Calculation of crystalline lens power in chickens with a customized version of Bennett's equation.

Science.gov (United States)

Iribarren, Rafael; Rozema, Jos J; Schaeffel, Frank; Morgan, Ian G

2014-03-01

This paper customizes Bennett's equation for calculating lens power in chicken eyes from refraction, keratometry and biometry. Previously published data on refraction, corneal power, anterior chamber depth, lens thickness, lens radii of curvature, axial length and eye power in chickens aged 10-90 days were used to estimate Gullstrand's lens power and Bennett's lens power for chicken eyes, and to calculate the lens equivalent refractive index. Bennett's A and B constants for the front and back surface powers of the lens were calculated for data measured from day 10 to 90 at 10 day intervals, and mean customized constants were calculated. The mean customized constants for Bennett's equation for chicks were A=0.574±0.023 and B=0.379±0.021. As found previously, lens power decreases with age in chicks, while corneal power decreases and axial length increases. The lens equivalent refractive index decreases with age from 10 to 90 days after hatching. Bennett's equation can be used to calculate lens power in chicken eyes for studies on animal myopia, using standard biometry. Copyright © 2014 Elsevier B.V. All rights reserved.

Calculation of statistic estimates of kinetic parameters from substrate uncompetitive inhibition equation using the median method

Directory of Open Access Journals (Sweden)

Pedro L. Valencia

2017-04-01

Full Text Available We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974. The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis–Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax, Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].

Calculation of proper values {lambda}{sub mn}(c) of the spheroidal equation; Calcul des valeurs propres {lambda}{sub mn}(c) de l'equation spheroidale

Energy Technology Data Exchange (ETDEWEB)

Dufour, J M [CEA Limeil Valenton, 94 - Villeneuve-Saint-Georges (France)

1969-05-01

The aim of this report is to find, with a fair accuracy, a proper value {lambda}{sub mn}(c) for the spheroidal differential equation: d/dz[(1-z{sup 2})du/dz]+[ {lambda} - c{sup 2}z{sup 2} - m{sup 2}/(1-z{sup 2})]u = 0 obtained by the separation of the three variables of the wave equation: {delta}{sup 2}u + k{sup 2}u = 0 with rotational elongated or flattened ellipsoidal coordinates. The program drawn up calculates {lambda}{sub mn}(c) for any values of (mnc) chosen in the zones 0 {<=} | m | {<=} 10, a whole number; |m| {<=} n {<=} 20, n a whole number; 0 {<=} |c | {<=} 30; previous work has covered a smaller field of values. The function to be solved by the approximation method of the Newton-Raphson type, and the initial value, are chosen so as to converge towards the required solution. (author) [French] L'objet de ce rapport est de rechercher avec une tres bonne approximation, une valeur propre {lambda}{sub mn}(c) de l'equation differentielle spheroidale: d/dz[(1-z{sup 2})du/dz]+[ {lambda} - c{sup 2}z{sup 2} - m{sup 2}/1-z{sup 2}]u = 0 obtenue par separation des 3 variables de l'equation des ondes: {delta}{sup 2}u + k{sup 2}u = 0 en coordonnees des ellipsoides de revolution allonges ou aplatis. Le programme etabli calcule {lambda}{sub mn}(c) quel que soit le jeu (mnc) choisi dans le domaine 0 {<=} | m | {<=} 10 entier; |m| {<=} n {<=} 20, n entier; 0 {<=} |c | {<=} 30; alors que les etudes precedentes portaient sur un domaine plus restreint. La fonction a resoudre par la methode d'approximation du type NEWTON-RAPHSON et la valeur initiale, sont choisies de facon a converger vers la solution desiree. (auteur)

Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence

OpenAIRE

Hardouin, Charlotte; Minchenko, Andrei; Ovchinnikov, Alexey

2015-01-01

The main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential equations, via the parameterized differential and Galois theories. To achieve this, we expand the representation theory of linear differential algebraic groups and develop new algorithms that calculate unipotent radicals of parameterized differential Galois groups for differential equations whose coefficients are rational functions. P. Berman and M.F. Singer ...

Development and validation of risk prediction equations to estimate survival in patients with colorectal cancer: cohort study

OpenAIRE

Hippisley-Cox, Julia; Coupland, Carol

2017-01-01

Objective: To develop and externally validate risk prediction equations to estimate absolute and conditional survival in patients with colorectal cancer. \\ud \\ud Design: Cohort study.\\ud \\ud Setting: General practices in England providing data for the QResearch database linked to the national cancer registry.\\ud \\ud Participants: 44 145 patients aged 15-99 with colorectal cancer from 947 practices to derive the equations. The equations were validated in 15 214 patients with colorectal cancer ...

A deterministic partial differential equation model for dose calculation in electron radiotherapy.

Science.gov (United States)

Duclous, R; Dubroca, B; Frank, M

2010-07-07

High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g.Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung

A deterministic partial differential equation model for dose calculation in electron radiotherapy

Science.gov (United States)

Duclous, R.; Dubroca, B.; Frank, M.

2010-07-01

High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g. Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung

Calculation of prevalence estimates through differential equations: application to stroke-related disability.

Science.gov (United States)

Mar, Javier; Sainz-Ezkerra, María; Moler-Cuiral, Jose Antonio

2008-01-01

Neurological diseases now make up 6.3% of the global burden of disease mainly because they cause disability. To assess disability, prevalence estimates are needed. The objective of this study is to apply a method based on differential equations to calculate the prevalence of stroke-related disability. On the basis of a flow diagram, a set of differential equations for each age group was constructed. The linear system was solved analytically and numerically. The parameters of the system were obtained from the literature. The model was validated and calibrated by comparison with previous results. The stroke prevalence rate per 100,000 men was 828, and the rate for stroke-related disability was 331. The rates steadily rose with age, but the group between the ages of 65 and 74 years had the highest total number of individuals. Differential equations are useful to represent the natural history of neurological diseases and to make possible the calculation of the prevalence for the various states of disability. In our experience, when compared with the results obtained by Markov models, the benefit of the continuous use of time outweighs the mathematical requirements of our model. (c) 2008 S. Karger AG, Basel.

Nonperturbative non-Markovian quantum master equation: Validity and limitation to calculate nonlinear response functions

Science.gov (United States)

Ishizaki, Akihito; Tanimura, Yoshitaka

2008-05-01

Based on the influence functional formalism, we have derived a nonperturbative equation of motion for a reduced system coupled to a harmonic bath with colored noise in which the system-bath coupling operator does not necessarily commute with the system Hamiltonian. The resultant expression coincides with the time-convolutionless quantum master equation derived from the second-order perturbative approximation, which is also equivalent to a generalized Redfield equation. This agreement occurs because, in the nonperturbative case, the relaxation operators arise from the higher-order system-bath interaction that can be incorporated into the reduced density matrix as the influence operator; while the second-order interaction remains as a relaxation operator in the equation of motion. While the equation describes the exact dynamics of the density matrix beyond weak system-bath interactions, it does not have the capability to calculate nonlinear response functions appropriately. This is because the equation cannot describe memory effects which straddle the external system interactions due to the reduced description of the bath. To illustrate this point, we have calculated the third-order two-dimensional (2D) spectra for a two-level system from the present approach and the hierarchically coupled equations approach that can handle quantal system-bath coherence thanks to its hierarchical formalism. The numerical demonstration clearly indicates the lack of the system-bath correlation in the present formalism as fast dephasing profiles of the 2D spectra.

Fast Near-Field Calculation for Volume Integral Equations for Layered Media

DEFF Research Database (Denmark)

Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav

2005-01-01

. Afterwards, the scattered electric field can be easily computed at a regular rectangular grid on any horizontal plane us-ing a 2-dimensional FFT. This approach provides significant speedup in the near-field calculation in comparison to a straightforward numerical evaluation of the ra-diation integral since......An efficient technique based on the Fast Fourier Transform (FFT) for calculating near-field scattering by dielectric objects in layered media is presented. A higher or-der method of moments technique is employed to solve the volume integral equation for the unknown induced volume current density...

Abstract of programs for nuclear reactor calculation and kinetic equations solution

International Nuclear Information System (INIS)

Marakazov, A.A.

1977-01-01

The collection includes about 50 annotations of programmes,developed in the Kurchatov Atomic Energy Institute in 1971-1976. The programmes are intended for calculating the neutron flux, for solving systems of multigroup equations in P 3 approximation, for calculating the reactor cell, for analysing the system stability, breeding ratio etc. The programme annotations are compiled according to the following diagram: 1.Programme title. 2.Computer type. 3.Physical problem. 4.Solution method. 5.Calculation limitations. 6.Characteristic computer time. 7.Programme characteristic features. 8.Bound programmes. 9.Programme state. 10.Literature allusions in the programme. 11.Required memory resourses. 12.Programming language. 13.Operation system. 14.Names of authors and place of programme adjusting

Automatic calculation of supersymmetric renormalization group equations and loop corrections

Science.gov (United States)

Staub, Florian

2011-03-01

SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. This information can be used by SARAH to write model files for CalcHep/ CompHep or FeynArts/ FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the superpotential and soft-breaking parameters at one- and two-loop level. Furthermore, it calculates the one-loop self-energies and the one-loop corrections to the tadpoles. SARAH can handle all N=1 SUSY models whose gauge sector is a direct product of SU(N) and U(1) gauge groups. The particle content of the model can be an arbitrary number of chiral superfields transforming as any irreducible representation with respect to the gauge groups. To implement a new model, the user has just to define the gauge sector, the particle, the superpotential and the field rotations to mass eigenstates. Program summaryProgram title: SARAH Catalogue identifier: AEIB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIB_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.: 97 577 No. of bytes in distributed program, including test data, etc.: 2 009 769 Distribution format: tar.gz Programming language: Mathematica Computer: All systems that Mathematica is available for Operating system: All systems that Mathematica is available for Classification: 11.1, 11.6 Nature of problem: A supersymmetric model is usually characterized by the particle content, the gauge sector and the superpotential. It is a time consuming process to obtain all necessary information for phenomenological studies from these basic ingredients. Solution method: SARAH calculates the complete Lagrangian for a given model whose

Variational Calculation for the Equation of State of Hot Asymmetric Nuclear Matter

International Nuclear Information System (INIS)

Togashi, Hajime; Kanzawa, Hiroaki; Takano, Masatoshi

2010-01-01

We calculate the equation of state (EOS) of asymmetric nuclear matter at finite temperatures with the cluster variational method based on the realistic nuclear Hamiltonian composed of the AV18 and UIX nuclear potentials. The free energy is calculated with an extension of the variational method proposed by Schmidt and Pandharipande. The obtained thermodynamic quantities such as entropy, internal energy, pressure and chemical potential derived from the free energy are reasonable. It is also found that the present variational calculation is self-consistent. These thermodynamic quantities are essential ingredients in our project for constructing a new nuclear EOS applicable to supernova simulations.

Isothermal Multiphase Flash Calculations with the PC-SAFT Equation of State

International Nuclear Information System (INIS)

Justo-Garcia, Daimler N.; Garcia-Sanchez, Fernando; Romero-Martinez, Ascencion

2008-01-01

A computational approach for isothermal multiphase flash calculations with the PC-SAFT (Perturbed-Chain Statistical Associating Fluid Theory) equation of state is presented. In the framework of the study of fluid phase equilibria of multicomponent systems, the general multiphase problem is the single most important calculation which consists of finding the correct number and types of phases and their corresponding equilibrium compositions such that the Gibbs energy of the system is a minimum. For solving this problem, the system Gibbs energy was minimized using a rigorous method for thermodynamic stability analysis to find the most stable state of the system. The efficiency and reliability of the approach to predict and calculate complex phase equilibria are illustrated by solving three typical problems encountered in the petroleum industry

Equations for calculating hydrogeochemical reactions of minerals and gases such as CO2 at high pressures and temperatures

Science.gov (United States)

Appelo, C. A. J.; Parkhurst, D. L.; Post, V. E. A.

2014-01-01

Calculating the solubility of gases and minerals at the high pressures of carbon capture and storage in geological reservoirs requires an accurate description of the molar volumes of aqueous species and the fugacity coefficients of gases. Existing methods for calculating the molar volumes of aqueous species are limited to a specific concentration matrix (often seawater), have been fit for a limited temperature (below 60 °C) or pressure range, apply only at infinite dilution, or are defined for salts instead of individual ions. A more general and reliable calculation of apparent molar volumes of single ions is presented, based on a modified Redlich-Rosenfeld equation. The modifications consist of (1) using the Born equation to calculate the temperature dependence of the intrinsic volumes, following Helgeson-Kirkham-Flowers (HKF), but with Bradley and Pitzer’s expression for the dielectric permittivity of water, (2) using the pressure dependence of the extended Debye-Hückel equation to constrain the limiting slope of the molar volume with ionic strength, and (3) adopting the convention that the proton has zero volume at all ionic strengths, temperatures and pressures. The modifications substantially reduce the number of fitting parameters, while maintaining or even extending the range of temperature and pressure over which molar volumes can be accurately estimated. The coefficients in the HKF-modified-Redlich-Rosenfeld equation were fitted by least-squares on measured solution densities. The limiting volume and attraction factor in the Van der Waals equation of state can be estimated with the Peng-Robinson approach from the critical temperature, pressure, and acentric factor of a gas. The Van der Waals equation can then be used to determine the fugacity coefficients for pure gases and gases in a mixture, and the solubility of the gas can be calculated from the fugacity, the molar volume in aqueous solution, and the equilibrium constant. The coefficients for the

Simple renormalization group method for calculating geometrical and other equations of states

International Nuclear Information System (INIS)

Tsallis, C.; Schwaccheim, G.; Coniglio, A.

1984-01-01

A real space renormalization group procedure to calculate geometrical and thermal equations of states for the entire range of values of the external parameters is described. Its use is as simple as a Mean Field Approximation; however, it yields non trivial results and can be systematically improved. Such a procedure is illustrated by calculating, for all bond concentrations, the site mass density for the complete and the backbone percolating infinite clusters in square lattice: the results are quite satisfactory. (Author) [pt

Numerical calculation of the cross section by the solution of the wave equation

International Nuclear Information System (INIS)

Drewko, J.

1982-01-01

A numerical method of solving of the wave equation is described for chosen vibrational eigenfunctions. A prepared program calculates the total cross sections for the resonant vibrational excitation for diatomic molecules on the basis of introduced molecular data. (author)

Equations for calculating hydrogeochemical reactions of minerals and gases such as CO2 at high pressures and temperatures

Science.gov (United States)

Appelo, C.A.J.; Parkhurst, David L.; Post, V.E.A.

2014-01-01

Calculating the solubility of gases and minerals at the high pressures of carbon capture and storage in geological reservoirs requires an accurate description of the molar volumes of aqueous species and the fugacity coefficients of gases. Existing methods for calculating the molar volumes of aqueous species are limited to a specific concentration matrix (often seawater), have been fit for a limited temperature (below 60 °C) or pressure range, apply only at infinite dilution, or are defined for salts instead of individual ions. A more general and reliable calculation of apparent molar volumes of single ions is presented, based on a modified Redlich–Rosenfeld equation. The modifications consist of (1) using the Born equation to calculate the temperature dependence of the intrinsic volumes, following Helgeson–Kirkham–Flowers (HKF), but with Bradley and Pitzer’s expression for the dielectric permittivity of water, (2) using the pressure dependence of the extended Debye–Hückel equation to constrain the limiting slope of the molar volume with ionic strength, and (3) adopting the convention that the proton has zero volume at all ionic strengths, temperatures and pressures. The modifications substantially reduce the number of fitting parameters, while maintaining or even extending the range of temperature and pressure over which molar volumes can be accurately estimated. The coefficients in the HKF-modified-Redlich–Rosenfeld equation were fitted by least-squares on measured solution densities.The limiting volume and attraction factor in the Van der Waals equation of state can be estimated with the Peng–Robinson approach from the critical temperature, pressure, and acentric factor of a gas. The Van der Waals equation can then be used to determine the fugacity coefficients for pure gases and gases in a mixture, and the solubility of the gas can be calculated from the fugacity, the molar volume in aqueous solution, and the equilibrium constant. The

High energy ion range and deposited energy calculation using the Boltzmann-Fokker-Planck splitting of the Boltzmann transport equation

International Nuclear Information System (INIS)

Mozolevski, I.E.

2001-01-01

We consider the splitting of the straight-ahead Boltzmann transport equation in the Boltzmann-Fokker-Planck equation, decomposing the differential cross-section into a singular part, corresponding to small energy transfer events, and in a regular one, which corresponds to large energy transfer. The convergence of implantation profile, nuclear and electronic energy depositions, calculated from the Boltzmann-Fokker-Planck equation, to the respective exact distributions, calculated from Monte-Carlo method, was exanimate in a large-energy interval for various values of splitting parameter and for different ion-target mass relations. It is shown that for the universal potential there exists an optimal value of splitting parameter, for which range and deposited energy distributions, calculated from the Boltzmann-Fokker-Planck equation, accurately approximate the exact distributions and which minimizes the computational expenses

Calculation of the Intensity of electrical field at the end of the loaded path in the solid-state nuclear track detectors by using the numerical calculation of Laplace equations

International Nuclear Information System (INIS)

Kolahdooz, M.; Abotalebi, A.; Sheikh Aleslam, F.

2011-01-01

The goal of this article is calculation of the electric field at the end of loaded path in solid-state track detectors. For the calculation, Laplace-Equation has been solved numerically. By solving the equation, upon considering a specific potential at the boundary of the region, in addition to calculating the electric field at the end of path, the parameters which are affecting the electric field have also been investigated.

A Poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows

Science.gov (United States)

Sohn, J. L.; Heinrich, J. C.

1990-01-01

The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.

A model expansion criterion for treating surface topography in ray path calculations using the eikonal equation

International Nuclear Information System (INIS)

Ma, Ting; Zhang, Zhongjie

2014-01-01

Irregular surface topography has revolutionized how seismic traveltime is calculated and the data are processed. There are two main schemes for dealing with an irregular surface in the seismic first-arrival traveltime calculation: (1) expanding the model and (2) flattening the surface irregularities. In the first scheme, a notional infill medium is added above the surface to expand the physical space into a regular space, as required by the eikonal equation solver. Here, we evaluate the chosen propagation velocity in the infill medium through ray path tracking with the eikonal equation-solved traveltime field, and observe that the ray paths will be physically unrealistic for some values of this propagation velocity. The choice of a suitable propagation velocity in the infill medium is crucial for seismic processing of irregular topography. Our model expansion criterion for dealing with surface topography in the calculation of traveltime and ray paths using the eikonal equation highlights the importance of both the propagation velocity of the infill physical medium and the topography gradient. (paper)

Interaction and collective effects in classical-equations-of-motion calculations

International Nuclear Information System (INIS)

Bodmer, A.R.

1981-01-01

We discuss results obtained with the classical-equations-of-motion (CEOM) approach, with particular reference to interaction (potential energy) and collective effects in central collisions of equal mass nuclei. The essence of the CEOM approach is the classical calculation of all A = A/sub P/ + A/sub T/ trajectories using a 2-body potential V between all pairs of nucleons; V = V/sub short/ + V/sub long/ has a short range repulsion and a longer range attractive tail. In contrast to hydrodynamics, the CEOM approach is microscopic and includes transparency and nonequilibrium effects

A four-equation friction model for water hammer calculation in quasi-rigid pipelines

International Nuclear Information System (INIS)

Ghodhbani, Abdelaziz; Haj Taïeb, Ezzeddine

2017-01-01

Friction coupling affects water hammer evolution in pipelines according to the initial flow regime. Unsteady friction models are only validated with uncoupled formulation. On the other hand, coupled models such as four-equation model, provide more accurate prediction of water hammer since fluid-structure interaction (FSI) is taken into account, but they are limited to steady-state friction formulation. This paper deals with the creation of the “four-equation friction model” which is based on the incorporation of the unsteady head loss given by an unsteady friction model into the four-equation model. For transient laminar flow cases, the Zielke model is considered. The proposed model is applied to a quasi-rigid pipe with axial moving valve, and then calculated by the method of characteristics (MOC). Damping and shape of the numerical solution are in good agreement with experimental data. Thus, the proposed model can be incorporated into a new computer code. - Highlights: • Both Zielke model and four-equation model are insufficient to predict water hammer. • The four-equation friction model proposed is obtained by incorporating the unsteady head loss in the four-equation model. • The solution obtained by the proposed model is in good agreement with experimental data. • The wave-speed adjustment scheme is more efficient than interpolations schemes.

The two-wave X-ray field calculated by means of integral-equation methods

International Nuclear Information System (INIS)

Bremer, J.

1984-01-01

The problem of calculating the two-wave X-ray field on the basis of the Takagi-Taupin equations is discussed for the general case of curved lattice planes. A two-dimensional integral equation which incorporates the nature of the incoming radiation, the form of the crystal/vacuum boundary, and the curvature of the structure, is deduced. Analytical solutions for the symmetrical Laue case with incoming plane waves are obtained directly for perfect crystals by means of iteration. The same method permits a simple derivation of the narrow-wave Laue and Bragg cases. Modulated wave fronts are discussed, and it is shown that a cut-off in the width of an incoming plane wave leads to lateral oscillations which are superimposed on the Pendelloesung fringes. Bragg and Laue shadow fields are obtained. The influence of a non-zero kernel is discussed and a numerical procedure for calculating wave amplitudes in curved crystals is presented. (Auth.)

On the calculation of linear stability with the aid of asymptotic solutions of Orr-Sommerfeld equation, 1

International Nuclear Information System (INIS)

Fujimura, Kaoru

1980-11-01

The numerical treatment of Orr-Sommerfeld equation which is the fundamental equation of linear hydrodynamic stability theory is described. Present calculation procedure is applied to the two-dimensional quasi-parallel flow for which linearized disturbance equation (Orr-Sommerfeld equation) contains one simple turning point and αR >> 1. The numerical procedure for this problem and one numerical example for Jeffery-Hamel flow (J-H III 1 ) are presented. These treatment can be extended to the other velocity profiles by slight midifications. (author)

The transition equation of the state intensities for exciton model and the calculation program

International Nuclear Information System (INIS)

Yu Xian; Zheng Jiwen; Liu Guoxing; Chen Keliang

1995-01-01

An equation set of the exciton model is given and calculation program is developed. The process of approaching to equilibrium state has been investigated with the program for 12 C + 64 Ni reaction at energy 72 MeV

Efficient implementation of core-excitation Bethe-Salpeter equation calculations

Science.gov (United States)

Gilmore, K.; Vinson, John; Shirley, E. L.; Prendergast, D.; Pemmaraju, C. D.; Kas, J. J.; Vila, F. D.; Rehr, J. J.

2015-12-01

We present an efficient implementation of the Bethe-Salpeter equation (BSE) method for obtaining core-level spectra including X-ray absorption (XAS), X-ray emission (XES), and both resonant and non-resonant inelastic X-ray scattering spectra (N/RIXS). Calculations are based on density functional theory (DFT) electronic structures generated either by ABINIT or QuantumESPRESSO, both plane-wave basis, pseudopotential codes. This electronic structure is improved through the inclusion of a GW self energy. The projector augmented wave technique is used to evaluate transition matrix elements between core-level and band states. Final two-particle scattering states are obtained with the NIST core-level BSE solver (NBSE). We have previously reported this implementation, which we refer to as OCEAN (Obtaining Core Excitations from Ab initio electronic structure and NBSE) (Vinson et al., 2011). Here, we present additional efficiencies that enable us to evaluate spectra for systems ten times larger than previously possible; containing up to a few thousand electrons. These improvements include the implementation of optimal basis functions that reduce the cost of the initial DFT calculations, more complete parallelization of the screening calculation and of the action of the BSE Hamiltonian, and various memory reductions. Scaling is demonstrated on supercells of SrTiO3 and example spectra for the organic light emitting molecule Tris-(8-hydroxyquinoline)aluminum (Alq3) are presented. The ability to perform large-scale spectral calculations is particularly advantageous for investigating dilute or non-periodic systems such as doped materials, amorphous systems, or complex nano-structures.

Standardization of equations for radiochemical calculations

International Nuclear Information System (INIS)

Danahy, R.J.; Dugan, T.A.; Tomlinson, F.K.; Jones, H.W.

1994-01-01

In mid 1993, the Fernald Environmental Restoration Management Corporation (FERMCO), with USEPA approval implemented a project quality assurance plan containing performance-based specifications for radiochemical sample analyses conducted in support of the Fernald site remediation activities. FERMCO's initial approach to acquiring performance-based radioanalytical services was to provide limited guidance regarding equations for computation of the quantities required in each analysis report. It became evident that there was a significant divergence of opinion on how to compute some very basic radiochemical quantities. The use of a standardized set of equations was needed in order to ensure comparability of data from different laboratories. In a remediation project of this magnitude, use of multiple laboratories is a virtual necessity. Consequently comparability of data becomes an extremely important issue. A critical issue in the Remedial Investigation/Feasibility Study (RI/FS) phase of the dean up project is to avoid the occurrence of excessive false positive sample results. Such results could lead to unnecessary clean up and significant additional cost. This paper describes the specific formulas FERMCO is currently using to define such quantities as net sample count rate, sample radionuclide concentration, radiometric tracer and gravimetric carrier recovery. Equations have also been produced to define the uncertainty in each of the above quantities. Equations for the Total Propagated Uncertainty (TPU) and for a sample-specific Minimum Detectable Concentration (MDC) have also been specified. Generalized equations have been reformulated to address the specific conditions which apply to the analysis of FERMCO samples. In particular, FERMCO requires results which have been corrected for the radioactivity in the blank while in other instances, sample results without blank correction are required

Resolution of the multigroup scattering equation in a one-dimensional geometry and subsidiary calculations: the MUDE code; Resolution de l'equation multigroupe de la diffusion dans une geometrie a une dimension et calculs annexes: code MUDE

Energy Technology Data Exchange (ETDEWEB)

Bore, C; Dandeu, Y; Saint-Amand, Ch [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1965-07-01

MUDE is a nuclear code written in FORTRAN II for IBM 7090-7094. It resolves a system of difference equations approximating to the one-dimensional multigroup neutron scattering problem. More precisely, this code makes it possible to: 1. Calculate the critical condition of a reactor (k{sub eff}, critical radius, critical composition) and the corresponding fluxes; 2. Calculate the associated fluxes and various subsidiary results; 3. Carry out perturbation calculations; 4. Study the propagation of fluxes at a distance; 5. Estimate the relative contributions of the cross sections (macroscopic or microscopic); 6. Study the changes with time of the composition of the reactor. (authors) [French] MUDE est un code nucleaire ecrit en FORTRAN II pour IBM 7090-7094. Il resout un systeme d'equations aux differences approchant le probleme de diffusion neutronique multigroupe a une dimension. Plus precisement ce code permet de: 1. Calculer la condition critique d'un reacteur (k{sub eff}, rayon critique, composition critique) et les flux correspondants; 2. Calculer les flux adjoints et divers resultats connexes; 3. Effectuer des calculs de perturbation; 4. Etudier la propagation des flux a longue distance; 5. Ponderer des sections efficaces (macroscopiques ou microscopiques); 6. Etudier l'evolution de la composition du reacteur au cours du temps. (auteurs)

Calculation of similarity solutions of partial differential equations

International Nuclear Information System (INIS)

Dresner, L.

1980-08-01

When a partial differential equation in two independent variables is invariant to a group G of stretching transformations, it has similarity solutions that can be found by solving an ordinary differential equation. Under broad conditions, this ordinary differential equation is also invariant to another stretching group G', related to G. The invariance of the ordinary differential equation to G' can be used to simplify its solution, particularly if it is of second order. Then a method of Lie's can be used to reduce it to a first-order equation, the study of which is greatly facilitated by analysis of its direction field. The method developed here is applied to three examples: Blasius's equation for boundary layer flow over a flat plate and two nonlinear diffusion equations, cc/sub t/ = c/sub zz/ and c/sub t/ = (cc/sub z/)/sub z/

Statistical Average of Spin Operators for Calculation of Three-Component Magnetization (II): Solution of Equation

International Nuclear Information System (INIS)

Wang Huaiyu; Long Yao; Chen Nanxian

2006-01-01

In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green's function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.

Calculating the renormalisation group equations of a SUSY model with Susyno

Science.gov (United States)

Fonseca, Renato M.

2012-10-01

Susyno is a Mathematica package dedicated to the computation of the 2-loop renormalisation group equations of a supersymmetric model based on any gauge group (the only exception being multiple U(1) groups) and for any field content. Program summary Program title: Susyno Catalogue identifier: AEMX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMX_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.: 30829 No. of bytes in distributed program, including test data, etc.: 650170 Distribution format: tar.gz Programming language: Mathematica 7 or higher. Computer: All systems that Mathematica 7+ is available for (PC, Mac). Operating system: Any platform supporting Mathematica 7+ (Windows, Linux, Mac OS). Classification: 4.2, 5, 11.1. Nature of problem: Calculating the renormalisation group equations of a supersymmetric model involves using long and complicated general formulae [1, 2]. In addition, to apply them it is necessary to know the Lagrangian in its full form. Building the complete Lagrangian of models with small representations of SU(2) and SU(3) might be easy but in the general case of arbitrary representations of an arbitrary gauge group, this task can be hard, lengthy and error prone. Solution method: The Susyno package uses group theoretical functions to calculate the super-potential and the soft-SUSY-breaking Lagrangian of a supersymmetric model, and calculates the two-loop RGEs of the model using the general equations of [1, 2]. Susyno works for models based on any representation(s) of any gauge group (the only exception being multiple U(1) groups). Restrictions: As the program is based on the formalism of [1, 2], it shares its limitations. Running time can also be a significant restriction, in particular for models with many fields. Unusual features

Choosing of mode and calculation of multiple regression equation parameters in X-ray radiometric analysis

International Nuclear Information System (INIS)

Mamikonyan, S.V.; Berezkin, V.V.; Lyubimova, S.V.; Svetajlo, Yu.N.; Shchekin, K.I.

1978-01-01

A method to derive multiple regression equations for X-ray radiometric analysis is described. Te method is realized in the form of the REGRA program in an algorithmic language. The subprograms included in the program are describe. In analyzing cement for Mg, Al, Si, Ca and Fe contents as an example, the obtainment of working equations in the course of calculations by the program is shown to simpliy the realization of computing devices in instruments for X-ray radiometric analysis

DIFFERENTIAL EQUATION SIMULATION IN CALCULATION OF LATERAL AND TRANSVERSE-LONGITUDINAL BENDING OF FRAME STRUCTURES WITHOUT AND WITH DUE ACCOUNT OF VISCOELASTIC MATERIAL PROPERTIES

Directory of Open Access Journals (Sweden)

V. M. Ovsianko

2012-01-01

Full Text Available The paper reveals a brand-new direction in simulation of frame and continual structures while calculating static and dynamic loads and stability.  An electronic model has been synthesized  for an investigated object and then it has been analyzed not with the help of  specialized analog computing techniques but by means of high-performance software package for electronic circuit calculation using a personal computer.The given paper contains exact algebraic equations corresponding to differential equations for lateral bending calculation of frame structures without and with due account of viscoelastic material properties in compliance with the Kelvin model.The exact algebraic equation for a beam on elastic supports (or elastic Winkler foundation has been derived for quartic differential equation.The paper presents a number of exact algebraic equations which are equivalent to differential equations for transverse-longitudinal bending calculation of frame structures without and with due account of viscoelastic material properties when lateral and longitudinal loads are applied in the form of  impulses with any periods of their duration and any interchangeability. 

Development and external multicenter validation of Chinese Prostate Cancer Consortium prostate cancer risk calculator for initial prostate biopsy.

