimates of light transport in strongly scattering tissue. The diffusion approximation is a greatly simplified model and produces analytical solutions for the reflectance and absorbance in tissue. However, the diffusion approximation breaks down if tissue is strongly absorbing, which is common in the visible part of the spectrum or in applications that involve darkly pigmented skin and/or high local volumes of blood such as port-wine stain therapy or reconstructive flap monitoring. In these cases, a model of light transfer that can accommodate both strongly and weakly absorbing regimes is required. Here we present a model of light transfer through layered biological media that represents skin with two strongly scattering and one strongly absorbing layer.

The Bogolubov Representation of the Polaron Model and Its Completely Integrable RPA-Approximation

International Nuclear Information System (INIS)

Bogolubov, Nikolai N. Jr.; Prykarpatsky, Yarema A.; Ghazaryan, Anna A.

2009-12-01

The polaron model in ionic crystal is studied in the N. Bogolubov representation using a special RPA-approximation. A new exactly solvable approximated polaron model is derived and described in detail. Its free energy at finite temperature is calculated analytically. The polaron free energy in the constant magnetic field at finite temperature is also discussed. Based on the structure of the N. Bogolubov unitary transformed polaron Hamiltonian a very important new result is stated: the full polaron model is exactly solvable. (author)

Analytical Propagation of Uncertainty in Life Cycle Assessment Using Matrix Formulation

DEFF Research Database (Denmark)

Imbeault-Tétreault, Hugues; Jolliet, Olivier; Deschênes, Louise

2013-01-01

with Monte Carlo results. The sensitivity and contribution of input parameters to output uncertainty were also analytically calculated. This article outlines an uncertainty analysis of the comparison between two case study scenarios. We conclude that the analytical method provides a good approximation...... on uncertainty calculation. This article shows the importance of the analytical method in uncertainty calculation, which could lead to a more complete uncertainty analysis in LCA practice....... uncertainty assessment is not a regular step in LCA. An analytical approach based on Taylor series expansion constitutes an effective means to overcome the drawbacks of the Monte Carlo method. This project aimed to test the approach on a real case study, and the resulting analytical uncertainty was compared...

Analytic integration of real-virtual counterterms in NNLO jet cross sections II

Energy Technology Data Exchange (ETDEWEB)

Bolzoni, Paolo; Moch, Sven-Olaf [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Somogyi, Gabor [Zurich Univ. (Switzerland). Inst. fuer Theoretische Physik; Trocsanyi, Zoltan [Debrecen Univ. (Hungary); Hungarian Academy of Sciences, Debrecen (Hungary). Inst. of Nuclear Research

2009-05-15

We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in 4-2{epsilon} dimensions to obtain the coefficients of their Laurent expansions around {epsilon}=0. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in {epsilon} both numerically and analytically by complex integration over the Mellin-Barnes contours. (orig.)

Analytic integration of real-virtual counterterms in NNLO jet cross sections II

International Nuclear Information System (INIS)

Bolzoni, Paolo; Moch, Sven-Olaf; Somogyi, Gabor; Trocsanyi, Zoltan

2009-01-01

We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in 4 - 2ε dimensions to obtain the coefficients of their Laurent expansions around ε = 0. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in ε both numerically and analytically by complex integration over the Mellin-Barnes contours.

Analytic integration of real-virtual counterterms in NNLO jet cross sections II

Science.gov (United States)

Bolzoni, Paolo; Moch, Sven-Olaf; Somogyi, Gábor; Trócsányi, Zoltán

2009-08-01

We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in 4 - 2epsilon dimensions to obtain the coefficients of their Laurent expansions around epsilon = 0. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in epsilon both numerically and analytically by complex integration over the Mellin-Barnes contours.

Analytic integration of real-virtual counterterms in NNLO jet cross sections II

International Nuclear Information System (INIS)

Bolzoni, Paolo; Moch, Sven-Olaf; Somogyi, Gabor; Trocsanyi, Zoltan; Hungarian Academy of Sciences, Debrecen

2009-05-01

We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in 4-2ε dimensions to obtain the coefficients of their Laurent expansions around ε=0. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in ε both numerically and analytically by complex integration over the Mellin-Barnes contours. (orig.)

Assessment of analytical techniques for characterization of crystalline clopidogrel forms in patent applications

Directory of Open Access Journals (Sweden)

Luiz Marcelo Lira

2014-04-01

Full Text Available The aim of this study was to evaluate two important aspects of patent applications of crystalline forms of drugs: (i the physicochemical characterization of the crystalline forms; and (ii the procedure for preparing crystals of the blockbuster drug clopidogrel. To this end, searches were conducted using online patent databases. The results showed that: (i the majority of patent applications for clopidogrel crystalline forms failed to comply with proposed Brazilian Patent Office guidelines. This was primarily due to insufficient number of analytical techniques evaluating the crystalline phase. In addition, some patent applications lacked assessment of chemical/crystallography purity; (ii use of more than two analytical techniques is important; and (iii the crystallization procedure for clopidogrel bisulfate form II were irreproducible based on the procedure given in the patent application.

Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.

Science.gov (United States)

Liu, Haofei; Sun, Wei

2017-08-01

Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

Bilinear reduced order approximate model of parabolic distributed solar collectors

KAUST Repository

Elmetennani, Shahrazed

2015-07-01

This paper proposes a novel, low dimensional and accurate approximate model for the distributed parabolic solar collector, by means of a modified gaussian interpolation along the spatial domain. The proposed reduced model, taking the form of a low dimensional bilinear state representation, enables the reproduction of the heat transfer dynamics along the collector tube for system analysis. Moreover, presented as a reduced order bilinear state space model, the well established control theory for this class of systems can be applied. The approximation efficiency has been proven by several simulation tests, which have been performed considering parameters of the Acurex field with real external working conditions. Model accuracy has been evaluated by comparison to the analytical solution of the hyperbolic distributed model and its semi discretized approximation highlighting the benefits of using the proposed numerical scheme. Furthermore, model sensitivity to the different parameters of the gaussian interpolation has been studied.

Experimental and analytical evaluation of preheating temperature during multipass repair welding

Directory of Open Access Journals (Sweden)

Sedmak Aleksandar S.

2017-01-01

Full Text Available Experimental measurement and analytical calculation of preheating, i. e. interpass temperature during multi-pass repair welding has been presented. Analytical calculation is based on heat transfer analysis, whereas measurements have been performed by thermovision camera. Repair welding was performed on crane wheels in the Steelworks Smederevo. Comparison of results indicated that analytical calculation is good enough as the first approximation, but it needs further elaboration, e. g. taking into account the radiation component of heat dissipation and/or temperature dependence of material thermomechanical properties.

Analytical electromagnetic calculations for practical superconductors

International Nuclear Information System (INIS)

Tominaka, T

2008-01-01

The current distributions of twisted long filamentary composites are studied during the current sweep and under the transverse and longitudinal external field, using the inductance matrix among superconducting helical filaments and the inductive voltage between filaments and the external coil in the circuit equation. The self- and mutual inductances of helical conductors with a uniform helical current density are approximately calculated from the analytical expressions of long helical thin conductors. In addition, the magnetic field and the vector potential distributions of a twisted superconducting composite are also obtained by the numerical integral calculation over the cross section of the analytical expressions for the magnetic field and vector potential due to an infinitely long helical conductor

Workshop on Analytical Methods in Statistics

CERN Document Server

Jurečková, Jana; Maciak, Matúš; Pešta, Michal

2017-01-01

This volume collects authoritative contributions on analytical methods and mathematical statistics. The methods presented include resampling techniques; the minimization of divergence; estimation theory and regression, eventually under shape or other constraints or long memory; and iterative approximations when the optimal solution is difficult to achieve. It also investigates probability distributions with respect to their stability, heavy-tailness, Fisher information and other aspects, both asymptotically and non-asymptotically. The book not only presents the latest mathematical and statistical methods and their extensions, but also offers solutions to real-world problems including option pricing. The selected, peer-reviewed contributions were originally presented at the workshop on Analytical Methods in Statistics, AMISTAT 2015, held in Prague, Czech Republic, November 10-13, 2015.

Synthesis and studies on Cu(II), Co(II), Ni(II) complexes of Knoevenagel β-diketone ligands

Science.gov (United States)

Sumathi, S.; Tharmaraj, P.; Sheela, C. D.; Anitha, C.

2012-11-01

Transition metal complexes of various acetylacetone based ligands of the type ML [where M = Cu(II), Ni(II), Co(II); L = 3-(aryl)-pentane-2,4-dione] have been synthesized. The structural features have been derived from their elemental analysis, magnetic susceptibility, molar conductance, IR, UV-Vis, 1H NMR, Mass and ESR spectral studies. Conductivity measurements reveal that all the complexes are non-electrolytic in nature. Spectroscopic and other analytical data of the complexes suggest octahedral geometry for other metal(II) complexes. The redox behavior of the copper(II) complexes have been studied by cyclic voltammetry. The free ligands and their metal complexes have been screened for their in vitro biological activities against the bacteria Pseudomonas aeruginosa, Escherichia coli and Staphylococcus aureus as well as the fungus Candida albicans by well diffusion method. The zone of inhibition value indicates that the most of the metal(II) complexes are found to possess increased activities compared to those of the free ligands. All synthesized compounds may serve as potential photoactive materials as indicated from their characteristic fluorescence properties. The second harmonic generation (SHG) efficiency of the ligands (L1-L3) was found to be considerable effect than that of urea and KDP (potassium dihydrogen phosphate).

An analytical method for neutron thermalization calculations in heterogenous reactors

Energy Technology Data Exchange (ETDEWEB)

Pop-Jordanov, J [Boris Kidric Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1965-07-01

It is well known that the use of the diffusion approximation for stuapproximation in absorbing media has been avoided, but the treatment remained analytical, thus simplifying practical calculations.

An analytical method for neutron thermalization calculations in heterogenous reactors

International Nuclear Information System (INIS)

Pop-Jordanov, J.

1965-01-01

It is well known that the use of the diffusion approximation for studying neutron thermalization in heterogeneous reactors may result in considerable errors. On the other hand, more exact numerical methods are rather laborious and require the use of large digital computers. In this paper, the use of the diffusion approximation in absorbing media has been avoided, but the treatment remained analytical, thus simplifying practical calculations

Solvent effects in time-dependent self-consistent field methods. II. Variational formulations and analytical gradients

International Nuclear Information System (INIS)

Bjorgaard, J. A.; Velizhanin, K. A.; Tretiak, S.

2015-01-01

This study describes variational energy expressions and analytical excited state energy gradients for time-dependent self-consistent field methods with polarizable solvent effects. Linear response, vertical excitation, and state-specific solventmodels are examined. Enforcing a variational ground stateenergy expression in the state-specific model is found to reduce it to the vertical excitation model. Variational excited state energy expressions are then provided for the linear response and vertical excitation models and analytical gradients are formulated. Using semiempiricalmodel chemistry, the variational expressions are verified by numerical and analytical differentiation with respect to a static external electric field. Lastly, analytical gradients are further tested by performing microcanonical excited state molecular dynamics with p-nitroaniline

Laplace transform homotopy perturbation method for the approximation of variational problems.

Science.gov (United States)

Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R

2016-01-01

This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.

Analytic characterization of linear accelerator radiosurgery dose distributions for fast optimization

International Nuclear Information System (INIS)

Meeks, S.L.; Buatti, J.M.; Eyster, B.; Kendrick, L.A.

1999-01-01

Linear accelerator (linac) radiosurgery utilizes non-coplanar arc therapy delivered through circular collimators. Generally, spherically symmetric arc sets are used, resulting in nominally spherical dose distributions. Various treatment planning parameters may be manipulated to provide dose conformation to irregular lesions. Iterative manipulation of these variables can be a difficult and time-consuming task, because (a) understanding the effect of these parameters is complicated and (b) three-dimensional (3D) dose calculations are computationally expensive. This manipulation can be simplified, however, because the prescription isodose surface for all single isocentre distributions can be approximated by conic sections. In this study, the effects of treatment planning parameter manipulation on the dimensions of the treatment isodose surface were determined empirically. These dimensions were then fitted to analytic functions, assuming that the dose distributions were characterized as conic sections. These analytic functions allowed real-time approximation of the 3D isodose surface. Iterative plan optimization, either manual or automated, is achieved more efficiently using this real time approximation of the dose matrix. Subsequent to iterative plan optimization, the analytic function is related back to the appropriate plan parameters, and the dose distribution is determined using conventional dosimetry calculations. This provides a pseudo-inverse approach to radiosurgery optimization, based solely on geometric considerations. (author)

About APPLE II Operation

International Nuclear Information System (INIS)

Schmidt, T.; Zimoch, D.

2007-01-01

The operation of an APPLE II based undulator beamline with all its polarization states (linear horizontal and vertical, circular and elliptical, and continous variation of the linear vector) requires an effective description allowing an automated calculation of gap and shift parameter as function of energy and operation mode. The extension of the linear polarization range from 0 to 180 deg. requires 4 shiftable magnet arrrays, permitting use of the APU (adjustable phase undulator) concept. Studies for a pure fixed gap APPLE II for the SLS revealed surprising symmetries between circular and linear polarization modes allowing for simplified operation. A semi-analytical model covering all types of APPLE II and its implementation will be presented

Analytical construction of peaked solutions for the nonlinear ...

African Journals Online (AJOL)

These results demonstrate the existence of peaked pulses propagating through a pair plasma. The algebraic decay rate of the pulses are determined analytically, as well. The method discussed here can be applied to approximate solutions to similar nonlinear partial differential equations of nonlinear Schrödinger type.

Synthesis, spectral, thermal and antimicrobial studies on cobalt(II), nickel(II), copper(II), zinc(II) and palladium(II) complexes containing thiosemicarbazone ligand

Science.gov (United States)

El-Sawaf, Ayman K.; El-Essawy, Farag; Nassar, Amal A.; El-Samanody, El-Sayed A.

2018-04-01

The coordination characteristic of new N4-morpholinyl isatin-3-thiosemicarbazone (HL) towards Co(II), Ni(II), Cu(II), Zn(II) and Pd(II) has been studies. The structures of the complexes were described by elemental analyses, molar conductivity, magnetic, thermal and spectral (IR, UV-Vis, 1H and 13C NMR and ESR) studies. On the basis of analytical and spectral studies the ligand behaves as monobasic tridentate ONS donor forming two five membered rings towards cobalt, copper and palladium and afforded complexes of the kind [M(L)X], (Mdbnd Co, Cu or Pd; Xdbnd Cl, Br or OAc). Whereas the ligand bound to NiCl2 as neutral tridentate ONS donor and with ZnCl2 as neutral bidentate NS donor. The newly synthesized thiosemicarbazone ligand and some of its complexes were examined for antimicrobial activity against 2 gram negative bacterial strains (Escherichia coli Pseudomonas and aeruginosa), 2 gram positive bacterial strains (Streptococcus pneumoniae and Staphylococcus aureus)} and two Pathogenic fungi (Aspergillus fumigatus and Candida albicans). All metal complexes possess higher antimicrobial activity comparing with the free thiosemicarbazone ligand. The high potent activities of the complexes may arise from the coordination and chelation, which tends to make metal complexes act as more controlling and potent antimicrobial agents, thus hindering the growing of the microorganisms. The antimicrobial results also show that copper bromide complex is better antimicrobial agent as compared to the Schiff base and its metal complexes.