Science.gov (United States)

Chen, Rui; Xie, Liping; Xue, Wei; Ye, Zhangqun; Ma, Lulin; Gao, Xu; Ren, Shancheng; Wang, Fubo; Zhao, Lin; Xu, Chuanliang; Sun, Yinghao

2016-09-01

Substantial differences exist in the relationship of prostate cancer (PCa) detection rate and prostate-specific antigen (PSA) level between Western and Asian populations. Classic Western risk calculators, European Randomized Study for Screening of Prostate Cancer Risk Calculator, and Prostate Cancer Prevention Trial Risk Calculator, were shown to be not applicable in Asian populations. We aimed to develop and validate a risk calculator for predicting the probability of PCa and high-grade PCa (defined as Gleason Score sum 7 or higher) at initial prostate biopsy in Chinese men. Urology outpatients who underwent initial prostate biopsy according to the inclusion criteria were included. The multivariate logistic regression-based Chinese Prostate Cancer Consortium Risk Calculator (CPCC-RC) was constructed with cases from 2 hospitals in Shanghai. Discriminative ability, calibration and decision curve analysis were externally validated in 3 CPCC member hospitals. Of the 1,835 patients involved, PCa was identified in 338/924 (36.6%) and 294/911 (32.3%) men in the development and validation cohort, respectively. Multivariate logistic regression analyses showed that 5 predictors (age, logPSA, logPV, free PSA ratio, and digital rectal examination) were associated with PCa (Model 1) or high-grade PCa (Model 2), respectively. The area under the curve of Model 1 and Model 2 was 0.801 (95% CI: 0.771-0.831) and 0.826 (95% CI: 0.796-0.857), respectively. Both models illustrated good calibration and substantial improvement in decision curve analyses than any single predictors at all threshold probabilities. Higher predicting accuracy, better calibration, and greater clinical benefit were achieved by CPCC-RC, compared with European Randomized Study for Screening of Prostate Cancer Risk Calculator and Prostate Cancer Prevention Trial Risk Calculator in predicting PCa. CPCC-RC performed well in discrimination and calibration and decision curve analysis in external validation compared

Empirical rate equation model and rate calculations of hydrogen generation for Hanford tank waste

International Nuclear Information System (INIS)

HU, T.A.

1999-01-01

Empirical rate equations are derived to estimate hydrogen generation based on chemical reactions, radiolysis of water and organic compounds, and corrosion processes. A comparison of the generation rates observed in the field with the rates calculated for twenty eight tanks shows agreement within a factor of two to three

Development and External Validation of the Korean Prostate Cancer Risk Calculator for High-Grade Prostate Cancer: Comparison with Two Western Risk Calculators in an Asian Cohort.

Science.gov (United States)

Park, Jae Young; Yoon, Sungroh; Park, Man Sik; Choi, Hoon; Bae, Jae Hyun; Moon, Du Geon; Hong, Sung Kyu; Lee, Sang Eun; Park, Chanwang; Byun, Seok-Soo

2017-01-01

We developed the Korean Prostate Cancer Risk Calculator for High-Grade Prostate Cancer (KPCRC-HG) that predicts the probability of prostate cancer (PC) of Gleason score 7 or higher at the initial prostate biopsy in a Korean cohort (http://acl.snu.ac.kr/PCRC/RISC/). In addition, KPCRC-HG was validated and compared with internet-based Western risk calculators in a validation cohort. Using a logistic regression model, KPCRC-HG was developed based on the data from 602 previously unscreened Korean men who underwent initial prostate biopsies. Using 2,313 cases in a validation cohort, KPCRC-HG was compared with the European Randomized Study of Screening for PC Risk Calculator for high-grade cancer (ERSPCRC-HG) and the Prostate Cancer Prevention Trial Risk Calculator 2.0 for high-grade cancer (PCPTRC-HG). The predictive accuracy was assessed using the area under the receiver operating characteristic curve (AUC) and calibration plots. PC was detected in 172 (28.6%) men, 120 (19.9%) of whom had PC of Gleason score 7 or higher. Independent predictors included prostate-specific antigen levels, digital rectal examination findings, transrectal ultrasound findings, and prostate volume. The AUC of the KPCRC-HG (0.84) was higher than that of the PCPTRC-HG (0.79, pexternal validation. Calibration plots also revealed better performance of KPCRC-HG and ERSPCRC-HG than that of PCPTRC-HG on external validation. At a cut-off of 5% for KPCRC-HG, 253 of the 2,313 men (11%) would not have been biopsied, and 14 of the 614 PC cases with Gleason score 7 or higher (2%) would not have been diagnosed. KPCRC-HG is the first web-based high-grade prostate cancer prediction model in Korea. It had higher predictive accuracy than PCPTRC-HG in a Korean population and showed similar performance with ERSPCRC-HG in a Korean population. This prediction model could help avoid unnecessary biopsy and reduce overdiagnosis and overtreatment in clinical settings.

A Direct Radiative Transfer Equation Solver for Path Loss Calculation of Underwater Optical Wireless Channels

KAUST Repository

Li, Changping; Park, Ki-Hong; Alouini, Mohamed-Slim

2014-01-01

In this report, we propose a fast numerical solution for the steady state radiative transfer equation in order to calculate the path loss due to light absorption and scattering in various type of underwater channels. In the proposed scheme, we apply a direct non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. The accuracy and efficiency of the proposed scheme is validated by Monte Carlo simulations.

A Direct Radiative Transfer Equation Solver for Path Loss Calculation of Underwater Optical Wireless Channels

KAUST Repository

Li, Changping

2014-11-10

In this report, we propose a fast numerical solution for the steady state radiative transfer equation in order to calculate the path loss due to light absorption and scattering in various type of underwater channels. In the proposed scheme, we apply a direct non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. The accuracy and efficiency of the proposed scheme is validated by Monte Carlo simulations.

Microscopic equation of state calculations: 1. Nuclear matter. 2. Liquid helium 3

International Nuclear Information System (INIS)

Heyer, J.P.

1989-01-01

A new method for calculating the equation of state of extended Fermi systems is proposed and applied to nuclear matter and liquid 3 He. New techniques are developed for summing up the particle-particle (pp) and particle-hole (ph) ring diagrams to all orders in the calculation of the ground state shift ΔE 0 for many-body systems. Analytic expressions for ΔE pp P 0 , the contribution from all of the pp ring diagrams to ΔE 0 , and ΔE ph 0 , the corresponding contribution from all of the ph ring diagrams, have been obtained. It has been shown that the pp ring diagram sum may be written as an integral over frequency, involving the particle-particle Green's function. A similar integral expression is derived for the ph ring diagram sum. Two methods are developed for carrying out the frequency integrations, namely the multipole and transition amplitude methods. These methods have been tested on an exactly-solvable many-fermion model, a modified Lipkin model, and compared. The author has studied the instability of nuclear matter at both zero and finite temperature within the pp ring diagram framework. He has found using the Gogny D1 effective nucleon-nucleon interaction, complex eigenvalues of an RPA-type secular equation are obtained in a well-defined temperature-density region. When complex eigenvalues occur, the thermodynamic potential becomes complex. The possible connection between the occurrence of complex eigenvalues and liquid-gas phase separation is discussed. The pp ring diagrams are also found to lower the compression modulus of nuclear matter. Lastly, the pp ring diagram method is applied to the calculation of the ground state energy of normal and spin-polarized liquid 3 He. We have found a binding energy per particle (BE/A) of 1.45 degree K and 1.79 degree K for the normal and spin-polarized systems, respectively

Quadratic-linear pattern in cancer fractional radiotherapy. Equations for a computering program

International Nuclear Information System (INIS)

Burgos, D.; Bullejos, J.; Garcia Puche, J.L.; Pedraza, V.

1990-01-01

Knowledge of equivalence between different tratment schemes with the same iso-effect is the essential thing in clinical cancer radiotherapy. For this purpose it is very useful the group of ideas derived from quadratic-linear pattern (Q-L) proposed in order to analyze cell survival curve to radiation. Iso-effect definition caused by several irradiation rules is done by extrapolated tolerance dose (ETD). Because equations for ETD are complex, a computering program have been carried out. In this paper, iso-effect equations for well defined therapeutic situations and flow diagram proposed for resolution, have been studied. (Author)

A reduction method for phase equilibrium calculations with cubic equations of state

Directory of Open Access Journals (Sweden)

D. V. Nichita

2006-09-01

Full Text Available In this work we propose a new reduction method for phase equilibrium calculations using a general form of cubic equations of state (CEOS. The energy term in the CEOS is a quadratic form, which is diagonalized by applying a linear transformation. The number of the reduction parameters is related to the rank of the matrix C with elements (1-Cij, where Cij denotes the binary interaction parameters (BIPs. The dimensionality of the problem depends only on the number of reduction parameters, and is independent of the number of components in the mixture.

Calculational and experimental approaches to the equation of state of irradiated fuel

International Nuclear Information System (INIS)

Bober, M.; Breitung, W.; Karow, H.U.; Schumacher, G.

1977-07-01

The oxygen potential is an important parameter for the estimation of the vapor pressure of mixed oxide fuel and fission products. Dissolved fission products can have great influence on this potential in hypostoichiometric fuel. Therefore an attempt was made to calculate oxygen potentials of uranium-plutonium mixed oxides which contain fission products using models based on the equilibrium of oxygen defects. Vapor pressures have been calculated applying these data. The results of the calculation with various models differ especially at high temperatures above 4,000 K. Experimental work has been done to determine the vapor pressure of oxide fuel material at temperatures between 3,000 K and 5,000 K using laser beam heating. A measuring technique and a detailed evaluation model of laser evaporation measurements have been developed. The evaluation model describes the complex phenomena occurring during surface evaporation of liquid oxide fuel. Vapor pressure measurements with UO 2 have been carried out in the temperature region up to 4,500 K. With thermodynamic calculations the required equilibrium vapor pressures (EOS) can be derived from the vapor pressures measured. The caloric equation-of-state of the liquid-vapor equilibrium of the fuel up to temperatures of 5,000 K has been considered theoretically. (orig.) [de

Application of the method of integral equations to calculating the electrodynamic characteristics of periodically corrugated waveguides

International Nuclear Information System (INIS)

Belov, V.E.; Rodygin, L.V.; Fil'chenko, S.E.; Yunakovskii, A.D.

1988-01-01

A method is described for calculating the electrodynamic characteristics of periodically corrugated waveguide systems. This method is based on representing the field as the solution of the Helmholtz vector equation in the form of a simple layer potential, transformed with the use of the Floquet conditions. Systems of compound integral equations based on a weighted vector function of the simple layer potential are derived for waveguides with azimuthally symmetric and helical corrugations. A numerical realization of the Fourier method is cited for seeking the dispersion relation of azimuthally symmetric waves of a circular corrugated waveguide

Toward enabling large-scale open-shell equation-of-motion coupled cluster calculations: triplet states of β-carotene

Energy Technology Data Exchange (ETDEWEB)

Hu, Hanshi; Bhaskaran-Nair, Kiran; Apra, Edoardo; Govind, Niranjan; Kowalski, Karol

2014-10-02

In this paper we discuss the application of novel parallel implementation of the coupled cluster (CC) and equation-of-motion coupled cluster methods (EOMCC) in calculations of excitation energies of triplet states in beta-carotene. Calculated excitation energies are compared with experimental data, where available. We also provide a detailed description of the new parallel algorithms for iterative CC and EOMCC models involving single and doubles excitations.

Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Convergence and Testing

International Nuclear Information System (INIS)

Reynolds, J. M.; Lopez-Bruna, D.

2009-01-01

This report is the third of a series [Informes Tecnicos Ciemat 1165 y 1172] devoted to the development of a new numerical code to solve the guiding center equation for electrons and ions in toroidal plasmas. Two calculation meshes corresponding to axisymmetric tokamaks are now prepared and the kinetic equation is expanded so the standard terms of neoclassical theory --fi rst order terms in the Larmor radius expansion-- can be identified, restricting the calculations correspondingly. Using model density and temperature profiles for the plasma, several convergence test are performed depending on the calculation meshes and the expansions of the distribution function; then the results are compared with the theory [Hinton and Hazeltine, Rev. Mod. Phys. (1976)]. (Author) 18 refs

A Study on the Consistency of Discretization Equation in Unsteady Heat Transfer Calculations

Directory of Open Access Journals (Sweden)

Wenhua Zhang

2013-01-01

Full Text Available The previous studies on the consistency of discretization equation mainly focused on the finite difference method, but the issue of consistency still remains with several problems far from totally solved in the actual numerical computation. For instance, the consistency problem is involved in the numerical case where the boundary variables are solved explicitly while the variables away from the boundary are solved implicitly. And when the coefficient of discretization equation of nonlinear numerical case is the function of variables, calculating the coefficient explicitly and the variables implicitly might also give rise to consistency problem. Thus the present paper mainly researches the consistency problems involved in the explicit treatment of the second and third boundary conditions and that of thermal conductivity which is the function of temperature. The numerical results indicate that the consistency problem should be paid more attention and not be neglected in the practical computation.

Evaluation of the Prostate Cancer Prevention Trial Risk Calculator in a High-Risk Screening Population

Science.gov (United States)

Kaplan, David J.; Boorjian, Stephen A.; Ruth, Karen; Egleston, Brian L.; Chen, David Y.T.; Viterbo, Rosalia; Uzzo, Robert G.; Buyyounouski, Mark K.; Raysor, Susan; Giri, Veda N.

2009-01-01

Introduction Clinical factors in addition to PSA have been evaluated to improve risk assessment for prostate cancer. The Prostate Cancer Prevention Trial (PCPT) risk calculator provides an assessment of prostate cancer risk based on age, PSA, race, prior biopsy, and family history. This study evaluated the risk calculator in a screening cohort of young, racially diverse, high-risk men with a low baseline PSA enrolled in the Prostate Cancer Risk Assessment Program. Patients and Methods Eligibility for PRAP include men ages 35-69 who are African-American, have a family history of prostate cancer, or have a known BRCA1/2 mutation. PCPT risk scores were determined for PRAP participants, and were compared to observed prostate cancer rates. Results 624 participants were evaluated, including 382 (61.2%) African-American men and 375 (60%) men with a family history of prostate cancer. Median age was 49.0 years (range 34.0-69.0), and median PSA was 0.9 (range 0.1-27.2). PCPT risk score correlated with prostate cancer diagnosis, as the median baseline risk score in patients diagnosed with prostate cancer was 31.3%, versus 14.2% in patients not diagnosed with prostate cancer (p<0.0001). The PCPT calculator similarly stratified the risk of diagnosis of Gleason score ≥7 disease, as the median risk score was 36.2% in patients diagnosed with Gleason ≥7 prostate cancer versus 15.2% in all other participants (p<0.0001). Conclusion PCPT risk calculator score was found to stratify prostate cancer risk in a cohort of young, primarily African-American men with a low baseline PSA. These results support further evaluation of this predictive tool for prostate cancer risk assessment in high-risk men. PMID:19709072

Hysterectomy and its impact on the calculated incidence of cervical cancer and screening coverage in Denmark

DEFF Research Database (Denmark)

Lam, Janni Uyen Hoa; Lynge, Elsebeth; Njor, Sisse Helle

2015-01-01

sense to determine the indicators also for the true at-risk populations. We described the frequency of total hysterectomy in Denmark and its impact on the calculated incidence of cervical cancer and the screening coverage. MATERIAL AND METHODS: With data from five Danish population-based registries......% (adjusted). In Denmark, hysterectomies do not have a large overall impact on the calculated cancer incidence and screening coverage. Nevertheless, at ≥ 65 years adjusted rates would increase by almost 20% compared to unadjusted rates. This suggests that calculating disease risks per organ-years may have......, the incidence rate of cervical cancer and the screening coverage for women aged 23-64 years on 31 December 2010 were calculated with and without adjustments for hysterectomies undertaken for reasons other than cervical cancer. They were calculated as the number of cases divided by 1) the total number of woman...

Phase stability, electronic structure and equation of state of cubic TcN from first-principles calculations

International Nuclear Information System (INIS)

Song, T.; Ma, Q.; Sun, X.W.; Liu, Z.J.; Fu, Z.J.; Wei, X.P.; Wang, T.; Tian, J.H.

2016-01-01

The phase transition, electronic band structure, and equation of state (EOS) of cubic TcN are investigated by first-principles pseudopotential method based on density-functional theory. The calculated enthalpies show that TcN has a transformation between zincblende and rocksalt phases and the pressure determined by the relative enthalpy is 32 GPa. The calculated band structure indicates the metallic feature and it might make cubic TcN a better candidate for hard materials. Particular attention is paid to the predictions of volume, bulk modulus and its pressure derivative which play a central role in the formulation of approximate EOSs using the quasi-harmonic Debye model. - Highlights: • The phase transition pressure and electronic band structure for cubic TcN are determined. • Particular attention is paid to investigate the equation of state parameters for cubic TcN. • The thermodynamic properties up to 80 GPa and 3000 K are successfully predicted.

Coupling of atom-by-atom calculations of extended defects with B kick-out equations: application to the simulation of boron ted

International Nuclear Information System (INIS)

Lampin, E.; Cristiano, F.; Lamrani, Y.; Colombeau, B.

2004-01-01

We present simulations of B TED based on a complete calculation of the extended defect growth/shrinkage during annealing. The Si self-interstitial supersaturation calculated at the extended defect depth is coupled to the set of equations for the B kick-out diffusion through a generation/recombination term in the diffusion equation of the Si self-interstitials. The simulations are compared to the measurements performed on a Si wafer containing several B marker layers, where the amount of TED varies from one peak to the other. The good agreement obtained on this experiment is very promising for the application of these calculations to the case of ultra-shallow B + implants

Calculation of Rayleigh type sums for zeros of the equation arising in spectral problem

Science.gov (United States)

Kostin, A. B.; Sherstyukov, V. B.

2017-12-01

For zeros of the equation (arising in the oblique derivative problem) μ J n ‧ ( μ ) cos α + i n J n ( μ ) sin α = 0 , μ ∈ ℂ , with parameters n ∈ ℤ, α ∈ [-π/2, π/2] and the Bessel function Jn (μ) special summation relationships are proved. The obtained results are consistent with the theory of well-known Rayleigh sums calculating by zeros of the Bessel function.

Correction of the calculation of beam loading based in the RF power diffusion equation

International Nuclear Information System (INIS)

Silva, R. da.

1980-01-01

It is described an empirical correction based upon experimental datas of others authors in ORELA, GELINA and SLAC accelerators, to the calculation of the energy loss due to the beam loading effect as stated by the RF power diffusion equation theory an accelerating structure. It is obtained a dependence of this correction with the electron pulse full width half maximum, but independent of the electron energy. (author) [pt

A nodal collocation method for the calculation of the lambda modes of the P L equations

International Nuclear Information System (INIS)

Capilla, M.; Talavera, C.F.; Ginestar, D.; Verdu, G.

2005-01-01

P L equations are classical approximations to the neutron transport equation admitting a diffusive form. Using this property, a nodal collocation method is developed for the P L approximations, which is based on the expansion of the flux in terms of orthonormal Legendre polynomials. This method approximates the differential lambda modes problem by an algebraic eigenvalue problem from which the fundamental and the subcritical modes of the system can be calculated. To test the performance of this method, two problems have been considered, a homogeneous slab, which admits an analytical solution, and a seven-region slab corresponding to a more realistic problem

Calculation of the critical buckling of a lattice based on the integral form of the transport equation

International Nuclear Information System (INIS)

Benoist, P.

1990-06-01

The migration area, which relates the buckling to the multiplication factor, can be calculated by means of the Deniz formula. This formula involves the direct and adjoint angular fluxes. It is shown in this note that it is possible, using the integral form of the transport equation, to establish an equivalent formula in which only angle-integrated quantities appear. This formulation is more suitable for the calculation by the collision probably method [fr

New explicit equations for the accurate calculation of the growth and evaporation of hydrometeors by the diffusion of water vapor

Science.gov (United States)

Srivastava, R. C.; Coen, J. L.

1992-01-01

The traditional explicit growth equation has been widely used to calculate the growth and evaporation of hydrometeors by the diffusion of water vapor. This paper reexamines the assumptions underlying the traditional equation and shows that large errors (10-30 percent in some cases) result if it is used carelessly. More accurate explicit equations are derived by approximating the saturation vapor-density difference as a quadratic rather than a linear function of the temperature difference between the particle and ambient air. These new equations, which reduce the error to less than a few percent, merit inclusion in a broad range of atmospheric models.

Nucleon matter equation of state, particle number fluctuations, and shear viscosity within UrQMD box calculations

Science.gov (United States)

Motornenko, A.; Bravina, L.; Gorenstein, M. I.; Magner, A. G.; Zabrodin, E.

2018-03-01

Properties of equilibrated nucleon system are studied within the ultra-relativistic quantum molecular dynamics (UrQMD) transport model. The UrQMD calculations are done within a finite box with periodic boundary conditions. The system achieves thermal equilibrium due to nucleon-nucleon elastic scattering. For the UrQMD-equilibrium state, nucleon energy spectra, equation of state, particle number fluctuations, and shear viscosity η are calculated. The UrQMD results are compared with both, statistical mechanics and Chapman-Enskog kinetic theory, for a classical system of nucleons with hard-core repulsion.

Comparison of Benedict-Webb-Rubin, Starling and Lee-Kesler equations of state for use in P-V-T calculations

International Nuclear Information System (INIS)

McFee, D.G.; Mueller, K.H.; Lielmezs, J.

1982-01-01

By means of the available experimental gas compressibility data, the predictive accuracy of the Benedict-Webb-Rubin, Starling and Lee-Kesler equations was tested over wide temperature and pressure ranges for the following commonly used industrial gases: CH 4 , C 2 H 6 , C 3 H 8 , CO 2 , Ar, He, H 2 and N 2 . The root mean square (RMS) percent errors calculated over the T-P range investigated for all compounds, showed a degree of superiority and ease of use of the Lee-Kesler equation over the Benedict-Webb-Rubin and Starling equations. In order to treat quantal fluids H 2 and He, the Benedict-Webb-Rubin equation was modified by making constant B 0 temperature dependent, while the Starling and Lee-Kesler equations were rewritten through inclusion of quantum effect corrected pseudo-critical state parameters. (orig.)

The Dirac equation in electronic structure calculations: Accurate evaluation of DFT predictions for actinides

International Nuclear Information System (INIS)

Wills, John M.; Mattsson, Ann E.

2012-01-01

Brooks, Johansson, and Skriver, using the LMTO-ASA method and considerable insight, were able to explain many of the ground state properties of the actinides. In the many years since this work was done, electronic structure calculations of increasing sophistication have been applied to actinide elements and compounds, attempting to quantify the applicability of DFT to actinides and actinide compounds and to try to incorporate other methodologies (i.e. DMFT) into DFT calculations. Through these calculations, the limits of both available density functionals and ad hoc methodologies are starting to become clear. However, it has also become clear that approximations used to incorporate relativity are not adequate to provide rigorous tests of the underlying equations of DFT, not to mention ad hoc additions. In this talk, we describe the result of full-potential LMTO calculations for the elemental actinides, comparing results obtained with a full Dirac basis with those obtained from scalar-relativistic bases, with and without variational spin-orbit. This comparison shows that the scalar relativistic treatment of actinides does not have sufficient accuracy to provide a rigorous test of theory and that variational spin-orbit introduces uncontrolled errors in the results of electronic structure calculations on actinide elements.

Development of the balance equations model for calculation of ion charge-state distribution in ECR ion sources

International Nuclear Information System (INIS)

Filippov, A.V.; Shirkov, G.D.; Consoli, F.; Gammino, S.; Ciavola, G.; Celona, L.; Barbarino, S.

2008-01-01

The investigation of the widespread model for the calculation of ion charge-state distributions (CSD) in electron cyclotron-resonance ion source based on the set of balance equations is given. The modification of this model that allows one to describe the confinement and accumulation processes of highly charged ions in ECR plasma for gas mixing case more precisely is discussed. The new approach for the time confinement calculation (ions and electrons) based on the theory of Pastukhov is offered, viz. - calculation of confinement times during two step minimization of special type functionals. The results obtained by this approach have been compared with available experimental data

Integration of second cancer risk calculations in a radiotherapy treatment planning system

International Nuclear Information System (INIS)

Hartmann, M; Schneider, U

2014-01-01

Second cancer risk in patients, in particular in children, who were treated with radiotherapy is an important side effect. It should be minimized by selecting an appropriate treatment plan for the patient. The objectives of this study were to integrate a risk model for radiation induced cancer into a treatment planning system which allows to judge different treatment plans with regard to second cancer induction and to quantify the potential reduction in predicted risk. A model for radiation induced cancer including fractionation effects which is valid for doses in the radiotherapy range was integrated into a treatment planning system. From the three-dimensional (3D) dose distribution the 3D-risk equivalent dose (RED) was calculated on an organ specific basis. In addition to RED further risk coefficients like OED (organ equivalent dose), EAR (excess absolute risk) and LAR (lifetime attributable risk) are computed. A risk model for radiation induced cancer was successfully integrated in a treatment planning system. Several risk coefficients can be viewed and used to obtain critical situations were a plan can be optimised. Risk-volume-histograms and organ specific risks were calculated for different treatment plans and were used in combination with NTCP estimates for plan evaluation. It is concluded that the integration of second cancer risk estimates in a commercial treatment planning system is feasible. It can be used in addition to NTCP modelling for optimising treatment plans which result in the lowest possible second cancer risk for a patient.

Use of the Boltzmann equation for calculating the scattering law in gas mixtures

International Nuclear Information System (INIS)

Eder, O.J.; Lackner, T.

1989-01-01

A new approach is presented for the calculation of the dynamical incoherent structure factor S s (q, ω) for a dilute binary gas mixture. The starting point is the linearized one-dimensional Boltzmann equation for a mixture of particles interacting via a quasi-Maxwell potential (V(r) ≅ 1/r ν , ν=4). It is shown how - in the Fourier-Laplace space (q, ω) - the solution of the Boltzman equation can be expressed as an infinite continued fraction. The well known hydrodynamic limit (q→0) and the free gas limit (q→∞) are correctly reproduced as the appropriate limits of the continued fraction. A brief comparison between S s (q, ω) for two interaction potentials (quasi-Maxwell potential, ν=4, and hard core potential, ν=∞) is presented, and it is found that, after scaling the variables to the respective diffusion coefficients, only little dependence on the potential remains. Furthermore, for a one-component system in three dimensions results are summarized for the dynamical incoherent and coherent structure factor. (orig.) [de

Prediction of prostate cancer in unscreened men: external validation of a risk calculator.

Science.gov (United States)

van Vugt, Heidi A; Roobol, Monique J; Kranse, Ries; Määttänen, Liisa; Finne, Patrik; Hugosson, Jonas; Bangma, Chris H; Schröder, Fritz H; Steyerberg, Ewout W

2011-04-01

Prediction models need external validation to assess their value beyond the setting where the model was derived from. To assess the external validity of the European Randomized study of Screening for Prostate Cancer (ERSPC) risk calculator (www.prostatecancer-riskcalculator.com) for the probability of having a positive prostate biopsy (P(posb)). The ERSPC risk calculator was based on data of the initial screening round of the ERSPC section Rotterdam and validated in 1825 and 531 men biopsied at the initial screening round in the Finnish and Swedish sections of the ERSPC respectively. P(posb) was calculated using serum prostate specific antigen (PSA), outcome of digital rectal examination (DRE), transrectal ultrasound and ultrasound assessed prostate volume. The external validity was assessed for the presence of cancer at biopsy by calibration (agreement between observed and predicted outcomes), discrimination (separation of those with and without cancer), and decision curves (for clinical usefulness). Prostate cancer was detected in 469 men (26%) of the Finnish cohort and in 124 men (23%) of the Swedish cohort. Systematic miscalibration was present in both cohorts (mean predicted probability 34% versus 26% observed, and 29% versus 23% observed, both pscreened men, but overestimated the risk of a positive biopsy. Further research is necessary to assess the performance and applicability of the ERSPC risk calculator when a clinical setting is considered rather than a screening setting. Copyright © 2010 Elsevier Ltd. All rights reserved.

Backscattering Properties of Nonspherical Ice Particles Calculated by Geometrical-Optics-Integral-Equation Method

Directory of Open Access Journals (Sweden)

Masuda Kazuhiko

2016-01-01

Full Text Available Backscattering properties of ice crystal models (Voronoi aggregates (VA, hexagonal columns (COL, and six-branched bullet rosettes (BR6 are calculated by using geometrical-opticsintegral-equation (GOIE method. Characteristics of depolarization ratio (δ and lidar ratio (L of the crystal models are examined. δ (L values are 0.2~0.3 (4~50, 0.3~0.4 (10~25, and 0.5~0.6 (50~100 for COL, BR6, and VA, respectively, at wavelength λ=0.532 μm. It is found that small deformation of COL model could produce significant changes in δ and L.

A method for calculating effective lifetime risk of radiation-induced cancer from screening mammography

International Nuclear Information System (INIS)

Ali, R.M.; England, A.; McEntee, M.F.; Hogg, P.

2015-01-01

Purpose: To propose a method for evaluating the effective lifetime risk of radiation-induced cancer from screening mammography and to present initial data for the UK National Breast Screening Programme. Material and methods: The imaging was undertaken using a Hologic Selenia full field digital mammographic unit. The proposed method utilises an ATOM phantom containing thermoluminescent dosimeters and a perspex-polyethylene breast phantom to measure organ doses during a standard four view screening mammogram. Effective dose was calculated and effective risk was modelled for a range of client ages. The total lifetime effective risk was then calculated for the UK national screening programme. Calculation of effective risk includes the radiation dose to examined and contralateral breasts in addition to other body organs; this is an advantage over the mean glandular dose. Results: The contralateral breast, thyroid, thymus, brain, lung, salivary glands, and bone marrow all receive more than 1 μGy radiation dose during screening mammography. A major difference exists for total effective lifetime risk of radiation-induced cancer between clients with average and high breast cancer risk. Differences are attributed to the commencement age of screening and time interval between screens. Conclusion: This study proposes a method to evaluate effective lifetime risk of radiation-induced cancer from screening mammography in order to compare different mammography screening programmes. - Highlights: • We proposed a method for the calculation of radiation-induced cancer from screening mammography. • We measured the radiation absorbed dose of different organs during screening mammography. • There are major differences between mammography screening programme categories with regard to radiation effective risk.

Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. II. Application of the local basis equation.

Science.gov (United States)

Ferenczy, György G

2013-04-05

The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009, 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self-consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree-Fock-Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self-consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave-function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem. Copyright © 2013 Wiley Periodicals, Inc.

Calculating disability-adjusted life years (DALY) as a measure of excess cancer risk following radiation exposure

International Nuclear Information System (INIS)

Shimada, K; Kai, M

2015-01-01

This paper has proposed that disability-adjusted life year (DALY) can be used as a measure of radiation health risk. DALY is calculated as the sum of years of life lost (YLL) and years lived with disability (YLD). This multidimensional concept can be expressed as a risk index without a probability measure to avoid the misuse of the current radiation detriment at low doses. In this study, we calculated YLL and YLD using Japanese population data by gender. DALY for all cancers in Japan per 1 Gy per person was 0.84 year in men and 1.34 year in women. The DALY for all cancers in the Japanese baseline was 4.8 in men and 3.5 in women. When we calculated the ICRP detriment from the same data, DALYs for the cancer sites were similar to the radiation detriment in the cancer sites, excluding leukemia, breast and thyroid cancer. These results suggested that the ICRP detriment overestimate the weighting fraction of leukemia risk and underestimate the weighting fraction of breast and thyroid cancer. A big advantage over the ICRP detriment is that DALY can calculate the risk components for non-fatal diseases without the data of lethality. This study showed that DALY is a practical tool that can compare many types of diseases encountered in public health. (paper)

Calculations of reactivity based in the solution of the Neutron transport equation in X Y geometry and Lineal perturbation theory

International Nuclear Information System (INIS)

Valle G, E. del; Mugica R, C.A.