Radiative heat transfer in honeycomb structures-New simple analytical and numerical approaches

International Nuclear Information System (INIS)

Baillis, D; Coquard, R; Randrianalisoa, J

2012-01-01

Porous Honeycomb Structures present the interest of combining, at the same time, high thermal insulating properties, low density and sufficient mechanical resistance. However, their thermal properties remain relatively unexplored. The aim of this study is the modelling of the combined heat transfer and especially radiative heat transfer through this type of anisotropic porous material. The equivalent radiative properties of the material are determined using ray-tracing procedures inside the honeycomb porous structure. From computational ray-tracing results, simple new analytical relations have been deduced. These useful analytical relations permit to determine radiative properties such as extinction, absorption and scattering coefficients and phase function functions of cell dimensions and optical properties of cell walls. The radiative properties of honeycomb material strongly depend on the direction of propagation. From the radiative properties computed, we have estimated the radiative heat flux passing through slabs of honeycomb core materials submitted to a 1-D temperature difference between a hot and a cold plate. We have compared numerical results obtained from Discrete Ordinate Method with analytical results obtained from Rosseland-Deissler approximation. This approximation is usually used in the case of isotropic materials. We have extended it to anisotropic honeycomb materials. Indeed a mean over incident directions of Rosseland extinction coefficient is proposed. Results tend to show that Rosseland-Deissler extended approximation can be used as a first approximation. Deviation on radiative conductivity obtained from Rosseland-Deissler approximation and from the Discrete Ordinated Method are lower than 6.7% for all the cases studied.

Inverse periodic problem for the discrete approximation of the Schroedinger nonlinear equation

International Nuclear Information System (INIS)

Bogolyubov, N.N.; Prikarpatskij, A.K.; AN Ukrainskoj SSR, Lvov. Inst. Prikladnykh Problem Mekhaniki i Matematiki)

1982-01-01

The problem of numerical solution of the Schroedinger nonlinear equation (1) iPSIsub(t) = PSIsub(xx)+-2(PSI)sup(2)PSI. The numerical solution of nonlinear differential equation supposes its discrete approximation is required for the realization of the computer calculation process. Tor the equation (1) there exists the following discrete approximation by variable x(2) iPSIsub(n, t) = (PSIsub(n+1)-2PSIsub(n)+PSIsub(n-1))/(Δx)sup(2)+-(PSIsub(n))sup(2)(PSIsub(n+1)+PSIsub(n-1)), n=0, +-1, +-2... where PSIsub(n)(+) is the corresponding value of PSI(x, t) function in the node and divisions with the equilibrium step Δx. The main problem is obtaining analytically exact solutions of the equations (2). The analysis of the equation system (2) is performed on the base of the discrete analogue of the periodic variant of the inverse scattering problem method developed with the aid of nonlinear equations of the Korteweg-de Vries type. Obtained in explicit form are analytical solutions of the equations system (2). The solutions are expressed through the Riemann THETA-function [ru

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

International Nuclear Information System (INIS)

Peralta, J.; López-Valverde, M. A.; Imamura, T.; Read, P. L.; Luz, D.; Piccialli, A.

2014-01-01

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 background 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

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

Energy Technology Data Exchange (ETDEWEB)

Peralta, J.; López-Valverde, M. A. [Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Imamura, T. [Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan); Read, P. L. [Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford (United Kingdom); Luz, D. [Centro de Astronomia e Astrofísica da Universidade de Lisboa (CAAUL), Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa (Portugal); Piccialli, A., E-mail: peralta@iaa.es [LATMOS, UVSQ, 11 bd dAlembert, 78280 Guyancourt (France)

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 background 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.

Transport of optical excitations on dendrimers in the continuum approximation

International Nuclear Information System (INIS)

Vlaming, S.M.; Heijs, D.J.; Knoester, J.

2005-01-01

We study the incoherent transport of optical excitations created at the rim of a dendritic molecule to a trap occurring at the core. The corresponding discrete random walk is treated in a continuum approximation, resulting in a diffusion-like process which admits semi-analytical solutions. The thus obtained arrival time distribution for the excitation at the trap is compared with the one for the original, discrete problem. In the case of an inward bias or even a weak outward one, the agreement is very good and the continuum approximation provides a good alternative description of the energy transfer process, even for small dendrimers. In the case of a strong outward bias, the mean trapping time, which sets the time scale for the entire distribution, depends exponentially on the number of generations in both approaches, but with a different base. The failure of the continuum approximation for this case is explained from the peaked behavior of the excitation density near the rim

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

Science.gov (United States)

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.

Analytical effective tensor for flow-through composites

Science.gov (United States)

Sviercoski, Rosangela De Fatima [Los Alamos, NM

2012-06-19

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

A SIMPLE ANALYTICAL METHOD TO DETERMINE SOLAR ENERGETIC PARTICLES' MEAN FREE PATH

International Nuclear Information System (INIS)

He, H.-Q.; Qin, G.

2011-01-01

To obtain the mean free path of solar energetic particles (SEPs) for a solar event, one usually has to fit time profiles of both flux and anisotropy from spacecraft observations to numerical simulations of SEPs' transport processes. This method can be called a simulation method. But a reasonably good fitting needs a lot of simulations, which demand a large amount of calculation resources. Sometimes, it is necessary to find an easy way to obtain the mean free path of SEPs quickly, for example, in space weather practice. Recently, Shalchi et al. provided an approximate analytical formula of SEPs' anisotropy time profile as a function of particles' mean free path for impulsive events. In this paper, we determine SEPs' mean free path by fitting the anisotropy time profiles from Shalchi et al.'s analytical formula to spacecraft observations. This new method can be called an analytical method. In addition, we obtain SEPs' mean free path with the traditional simulation methods. Finally, we compare the mean free path obtained with the simulation method to that of the analytical method to show that the analytical method, with some minor modifications, can give us a good, quick approximation of SEPs' mean free path for impulsive events.

Analytical mechanics for relativity and quantum mechanics

CERN Document Server

Johns, Oliver Davis

2011-01-01

Analytical Mechanics for Relativity and Quantum Mechanics is an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the introductory graduate level. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum...

Spin-glass in low dimension and the Midgal Kadanoff approximation

International Nuclear Information System (INIS)

Curado, E.M.F.

1987-01-01

We study the spin glass problem within the Migdal Kadanoff approximation of the hyper cubic lattices. Using various technics, both analytical and numerical, we perform the real space renormalization of the problem. We find that a Spin Glass transition occurs in 3 dimensions while it does not occur in two dimensions. The specific heat critical exponent for the transition is found to be large and negative in agreement with the experimental results. (author) [pt

Analytic plane wave solutions for the quaternionic potential step

International Nuclear Information System (INIS)

De Leo, Stefano; Ducati, Gisele C.; Madureira, Tiago M.

2006-01-01

By using the recent mathematical tools developed in quaternionic differential operator theory, we solve the Schroedinger equation in the presence of a quaternionic step potential. The analytic solution for the stationary states allows one to explicitly show the qualitative and quantitative differences between this quaternionic quantum dynamical system and its complex counterpart. A brief discussion on reflected and transmitted times, performed by using the stationary phase method, and its implication on the experimental evidence for deviations of standard quantum mechanics is also presented. The analytic solution given in this paper represents a fundamental mathematical tool to find an analytic approximation to the quaternionic barrier problem (up to now solved by numerical method)

Analytical theory of noncollinear amorphous metallic magnetism

International Nuclear Information System (INIS)

Kakehashi, Y.; Uchida, T.

2001-01-01

Analytical theory of noncollinear magnetism in amorphous metals is proposed on the basis of the Gaussian model for the distribution of the interatomic distance and the saddle-point approximation. The theory removes the numerical difficulty in the previous theory based on the Monte-Carlo sampling method, and reasonably describes the magnetic properties of amorphous transition metals

Preliminary feasibility study on storage of radioactive wastes in Columbia River basalts. Volume II

Energy Technology Data Exchange (ETDEWEB)

,

1976-11-01

Volume II comprises four appendices: analytical data and sample locations for basalt flow type localities; Analytical data and sample locations for measured field sections in Yakima basalts; core hole lithology and analytical data; and geophysical logs. (LK)

Higher order saddlepoint approximations in the Vasicek portfolio credit loss model

NARCIS (Netherlands)

Huang, X.; Oosterlee, C.W.; van der Weide, J.A.M.

2006-01-01

This paper utilizes the saddlepoint approximation as an efficient tool to estimate the portfolio credit loss distribution in the Vasicek model. Value at Risk (VaR), the risk measure chosen in the Basel II Accord for the evaluation of capital requirement, can then be found by inverting the loss

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

Energy Technology Data Exchange (ETDEWEB)

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)

2017-06-15

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.

An extreme Fe II emitter the narrow line quasar PHL 1092

CERN Document Server

Bergeron, J

1980-01-01

A search for Fe II emission in a sample of radio-quiet quasars has revealed the outstanding properties of PHL 1092. Intense Fe II lines dominate the entire spectrum, and the Fe II UV multiplets are nearly as strong as the optical ones. In contrast the extreme weakness of the Balmer and Mg II lines is striking. For the first time, Fe I lines are identified in an extra-galactic object. The lines are narrow, with a FWHM of 1300 km s/sup -1/. The presence of Fe II UV lines and Fe I lines from the ground state requires moderate column densities. However Fe/sup 0/ can exist only in a region completely shielded from the UV continuum. The weakness of Mg II and H beta relative to Fe II lines is best explained by their thermalization. The emitting region is of high electron density n/sub e/ approximately=10/sup 12/ cm/sup -3/, low temperature T approximately=10000K, and has an optical depth in the Fe II UV lines tau /sub UV/ approximately=10/sup 3/-10/sup 4/. It is speculated that for higher densities all the lines wou...

The analytic renormalization group

Directory of Open Access Journals (Sweden)

Frank Ferrari

2016-08-01

Full Text Available Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k∈Z, associated with the Matsubara frequencies νk=2πk/β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct “Analytic Renormalization Group” linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk|<μ (with the possible exception of the zero mode G0, together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk|≥μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.

Analytical treatment of the runaway-effect

International Nuclear Information System (INIS)

Kaeppeler, H.J.

1980-09-01

In the analytical treatment of the runaway-effect there appear the integrals Isub(m)(α). For m = 1, 2 and 3, series expansions for these integrals can be found in the literature. Furthermore, asymptotic solutions for Isub(m)(α) are known. It is shown here that the solutions for Isub(m)(α) can be approximated by the modified Bessel Function Ksub(n)(αsup(ν)) in such a way that for α → 0 the exact limiting value for Isub(m)(α) follows and that for α → infinite essentially the known asymptotic solutions for Isub(m)(α) follow. The maximum error for this approximation in the order of percent is considered justifiable for the application considered. (orig.)

Rule-Based Analytic Asset Management for Space Exploration Systems (RAMSES), Phase II

Data.gov (United States)

National Aeronautics and Space Administration — Payload Systems Inc. (PSI) and the Massachusetts Institute of Technology (MIT) were selected to jointly develop the Rule-based Analytic Asset Management for Space...

Evaluation of Analytical Modeling Functions for the Phonation Onset Process

Directory of Open Access Journals (Sweden)

Simon Petermann

2016-01-01

Full Text Available 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.

Developments in analytical instrumentation

Science.gov (United States)

Petrie, G.

The situation regarding photogrammetric instrumentation has changed quite dramatically over the last 2 or 3 years with the withdrawal of most analogue stereo-plotting machines from the market place and their replacement by analytically based instrumentation. While there have been few new developments in the field of comparators, there has been an explosive development in the area of small, relatively inexpensive analytical stereo-plotters based on the use of microcomputers. In particular, a number of new instruments have been introduced by manufacturers who mostly have not been associated previously with photogrammetry. Several innovative concepts have been introduced in these small but capable instruments, many of which are aimed at specialised applications, e.g. in close-range photogrammetry (using small-format cameras); for thematic mapping (by organisations engaged in environmental monitoring or resources exploitation); for map revision, etc. Another innovative and possibly significant development has been the production of conversion kits to convert suitable analogue stereo-plotting machines such as the Topocart, PG-2 and B-8 into fully fledged analytical plotters. The larger and more sophisticated analytical stereo-plotters are mostly being produced by the traditional mainstream photogrammetric systems suppliers with several new instruments and developments being introduced at the top end of the market. These include the use of enlarged photo stages to handle images up to 25 × 50 cm format; the complete integration of graphics workstations into the analytical plotter design; the introduction of graphics superimposition and stereo-superimposition; the addition of correlators for the automatic measurement of height, etc. The software associated with this new analytical instrumentation is now undergoing extensive re-development with the need to supply photogrammetric data as input to the more sophisticated G.I.S. systems now being installed by clients, instead

Accuracy of the Bethe approximation for hyperparameter estimation in probabilistic image processing

International Nuclear Information System (INIS)

Tanaka, Kazuyuki; Shouno, Hayaru; Okada, Masato; Titterington, D M

2004-01-01

We investigate the accuracy of statistical-mechanical approximations for the estimation of hyperparameters from observable data in probabilistic image processing, which is based on Bayesian statistics and maximum likelihood estimation. Hyperparameters in statistical science correspond to interactions or external fields in the statistical-mechanics context. In this paper, hyperparameters in the probabilistic model are determined so as to maximize a marginal likelihood. A practical algorithm is described for grey-level image restoration based on a Gaussian graphical model and the Bethe approximation. The algorithm corresponds to loopy belief propagation in artificial intelligence. We examine the accuracy of hyperparameter estimation when we use the Bethe approximation. It is well known that a practical algorithm for probabilistic image processing can be prescribed analytically when a Gaussian graphical model is adopted as a prior probabilistic model in Bayes' formula. We are therefore able to compare, in a numerical study, results obtained through mean-field-type approximations with those based on exact calculation

Calculation of the atomic states energies in the Thomas - Fermi approximation

Directory of Open Access Journals (Sweden)

S. N. Fedotkin

2017-12-01

Full Text Available A method for calculating the energies of levels for many-electron neutral atoms is proposed. In this case, in addition to the Coulomb field of the nucleus, an important contribution to the energy is connected with the interaction between the electrons. This interaction is taken into account approximately by perturbation theory in the framework of the Thomas - Fermi statistical model. Using the Taytz approximation for the mean potential the analytical expressions for the energies of s-states are obtained with principal quantum numbers n = 1, 2, 3, 4. The energies are calculated for the nuclear charges in the interval 1 < Z ≤ 100. A good agreement with the experimental values of the energies was obtained.

Approximation of the Doppler broadening function by Frobenius method; Aproximacao da funcao de alargamento doppler atraves do metodo de Frobenius

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P. [Centro Federal de Educacao Tecnologica de Quimica de Nilopolis/RJ (CEFET), RJ (Brazil)]. E-mail: dpalma@cefeteq.br; Martinez, Aquilino S.; Silva, Fernando C. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]. E-mail: aquilino@lmp.ufrj.br; fernando@lmn.con.ufrj.br

2005-07-01

An analytical approximation of the Doppler broadening function {psi}(x,{xi}) is proposed. This approximation is based on the solution of the differential equation for {psi}(x,{xi}) using the methods of Frobenius and the parameters variation. The analytical form derived for {psi}(x,{xi}) in terms of elementary functions is very simple and precise. It can be useful for applications related to the treatment of nuclear resonances mainly for the calculations of multigroup parameters and self-protection factors of the resonances, being the last used to correct microscopic cross-sections measurements by the activation technique. (author)

Multiplier ideal sheaves and analytic methods in algebraic geometry

International Nuclear Information System (INIS)

Demailly, J.-P.