2005-01-01

In our country, in last congresses, Gomez et al carried out reactivity calculations based on the solution of the diffusion equation for an energy group using nodal methods in one dimension and the TPL approach (Lineal Perturbation Theory). Later on, Mugica extended the application to the case of multigroup so much so much in one as in two dimensions (X Y geometry) with excellent results. Presently work is carried out similar calculations but this time based on the solution of the neutron transport equation in X Y geometry using nodal methods and again the TPL approximation. The idea is to provide a calculation method that allows to obtain in quick form the reactivity solving the direct problem as well as the enclosed problem of the not perturbed problem. A test problem for the one that results are provided for the effective multiplication factor is described and its are offered some conclusions. (Author)

Method for calculating the variance and prediction intervals for biomass estimates obtained from allometric equations

CSIR Research Space (South Africa)

Kirton, A

2010-08-01

Full Text Available for calculating the variance and prediction intervals for biomass estimates obtained from allometric equations A KIRTON B SCHOLES S ARCHIBALD CSIR Ecosystem Processes and Dynamics, Natural Resources and the Environment P.O. BOX 395, Pretoria, 0001, South... intervals (confidence intervals for predicted values) for allometric estimates can be obtained using an example of estimating tree biomass from stem diameter. It explains how to deal with relationships which are in the power function form - a common form...

Calculation of bulk etch rate’s semi-empirical equation for polymer track membranes in stationary and dynamic modes

Directory of Open Access Journals (Sweden)

A. Mashentseva

2013-05-01

Full Text Available One of the most urgent and extremely social problems in environmental safeties area in Kazakhstan is providing the population of all regions of the country with quality drinking water. Development of filter elements based on nuclear track-etch membranes may be considered as one of best solutions this problem. The values of bulk etch rate and activation energy were calculated in view the effect of temperature, alkaline solution concentration as well as stirring effect. The semi-empirical equation of the bulk etch rate for PET track membranes was calculated. As a result of theoretical and experimental studies a semi-empirical equation of the bulk etch rate VB=3.4∙1012∙C2.07∙exp(-0.825/kT for 12 microns PET film, irradiated by ions 84Kr15+ (energy of 1.75 MeV/nucleon at the heavy ion accelerator DC-60 in Astana branch of the INP NNC RK, was obtained. 

Time-dependent magnetization of a type-II superconductor numerically calculated by using the flux-creep equation

International Nuclear Information System (INIS)

Lee, J. H.; Park, I. S.; Ahmad, D.; Kim, D.; Kim, Y. C.; Ko, R. K.; Jeong, D. Y.

2012-01-01

The macroscopic magnetic behaviors of a type-II superconductor, such as the field- or the temperature-dependent magnetization, have been described by using critical state models. However, because the models are time-independent, the magnetic relaxation in a type-II superconductor cannot be described by them, and the time dependence of the magnetization can affect the field or the temperature-dependent magnetization curve described by the models. In order to avoid the time independence of critical state models, we try the numerical calculation used by Qin et al., who mainly calculated the temperature dependence of the ac susceptibility χ(T). Their calculation showed that the frequency-dependent χ(T) could be obtained by using the flux-creep equation. We calculated the field-dependent magnetization and magnetic relaxation by using a numerical method. The calculated field-dependent magnetization M(H) curves shows the shapes of a typical type-II superconductor. The calculated magnetic relaxation do not show a logarithmic decay of the magnetization, but the addition of a surface barrier to the relaxation calculation caused a clear logarithmic decay of the magnetization, producing a crossover at a mid-time. This means that the logarithmic magnetic relaxation is caused by not only flux creep but also a combination of flux creep and a surface barrier.

Numerical Calculation of Transport Based on the Drift Kinetic Equation for plasmas in General Toroidal Magnetic Geometry

International Nuclear Information System (INIS)

Reynolds, J. M.; Lopez-Bruna, D.

2009-01-01

This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs

Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry

International Nuclear Information System (INIS)

Yasa, F.; Anli, F.; Guengoer, S.

2007-01-01

We present analytical calculations of spherically symmetric radioactive transfer and neutron transport using a hypothesis of P1 and T1 low order polynomial approximation for diffusion coefficient D. Transport equation in spherical geometry is considered as the pseudo slab equation. The validity of polynomial expansionion in transport theory is investigated through a comparison with classic diffusion theory. It is found that for causes when the fluctuation of the scattering cross section dominates, the quantitative difference between the polynomial approximation and diffusion results was physically acceptable in general

Sound Propagation Around Off-Shore Wind Turbines. Long-Range Parabolic Equation Calculations for Baltic Sea Conditions

Energy Technology Data Exchange (ETDEWEB)

Johansson, Lisa

2003-07-01

Low-frequency, long-range sound propagation over a sea surface has been calculated using a wide-angel Cranck-Nicholson Parabolic Equation method. The model is developed to investigate noise from off-shore wind turbines. The calculations are made using normal meteorological conditions of the Baltic Sea. Special consideration has been made to a wind phenomenon called low level jet with strong winds on rather low altitude. The effects of water waves on sound propagation have been incorporated in the ground boundary condition using a boss model. This way of including roughness in sound propagation models is valid for water wave heights that are small compared to the wave length of the sound. Nevertheless, since only low frequency sound is considered, waves up to the mean wave height of the Baltic Sea can be included in this manner. The calculation model has been tested against benchmark cases and agrees well with measurements. The calculations show that channelling of sound occurs at downwind conditions and that the sound propagation tends towards cylindrical spreading. The effects of the water waves are found to be fairly small.

Calculation of coherent synchrotron radiation in toroidal waveguides by paraxial wave equation

Directory of Open Access Journals (Sweden)

D. R. Gillingham

2007-05-01

Full Text Available A new technique for the simulation of coherent synchrotron radiation (CSR and space-charge fields from a single electron bunch in straight or toroidal rectangular waveguide sections has been developed. It is based on the integration of the paraxial approximation to the wave equations, using the perturbation technique where the bending radius is large compared to the dimension of the waveguide. We have implemented an unconditionally stable integration method in the time domain with transparent boundary conditions that allows the use of a minimally sized computational domain about the bunch. This technique explicitly enforces the causality condition so that no portion of the fields can propagate faster than the speed of light, can be used with arbitrary three-dimensional charge distributions, and contains corrections for finite energy. We have also developed a method for the calculation of the transverse forces within the bunch including space-charge. This method has been developed for incorporation with a particle-in-cell code so that we may self-consistently model CSR and space-charge in combinations of bending sections with a fully dynamic electron bunch in an efficient manner. In this paper we describe the model and methods for calculation of the fields in detail and compare results to theory wherever possible.

equateIRT: An R Package for IRT Test Equating

Directory of Open Access Journals (Sweden)

Michela Battauz

2015-12-01

Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

Approach to calculation of mass spectra and two-photon decays of c c¯ mesons in the framework of Bethe-Salpeter equation

Science.gov (United States)

Bhatnagar, Shashank; Alemu, Lmenew

2018-02-01

In this work we calculate the mass spectra of charmonium for 1 P ,…,4 P states of 0++ and 1++, for 1 S ,…,5 S states of 0-+, and for 1 S ,…,4 D states of 1- along with the two-photon decay widths of the ground and first excited states of 0++ quarkonia for the process O++→γ γ in the framework of a QCD-motivated Bethe-Salpeter equation (BSE). In this 4 ×4 BSE framework, the coupled Salpeter equations are first shown to decouple for the confining part of the interaction (under the heavy-quark approximation) and are analytically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to mass spectral equations for various quarkonia. The analytic forms of wave functions obtained are used for the calculation of the two-photon decay widths of χc 0. Our results are in reasonable agreement with data (where available) and other models.

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

Science.gov (United States)

Karney, C. F. F.

1977-01-01

Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

Magnetic resonance only workflow and validation of dose calculations for radiotherapy of prostate cancer

DEFF Research Database (Denmark)

Lübeck Christiansen, Rasmus; Jensen, Henrik R.; Brink, Carsten

2017-01-01

Background: Current state of the art radiotherapy planning of prostate cancer utilises magnetic resonance (MR) for soft tissue delineation and computed tomography (CT) to provide an electron density map for dose calculation. This dual scan workflow is prone to setup and registration error....... This study evaluates the feasibility of an MR-only workflow and the validity of dose calculation from an MR derived pseudo CT. Material and methods: Thirty prostate cancer patients were CT and MR scanned. Clinical treatment plans were generated on CT using a single 18 MV arc volumetric modulated arc therapy...... was successfully delivered to one patient, including manually performed daily IGRT. Conclusions: Median gamma pass rates were high for pseudo CT and proved superior to uniform density. Local differences in dose calculations were concluded not to have clinical relevance. Feasibility of the MR-only workflow...

[Macro-economic calculation of spending versus micro-economic follow-up of costs of breast cancer].

Science.gov (United States)

Borella, L; Paraponaris, A

2002-12-01

In the healthcare field, the ability to make economic forecasts requires knowledge of the costs of caring for major diseases. In the case of a semi-chronic condition like cancer, this cost covers all the episodes of care associated with a patient. An evaluation of a macro-economic method of calculating costs for treating non-metastatic cancer, covering all hospital episodes, is proposed. This method is based entirely on the use of annual hospital activity databases, linked to data concerning the incidence of cancer. It allows us to obtain the global cost of care for a neoplasm of a particular site, without the need to reconstruct the whole care pathway of the patients. The model was assessed by comparing it's own results, in the particular case of breast cancer to those issuing from a micro-economic follow-up of 115 patients. Data for macro-economic calculation are extracted from the national French hospital database for the year 1999 and from cancer incidence data. The prospective study was done in 1995, in a comprehensive cancer centre. Macro-economic calculation leads to a cost of 14,555 Euro, for primary breast cancer. Prospective follow-up showed a cost of 14,350 Euro (data corrected, 1999 value). With a difference of 1%, there was a clear cohesion of the two results, while a higher level of divergence was noticed (from 1 to 15%) in the comparison between therapeutic techniques. Accuracy and reliability of results were evaluated. This method may be extended to all types of neoplasms. This method cannot be used instead of follow-up studies, for cost-efficacy or cost-severity analysis, but may be interesting beyond economic forecasts, in the field of payment per pathology.

Numerical Calculation and Exergy Equations of Spray Heat Exchanger Attached to a Main Fan Diffuser

Science.gov (United States)

Cui, H.; Wang, H.; Chen, S.

2015-04-01

In the present study, the energy depreciation rule of spray heat exchanger, which is attached to a main fan diffuser, is analyzed based on the second law of thermodynamics. Firstly, the exergy equations of the exchanger are deduced. The equations are numerically calculated by the fourth-order Runge-Kutta method, and the exergy destruction is quantitatively effected by the exchanger structure parameters, working fluid (polluted air, i.e., PA; sprayed water, i.e., SW) initial state parameters and the ambient reference parameters. The results are showed: (1) heat transfer is given priority to latent transfer at the bottom of the exchanger, and heat transfer of convection and is equivalent to that of condensation in the upper. (2) With the decrease of initial temperature of SW droplet, the decrease of PA velocity or the ambient reference temperature, and with the increase of a SW droplet size or initial PA temperature, exergy destruction both increase. (3) The exergy efficiency of the exchanger is 72.1 %. An approach to analyze the energy potential of the exchanger may be provided for engineering designs.

SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation

Energy Technology Data Exchange (ETDEWEB)

Hong, X; Gao, H [Shanghai Jiao Tong University, Shanghai, Shanghai (China); Paganetti, H [Massachusetts General Hospital, Boston, MA (United States)

2015-06-15

Purpose: The Boltzmann-Fokker-Planck equation (BFPE) accurately models the migration of photons/charged particles in tissues. While the Monte Carlo (MC) method is popular for solving BFPE in a statistical manner, we aim to develop a deterministic BFPE solver based on various state-of-art numerical acceleration techniques for rapid and accurate dose calculation. Methods: Our BFPE solver is based on the structured grid that is maximally parallelizable, with the discretization in energy, angle and space, and its cross section coefficients are derived or directly imported from the Geant4 database. The physical processes that are taken into account are Compton scattering, photoelectric effect, pair production for photons, and elastic scattering, ionization and bremsstrahlung for charged particles.While the spatial discretization is based on the diamond scheme, the angular discretization synergizes finite element method (FEM) and spherical harmonics (SH). Thus, SH is used to globally expand the scattering kernel and FFM is used to locally discretize the angular sphere. As a Result, this hybrid method (FEM-SH) is both accurate in dealing with forward-peaking scattering via FEM, and efficient for multi-energy-group computation via SH. In addition, FEM-SH enables the analytical integration in energy variable of delta scattering kernel for elastic scattering with reduced truncation error from the numerical integration based on the classic SH-based multi-energy-group method. Results: The accuracy of the proposed BFPE solver was benchmarked against Geant4 for photon dose calculation. In particular, FEM-SH had improved accuracy compared to FEM, while both were within 2% of the results obtained with Geant4. Conclusion: A deterministic solver of the Boltzmann-Fokker-Planck equation is developed for dose calculation, and benchmarked against Geant4. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang

Cálculo do volume na equação de van der Waals pelo método de cardano Volume calculation in van der Waals equation by the cardano method

Directory of Open Access Journals (Sweden)

Nelson H. T. Lemes

2010-01-01

Full Text Available Analytical solutions of a cubic equation with real coefficients are established using the Cardano method. The method is first applied to simple third order equation. Calculation of volume in the van der Waals equation of state is afterwards established. These results are exemplified to calculate the volumes below and above critical temperatures. Analytical and numerical values for the compressibility factor are presented as a function of the pressure. As a final example, coexistence volumes in the liquid-vapor equilibrium are calculated. The Cardano approach is very simple to apply, requiring only elementary operations, indicating an attractive method to be used in teaching elementary thermodynamics.

A clinical study of lung cancer dose calculation accuracy with Monte Carlo simulation.

Science.gov (United States)

Zhao, Yanqun; Qi, Guohai; Yin, Gang; Wang, Xianliang; Wang, Pei; Li, Jian; Xiao, Mingyong; Li, Jie; Kang, Shengwei; Liao, Xiongfei

2014-12-16

The accuracy of dose calculation is crucial to the quality of treatment planning and, consequently, to the dose delivered to patients undergoing radiation therapy. Current general calculation algorithms such as Pencil Beam Convolution (PBC) and Collapsed Cone Convolution (CCC) have shortcomings in regard to severe inhomogeneities, particularly in those regions where charged particle equilibrium does not hold. The aim of this study was to evaluate the accuracy of the PBC and CCC algorithms in lung cancer radiotherapy using Monte Carlo (MC) technology. Four treatment plans were designed using Oncentra Masterplan TPS for each patient. Two intensity-modulated radiation therapy (IMRT) plans were developed using the PBC and CCC algorithms, and two three-dimensional conformal therapy (3DCRT) plans were developed using the PBC and CCC algorithms. The DICOM-RT files of the treatment plans were exported to the Monte Carlo system to recalculate. The dose distributions of GTV, PTV and ipsilateral lung calculated by the TPS and MC were compared. For 3DCRT and IMRT plans, the mean dose differences for GTV between the CCC and MC increased with decreasing of the GTV volume. For IMRT, the mean dose differences were found to be higher than that of 3DCRT. The CCC algorithm overestimated the GTV mean dose by approximately 3% for IMRT. For 3DCRT plans, when the volume of the GTV was greater than 100 cm(3), the mean doses calculated by CCC and MC almost have no difference. PBC shows large deviations from the MC algorithm. For the dose to the ipsilateral lung, the CCC algorithm overestimated the dose to the entire lung, and the PBC algorithm overestimated V20 but underestimated V5; the difference in V10 was not statistically significant. PBC substantially overestimates the dose to the tumour, but the CCC is similar to the MC simulation. It is recommended that the treatment plans for lung cancer be developed using an advanced dose calculation algorithm other than PBC. MC can accurately

The CPA Equation of State and an Activity Coefficient Model for Accurate Molar Enthalpy Calculations of Mixtures with Carbon Dioxide and Water/Brine

Energy Technology Data Exchange (ETDEWEB)

Myint, P. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Hao, Y. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Firoozabadi, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2015-03-27

Thermodynamic property calculations of mixtures containing carbon dioxide (CO₂) and water, including brines, are essential in theoretical models of many natural and industrial processes. The properties of greatest practical interest are density, solubility, and enthalpy. Many models for density and solubility calculations have been presented in the literature, but there exists only one study, by Spycher and Pruess, that has compared theoretical molar enthalpy predictions with experimental data [1]. In this report, we recommend two different models for enthalpy calculations: the CPA equation of state by Li and Firoozabadi [2], and the CO₂ activity coefficient model by Duan and Sun [3]. We show that the CPA equation of state, which has been demonstrated to provide good agreement with density and solubility data, also accurately calculates molar enthalpies of pure CO₂, pure water, and both CO₂-rich and aqueous (H₂O-rich) mixtures of the two species. It is applicable to a wider range of conditions than the Spycher and Pruess model. In aqueous sodium chloride (NaCl) mixtures, we show that Duan and Sun’s model yields accurate results for the partial molar enthalpy of CO₂. It can be combined with another model for the brine enthalpy to calculate the molar enthalpy of H₂O-CO₂-NaCl mixtures. We conclude by explaining how the CPA equation of state may be modified to further improve agreement with experiments. This generalized CPA is the basis of our future work on this topic.

Mobile application-based Seoul National University Prostate Cancer Risk Calculator: development, validation, and comparative analysis with two Western risk calculators in Korean men.

Directory of Open Access Journals (Sweden)

Chang Wook Jeong

Full Text Available OBJECTIVES: We developed a mobile application-based Seoul National University Prostate Cancer Risk Calculator (SNUPC-RC that predicts the probability of prostate cancer (PC at the initial prostate biopsy in a Korean cohort. Additionally, the application was validated and subjected to head-to-head comparisons with internet-based Western risk calculators in a validation cohort. Here, we describe its development and validation. PATIENTS AND METHODS: As a retrospective study, consecutive men who underwent initial prostate biopsy with more than 12 cores at a tertiary center were included. In the development stage, 3,482 cases from May 2003 through November 2010 were analyzed. Clinical variables were evaluated, and the final prediction model was developed using the logistic regression model. In the validation stage, 1,112 cases from December 2010 through June 2012 were used. SNUPC-RC was compared with the European Randomized Study of Screening for PC Risk Calculator (ERSPC-RC and the Prostate Cancer Prevention Trial Risk Calculator (PCPT-RC. The predictive accuracy was assessed using the area under the receiver operating characteristic curve (AUC. The clinical value was evaluated using decision curve analysis. RESULTS: PC was diagnosed in 1,240 (35.6% and 417 (37.5% men in the development and validation cohorts, respectively. Age, prostate-specific antigen level, prostate size, and abnormality on digital rectal examination or transrectal ultrasonography were significant factors of PC and were included in the final model. The predictive accuracy in the development cohort was 0.786. In the validation cohort, AUC was significantly higher for the SNUPC-RC (0.811 than for ERSPC-RC (0.768, p<0.001 and PCPT-RC (0.704, p<0.001. Decision curve analysis also showed higher net benefits with SNUPC-RC than with the other calculators. CONCLUSIONS: SNUPC-RC has a higher predictive accuracy and clinical benefit than Western risk calculators. Furthermore, it is easy

Statistical mechanics of stochastic neural networks: Relationship between the self-consistent signal-to-noise analysis, Thouless-Anderson-Palmer equation, and replica symmetric calculation approaches

International Nuclear Information System (INIS)

Shiino, Masatoshi; Yamana, Michiko

2004-01-01

We study the statistical mechanical aspects of stochastic analog neural network models for associative memory with correlation type learning. We take three approaches to derive the set of the order parameter equations for investigating statistical properties of retrieval states: the self-consistent signal-to-noise analysis (SCSNA), the Thouless-Anderson-Palmer (TAP) equation, and the replica symmetric calculation. On the basis of the cavity method the SCSNA can be generalized to deal with stochastic networks. We establish the close connection between the TAP equation and the SCSNA to elucidate the relationship between the Onsager reaction term of the TAP equation and the output proportional term of the SCSNA that appear in the expressions for the local fields

CT-based dose calculations and in vivo dosimetry for lung cancer treatment

International Nuclear Information System (INIS)

Essers, M.; Lanson, J.H.; Leunens, G.; Schnabel, T.; Mijnheer, B.J.

1995-01-01

Reliable CT-based dose calculations and dosimetric quality control are essential for the introduction of new conformal techniques for the treatment of lung cancer. The first aim of this study was therefore to check the accuracy of dose calculations based on CT-densities, using a simple inhomogeneity correction model, for lung cancer patients irradiated with an AP-PA treatment technique. Second, the use of diodes for absolute exit dose measurements and an Electronic Portal Imaging Device (EPID) for relative transmission dose verification was investigated for 22 and 12 patients, respectively. The measured dose values were compared with calculations performed using our 3-dimensional treatment planning system, using CT-densities or assuming the patient to be water-equivalent. Using water-equivalent calculations, the actual exit dose value under lung was, on average, underestimated by 30%, with an overall spread of 10% (1 SD). Using inhomogeneity corrections, the exit dose was, on average, overestimated by 4%, with an overall spread of 6% (1 SD). Only 2% of the average deviation was due to the inhomogeneity correction model. An uncertainty in exit dose calculation of 2.5% (1 SD) could be explained by organ motion, resulting from the ventilatory or cardiac cycle. The most important reason for the large overall spread was, however, the uncertainty involved in performing point measurements: about 4% (1 SD). This difference resulted from the systematic and random deviation in patient set-up and therefore in diode position with respect to patient anatomy. Transmission and exit dose values agreed with an average difference of 1.1%. Transmission dose profiles also showed good agreement with calculated exit dose profiles. Our study shows that, for this treatment technique, the dose in the thorax region is quite accurately predicted using CT-based dose calculations, even if a simple inhomogeneity correction model is used. Point detectors such as diodes are not suitable for exit

Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. Part I. Application of the Huzinaga equation.

Science.gov (United States)

Ferenczy, György G

2013-04-05

Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods. Copyright © 2012 Wiley Periodicals, Inc.

Shielding calculations using FLUKA

International Nuclear Information System (INIS)

Yamaguchi, Chiri; Tesch, K.; Dinter, H.

1988-06-01

The dose equivalent on the surface of concrete shielding has been calculated using the Monte Carlo code FLUKA86 for incident proton energies from 10 to 800 GeV. The results have been compared with some simple equations. The value of the angular dependent parameter in Moyer's equation has been calculated from the locations where the values of the maximum dose equivalent occur. (author)

Feynman integrals and difference equations

International Nuclear Information System (INIS)

Moch, S.; Schneider, C.

2007-09-01

We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)

Lung Dose Calculation With SPECT/CT for 90Yittrium Radioembolization of Liver Cancer

International Nuclear Information System (INIS)

Yu, Naichang; Srinivas, Shaym M.; DiFilippo, Frank P.; Shrikanthan, Sankaran; Levitin, Abraham; McLennan, Gordon; Spain, James; Xia, Ping; Wilkinson, Allan

2013-01-01

Purpose: To propose a new method to estimate lung mean dose (LMD) using technetium-99m labeled macroaggregated albumin ( 99m Tc-MAA) single photon emission CT (SPECT)/CT for 90 Yttrium radioembolization of liver tumors and to compare the LMD estimated using SPECT/CT with clinical estimates of LMD using planar gamma scintigraphy (PS). Methods and Materials: Images of 71 patients who had SPECT/CT and PS images of 99m Tc-MAA acquired before TheraSphere radioembolization of liver cancer were analyzed retrospectively. LMD was calculated from the PS-based lung shunt assuming a lung mass of 1 kg and 50 Gy per GBq of injected activity shunted to the lung. For the SPECT/CT-based estimate, the LMD was calculated with the activity concentration and lung volume derived from SPECT/CT. The effect of attenuation correction and the patient's breathing on the calculated LMD was studied with the SPECT/CT. With these effects correctly taken into account in a more rigorous fashion, we compared the LMD calculated with SPECT/CT with the LMD calculated with PS. Results: The mean dose to the central region of the lung leads to a more accurate estimate of LMD. Inclusion of the lung region around the diaphragm in the calculation leads to an overestimate of LMD due to the misregistration of the liver activity to the lung from the patient's breathing. LMD calculated based on PS is a poor predictor of the actual LMD. For the subpopulation with large lung shunt, the mean overestimation from the PS method for the lung shunt was 170%. Conclusions: A new method of calculating the LMD for TheraSphere and SIR-Spheres radioembolization of liver cancer based on 99m Tc-MAA SPECT/CT is presented. The new method provides a more accurate estimate of radiation risk to the lungs. For patients with a large lung shunt calculated from PS, a recalculation of LMD based on SPECT/CT is recommended

Non-perturbative background field calculations

International Nuclear Information System (INIS)

Stephens, C.R.; Department of Physics, University of Utah, Salt Lake City, Utah 84112)

1988-01-01

New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation: perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation. copyright 1988 Academic Press, Inc

Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection

Science.gov (United States)

Chen, Xueli; Yang, Defu; Qu, Xiaochao; Hu, Hao; Liang, Jimin; Gao, Xinbo; Tian, Jie

2012-06-01

Bioluminescence tomography (BLT) has been successfully applied to the detection and therapeutic evaluation of solid cancers. However, the existing BLT reconstruction algorithms are not accurate enough for cavity cancer detection because of neglecting the void problem. Motivated by the ability of the hybrid radiosity-diffusion model (HRDM) in describing the light propagation in cavity organs, an HRDM-based BLT reconstruction algorithm was provided for the specific problem of cavity cancer detection. HRDM has been applied to optical tomography but is limited to simple and regular geometries because of the complexity in coupling the boundary between the scattering and void region. In the provided algorithm, HRDM was first applied to three-dimensional complicated and irregular geometries and then employed as the forward light transport model to describe the bioluminescent light propagation in tissues. Combining HRDM with the sparse reconstruction strategy, the cavity cancer cells labeled with bioluminescent probes can be more accurately reconstructed. Compared with the diffusion equation based reconstruction algorithm, the essentiality and superiority of the HRDM-based algorithm were demonstrated with simulation, phantom and animal studies. An in vivo gastric cancer-bearing nude mouse experiment was conducted, whose results revealed the ability and feasibility of the HRDM-based algorithm in the biomedical application of gastric cancer detection.

State equation approximation of transfer matrices and its application to the phase domain calculation of electromagnetic transients

International Nuclear Information System (INIS)

Soysal, A.O.; Semlyen, A.

1994-01-01

A general methodology is presented for the state equation approximation of a multiple input-output linear system from transfer matrix data. A complex transformation matrix, obtained by eigen analysis at a fixed frequency, is used for diagonalization of the transfer matrix over the whole frequency range. A scalar estimation procedure is applied for identification of the modal transfer functions. The state equations in the original coordinates are obtained by inverse transformation. An iterative Gauss-Newton refinement process is used to reduce the overall error of the approximation. The developed methodology is applied to the phase domain modeling of untransposed transmission lines. The approach makes it possible to perform EMTP calculations directly in the phase domain. This results in conceptual simplification and savings in computation time since modal transformations are not needed in the sequences of the transient analysis. The presented procedure is compared with the conventional modal approach in terms of accuracy and computation time

Can multiparametric MRI replace Roach equations in staging prostate cancer before external beam radiation therapy?

International Nuclear Information System (INIS)

Girometti, Rossano; Signor, Marco Andrea; Pancot, Martina; Cereser, Lorenzo; Zuiani, Chiara

2016-01-01

Purpose: To investigate the agreement between Roach equations (RE) and multiparametric magnetic resonance imaging (mpMRI) in assessing the T-stage of prostate cancer (PCa). Materials and methods: Seventy-three patients with biopsy-proven PCa and previous RE assessment prospectively underwent mpMRI on a 3.0T magnet before external beam radiation therapy (EBRT). Using Cohen’s kappa statistic, we assessed the agreement between RE and mpMRI in defining the T-stage (≥T3 vs.T ≤ 2) and risk category according to the National comprehensive cancer network criteria (≤intermediate vs. ≥high). We also calculated sensitivity and specificity for ≥T3 stage in an additional group of thirty-seven patients with post-prostatectomy histological examination (mpMRI validation group). Results: The agreement between RE and mpMRI in assessing the T stage and risk category was moderate (k = 0.53 and 0.56, respectively). mpMRI changed the T stage and risk category in 21.9% (95%C.I. 13.4–33-4) and 20.5% (95%C.I. 12.3–31.9), respectively, prevalently downstaging PCa compared to RE. Sensitivity and specificity for ≥T3 stage in the mpMRI validation group were 81.8% (95%C.I. 65.1–91.9) and 88.5% (72.8–96.1). Conclusion: RE and mpMRI show moderate agreement only in assessing the T-stage of PCa, translating into an mpMRI-induced change in risk assessment in about one fifth of patients. As supported by high sensitivity/specificity for ≥T3 stage in the validation group, the discrepancy we found is in favour of mpMRI as a tool to stage PCa before ERBT.

Can multiparametric MRI replace Roach equations in staging prostate cancer before external beam radiation therapy?

Energy Technology Data Exchange (ETDEWEB)

Girometti, Rossano, E-mail: rgirometti@sirm.org [Institute of Diagnostic Radiology, Department of Medical and Biological Sciences, University of Udine, Azienda Ospedaliero-Universitaria Santa Maria della Misericordia − via Colugna, 50–33100, Udine (Italy); Signor, Marco Andrea, E-mail: marco.signor@asuiud.sanita.fvg.it [Department of Oncological Radiation Therapy, Azienda Ospedaliero-Universitaria Santa Maria della Misericordia, Piazzale S. M. della Misericordia, 15–33100, Udine (Italy); Pancot, Martina, E-mail: martypancot@libero.it [Institute of Diagnostic Radiology, Department of Medical and Biological Sciences, University of Udine, Azienda Ospedaliero-Universitaria Santa Maria della Misericordia − via Colugna, 50–33100, Udine (Italy); Cereser, Lorenzo, E-mail: lcereser@sirm.org [Institute of Diagnostic Radiology, Department of Medical and Biological Sciences, University of Udine, Azienda Ospedaliero-Universitaria Santa Maria della Misericordia − via Colugna, 50–33100, Udine (Italy); Zuiani, Chiara, E-mail: chiara.zuiani@uniud.it [Institute of Diagnostic Radiology, Department of Medical and Biological Sciences, University of Udine, Azienda Ospedaliero-Universitaria Santa Maria della Misericordia − via Colugna, 50–33100, Udine (Italy)

2016-12-15

Purpose: To investigate the agreement between Roach equations (RE) and multiparametric magnetic resonance imaging (mpMRI) in assessing the T-stage of prostate cancer (PCa). Materials and methods: Seventy-three patients with biopsy-proven PCa and previous RE assessment prospectively underwent mpMRI on a 3.0T magnet before external beam radiation therapy (EBRT). Using Cohen’s kappa statistic, we assessed the agreement between RE and mpMRI in defining the T-stage (≥T3 vs.T ≤ 2) and risk category according to the National comprehensive cancer network criteria (≤intermediate vs. ≥high). We also calculated sensitivity and specificity for ≥T3 stage in an additional group of thirty-seven patients with post-prostatectomy histological examination (mpMRI validation group). Results: The agreement between RE and mpMRI in assessing the T stage and risk category was moderate (k = 0.53 and 0.56, respectively). mpMRI changed the T stage and risk category in 21.9% (95%C.I. 13.4–33-4) and 20.5% (95%C.I. 12.3–31.9), respectively, prevalently downstaging PCa compared to RE. Sensitivity and specificity for ≥T3 stage in the mpMRI validation group were 81.8% (95%C.I. 65.1–91.9) and 88.5% (72.8–96.1). Conclusion: RE and mpMRI show moderate agreement only in assessing the T-stage of PCa, translating into an mpMRI-induced change in risk assessment in about one fifth of patients. As supported by high sensitivity/specificity for ≥T3 stage in the validation group, the discrepancy we found is in favour of mpMRI as a tool to stage PCa before ERBT.

Calculation of radiation effects in solids by direct numerical solution of the adjoint transport equation

International Nuclear Information System (INIS)

Matthes, W.K.

1998-01-01

The 'adjoint transport equation in its integro-differential form' is derived for the radiation damage produced by atoms injected into solids. We reduce it to the one-dimensional form and prepare it for a numerical solution by: --discretizing the continuous variables energy, space and direction, --replacing the partial differential quotients by finite differences and --evaluating the collision integral by a double sum. By a proper manipulation of this double sum the adjoint transport equation turns into a (very large) set of linear equations with tridiagonal matrix which can be solved by a special (simple and fast) algorithm. The solution of this set of linear equations contains complete information on a specified damage type (e.g. the energy deposited in a volume V) in terms of the function D(i,E,c,x) which gives the damage produced by all particles generated in a cascade initiated by a particle of type i starting at x with energy E in direction c. It is essential to remark that one calculation gives the damage function D for the complete ranges of the variables {i,E,c and x} (for numerical reasons of course on grid-points in the {E,c,x}-space). This is most useful to applications where a general source-distribution S(i,E,c,x) of particles is given by the experimental setup (e.g. beam-window and and target in proton accelerator work. The beam-protons along their path through the window--or target material generate recoil atoms by elastic collisions or nuclear reactions. These recoil atoms form the particle source S). The total damage produced then is eventually given by: D = (Σ)i ∫ ∫ ∫ S(i, E, c, x)*D(i, E, c, x)*dE*dc*dx A Fortran-77 program running on a PC-486 was written for the overall procedure and applied to some problems

REGRES: A FORTRAN-77 program to calculate nonparametric and ``structural'' parametric solutions to bivariate regression equations

Science.gov (United States)

Rock, N. M. S.; Duffy, T. R.

REGRES allows a range of regression equations to be calculated for paired sets of data values in which both variables are subject to error (i.e. neither is the "independent" variable). Nonparametric regressions, based on medians of all possible pairwise slopes and intercepts, are treated in detail. Estimated slopes and intercepts are output, along with confidence limits, Spearman and Kendall rank correlation coefficients. Outliers can be rejected with user-determined stringency. Parametric regressions can be calculated for any value of λ (the ratio of the variances of the random errors for y and x)—including: (1) major axis ( λ = 1); (2) reduced major axis ( λ = variance of y/variance of x); (3) Y on Xλ = infinity; or (4) X on Y ( λ = 0) solutions. Pearson linear correlation coefficients also are output. REGRES provides an alternative to conventional isochron assessment techniques where bivariate normal errors cannot be assumed, or weighting methods are inappropriate.

Feynman integrals and difference equations

Energy Technology Data Exchange (ETDEWEB)

Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation

2007-09-15

We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)

Comparison of the Koster-Slater and the equation-of-motion method for calculation of the electronic structure of defects in compound semiconductors

International Nuclear Information System (INIS)

Tit, N.; Halley, J.W.

1992-01-01

Traditional methods of calculating the electronic structure of defects in semiconductors rely on matrix-diagonalization methods which use the unperturbed crystalline wave functions as a basis. Equation-of-motion (EOM) methods, on the other hand, give excellent results with strong disorder and many defects and make no use of the basis of unperturbed wave functions, but require self-averaging properties of the wave functions which appear superficially to make them unsuitable for study of local properties. We show here that EOM methods are better than traditional methods for calculating the electronic structure of essentially any finite-range impurity potential. The reason is basically that the numerical cost of the traditional Green's-function methods grows approximately as R 7 o/Iper sitet/P, where R is the range of the potential, whereas the cost of the EOM methods per site is independent of the range of the potential. Our detailed calculations on a model of an oxygen vacancy in rutile TiO 2 show that a crossover occurs very soon, so that equation-of-motion methods are better than the traditional ones in the case of potentials of realistic range

On the calculation of the eigenvalues of the Faddeev equation kernel on the nonphysical sheet of energy

International Nuclear Information System (INIS)

Moeller, K.

1978-01-01

A system of three particles is considered which interacts by rank-1 separable potential. For the Faddeev equation kernel of this system a method is proposed for calculating the eigenvalues on the nonphysical sheet of the three-particle cms-energy. From the consideration of the analytical structure of the eigenvalues in the energy plane it follows that the analytical continuations of the eigenvalues from the physical to the nonphysical region are different above and below the three-particle threshold. In this paper the continuation below the threshold is discussed. (author)

Empirical equations of the solvent extraction of the energetic inputs, uranium and plutonium, calculated by using the program Microsoft Excel

International Nuclear Information System (INIS)

Bento, Dercio Lopes

2006-01-01

PUREX is one of the purification process for irradiated nuclear fuel. In the flowchart the program uses various uranium and plutonium extraction phases by using organic solvent contained in the aqueous phase obtained in the dissolution of the fuel element. A posterior extraction U and Pu are changed to the aqueous phase. So it is fundamental to know the distribution coefficient (dS), at the temperature (tc), of the substances among the two immiscible phases, for better calculation the suitable flowchart. A mathematical model was elaborated based on experimental data, for the calculation of the dS and applied to a referential band of substance concentrations in the aqueous phase (xS) and organic (yS). By using the program Excel, we personalized the empirical equations calculated by the root mean square. The relative deviation, among the calculated values and the experimental ones are the standards

Transport equation solving methods

International Nuclear Information System (INIS)

Granjean, P.M.

1984-06-01

This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr

Non-perturbative background field calculations

Science.gov (United States)

Stephens, C. R.

1988-01-01

New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation—perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation.

The numerical solution of linear multi-term fractional differential equations: systems of equations

Science.gov (United States)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

Stable solution of the energy equation for the calculation of transitory regimes of natural convection in sodium circuits

International Nuclear Information System (INIS)

Walsh, L.M.

1988-01-01

A new treatment is given to the problem studied in the previous work 'Conveccao Natural em um Circuito Termico a Sodio' (1981) by the same author. It consists of another method of the solution of the energy equation. It was obtained some stability in the numerical calculation independent of the value of the step; it was also obtained a considerable reduction in the machine time. A new program is being elaborated for testing the time reduction as compared to the previous one. (author) [pt

On the Use of a Direct Radiative Transfer Equation Solver for Path Loss Calculation in Underwater Optical Wireless Channels

KAUST Repository

Li, Changping; Park, Kihong; Alouini, Mohamed-Slim

2015-01-01

In this letter, we propose a fast numerical solution for the steady state radiative transfer equation based on the approach in [1] in order to calculate the optical path loss of light propagation suffering from attenuation due to the absorption and scattering in various water types. We apply an optimal non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. Finally, we extend the resulting radiance in 2-dimensional to 3-dimensional by the azimuthal symmetric assumption to compute the received optical power under the given receiver aperture and field of view. The accuracy and efficiency of the proposed scheme are validated by uniform RTE solver and Monte Carlo simulations.

On the Use of a Direct Radiative Transfer Equation Solver for Path Loss Calculation in Underwater Optical Wireless Channels

KAUST Repository

Li, Changping

2015-07-22

In this letter, we propose a fast numerical solution for the steady state radiative transfer equation based on the approach in [1] in order to calculate the optical path loss of light propagation suffering from attenuation due to the absorption and scattering in various water types. We apply an optimal non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. Finally, we extend the resulting radiance in 2-dimensional to 3-dimensional by the azimuthal symmetric assumption to compute the received optical power under the given receiver aperture and field of view. The accuracy and efficiency of the proposed scheme are validated by uniform RTE solver and Monte Carlo simulations.

Lung Dose Calculation With SPECT/CT for {sup 90}Yittrium Radioembolization of Liver Cancer

Energy Technology Data Exchange (ETDEWEB)

Yu, Naichang, E-mail: yun@ccf.org [Department of Radiation Oncology, Cleveland Clinic, Cleveland, OH (United States); Srinivas, Shaym M.; DiFilippo, Frank P.; Shrikanthan, Sankaran [Department of Nuclear Medicine, Cleveland Clinic, Cleveland, OH (United States); Levitin, Abraham; McLennan, Gordon; Spain, James [Department of Interventional Radiology, Cleveland Clinic, Cleveland, OH (United States); Xia, Ping; Wilkinson, Allan [Department of Radiation Oncology, Cleveland Clinic, Cleveland, OH (United States)

2013-03-01

Purpose: To propose a new method to estimate lung mean dose (LMD) using technetium-99m labeled macroaggregated albumin ({sup 99m}Tc-MAA) single photon emission CT (SPECT)/CT for {sup 90}Yttrium radioembolization of liver tumors and to compare the LMD estimated using SPECT/CT with clinical estimates of LMD using planar gamma scintigraphy (PS). Methods and Materials: Images of 71 patients who had SPECT/CT and PS images of {sup 99m}Tc-MAA acquired before TheraSphere radioembolization of liver cancer were analyzed retrospectively. LMD was calculated from the PS-based lung shunt assuming a lung mass of 1 kg and 50 Gy per GBq of injected activity shunted to the lung. For the SPECT/CT-based estimate, the LMD was calculated with the activity concentration and lung volume derived from SPECT/CT. The effect of attenuation correction and the patient's breathing on the calculated LMD was studied with the SPECT/CT. With these effects correctly taken into account in a more rigorous fashion, we compared the LMD calculated with SPECT/CT with the LMD calculated with PS. Results: The mean dose to the central region of the lung leads to a more accurate estimate of LMD. Inclusion of the lung region around the diaphragm in the calculation leads to an overestimate of LMD due to the misregistration of the liver activity to the lung from the patient's breathing. LMD calculated based on PS is a poor predictor of the actual LMD. For the subpopulation with large lung shunt, the mean overestimation from the PS method for the lung shunt was 170%. Conclusions: A new method of calculating the LMD for TheraSphere and SIR-Spheres radioembolization of liver cancer based on {sup 99m}Tc-MAA SPECT/CT is presented. The new method provides a more accurate estimate of radiation risk to the lungs. For patients with a large lung shunt calculated from PS, a recalculation of LMD based on SPECT/CT is recommended.

Lung dose calculation with SPECT/CT for ⁹⁰Yittrium radioembolization of liver cancer.

Science.gov (United States)

Yu, Naichang; Srinivas, Shaym M; Difilippo, Frank P; Shrikanthan, Sankaran; Levitin, Abraham; McLennan, Gordon; Spain, James; Xia, Ping; Wilkinson, Allan

2013-03-01

To propose a new method to estimate lung mean dose (LMD) using technetium-99m labeled macroaggregated albumin ((99m)Tc-MAA) single photon emission CT (SPECT)/CT for (90)Yttrium radioembolization of liver tumors and to compare the LMD estimated using SPECT/CT with clinical estimates of LMD using planar gamma scintigraphy (PS). Images of 71 patients who had SPECT/CT and PS images of (99m)Tc-MAA acquired before TheraSphere radioembolization of liver cancer were analyzed retrospectively. LMD was calculated from the PS-based lung shunt assuming a lung mass of 1 kg and 50 Gy per GBq of injected activity shunted to the lung. For the SPECT/CT-based estimate, the LMD was calculated with the activity concentration and lung volume derived from SPECT/CT. The effect of attenuation correction and the patient's breathing on the calculated LMD was studied with the SPECT/CT. With these effects correctly taken into account in a more rigorous fashion, we compared the LMD calculated with SPECT/CT with the LMD calculated with PS. The mean dose to the central region of the lung leads to a more accurate estimate of LMD. Inclusion of the lung region around the diaphragm in the calculation leads to an overestimate of LMD due to the misregistration of the liver activity to the lung from the patient's breathing. LMD calculated based on PS is a poor predictor of the actual LMD. For the subpopulation with large lung shunt, the mean overestimation from the PS method for the lung shunt was 170%. A new method of calculating the LMD for TheraSphere and SIR-Spheres radioembolization of liver cancer based on (99m)Tc-MAA SPECT/CT is presented. The new method provides a more accurate estimate of radiation risk to the lungs. For patients with a large lung shunt calculated from PS, a recalculation of LMD based on SPECT/CT is recommended. Copyright © 2013 Elsevier Inc. All rights reserved.

Calculating qP-wave traveltimes in 2-D TTI media by high-order fast sweeping methods with a numerical quartic equation solver

Science.gov (United States)

Han, Song; Zhang, Wei; Zhang, Jie

2017-09-01

A fast sweeping method (FSM) determines the first arrival traveltimes of seismic waves by sweeping the velocity model in different directions meanwhile applying a local solver. It is an efficient way to numerically solve Hamilton-Jacobi equations for traveltime calculations. In this study, we develop an improved FSM to calculate the first arrival traveltimes of quasi-P (qP) waves in 2-D tilted transversely isotropic (TTI) media. A local solver utilizes the coupled slowness surface of qP and quasi-SV (qSV) waves to form a quartic equation, and solve it numerically to obtain possible traveltimes of qP-wave. The proposed quartic solver utilizes Fermat's principle to limit the range of the possible solution, then uses the bisection procedure to efficiently determine the real roots. With causality enforced during sweepings, our FSM converges fast in a few iterations, and the exact number depending on the complexity of the velocity model. To improve the accuracy, we employ high-order finite difference schemes and derive the second-order formulae. There is no weak anisotropy assumption, and no approximation is made to the complex slowness surface of qP-wave. In comparison to the traveltimes calculated by a horizontal slowness shooting method, the validity and accuracy of our FSM is demonstrated.

Volume Estimates in Chronic Hemodialysis Patients by the Watson Equation and Bioimpedance Spectroscopy and the Impact on the Kt/Vurea calculation.

Science.gov (United States)

Noori, Nazanin; Wald, Ron; Sharma Parpia, Arti; Goldstein, Marc B

2018-01-01

Accurate assessment of total body water (TBW) is essential for the evaluation of dialysis adequacy (Kt/V urea ). The Watson formula, which is recommended for the calculation of TBW, was derived in healthy volunteers thereby leading to potentially inaccurate TBW estimates in maintenance hemodialysis recipients. Bioimpedance spectroscopy (BIS) may be a robust alternative for the measurement of TBW in hemodialysis recipients. The primary objective of this study was to evaluate the accuracy of Watson formula-derived TBW estimates as compared with TBW measured with BIS. Second, we aimed to identify the anthropometric characteristics that are most likely to generate inaccuracy when using the Watson formula to calculate TBW. Finally, we derived novel anthropometric equations for the more accurate estimation of TBW. This was a cross-sectional study of prevalent in-center HD patients at St Michael's Hospital. One hundred eighty-four hemodialysis patients (109 men and 75 women) were evaluated in this study. Anthropometric measurements including weight, height, waist circumference, midarm circumference, and 4-site skinfold (biceps, triceps, subscapular, and suprailiac) thickness were measured; fat mass was measured using the formula by Durnin and Womersley. We measured TBW by BIS using the Body Composition Monitor (Fresenius Medical Care, Bad Homburg, Germany). We used the Bland-Altman method to calculate the difference between the TBW derived from the Watson method and the BIS. To derive new equations for TBW estimation, Pearson's correlation coefficients between BIS-TBW (the reference test) and other variables were examined. We used the least squares regression analysis to develop parsimonious equations to predict TBW. TBW values based on the Watson method had a high correlation with BIS-TBW (correlation coefficients = 0.87 and P Watson formula overestimated TBW by 5.1 (4.5-5.8) liters and 3.8 (3.0-4.5) liters, in men and women, respectively. Higher fat mass and waist

Relativistic three-particle dynamical equations: I. Theoretical development

International Nuclear Information System (INIS)

Adhikari, S.K.; Tomio, L.; Frederico, T.

1993-11-01

Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, three dimensional scattering integral equations satisfying constrains of relativistic unitarity and covariance are rederived. These equations were first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence it is shown to perform and relate dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, several three dimensional three-particle scattering equations satisfying constraints of relativistic unitary and covariance are derived. Two of these three-particle equations are related by a transformation of variables as in the two-particle case. The three-particle equations obtained are very practical and suitable for performing relativistic scattering calculations. (author)

Calculation of radon concentration in water by toluene extraction method

Energy Technology Data Exchange (ETDEWEB)

Saito, Masaaki [Tokyo Metropolitan Isotope Research Center (Japan)

1997-02-01

Noguchi method and Horiuchi method have been used as the calculation method of radon concentration in water. Both methods have two problems in the original, that is, the concentration calculated is changed by the extraction temperature depend on the incorrect solubility data and the concentration calculated are smaller than the correct values, because the radon calculation equation does not true to the gas-liquid equilibrium theory. However, the two problems are solved by improving the radon equation. I presented the Noguchi-Saito equation and the constant B of Horiuchi-Saito equation. The calculating results by the improved method showed about 10% of error. (S.Y.)

Spurious solutions in few-body equations. II. Numerical investigations

International Nuclear Information System (INIS)

Adhikari, S.K.

1979-01-01

A recent analytic study of spurious solutions in few-body equations by Adhikari and Gloeckle is here complemented by numerical investigations. As proposed by Adhikari and Gloeckle we study numerically the spurious solutions in the three-body Weinberg type equations and draw some general conclusions about the existence of spurious solutions in three-body equations with the Weinberg kernel and in other few-body formulations. In particular we conclude that for most of the potentials we encounter in problems of nuclear physics the three-body Weinberg type equation will not have a spurious solution which may interfere with the bound state or scattering calculation. Hence, if proven convenient, the three-body Weinberg type equation can be used in practical calculations. The same conclusion is true for the three-body channel coupling array scheme of Kouri, Levin, and Tobocman. In the case of the set of six coupled four-body equations proposed by Rosenberg et al. and the set of the Bencze-Redish-Sloan equations a careful study of the possible spurious solutions is needed before using these equations in practical calculations

On the water saturation calculation in hydrocarbon sandstone reservoirs

Energy Technology Data Exchange (ETDEWEB)

Stalheim, Stein Ottar

2002-07-01

The main goal of this work was to identify the most important uncertainty sources in water saturation calculation and examine the possibility for developing new S{sub w} - equations or possibility to develop methods to remove weaknesses and uncertainties in existing S{sub w} - equations. Due to the need for industrial applicability of the equations we aimed for results with the following properties: The accuracy in S{sub w} should increase compared with existing S{sub w} - equations. The equations should be simple to use in petrophysical evaluations. The equations should be based on conventional logs and use as few as possible input parameters. The equations should be numerical stable. This thesis includes an uncertainty and sensitivity analysis of the most common S{sub w} equations. The results are addressed in chapter 3 and were intended to find the most important uncertainty sources in water saturation calculation. To increase the knowledge of the relationship between R{sub t} and S{sub w} in hydrocarbon sandstone reservoirs and to understand how the pore geometry affects the conductivity (n and m) of the rock a theoretical study was done. It was also an aim to examine the possibility for developing new S{sub w} - equations (or investigation an effective medium model) valid inhydrocarbon sandstone reservoirs. The results are presented in paper 1. A new equation for water saturation calculation in clean sandstone oil reservoirs is addressed in paper 2. A recommendation for best practice of water saturation calculation in non water wet formation is addressed in paper 3. Finally a new equation for water saturation calculation in thinly interbedded sandstone/mudstone reservoirs is presented in paper 4. The papers are titled: 1) Is the saturation exponent n a constant. 2) A New Model for Calculating Water Saturation In 3) Influence of wettability on water saturation modeling. 4) Water Saturation Calculations in Thinly Interbedded Sandstone/mudstone Reservoirs. A

Derivation of new 3D discrete ordinate equations

International Nuclear Information System (INIS)

Ahrens, C. D.

2012-01-01

The Sn equations have been the workhorse of deterministic radiation transport calculations for many years. Here we derive two new angular discretizations of the 3D transport equation. The first set of equations, derived using Lagrange interpolation and collocation, retains the classical Sn structure, with the main difference being how the scattering source is calculated. Because of the formal similarity with the classical S n equations, it should be possible to modify existing computer codes to take advantage of the new formulation. In addition, the new S n-like equations correctly capture delta function scattering. The second set of equations, derived using a Galerkin technique, does not retain the classical Sn structure because the streaming term is not diagonal. However, these equations can be cast into a form similar to existing methods developed to reduce ray effects. Numerical investigation of both sets of equations is under way. (authors)

Extraction of dynamical equations from chaotic data

International Nuclear Information System (INIS)

Rowlands, G.; Sprott, J.C.

1991-02-01

A method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise. The equations facilitate calculation of fractal dimension, Lyapunov exponents and short-term predictions. The method is applied to data derived from numerical solutions of the Logistic equation, the Henon equations, the Lorenz equations and the Roessler equations. 10 refs., 5 figs

Calculation Of Pneumatic Attenuation In Pressure Sensors

Science.gov (United States)

Whitmore, Stephen A.

1991-01-01

Errors caused by attenuation of air-pressure waves in narrow tubes calculated by method based on fundamental equations of flow. Changes in ambient pressure transmitted along narrow tube to sensor. Attenuation of high-frequency components of pressure wave calculated from wave equation derived from Navier-Stokes equations of viscous flow in tube. Developed to understand and compensate for frictional attenuation in narrow tubes used to connect aircraft pressure sensors with pressure taps on affected surfaces.

Biased calculations: Numeric anchors influence answers to math equations

Directory of Open Access Journals (Sweden)

Andrew R. Smith

2011-02-01

Full Text Available People must often perform calculations in order to produce a numeric estimate (e.g., a grocery-store shopper estimating the total price of his or her shopping cart contents. The current studies were designed to test whether estimates based on calculations are influenced by comparisons with irrelevant anchors. Previous research has demonstrated that estimates across a wide range of contexts assimilate toward anchors, but none has examined estimates based on calculations. In two studies, we had participants compare the answers to math problems with anchors. In both studies, participants' estimates assimilated toward the anchor values. This effect was moderated by time limit such that the anchoring effects were larger when the participants' ability to engage in calculations was limited by a restrictive time limit.

Radar equations for modern radar

CERN Document Server

Barton, David K

2012-01-01

Based on the classic Radar Range-Performance Analysis from 1980, this practical volume extends that work to ensure applicability of radar equations to the design and analysis of modern radars. This unique book helps you identify what information on the radar and its environment is needed to predict detection range. Moreover, it provides equations and data to improve the accuracy of range calculations. You find detailed information on propagation effects, methods of range calculation in environments that include clutter, jamming and thermal noise, as well as loss factors that reduce radar perfo

Low-density lipoprotein cholesterol and the risk of cancer: a mendelian randomization study

DEFF Research Database (Denmark)

Benn, Marianne; Tybjærg-Hansen, Anne; Stender, Stefan

2011-01-01

cholesterol was calculated using the Friedewald equation in samples in which the triglyceride level was less than 354 mg/dL and measured directly by colorimetry for samples with higher triglyceride levels. Risk of cancer was estimated prospectively using Cox proportional hazards regression analyses and cross...

The impact of using weight estimated from mammographic images vs. self-reported weight on breast cancer risk calculation

Science.gov (United States)

Nair, Kalyani P.; Harkness, Elaine F.; Gadde, Soujanye; Lim, Yit Y.; Maxwell, Anthony J.; Moschidis, Emmanouil; Foden, Philip; Cuzick, Jack; Brentnall, Adam; Evans, D. Gareth; Howell, Anthony; Astley, Susan M.

2017-03-01

Personalised breast screening requires assessment of individual risk of breast cancer, of which one contributory factor is weight. Self-reported weight has been used for this purpose, but may be unreliable. We explore the use of volume of fat in the breast, measured from digital mammograms. Volumetric breast density measurements were used to determine the volume of fat in the breasts of 40,431 women taking part in the Predicting Risk Of Cancer At Screening (PROCAS) study. Tyrer-Cuzick risk using self-reported weight was calculated for each woman. Weight was also estimated from the relationship between self-reported weight and breast fat volume in the cohort, and used to re-calculate Tyrer-Cuzick risk. Women were assigned to risk categories according to 10 year risk (below average =8%) and the original and re-calculated Tyrer-Cuzick risks were compared. Of the 716 women diagnosed with breast cancer during the study, 15 (2.1%) moved into a lower risk category, and 37 (5.2%) moved into a higher category when using weight estimated from breast fat volume. Of the 39,715 women without a cancer diagnosis, 1009 (2.5%) moved into a lower risk category, and 1721 (4.3%) into a higher risk category. The majority of changes were between below average and average risk categories (38.5% of those with a cancer diagnosis, and 34.6% of those without). No individual moved more than one risk group. Automated breast fat measures may provide a suitable alternative to self-reported weight for risk assessment in personalized screening.

Evaluation of mixing rules for VLE calculations

International Nuclear Information System (INIS)

Adachi, Y.; Chung, W.K.; Lu, B.C.Y.; Yu, J.M.

1983-01-01

This chapter calculates vapor-liquid equilibrium (VLE) values for a number of binary systems of cryogenic interest, including hydrogen- and helium-containing mixtures, by means of several selected cubic equations of state using different sets of mixing rules. The aim is to test the capabilities of these equations for representing VLE values for the selected mixtures, and to identify and recommend the most suitable equation of state together with its compatible mixing rules for the desired data representation. It is determined that the conventional mixing rules together with the modified van der Waals equation, or the four-parameter equation, are suitable for calculating VLE values for the selected systems at cryogenic conditions. The Peng-Robinson and four-parameter equations may yield slightly better results for helium-containing systems

Methods for the solution of the two-dimensional radiation-transfer equation

International Nuclear Information System (INIS)

Weaver, R.; Mihalas, D.; Olson, G.

1982-01-01

We use the variable Eddington factor (VEF) approximation to solve the time-dependent two-dimensional radiation transfer equation. The transfer equation and its moments are derived for an inertial frame of reference in cylindrical geometry. Using the VEF tensor to close the moment equations, we manipulate them into a combined moment equation that results in an energy equation, which is automatically flux limited. There are two separable facets in this method of solution. First, given the variable Eddington tensor, we discuss the efficient solution of the combined moment matrix equation. The second facet of the problem is the calculation of the variable Eddington tensor. Several options for this calculation, as well as physical limitations on the use of locally-calculated Eddington factors, are discussed

40 CFR 98.363 - Calculating GHG emissions.

Science.gov (United States)

2010-07-01

... combustion device (metric tons CH4/yr). V = Average annual volumetric flow rate, calculated in Equation JJ-7... CH4 flow to digester combustion device, as calculated in Equation JJ-6 of this section (metric tons CH4). DE = CH4 destruction efficiency from flaring or burning in engine (lesser of manufacturer's...

Optimum biasing of integral equations in Monte Carlo calculations

International Nuclear Information System (INIS)

Hoogenboom, J.E.

1979-01-01

In solving integral equations and estimating average values with the Monte Carlo method, biasing functions may be used to reduce the variancee of the estimates. A simple derivation was used to prove the existence of a zero-variance collision estimator if a specific biasing function and survival probability are applied. This optimum biasing function is the same as that used for the well known zero-variance last-event estimator

Exergy analysis on throttle reduction efficiency based on real gas equations

International Nuclear Information System (INIS)

Luo, Yuxi; Wang, Xuanyin

2010-01-01

This paper proposes an approach to calculate the efficiency of throttling in which the exergy (available energy) is used to evaluate the energy conversion processes. In the exergy calculation for real gases, a difficult part of integration can be removed by judiciously advised thermodynamic paths; the compressibility factor is calculated by using Peng-Robinson (P-R) equation. It is found that the largest deviation between the exergies calculated by the real gas equation and ideal gas assumption is about 1%. Because the exergy is a function of the pressure and temperature, the Joule-Thomson coefficients are used to calculate the temperature changes of throttling, based on the compressibility factors of the Soave-Redlich-Kwong (S-R-K) and P-R equations, and the temperature decreases are compared with those calculated by empirical formula. The result shows that the heat exergy contributes very little in throttling. The simple equation of ideal gas is suggested to calculate the efficiency of throttling for air at atmospheric temperatures.

Green function of the double-fractional Fokker-Planck equation: Path integral and stochastic differential equations

Science.gov (United States)

Kleinert, H.; Zatloukal, V.

2013-11-01

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

Calculation of Critical Temperatures by Empirical Formulae

Directory of Open Access Journals (Sweden)

Trzaska J.

2016-06-01

Full Text Available The paper presents formulas used to calculate critical temperatures of structural steels. Equations that allow calculating temperatures Ac1, Ac3, Ms and Bs were elaborated based on the chemical composition of steel. To elaborate the equations the multiple regression method was used. Particular attention was paid to the collection of experimental data which was required to calculate regression coefficients, including preparation of data for calculation. The empirical data set included more than 500 chemical compositions of structural steel and has been prepared based on information available in literature on the subject.

Hamming generalized corrector for reactivity calculation

International Nuclear Information System (INIS)

Suescun-Diaz, Daniel; Ibarguen-Gonzalez, Maria C.; Figueroa-Jimenez, Jorge H.

2014-01-01

This work presents the Hamming method generalized corrector for numerically resolving the differential equation of delayed neutron precursor concentration from the point kinetics equations for reactivity calculation, without using the nuclear power history or the Laplace transform. A study was carried out of several correctors with their respective modifiers with different time step calculations, to offer stability and greater precision. Better results are obtained for some correctors than with other existing methods. Reactivity can be calculated with precision of the order h 5 , where h is the time step. (orig.)

Real-time fluorescence target/background (T/B) ratio calculation in multimodal endoscopy for detecting GI tract cancer

Science.gov (United States)

Jiang, Yang; Gong, Yuanzheng; Wang, Thomas D.; Seibel, Eric J.

2017-02-01

Multimodal endoscopy, with fluorescence-labeled probes binding to overexpressed molecular targets, is a promising technology to visualize early-stage cancer. T/B ratio is the quantitative analysis used to correlate fluorescence regions to cancer. Currently, T/B ratio calculation is post-processing and does not provide real-time feedback to the endoscopist. To achieve real-time computer assisted diagnosis (CAD), we establish image processing protocols for calculating T/B ratio and locating high-risk fluorescence regions for guiding biopsy and therapy in Barrett's esophagus (BE) patients. Methods: Chan-Vese algorithm, an active contour model, is used to segment high-risk regions in fluorescence videos. A semi-implicit gradient descent method was applied to minimize the energy function of this algorithm and evolve the segmentation. The surrounding background was then identified using morphology operation. The average T/B ratio was computed and regions of interest were highlighted based on user-selected thresholding. Evaluation was conducted on 50 fluorescence videos acquired from clinical video recordings using a custom multimodal endoscope. Results: With a processing speed of 2 fps on a laptop computer, we obtained accurate segmentation of high-risk regions examined by experts. For each case, the clinical user could optimize target boundary by changing the penalty on area inside the contour. Conclusion: Automatic and real-time procedure of calculating T/B ratio and identifying high-risk regions of early esophageal cancer was developed. Future work will increase processing speed to <5 fps, refine the clinical interface, and apply to additional GI cancers and fluorescence peptides.

On calculation of difference in specific heats at constant pressure and constant volume using an empiric Nernst-Lindeman equation

International Nuclear Information System (INIS)

Leont'ev, K.L.

1981-01-01

Known theoretical and empirical formulae are considered for the difference in specific heats at constant pressure and volume. On the basis of the Grunaiser law on the ratio of specific heat to thermal expansion and on the basis of the correlation proposed by the author, between this ratio and average velocity of elastic waves obtained in a new expression for the difference in specific heats and determined are conditions at which empiric Nernst-Lindeman equation can be considered to be strict. Results of calculations for metals with fcc lattice are presented

Electronic representation of wave equation

Energy Technology Data Exchange (ETDEWEB)

Veigend, Petr; Kunovský, Jiří, E-mail: kunovsky@fit.vutbr.cz; Kocina, Filip; Nečasová, Gabriela; Valenta, Václav [University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic); Šátek, Václav [IT4Innovations, VŠB Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba (Czech Republic); University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic)

2016-06-08

The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.

The Dirac Equation in the algebraic approximation. VII. A comparison of molecular finite difference and finite basis set calculations using distributed Gaussian basis sets

NARCIS (Netherlands)

Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E

2001-01-01

A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and

The MiAge Calculator: a DNA methylation-based mitotic age calculator of human tissue types.