2001-01-01

Our main purpose here is to describe a few analytic tools which are useful to study questions such as linear series and vanishing theorems for algebraic vector bundles. One of the early successes of analytic methods in this context is Kodaira's use of the Bochner technique in relation with the theory of harmonic forms, during the decade 1950-60.The idea is to represent cohomology classes by harmonic forms and to prove vanishing theorems by means of suitable a priori curvature estimates. We pursue the study of L2 estimates, in relation with the Nullstellenstatz and with the extension problem. We show how subadditivity can be used to derive an approximation theorem for (almost) plurisubharmonic functions: any such function can be approximated by a sequence of (almost) plurisubharmonic functions which are smooth outside an analytic set, and which define the same multiplier ideal sheaves. From this, we derive a generalized version of the hard Lefschetz theorem for cohomology with values in a pseudo-effective line bundle; namely, the Lefschetz map is surjective when the cohomology groups are twisted by the relevant multiplier ideal sheaves. These notes are essentially written with the idea of serving as an analytic tool- box for algebraic geometers. Although efficient algebraic techniques exist, our feeling is that the analytic techniques are very flexible and offer a large variety of guidelines for more algebraic questions (including applications to number theory which are not discussed here). We made a special effort to use as little prerequisites and to be as self-contained as possible; hence the rather long preliminary sections dealing with basic facts of complex differential geometry

Multiplier ideal sheaves and analytic methods in algebraic geometry

Energy Technology Data Exchange (ETDEWEB)

Demailly, J -P [Universite de Grenoble I, Institut Fourier, Saint-Martin d' Heres (France)

2001-12-15

Our main purpose here is to describe a few analytic tools which are useful to study questions such as linear series and vanishing theorems for algebraic vector bundles. One of the early successes of analytic methods in this context is Kodaira's use of the Bochner technique in relation with the theory of harmonic forms, during the decade 1950-60.The idea is to represent cohomology classes by harmonic forms and to prove vanishing theorems by means of suitable a priori curvature estimates. We pursue the study of L2 estimates, in relation with the Nullstellenstatz and with the extension problem. We show how subadditivity can be used to derive an approximation theorem for (almost) plurisubharmonic functions: any such function can be approximated by a sequence of (almost) plurisubharmonic functions which are smooth outside an analytic set, and which define the same multiplier ideal sheaves. From this, we derive a generalized version of the hard Lefschetz theorem for cohomology with values in a pseudo-effective line bundle; namely, the Lefschetz map is surjective when the cohomology groups are twisted by the relevant multiplier ideal sheaves. These notes are essentially written with the idea of serving as an analytic tool- box for algebraic geometers. Although efficient algebraic techniques exist, our feeling is that the analytic techniques are very flexible and offer a large variety of guidelines for more algebraic questions (including applications to number theory which are not discussed here). We made a special effort to use as little prerequisites and to be as self-contained as possible; hence the rather long preliminary sections dealing with basic facts of complex differential geometry.

SU-E-T-135: Assessing the Clinical Impact of Approximations in Analytical Dose Calculations for Proton Therapy

Energy Technology Data Exchange (ETDEWEB)

Schuemann, J; Giantsoudi, D; Grassberger, C; Paganetti, H [Massachusetts General Hospital, Boston, MA (United States)

2015-06-15

Purpose: To estimate the clinical relevance of approximations made in analytical dose calculation methods (ADCs) used for treatment planning on tumor coverage and tumor control probability (TCP) in proton therapy. Methods: We compared dose distributions planned with ADC to delivered dose distributions (as determined by TOPAS Monte Carlo (MC) simulations). We investigated 10 patients per site for 5 treatment sites (head-and-neck, lung, breast, prostate, liver). We evaluated differences between the two dose distributions analyzing dosimetric indices based on the dose-volume-histograms, the γ-index and the TCP. The normal tissue complication probability (NTCP) was estimated for the bladder and anterior rectum for the prostate patients. Results: We find that the target doses are overestimated by the ADC by 1–2% on average for all patients considered. All dosimetric indices (the mean dose, D95, D50 and D02, the dose values covering 95%, 50% and 2% of the target volume, respectively) are predicted within 5% of the delivered dose. A γ-index with a 3%/3mm criteria had a passing rate for target volumes above 96% for all patients. The TCP predicted by the two algorithms was up to 2%, 2.5%, 6%, 6.5%, and 11% for liver and breast, prostate, head-and-neck and lung patients, respectively. Differences in NTCP for anterior-rectum and bladder for prostate patients were less than 3%. Conclusion: We show that ADC provide adequate dose distributions for most patients, however, they can Result in underdosage of the target by as much as 5%. The TCP was found to be up to 11% lower than predicted. Advanced dose-calculation methods like MC simulations may be necessary in proton therapy to ensure target coverage for heterogeneous patient geometries, in clinical trials comparing proton therapy to conventional radiotherapy to avoid biases due to systematic discrepancies in calculated dose distributions, and, if tighter range margins are considered. Fully funded by NIH grants.

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

Guo Jin-Li

2010-01-01

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. (general)

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

International Nuclear Information System (INIS)

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

2013-01-01

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. (paper)

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem

KAUST Repository

Younis, Mohammad I.

2014-08-17

We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data in the literature and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximations they are based on. In such cases, multi-mode reduced order models need to be utilized.

The big bang and inflation united by an analytic solution

International Nuclear Information System (INIS)

Bars, Itzhak; Chen, Shih-Hung

2011-01-01

Exact analytic solutions for a class of scalar-tensor gravity theories with a hyperbolic scalar potential are presented. Using an exact solution we have successfully constructed a model of inflation that produces the spectral index, the running of the spectral index, and the amplitude of scalar perturbations within the constraints given by the WMAP 7 years data. The model simultaneously describes the big bang and inflation connected by a specific time delay between them so that these two events are regarded as dependent on each other. In solving the Friedmann equations, we have utilized an essential Weyl symmetry of our theory in 3+1 dimensions which is a predicted remaining symmetry of 2T-physics field theory in 4+2 dimensions. This led to a new method of obtaining analytic solutions in the 1T field theory which could in principle be used to solve more complicated theories with more scalar fields. Some additional distinguishing properties of the solution includes the fact that there are early periods of time when the slow-roll approximation is not valid. Furthermore, the inflaton does not decrease monotonically with time; rather, it oscillates around the potential minimum while settling down, unlike the slow-roll approximation. While the model we used for illustration purposes is realistic in most respects, it lacks a mechanism for stopping inflation. The technique of obtaining analytic solutions opens a new window for studying inflation, and other applications, more precisely than using approximations.

Analytical and numerical investigation of double diffusion in thermally anisotropy multilayer porous medium

Energy Technology Data Exchange (ETDEWEB)

Bennacer, R. [Neuville sur Oise, LEEVAM 5 mail Gay Lussac, Cergy-Pontoise Cedex (France); Mohamad, A.A. [CEERE University of Calgary, Department of Mechanical and Manufacturing Engineering, Calgary, Alberta (Canada); Ganaoui, M.El [Faculte des Sciences et Techniques de Limoges, Limoges (France)

2005-02-01

Double-diffusive natural convection within a multilayer anisotropic porous medium is studied numerically and analytically. The domain composed of two horizontal porous layers is subjected to a uniform horizontal heat flux and a vertical mass flux, where only the lower one is thermally anisotropic. Darcy model with classical Boussinesq approximation is used in formulating the mathematical model. The effect of thermal anisotropy and the relative width of the two layers on the flow and transfers is illustrated with characterising the transitions from the diffusive to the convective solution. Results were well compared with respect to a developed analytical approach, based on a parallel flow approximation for thermally anisotropic multilayer media. (orig.)

Analytical phase diagrams for colloids and non-adsorbing polymer.

Science.gov (United States)

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

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

Directory of Open Access Journals (Sweden)

Lakshmi Narayana Suvarapu

2015-01-01

Full Text Available 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.

Intelligent control-II: review of fuzzy systems and theory of approximate reasoning

International Nuclear Information System (INIS)

Nagrial, M.H.

2004-01-01

Fuzzy systems are knowledge-based or rule-based systems. The heart of a fuzzy systems knowledge base consisting of the so-called fuzzy IF -THEN rules. This paper reviews various aspects of fuzzy IF-THEN rules. The theory of approximate reasoning, which provides a powerful framework for reasoning the imprecise and uncertain information, , is also reviewed. Additional properties of fuzzy systems are also discussed. (author)

Fowler's approximation for the surface tension and surface energy of Lennard-Jones fluids revisited

Energy Technology Data Exchange (ETDEWEB)

Mulero, A [Departamento de Fisica, Universidad de Extremadura, 06071-Badajoz (Spain); Galan, C [Departamento de Fisica, Universidad de Extremadura, 06071-Badajoz (Spain); Cuadros, F [Departamento de Fisica, Universidad de Extremadura, 06071-Badajoz (Spain)

2003-04-16

We present a detailed study of the validity of Fowler's approximation for calculating the surface tension and the surface energy of Lennard-Jones fluids. To do so, we consider three different explicit analytical expressions for the radial distribution function (RDF), including one proposed by our research group, together with very accurate expressions for the liquid and vapour densities, also proposed by our group. The calculation of the surface tension from the direct correlation function using both the Percus-Yevick and the hypernetted-chain approximations is also considered. Finally, our results are compared with those obtained by other authors by computer simulations or through relevant theoretical approximations. In particular, we consider the analytical expression proposed by Kalikmanov and Hofmans (1994 J. Phys.: Condens. Matter 6 2207-14) for the surface tension. Our results indicate that the values for the surface energy in Fowler's approximation obtained by other authors are adequate, and can be calculated from the RDF models. For the surface tension, however, the values considered as valid in previous works seem to be incorrect. The correct values can be obtained from our model for the RDF or from the Kalikmanov and Hofmans expression with suitable inputs.

Transport with Astra in TJ-II; Transporte con Astra en TJ-II

Energy Technology Data Exchange (ETDEWEB)

Lopez-Bruna, D; Castejon, F; Fontdecaba, J M

2004-07-01

This report describes the adaptation of the numerical transport shell ASTRA for performing plasma calculations in the TJ-II stellarator device. Firstly, an approximation to the TJ-II geometry is made and a simple transport model is shared with two other codes in order to compare these codes (PROCTR, PRETOR-Stellarator) with ASTRA as calculation tool for TJ-II plasmas are provided: interpretative and predictive transport. The first consists in estimating the transport coefficients from real experimental data, thes being taken from three TJ-II discharges. The predictive facet is illustrated using a model that is able to includes self-consistently thedynamics of transport barriers. The report includes this model, written in the ASTRA programming language, to illustrate the use of ASTRA. (Author) 26 refs.

Parametric investigation of fracture of EBR-II ducts

International Nuclear Information System (INIS)

Chopra, P.S.; Moustakakis, B.

1977-01-01

Results of preliminary static and dynamic finite element fracture mechanics analyses that were conducted to analytically simulate the dynamic fracture behavior of EBR-II ducts are presented. The loads considered are those that may arise because of rapid release of fission gases from a failed fuel element inside a duct, obtained from some previous tests and a recent analytical model. In spite of the motivation for the present work, the analytical procedures described may have a wider general application in the fail-safe design of structures

Hierarchical low-rank approximation for high dimensional approximation

KAUST Repository

Nouy, Anthony

2016-01-07

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

Hierarchical low-rank approximation for high dimensional approximation

KAUST Repository

Nouy, Anthony

2016-01-01

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

Synthesis, Spectral and Antimicrobial Studies of Some Co(II, Ni(II and Cu(II Complexes Containing 2-Thiophenecarboxaldehyde Moiety

Directory of Open Access Journals (Sweden)

A. P. Mishra

2012-01-01

Full Text Available Some new Schiff base metal complexes of Co(II, Ni(II and Cu(II derived from 3-chloro-4-fluoroaniline (HL1 and 4-fluoroaniline (HL2 with 2-thiophenecarboxaldehyde have been synthesized and characterized by elemental analysis, FT-IR, FAB-mass, molar conductance, electronic spectra, ESR and magnetic susceptibility. The complexes exhibit coordination number 4 or 6. The complexes are colored and stable in air. Analytical data revealed that all the complexes exhibited 1:2 (metal: ligand ratio. FAB-mass data show degradation pattern of the complexes. The Schiff base and metal complexes show a good activity against the bacteria; B. subtilis, E. coli and S. aureus and fungi A. niger, A. flavus and C. albicans. The antimicrobial results also indicate that the metal complexes are better antimicrobial agents as compared to the Schiff bases.

Analytical solutions for ozone generation by point to plane corona discharge

International Nuclear Information System (INIS)

Bestman, A.R.

1990-12-01

A recent mathematical model developed for ozone production is tackled analytically by asymptotic approximation. The results obtained are compared with existing numerical solutions. The comparison shows good agreement. (author). 3 refs, 1 fig

Renormalization of self-consistent approximation schemes at finite temperature. II. Applications to the sunset diagram

International Nuclear Information System (INIS)

Hees, Hendrik van; Knoll, Joern

2002-01-01

The theoretical concepts for the renormalization of self-consistent Dyson resummations, devised in the first paper of this series, are applied to first example cases of φ 4 theory. In addition to the tadpole (Hartree) approximation, as a novel part the numerical solutions are presented, which include the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or the two-particle irreducible effective action concept

Renormalization of self-consistent approximation schemes at finite temperature II: applications to the sunset diagram

International Nuclear Information System (INIS)

Hees, H. van; Knoll, J.

2001-01-01

The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the φ 4 -theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or 2PI effective action concept. (orig.)

Quantum approximate optimization algorithm for MaxCut: A fermionic view

Science.gov (United States)

Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang; Rieffel, Eleanor G.

2018-02-01

Farhi et al. recently proposed a class of quantum algorithms, the quantum approximate optimization algorithm (QAOA), for approximately solving combinatorial optimization problems (E. Farhi et al., arXiv:1411.4028; arXiv:1412.6062; arXiv:1602.07674). A level-p QAOA circuit consists of p steps; in each step a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2 p times for which these two Hamiltonians are applied are the parameters of the algorithm, which are to be optimized classically for the best performance. As p increases, parameter optimization becomes inefficient due to the curse of dimensionality. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here we analytically and numerically study parameter setting for the QAOA applied to MaxCut. For the level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MaxCut, the "ring of disagrees," or the one-dimensional antiferromagnetic ring, we provide an analysis for an arbitrarily high level. Using a fermionic representation, the evolution of the system under the QAOA translates into quantum control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of the QAOA for any p . It also greatly simplifies the numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional submanifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

Social Set Visualizer (SoSeVi) II

DEFF Research Database (Denmark)

Flesch, Benjamin; Vatrapu, Ravi

2016-01-01

This paper reports the second iteration of the Social Set Visualizer (SoSeVi), a set theoretical visual analytics dashboard of big social data. In order to further demonstrate its usefulness in large-scale visual analytics tasks of individual and collective behavior of actors in social networks......, the current iteration of the Social Set Visualizer (SoSeVi) in version II builds on recent advancements in visualizing set intersections. The development of the SoSeVi dashboard involved cutting-edge open source visual analytics libraries (D3.js) and creation of new visualizations such as of actor mobility...

Synthetic salt cake standards for analytical laboratory quality control

International Nuclear Information System (INIS)

Schilling, A.E.; Miller, A.G.

1980-01-01

The validation of analytical results in the characterization of Hanford Nuclear Defense Waste requires the preparation of synthetic waste for standard reference materials. Two independent synthetic salt cake standards have been prepared to monitor laboratory quality control for the chemical characterization of high-level salt cake and sludge waste in support of Rockwell Hanford Operations' High-Level Waste Management Program. Each synthetic salt cake standard contains 15 characterized chemical species and was subjected to an extensive verification/characterization program in two phases. Phase I consisted of an initial verification of each analyte in salt cake form in order to determine the current analytical capability for chemical analysis. Phase II consisted of a final characterization of those chemical species in solution form where conflicting verification data were observed. The 95 percent confidence interval on the mean for the following analytes within each standard is provided: sodium, nitrate, nitrite, phosphate, carbonate, sulfate, hydroxide, chromate, chloride, fluoride, aluminum, plutonium-239/240, strontium-90, cesium-137, and water

On numerical-analytic techniques for boundary value problems

Czech Academy of Sciences Publication Activity Database

Rontó, András; Rontó, M.; Shchobak, N.