Science.gov (United States)

Youn, Ahrim; Wang, Shuang

2018-01-01

Cell division is important in human aging and cancer. The estimation of the number of cell divisions (mitotic age) of a given tissue type in individuals is of great interest as it allows not only the study of biological aging (using a new molecular aging target) but also the stratification of prospective cancer risk. Here, we introduce the MiAge Calculator, a mitotic age calculator based on a novel statistical framework, the MiAge model. MiAge is designed to quantitatively estimate mitotic age (total number of lifetime cell divisions) of a tissue using the stochastic replication errors accumulated in the epigenetic inheritance process during cell divisions. With the MiAge model, the MiAge Calculator was built using the training data of DNA methylation measures of 4,020 tumor and adjacent normal tissue samples from eight TCGA cancer types and was tested using the testing data of DNA methylation measures of 2,221 tumor and adjacent normal tissue samples of five other TCGA cancer types. We showed that within each of the thirteen cancer types studied, the estimated mitotic age is universally accelerated in tumor tissues compared to adjacent normal tissues. Across the thirteen cancer types, we showed that worse cancer survivals are associated with more accelerated mitotic age in tumor tissues. Importantly, we demonstrated the utility of mitotic age by showing that the integration of mitotic age and clinical information leads to improved survival prediction in six out of the thirteen cancer types studied. The MiAge Calculator is available at http://www.columbia.edu/∼sw2206/softwares.htm .

Calculation of Volterra kernels for solutions of nonlinear differential equations

NARCIS (Netherlands)

van Hemmen, JL; Kistler, WM; Thomas, EGF

2000-01-01

We consider vector-valued autonomous differential equations of the form x' = f(x) + phi with analytic f and investigate the nonanticipative solution operator phi bar right arrow A(phi) in terms of its Volterra series. We show that Volterra kernels of order > 1 occurring in the series expansion of

Improved g-level calculations for coil planet centrifuges.

Science.gov (United States)

van den Heuvel, Remco N A M; König, Carola S

2011-09-09

Calculation of the g-level is often used to compare CCC centrifuges, either against each other or to allow for comparison with other centrifugal techniques. This study shows the limitations of calculating the g-level in the traditional way. Traditional g-level calculations produce a constant value which does not accurately reflect the dynamics of the coil planet centrifuge. This work has led to a new equation which can be used to determine the improved non-dimensional values. The new equations describe the fluctuating radial and tangential g-level associated with CCC centrifuges and the mean radial g-level value. The latter has been found to be significantly different than that determined by the traditional equation. This new equation will give a better understanding of forces experienced by sample components and allows for more accurate comparison between centrifuges. Although the new equation is far better than the traditional equation for comparing different types of centrifuges, other factors such as the mixing regime may need to be considered to improve the comparison further. Copyright © 2011 Elsevier B.V. All rights reserved.

Sensitivity of rocky planet structures to the equation of state

International Nuclear Information System (INIS)

Swift, D.C.

2009-01-01

Structures were calculated for Mercury, Venus, Earth, the Moon, and Mars, using a core-mantle model and adjusting the core radius to reproduce the observed mass and diameter of each body. Structures were calculated using Fe and basalt equations of state of different degrees of sophistication for the core and mantle. The choice of equation of state had a significant effect on the inferred structure. For each structure, the moment of inertia ratio was calculated and compared with observed values. Linear Grueneisen equations of state fitted to limited portions of shock data reproduced the observed moments of inertia significantly better than did more detailed equations of state incorporating phase transitions, presumably reflecting the actual compositions of the bodies. The linear Grueneisen equations of state and corresponding structures seem however to be a reasonable starting point for comparative simulations of large-scale astrophysical impacts.

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

Science.gov (United States)

Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

2015-12-01

The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

Comparing the measured basal metabolic rates in patients with chronic disorders of consciousness to the estimated basal metabolic rate calculated from common predictive equations.

Science.gov (United States)

Xiao, Guizhen; Xie, Qiuyou; He, Yanbin; Wang, Ziwen; Chen, Yan; Jiang, Mengliu; Ni, Xiaoxiao; Wang, Qinxian; Murong, Min; Guo, Yequn; Qiu, Xiaowen; Yu, Ronghao

2017-10-01

Accurately predicting the basal metabolic rate (BMR) of patients in a vegetative state (VS) or minimally conscious state (MCS) is critical to proper nutritional therapy, but commonly used equations have not been shown to be accurate. Therefore, we compared the BMR measured by indirect calorimetry (IC) to BMR values estimated using common predictive equations in VS and MCS patients. Body composition variables were measured using the bioelectric impedance analysis (BIA) technique. BMR was measured by IC in 82 patients (64 men and 18 women) with VS or MCS. Patients were classified by body mass index as underweight (BMR was estimated for each group using the Harris-Benedict (H-B), Schofield, or Cunningham equations and compared to the measured BMR using Bland-Altman analyses. For the underweight group, there was a significant difference between the measured BMR values and the estimated BMR values calculated using the H-B, Schofield, and Cunningham equations (p BMR values estimated using the H-B and Cunningham equations were different significantly from the measured BMR (p BMR in the normal-weight group. The Schofield equation showed the best concordance (only 41.5%) with the BMR values measured by IC. None of the commonly used equations to estimate BMR were suitable for the VS or MCS populations. Indirect calorimetry is the preferred way to avoid either over or underestimate of BMR values. Copyright © 2016. Published by Elsevier Ltd.

New lumps of Veselov-Novikov integrable nonlinear equation and new exact rational potentials of two-dimensional stationary Schroedinger equation via ∂-macron-dressing method

International Nuclear Information System (INIS)

Dubrovsky, V.G.; Formusatik, I.B.

2003-01-01

The scheme for calculating via Zakharov-Manakov ∂-macron-dressing method of new rational solutions with constant asymptotic values at infinity of the famous two-dimensional Veselov-Novikov (VN) integrable nonlinear evolution equation and new exact rational potentials of two-dimensional stationary Schroedinger (2DSchr) equation with multiple pole wave functions is developed. As examples new lumps of VN nonlinear equation and new exact rational potentials of 2DSchr equation with multiple pole of order two wave functions are calculated. Among the constructed rational solutions are as nonsingular and also singular

A structural equation modelling approach to explore the role of B vitamins and immune markers in lung cancer risk.

Science.gov (United States)

Baltar, Valéria Troncoso; Xun, Wei W; Johansson, Mattias; Ferrari, Pietro; Chuang, Shu-Chun; Relton, Caroline; Ueland, Per Magne; Midttun, Øivind; Slimani, Nadia; Jenab, Mazda; Clavel-Chapelon, Françoise; Boutron-Ruault, Marie-Christine; Fagherazzi, Guy; Kaaks, Rudolf; Rohrmann, Sabine; Boeing, Heiner; Weikert, Cornelia; Bueno-de-Mesquita, Bas; Boshuizen, Hendriek; van Gils, Carla H; Onland-Moret, N Charlotte; Agudo, Antonio; Barricarte, Aurelio; Navarro, Carmen; Rodríguez, Laudina; Castaño, José Maria Huerta; Larrañaga, Nerea; Khaw, Kay-Tee; Wareham, Nick; Allen, Naomi E; Crowe, Francesca; Gallo, Valentina; Norat, Teresa; Krogh, Vittorio; Masala, Giovanna; Panico, Salvatore; Sacerdote, Carlotta; Tumino, Rosario; Trichopoulou, Antonia; Lagiou, Pagona; Trichopoulos, Dimitrios; Rasmuson, Torgny; Hallmans, Göran; Roswall, Nina; Tjønneland, Anne; Riboli, Elio; Brennan, Paul; Vineis, Paolo

2013-08-01

The one-carbon metabolism (OCM) is considered key in maintaining DNA integrity and regulating gene expression, and may be involved in the process of carcinogenesis. Several B-vitamins and amino acids have been implicated in lung cancer risk, via the OCM directly as well as immune system activation. However it is unclear whether these factors act independently or through complex mechanisms. The current study applies structural equations modelling (SEM) to further disentangle the mechanisms involved in lung carcinogenesis. SEM allows simultaneous estimation of linear relations where a variable can be the outcome in one equation and the predictor in another, as well as allowing estimation using latent variables (factors estimated by correlation matrix). A large number of biomarkers have been analysed from 891 lung cancer cases and 1,747 controls nested within the European Prospective Investigation into Cancer and Nutrition (EPIC) cohort. Four putative mechanisms in the OCM and immunity were investigated in relation to lung cancer risk: methionine-homocysteine metabolism, folate cycle, transsulfuration, and mechanisms involved in inflammation and immune activation, all adjusted for tobacco exposure. The hypothesized SEM model confirmed a direct and protective effect for factors representing methionine-homocysteine metabolism (p = 0.020) and immune activation (p = 0.021), and an indirect protective effect of folate cycle (p = 0.019), after adjustment for tobacco smoking. In conclusion, our results show that in the investigation of the involvement of the OCM, the folate cycle and immune system in lung carcinogenesis, it is important to consider complex pathways (by applying SEM) rather than the effects of single vitamins or nutrients (e.g. using traditional multiple regression). In our study SEM were able to suggest a greater role of the methionine-homocysteine metabolism and immune activation over other potential mechanisms.

A novel lattice energy calculation technique for simple inorganic crystals

Energy Technology Data Exchange (ETDEWEB)

Kaya, Cemal [Department of Chemistry, Faculty of Science, Cumhuriyet University, 58140 Sivas (Turkey); Kaya, Savaş, E-mail: savaskaya@cumhuriyet.edu.tr [Department of Chemistry, Faculty of Science, Cumhuriyet University, 58140 Sivas (Turkey); Banerjee, Priyabrata [Surface Engineering and Tribology Group, CSIR-Central Mechanical Engineering Research Institute, Mahatma Gandhi Avenue, Durgapur 713209 (India)

2017-01-01

In this pure theoretical study, a hitherto unexplored equation based on Shannon radii of the ions forming that crystal and chemical hardness of any crystal to calculate the lattice energies of simple inorganic ionic crystals has been presented. To prove the credibility of this equation, the results of the equation have been compared with experimental outcome obtained from Born-Fajans-Haber- cycle which is fundamentally enthalpy-based thermochemical cycle and prevalent theoretical approaches proposed for the calculation of lattice energies of ionic compounds. The results obtained and the comparisons made have demonstrated that the new equation is more useful compared to other theoretical approaches and allows to exceptionally accurate calculation of lattice energies of inorganic ionic crystals without doing any complex calculations.

Solving the neutron diffusion equation on combinatorial geometry computational cells for reactor physics calculations

International Nuclear Information System (INIS)

Azmy, Y. Y.

2004-01-01

An approach is developed for solving the neutron diffusion equation on combinatorial geometry computational cells, that is computational cells composed by combinatorial operations involving simple-shaped component cells. The only constraint on the component cells from which the combinatorial cells are assembled is that they possess a legitimate discretization of the underlying diffusion equation. We use the Finite Difference (FD) approximation of the x, y-geometry diffusion equation in this work. Performing the same combinatorial operations involved in composing the combinatorial cell on these discrete-variable equations yields equations that employ new discrete variables defined only on the combinatorial cell's volume and faces. The only approximation involved in this process, beyond the truncation error committed in discretizing the diffusion equation over each component cell, is a consistent-order Legendre series expansion. Preliminary results for simple configurations establish the accuracy of the solution to the combinatorial geometry solution compared to straight FD as the system dimensions decrease. Furthermore numerical results validate the consistent Legendre-series expansion order by illustrating the second order accuracy of the combinatorial geometry solution, the same as standard FD. Nevertheless the magnitude of the error for the new approach is larger than FD's since it incorporates the additional truncated series approximation. (authors)

The 'strength' of a system of differential equations

International Nuclear Information System (INIS)

Hoenselaers, C.

1977-01-01

A review of Einstein's concept of ''strength'' of a system of differential equations is given. As an example the strength of the Einstein-Maxwell equations for non-null Maxwell field is calculated and shown to be the same as for the pure vacuum Einstein equations. (auth.)

Macroscopic and microscopic description of HE-HI collisions; classical equations of motion calculations

International Nuclear Information System (INIS)

Bodmer, A.R.

1978-01-01

The study of high energy heavy ion reactions includes the three principle a priori approaches used for central collisions, namely, hydrodynamics, cascade--Boltzman equation, and the classical equations of motion. While no clearly justified central or near central collisions are found, the classical equations of motion are used to illustrate some general features of these reactions. It is expected that the hot nuclear matter produced in such collisions is a dense, viscous, and thermally conductive fluid with important nonequilibrium and nonclassical features, rapidity, distribution, noncentral collisions, potential dependent effects for a given two-body scattering, and c.m. cross sections for a central collision with given parameters are among the properties considered. 12 references

The Euler’s Graphical User Interface Spreadsheet Calculator for Solving Ordinary Differential Equations by Visual Basic for Application Programming

Science.gov (United States)

Gaik Tay, Kim; Cheong, Tau Han; Foong Lee, Ming; Kek, Sie Long; Abdul-Kahar, Rosmila

2017-08-01

In the previous work on Euler’s spreadsheet calculator for solving an ordinary differential equation, the Visual Basic for Application (VBA) programming was used, however, a graphical user interface was not developed to capture users input. This weakness may make users confuse on the input and output since those input and output are displayed in the same worksheet. Besides, the existing Euler’s spreadsheet calculator is not interactive as there is no prompt message if there is a mistake in inputting the parameters. On top of that, there are no users’ instructions to guide users to input the derivative function. Hence, in this paper, we improved previous limitations by developing a user-friendly and interactive graphical user interface. This improvement is aimed to capture users’ input with users’ instructions and interactive prompt error messages by using VBA programming. This Euler’s graphical user interface spreadsheet calculator is not acted as a black box as users can click on any cells in the worksheet to see the formula used to implement the numerical scheme. In this way, it could enhance self-learning and life-long learning in implementing the numerical scheme in a spreadsheet and later in any programming language.

Analytical solution to the hybrid diffusion-transport equation

International Nuclear Information System (INIS)

Nanneh, M.M.; Williams, M.M.R.

1986-01-01

A special integral equation was derived in previous work using a hybrid diffusion-transport theory method for calculating the flux distribution in slab lattices. In this paper an analytical solution of this equation has been carried out on a finite reactor lattice. The analytical results of disadvantage factors are shown to be accurate in comparison with the numerical results and accurate transport theory calculations. (author)

Rotor calculations for neutron spectroscopy; Calculs des rotors de spectrometres a neutrons

Energy Technology Data Exchange (ETDEWEB)

Gobert, G [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1968-07-01

The determination of stress in a rotating disk plane of symmetry normal to the axis of rotation has been studied by a number of investigators. In a recent paper Reich gives an operating process for an analytical solution in an asymmetric rotating disk. In the report we give the calculation of finite difference stress solutions applicable to the two rotating disks. The equations are then programmed for the 360.75 computer by Fortran methods concerning the rotors of choppers. (author) [French] La determination des contraintes dans les disques symetriques, en rotation a ete etudiee par de nombreux auteurs. Dans un recent rapport, Reich donne une solution pour le calcul des disques asymetriques. Ce rapport concerne l'application du calcul des contraintes par differences finies aux deux types de rotors. Les equations ecrites en langage Fortran pour l'ordinateur 360.75 concerne les rotors de choppers. (auteur)

Current evaluation of dose rate calculation - analytical method

International Nuclear Information System (INIS)

Tello, Marcos; Vilhena, Marco Tulio

1996-01-01

The accuracy of the dose calculations based on pencil beam formulas such as Fokker-Plank equations and Fermi equations for charged particle transport are studied and a methodology to solve the Boltzmann transport equation is suggested

Adjoint spectrum calculation in fuel heterogeneous cells

International Nuclear Information System (INIS)

Suster, Luis Carlos

1998-01-01

In most codes for cells calculation, the multigroup cross sections are generated taking into consideration the conservation of the reaction rates in the forward spectrum. However, for certain uses of the perturbation theory it's necessary to use the average of the parameters for energy macrogroups over the forward and the adjoint spectra. In this thesis the adjoint spectrum was calculated from the adjoint neutron balance equations, that were obtained for a heterogeneous unit cell. The collision probabilities method was used to obtain these equations. In order optimize the computational run-time, the Gaussian quadrature method was used in the calculation of the neutron balance equations, forward and adjoint. This method of integration was also used for the Doppler broadening functions calculation, necessary for obtaining the energy dependent cross sections. In order to calculate the reaction rates and the average cross sections, using both the forward and the adjoint neutron spectra, the most important resonances of the U 238 were considered. The results obtained with the method show significant differences for the different cross sections weighting schemes. (author)

Calculation of the quantities of radiation risk in Japanese population

International Nuclear Information System (INIS)

Nakamura, Yuji

1993-01-01

The purpose of this study was to reevaluate various kinds of indicators of radiation risks using additive projection and multiplicative projection models, as proposed by ICRP. Total death probability rate (1985) and probability rate of cancer death (1983 to 1987) were used as data base. The following indicators were calculated: total conditional death probability rate and conditional death probability rate; normalized death age probability density and unconditional death probability rate; attributable life-time probability of cancer death; and other risk indicators, including mean loss of life expectancy, reduction of life expectancy, mean annually committed probability of attributable cancer deaths, annual extra probability of cancer death, probability density of the age of death, maximum relative death probability rate (age at maximum relative rate), and probabilistic aging. In terms of calculations of these risk indicators for the comprehensive cancer death, there was no great difference between the Japanese population and ICRP. When calculating according to sites of cancer, calculations of indicators for cancer mortality (or cancer cure rate) in the Japanese population might bedifferent from ICRP's calculation. (N.K.) different from ICRP's calculations. (N.K.)

Magnetic Resonance Imaging Provides Added Value to the Prostate Cancer Prevention Trial Risk Calculator for Patients With Estimated Risk of High-grade Prostate Cancer Less Than or Equal to 10.

Science.gov (United States)

Kim, Eric H; Weaver, John K; Shetty, Anup S; Vetter, Joel M; Andriole, Gerald L; Strope, Seth A

2017-04-01

To determine the added value of prostate magnetic resonance imaging (MRI) to the Prostate Cancer Prevention Trial risk calculator. Between January 2012 and December 2015, 339 patients underwent prostate MRI prior to biopsy at our institution. MRI was considered positive if there was at least 1 Prostate Imaging Reporting and Data System 4 or 5 MRI suspicious region. Logistic regression was used to develop 2 models: biopsy outcome as a function of the (1) Prostate Cancer Prevention Trial risk calculator alone and (2) combined with MRI findings. When including all patients, the Prostate Cancer Prevention Trial with and without MRI models performed similarly (area under the curve [AUC] = 0.74 and 0.78, P = .06). When restricting the cohort to patients with estimated risk of high-grade (Gleason ≥7) prostate cancer ≤10%, the model with MRI outperformed the Prostate Cancer Prevention Trial alone model (AUC = 0.69 and 0.60, P = .01). Within this cohort of patients, there was no significant difference in discrimination between models for those with previous negative biopsy (AUC = 0.61 vs 0.63, P = .76), whereas there was a significant improvement in discrimination with the MRI model for biopsy-naïve patients (AUC = 0.72 vs 0.60, P = .01). The use of prostate MRI in addition to the Prostate Cancer Prevention Trial risk calculator provides a significant improvement in clinical risk discrimination for patients with estimated risk of high-grade (Gleason ≥7) prostate cancer ≤10%. Prebiopsy prostate MRI should be strongly considered for these patients. Copyright © 2016 Elsevier Inc. All rights reserved.

Sandia equation of state data base: seslan File

Energy Technology Data Exchange (ETDEWEB)

Kerley, G.I. [Sandia National Labs., Albuquerque, NM (US); Christian-Frear, T.L. [RE/SPEC Inc., Albuquerque, NM (US)

1993-06-24

Sandia National Laboratories maintains several libraries of equation of state tables, in a modified Sesame format, for use in hydrocode calculations and other applications. This report discusses one of those libraries, the seslan file, which contains 78 tables from the Los Alamos equation of state library. Minor changes have been made to these tables, making them more convenient for code users and reducing numerical difficulties that occasionally arise in hydrocode calculations.

The equation of state and ionization equilibrium of dense aluminum plasma with conductivity verification

International Nuclear Information System (INIS)

Wang, Kun; Shi, Zongqian; Shi, Yuanjie; Bai, Jun; Wu, Jian; Jia, Shenli

2015-01-01

The equation of state, ionization equilibrium, and conductivity are the most important parameters for investigation of dense plasma. The equation of state is calculated with the non-ideal effects taken into consideration. The electron chemical potential and pressure, which are commonly used thermodynamic quantities, are calculated by the non-ideal free energy and compared with results of a semi-empirical equation of state based on Thomas-Fermi-Kirzhnits model. The lowering of ionization potential, which is a crucial factor in the calculation of non-ideal Saha equation, is settled according to the non-ideal free energy. The full coupled non-ideal Saha equation is applied to describe the ionization equilibrium of dense plasma. The conductivity calculated by the Lee-More-Desjarlais model combined with non-ideal Saha equation is compared with experimental data. It provides a possible approach to verify the accuracy of the equation of state and ionization equilibrium

Differentiated thyroid cancer treatment with therapeutic doses of 131I calculated by dosimetry: our experience

International Nuclear Information System (INIS)

Fadel, Ana M.; Chebel, G.M.; Valdivieso, C.M.; Degrossi, Osvaldo J.; Cabrejas, R.; Cabrejas, M.L.

2006-01-01

The optimum dose for the differentiated thyroid cancer treatment is a motive of controversy. There exist two ways of deciding the dose to administer: the empirical method (fixed doses) and dosimetric calculation method. The use of fixed doses has demonstrated safety and effectiveness. Nevertheless there are cases in which the use of several small doses not resolves the metastases illness of the patients. Using the Benua-Leeper method for dosimetric calculation we have evaluated the maximum dose treatment that could be administered to 20 patients who showed persistent disease after several treatments with 131 I. (author) [es

Assessment of leakage dose in vivo in patients undergoing radiotherapy for breast cancer

Directory of Open Access Journals (Sweden)

Peta Lonski

2018-01-01

Full Text Available Background and purpose: Accurate quantification of the relatively small radiation doses delivered to untargeted regions during breast irradiation in patients with breast cancer is of increasing clinical interest for the purpose of estimating long-term radiation-related risks. Out-of-field dose calculations from commercial planning systems however may be inaccurate which can impact estimates for long-term risks associated with treatment. This work compares calculated and measured dose out-of-field and explores the application of a correction for leakage radiation. Materials and methods: Dose calculations of a Boltzmann transport equation solver, pencil beam-type, and superposition-type algorithms from a commercial treatment planning system (TPS were compared with in vivo thermoluminescent dosimetry (TLD measurements conducted out-of-field on the contralateral chest at points corresponding to the thyroid, axilla and contralateral breast of eleven patients undergoing tangential beam radiotherapy for breast cancer. Results: Overall, the TPS was found to under-estimate doses at points distal to the radiation field edge with a modern linear Boltzmann transport equation solver providing the best estimates. Application of an additive correction for leakage (0.04% of central axis dose improved correlation between the measured and calculated doses at points greater than 15 cm from the field edge. Conclusions: Application of a correction for leakage doses within peripheral regions is feasible and could improve accuracy of TPS in estimating out-of-field doses in breast radiotherapy. Keywords: Breast radiotherapy, TLD, Leakage dose, Dose calculation algorithm

Two-state approximation of the Fadeev-Hahn equations

International Nuclear Information System (INIS)

Brener, S.E.

1993-01-01

The equations have been chosen which allow both to solve the scattering problems and to calculate the parameters of bound states of three particles with Coulomb interaction when the system energy is below the decay to three separate particles. The method of constructing of equations which are most suitable for concrete problems is considered. Different numerical schemes to calculate the low energy scattering cross sections with two-particle clusterization in 'in' and 'out' collision's channels have been developed. The bounds of applied approaches were determined and the peculiarities connected with differently defined reaction amplitudes under these approaches have been considered. The interpretation of obtained results at different definitions of reaction amplitudes was demonstrated, and the elastic, inelastic cross sections and muon transfer rates in hydrogen isotope mesic atom collisions have been calculated using Fadeev-Hahn equations. (author)

Gravitational closure of matter field equations

Science.gov (United States)

Düll, Maximilian; Schuller, Frederic P.; Stritzelberger, Nadine; Wolz, Florian

2018-04-01

The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for diffeomorphism-invariant gravitational dynamics that can equip the coefficients of a given system of matter field equations with causally compatible canonical dynamics. Concretely, we show how starting from any linear local matter field equations whose principal polynomial satisfies three physicality conditions, one may calculate coefficient functions which then enter an otherwise immutable set of countably many linear homogeneous partial differential equations. Any solution of these so-called gravitational closure equations then provides a Lagrangian density for any type of tensorial geometry that features ultralocally in the initially specified matter Lagrangian density. Thus the given system of matter field equations is indeed closed by the so obtained gravitational equations. In contrast to previous work, we build the theory on a suitable associated bundle encoding the canonical configuration degrees of freedom, which allows one to include necessary constraints on the geometry in practically tractable fashion. By virtue of the presented mechanism, one thus can practically calculate, rather than having to postulate, the gravitational theory that is required by specific matter field dynamics. For the special case of standard model matter one obtains general relativity.

Development of Calculation Algorithm for ECCS Kinematic Shock

Energy Technology Data Exchange (ETDEWEB)

Lee, Seung-Chan; Yoon, Duk-Joo; Ha, Sang-Jun [KHNP-CRI, Daejeon (Korea, Republic of)

2014-10-15

The void fraction of inverted U-pipes in front of SI(Safety Injection) pumps impact on the pipe system of ECCS(Emergency Core Cooling Systems). This phenomena is called as 'Kinematic Shock'. The purpose of this paper is to achieve the more exactly calculation when the kinematic shock is calculated by simplified equation. The behavior of the void packet of the ECCS pipes is illustrated by the simplified (other name is kinematic shock equation).. The kinematic shock is defined as the depth of total length of void clusters in the pipes of ECCS when the void cluster is continually reached along the part of pipes in vertical direction. In this paper, the simplified equation is evaluated by comparing calculation error each other.]. The more exact methods of calculating the depth of the kinematic shock in ECCS is achieved. The error of kinematic shock calculation is strongly depended on the calculation search gap and the order of Taylor's expansion. From this study, to select the suitable search gap and the suitable calculation order, differential root method, secant method, and Taylor's expansion form are compared one another.

Complex solutions for generalised fitzhughnagumo equation

International Nuclear Information System (INIS)

Neirameh, A.

2014-01-01

During present investigation, a direct algebraic method on complex solutions of nonlinear partial differential equation is developed and tested in the case of generalized Burgers-Huxley equation. The proposed scheme can be used in a wide class of nonlinear reaction-diffusion equations. These calculations demonstrate that the accuracy of the direct algebraic solutions is quite high even in the case of a small number of grid points. This method is a very reliable, simple, small computation costs, flexible, and convenient alternative method. (author)

Calculation of propellant gas pressure by simple extended corresponding state principle

Directory of Open Access Journals (Sweden)

Bin Xu

2016-04-01

Full Text Available The virial equation can well describe gas state at high temperature and pressure, but the difficulties in virial coefficient calculation limit the use of virial equation. Simple extended corresponding state principle (SE-CSP is introduced in virial equation. Based on a corresponding state equation, including three characteristic parameters, an extended parameter is introduced to describe the second virial coefficient expressions of main products of propellant gas. The modified SE-CSP second virial coefficient expression was extrapolated based on the virial coefficients experimental temperature, and the second virial coefficients obtained are in good agreement with the experimental data at a low temperature and the theoretical values at high temperature. The maximum pressure in the closed bomb test was calculated with modified SE-CSP virial coefficient expressions with the calculated error of less than 2%, and the error was smaller than the result calculated with the reported values under the same calculation conditions. The modified SE-CSP virial coefficient expression provides a convenient and efficient method for practical virial coefficient calculation without resorting to complicated molecular model design and integral calculation.

Calculation code NIRVANA for free boundary MHD equilibrium

International Nuclear Information System (INIS)

Ninomiya, Hiromasa; Suzuki, Yasuo; Kameari, Akihisa

1975-03-01

The calculation method and code of solving the free boundary problem for MHD equilibrium has been developed. Usage of the code ''NIRVANA'' is described. The toroidal plasma current density determined as a function of the flux function PSI is substituted by a group of the ring currents, whereby the equation of MHD equilibrium is transformed into an integral equation. Either of the two iterative methods is chosen to solve the integral equation, depending on the assumptions made of the plasma surface points. Calculation of the magnetic field configurations is possible when the plasma surface coincides self-consistently with the magnetic flux including the separatrix points. The code is usable in calculation of the circular or non-circular shell-less Tokamak equilibrium. (auth.)

Validation of an online risk calculator for the prediction of anastomotic leak after colon cancer surgery and preliminary exploration of artificial intelligence-based analytics.

Science.gov (United States)

Sammour, T; Cohen, L; Karunatillake, A I; Lewis, M; Lawrence, M J; Hunter, A; Moore, J W; Thomas, M L

2017-11-01

Recently published data support the use of a web-based risk calculator ( www.anastomoticleak.com ) for the prediction of anastomotic leak after colectomy. The aim of this study was to externally validate this calculator on a larger dataset. Consecutive adult patients undergoing elective or emergency colectomy for colon cancer at a single institution over a 9-year period were identified using the Binational Colorectal Cancer Audit database. Patients with a rectosigmoid cancer, an R2 resection, or a diverting ostomy were excluded. The primary outcome was anastomotic leak within 90 days as defined by previously published criteria. Area under receiver operating characteristic curve (AUROC) was derived and compared with that of the American College of Surgeons National Surgical Quality Improvement Program ® (ACS NSQIP) calculator and the colon leakage score (CLS) calculator for left colectomy. Commercially available artificial intelligence-based analytics software was used to further interrogate the prediction algorithm. A total of 626 patients were identified. Four hundred and fifty-six patients met the inclusion criteria, and 402 had complete data available for all the calculator variables (126 had a left colectomy). Laparoscopic surgery was performed in 39.6% and emergency surgery in 14.7%. The anastomotic leak rate was 7.2%, with 31.0% requiring reoperation. The anastomoticleak.com calculator was significantly predictive of leak and performed better than the ACS NSQIP calculator (AUROC 0.73 vs 0.58) and the CLS calculator (AUROC 0.96 vs 0.80) for left colectomy. Artificial intelligence-predictive analysis supported these findings and identified an improved prediction model. The anastomotic leak risk calculator is significantly predictive of anastomotic leak after colon cancer resection. Wider investigation of artificial intelligence-based analytics for risk prediction is warranted.

Resting energy expenditure and body composition in patients with head and neck cancer: An observational study leading to a new predictive equation.

Science.gov (United States)

Souza, Micheline Tereza Pires; Singer, Pierre; Ozorio, Gislaine Aparecida; Rosa, Vitor Modesto; Alves, Maria Manuela Ferreira; Mendoza López, Rossana Verónica; Waitzberg, Dan L

2018-02-05

Patients with head and neck cancer have changes in body composition and resting energy expenditure (REE) related to significant inflammatory processes. We investigated REE and body composition in a population of patients with head and neck cancer, comparing the measured REE with predicted energy expenditure and deriving an equation of anthropometric values and body composition. This retrospective, observational, descriptive study of a single center included patients with head and neck cancer. We evaluated nutritional status by body mass index (BMI) and Patient-Generated Subjective Global Assessment (PG-SGA), body composition by electric bioimpedance, and REE by indirect calorimetry (IC). We included 140 patients, most of whom were men (80.7%), 60 y or older (58.6%), and had advanced disease (77.9%). Most were malnourished by BMI standards (77.9%) and severely malnourished according to the PG-SGA (49.3%), with a fat-free mass below the ideal values (82.9%) associated with sarcopenia (92.1%). Hypermetabolism was 57%. When comparing REE with the Harris-Benedict formula, we found the agreement limits from -546 613 to 240 708, the mean difference was -152 953 (95% confidence interval [CI], -185 844 to -120 062) and Pitman's variance test was r = -0.294 (P = 0.001). When we included the activity factor and the thermogenesis factor in REE and compared with Harris-Benedict, we found the agreement limits from -764.423 to 337.087, a mean difference of -213.668 (95% CI -259.684 to -167.652), and the Pitman's variance text at r = -0.292 (P = 0.001). Predictive equations, generally recommended by guidelines, are imprecise when compared with IC measures. Therefore, we suggest a new predictive equation. Copyright © 2018 Elsevier Inc. All rights reserved.