2012-01-01

Roč. 12, č. 3 (2012), s. 5-10 ISSN 1335-8243 Institutional support: RVO:67985840 Keywords : numerical-analytic method * periodic successive approximations * Lyapunov-Schmidt method Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/aeei.2012.12.issue-3/v10198-012-0035-1/v10198-012-0035-1.xml?format=INT

Practical implementation of a higher order transverse leakage approximation

International Nuclear Information System (INIS)

Prinsloo, Rian H.; Tomašević

2011-01-01

Transverse integrated nodal diffusion methods currently represent the standard in full core neutronic simulation. The primary shortcoming in this approach, be it via the Analytic Nodal Method or Nodal Expansion Method, is the utilization of the quadratic transverse leakage approximation. This approach, although proven to work well for typical LWR problems, is not consistent with the formulation of nodal methods and can cause accuracy and convergence problems. In this work an improved, consistent quadratic leakage approximation is formulated, which derives from the class of higher order nodal methods developed some years ago. In this new approach, only information relevant to describing the transverse leak- age terms in the zero-order nodal equations are obtained from the higher order formalism. The method yields accuracy comparable to full higher order methods, but does not suffer from the same computational burden which these methods typically incur. (author)

A new formulation for the Doppler broadening function relaxing the approximations of Beth–Plackzec

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Gonçalves, Alessandro C.; Martinez, Aquilino S.; Mesquita, Amir Z.

2016-01-01

Highlights: • One of the Beth–Placzek approximation were relaxed. • An additional term in the form of an integral is obtained. • A new mathematical formulation for the Doppler broadening function is proposed. - Abstract: In all nuclear reactors some neutrons can be absorbed in the resonance region and, in the design of these reactors, an accurate treatment of the resonant absorptions is essential. Apart from that, the resonant absorption varies with fuel temperature due to the Doppler broadening of the resonances. The thermal agitation movement in the reactor core is adequately represented in the microscopic cross-section of the neutron-core interaction through the Doppler broadening function. This function is calculated numerically in modern systems for the calculation of macro-group constants, necessary to determine the power distribution of a nuclear reactor. It can also be applied to the calculation of self-shielding factors to correct the measurements of the microscopic cross-sections through the activation technique and used for the approximate calculations of the resonance integrals in heterogeneous fuel cells. In these types of application we can point at the need to develop precise analytical approximations for the Doppler broadening function to be used in the calculation codes that calculate the values of this function. However, the Doppler broadening function is based on a series of approximations proposed by Beth–Plackzec. In this work a relaxation of these approximations is proposed, generating an additional term in the form of an integral. Analytical solutions of this additional term are discussed. The results obtained show that the new term is important for high temperatures.

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.

Science.gov (United States)

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.

Accelerating SPARQL Queries and Analytics on RDF Data

KAUST Repository

Al-Harbi, Razen

2016-11-09

The complexity of SPARQL queries and RDF applications poses great challenges on distributed RDF management systems. SPARQL workloads are dynamic and con- sist of queries with variable complexities. Hence, systems that use static partitioning su↵er from communication overhead for workloads that generate excessive communi- cation. Concurrently, RDF applications are becoming more sophisticated, mandating analytical operations that extend beyond SPARQL queries. Being primarily designed and optimized to execute SPARQL queries, which lack procedural capabilities, exist- ing systems are not suitable for rich RDF analytics. This dissertation tackles the problem of accelerating SPARQL queries and RDF analytics on distributed shared-nothing RDF systems. First, a distributed RDF en- gine, coined AdPart, is introduced. AdPart uses lightweight hash partitioning for sharding triples using their subject values; rendering its startup overhead very low. The locality-aware query optimizer of AdPart takes full advantage of the partition- ing to (i) support the fully parallel processing of join patterns on subjects and (ii) minimize data communication for general queries by applying hash distribution of intermediate results instead of broadcasting, wherever possible. By exploiting hash- based locality, AdPart achieves better or comparable performance to systems that employ sophisticated partitioning schemes. To cope with workloads dynamism, AdPart is extended to dynamically adapt to workload changes. AdPart monitors the data access patterns and dynamically redis- tributes and replicates the instances of the most frequent patterns among workers.Consequently, the communication cost for future queries is drastically reduced or even eliminated. Experiments with synthetic and real data verify that AdPart starts faster than all existing systems and gracefully adapts to the query load. Finally, to support and accelerate rich RDF analytical tasks, a vertex-centric RDF analytics framework is

Analytical results for a hole in an antiferromagnet

International Nuclear Information System (INIS)

Li, Y.M.; d'Ambrumenil, N.; Su, Z.B.

1996-04-01

The Green's function for a hole moving in an antiferromagnet is derived analytically in the long-wavelength limit. We find that the infrared divergence is eliminated in two and higher dimensions so that the quasiparticle weight is finite. Our results also suggest that the hole motion is polaronic in nature with a bandwidth proportional to t 2 /J exp[-c(t/J) 2 ] (c is a constant) for J/t >or approx 0.5. The connection of the long-wavelength approximation to the first-order approximation in the cumulant expansion is also clarified. (author). 23 refs, 2 figs

Evaluation of the effect of coal cleaning of fugitive elements. Part II. Analytical methods. Final report, Phase II

Energy Technology Data Exchange (ETDEWEB)

Bosshart, R.E.; Price, A.A.; Ford, C.T.

1980-03-01

This report contains the analytical and test methods which were used routinely at Bituminous Coal Research, Inc. during the project. The procedures contained herein should aid coal industry laboratories and others, including commercial laboratories, who might be required to determine trace elements in coal. Some of the procedures have been presented in previous BCR reports; however, this report includes additional procedures which are described in greater detail. Also presented are many as the more basic coal methods which have been in use at BCR for many years, or which have been adapted or refined from other standard reference sources for coal and water. The basis for choosing specific analytical procedures for trace elements in coal is somewhat complex. At BCR, atomic absorption was selected as the basic method in the development of these procedures. The choice was based on sensitivity, selectivity, accuracy, precision, practicability, and economy. Whenever possible, the methods developed had to be both adequate and amenable for use by coal industry laboratories by virtue of relative simplicity and cost. This is not to imply that the methods described are simple or inexpensive; however, atomic abosrption techniques do meet these criteria in relation to more complex and costly methods such as neutron activation, mass spectrometry, and x-ray fluorescence, some of which require highly specialized personnel as well as access to sophisticated nuclear and computational facilities. Many of the analytical procedures for trace elements in coal have been developed or adapted specifically for the BCR studies. Their presentation is the principal purpose of this report.

Kirchhoff approximation and closed-form expressions for atom-surface scattering

International Nuclear Information System (INIS)

Marvin, A.M.

1980-01-01

In this paper an approximate solution for atom-surface scattering is presented beyond the physical optics approximation. The potential is well represented by a hard corrugated surface but includes an attractive tail in front. The calculation is carried out analytically by two different methods, and the limit of validity of our formulas is well established in the text. In contrast with other workers, I find those expressions to be exact in both limits of small (Rayleigh region) and large momenta (classical region), with the correct behavior at the threshold. The result is attained through a particular use of the extinction theorem in writing the scattered amplitudes, hitherto not employed, and not for particular boundary values of the field. An explicit evaluation of the field on the surface shows in fact the present formulas to be simply related to the well known Kirchhoff approximation (KA) or more generally to an ''extended'' KA fit to the potential model above. A possible application of the theory to treat strong resonance-overlapping effects is suggested in the last part of the work

Analytic moment method calculations of the drift wave spectrum

International Nuclear Information System (INIS)

Thayer, D.R.; Molvig, K.

1985-11-01

A derivation and approximate solution of renormalized mode coupling equations describing the turbulent drift wave spectrum is presented. Arguments are given which indicate that a weak turbulence formulation of the spectrum equations fails for a system with negative dissipation. The inadequacy of the weak turbulence theory is circumvented by utilizing a renormalized formation. An analytic moment method is developed to approximate the solution of the nonlinear spectrum integral equations. The solution method employs trial functions to reduce the integral equations to algebraic equations in basic parameters describing the spectrum. An approximate solution of the spectrum equations is first obtained for a mode dissipation with known solution, and second for an electron dissipation in the NSA

Chemically modified activated carbon with 1-acylthiosemicarbazide for selective solid-phase extraction and preconcentration of trace Cu(II), Hg(II) and Pb(II) from water samples.

Science.gov (United States)

Gao, Ru; Hu, Zheng; Chang, Xijun; He, Qun; Zhang, Lijun; Tu, Zhifeng; Shi, Jianping

2009-12-15

A new sorbent 1-acylthiosemicarbazide-modified activated carbon (AC-ATSC) was prepared as a solid-phase extractant and applied for removing of trace Cu(II), Hg(II) and Pb(II) prior to their determination by inductively coupled plasma optical emission spectrometry (ICP-OES). The separation/preconcentration conditions of analytes were investigated, including effects of pH, the shaking time, the sample flow rate and volume, the elution condition and the interfering ions. At pH 3, the maximum static adsorption capacity of Cu(II), Hg(II) and Pb(II) onto the AC-ATSC were 78.20, 67.80 and 48.56 mg g(-1), respectively. The adsorbed metal ions were quantitatively eluted by 3.0 mL of 2% CS(NH2)2 and 2.0 mol L(-1) HCl solution. Common coexisting ions did not interfere with the separation. According to the definition of IUPAC, the detection limits (3sigma) of this method for Cu(II), Hg(II) and Pb(II) were 0.20, 0.12 and 0.45 ng mL(-1), respectively. The relative standard deviation under optimum conditions is less than 4.0% (n=8). The prepared sorbent was applied for the preconcentration of trace Cu(II), Hg(II) and Pb(II) in certified and water samples with satisfactory results.

Analytical relativistic self-consistent-field calculations for atoms

International Nuclear Information System (INIS)

Barthelat, J.C.; Pelissier, M.; Durand, P.

1980-01-01

A new second-order representation of the Dirac equation is presented. This representation which is exact for a hydrogen atom is applied to approximate analytical self-consistent-field calculations for atoms. Results are given for the rare-gas atoms from helium to radon and for lead. The results compare favorably with numerical Dirac-Hartree-Fock solutions

An approximate method to calculate ionization of LTE and non-LTE plasma

International Nuclear Information System (INIS)

Zhang Jun; Gu Peijun

1987-01-01

When matter, especially high Z element, is heated to high temperature, it will be ionized many times. The degree of ionization has a strong effect on many plasma properties. So an approximate method to calculate the mean ionization degree is needed for solving many practical problems. An analytical expression which is convenient for the approximate numerical calculation is given by fitting it to the scaling law and numerical results of the ionization potential of Thomas-Fermi statistical model. In LTE case, the ionization degree of Au calculated by using the approximate method is in agreement with that of the average ion model. By extending the approximate method to non-LTE case, the ionization degree of Au is similarly calculated according to Corona model and Collision-Radiatoin model(C-R). The results of Corona model agree with the published data quite well, while the results of C-R approach those of Corona model as the density is reduced and approach those of LTE as the density is increased. Finally, all approximately calculated results of ionization degree of Au and the comparision of them are given in figures and tables

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

Science.gov (United States)

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.

Dust in H II regions

International Nuclear Information System (INIS)

Isobe, S.

1977-01-01

Several pieces of evidence indicate that H II regions may contain dust: 1) the continuum light scattered by dust grains (O'Dell and Hubbard, 1965), 2) thermal radiation from dust grains at infrared wavelengths (Ney and Allen, 1969), 3) the abnormal helium abundance in some H II regions (Peimbert and Costero, 1969), etc. Although observations of the scattered continuum suggest that the H II region cores may be dust-free, dust grains and gas must be well mixed in view of the infrared observations. This difficulty may be solved by introducing globules with sizes approximately 0.001 pc. These globules and the molecular clouds adjacent to H II regions are the main sources supplying dust to H II regions. (Auth.)

Multi-level methods and approximating distribution functions

International Nuclear Information System (INIS)

Wilson, D.; Baker, R. E.

2016-01-01

Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie’s direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146–179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.

Multi-level methods and approximating distribution functions

Energy Technology Data Exchange (ETDEWEB)

Wilson, D., E-mail: daniel.wilson@dtc.ox.ac.uk; Baker, R. E. [Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG (United Kingdom)

2016-07-15

Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie’s direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146–179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.

Numerical Test of Different Approximations Used in the Transport Theory of Energetic Particles

Science.gov (United States)

Qin, G.; Shalchi, A.

2016-05-01

Recently developed theories for perpendicular diffusion work remarkably well. The diffusion coefficients they provide agree with test-particle simulations performed for different turbulence setups ranging from slab and slab-like models to two-dimensional and noisy reduced MHD turbulence. However, such theories are still based on different analytical approximations. In the current paper we use a test-particle code to explore the different approximations used in diffusion theory. We benchmark different guiding center approximations, simplifications of higher-order correlations, and the Taylor-Green-Kubo formula. We demonstrate that guiding center approximations work very well as long as the particle's unperturbed Larmor radius is smaller than the perpendicular correlation length of the turbulence. Furthermore, the Taylor-Green-Kubo formula and the definition of perpendicular diffusion coefficients via mean square displacements provide the same results. The only approximation that was used in the past in nonlinear diffusion theory that fails is to replace fourth-order correlations by a product of two second-order correlation functions. In more advanced nonlinear theories, however, this type of approximation is no longer used. Therefore, we confirm the validity of modern diffusion theories as a result of the work presented in the current paper.

Semi-analytic calculations for the impact parameter dependence of electromagnetic multi-lepton pair production

International Nuclear Information System (INIS)

Gueclue, M.C.

2000-01-01

We provide a new general semi-analytic derivation of the impact parameter dependence of lowest order electromagnetic lepton-pair production in relativistic heavy-ion collisions. By using this result we have also calculated the related analytic multiple-pair production in the two-photon external-field model. We have compared our results with the equivalent-photon approximation and other calculations

Analytical approach for the Floquet theory of delay differential equations.

Science.gov (United States)

Simmendinger, C; Wunderlin, A; Pelster, A

1999-05-01

We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincaré-Lindstedt and the Shohat expansions, which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows us to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions.

Analytical calculation of the average scattering cross sections using fourier series

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P. [Instituto Federal do Rio de Janeiro, Nilopolis, RJ (Brazil)], e-mail: dpalmaster@gmail.com; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da [Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear], e-mail: asilva@con.ufrj.br, e-mail: agoncalves@con.ufrj.br, e-mail: aquilino@lmp.ufrj.br, e-mail: fernando@con.ufrj.br

2009-07-01

The precise determination of the Doppler broadening functions is very important in different applications of reactors physics, mainly in the processing of nuclear data. Analytical approximations are obtained in this paper for average scattering cross section using expansions in Fourier series, generating an approximation that is simple and precise. The results have shown to be satisfactory from the point-of-view of accuracy and do not depend on the type of resonance considered. (author)

Analytical calculation of the average scattering cross sections using fourier series

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da

2009-01-01

The precise determination of the Doppler broadening functions is very important in different applications of reactors physics, mainly in the processing of nuclear data. Analytical approximations are obtained in this paper for average scattering cross section using expansions in Fourier series, generating an approximation that is simple and precise. The results have shown to be satisfactory from the point-of-view of accuracy and do not depend on the type of resonance considered. (author)

The Eddington approximation calculation of radiation flux in the atmosphere–ocean system

International Nuclear Information System (INIS)

Shi, Chong; Nakajima, Teruyuki

2015-01-01

An analytical approximation method is presented to calculate the radiation flux in the atmosphere–ocean system using the Eddington approximation when the upwelling radiation from the ocean body is negligibly small. Numerical experiments were carried out to investigate the feasibility of the method in two cases: flat and rough ocean surfaces. The results show good consistency for the reflectivity at the top of atmosphere and transmissivity just above the ocean surface, in comparison with the exact values calculated by radiative transfer models in each case. Moreover, an obvious error might be introduced for the calculation of radiation flux at larger solar zenith angles when the roughness of the ocean surface is neglected. - Highlights: • The Eddington approximation method is extended to the atmosphere–ocean system. • The roughness of ocean surface cannot be neglected at lager solar zenith angles. • Unidirectional reflectivity for rough ocean surface is proposed

Analytic properties of the whistler dispersion function

International Nuclear Information System (INIS)

Daniell, G.J.