'Prostate Cancer Risk Calculator' mobile applications (Apps): a systematic review and scoring using the validated user version of the Mobile Application Rating Scale (uMARS).

Science.gov (United States)

Adam, Ahmed; Hellig, Julian C; Perera, Marlon; Bolton, Damien; Lawrentschuk, Nathan

2018-04-01

The use of mobile phone applications (Apps) has modernised the conventional practice of medicine. The diagnostic ability of the current Apps in prostate specific antigen monitoring, and its diagnostic ability within prostate cancer (PCa) risk calculators have not yet been appraised. We aimed to review, rate and assess the everyday functionality, and utility of all the currently available PCa risk calculator Apps. A systematic search on iTunes, Google Play Store, Blackberry World and Windows Apps Store, was performed on 23/11/2017, using the search term 'prostate cancer risk calculator'. After applying the exclusion criteria, each App was individually assessed and rated using pre-set criteria and grading was performed using the validated uMARS scale. In total, 83 Apps were retrieved. After applying our exclusion criteria, only 9 Apps were relevant, with 2 duplicated, and the remaining 7 were suitable for critical review. Data sizes ranged from 414 kb to 10.1 Mb. The cost of the Apps ranged from South African rand (ZAR) 0.00 to ZAR 29.99. The overall mean category uMARS scores ranged from 2.8/5 to 4.5/5. Apps such as Rotterdam Prostate Cancer Risk Calculator, Coral-Prostate Cancer Nomogram Calculator and CPC Risk Calculator, performed the best. The current PCa risk calculator mobile Apps available may be beneficial in counselling the concerned at risk patient. These Apps have potential to assist both the patient and the urologist alike. The PCa risk calculator App 'predictability' may be further enhanced by the incorporation of newly validated risk factors and predictors for PCa.

New equations to calculate temperature correction factors for PO2 in human blood.

Science.gov (United States)

Inaba, H; Ohwada, T; Sato, J; Mizuguchi, T; Hirasawa, H

1986-01-01

Effects of hemoglobin concentration (Hb), pH, and body temperature (T) on the relationships between delta log PO2/delta T and PO2 were studied by means of a mathematical model using a Newton-Raphson iteration method. The functions between delta log PO2/delta T and PO2 were affected by the above three factors. New equations considering the effects of Hb, pH, and T were proposed by modifying the equation reported by Severinghaus: delta log PO2/delta T = (L +(U-L)/(A(vPO237)B + 1))(10(-2) where U = 3.15-0.45(7.4-pH37) L = 0.68-0.09(7.4-pH37) A = 5.86(exp10(0.074(T)-0.294(7.4-pH37)-11))((Hb)0.913) B = 6.33(exp10(-0.0051(T)))((Hb)-0.113) + 0.24(7.4-pH37) and vPO237 is virtual PO237 which may exist when PO237 is corrected to standard conditions (pH = 7.4, BE = 0) by the following equations: vPO237 = PO237(exp10(fB(7.4-pH37)-0.0013(BE))) fB = (PO237/26.6)0.08-1.52 where fB is the Bohr factor. The above equations provided values of delta log PO2/delta T which fit closely to those obtained by the complex iteration method with maximum differences of less than 1.3 X 10(-3) at T = 27, indicating that maximum % errors for PO2 at T (PO2T) are less than 3.0% at T = 27 and that our equations can be applied over a wide range of Hb, pH37 and T.

Transport equation and shock waves

International Nuclear Information System (INIS)

Besnard, D.

1981-04-01

A multi-group method is derived from a one dimensional transport equation for the slowing down and spatial transport of energetic positive ions in a plasma. This method is used to calculate the behaviour of energetic charged particles in non homogeneous and non stationary plasma, and the effect of energy deposition of the particles on the heating of the plasma. In that purpose, an equation for the density of fast ions is obtained from the Fokker-Planck equation, and a closure condition for the second moment of this equation is deduced from phenomenological considerations. This method leads to a numerical method, simple and very efficient, which doesn't require much computer storage. Two types of numerical results are obtained. First, results on the slowing down of 3.5 MeV alpha particles in a 50 keV plasma plublished by Corman and al and Moses are compared with the results obtained with both our method and a Monte Carlo type method. Good agreement was obtained, even for energy deposition on the ions of the plasma. Secondly, we have calculated propagation of alpha particles heating a cold plasma. These results are in very good agreement with those given by an accurate Monte Carlo method, for both the thermal velocity, and the energy deposition in the plasma

SU-F-T-683: Cancer Stem Cell Hypothesis and Radiation Treatments

International Nuclear Information System (INIS)

Fourkal, E

2016-01-01

Purpose: The tumor control probability in radiation therapy allows comparing different radiation treatments to each other by means of calculating the probability that a prescribed dose of radiation eradicates or controls the tumor. In the conventional approach, all cancer cells can divide unlimited number of times and the tumor control often means eradicating every malignant cell by the radiation. In recent years however, there is a mounting consensus that in a given tumor volume there is a sub-population of cells, known as cancer stem cells (CSCs) that are responsible for tumor initiation and growth. Other or progenitor cancer cells can only divide limited number of times. This entails that only cancer stem cells may nned to be eliminated in order to control the tumor. Thus one may define TCP as the probability of eliminating CSCs for the given dose of radiation. Methods: Using stochastic methods, specifically the birth-and-death Markov processes, an infinite system of equations is set for probabilities of having m cancer stem cells at time t after the start of radiation. The TCP is calculated as the probability of no cancer stem cells surviving the radiation. Two scenarios are studied. In the first situation, the TCP is calculated for a unidirectional case when CSC gives birth to another CSC or a progenitor cell. In the second scenario, a bidirectional model is studied where the progenitor cell gives rise to CSC. Results: The proposed calculations show that the calculated TCP for CSC depends on whether one adopts unidirectional or bidirectional conversion models. The bidirectional model shows significantly lower TCP values for the given dose delivered to the tumor. Conclusion: Incorporating CSC hypothesis into the TCP modeling may notably influence the dose prescription as well as the concept of the expected TCP after the radiation treatments.

SU-F-T-683: Cancer Stem Cell Hypothesis and Radiation Treatments

Energy Technology Data Exchange (ETDEWEB)

Fourkal, E [Pinnacle Health Cancer Center, Harrisburg, PA (United States)

2016-06-15

Purpose: The tumor control probability in radiation therapy allows comparing different radiation treatments to each other by means of calculating the probability that a prescribed dose of radiation eradicates or controls the tumor. In the conventional approach, all cancer cells can divide unlimited number of times and the tumor control often means eradicating every malignant cell by the radiation. In recent years however, there is a mounting consensus that in a given tumor volume there is a sub-population of cells, known as cancer stem cells (CSCs) that are responsible for tumor initiation and growth. Other or progenitor cancer cells can only divide limited number of times. This entails that only cancer stem cells may nned to be eliminated in order to control the tumor. Thus one may define TCP as the probability of eliminating CSCs for the given dose of radiation. Methods: Using stochastic methods, specifically the birth-and-death Markov processes, an infinite system of equations is set for probabilities of having m cancer stem cells at time t after the start of radiation. The TCP is calculated as the probability of no cancer stem cells surviving the radiation. Two scenarios are studied. In the first situation, the TCP is calculated for a unidirectional case when CSC gives birth to another CSC or a progenitor cell. In the second scenario, a bidirectional model is studied where the progenitor cell gives rise to CSC. Results: The proposed calculations show that the calculated TCP for CSC depends on whether one adopts unidirectional or bidirectional conversion models. The bidirectional model shows significantly lower TCP values for the given dose delivered to the tumor. Conclusion: Incorporating CSC hypothesis into the TCP modeling may notably influence the dose prescription as well as the concept of the expected TCP after the radiation treatments.

Course on hybrid calculation

International Nuclear Information System (INIS)

Weill, J.; Tellier; Bonnemay; Craigne; Chareton; Di Falco

1969-02-01

After a definition of hybrid calculation (combination of analogue and digital calculation) with a distinction between series and parallel hybrid computing, and a description of a hybrid computer structure and of task sharing between computers, this course proposes a description of hybrid hardware used in Saclay and Cadarache computing centres, and of operations performed by these systems. The next part addresses issues related to programming languages and software. The fourth part describes how a problem is organised for its processing on these computers. Methods of hybrid analysis are then addressed: resolution of optimisation problems, of partial differential equations, and of integral equations by means of different methods (gradient, maximum principle, characteristics, functional approximation, time slicing, Monte Carlo, Neumann iteration, Fischer iteration)

Using the charge-stabilization technique in the double ionization potential equation-of-motion calculations with dianion references.

Science.gov (United States)

Kuś, Tomasz; Krylov, Anna I

2011-08-28

The charge-stabilization method is applied to double ionization potential equation-of-motion (EOM-DIP) calculations to stabilize unstable dianion reference functions. The auto-ionizing character of the dianionic reference states spoils the numeric performance of EOM-DIP limiting applications of this method. We demonstrate that reliable excitation energies can be computed by EOM-DIP using a stabilized resonance wave function instead of the lowest energy solution corresponding to the neutral + free electron(s) state of the system. The details of charge-stabilization procedure are discussed and illustrated by examples. The choice of optimal stabilizing Coulomb potential, which is strong enough to stabilize the dianion reference, yet, minimally perturbs the target states of the neutral, is the crux of the approach. Two algorithms of choosing optimal parameters of the stabilization potential are presented. One is based on the orbital energies, and another--on the basis set dependence of the total Hartree-Fock energy of the reference. Our benchmark calculations of the singlet-triplet energy gaps in several diradicals show a remarkable improvement of the EOM-DIP accuracy in problematic cases. Overall, the excitation energies in diradicals computed using the stabilized EOM-DIP are within 0.2 eV from the reference EOM spin-flip values. © 2011 American Institute of Physics

Calculation of cell face velocity of non-staggered grid system

KAUST Repository

Li, Wang

2012-07-28

In this paper, the cell face velocities in the discretization of the continuity equation, the momentum equation, and the scalar equation of a non-staggered grid system are calculated and discussed. Both the momentum interpolation and the linear interpolation are adopted to evaluate the coefficients in the discretized momentum and scalar equations. Their performances are compared. When the linear interpolation is used to calculate the coefficients, the mass residual term in the coefficients must be dropped to maintain the accuracy and convergence rate of the solution. © Shanghai University and Springer-Verlag Berlin Heidelberg 2012.

The calculated reference value of the tubular extraction rate in infants and children. An attempt to use a new regression equation

International Nuclear Information System (INIS)

Watanabe, Nami; Sugai Yukio; Komatani, Akio; Yamaguchi, Koichi; Takahashi, Kazuei

1999-01-01

This study was designed to investigate the empirical tubular extraction rate (TER) of the normal renal function in childhood and then propose a new equation to obtain TER theoretically. The empirical TER was calculated using Russell's method for determination of single-sample plasma clearance and 99m Tc-MAG 3 in 40 patients with renal disease younger than 10 years of age who were classified as having normal renal function using diagnostic criteria defined by the Paediatric Task Group of EANM. First, we investigated the relationships of the empirical value of absolute TER to age, body weight, body surface area (BSA) and distribution volume. Next we investigated the relationships of the empirical value of BSA corrected TER to age, body weight, BSA and distribution volume. Linear relationship was indicated between the absolute TER and each body dimensional factors, especially regarding to BSA, its correlation coefficient was 0.90 (p value). The BSA-corrected TER showed a logarithmic relationship with BSA, but linear regression did not show any significant correlation. Therefore, it was thought that the normal value of TER could be calculated theoretically using the body surface area, and here we proposed the following linear regression equation; Theoretical TER (ml/min/1.73 m 2 )=(-39.8+257.2 x BSA)/BSA/1.73. The theoretical TER could be one of the reference values of the renal function in the period of the renal maturation. (author)

On computation of relaxation constant α in Landau–Lifshitz–Gilbert equation

Energy Technology Data Exchange (ETDEWEB)

Gladkov, Serguey, E-mail: sglad@newmail.ru; Bogdanova, Sofiya, E-mail: sonjaf@list.ru

2014-11-15

Due to the quasi-classical kinetic equation (QKE) for the magnon distribution function to calculate the velocity of the domain wall motion V in magnetic fields H>H{sub a}, where H{sub a}− magnetic anisotropy field. Based on the comparison of this formula for Vthe analytic expression of relaxation constant α in Landau–Lifshitz–Gilbert equation was found. We used the detected correlation between the system's entropy and the environment's resistance force, and obtained an expression for the spin-lattice braking force that is applied to the moving domain wall. We calculated the mobility ratio of the domain wall. - Highlights: • The resistance force acting on the domain wall was calculated. • Mobility coefficient of domain wall was calculated. • The strict calculation of relaxation constant in equation Landau-Lifshitz- Gilbert.

3-D resistive MHD calculations for tokamak plasmas: beyond the simple reduced set of equations

International Nuclear Information System (INIS)

Carreras, B.A.; Garcia, L.; Hender, T.C.; Hicks, H.R.; Holmes, J.A.; Lynch, V.E.; Masden, B.F.

1983-01-01

Numerical studies of the resistive stability of tokamak plasmas in cylindrical geometry have been performed using: (1) the full set of resistive Magnetohydrodynamic (MHD) equations and (2) an extended version of the reduced set of resistive MHD equations including diamagnetic and electron temperature effects. In particular, the nonlinear interaction of tearing modes of many helicities has been investigated. The numerical results confirm many of the features uncovered previously using the simple reduced equations. (author)

Navier-Stokes-like equations for traffic flow.

Science.gov (United States)

Velasco, R M; Marques, W

2005-10-01

The macroscopic traffic flow equations derived from the reduced Paveri-Fontana equation are closed starting with the maximization of the informational entropy. The homogeneous steady state taken as a reference is obtained for a specific model of the desired velocity and a kind of Chapman-Enskog method is developed to calculate the traffic pressure at the Navier-Stokes level. Numerical solution of the macroscopic traffic equations is obtained and its characteristics are analyzed.

Câbles electriques - Calcul du courant admissible - Partie 1: Equations de l'intensité du courant admissible (facteur de charge 100%) et calcul des pertes - Section 2: Facteurs de pertes par courants de Foucault dans les gaines dans le cas de deux circuits disposés en nappe

CERN Document Server

International Electrotechnical Commission. Geneva

1993-01-01

Câbles electriques - Calcul du courant admissible - Partie 1: Equations de l'intensité du courant admissible (facteur de charge 100%) et calcul des pertes - Section 2: Facteurs de pertes par courants de Foucault dans les gaines dans le cas de deux circuits disposés en nappe

EQUATIONS FOR GAS RELEASING PROCESS FROM PRESSURIZED VESSELS IN ODH EVALUATION

International Nuclear Information System (INIS)

JIA, L.X.; WANG, L.

2001-01-01

IN THE EVALUATION OF ODH, THE CALCULATION OF THE SPILL RATE FROM THE PRESSURIZED VESSEL IS THE CENTRAL TASK. THE ACCURACY OF THE ENGINEERING ESTIMATION BECOMES ONE OF THE SAFETY DESIGN ISSUES. THIS PAPER SUMMARIZES THE EQUATIONS FOR THE OXYGEN CONCENTRATION CALCULATION IN DIFFERENT CASES, AND DISCUSSES THE EQUATIONS FOR THE GAS RELEASE PROCESS CALCULATION BOTH FOR THE HIGH-PRESSURE GAS TANK AND THE LOW-TEMPERATURE LIQUID CONTAINER

Bound states of quarks calculated with stochastic integration of the Bethe-Salpeter equation

International Nuclear Information System (INIS)

Salomon, M.

1992-07-01

We have computed the masses, wave functions and sea quark content of mesons in their ground state by integrating the Bethe-Salpeter equation with a stochastic algorithm. This method allows the inclusion of a large set of diagrams. Inspection of the kernel of the equation shows that q-q-bar pairs with similar constituent masses in a singlet spin state exhibit a high bound state which is not present in other pairs. The pion, kaon and eta belongs to this category. 19 refs., 2 figs., 2 tabs

Regression equations for calculation of z scores for echocardiographic measurements of right heart structures in healthy Han Chinese children.

Science.gov (United States)

Wang, Shan-Shan; Zhang, Yu-Qi; Chen, Shu-Bao; Huang, Guo-Ying; Zhang, Hong-Yan; Zhang, Zhi-Fang; Wu, Lan-Ping; Hong, Wen-Jing; Shen, Rong; Liu, Yi-Qing; Zhu, Jun-Xue

2017-06-01

Clinical decision making in children with congenital and acquired heart disease relies on measurements of cardiac structures using two-dimensional echocardiography. We aimed to establish z-score regression equations for right heart structures in healthy Chinese Han children. Two-dimensional and M-mode echocardiography was performed in 515 patients. We measured the dimensions of the pulmonary valve annulus (PVA), main pulmonary artery (MPA), left pulmonary artery (LPA), right pulmonary artery (RPA), right ventricular outflow tract at end-diastole (RVOTd) and at end-systole (RVOTs), tricuspid valve annulus (TVA), right ventricular inflow tract at end-diastole (RVIDd) and at end-systole (RVIDs), and right atrium (RA). Regression analyses were conducted to relate the measurements of right heart structures to 4body surface area (BSA). Right ventricular outflow-tract fractional shortening (RVOTFS) was also calculated. Several models were used, and the best model was chosen to establish a z-score calculator. PVA, MPA, LPA, RPA, RVOTd, RVOTs, TVA, RVIDd, RVIDs, and RA (R 2  = 0.786, 0.705, 0.728, 0.701, 0.706, 0.824, 0.804, 0.663, 0.626, and 0.793, respectively) had a cubic polynomial relationship with BSA; specifically, measurement (M) = β0 + β1 × BSA + β2 × BSA 2  + β3 × BSA. 3 RVOTFS (0.28 ± 0.02) fell within a narrow range (0.12-0.51). Our results provide reference values for z scores and regression equations for right heart structures in Han Chinese children. These data may help interpreting the routine clinical measurement of right heart structures in children with congenital or acquired heart disease. © 2016 Wiley Periodicals, Inc. J Clin Ultrasound 45:293-303, 2017. © 2017 Wiley Periodicals, Inc.

The Boltzmann equation in the difference formulation

Energy Technology Data Exchange (ETDEWEB)

Szoke, Abraham [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Brooks III, Eugene D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2015-05-06

First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.

Universal equation for estimating ideal body weight and body weight at any BMI.

Science.gov (United States)

Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B

2016-05-01

Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5-0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. © 2016 American Society for Nutrition.

Direct Discrete Method for Neutronic Calculations

International Nuclear Information System (INIS)

Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid

2002-01-01

The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for a cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)

Darboux invariants of integrable equations with variable spectral parameters

International Nuclear Information System (INIS)

Shin, H J

2008-01-01

The Darboux transformation for integrable equations with variable spectral parameters is introduced. Darboux invariant quantities are calculated, which are used in constructing the Lax pair of integrable equations. This approach serves as a systematic method for constructing inhomogeneous integrable equations and their soliton solutions. The structure functions of variable spectral parameters determine the integrability and nonlinear coupling terms. Three cases of integrable equations are treated as examples of this approach

State-dependent neutral delay equations from population dynamics.

Science.gov (United States)

Barbarossa, M V; Hadeler, K P; Kuttler, C

2014-10-01

A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.

Non-Equilibrium Properties from Equilibrium Free Energy Calculations

Science.gov (United States)

Pohorille, Andrew; Wilson, Michael A.

2012-01-01

Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.

New Numerical Solution of von Karman Equation of Lengthwise Rolling

Directory of Open Access Journals (Sweden)

Rudolf Pernis

2015-01-01

Full Text Available The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: (a by polygonal curve and (b by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. The new term relative stress as nondimensional variable was defined. The result from derived mathematical models can be calculated following variables: normal contact stress distribution, front and back tensions, angle of neutral point, coefficient of the arm of rolling force, rolling force, and rolling torque during rolling process. Laboratory cold rolled experiment of CuZn30 brass material was performed. Work hardening during brass processing was calculated. Comparison of theoretical values of normal contact stress with values of normal contact stress obtained from cold rolling experiment was performed. The calculations were not concluded with roll flattening.

Analytical approach to (2+1)-dimensional Boussinesq equation and (3+1)-dimensional Kadomtsev-Petviashvili equation

Energy Technology Data Exchange (ETDEWEB)

Sariaydin, Selin; Yildirim, Ahmet [Ege Univ., Dept. of Mathematics, Bornova-Izmir (Turkey)

2010-05-15

In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation u{sub tt} - u{sub xx} - u{sub yy} - (u{sup 2}){sub xx} - u{sub xxxx} = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation u{sub xt} - 6u{sub x}{sup 2} + 6uu{sub xx} - u{sub xxxx} - u{sub yy} - u{sub zz} = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically. (orig.)

Equilibrium calculations for helical axis stellarators

International Nuclear Information System (INIS)

Hender, T.C.; Carreras, B.A.

1984-04-01

An average method based on a vacuum flux coordinate system is presented. This average method permits the study of helical axis stellarators with toroidally dominated shifts. An ordering is introduced, and to lowest order the toroidally averaged equilibrium equations are reduced to a Grad-Shafranov equation. Also, to lowest order, a Poisson-type equation is obtained for the toroidally varying corrections to the equilibium. By including these corrections, systems that are toroidally dominated, but with significant helical distortion to the equilibrium, may be studied. Numerical solutions of the average method equations are shown to agree well with three-dimensional calculations

Calculations in solvent extraction of rare earth metals

International Nuclear Information System (INIS)

Sadanandam, R.; Sharma, A.K.; Fonseca, M.F.; Hubli, R.C.; Suri, A.K.; Singh, D.K.

2010-01-01

The paper deals with calculation of number of countercurrent stages in solvent extraction of rare earths both under total reflux and partial reflux conditions to achieve a given degree of purification and recovery. The use of Fenske's equation normally used for separation by distillation is proposed to calculate the number of stages required under total reflux, replacing relative volatility by separation factor. Kremser's equations for extraction and scrubbing are used to calculate the number of stages in extraction and scrubbing modules under partial reflux conditions. McCabe-Thiele's approach is also adopted to arrive at the number of scrubbing stages. (author)

Using Financial Calculators in a Business Mathematics Course.

Science.gov (United States)

Heller, William H.; Taylor, Monty B.

2000-01-01

Discusses the authors' experiences with integrating financial calculators into a business mathematics course. Presents a brief overview of the operation of financial calculators, reviews some of the more common models, discusses how to use the equation solver utility on other calculators to emulate a financial calculator, and explores the…

Analysis of error in Monte Carlo transport calculations

International Nuclear Information System (INIS)

Booth, T.E.

1979-01-01

The Monte Carlo method for neutron transport calculations suffers, in part, because of the inherent statistical errors associated with the method. Without an estimate of these errors in advance of the calculation, it is difficult to decide what estimator and biasing scheme to use. Recently, integral equations have been derived that, when solved, predicted errors in Monte Carlo calculations in nonmultiplying media. The present work allows error prediction in nonanalog Monte Carlo calculations of multiplying systems, even when supercritical. Nonanalog techniques such as biased kernels, particle splitting, and Russian Roulette are incorporated. Equations derived here allow prediction of how much a specific variance reduction technique reduces the number of histories required, to be weighed against the change in time required for calculation of each history. 1 figure, 1 table

Electron transfer dynamics: Zusman equation versus exact theory

International Nuclear Information System (INIS)

Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing

2009-01-01

The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.

Program for TI programmable 59 calculator for calculation of 3H concentration of water samples

International Nuclear Information System (INIS)

Hussain, S.D.; Asghar, G.

1982-09-01

A program has been developed for TI Programmable 59 Calculator of Texas Instruments Inc. to calculate from the observed parameters such as count rate etc. the 3 H (tritium) concentration of water samples processed with/without prior electrolytic enrichment. Procedure to use the program has been described in detail. A brief description of the laboratory treatment of samples and the mathematical equations used in the calculations have been given. (orig./A.B.)

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

Science.gov (United States)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

THE CONTENT MODEL AND THE EQUATIONS OF MOTION OF ELECTRIC VEHICLE

Directory of Open Access Journals (Sweden)

K. O. Soroka

2015-06-01

Full Text Available Purpose. The calculation methods improvement of the electric vehicle curve movement and the cost of electricity with the aim of performance and accuracy of calculations improving are considered in the paper. Methodology. The method is based upon the general principles of mathematical simulation, when a conceptual model of problem domain is created and then a mathematic model is formulated according to the conceptual model. Development of an improved conceptual model of electric vehicles motion is proposed and a corresponding mathematical model is studied. Findings. The authors proposed model in which the vehicle considers as a system of interacting point-like particles with defined interactions under the influence of external forces. As a mathematical model the Euler-Lagrange equation of the second kind is used. Conservative and dissipative forces affecting the system dynamics are considered. Equations for calculating motion of electric vehicles with taking into account the energy consumption are proposed. Originality. In the paper the conceptual model of motion for electric vehicles with distributed masses has been developed as a system of interacting point-like particles. In the easiest case the system has only one degree of freedom. The mathematical model is based on Lagrange equations. The shown approach allows a detailed and physically based description of the electric vehicles dynamics. The derived motion equations for public electric transport are substantially more precise than the equations recommended in textbooks and the reference documentation. The motion equations and energy consumption calculations for transportation of one passenger with a trolleybus are developed. It is shown that the energy consumption depends on the data of vehicle and can increase when the manload is above the certain level. Practical value. The authors received the equations of motion and labour costs in the calculations focused on the use of computer methods

Scalar potentials and the Dirac equation

International Nuclear Information System (INIS)

Bergerhoff, B.; Soff, G.

1994-01-01

The Dirac equation is solved for various types of scalar potentials. Energy eigenvalues and normalized bound-state wave functions are calculated analytically for a scalar 1/r-potential as well as for a mixed scalar and Coulomb 1/r-potential. Also continuum wave functions for positive and negative energies are derived. Similarly, we investigate the solutions of the Dirac equation for a scalar square-well potential. Relativistic wave functions for scalar Yukawa and exponential potentials are determined numerically. Finally, we also discuss solutions of the Dirac equation for scalar linear and quadratic potentials which are frequently used to simulate quark confinement. (orig.)

Calculation of cell face velocity of non-staggered grid system

KAUST Repository

Li, Wang; Yu, Bo; Wang, Xinran; Sun, Shuyu

2012-01-01

In this paper, the cell face velocities in the discretization of the continuity equation, the momentum equation, and the scalar equation of a non-staggered grid system are calculated and discussed. Both the momentum interpolation and the linear

Calculations of stationary solutions for the non linear viscous resistive MHD equations in slab geometry

International Nuclear Information System (INIS)

Edery, D.

1983-11-01

The reduced system of the non linear resistive MHD equations is used in the 2-D one helicity approximation in the numerical computations of stationary tearing modes. The critical magnetic Raynolds number S (S=tausub(r)/tausub(H) where tausub(R) and tausub(H) are respectively the characteristic resistive and hydro magnetic times) and the corresponding linear solution are computed as a starting approximation for the full non linear equations. These equations are then treated numerically by an iterative procedure which is shown to be rapidly convergent. A numerical application is given in the last part of this paper

Perturbation theory for continuous stochastic equations

International Nuclear Information System (INIS)

Chechetkin, V.R.; Lutovinov, V.S.

1987-01-01

The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)

Nodal spectrum method for solving neutron diffusion equation

International Nuclear Information System (INIS)

Sanchez, D.; Garcia, C. R.; Barros, R. C. de; Milian, D.E.

1999-01-01

Presented here is a new numerical nodal method for solving static multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X, Y directions and then considering flat approximations for the current. These flat approximations are the only approximations that are considered in this method, as a result the numerical solutions are completely free from truncation errors. We show numerical results to illustrate the methods accuracy for coarse mesh calculations

Plasma physics on the TI-85 calculator or Down with supercomputers

International Nuclear Information System (INIS)

Sedlacek, Z.

1998-10-01

In the Fourier transformed velocity space the Vlasov plasma oscillations may be interpreted as a wave propagation process corresponding to an imperfectly trapped (leaking) wave. The Landau damped solutions of the Vlasov-Poisson equation then become genuine Eigenmodes corresponding to complex eigenvalues. To illustrate this new interpretation we solve numerically the Fourier transformed Vlasov-Poisson equation, essentially a perturbed advective equation, on the TI-85 pocket graphics calculator. A program is described, based on the method of lines: A finite-difference scheme is utilized to discretize the transformed equation and the resulting set of ordinary differential equations is then solved in time. The user can choose from several possible finite-difference differentiation schemes differing in the total number of points and the number of downwind points. The resulting evolution of the electric field showing the Landau damped plasma oscillations is displayed on the screen of the calculator. In addition, calculation of the eigenvalues of the Fourier transformed Vlasov-Poisson operator is possible. The user can also experiment with the numerical solution of the advective equation which describes free streaming. (author)

Kinetic equation solution by inverse kinetic method

International Nuclear Information System (INIS)

Salas, G.

1983-01-01

We propose a computer program (CAMU) which permits to solve the inverse kinetic equation. The CAMU code is written in HPL language for a HP 982 A microcomputer with a peripheral interface HP 9876 A ''thermal graphic printer''. The CAMU code solves the inverse kinetic equation by taking as data entry the output of the ionization chambers and integrating the equation with the help of the Simpson method. With this program we calculate the evolution of the reactivity in time for a given disturbance

Integro-differential equation approach extended to larger nuclei

International Nuclear Information System (INIS)

Adam, R.M.; Sofianos, S.A.; Fiedeldey, H.; Fabre de la Ripelle, M.

1992-01-01

We extend the integro-differential equation approach (IDEA) from few-nucleon to closed-shell and closed-subshell nuclei and outline the analytical methods required for the calculation of the density functions, which enter into the integro-differential equations. These contain all the physics for a system of fermions associated with the Pauli principle. In order to test the accuracy of the IDEA comparisons are made of the binding energies of 4 He, 12 C and 16 O obtained with effective potentials using the hypercentral approximation (HCA) providing a variational solution without correlations, the IDEA which fully includes the two-body correlations, the S-states integro-differential equation (SIDE) valid for potentials operating only on pairs in the S-state and those calculated by several variational or perturbative methods in the literature. (author)

NLOM - a program for nonlocal optical model calculations

International Nuclear Information System (INIS)

Kim, B.T.; Kyum, M.C.; Hong, S.W.; Park, M.H.; Udagawa, T.

1992-01-01

A FORTRAN program NLOM for nonlocal optical model calculations is described. It is based on a method recently developed by Kim and Udagawa, which utilizes the Lanczos technique for solving integral equations derived from the nonlocal Schroedinger equation. (orig.)

CALCULATION OF REACTION COMPLETENESS AND SUBSTANCE TRANSFORMATION AT WATER-COAL GASIFICATION

Directory of Open Access Journals (Sweden)

N. S. Nazarov

2007-01-01

Full Text Available Process of water-coal gasification is satisfactorily described by three thermal and chemical equations; using these equations composition of gasification product (water carbon monoxide gas has been calculated in accordance with a temperature. Results of the calculations are presented in the form of charts. 

On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations; Sur la stabilite, les solutions periodiques et la resolution de certaines categories d'equations et systemes d'equations differentielles couplees non lineaires apparaissant dans les oscillations betatroniques

Energy Technology Data Exchange (ETDEWEB)

Valat, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1960-12-15

Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [French] Pour les equations du genre de Hill-Meissner a coefficients creneles, on a calcule des diagrammes universels de stabilite et ceux-ci ont ete verifies experimentalement. L'etude de ces equations dans le plan de phase a permis ensuite d'etendre le calcul des solutions periodiques au cas des equations differentielles non lineaires a coefficients periodiques creneles. Cette theorie a ete verifiee experimentalement. Pour Jes systemes couples non lineaires a coefficients constants, on a d'abord cherche les solutions menant a des mouvements algebriques. Les fonctions elliptiques et fuchsiennes uniformisent de tels mouvements. L'etude de mouvements non algebriques est plus delicate, a part l'etude des mouvements de Lissajous non lineaires. Une analyse fonctionnelle montre qu'il est toutefois possible dans certains cas de decoupler le systeme et de trouver des solutions generales. Pour les

Spin-orbit couplings within the equation-of-motion coupled-cluster framework: Theory, implementation, and benchmark calculations

Energy Technology Data Exchange (ETDEWEB)

Epifanovsky, Evgeny [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States); Department of Chemistry, University of California, Berkeley, California 94720 (United States); Q-Chem Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588 (United States); Klein, Kerstin; Gauss, Jürgen [Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz (Germany); Stopkowicz, Stella [Department of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, N-0315 Oslo (Norway); Krylov, Anna I. [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States)

2015-08-14

We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.

Explicit presentation of the Colebrook's friction factor equation ...

African Journals Online (AJOL)

Two explicit and very accurate equations for calculating the friction factor of pipes over the entire range of relative roughness and Reynold's Number covered by the Colebrook's Equation have been developed. A rectangular array of relative Roughness and Reynold's Number was used to test the accuracy of the new ...

Equations of macrotransport in reactor fuel assemblies

International Nuclear Information System (INIS)

Sorokin, A.P.; Zhukov, A.V.; Kornienko, Yu.N.; Ushakov, P.A.

1986-01-01

The rigorous statement of equations of macrotransport is obtained. These equations are bases for channel-by-channel methods of thermohydraulic calculations of reactor fuel assemblies within the scope of the model of discontinuous multiphase coolant flow (including chemical reactions); they also describe a wide range of problems on thermo-physical reactor fuel assembly justification. It has been carried out by smoothing equations of mass, momentum and enthalpy transfer in cross section of each phase of the elementary fuel assembly subchannel. The equation for cross section flows is obtaind by smoothing the equation of momentum transfer on the interphase. Interaction of phases on the channel boundary is described using the Stanton number. The conclusion is performed using the generalized equation of substance transfer. The statement of channel-by-channel method without the scope of homogeneous flow model is given

Equation of state calculations for two-dimensional dust coulomb crystal at near zero temperature by molecular dynamics simulations

Energy Technology Data Exchange (ETDEWEB)

Djouder, M., E-mail: djouder-madjid@ummto.dz; Kermoun, F.; Mitiche, M. D.; Lamrous, O. [Laboratoire de Physique et Chimie Quantique, Université Mouloud Mammeri Tizi-Ouzou, BP 17 RP, 15000 Tizi-Ouzou (Algeria)

2016-01-15

Dust particles observed in universe as well as in laboratory and technological plasma devices are still under investigation. At low temperature, these particles are strongly negatively charged and are able to form a 2D or 3D coulomb crystal. In this work, our aim was to check the ideal gas law validity for a 2D single-layer dust crystal recently reported in the literature. For this purpose, we have simulated, using the molecular dynamics method, its thermodynamic properties for different values of dust particles number and confinement parameters. The obtained results have allowed us to invalidate the ideal gas behaviour and to propose an effective equation of state which assumes a near zero dust temperature. Furthermore, the value of the calculated sound velocity was found to be in a good agreement with experimental data published elsewhere.

Equation of state calculations for two-dimensional dust coulomb crystal at near zero temperature by molecular dynamics simulations

International Nuclear Information System (INIS)

Djouder, M.; Kermoun, F.; Mitiche, M. D.; Lamrous, O.

2016-01-01

Dust particles observed in universe as well as in laboratory and technological plasma devices are still under investigation. At low temperature, these particles are strongly negatively charged and are able to form a 2D or 3D coulomb crystal. In this work, our aim was to check the ideal gas law validity for a 2D single-layer dust crystal recently reported in the literature. For this purpose, we have simulated, using the molecular dynamics method, its thermodynamic properties for different values of dust particles number and confinement parameters. The obtained results have allowed us to invalidate the ideal gas behaviour and to propose an effective equation of state which assumes a near zero dust temperature. Furthermore, the value of the calculated sound velocity was found to be in a good agreement with experimental data published elsewhere

Cryostatic stability equation

International Nuclear Information System (INIS)

Sydoriak, S.G.

1976-01-01

Although criteria for cryostatic stability of superconducting magnets cooled by pool boiling of liquid helium have been widely discussed the same cannot be said for magnets cooled by natural convection or forced flow boiling in channels. Boiling in narrow channels is shown to be qualitatively superior to pool boiling because the recovery heat flux equals the breakaway flux for narrow channels, whereas the two are markedly different in pool boiling. A second advantage of channel boiling is that it is well understood and calculable; pool peak nucleate boiling heat flux has been adequately measured only for boiling from the top of an immersed heated body. Peak boiling from the bottom is much less and (probably) depends strongly on the extent of the bottom surface. Equations are presented by which one can calculate the critical boiling heat flux for parallel wall vertical channels subject to either natural convection or forced flow boiling, with one or both walls heated. The one-heated-wall forced flow equation is discussed with regard to design of a spiral wound solenoid (pancake magnet) having a slippery insulating tape between the windings

Meson spectra from two-body dirac equations with minimal interactions

International Nuclear Information System (INIS)

Crater, H.W.; Becker, R.L.; Wong, C.Y.

1991-01-01

Many authors have used two-body relativistic wave equations with spin in nonperturbative numerical quark model calculations of the meson spectrum. Usually, they adopt a truncation of the Bethe-Salpeter equation of QED and/or scalar. QED and replace the static Coulomb interactions of those field theories with a semiphenomenological Q bar Q potential whose insertion in the Breit terms give the corresponding spin corrections. However, the successes of these wave equations in QED have invariably depended on perturbative treatment of the terms in each beyond the Coulomb terms. There have been no successful nonperturbative numerical test of two-body quantum wave equations in QED, because in most equations the effective potentials beyond the Coulomb are singular and can only be treated perturbatively. This is a glaring omission that we rectify here for the case of the two-body Dirac equations of constraint dynamics. We show in this paper that a nonperturbative numerical treatment of these equations for QED yields the same spectral results as a perturbative treatment of them which in turn agrees with the standard spectral results for positronium and muonium. This establishes that the vector and scalar interaction structures of our equations accurately incorporate field theoretic interactions in a bone fide relativistic wave equation. The last portion of this work will report recent quark model calculations using these equations with the Adler-Piran static Q bar Q potential

Validity of the modified Reynolds equation for incompressible active lubrication

DEFF Research Database (Denmark)

Cerda Varela, Alejandro Javier; Santos, Ilmar

2016-01-01

The modified Reynolds equation for active lubrication has been the cornerstone around which the theoretical investigations regarding actively lubricated bearings have evolved over the years. Introduced originally in 1994, it enables to calculate in a simplified manner the bearing pressure field...... as a function of servovalve controlled pressurized oil injection. This article deals with a preliminary critical review of the simplificatory assumptions that are introduced into the modified Reynolds equation in order to model the phenomena taking place in the interface between the injection nozzle...... and the bearing clearance. The analysis is performed by means of direct comparison of the results of the modified Reynolds equation model versus benchmark CFD calculations, applied to a geometry representative of the system analyzed. The results show that the modified Reynolds equation mathematical simplicity...

Theoretical calculation of solid particles deposition from the air

Directory of Open Access Journals (Sweden)

Bobro Milan

2002-03-01

Full Text Available This paper presents the calculation of harmful substance deposition (air pollution from the point source (Slanèo, et al., 2001 using equation (1. The point source shall be understood as e.g. chimneys of factory, heat plant, incinerator, boiler plant, local heating plant, etc.The theoretical calculation of concentration (1, or deposition (8 is based on the study of transfer and dispersion of pollution in air (Slanèo, et al., 2000a. The movement of pollution in air consists of a movement of the air itself and a relative movement of pollution particles and air, while the movement of harmful substance in the smoke trail is under the influence of turbulent diffusion, convection and gravitation. Molecular diffusion is not important in this process. When calculating concentrations (1 and deposition (8 of air pollution on a particular place near the source, it is assumed that the air speed is constant, the direction of wind does not change with the height and the source of air pollution is time-constant. The change in the wind speed with the height depends on the stability class of atmosphere (temperature gradient (Slanèo, et al., 2000a and it is calculated using equation (10.The theoretical calculation of concentration and or deposition of harmful substance from the point source (1 and (8 shall be applied if the harmful substance particles, which leave the source, have the same density (composition, shape (spherical and size.The experimental observations of dust deposition showed the significance of 0.1-20 µm particles. The application of equation (1 to calculate the concentration is conditioned, in addition to the recognition of source parameters and meteorological conditions, by the recognition of the particle sedimentation speed, which changes with the size of particle radius (2.For a practical calculation of deposition it is therefore necessary to know the differential distribution function f(r of particle radii, which can be made on the basis

Bubble-point and dew-point equation for binary refrigerant mixture R22-R142b

Energy Technology Data Exchange (ETDEWEB)

Liancheng Tan; Zhongyou Zhao; Yonghong Duan (Xi' an Jiaotong Univ., Xi' an (China). Dept. of Power Machinery Engineering)

1992-01-01

A bubble-point and dew-point equation (in terms either of temperature or of pressure is suggested for the refrigerant mixture R22-R142b), which is regarded as one of the alternatives to R12. This equation has been examined with experimental data. A modified Rackett equation for the calculation of the bubble-point volume is also proposed. Compared with the experimental data, the rms errors in the calculated values of the bubble-point temperature, the dew-point temperature, and the bubble-point volume are 1.093%, 0.947%, and 1.120%, respectively. The calculation covers a wide range of temperatures and pressures, even near the critical point. It is shown how the equations are extrapolated to calculate other binary refrigerant mixtures. (author)

Nonlinear dynamics in the Einstein-Friedmann equation

International Nuclear Information System (INIS)

Tanaka, Yosuke; Mizuno, Yuji; Ohta, Shigetoshi; Mori, Keisuke; Horiuchi, Tanji

2009-01-01

We have studied the gravitational field equations on the basis of general relativity and nonlinear dynamics. The space component of the Einstein-Friedmann equation shows the chaotic behaviours in case the following conditions are satisfied: (i)the expanding ratio: h=x . /x max = +0.14) for the occurrence of the chaotic behaviours in the Einstein-Friedmann equation (0 ≤ λ ≤ +0.14). The numerical calculations are performed with the use of the Microsoft EXCEL(2003), and the results are shown in the following cases; λ = 2b = +0.06 and +0.14.

SU-E-T-191: First Principle Calculation of Quantum Yield in Photodynamic Therapy

Energy Technology Data Exchange (ETDEWEB)

Abolfath, R; Guo, F; Chen, Z; Nath, R [Yale New Haven Hospital, New Haven, CT (United States)

2014-06-01

Purpose: We present a first-principle method to calculate the spin transfer efficiency in oxygen induced by any photon fields especially in MeV energy range. The optical pumping is mediated through photosensitizers, e.g., porphyrin and/or ensemble of quantum dots. Methods: Under normal conditions, oxygen molecules are in the relatively non-reactive triplet state. In the presence of certain photosensitizer compounds such as porphyrins, electromagnetic radiation of specific wavelengths can excite oxygen to highly reactive singlet state. With selective uptake of photosensitizers by certain malignant cells, photon irradiation of phosensitized tumors can lead to selective killing of cancer cells. This is the basis of photodynamic therapy (PDT). Despite several attempts, PDT has not been clinically successful except in limited superficial cancers. Many parameters such as photon energy, conjugation with quantum dots etc. can be potentially combined with PDT in order to extend the role of PDT in cancer management. The key quantity for this optimization is the spin transfer efficiency in oxygen by any photon field. The first principle calculation model presented here, is an attempt to fill this need. We employ stochastic density matrix description of the quantum jumps and the rate equation methods in quantum optics based on Markov/Poisson processes and calculate time evolution of the population of the optically pumped singlet oxygen. Results: The results demonstrate the feasibility of our model in showing the dependence of the optical yield in generating spin-singlet oxygen on the experimental conditions. The adjustable variables can be tuned to maximize the population of the singlet oxygen hence the efficacy of the photodynamic therapy. Conclusion: The present model can be employed to fit and analyze the experimental data and possibly to assist researchers in optimizing the experimental conditions in photodynamic therapy.

On calculating of squared-off cascades for multicomponent isotope separation

International Nuclear Information System (INIS)

Potapov, D.V.; Soulaberidze, G.A.; Chuzhinov, V.A.; Filipppov, I.G.

1996-01-01

Calculation on a cascade of specified configuration (specified number of stages and flows in the enriching and stripping sections of the cascade) is performed with two approaches. The first one, which is advisable to use for for calculation of so-called 'long' cascades (for example, squared-off cascades of distillation columns), is based on either analytical transitions enabling the problem to be reduced to to the algebraic transcendental equations, or based on the direct integration of the equations describing the cascade separation process, with the subsequent iteration on the boundary conditions and the balance equations. This approach also involves the orthogonal-collocation technique consisting in the approximation of the differential equations solution by an Lagrangian polynomial interpolation

BADGER v1.0: A Fortran equation of state library

Science.gov (United States)

Heltemes, T. A.; Moses, G. A.

2012-12-01

The BADGER equation of state library was developed to enable inertial confinement fusion plasma codes to more accurately model plasmas in the high-density, low-temperature regime. The code had the capability to calculate 1- and 2-T plasmas using the Thomas-Fermi model and an individual electron accounting model. Ion equation of state data can be calculated using an ideal gas model or via a quotidian equation of state with scaled binding energies. Electron equation of state data can be calculated via the ideal gas model or with an adaptation of the screened hydrogenic model with ℓ-splitting. The ionization and equation of state calculations can be done in local thermodynamic equilibrium or in a non-LTE mode using a variant of the Busquet equivalent temperature method. The code was written as a stand-alone Fortran library for ease of implementation by external codes. EOS results for aluminum are presented that show good agreement with the SESAME library and ionization calculations show good agreement with the FLYCHK code. Program summaryProgram title: BADGERLIB v1.0 Catalogue identifier: AEND_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEND_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.: 41 480 No. of bytes in distributed program, including test data, etc.: 2 904 451 Distribution format: tar.gz Programming language: Fortran 90. Computer: 32- or 64-bit PC, or Mac. Operating system: Windows, Linux, MacOS X. RAM: 249.496 kB plus 195.630 kB per isotope record in memory Classification: 19.1, 19.7. Nature of problem: Equation of State (EOS) calculations are necessary for the accurate simulation of high energy density plasmas. Historically, most EOS codes used in these simulations have relied on an ideal gas model. This model is inadequate for low

Investigation of two and three parameter equations of state for cryogenic fluids

International Nuclear Information System (INIS)

Jenkins, S.L.; Majumdar, A.K.; Hendricks, R.C.

1990-01-01

Two-phase flows are a common occurrence in cryogenic engines and an accurate evaluation of the heat-transfer coefficient in two-phase flow is of significant importance in their analysis and design. The thermodynamic equation of state plays a key role in calculating the heat transfer coefficient which is a function of thermodynamic and thermophysical properties. An investigation has been performed to study the performance of two- and three-parameter equations of state to calculate the compressibility factor of cryogenic fluids along the saturation loci. The two-parameter equations considered here are van der Waals and Redlich-Kwong equations of state. The three-parameter equation represented here is the generalized Benedict-Webb-Rubin (BWR) equation of Lee and Kesler. Results have been compared with the modified BWR equation of Bender and the extended BWR equations of Stewart. Seven cryogenic fluids have been tested; oxygen, hydrogen, helium, nitrogen, argon, neon, and air. The performance of the generalized BWR equation is poor for hydrogen and helium. The van der Waals equation is found to be inaccurate for air near the critical point. For helium, all three equations of state become inaccurate near the critical point. 13 refs

Extension of a GIS procedure for calculating the RUSLE equation LS factor

NARCIS (Netherlands)

Zhang, H.; Yang, Q.; Li, R.; Liu, Q.; Moore, D.; He, P.; Ritsema, C.J.; Geissen, V.

2013-01-01

The Universal Soil Loss Equation (USLE) and revised USLE (RUSLE) are often used to estimate soil erosion at regional landscape scales, however a major limitation is the difficulty in extracting the LS factor. The geographic information system-based (GIS-based) methods which have been developed for

New equations to calculate 3D joint centres in the lower extremities

DEFF Research Database (Denmark)

Sandau, Martin; Heimbürger, Rikke V; Villa, Chiara

2015-01-01

Biomechanical movement analysis in 3D requires estimation of joint centres in the lower extremities and this estimation is based on extrapolation from markers placed on anatomical landmarks. The purpose of the present study was to quantify the accuracy of three established set of equations and pr...

Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Cherny, A.Yu.; Brand, J.

2004-01-01

A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the trapping potential, e.g., in quasi-1D or quasi-2D systems. It is shown that a simplified version of the Hartree-Fock-Bogoliubov approximation leads to a variational problem for both the condensate and a two-body wave function describing the behavior of a pair of bosons in the Bose-Einstein condensate. The resulting coupled equations are free of unphysical divergences. Particular cases of this scheme that admit analytical estimations are considered and compared to the literature. In addition to the well-known cases of low-dimensional trapping, crossover regimes can be studied. The values of the kinetic, interaction, external, and release energies in low dimensions are also evaluated and contributions due to short-range correlations are found to be substantial

Single-site Green function of the Dirac equation for full-potential electron scattering

Energy Technology Data Exchange (ETDEWEB)

Kordt, Pascal

2012-05-30

I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)

Single-site Green function of the Dirac equation for full-potential electron scattering

International Nuclear Information System (INIS)

Kordt, Pascal

2012-01-01

I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)

Self-similar solutions of the modified nonlinear schrodinger equation

International Nuclear Information System (INIS)

Kitaev, A.V.

1986-01-01

This paper considers a 2 x 2 matrix linear ordinary differential equation with large parameter t and irregular singular point of fourth order at infinity. The leading order of the monodromy data of this equation is calculated in terms of its coefficients. Isomonodromic deformations of the equation are self-similar solutions of the modified nonlinear Schrodinger equation, and therefore inversion of the expressions obtained for the monodromy data gives the leading term in the time-asymptotic behavior of the self-similar solution. The application of these results to the type IV Painleve equation is considered in detail

Calculation of thermodynamic properties of sodium and potassium vapors on the base of semiempirical state equation. Group integrals and virial coefficients

International Nuclear Information System (INIS)

Reva, T.D.; Semenov, A.M.

1984-01-01

Statistically significant estimations of the second, third and fourth group integrals of sodium and potassium vapors were obtained in the framework of the initial atom method on the basis of semiempirical equation of state derived by the authors. Possibility is duscussed of estimating dimer, trimer and tetramer concentrations from these data with account of unideality of vapors. High rate of convergence of density and pressure group expansion is demonstrated. Virial coefficients were calculated. It is shown that virial expansions of thermodynamic functions diverge at elevated densities of the gases under study. The estimations of senior virial coefficients of sodium and potassium vapors available in literature were proved to be faulty

Modifying Poisson equation for near-solute dielectric polarization and solvation free energy

Energy Technology Data Exchange (ETDEWEB)

Yang, Pei-Kun, E-mail: peikun@isu.edu.tw

2016-06-15

Highlights: • We modify the Poisson equation. • The dielectric polarization was calculated from the modified Poisson equation. • The solvation free energies of the solutes were calculated from the dielectric polarization. • The calculated solvation free energies were similar to those obtained from MD simulations. - Abstract: The dielectric polarization P is important for calculating the stability of protein conformation and the binding affinity of protein–protein/ligand interactions and for exploring the nonthermal effect of an external electric field on biomolecules. P was decomposed into the product of the electric dipole moment per molecule p; bulk solvent density N{sub bulk}; and relative solvent molecular density g. For a molecular solute, 4πr{sup 2}p(r) oscillates with the distance r to the solute, and g(r) has a large peak in the near-solute region, as observed in molecular dynamics (MD) simulations. Herein, the Poisson equation was modified for computing p based on the modified Gauss’s law of Maxwell’s equations, and the potential of the mean force was used for computing g. For one or two charged atoms in a water cluster, the solvation free energies of the solutes obtained by these equations were similar to those obtained from MD simulations.

Undergraduate paramedic students cannot do drug calculations

Science.gov (United States)

Eastwood, Kathryn; Boyle, Malcolm J; Williams, Brett

2012-01-01

BACKGROUND: Previous investigation of drug calculation skills of qualified paramedics has highlighted poor mathematical ability with no published studies having been undertaken on undergraduate paramedics. There are three major error classifications. Conceptual errors involve an inability to formulate an equation from information given, arithmetical errors involve an inability to operate a given equation, and finally computation errors are simple errors of addition, subtraction, division and multiplication. The objective of this study was to determine if undergraduate paramedics at a large Australia university could accurately perform common drug calculations and basic mathematical equations normally required in the workplace. METHODS: A cross-sectional study methodology using a paper-based questionnaire was administered to undergraduate paramedic students to collect demographical data, student attitudes regarding their drug calculation performance, and answers to a series of basic mathematical and drug calculation questions. Ethics approval was granted. RESULTS: The mean score of correct answers was 39.5% with one student scoring 100%, 3.3% of students (n=3) scoring greater than 90%, and 63% (n=58) scoring 50% or less, despite 62% (n=57) of the students stating they ‘did not have any drug calculations issues’. On average those who completed a minimum of year 12 Specialist Maths achieved scores over 50%. Conceptual errors made up 48.5%, arithmetical 31.1% and computational 17.4%. CONCLUSIONS: This study suggests undergraduate paramedics have deficiencies in performing accurate calculations, with conceptual errors indicating a fundamental lack of mathematical understanding. The results suggest an unacceptable level of mathematical competence to practice safely in the unpredictable prehospital environment. PMID:25215067

Undergraduate paramedic students cannot do drug calculations.

Science.gov (United States)

Eastwood, Kathryn; Boyle, Malcolm J; Williams, Brett

2012-01-01

Previous investigation of drug calculation skills of qualified paramedics has highlighted poor mathematical ability with no published studies having been undertaken on undergraduate paramedics. There are three major error classifications. Conceptual errors involve an inability to formulate an equation from information given, arithmetical errors involve an inability to operate a given equation, and finally computation errors are simple errors of addition, subtraction, division and multiplication. The objective of this study was to determine if undergraduate paramedics at a large Australia university could accurately perform common drug calculations and basic mathematical equations normally required in the workplace. A cross-sectional study methodology using a paper-based questionnaire was administered to undergraduate paramedic students to collect demographical data, student attitudes regarding their drug calculation performance, and answers to a series of basic mathematical and drug calculation questions. Ethics approval was granted. The mean score of correct answers was 39.5% with one student scoring 100%, 3.3% of students (n=3) scoring greater than 90%, and 63% (n=58) scoring 50% or less, despite 62% (n=57) of the students stating they 'did not have any drug calculations issues'. On average those who completed a minimum of year 12 Specialist Maths achieved scores over 50%. Conceptual errors made up 48.5%, arithmetical 31.1% and computational 17.4%. This study suggests undergraduate paramedics have deficiencies in performing accurate calculations, with conceptual errors indicating a fundamental lack of mathematical understanding. The results suggest an unacceptable level of mathematical competence to practice safely in the unpredictable prehospital environment.

Symmetrized neutron transport equation and the fast Fourier transform method

International Nuclear Information System (INIS)

Sinh, N.Q.; Kisynski, J.; Mika, J.

1978-01-01

The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations

Model equations for Calculating Rn-gas Concentrations in Air of Uranium Exploratory Tunnels, Allouga, West-Central Sinai , Egypt

International Nuclear Information System (INIS)

Abdel-Monem, A.A.; Soliman, S.F.H.; Abd El-Kader, F.H.; El-Naggar, A.M.; Eissa, H.M.; Abd El-Hafez, A.A.

2001-01-01

Gabal Allouga area is located some 40 km due east from Abu Zenima town on the east coast of the Gulf of Suez, West-Central Sinai, Egypt. A network of exploratory tunnels totaling 670m in length and approximately 2x2 m in cross section, were excavated within a paleosol clayey bed. They host (Fe, Mn)-, Cu-, and U-mineralizations. Portions of the tunnels are naturally ventilated and others portions are non-ventilated and show ground water seepage through fractures. Model equations were developed for calculating the Rn-gas concentrations in the air of the tunnels under dry conditions where Rn-gas transport is mainly by air flow through porous media as well as for wet conditions where Rn-gas transport is mainly by ground water flow into the tunnels. Under dry conditions the model calculated Rn-gas concentrations(15.2-60.6 PCi/1) are consistent with measured values by active techniques (3.26-22.85 pCi/1) and by SSNTD techniques (19-69.1 pCi/1) when the Rn-emanation coefficient (alpha= 0.05-0.2), the emanating rock thickness (X=10 cm) and U-concentration averages 30 ppm. Under wet and non-ventilated conditions the model calculated Rn-gas concentrations (159-1248 pCi/1) are consistent with the measured values by active techniques (231-1348 pCi/1) and by SSNTD techniques (144-999pCi/1), when the Rn-emanation coefficient (alpha=0.1-0.25), the ground water flow (F=0.04-0.10 ml/s -1 cm -2 ) and U-concertrations (100-250ppm)

Scattering integral equations and four nucleon problem

International Nuclear Information System (INIS)

Narodetskii, I.M.

1980-01-01

Existing results from the application of integral equation technique to the four-nucleon bound states and scattering are reviewed. The first numerical calculations of the four-body integral equations have been done ten years ago. Yet, it is still widely believed that these equations are too complicated to solve numerically. The purpose of this review is to provide a clear and elementary introduction in the integral equation method and to demonstrate its usefulness in physical applications. The presentation is based on the quasiparticle approach. This permits a simple interpretation of the equations in terms of quasiparticle scattering. The mathematical basis for the quasiparticle approach is the Hilbert-Schmidt method of the Fredholm integral equation theory. The first part of this review contains a detailed discussion of the Hilbert-Schmidt expansion as applied to the 2-particle amplitudes and to the kernel of the four-body equations. The second part contains the discussion of the four-body quasiparticle equations and of the resed forullts obtain bound states and scattering

Nonperturbative time-convolutionless quantum master equation from the path integral approach

International Nuclear Information System (INIS)

Nan Guangjun; Shi Qiang; Shuai Zhigang

2009-01-01

The time-convolutionless quantum master equation is widely used to simulate reduced dynamics of a quantum system coupled to a bath. However, except for several special cases, applications of this equation are based on perturbative calculation of the dissipative tensor, and are limited to the weak system-bath coupling regime. In this paper, we derive an exact time-convolutionless quantum master equation from the path integral approach, which provides a new way to calculate the dissipative tensor nonperturbatively. Application of the new method is demonstrated in the case of an asymmetrical two-level system linearly coupled to a harmonic bath.

Equation of state of warm condensed matter

Energy Technology Data Exchange (ETDEWEB)

Barbee, T.W., III; Young, D.A.; Rogers, F.J.

1998-03-01

Recent advances in computational condensed matter theory have yielded accurate calculations of properties of materials. These calculations have, for the most part, focused on the low temperature (T=0) limit. An accurate determination of the equation of state (EOS) at finite temperature also requires knowledge of the behavior of the electron and ion thermal pressure as a function of T. Current approaches often interpolate between calculated T=0 results and approximations valid in the high T limit. Plasma physics-based approaches are accurate in the high temperature limit, but lose accuracy below T{approximately}T{sub Fermi}. We seek to ``connect up`` these two regimes by using ab initio finite temperature methods (including linear-response[1] based phonon calculations) to derive an equation of state of condensed matter for T{<=}T{sub Fermi}. We will present theoretical results for the principal Hugoniot of shocked materials, including carbon and aluminum, up to pressures P>100 GPa and temperatures T>10{sup 4}K, and compare our results with available experimental data.

Thermohydraulic calculations of PWR primary circuits

International Nuclear Information System (INIS)

Botelho, D.A.

1984-01-01

Some mathematical and numerical models from Retran computer codes aiming to simulate reactor transients, are presented. The equations used for calculating one-dimensional flow are integrated using mathematical methods from Flash code, with steam code to correlate the variables from thermodynamic state. The algorithm obtained was used for calculating a PWR reactor. (E.G.) [pt

Selection of skin dose calculation methodologies

International Nuclear Information System (INIS)

Farrell, W.E.

1987-01-01

This paper reports that good health physics practice dictates that a dose assessment be performed for any significant skin contamination incident. There are, however, several methodologies that could be used, and while there is probably o single methodology that is proper for all cases of skin contamination, some are clearly more appropriate than others. This can be demonstrated by examining two of the more distinctly different options available for estimating skin dose the calculational methods. The methods compiled by Healy require separate beta and gamma calculations. The beta calculational method is the derived by Loevinger, while the gamma dose is calculated from the equation for dose rate from an infinite plane source with an absorber between the source and the detector. Healy has provided these formulas in graphical form to facilitate rapid dose rate determinations at density thicknesses of 7 and 20 mg/cm 2 . These density thicknesses equate to the regulatory definition of the sensitive layer of the skin and a more arbitrary value to account of beta absorption in contaminated clothing

Relativistic hydrodynamics with QHD-I equation of state

International Nuclear Information System (INIS)

Menezes, D.P.

1993-04-01

We derive the equation of state of the QHD-I lagrangian in a classical approach. The obtained equation of state is then used as input in a relativistic hydrodynamical numerical routine. Rapidity and transverse momentum distributions are calculated and compared with experimental data on heavy ion collisions obtained at BNL-AGS and CERN-SPS. (orig.). 7 figs

Exact renormalization group equation for the Lifshitz critical point

Science.gov (United States)

Bervillier, C.

2004-10-01

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.

COMPUTER PROGRAM FOR CALCULATION MICROCHANNEL HEAT EXCHANGERS FOR AIR CONDITIONING SYSTEMS

Directory of Open Access Journals (Sweden)

Olga V. Olshevska

2016-08-01

Full Text Available Creating a computer program to calculate microchannel air condensers to reduce design time and carrying out variant calculations. Software packages for thermophysical properties of the working substance and the coolant, the correlation equation for calculating heat transfer, aerodynamics and hydrodynamics, the thermodynamic equations for the irreversible losses and their minimization in the heat exchanger were used in the process of creating. Borland Delphi 7 is used for creating software package.

Reaction rate calculations via transmission coefficients

International Nuclear Information System (INIS)

Feit, M.D.; Alder, B.J.

1985-01-01

The transmission coefficient of a wavepacket traversing a potential barrier can be determined by steady state calculations carried out in imaginary time instead of by real time dynamical calculations. The general argument is verified for the Eckart barrier potential by a comparison of transmission coefficients calculated from real and imaginary time solutions of the Schroedinger equation. The correspondence demonstrated here allows a formulation for the reaction rate that avoids difficulties due to both rare events and explicitly time dependent calculations. 5 refs., 2 figs

Hirarchical emotion calculation model for virtual human modellin - biomed 2010.

Science.gov (United States)

Zhao, Yue; Wright, David

2010-01-01

This paper introduces a new emotion generation method for virtual human modelling. The method includes a novel hierarchical emotion structure, a group of emotion calculation equations and a simple heuristics decision making mechanism, which enables virtual humans to perform emotionally in real-time according to their internal and external factors. Emotion calculation equations used in this research were derived from psychologic emotion measurements. Virtual humans can utilise the information in virtual memory and emotion calculation equations to generate their own numerical emotion states within the hierarchical emotion structure. Those emotion states are important internal references for virtual humans to adopt appropriate behaviours and also key cues for their decision making. A simple heuristics theory is introduced and integrated into decision making process in order to make the virtual humans decision making more like a real human. A data interface which connects the emotion calculation and the decision making structure together has also been designed and simulated to test the method in Virtools environment.

Determination of Watershed Lag Equation for Philippine Hydrology

Science.gov (United States)

Cipriano, F. R.; Lagmay, A. M. F. A.; Uichanco, C.; Mendoza, J.; Sabio, G.; Punay, K. N.; Oquindo, M. R.; Horritt, M.