1986-01-01

The analytic properties of the dispersion function of a whistler are investigated in the complex frequency plane. It possesses a pole and a branch point at a frequency equal to the minimum value of the electron gyrofrequency along the path of propagation. An integral equation relates the dispersion function to the distribution of magnetospheric electrons along the path and the solution of this equation is obtained. It is found that the electron density in the equatorial plane is very simply related to the dispersion function. A discussion of approximate formulae to represent the dispersion shows how particular terms can be related to attributes of the electron density distribution, and a new approximate formula is proposed. (author)

Thermodynamics of Gas Turbine Cycles with Analytic Derivatives in OpenMDAO

Science.gov (United States)

Gray, Justin; Chin, Jeffrey; Hearn, Tristan; Hendricks, Eric; Lavelle, Thomas; Martins, Joaquim R. R. A.

2016-01-01

A new equilibrium thermodynamics analysis tool was built based on the CEA method using the OpenMDAO framework. The new tool provides forward and adjoint analytic derivatives for use with gradient based optimization algorithms. The new tool was validated against the original CEA code to ensure an accurate analysis and the analytic derivatives were validated against finite-difference approximations. Performance comparisons between analytic and finite difference methods showed a significant speed advantage for the analytic methods. To further test the new analysis tool, a sample optimization was performed to find the optimal air-fuel equivalence ratio, , maximizing combustion temperature for a range of different pressures. Collectively, the results demonstrate the viability of the new tool to serve as the thermodynamic backbone for future work on a full propulsion modeling tool.

Analytical model of the optical vortex microscope.

Science.gov (United States)

Płocinniczak, Łukasz; Popiołek-Masajada, Agnieszka; Masajada, Jan; Szatkowski, Mateusz

2016-04-20

This paper presents an analytical model of the optical vortex scanning microscope. In this microscope the Gaussian beam with an embedded optical vortex is focused into the sample plane. Additionally, the optical vortex can be moved inside the beam, which allows fine scanning of the sample. We provide an analytical solution of the whole path of the beam in the system (within paraxial approximation)-from the vortex lens to the observation plane situated on the CCD camera. The calculations are performed step by step from one optical element to the next. We show that at each step, the expression for light complex amplitude has the same form with only four coefficients modified. We also derive a simple expression for the vortex trajectory of small vortex displacements.

Finite approximations in discrete-time stochastic control quantized models and asymptotic optimality

CERN Document Server

Saldi, Naci; Yüksel, Serdar

2018-01-01

In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original mo...

Approximation of the cross-sections for charged-particle emission reactions near the threshold

International Nuclear Information System (INIS)

Badikov, S.A.; Pashchenko, A.B.

1990-01-01

We perform an analytical approximation of the energy dependence of the cross-sections for the reactions (n,p) and (n,γ) from the BOSPOR library, correct them for the latest differential and integral experimental data using the common features, characteristic of the energy dependence of the threshold reaction cross-section and making some physical assumptions. 19 refs, 1 fig., 1 tab

Analytical Results for Scaling Properties of the Spectrum of the Fibonacci Chain

Science.gov (United States)

Piéchon, Frédéric; Benakli, Mourad; Jagannathan, Anuradha

1995-06-01

We solve the approximate renormalization group found by Niu and Nori for a quasiperiodic tight-binding Hamiltonian on the Fibonacci chain. This enables us to characterize analytically the spectral properties of this model.

Approximate solutions: ramps and periodic variations. Chapter 5

International Nuclear Information System (INIS)

1998-01-01

The aim of reactor regulation is generally to maintain reactor power at the demand power, or to vary it slowly to attain a new demand power. On the other hand, the purpose of reactor shutdown systems (SDS) is to insert rapidly, on actuation, a large negative reactivity in order to minimize an overpower, or limit the energy released during a transient, so that fuel failure is improbable. Control mechanisms are therefore characterized by: their reactivity worth (mk), which must exceed the reactivity effect which the mechanism is designed to compensate; and their insertion rate (mk/s), which must be at least as fast as the effect to be controlled. Table 5.1 gives a summary of the various control mechanisms in a CANDU 6 reactor. The reactivity worth shown for each mechanism is the static reactivity change associated with full movement of the device. In reality, the dynamic reactivity will vary in a continuous manner, not suddenly, as assumed in the previous chapter. The realistic simulation of a reactivity insertion in the reactor must then take into account the rate of insertion of reactivity, which is governed by the insertion speed of the mechanism. We have seen in the previous chapter that it is possible to solved analytically the point-kinetics equations for constant reactivity. We could generalize these solutions to step-wise reactivity variations by linking together the analytic solutions to for a sequence of step changes. This approach is not necessarily the best from a numerical point of view. By introducing one or more simplifying assumptions, it will be possible to obtain an analytical solution of arbitrary variations in reactivity or in the external source. These assumptions will undoubtedly limit the applicability of the results, but the approximate solutions obtained will allow us to describe the reactor behaviour analytically. (author)

New approximation of a scale space kernel on SE(3) and applications in neuroimaging

NARCIS (Netherlands)

Portegies, J.M.; Sanguinetti, G.R.; Meesters, S.P.L.; Duits, R.

2015-01-01

We provide a new, analytic kernel for scale space filtering of dMRI data. The kernel is an approximation for the Green's function of a hypo-elliptic diffusion on the 3D rigid body motion group SE(3), for fiber enhancement in dMRI. The enhancements are described by linear scale space PDEs in the

Interacting Brownian Swarms: Some Analytical Results

Directory of Open Access Journals (Sweden)

Guillaume Sartoretti

2016-01-01

Full Text Available We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables. Implicitly, the implementation of rank-based mutual interactions, requires that agents have infinite interaction ranges. Using the probabilistic size of the swarm’s support, we analytically estimate the critical interaction range below that flocked swarms cannot survive. In the second part of the paper, we consider the interactions between two flocked swarms of Brownian agents with finite interaction ranges. Both swarms travel with different barycentric velocities, and agents from both swarms indifferently interact with each other. For appropriate initial configurations, both swarms eventually collide (i.e., all agents interact. Depending on the values of the control parameters, one of the following patterns emerges after collision: (i Both swarms remain essentially flocked, or (ii the swarms become ultimately quasi-free and recover their nominal barycentric speeds. We derive a set of analytical flocking conditions based on the generalized rank-based Brownian motion. An extensive set of numerical simulations corroborates our analytical findings.

SU-F-T-144: Analytical Closed Form Approximation for Carbon Ion Bragg Curves in Water

Energy Technology Data Exchange (ETDEWEB)

Tuomanen, S; Moskvin, V; Farr, J [St. Jude Children’s Research Hospital, Memphis, TN (United States)

2016-06-15

Purpose: Semi-empirical modeling is a powerful computational method in radiation dosimetry. A set of approximations exist for proton ion depth dose distribution (DDD) in water. However, the modeling is more complicated for carbon ions due to fragmentation. This study addresses this by providing and evaluating a new methodology for DDD modeling of carbon ions in water. Methods: The FLUKA, Monte Carlo (MC) general-purpose transport code was used for simulation of carbon DDDs for energies of 100–400 MeV in water as reference data model benchmarking. Based on Thomas Bortfeld’s closed form equation approximating proton Bragg Curves as a basis, we derived the critical constants for a beam of Carbon ions by applying models of radiation transport by Lee et. al. and Geiger to our simulated Carbon curves. We hypothesized that including a new exponential (κ) residual distance parameter to Bortfeld’s fluence reduction relation would improve DDD modeling for carbon ions. We are introducing an additional term to be added to Bortfeld’s equation to describe fragmentation tail. This term accounts for the pre-peak dose from nuclear fragments (NF). In the post peak region, the NF transport will be treated as new beams utilizing the Glauber model for interaction cross sections and the Abrasion- Ablation fragmentation model. Results: The carbon beam specific constants in the developed model were determined to be : p= 1.75, β=0.008 cm-1, γ=0.6, α=0.0007 cm MeV, σmono=0.08, and the new exponential parameter κ=0.55. This produced a close match for the plateau part of the curve (max deviation 6.37%). Conclusion: The derived semi-empirical model provides an accurate approximation of the MC simulated clinical carbon DDDs. This is the first direct semi-empirical simulation for the dosimetry of therapeutic carbon ions. The accurate modeling of the NF tail in the carbon DDD will provide key insight into distal edge dose deposition formation.

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

OpenAIRE

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 ...

Phase II of a Six sigma Initiative to Study DWPF SME Analytical Turnaround Times: SRNL's Evaluation of Carbonate-Based Dissolution Methods

International Nuclear Information System (INIS)

Edwards, Thomas

2005-01-01

The Analytical Development Section (ADS) and the Statistical Consulting Section (SCS) of the Savannah River National Laboratory (SRNL) are participating in a Six Sigma initiative to improve the Defense Waste Processing Facility (DWPF) Laboratory. The Six Sigma initiative has focused on reducing the analytical turnaround time of samples from the Slurry Mix Evaporator (SME) by developing streamlined sampling and analytical methods [1]. The objective of Phase I was to evaluate the sub-sampling of a larger sample bottle and the performance of a cesium carbonate (Cs 2 CO 3 ) digestion method. Successful implementation of the Cs 2 CO 3 fusion method in the DWPF would have important time savings and convenience benefits because this single digestion would replace the dual digestion scheme now used. A single digestion scheme would result in more efficient operations in both the DWPF shielded cells and the inductively coupled plasma--atomic emission spectroscopy (ICP-AES) laboratory. By taking a small aliquot of SME slurry from a large sample bottle and dissolving the vitrified SME sample with carbonate fusion methods, an analytical turnaround time reduction from 27 hours to 9 hours could be realized in the DWPF. This analytical scheme has the potential for not only dramatically reducing turnaround times, but also streamlining operations to minimize wear and tear on critical shielded cell components that are prone to fail, including the Hydragard(trademark) sampling valves and manipulators. Favorable results from the Phase I tests [2] led to the recommendation for a Phase II effort as outlined in the DWPF Technical Task Request (TTR) [3]. There were three major tasks outlined in the TTR, and SRNL issued a Task Technical and QA Plan [4] with a corresponding set of three major task activities: (1) Compare weight percent (wt%) total solids measurements of large volume samples versus peanut vial samples. (2) Evaluate Cs 2 CO 3 and K 2 CO 3 fusion methods using DWPF simulated

Systematic approximation of multi-scale Feynman integrals arXiv

CERN Document Server

Borowka, Sophia; Hulme, Daniel

An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman integrals, allowing for fast numerical evaluation. The results are valid in all kinematical regions, both above and below thresholds, up to in principle arbitrary orders in the dimensional regulator. The scope of the algorithm is demonstrated by presenting results for selected two-loop three-point and four-point integrals with an internal mass scale that appear in the two-loop amplitudes for Higgs+jet production.

Intensity-based hierarchical elastic registration using approximating splines.

Science.gov (United States)

Serifovic-Trbalic, Amira; Demirovic, Damir; Cattin, Philippe C

2014-01-01

We introduce a new hierarchical approach for elastic medical image registration using approximating splines. In order to obtain the dense deformation field, we employ Gaussian elastic body splines (GEBS) that incorporate anisotropic landmark errors and rotation information. Since the GEBS approach is based on a physical model in form of analytical solutions of the Navier equation, it can very well cope with the local as well as global deformations present in the images by varying the standard deviation of the Gaussian forces. The proposed GEBS approximating model is integrated into the elastic hierarchical image registration framework, which decomposes a nonrigid registration problem into numerous local rigid transformations. The approximating GEBS registration scheme incorporates anisotropic landmark errors as well as rotation information. The anisotropic landmark localization uncertainties can be estimated directly from the image data, and in this case, they represent the minimal stochastic localization error, i.e., the Cramér-Rao bound. The rotation information of each landmark obtained from the hierarchical procedure is transposed in an additional angular landmark, doubling the number of landmarks in the GEBS model. The modified hierarchical registration using the approximating GEBS model is applied to register 161 image pairs from a digital mammogram database. The obtained results are very encouraging, and the proposed approach significantly improved all registrations comparing the mean-square error in relation to approximating TPS with the rotation information. On artificially deformed breast images, the newly proposed method performed better than the state-of-the-art registration algorithm introduced by Rueckert et al. (IEEE Trans Med Imaging 18:712-721, 1999). The average error per breast tissue pixel was less than 2.23 pixels compared to 2.46 pixels for Rueckert's method. The proposed hierarchical elastic image registration approach incorporates the GEBS

Final project report: TA-35 Los Alamos Power Reactor Experiment No. II (LAPRE II) decommissioning project

International Nuclear Information System (INIS)

Montoya, G.M.

1993-02-01

This final report addresses the decommissioning of the LAPRE II Reactor, safety enclosure, fuel reservoir tanks, emergency fuel recovery system, primary pump pit, secondary loop, associated piping, and the post-remediation activities. Post-remedial action measurements are also included. The cost of the project including, Phase I assessment and Phase II remediation was approximately $496K. The decommissioning operation produced 533 M 3 of mixed waste

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

Science.gov (United States)

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.

Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC

Directory of Open Access Journals (Sweden)

Morten Hovd

2010-04-01

Full Text Available Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC. A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general.

Higher-order meshing of implicit geometries, Part II: Approximations on manifolds

Science.gov (United States)

Fries, T. P.; Schöllhammer, D.

2017-11-01

A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it enables a completely automatic workflow from the geometric description to the numerical analysis without any user-intervention. A master level-set function defines the shape of the manifold through its zero-isosurface which is then restricted to a finite domain by additional level-set functions. It is ensured that the surface elements are sufficiently continuous and shape regular which is achieved by manipulating the background mesh. The numerical results show that optimal convergence rates are obtained with a moderate increase in the condition number compared to handcrafted surface meshes.

Analysis of carbon transport in the EBR-II and FFTF primary sodium systems

International Nuclear Information System (INIS)

Snyder, R.B.; Natesan, K.; Kassner, T.F.

1976-01-01

An analysis of the carburization-decarburization behavior of austenitic stainless steels in the primary heat-transport systems of the EBR-II and FFTF has been made that is based upon a kinetic model for the diffusion process and the surface area of steel in contact with flowing sodium at various temperatures in the two systems. The analysis was performed for operating conditions that result in sodium outlet temperatures of 474 and 566 0 C in the FFTF and 470 0 C in the EBR-II. If there was no external source of carbon to the system, i.e., other than the carbon initially present in the steel and the sodium, the dynamic-equilibrium carbon concentrations calculated for the FFTF primary sodium were approximately 0.025 and approximately 0.065 ppm for the 474 and 566 0 C outlet temperatures, respectively, and approximately 0.018 ppm for the EBR-II primary system. The analysis indicated that a carbon-source rate of approximately 250 g/y would be required to increase the carbon concentration of the EBR-II sodium to the measured range of approximately 0.16--0.19 ppm. An evaluation of possible carbon sources and the amount of carbonaceous material introduced into the reactor cover gas and sodium suggests that the magnitude of the calculated contamination rate is reasonable. For a 566 0 C outlet temperature, carbonaceous material would have to be introduced into the FFTF primary system at a rate approximately 4--6 times higher than in EBR-II to achieve the same carbon concentration in the sodium in the two systems. Since contamination rates of approximately 1500 g/y are unlikely, high-temperature fuel cladding in the FFTF should exhibit decarburization similar to that observed in laboratory loop systems, in contrast to the minimal compositional changes that result after exposure of Type 316 stainless steel to EBR-II sodium at temperatures between approximately 625 and 650 0 C

Analytical Modeling for Underground Risk Assessment in Smart Cities

Directory of Open Access Journals (Sweden)

Israr Ullah

2018-06-01

Full Text Available In the developed world, underground facilities are increasing day-by-day, as it is considered as an improved utilization of available space in smart cities. Typical facilities include underground railway lines, electricity lines, parking lots, water supply systems, sewerage network, etc. Besides its utility, these facilities also pose serious threats to citizens and property. To preempt accidental loss of precious human lives and properties, a real time monitoring system is highly desirable for conducting risk assessment on continuous basis and timely report any abnormality before its too late. In this paper, we present an analytical formulation to model system behavior for risk analysis and assessment based on various risk contributing factors. Based on proposed analytical model, we have evaluated three approximation techniques for computing final risk index: (a simple linear approximation based on multiple linear regression analysis; (b hierarchical fuzzy logic based technique in which related risk factors are combined in a tree like structure; and (c hybrid approximation approach which is a combination of (a and (b. Experimental results shows that simple linear approximation fails to accurately estimate final risk index as compared to hierarchical fuzzy logic based system which shows that the latter provides an efficient method for monitoring and forecasting critical issues in the underground facilities and may assist in maintenance efficiency as well. Estimation results based on hybrid approach fails to accurately estimate final risk index. However, hybrid scheme reveals some interesting and detailed information by performing automatic clustering based on location risk index.

3D Analytical Calculation of Forces between Linear Halbach-Type Permanent Magnet Arrays

OpenAIRE

Allag , Hicham; Yonnet , Jean-Paul; Latreche , Mohamed E. H.

2009-01-01

International audience; Usely, in analytical calculation of magnetic and mechanical quantities of Halbach systems, the authors use the Fourier series approximation because the exact calculations are more difficult. In this work the interaction forces between linear Halbach arrays are analytically calculated thanks to our recent development 3D exact calculation of forces between two cuboïdal magnets with parallel and perpendicular magnetization. We essentially describe the way to separately ca...

Modelling of heating and evaporation of gasoline fuel droplets: A comparative analysis of approximations

KAUST Repository

Elwardani, Ahmed Elsaid

2013-09-01

Modelling of gasoline fuel droplet heating and evaporation processes is investigated using several approximations of this fuel. These are quasi-components used in the quasi-discrete model and the approximations of these quasi-components (Surrogate I (molar fractions: 83.0% n-C 6H14 + 15.6% n-C10H22 + 1.4% n-C14H30) and Surrogate II (molar fractions: 83.0% n-C7H16 + 15.6% n-C11H24 + 1.4% n-C15H32)). Also, we have used Surrogate A (molar fractions: 56% n-C7H16 + 28% iso-C8H 18 + 17% C7H8) and Surrogate B (molar fractions: 63% n-C7H16 + 20% iso-C8H 18 + 17% C7H8), originally introduced based on the closeness of the ignition delay of surrogates to that of gasoline fuel. The predictions of droplet radii and temperatures based on three quasi-components and their approximations (Surrogates I and II) are shown to be much more accurate than the predictions using Surrogates A and B. © 2013 Elsevier Ltd. All rights reserved.

Non-diverging analytic expression for the on-axis sensitivity of converging collimators: analytic derivation

International Nuclear Information System (INIS)

Accorsi, R; Metzler, S D

2006-01-01

The expressions for the sensitivity of converging collimators found in the literature diverge at points near the focal locus of the collimator. In this paper, an analytical formula that does not diverge is derived and compared to that available in the literature. An analysis is provided to predict the cases in which use of the new formula is advisable. Since the first expression derived is rather complex, approximations were made to reach simpler formulae. The formulae derived can be used to define and extend the realm of applicability of the literature expression in the cases identified in their derivation

Analytical approximations for thermophysical properties of supercritical nitrogen (SCN) to be used in futuristic high temperature superconducting (HTS) cables

Energy Technology Data Exchange (ETDEWEB)

Dondapati, Raja Sekhar, E-mail: drsekhar@ieee.org [School of Mechanical Engineering, Lovely Professional University, Phagwara, Punjab 144401 (India); Ravula, Jeswanth [School of Mechanical Engineering, Lovely Professional University, Phagwara, Punjab 144401 (India); Thadela, S. [Department of Mechanical Engineering, Andhra University, Visakhapatnam, Andhra Pradesh (India); Usurumarti, Preeti Rao [Department of Mechanical Engineering, P.V.K. Institute of Technology, Anantapur, Andhra Pradesh (India)

2015-12-15

Future power transmission applications demand higher efficiency due to the limited resources of energy. In order to meet such demand, a novel method of transmission is being developed using High Temperature Superconducting (HTS) cables. However, these HTS cables need to be cooled below the critical temperature of superconductors used in constructing the cable to retain the superconductivity. With the advent of new superconductors whose critical temperatures having reached up to 134 K (Hg based), a need arises to find a suitable coolant which can accommodate the heating loads on the superconductors. The present work proposes, Supercritical Nitrogen (SCN) to be a feasible coolant to achieve the required cooling. Further, the feasibility of proposed coolant to be used in futuristic HTS cables is investigated by studying the thermophysical properties such as density, viscosity, specific heat and thermal conductivity with respect to temperature (T{sub C} + 10 K) and pressure (P{sub C} + 10 bar). In addition, few temperature dependent analytical functions are developed for thermophysical properties of SCN which are useful in predicting thermohydraulic performance (pressure drop, pumping power and cooling capacity) using numerical or computational techniques. Also, the developed analytical functions are used to calculate the pumping power and the temperature difference between inlet and outlet of HTS cable. These results are compared with those of liquid nitrogen (LN2) and found that the circulating pumping power required to pump SCN is significantly smaller than that to pump LN2. Further, it is found that the temperature difference between the inlet and outlet is smaller as compared to that when LN2 is used, SCN can be preferred to cool long length Hg based HTS cables. - Highlights: • Analytical functions are developed for thermophysical properties of Supercritical Nitrogen. • Error analysis shows extremely low errors in the developed analytical functions. �

Analytical approximations for thermophysical properties of supercritical nitrogen (SCN) to be used in futuristic high temperature superconducting (HTS) cables

International Nuclear Information System (INIS)

Dondapati, Raja Sekhar; Ravula, Jeswanth; Thadela, S.; Usurumarti, Preeti Rao

2015-01-01

Future power transmission applications demand higher efficiency due to the limited resources of energy. In order to meet such demand, a novel method of transmission is being developed using High Temperature Superconducting (HTS) cables. However, these HTS cables need to be cooled below the critical temperature of superconductors used in constructing the cable to retain the superconductivity. With the advent of new superconductors whose critical temperatures having reached up to 134 K (Hg based), a need arises to find a suitable coolant which can accommodate the heating loads on the superconductors. The present work proposes, Supercritical Nitrogen (SCN) to be a feasible coolant to achieve the required cooling. Further, the feasibility of proposed coolant to be used in futuristic HTS cables is investigated by studying the thermophysical properties such as density, viscosity, specific heat and thermal conductivity with respect to temperature (T_C + 10 K) and pressure (P_C + 10 bar). In addition, few temperature dependent analytical functions are developed for thermophysical properties of SCN which are useful in predicting thermohydraulic performance (pressure drop, pumping power and cooling capacity) using numerical or computational techniques. Also, the developed analytical functions are used to calculate the pumping power and the temperature difference between inlet and outlet of HTS cable. These results are compared with those of liquid nitrogen (LN2) and found that the circulating pumping power required to pump SCN is significantly smaller than that to pump LN2. Further, it is found that the temperature difference between the inlet and outlet is smaller as compared to that when LN2 is used, SCN can be preferred to cool long length Hg based HTS cables. - Highlights: • Analytical functions are developed for thermophysical properties of Supercritical Nitrogen. • Error analysis shows extremely low errors in the developed analytical functions. �

Gaseous analytes of concern at Hanford Tank Farms. Topical report

International Nuclear Information System (INIS)

1996-01-01

Large amounts of toxic and radioactive waste materials are stored in underground tanks at DOE sites. When the vapors in the tank headspaces vent to the open atmosphere a potentially dangerous situation can occur for personnel in the area. An open-path atmospheric pollution monitor is being developed for DOE to monitor the open air space above these tanks. In developing this monitor it is important to know what hazardous gases are most likely to be found in dangerous concentrations. These gases are called the Analytes of Concern. At the present time, measurements in eight tanks have detected thirty-one analytes in at least two tanks and fifteen analytes in only one tank. In addition to these gases, Carbon tetrachloride is considered to be an Analyte of Concern because it permeates the ground around the tanks. These Analytes are described and ranked according to a Hazard Index which combines their vapor pressure, density, and approximate danger level. The top sixteen ranked analytes which have been detected in at least two tanks comprise an open-quotes Analytes of Concern Test Listclose quotes for determining the system performance of the atmospheric pollution monitor under development. A preliminary examination of the infrared spectra, barring atmospheric interferences, indicates that: The pollution monitor will detect all forty-seven Analytes exclamation point

Analytic solution for a quartic electron mirror

Energy Technology Data Exchange (ETDEWEB)

Straton, Jack C., E-mail: straton@pdx.edu

2015-01-15

A converging electron mirror can be used to compensate for spherical and chromatic aberrations in an electron microscope. This paper presents an analytical solution to a diode (two-electrode) electrostatic mirror including the next term beyond the known hyperbolic shape. The latter is a solution of the Laplace equation to second order in the variables perpendicular to and along the mirror's radius (z{sup 2}−r{sup 2}/2) to which we add a quartic term (kλz{sup 4}). The analytical solution is found in terms of Jacobi cosine-amplitude functions. We find that a mirror less concave than the hyperbolic profile is more sensitive to changes in mirror voltages and the contrary holds for the mirror more concave than the hyperbolic profile. - Highlights: • We find the analytical solution for electron mirrors whose curvature has z4 dependence added to the usual z{sup 2} – r{sup 2}/2 terms. • The resulting Jacobi cosine-amplitude function reduces to the well-known cosh solution in the limit where the new term is 0. • This quartic term gives a mirror designer additional flexibility for eliminating spherical and chromatic aberrations. • The possibility of using these analytical results to approximately model spherical tetrode mirrors close to axis is noted.

Transport of radionuclides in stochastic media. Pt. 1: The quasi-asymptotic approximation

International Nuclear Information System (INIS)

Devooght, J.; Smidts, O.F.

1996-01-01

A three-dimensional quasi-asymptotic approximate equation is developed for the transport of radionuclides in a stochastic velocity field. This approximation is derived from an integro-differential equation of transport in stochastic media, commonly encountered in hydrogeology. The quasi-asymptotic equation turns out to be a generalised Telegrapher's equation as found by Williams in the particular context of fractured media. We obtain the Telegrapher's equation without specifying the causes responsible for the random velocity field. Our model may thus be applied in porous media as well as in fractured media. We give the developments leading to the analytical solution of the three-dimensional Telegrapher's equation for constant parameters. This solution is then visualised for a source in the form of a square wave. (Author)

Numerical approximation for HIV infection of CD4+ T cells mathematical model

Directory of Open Access Journals (Sweden)

Vineet K. Srivastava

2014-06-01

Full Text Available A dynamical model of HIV infection of CD4+ T cells is solved numerically using an approximate analytical method so-called the differential transform method (DTM. The solution obtained by the method is an infinite power series for appropriate initial condition, without any discretization, transformation, perturbation, or restrictive conditions. A comparative study between the present method, the classical Euler’s and Runge–Kutta fourth order (RK4 methods is also carried out.

An analytical model of iceberg drift

Science.gov (United States)

Eisenman, I.; Wagner, T. J. W.; Dell, R.

2017-12-01

Icebergs transport freshwater from glaciers and ice shelves, releasing the freshwater into the upper ocean thousands of kilometers from the source. This influences ocean circulation through its effect on seawater density. A standard empirical rule-of-thumb for estimating iceberg trajectories is that they drift at the ocean surface current velocity plus 2% of the atmospheric surface wind velocity. This relationship has been observed in empirical studies for decades, but it has never previously been physically derived or justified. In this presentation, we consider the momentum balance for an individual iceberg, which includes nonlinear drag terms. Applying a series of approximations, we derive an analytical solution for the iceberg velocity as a function of time. In order to validate the model, we force it with surface velocity and temperature data from an observational state estimate and compare the results with iceberg observations in both hemispheres. We show that the analytical solution reduces to the empirical 2% relationship in the asymptotic limit of small icebergs (or strong winds), which approximately applies for typical Arctic icebergs. We find that the 2% value arises due to a term involving the drag coefficients for water and air and the densities of the iceberg, ocean, and air. In the opposite limit of large icebergs (or weak winds), which approximately applies for typical Antarctic icebergs with horizontal length scales greater than about 12 km, we find that the 2% relationship is not applicable and that icebergs instead move with the ocean current, unaffected by the wind. The two asymptotic regimes can be understood by considering how iceberg size influences the relative importance of the wind and ocean current drag terms compared with the Coriolis and pressure gradient force terms in the iceberg momentum balance.

On analytical fits for electron impact ionisation cross sections

International Nuclear Information System (INIS)

Godunov, A.L.; Ivanov, P.B.

1999-01-01

The problem of providing accurate recommended analytical fits for electron impact ionisation cross sections is discussed, and a number of approaches are considered on the sample case of neon and its ions. The previously known fits are being reassessed using complete experimental and theoretical data, with the preference for experiment, to avoid systematic shifts introduced by the present calculation methods. The feasibility of the standard BELI formula is investigated in detail, and a number of other analytical expressions is suggested, approximating single-ionization cross sections in the whole range of energies. The factors influencing the accuracy of the fits and the physical meaning of the parameters obtained are discussed. (orig.)

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.

Science.gov (United States)

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.

The analytical and numerical study of the fluorination of uranium dioxide particles

International Nuclear Information System (INIS)

Sazhin, S.S.

1997-01-01

A detailed analytical study of the equations describing the fluorination of UO 2 particles is presented for some limiting cases assuming that the mass flowrate of these particles is so small that they do not affect the state of the gas. The analytical solutions obtained can be used for approximate estimates of the effect of fluorination on particle diameter and temperature but their major application, however, is probably in the verification of self-consistent numerical solutions. Computational results are presented and discussed for a self-consistent problem in which both the effects of gas on particles and particles on gas are accounted for. It has been shown that in the limiting cases for which analytical solutions have been obtained, the coincidence between numerical and analytical results is almost exact. This can be considered as a verification of both the analytical and numerical solutions. (orig.)

An approximate analytical solution for the energy distribution of beta particles transmitted through metal foils

International Nuclear Information System (INIS)

Gurler, O.; Yalcin, S.; Gultekin, A.; Kaynak, G.; Gundogdu, O.

2006-01-01

The energy distributions of beta particles which penetrated a certain matter thickness were studied experimentally and theoretically by using a surface barrier solid state detector. A valid theoretical expression based on average values between energy and distance traveled during the slowing down of the electron was obtained. Two analytical expressions were proposed; one for the energy distribution of monoenergetic electrons which penetrated a certain matter thickness, and one for the response function in the detector for monoenergetic electrons detected with its entire energy. Response functions of the detector for beta particles emitted from 204 Tl isotope which penetrated a certain matter thickness were obtained for two different aluminum thicknesses, and the results were discussed by comparing with experimental energy spectra

An approximate analytical solution for the energy distribution of beta particles transmitted through metal foils

Energy Technology Data Exchange (ETDEWEB)

Gurler, O. [Faculty of Arts and Sciences, University of Uludag, 16059 Bursa (Turkey)]. E-mail: ogurler@uludag.edu.tr; Yalcin, S. [Gazi University Kastamonu, Education Faculty, 37200 Kastamonu (Turkey); Gultekin, A. [Faculty of Arts and Sciences, University of Uludag, 16059 Bursa (Turkey); Kaynak, G. [Faculty of Arts and Sciences, University of Uludag, 16059 Bursa (Turkey); Gundogdu, O. [School of Engineering, University of Surrey, Guildford GU2 7XH (United Kingdom)

2006-04-15

The energy distributions of beta particles which penetrated a certain matter thickness were studied experimentally and theoretically by using a surface barrier solid state detector. A valid theoretical expression based on average values between energy and distance traveled during the slowing down of the electron was obtained. Two analytical expressions were proposed; one for the energy distribution of monoenergetic electrons which penetrated a certain matter thickness, and one for the response function in the detector for monoenergetic electrons detected with its entire energy. Response functions of the detector for beta particles emitted from {sup 204}Tl isotope which penetrated a certain matter thickness were obtained for two different aluminum thicknesses, and the results were discussed by comparing with experimental energy spectra.

L.U.St: a tool for approximated maximum likelihood supertree reconstruction.

Science.gov (United States)

Akanni, Wasiu A; Creevey, Christopher J; Wilkinson, Mark; Pisani, Davide

2014-06-12

Supertrees combine disparate, partially overlapping trees to generate a synthesis that provides a high level perspective that cannot be attained from the inspection of individual phylogenies. Supertrees can be seen as meta-analytical tools that can be used to make inferences based on results of previous scientific studies. Their meta-analytical application has increased in popularity since it was realised that the power of statistical tests for the study of evolutionary trends critically depends on the use of taxon-dense phylogenies. Further to that, supertrees have found applications in phylogenomics where they are used to combine gene trees and recover species phylogenies based on genome-scale data sets. Here, we present the L.U.St package, a python tool for approximate maximum likelihood supertree inference and illustrate its application using a genomic data set for the placental mammals. L.U.St allows the calculation of the approximate likelihood of a supertree, given a set of input trees, performs heuristic searches to look for the supertree of highest likelihood, and performs statistical tests of two or more supertrees. To this end, L.U.St implements a winning sites test allowing ranking of a collection of a-priori selected hypotheses, given as a collection of input supertree topologies. It also outputs a file of input-tree-wise likelihood scores that can be used as input to CONSEL for calculation of standard tests of two trees (e.g. Kishino-Hasegawa, Shimidoara-Hasegawa and Approximately Unbiased tests). This is the first fully parametric implementation of a supertree method, it has clearly understood properties, and provides several advantages over currently available supertree approaches. It is easy to implement and works on any platform that has python installed. bitBucket page - https://afro-juju@bitbucket.org/afro-juju/l.u.st.git. Davide.Pisani@bristol.ac.uk.

Analytic continuation by duality estimation of the S parameter

International Nuclear Information System (INIS)

Ignjatovic, S. R.; Wijewardhana, L. C. R.; Takeuchi, T.

2000-01-01

We investigate the reliability of the analytic continuation by duality (ACD) technique in estimating the electroweak S parameter for technicolor theories. The ACD technique, which is an application of finite energy sum rules, relates the S parameter for theories with unknown particle spectra to known OPE coefficients. We identify the sources of error inherent in the technique and evaluate them for several toy models to see if they can be controlled. The evaluation of errors is done analytically and all relevant formulas are provided in appendixes including analytical formulas for approximating the function 1/s with a polynomial in s. The use of analytical formulas protects us from introducing additional errors due to numerical integration. We find that it is very difficult to control the errors even when the momentum dependence of the OPE coefficients is known exactly. In realistic cases in which the momentum dependence of the OPE coefficients is only known perturbatively, it is impossible to obtain a reliable estimate. (c) 2000 The American Physical Society

The calculation of hydrostatic pressures in SIMMER-II and the problem of connected tubes

International Nuclear Information System (INIS)

Schmuck, P.; Kleinheins, S.

1986-03-01

Some SIMMER-II calculations had shown that the hydrostatic equilibrium in connected tubes had not been simulated correctly under certain conditions. The present report documents the results of the investigations, which had been performed to understand these inconsistencies. The reasons are presented in analytical form and possibilities to avoid the mistakes or to keep their consequences as small as possible are given. For the verification of the analytical results some SIMMER-II, version 9 have been performed and their results are presented

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

Science.gov (United States)

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.

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

Directory of Open Access Journals (Sweden)

Wilten eNicola

2016-02-01

Full Text Available 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

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

Science.gov (United States)

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.

Analysis of Topaz-II reactor performance using MCNP and TFEHX

International Nuclear Information System (INIS)

Lee, H.H.; Klein, A.C.

1993-01-01

Data reported by Russian scientist and engineers for the TOPAZ-II Space Nuclear Power is compared with analytical results calculated using the Monte Carlo Neutron and Photon (MCNP) and TFEHX computer codes. The results of these comparisons show good agreement with the TOPAZ-II neutronics, thermionic and thermal hydraulics performance. A detailed description of the TOPAZ-II reactor and of the TFE should enhance the performance of the both codes in modeling the reactor and TFE performances

An accurate analytical solution of a zero-dimensional greenhouse model for global warming

International Nuclear Information System (INIS)

Foong, S K

2006-01-01

In introducing the complex subject of global warming, books and papers usually use the zero-dimensional greenhouse model. When the ratio of the infrared radiation energy of the Earth's surface that is lost to outer space to the non-reflected average solar radiation energy is small, the model admits an accurate approximate analytical solution-the resulting energy balance equation of the model is a quartic equation that can be solved analytically-and thus provides an alternative solution and instructional strategy. A search through the literature fails to find an analytical solution, suggesting that the solution may be new. In this paper, we review the model, derive the approximation and obtain its solution. The dependence of the temperature of the surface of the Earth and the temperature of the atmosphere on seven parameters is made explicit. A simple and convenient formula for global warming (or cooling) in terms of the percentage change of the parameters is derived. The dependence of the surface temperature on the parameters is illustrated by several representative graphs

Analytical solution for a coaxial plasma gun: Weak coupling limit

International Nuclear Information System (INIS)

Dietz, D.

1987-01-01

The analytical solution of the system of coupled ODE's which describes the time evolution of an ideal (i.e., zero resistance) coaxial plasma gun operating in the snowplow mode is obtained in the weak coupling limit, i.e, when the gun is fully influenced by the driving (RLC) circuit in which it resides but the circuit is negligibly influenced by the gun. Criteria for the validity of this limit are derived and numerical examples are presented. Although others have obtained approximate, asymptotic and numerical solutions of the equations, the present analytical results seem not to have appeared previously in the literature

A high resolution atlas of Mg II profiles

Science.gov (United States)

Ewald, R.; Nichols-Bohlin, Joy Y.; Kondo, Yoji

1990-01-01

An atlas of high dispersion Mg II profiles for standard stars of spectral types B0 through G9 is presented. The atlas contains plots of the Mg II profiles for approximately 65 stars and associated equivalent width measurements for both absorption and emission components, and the subordinate lines. The atlas is used to investigate systematic behavior of the Mg II profiles and correlation of the behavior with spectral classification.

Calculus II For Dummies

CERN Document Server

Zegarelli, Mark

2012-01-01

An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, wit

Immobilization of aqueous Hg(II) by mackinawite (FeS)

International Nuclear Information System (INIS)

Liu Jianrong; Valsaraj, Kalliat T.; Devai, Istvan; DeLaune, R.D.

2008-01-01

As one of the major constituents of acid volatile sulfide (AVS) in anoxic sediments, mackinawite (FeS) is known for its ability to scavenge trace metals. The interaction between aqueous Hg(II) (added as HgCl 2 ) and synthetic FeS was studied via batch sorption experiments conducted under anaerobic conditions. Due to the release of H + during formation of hydrolyzed Hg(II) species which is more reactive than Hg 2+ in surface adsorption, the equilibrium pH decreased with the increase in Hg(II)/FeS molar ratio. Counteracting the loss of FeS solids at lower pH, the maximum capacity for FeS to remove aqueous Hg(II) was approximately 0.75 mol Hg(II) (mol FeS) -1 . The comparison of X-ray power diffraction (XRPD) patterns of synthetic FeS sorbent before and after sorption showed that the major products formed from the interaction between FeS and the aqueous Hg(II) were metacinnabar, cinnabar, and mercury iron sulfides. With the addition of FeS at 0.4 g L -1 to a 1 mM Hg(II) solution with an initial pH of 5.6, Fe 2+ release was approximately 0.77 mol Fe 2+ per mol Hg(II) removed, suggesting that 77% of Hg(II) was removed via precipitation reaction under these conditions, with 23% of Hg(II) removed by adsorption. Aeration does not cause significant release of Hg(II) into the water phase

Accelerating Electrostatic Surface Potential Calculation with Multiscale Approximation on Graphics Processing Units

Science.gov (United States)

Anandakrishnan, Ramu; Scogland, Tom R. W.; Fenley, Andrew T.; Gordon, John C.; Feng, Wu-chun; Onufriev, Alexey V.

2010-01-01

Tools that compute and visualize biomolecular electrostatic surface potential have been used extensively for studying biomolecular function. However, determining the surface potential for large biomolecules on a typical desktop computer can take days or longer using currently available tools and methods. Two commonly used techniques to speed up these types of electrostatic computations are approximations based on multi-scale coarse-graining and parallelization across multiple processors. This paper demonstrates that for the computation of electrostatic surface potential, these two techniques can be combined to deliver significantly greater speed-up than either one separately, something that is in general not always possible. Specifically, the electrostatic potential computation, using an analytical linearized Poisson Boltzmann (ALPB) method, is approximated using the hierarchical charge partitioning (HCP) multiscale method, and parallelized on an ATI Radeon 4870 graphical processing unit (GPU). The implementation delivers a combined 934-fold speed-up for a 476,040 atom viral capsid, compared to an equivalent non-parallel implementation on an Intel E6550 CPU without the approximation. This speed-up is significantly greater than the 42-fold speed-up for the HCP approximation alone or the 182-fold speed-up for the GPU alone. PMID:20452792

Activities at Forschungszentrum Juelich in Safeguards Analytical Techniques and Measurements

International Nuclear Information System (INIS)

Duerr, M.; Knott, A.; Middendorp, R.; Niemeyer, I.; Kueppers, S.; Zoriy, M.; Froning, M.; Bosbach, D.

2015-01-01

The application of safeguards by the IAEA involves analytical measurements of samples taken during inspections. The development and advancement of analytical techniques with support from the Member States contributes to strengthened and more efficient verification of compliance with non-proliferation obligations. Since recently, a cooperation agreement has been established between Forschungszentrum Juelich and the IAEA in the field of analytical services. The current working areas of Forschungszentrum Juelich are: (i) Production of synthetic micro-particles as calibration standard and reference material for particle analysis, (ii) qualification of the Forschungszentrum Juelich as a member of the IAEA network of analytical laboratories for safeguards (NWAL), and (iii) analysis of impurities in nuclear material samples. With respect to the synthesis of particles, a dedicated setup for the production of uranium particles is being developed, which addresses the urgent need for material tailored for its use in quality assurance and quality control measures for particle analysis of environmental swipe samples. Furthermore, Forschungszentrum Juelich has been nominated as a candidate laboratory for membership in the NWAL network. To this end, analytical capabilities at Forschungszentrum Juelich have been joined to form an analytical service within a dedicated quality management system. Another activity is the establishment of analytical techniques for impurity analysis of uranium-oxide, mainly focusing on inductively coupled mass spectrometry. This contribution will present the activities at Forschungszentrum Juelich in the area of analytical measurements and techniques for nuclear verification. (author)

Exact and analytic solutions of the Ernst equation governing axially symmetric stationary vacuum gravitational fields

International Nuclear Information System (INIS)

Baxter, Mathew; Van Gorder, Robert A

2013-01-01

We obtain solutions to a transformation of the axially symmetric Ernst equation, which governs a class of exact solutions of Einstein's field equations. Physically, the equation serves as a model of axially symmetric stationary vacuum gravitational fields. By an application of the method of homotopy analysis, we are able to construct approximate analytic solutions to the relevant boundary value problem in the case where exact solutions are not possible. The results presented constitute a solution for a complicated nonlinear and singular initial value problem. Through appropriate selection of the auxiliary linear operator and convergence control parameter, we are able to obtain low order approximations which minimize residual error over the problem domain. The benefit to such approach is that we obtain very accurate approximations after computing very few terms, hence the computational efficiency is high. Finally, an exact solution is provided in a special case, and this corresponds to the analytical solutions obtained in the more general case. The approximate solutions agree qualitatively with the exact solutions. (paper)

Analytic model for ultrasound energy receivers and their optimal electric loads II: Experimental validation

Science.gov (United States)

Gorostiaga, M.; Wapler, M. C.; Wallrabe, U.

2017-10-01

In this paper, we verify the two optimal electric load concepts based on the zero reflection condition and on the power maximization approach for ultrasound energy receivers. We test a high loss 1-3 composite transducer, and find that the measurements agree very well with the predictions of the analytic model for plate transducers that we have developed previously. Additionally, we also confirm that the power maximization and zero reflection loads are very different when the losses in the receiver are high. Finally, we compare the optimal load predictions by the KLM and the analytic models with frequency dependent attenuation to evaluate the influence of the viscosity.

Comparison of analytical and Monte Carlo calculations of multi-photon effects in bremsstrahlung emission by high-energy electrons

DEFF Research Database (Denmark)

Mangiarotti, Alessio; Sona, Pietro; Ballestrero, Sergio

2012-01-01

Approximate analytical calculations of multi-photon effects in the spectrum of total radiated energy by high-energy electrons crossing thin targets are compared to the results of Monte Carlo type simulations. The limits of validity of the analytical expressions found in the literature are establi...

Nuclear analytical techniques with neutron beams at the Univ. of Texas at Austin

International Nuclear Information System (INIS)

Uenlue, K.; Wehring, B.W.

1996-01-01

Neutron beams produced by nuclear research reactors can be used for analytical chemical analysis by measuring nuclear radiation produced by neutron capture. Prompt gamma activation analysis (PGAA) and neutron depth profiling (NDP) are two such analytical techniques. For the last three decades, these techniques have been applied at a number of research reactors around the world. Within the last 4 yr, we have developed NDP and PGAA facilities at The University of Texas at Austin research reactor, a 1-MW TRIGA Mark II reactor. Brief descriptions of the facilities and summaries of activities for these analytical techniques at the University of Texas at Austin are provided in this paper

Formulation and Analysis of an Approximate Expression for Voltage Sensitivity in Radial DC Distribution Systems

Directory of Open Access Journals (Sweden)

Ho-Yong Jeong

2015-08-01

Full Text Available Voltage is an important variable that reflects system conditions in DC distribution systems and affects many characteristics of a system. In a DC distribution system, there is a close relationship between the real power and the voltage magnitude, and this is one of major differences from the characteristics of AC distribution systems. One such relationship is expressed as the voltage sensitivity, and an understanding of voltage sensitivity is very useful to describe DC distribution systems. In this paper, a formulation for a novel approximate expression for the voltage sensitivity in a radial DC distribution system is presented. The approximate expression is derived from the power flow equation with some additional assumptions. The results of approximate expression is compared with an exact calculation, and relations between the voltage sensitivity and electrical quantities are analyzed analytically using both the exact form and the approximate voltage sensitivity equation.

A New Closed Form Approximation for BER for Optical Wireless Systems in Weak Atmospheric Turbulence

Science.gov (United States)

Kaushik, Rahul; Khandelwal, Vineet; Jain, R. C.

2018-04-01

Weak atmospheric turbulence condition in an optical wireless communication (OWC) is captured by log-normal distribution. The analytical evaluation of average bit error rate (BER) of an OWC system under weak turbulence is intractable as it involves the statistical averaging of Gaussian Q-function over log-normal distribution. In this paper, a simple closed form approximation for BER of OWC system under weak turbulence is given. Computation of BER for various modulation schemes is carried out using proposed expression. The results obtained using proposed expression compare favorably with those obtained using Gauss-Hermite quadrature approximation and Monte Carlo Simulations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

Science.gov (United States)

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens

International Nuclear Information System (INIS)

Yildirim, A.; Gökdoğan, A.; Merdan, M.; Lakshminarayanan, V.

2012-01-01

An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed, using the multi-step differential transform method based on the classical differential transformation method. Numerical results are compared to those obtained by the fourth-order Runge—Kutta method to illustrate the precision and effectiveness of the proposed method. Results are given in explicit and graphical forms. (fundamental areas of phenomenology(including applications))

Determination of tin(II) in reagents for radiopharmaceuticals

International Nuclear Information System (INIS)

Morosanova, E.I.; Loginova, K. A.; Epstein, N.B.

2003-01-01

The goal of this work is to elaborate a procedure for rapid and simple determination of tin(II) in reagents for preparation of radiopharmaceuticals based on a system albumin-Tc-99m. Original test tools for the determination of various analytes have been suggested in our lab based on the use of small glass tubes (1-2 mm i.d. - 50-70 mm) filled with indicator powders containing suitable immobilized chromogenic reagents. An analytical signal (a length of colored zone which is proportional to the concentration of an analyte) is detected after a sample passing through the indicator tube. Heteropoly compounds are well-known analytical reagents for a photometric determination of various reductants. For elaboration of indicator tubes abilities of Mo,P-heteropoly compounds to give deeply colored blue compounds after reduction were used. (authors)

Vortex sheet approximation of boundary layers

International Nuclear Information System (INIS)

Chorin, A.J.

1978-01-01

a grid free method for approximating incomprssible boundary layers is introduced. The computational elements are segments of vortex sheets. The method is related to the earlier vortex method; simplicity is achieved at the cost of replacing the Navier-Stokes equations by the Prandtl boundary layer equations. A new method for generating vorticity at boundaries is also presented; it can be used with the earlier voartex method. The applications presented include (i) flat plate problems, and (ii) a flow problem in a model cylinder- piston assembly, where the new method is used near walls and an improved version of the random choice method is used in the interior. One of the attractive features of the new method is the ease with which it can be incorporated into hybrid algorithms

Capacity of the circular plate condenser: analytical solutions for large gaps between the plates

International Nuclear Information System (INIS)

Rao, T V

2005-01-01

A solution of Love's integral equation (Love E R 1949 Q. J. Mech. Appl. Math. 2 428), which forms the basis for the analysis of the electrostatic field due to two equal circular co-axial parallel conducting plates, is considered for the case when the ratio, τ, of distance of separation to radius of the plates is greater than 2. The kernel of the integral equation is expanded into an infinite series in odd powers of 1/τ and an approximate kernel accurate to O(τ -(2N+1) ) is deduced therefrom by terminating the series after an arbitrary but finite number of terms, N. The approximate kernel is rearranged into a degenerate form and the integral equation with this kernel is reduced to a system of N linear equations. An explicit analytical solution is obtained for N = 4 and the resulting analytical expression for the capacity of the circular plate condenser is shown to be accurate to O(τ -9 ). Analytical expressions of lower orders of accuracy with respect to 1/τ are deduced from the four-term (i.e., N 4) solution and predictions (of capacity) from the expressions of different orders of accuracy (with respect to 1/τ) are compared with very accurate numerical solutions obtained by solving the linear system for large enough N. It is shown that the O(τ -9 ) approximation predicts the capacity extremely well for any τ ≥ 2 and an O(τ -3 ) approximation gives, for all practical purposes, results of adequate accuracy for τ ≥ 4. It is further shown that an approximate solution, applicable for the case of large distances of separation between the plates, due to Sneddon (Sneddon I N 1966 Mixed Boundary Value Problems in Potential Theory (Amsterdam: North-Holland) pp 230-46) is accurate to O(τ -6 ) for τ ≥ 2

Comparison of analytic models of instability of rarefied gas flow in a channel

Energy Technology Data Exchange (ETDEWEB)

Aksenova, Olga A. [St.-Petersburg State University, Department of Mathematics and Mechanics, 198504, Universitetskiy pr., 28, Peterhof, St.-Petersburg (Russian Federation); Khalidov, Iskander A. [St.-Petersburg State Polytechnic University, Department of Mathematics and Mechanics, 195251, Polytechnicheskaya ul., 29, St.-Petersburg (Russian Federation)

2014-12-09

Numerical and analytical results are compared concerning the limit properties of the trajectories, attractors and bifurcations of rarefied gas flows in channels. The cascade of bifurcations obtained in our previous analytical and numerical investigations is simulated numerically for different scattering functions V generalizing the ray-diffuse reflection of gas particles from the surface. The main purpose of numerical simulation by Monte Carlo method is the investigation of the properties of different analytic nonlinear dynamic systems corresponding to rarefied gas flow in a channel. The results are compared as well for the models suggested originally by R. N. Miroshin, as for the approximations considered for the first time or for studied in our subsequent papers. Analytical solutions we obtained earlier for the ray reflection which means only one determined velocity of scattered from the walls gas atoms, generally different from the specular reflection. The nonlinear iterative equation describing a rarefied gas flow in a long channel becomes unstable in some regions of corresponding parameters of V (it means the sensitivity to boundary conditions). The values of the parameters are found from analytical approximations in these regions. Numerical results show that the chaotic behavior of the nonlinear dynamic system corresponds to strange attractors and distinguishes clearly from Maxwellian distribution and from the equilibrium on the whole. In the regions of instability (as the dimension of the attractor increases) the search for a corresponding state requires a lot more computation time and a lot of data (the amount of data required increases exponentially with embedding dimension). Therefore the main complication in the computation is reducing as well the computing time as the amount of data to find a suitably close solution. To reduce the computing time our analytical results are applied. Flow conditions satisfying the requirements to the experiment are

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

International Nuclear Information System (INIS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2017-01-01

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics. (topical review)

Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization

Science.gov (United States)

Zhang, Li-qiang; Ma, Ting-ting; Yu, Chang-shui

2018-03-01

The computability of the quantifier of a given quantum resource is the essential challenge in the resource theory and the inevitable bottleneck for its application. Here we focus on the measurement-induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the noncontractivity of the measurement-induced nonlocality and has analytic expressions for pure states, (2 ⊗d )-dimensional quantum states, and some particular high-dimensional quantum states. Most importantly, an inverse approximate joint diagonalization algorithm, due to its simplicity, high efficiency, stability, and state independence, is presented to provide almost-analytic expressions for any quantum state, which can also shed light on other aspects in physics. To illustrate applications as well as demonstrate the validity of the algorithm, we compare the analytic and numerical expressions of various examples and show their perfect consistency.

The energy spectrum of delayed neutrons from thermal neutron induced fission of 235U and its analytical approximation

International Nuclear Information System (INIS)

Doroshenko, A.Yu.; Tarasko, M.Z.; Piksaikin, V.M.

2002-01-01

The energy spectrum of the delayed neutrons is the poorest known of all input data required in the calculation of the effective delayed neutron fractions. In addition to delayed neutron spectra based on the aggregate spectrum measurements there are two different approaches for deriving the delayed neutron energy spectra. Both of them are based on the data related to the delayed neutron spectra from individual precursors of delayed neutrons. In present work these two different data sets were compared with the help of an approximation by gamma-function. The choice of this approximation function instead of the Maxwellian or evaporation type of distribution is substantiated. (author)

Cosmological models constructed by van der Waals fluid approximation and volumetric expansion

Science.gov (United States)

Samanta, G. C.; Myrzakulov, R.

The universe modeled with van der Waals fluid approximation, where the van der Waals fluid equation of state contains a single parameter ωv. Analytical solutions to the Einstein’s field equations are obtained by assuming the mean scale factor of the metric follows volumetric exponential and power-law expansions. The model describes a rapid expansion where the acceleration grows in an exponential way and the van der Waals fluid behaves like an inflation for an initial epoch of the universe. Also, the model describes that when time goes away the acceleration is positive, but it decreases to zero and the van der Waals fluid approximation behaves like a present accelerated phase of the universe. Finally, it is observed that the model contains a type-III future singularity for volumetric power-law expansion.

Mean field approximation versus exact treatment of collisions in few-body systems

International Nuclear Information System (INIS)

Lemm, J.; Weiguny, A.; Giraud, B.G.

1990-01-01

A variational principle for calculating matrix elements of the full resolvent operator for a many-body system is studied. Its mean field approximation results in non-linear equations of Hartree (-Fock) type, with initial and final channel wave functions as driving terms. The mean field equations will in general have many solutions whereas the exact problem being linear, has a unique solution. In a schematic model with separable forces the mean field equations are analytically soluble, and for the exact problem the resulting integral equations are solved numerically. Comparing exact and mean field results over a wide range of system parameters, the mean field approach proves to be a very reliable approximation, which is not plagued by the notorious problem of defining asymptotic channels in the time-dependent mean field method. (orig.)

A simple stationary semi-analytical wake model

DEFF Research Database (Denmark)

Larsen, Gunner Chr.

We present an idealized simple, but fast, semi-analytical algorithm for computation of stationary wind farm wind fields with a possible potential within a multi-fidelity strategy for wind farm topology optimization. Basically, the model considers wakes as linear perturbations on the ambient non......-linear. With each of these approached, a parabolic system are described, which is initiated by first considering the most upwind located turbines and subsequently successively solved in the downstream direction. Algorithms for the resulting wind farm flow fields are proposed, and it is shown that in the limit......-uniform mean wind field, although the modelling of the individual stationary wake flow fields includes non-linear terms. The simulation of the individual wake contributions are based on an analytical solution of the thin shear layer approximation of the NS equations. The wake flow fields are assumed...

Time-dependent Hartree approximation and time-dependent harmonic oscillator model

International Nuclear Information System (INIS)

Blaizot, J.P.

1982-01-01

We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schroedinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory. (orig.)

Magnetic analysis of tokamak plasma with approximate MHD equilibrium solution

International Nuclear Information System (INIS)

Moriyama, Shin-ichi; Hiraki, Naoji

1993-01-01

A magnetic analysis method for determining equilibrium configuration parameters (plasma shape, poloidal beta and internal inductance) on a non-circular tokamak is described. The feature is to utilize an approximate MHD equilibrium solution which explicitly relates the configuration parameters with the magnetic fields picked up by magnetic sensors. So this method is suitable for the real-time analysis performed during a tokamak discharge. A least-squares fitting procedure is added to the analytical algorithm in order to reduce the errors in the magnetic analysis. The validity is investigated through the numerical calculation for a tokamak equilibrium model. (author)

The P1-approximation for the Distribution of Neutrons from a Pulsed Source in Hydrogen

International Nuclear Information System (INIS)

Claesson, A.

1963-12-01

The asymptotic distribution of neutrons from a pulsed, high energy source in an infinite moderator has been obtained earlier in a 'diffusion' approximation. In that paper the cross section was assumed to be constant over the whole energy region and the time derivative of the first moment was disregarded. Here, first, an analytic expression is obtained for the density in a P 1 -approximation. However, the result is very complicated, and it is shown that an asymptotic solution can be found in a simpler way. By taking into account the low hydrogen scattering cross section at the source energy it follows that the space dependence of the distribution is less than that obtained earlier. The importance of keeping the time derivative of the first moment is further shown in a perturbation approximation

First plasmas in the TJ-II flexible Heliac

NARCIS (Netherlands)

Alejaldre, C.; Alonso, J.; Almoguera, L.; Ascasibar, E.; Baciero, A.; Balbin, R.; Blaumoser, M.; Botija, J.; Branas, B.; De La Cal, E.; Cappa, A.; Carrasco, R.; Castejon, F.; Cepero, J. R.; Cremy, C.; Doncel, J.; Dulya, C.; Estrada, T.; Fernandez, A.; Frances, M.; Fuentes, C.; Garcia, A.; Garcia-Cortes, I.; Guasp, J.; Herranz, J.; Hidalgo, C.; Jimenez, J. A.; Kirpitchev, I.; Krivenski, V.; Labrador, I.; Lapayese, F.; Likin, K.; Liniers, M.; Lopez-Fraguas, A.; Lopez-Sanchez, A.; de la Luna, E.; Martin, R.; Martinez, A.; Medrano, M.; Mendez, P.; McCarthy, K.; Medina, F.; van Milligen, B.; Ochando, M.; Pacios, L.; Pastor, I.; Pedrosa, M. A.; de la Pena, A.; Portas, A.; Qin, J.; Rodriguez-Rodrigo, L.; Salas, A.; Sanchez, E.; Sanchez, J.; Tabares, F.; Tafalla, D.; Tribaldos, V.; Vaga, J.; Zurro, B.; Akulina, D.; Fadyanin, O. I.; Grebenshchicov, S.; Kharchev, N.; Meshcheryakov, A.; Barth, R.; van Dijk, G.; van der Meiden, H.; Petrov, S.

1999-01-01

The first experimental campaign of the TJ-II stellarator has been conducted using electron cyclotron resonance heating (f = 53.2 GHz, P-ECRH approximate to 250 kW) with a pulse length of Delta t approximate to (80-200) ms. The flexibility of the device has been used to study five different

Analytical Evaluation to Determine Selected PAHs in a Contaminated Soil With Type II Fuel; Metodo Optimizado de Extraccion por Ultrasonidos para la Determinacion de PAHs Seleccionados en un Suelo Contaminado con Fuel de Tipo II

Energy Technology Data Exchange (ETDEWEB)

Garcia Alonso, S.; Perez Pastor, R. M.; Sevillano Castano, M. L.; Garcia Frutos, F. J.

2010-10-21

A study on the optimization of an ultrasonic extraction method for selected PAHs determination in soil contaminated by type II fuel and by using HPLC with fluorescence detector is presented. The main objective was optimize the analytical procedure, minimizing the volume of solvent and analysis time and avoiding possible loss by evaporation. This work was carried out as part of a project that investigated a remediation process of agricultural land affected by an accidental spillage of fuel (Plan Nacional I + D + i, CTM2007-64 537). The paper is structured as: Optimization of wavelengths in the chromatographic conditions to improve resolution in the analysis of fuel samples. Optimization of the main parameters affecting in the extraction process by sonication. Comparison of results with those obtained by accelerated solvent extraction. (Author) 3 refs.

Series-produced Helium II Cryostats for the LHC Magnets Technical Choices, Industrialisation, Costs

CERN Document Server

Poncet, A

2008-01-01

Assembled in 8 continuous segments of approximately 2.7 km length each, the He II cryostats for the 1232 cryodipoles and 474 Short Straight Sections (SSS housing the quadrupoles) must fulfil tight technical requirements. They have been produced by industry in large series according to cost-effective industrial production methods to keep expenditure within the financial constraints of the project and assembled under contract at CERN. The specific technical requirements of the generic systems of the cryostat (vacuum, cryogenic, electrical distribution, magnet alignment) are briefly recalled, as well as the basic design choices leading to the definition of their components (vacuum vessels, thermal shielding, supporting systems). Early in the design process emphasis was placed on the feasibility of manufacturing techniques adequate for large series production of components, optimal tooling for time-effective assembly methods, and reliable quality assurance systems. An analytical review of the costs of the cryosta...

Does the Berry phase in a quantum optical system originate from the rotating wave approximation?

International Nuclear Information System (INIS)

Wang, Minghao; Wei, L.F.; Liang, J.Q.

2015-01-01

The Berry phase (BP) in a quantized light field demonstrated more than a decade ago (Fuentes-Guridi et al., 2002 [9]) has attracted considerable attention, since it plays an important role in the cavity quantum electrodynamics. However, it is argued in Larson (2012) [15] that such a BP is just due to the rotating wave approximation (RWA) and the relevant BP should vanish beyond this approximation. Based on a consistent analysis we conclude in this letter that the BP in a generic Rabi model actually exists, no matter whether the RWA is applied. The existence of BP is also generalized to a three-level atom in the quantized cavity field. - Highlights: • Non-zero Berry phases for the Rabi model (without rotating wave approximation) are verified. • A general formulation of Berry phases for both the JC model and the Rabi model is presented. • The claim of vanishing Berry phase in the Rabi model is a result of improper semiclassical approximation. • Analytic solutions for the Rabi model is presented in the semiclassical approximation

Finite-rank potential that reproduces the Pade approximant

International Nuclear Information System (INIS)

Tani, S.

1979-01-01