2014-12-01

Widespread flooding is a major problem in the Philippines. The country experiences heavy amount of rainfall throughout the year and several areas are prone to flood hazards because of its unique topography. Human casualties and destruction of infrastructure are some of the damages caused by flooding and the country's government has undertaken various efforts to mitigate these hazards. One of the solutions was to create flood hazard maps of different floodplains and use them to predict the possible catastrophic results of different rain scenarios. To produce these maps, different types of data were needed and part of that is calculating hydrological components to come up with an accurate output. This paper presents how an important parameter, the time-to-peak of the watershed (Tp) was calculated. Time-to-peak is defined as the time at which the largest discharge of the watershed occurs. This is computed by using a lag time equation that was developed specifically for the Philippine setting. The equation involves three measurable parameters, namely, watershed length (L), maximum potential retention (S), and watershed slope (Y). This approach is based on a similar method developed by CH2M Hill and Horritt for Taiwan, which has a similar set of meteorological and hydrological parameters with the Philippines. Data from fourteen water level sensors covering 67 storms from all the regions in the country were used to estimate the time-to-peak. These sensors were chosen by using a screening process that considers the distance of the sensors from the sea, the availability of recorded data, and the catchment size. Values of Tp from the different sensors were generated from the general lag time equation based on the Natural Resource Conservation Management handbook by the US Department of Agriculture. The calculated Tp values were plotted against the values obtained from the equation L0.8(S+1)0.7/Y0.5. Regression analysis was used to obtain the final equation that would be

Boltzmann-Fokker-Planck calculations using standard discrete-ordinates codes

International Nuclear Information System (INIS)

Morel, J.E.

1987-01-01

The Boltzmann-Fokker-Planck (BFP) equation can be used to describe both neutral and charged-particle transport. Over the past several years, the author and several collaborators have developed methods for representing Fokker-Planck operators with standard multigroup-Legendre cross-section data. When these data are input to a standard S/sub n/ code such as ONETRAN, the code actually solves the Boltzmann-Fokker-Planck equation rather than the Boltzmann equation. This is achieved wihout any modification to the S/sub n/ codes. Because BFP calculations can be more demanding from a numerical viewpoint than standard neutronics calculations, we have found it useful to implement new quadrature methods ad convergence acceleration methods in the standard discrete-ordinates code, ONETRAN. We discuss our BFP cross-section representation techniques, our improved quadrature and acceleration techniques, and present results from BFP coupled electron-photon transport calculations performed with ONETRAN. 19 refs., 7 figs

Reciprocity relationships in vector acoustics and their application to vector field calculations.

Science.gov (United States)

Deal, Thomas J; Smith, Kevin B

2017-08-01

The reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. A similar equation that governs the orthogonal components of the particle velocity field is needed to enable this computational method to be used for acoustic vector sensors. This paper derives a general reciprocity equation that accounts for both monopole and dipole sources. This vector-scalar reciprocity equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each vector field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-dependent environment using a parabolic equation model.

POISSON SUPERFISH, Poisson Equation Solver for Radio Frequency Cavity

International Nuclear Information System (INIS)

Colman, J.

2001-01-01

1 - Description of program or function: POISSON, SUPERFISH is a group of (1) codes that solve Poisson's equation and are used to compute field quality for both magnets and fixed electric potentials and (2) RF cavity codes that calculate resonant frequencies and field distributions of the fundamental and higher modes. The group includes: POISSON, PANDIRA, SUPERFISH, AUTOMESH, LATTICE, FORCE, MIRT, PAN-T, TEKPLOT, SF01, and SHY. POISSON solves Poisson's (or Laplace's) equation for the vector (scalar) potential with nonlinear isotropic iron (dielectric) and electric current (charge) distributions for two-dimensional Cartesian or three-dimensional cylindrical symmetry. It calculates the derivatives of the potential, the stored energy, and performs harmonic (multipole) analysis of the potential. PANDIRA is similar to POISSON except it allows anisotropic and permanent magnet materials and uses a different numerical method to obtain the potential. SUPERFISH solves for the accelerating (TM) and deflecting (TE) resonant frequencies and field distributions in an RF cavity with two-dimensional Cartesian or three-dimensional cylindrical symmetry. Only the azimuthally symmetric modes are found for cylindrically symmetric cavities. AUTOMESH prepares input for LATTICE from geometrical data describing the problem, (i.e., it constructs the 'logical' mesh and generates (x,y) coordinate data for straight lines, arcs of circles, and segments of hyperbolas). LATTICE generates an irregular triangular (physical) mesh from the input data, calculates the 'point current' terms at each mesh point in regions with distributed current density, and sets up the mesh point relaxation order needed to write the binary problem file for the equation-solving POISSON, PANDIRA, or SUPERFISH. FORCE calculates forces and torques on coils and iron regions from POISSON or PANDIRA solutions for the potential. MIRT optimizes magnet profiles, coil shapes, and current densities from POISSON output based on a

Seismic tomography analysis using finite differential calculation of the eikonal equation and reciplocal principle; Eikonal equation no sabunkaiho to sohan genri wo riyoshita danseiha tomography kaiseki

Energy Technology Data Exchange (ETDEWEB)

Fujimoto, M; Ashida, Y; Watanabe, T; Sassa, K [Kyoto University, Kyoto (Japan)

1996-10-01

This paper describes the seismic tomography analysis of underground structures using finite differential calculation (FDC) and a reciprocal principle which points out that a propagation path is constant even if a source and receiver are exchanged with each other. Tomography analysis generally determines a ray length across each underground cell structure by ray tracing method to modify each cell slowness (inverse of velocity). Travel time field was determined by FDC of eikonal equation among ray tracing methods, and a wave propagation path was determined by reciprocity of elastic wave to carry out inversion. In conventional methods, since a wave length is assumed to be infinitesimal by ray theory, false modified slowness structures frequently appears depending on the density of a ray. Wave propagates in a certain width, and is affected by environment. The slowness was thus modified on the basis of the wave propagation path with a certain width by using not ray-tracing but reciprocity. By this modification, false structures were hardly found under a fine grid, and several propagation paths could be considered. 6 refs., 9 figs.

Ab-initio ZORA calculations

NARCIS (Netherlands)

Faas, S.; Snijders, Jaap; van Lenthe, J.H.; HernandezLaguna, A; Maruani, J; McWeeny, R; Wilson, S

2000-01-01

In this paper we present the first application of the ZORA (Zeroth Order Regular Approximation of the Dirac Fock equation) formalism in Ab Initio electronic structure calculations. The ZORA method, which has been tested previously in the context of Density Functional Theory, has been implemented in

Set of difference spitting schemes for solving the Navier-Stokes incompressible equations in natural variables

International Nuclear Information System (INIS)

Koleshko, S.B.

1989-01-01

A three-parametric set of difference schemes is suggested to solve Navier-Stokes equations with the use of the relaxation form of the continuity equation. The initial equations are stated for time increments. Use is made of splitting the operator into one-dimensional forms that reduce calculations to scalar factorizations. Calculated results for steady- and unsteady-state flows in a cavity are presented

Saha's ionization equation for high Z elements

International Nuclear Information System (INIS)

Godwal, B.K.; Sikka, S.K.

1977-01-01

Saha's ionization equation has been solved for high Z elements with the aim of providing input for opacity calculations. Results are presented for two elements, tungsten and uranium. The ionization potentials have been evaluated using the simple Bhor's formula with suitable effective charges for ions. The reliability of the free electron density, ion concentrations, etc., obtained from the Saha's equation solutions has been checked by comparing the P and E computed from them with those given by the Thomas-Fermi-Dirac equation of state. The agreement between the two is good from temperatures above 0.2 keV. (author)

Revision to the humidity correction equation in the calculation formulae of the air refractive index based on a phase step interferometer with three frequency-stabilized lasers

International Nuclear Information System (INIS)

Chen, Qianghua; Zhang, Mengce; Liu, Shuaijie; He, Yongxi; Luo, Huifu; Luo, Jun; Lv, Weiwei

2016-01-01

At present the formulae proposed by G Boensch and E Potulski in 1998 (Boensch and Potulski 1998 Metrologia 35 133–9) are mostly used to calculate the air refractive index. However, the humidity correction equation in the formulae is derived by using the light source of a Cd lamp whose light frequency stability is poor and at a narrow temperature range, around 20 °C. So it is no longer suitable in present optical precision measurements. To solve this problem, we propose a refractive index measurement system based on phase step interferometer with three frequency stabilized lasers (532 nm, 633 nm, 780 nm), corrected coefficients of the humidity are measured and a corresponding revised humidity correction equation is acquired. Meanwhile, the application temperature range is extended from 14.6 °C to 25.0 °C. The experiment comparison results at the temperature of 22.2–23.2 °C show the accuracy by the presented equation is better than that of Boensch and Potulski. (paper)

Solution of multigroup diffusion equations in cylindrical configuration by local polynomial approximation

International Nuclear Information System (INIS)

Jakab, J.

1979-05-01

Local approximations of neutron flux density by 2nd degree polynomials are used in calculating light water reactors. The calculations include spatial kinetics tasks for the models of two- and three-dimensional reactors in the Cartesian geometry. The resulting linear algebraic equations are considered to be formally identical to the results of the differential method of diffusion equation solution. (H.S.)

COMRAD96, Nuclear Fuel Burnup and Depletion Calculation System

International Nuclear Information System (INIS)

Suyama, K.; Masukawa, F.; Ido, M.; Enomoto, M.; Takyu, S.; Hara, T.

2002-01-01

1 - Description of program or function: Burn-up calculation of nuclear fuel. 2 - Methods: Matrix exponential method, Bateman Equation. 3 - Restrictions on the complexity of the problem: a) One-grouped cross section library should be prepared for the fuel system to be analyzed using UNITBURN. However, UNITBURN is not available now for UNIX systems. b) Gamma ray spectrometry calculation will fail using the attached piflib routine. This problem has already been rectified in the internal version. 4 - Typical running time: Two minutes for standard burn-up calculation on Sun ULTRA 30. 5 - Unusual features - a) Selection of Matrix exponential method, or Bateman Equation. b) JDDL, a detailed decay chain data based on ENSDF. 6 - Related or auxiliary programs: UNITBURN: Burnup calculation code unit cell system

Calculation of transport coefficients in an axisymmetric plasma

International Nuclear Information System (INIS)

Shumaker, D.E.

1977-01-01

A method of calculating the transport coefficient in an axisymmetric toroidal plasma is presented. This method is useful in calculating the transport coefficients in a Tokamak plasma confinement device. The particle density and temperature are shown to be a constant on a magnetic flux surface. Transport equations are given for the total particle flux and total energy flux crossing a closed toroidal surface. Also transport equations are given for the toroidal magnetic flux. A computer code was written to calculate the transport coefficients for a three species plasma, electrons and two species of ions. This is useful for calculating the transport coefficients of a plasma which contains impurities. It was found that the particle and energy transport coefficients are increased by a large amount, and the transport coefficients for the toroidal magnetic field are reduced by a small amount

On FEL integral equation and electron energy loss in intermediate gain regime

International Nuclear Information System (INIS)

Takao, Masaru

1994-03-01

The FEL pendulum equation in a intermediate gain small signal regime is investigated. By calculating the energy loss of the electron beam in terms of the solution of the pendulum equation, we confirm the consistency of the FEL equation in intermediate gain regime. (author)

Subcriticality calculation in nuclear reactors with external neutron sources

Energy Technology Data Exchange (ETDEWEB)

Silva, Adilson Costa da; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE). Programa de Engenharia Nuclear]. E-mails: asilva@con.ufrj.br; aquilino@lmp.ufrj.br; fernando@con.ufrj.br

2007-07-01

The main objective of this paper consists on the development of a methodology to monitor subcriticality. We used the inverse point kinetic equation with 6 precursor groups and external neutron sources for the calculation of reactivity. The input data for the inverse point kinetic equation was adjusted, in order to use the neutron counting rates obtained from the subcritical multiplication (1/M) in a nuclear reactor. In this paper, we assumed that the external neutron sources strength is constant and we define it in terms of a known initial condition. The results obtained from inverse point kinetic equation with external neutron sources were compared with the results obtained with a benchmark calculation, and showed good accuracy (author)

Subcriticality calculation in nuclear reactors with external neutron sources

International Nuclear Information System (INIS)

Silva, Adilson Costa da; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

2007-01-01

The main objective of this paper consists on the development of a methodology to monitor subcriticality. We used the inverse point kinetic equation with 6 precursor groups and external neutron sources for the calculation of reactivity. The input data for the inverse point kinetic equation was adjusted, in order to use the neutron counting rates obtained from the subcritical multiplication (1/M) in a nuclear reactor. In this paper, we assumed that the external neutron sources strength is constant and we define it in terms of a known initial condition. The results obtained from inverse point kinetic equation with external neutron sources were compared with the results obtained with a benchmark calculation, and showed good accuracy (author)

Pan tropical biomass equations for Mexico's dry forests

Directory of Open Access Journals (Sweden)

José Návar

2014-12-01

Full Text Available This study reports a set of robust regional M-tree allometric equations for Mexico's tropical dry forests and their application to a forest inventory dataset for the States of Durango and Sinaloa, Mexico. Calculated M data from 15 reported equations were fitted, applied and validated for regional and global models. Proposed theoretical models, empirically derived equations, as well as global and local reported equations were fitted and applied to calculated M-tree data using wood specific gravity, diameter at breast height, and top height as exogenous variables. Empirically-derived, computer-based equations assessed the M-tree evaluations slightly better than the theoretical, the global and the local models. However, the theoretical models projected compatible M-tree values and deserve further attention once wood specific gravity data are collected in the field. Using the best fit equation, mean M plot density values of 30, 41 and 35 Mg ha-1 were estimated from 57 plots (1,600 m² each, 217 plots (1,000 m² each and 166 plots (1,000 m² each in the tropical dry forests of the States of Durango, Tiniaquis and Vado Hondo (Sinaloa, respectively. The large sample size, the richness of the tested allometric models, the economic and ecological importance of this data-source, and the spatial coverage of these equations made this dataset uniquely useful for biomass, charcoal, and other bio-energy estimations, as well as for understanding the inherent heterogeneity of the stand-structure in dynamic tropical forest environments.

Application of Ruze Equation for Inflatable Aperture Antennas

Science.gov (United States)

Welch, Bryan W.

2008-01-01

Inflatable aperture reflector antennas are an emerging technology that NASA is investigating for potential uses in science and exploration missions. As inflatable aperture antennas have not been proven fully qualified for space missions, they must be characterized properly so that the behavior of the antennas can be known in advance. To properly characterize the inflatable aperture antenna, testing must be performed in a relevant environment, such as a vacuum chamber. Since the capability of having a radiofrequency (RF) test facility inside a vacuum chamber did not exist at NASA Glenn Research Center, a different methodology had to be utilized. The proposal to test an inflatable aperture antenna in a vacuum chamber entailed performing a photogrammetry study of the antenna surface by using laser ranging measurements. A root-mean-square (rms) error term was derived from the photogrammetry study to calculate the antenna surface loss as described by the Ruze equation. However, initial testing showed that problems existed in using the Ruze equation to calculate the loss due to errors on the antenna surface. This study utilized RF measurements obtained in a near-field antenna range and photogrammetry data taken from a laser range scanner to compare the expected performance of the test antenna (via the Ruze equation) with the actual RF patterns and directivity measurements. Results showed that the Ruze equation overstated the degradation in the directivity calculation. Therefore, when the photogrammetry study is performed on the test antennas in the vacuum chamber, a more complex equation must be used in light of the fact that the Ruze theory overstates the loss in directivity for inflatable aperture reflector antennas.

Dressing symmetry of the uniformization solution of Liouville equation

International Nuclear Information System (INIS)

Shen Jianmin.

1994-10-01

In this paper, the relations between monodromy group and dressing group for Liouville equation in uniformization theorem are discussed. The representation of monodromy transformation, acting on the chiral components of the solution of Liouville equation, is obtained. The non-trivial exchange algebra for monodromy transformation is calculated. (author). 14 refs

Perfect fluid cosmological Universes: One equation of state and the ...

Indian Academy of Sciences (India)

Anadijiban Das

2018-01-04

Jan 4, 2018 ... equation of state, one may calculate the geometric vari- ables, such as the ... connected by any analytic function ψ, the evolutions equations, mainly ... [3] J E Marsden and A J Tromba, Vector calculus, 3rd edn. (W. H. Freeman ...

Burnout calculation

International Nuclear Information System (INIS)

Li, D.

1980-01-01

Reviewed is the effect of heat flux of different system parameters on critical density in order to give an initial view on the value of several parameters. A thorough analysis of different equations is carried out to calculate burnout is steam-water flows in uniformly heated tubes, annular, and rectangular channels and rod bundles. Effect of heat flux density distribution and flux twisting on burnout and storage determination according to burnout are commended [ru

Solution of Duffin-Kemmer-Petiau equations for finite and infinite square well potential

International Nuclear Information System (INIS)

Boztosun, I.; Taskin, F.; Burtebayev, N.

2002-01-01

The solution of the Duffin-Kemmer-Petiau relativistic equation for spinless boson in a central field has a long standing problem and the mathematical difficulty in attempting to reach the solution even for simple problems has caused the use this equation to be regarded as quite unattractive among scientists. In this paper we first derive the system of the first-order coupled differential equation which enable the energy eigenvalues to be evaluated and show that these equations can be reduced to the second-order Schroedinger type radial differential equation. We then consider some of the properties of this equation, which are needed for practical calculations, and show that using this the second-order radial equation, the physical observables can be found in a very simple way. As an example, we consider a pionic atoms in the finite and infinite square-well potentials and calculate the eigen-energies as well as the wave functions using the relativistic Duffin-Kemmer-Petiau equation. We show that our findings are in excellent agreement with the results of the Klein-Gordon equation

Modeling protective anti-tumor immunity via preventative cancer vaccines using a hybrid agent-based and delay differential equation approach.

Science.gov (United States)

Kim, Peter S; Lee, Peter P

2012-01-01

A next generation approach to cancer envisions developing preventative vaccinations to stimulate a person's immune cells, particularly cytotoxic T lymphocytes (CTLs), to eliminate incipient tumors before clinical detection. The purpose of our study is to quantitatively assess whether such an approach would be feasible, and if so, how many anti-cancer CTLs would have to be primed against tumor antigen to provide significant protection. To understand the relevant dynamics, we develop a two-compartment model of tumor-immune interactions at the tumor site and the draining lymph node. We model interactions at the tumor site using an agent-based model (ABM) and dynamics in the lymph node using a system of delay differential equations (DDEs). We combine the models into a hybrid ABM-DDE system and investigate dynamics over a wide range of parameters, including cell proliferation rates, tumor antigenicity, CTL recruitment times, and initial memory CTL populations. Our results indicate that an anti-cancer memory CTL pool of 3% or less can successfully eradicate a tumor population over a wide range of model parameters, implying that a vaccination approach is feasible. In addition, sensitivity analysis of our model reveals conditions that will result in rapid tumor destruction, oscillation, and polynomial rather than exponential decline in the tumor population due to tumor geometry.

Applying the Nernst equation to simulate redox potential variations for biological nitrification and denitrification processes.

Science.gov (United States)

Chang, Cheng-Nan; Cheng, Hong-Bang; Chao, Allen C

2004-03-15

In this paper, various forms of Nernst equations have been developed based on the real stoichiometric relationship of biological nitrification and denitrification reactions. Instead of using the Nernst equation based on a one-to-one stoichiometric relation for the oxidizing and the reducing species, the basic Nernst equation is modified into slightly different forms. Each is suitable for simulating the redox potential (ORP) variation of a specific biological nitrification or denitrification process. Using the data published in the literature, the validity of these developed Nernst equations has been verified by close fits of the measured ORP data with the calculated ORP curve. The simulation results also indicate that if the biological process is simulated using an incorrect form of Nernst equation, the calculated ORP curve will not fit the measured data. Using these Nernst equations, the ORP value that corresponds to a predetermined degree of completion for the biochemical reaction can be calculated. Thus, these Nernst equations will enable a more efficient on-line control of the biological process.

MINPACK-1, Subroutine Library for Nonlinear Equation System

International Nuclear Information System (INIS)

Garbow, Burton S.

1984-01-01

1 - Description of problem or function: MINPACK1 is a package of FORTRAN subprograms for the numerical solution of systems of non- linear equations and nonlinear least-squares problems. The individual programs are: Identification/Description: - CHKDER: Check gradients for consistency with functions, - DOGLEG: Determine combination of Gauss-Newton and gradient directions, - DPMPAR: Provide double precision machine parameters, - ENORM: Calculate Euclidean norm of vector, - FDJAC1: Calculate difference approximation to Jacobian (nonlinear equations), - FDJAC2: Calculate difference approximation to Jacobian (least squares), - HYBRD: Solve system of nonlinear equations (approximate Jacobian), - HYBRD1: Easy-to-use driver for HYBRD, - HYBRJ: Solve system of nonlinear equations (analytic Jacobian), - HYBRJ1: Easy-to-use driver for HYBRJ, - LMDER: Solve nonlinear least squares problem (analytic Jacobian), - LMDER1: Easy-to-use driver for LMDER, - LMDIF: Solve nonlinear least squares problem (approximate Jacobian), - LMDIF1: Easy-to-use driver for LMDIF, - LMPAR: Determine Levenberg-Marquardt parameter - LMSTR: Solve nonlinear least squares problem (analytic Jacobian, storage conserving), - LMSTR1: Easy-to-use driver for LMSTR, - QFORM: Accumulate orthogonal matrix from QR factorization QRFAC Compute QR factorization of rectangular matrix, - QRSOLV: Complete solution of least squares problem, - RWUPDT: Update QR factorization after row addition, - R1MPYQ: Apply orthogonal transformations from QR factorization, - R1UPDT: Update QR factorization after rank-1 addition, - SPMPAR: Provide single precision machine parameters. 4. Method of solution - MINPACK1 uses the modified Powell hybrid method and the Levenberg-Marquardt algorithm

Evaluating organ delineation, dose calculation and daily localization in an open-MRI simulation workflow for prostate cancer patients

International Nuclear Information System (INIS)

Doemer, Anthony; Chetty, Indrin J; Glide-Hurst, Carri; Nurushev, Teamour; Hearshen, David; Pantelic, Milan; Traughber, Melanie; Kim, Joshua; Levin, Kenneth; Elshaikh, Mohamed A; Walker, Eleanor; Movsas, Benjamin

2015-01-01

This study describes initial testing and evaluation of a vertical-field open Magnetic Resonance Imaging (MRI) scanner for the purpose of simulation in radiation therapy for prostate cancer. We have evaluated the clinical workflow of using open MRI as a sole modality for simulation and planning. Relevant results related to MRI alignment (vs. CT) reference dataset with Cone-Beam CT (CBCT) for daily localization are presented. Ten patients participated in an IRB approved study utilizing MRI along with CT simulation with the intent of evaluating the MRI-simulation process. Differences in prostate gland volume, seminal vesicles, and penile bulb were assessed with MRI and compared to CT. To evaluate dose calculation accuracy, bulk-density-assignments were mapped onto respective MRI datasets and treated IMRT plans were re-calculated. For image localization purposes, 400 CBCTs were re-evaluated with MRI as the reference dataset and daily shifts compared against CBCT-to-CT registration. Planning margins based on MRI/CBCT shifts were computed using the van Herk formalism. Significant organ contour differences were noted between MRI and CT. Prostate volumes were on average 39.7% (p = 0.002) larger on CT than MRI. No significant difference was found in seminal vesicle volumes (p = 0.454). Penile bulb volumes were 61.1% higher on CT, without statistical significance (p = 0.074). MRI-based dose calculations with assigned bulk densities produced agreement within 1% with heterogeneity corrected CT calculations. The differences in shift positions for the cohort between CBCT-to-CT registration and CBCT-to-MRI registration are −0.15 ± 0.25 cm (anterior-posterior), 0.05 ± 0.19 cm (superior-inferior), and −0.01 ± 0.14 cm (left-right). This study confirms the potential of using an open-field MRI scanner as primary imaging modality for prostate cancer treatment planning simulation, dose calculations and daily image localization

Influence of intravenous contrast agent on dose calculations of intensity modulated radiation therapy plans for head and neck cancer

International Nuclear Information System (INIS)

Choi, Youngmin; Kim, Jeung-Kee; Lee, Hyung-Sik; Hur, Won-Joo; Hong, Young-Seoub; Park, Sungkwang; Ahn, Kijung; Cho, Heunglae

2006-01-01

Background and purpose: To evaluate the effect of an intravenous contrast agent (CA) on dose calculations and its clinical significance in intensity modulated radiation therapy (IMRT) plans for head and neck cancer. Materials and methods: Fifteen patients with head and neck cancer and involved neck nodes were enrolled. Each patient took two sets of computerized tomography (CT) in the same position before and after intravenous CA injections. Target volumes and organs at risk (OAR) were contoured on the enhanced CT, and then an IMRT plan of nine equiangular beams with a 6 MV X-ray was created. After the fusion of non-enhanced and enhanced CTs, the contours and the IMRT plan created from the enhanced CT were copied and placed to the non-enhanced CT. Doses were calculated again from the non-enhanced CT by the same IMRT plan. The radiation doses calculated from the two sets of CTs were compared with regard to planning target volumes (PTV) and the three OARs, both parotid glands and the spinal cord, by Wilcoxon's signed rank test. Results: The doses (maximum, mean, and the dose of 95% of PTV received (D 95% )) of PTV70 and PTV59.4 calculated from the enhanced CTs were lower than those from the non-enhanced CTs (p < 0.05), but the dose differences were less than 1% compared to the doses calculated from the enhanced CTs. The doses of PTV50.4, parotid glands, and spinal cord were not significantly different between the non-enhanced and enhanced CTs. Conclusions: The difference between the doses calculated from the CTs with and without CA enhancement was tolerably small, therefore using intravenous CA could be recommended for the planning CT of head and neck IMRT

Resolution of hydrodynamical equations for transverse expansions

International Nuclear Information System (INIS)

Hama, Y.; Pottag, F.W.

1984-01-01

The three-dimensional hydrodynamical expansion is treated with a method similar to that of Milekhin, but more explicit. Although in the final stage one have to appeal to numerical calculation, the partial differential equations governing the transverse expansions are treated without transforming them into ordinary equations with an introduction of averaged quantities. It is only concerned with the formalism and the numerical results will be given in the next paper. (Author) [pt

Resolution of hydrodynamical equations for transverse expansions

International Nuclear Information System (INIS)

Hama, Y.; Pottag, F.W.

1985-01-01

The three-dimensional hydrodynamical expansion is treated with a method similar to that of Milekhin, but more explicit. Although in the final stage we have to appeal to numerical calculation, the partial differential equations governing the transverse expansions are treated without transforming them into ordinary equations with an introduction of averaged quantities. The present paper is concerned with the formalism and the numerical results will be reported in another paper. (Author) [pt

Consistent three-equation model for thin films

Science.gov (United States)

Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

2017-11-01

Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Convergence and Testing; Calculo Numerico del Transporte mediante la Ecuacion Cinetica de Deriva para Plasmas en Geometria Magnetica Toroidal: Convergencia y Comprobaciones

Energy Technology Data Exchange (ETDEWEB)

Reynolds, J. M.; Lopez-Bruna, D.

2009-12-11

This report is the third of a series [Informes Tecnicos Ciemat 1165 y 1172] devoted to the development of a new numerical code to solve the guiding center equation for electrons and ions in toroidal plasmas. Two calculation meshes corresponding to axisymmetric tokamaks are now prepared and the kinetic equation is expanded so the standard terms of neoclassical theory --fi rst order terms in the Larmor radius expansion-- can be identified, restricting the calculations correspondingly. Using model density and temperature profiles for the plasma, several convergence test are performed depending on the calculation meshes and the expansions of the distribution function; then the results are compared with the theory [Hinton and Hazeltine, Rev. Mod. Phys. (1976)]. (Author) 18 refs.

Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

Science.gov (United States)

Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2018-05-01

The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.

Numerical calculations near spatial infinity

International Nuclear Information System (INIS)

Zenginoglu, Anil

2007-01-01

After describing in short some problems and methods regarding the smoothness of null infinity for isolated systems, I present numerical calculations in which both spatial and null infinity can be studied. The reduced conformal field equations based on the conformal Gauss gauge allow us in spherical symmetry to calculate numerically the entire Schwarzschild-Kruskal spacetime in a smooth way including spacelike, null and timelike infinity and the domain close to the singularity

Inverse Schroedinger equation and the exact wave function

International Nuclear Information System (INIS)

Nakatsuji, Hiroshi

2002-01-01

Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem

Ordinary differential equation for local accumulation time.

Science.gov (United States)

Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

Updates to In-Line Calculation of Photolysis Rates

Science.gov (United States)

How photolysis rates are calculated affects ozone and aerosol concentrations predicted by the CMAQ model and the model?s run-time. The standard configuration of CMAQ uses the inline option that calculates photolysis rates by solving the radiative transfer equation for the needed ...

Computer local construction of a general solution for the Chew-Low equations

International Nuclear Information System (INIS)

Gerdt, V.P.

1980-01-01

General solution of the dynamic form of the Chew-Low equations in the vicinity of the restpoint is considered. A method for calculating coefficients of series being members of such solution is suggested. The results of calculations, coefficients of power series and expansions carried out by means of the SCHOONSCHIP and SYMBAL systems are given. It is noted that the suggested procedure of the Chew-Low equation solutions basing on using an electronic computer as an instrument for analytical calculations permits to obtain detail information on the local structure of general solution

Numerical procedure for the calculation of nonsteady spherical shock fronts with radiation

International Nuclear Information System (INIS)

Winkler, K.H.

The basis of the numerical method is an implicit difference scheme with time backward differences to a freely moving coordinate system. The coordinate system itself is determined simultaneously with the iterative solution of the physical equations as a function of the physical variables. Shock fronts, even nonsteady ones, are calculated as discontinuities according to the Rankine--Hugoniot equations. The radiation field is obtained from the two-dimensional, static, spherically symmetric transport equation in conjunction with the time-dependent one-dimensional moment equations. No artificial viscosity of any type is ever used. The applicability of the method developed is demonstrated by an example involving the calculation of protostar collapse. 11 figures

Adiabatic invariants of the extended KdV equation

Energy Technology Data Exchange (ETDEWEB)

Karczewska, Anna [Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Rozmej, Piotr, E-mail: p.rozmej@if.uz.zgora.pl [Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Infeld, Eryk [National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa (Poland); Rowlands, George [Department of Physics, University of Warwick, Coventry, CV4 7A (United Kingdom)

2017-01-30

When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic invariants (AI) can be found. When the KdV expansion parameters are zero, exact invariants are recovered. Existence of adiabatic invariants results from general theory of near-identity transformations (NIT) which allow us to transform higher order nonintegrable equations to asymptotically equivalent (when small parameters tend to zero) integrable form. Here we present a direct method of calculations of adiabatic invariants. It does not need a transformation to a moving reference frame nor performing a near-identity transformation. Numerical tests show that deviations of AI from constant values are indeed small. - Highlights: • We suggest a new and simple method for calculating adiabatic invariants of second order wave equations. • It is easy to use and we hope that it will be useful if published. • Interesting numerics included.

Relativistic wave equations and compton scattering

International Nuclear Information System (INIS)

Sutanto, S.H.; Robson, B.A.

1998-01-01

Full text: Recently an eight-component relativistic wave equation for spin-1/2 particles was proposed.This equation was obtained from a four-component spin-1/2 wave equation (the KG1/2 equation), which contains second-order derivatives in both space and time, by a procedure involving a linearisation of the time derivative analogous to that introduced by Feshbach and Villars for the Klein-Gordon equation. This new eight-component equation gives the same bound-state energy eigenvalue spectra for hydrogenic atoms as the Dirac equation but has been shown to predict different radiative transition probabilities for the fine structure of both the Balmer and Lyman a-lines. Since it has been shown that the new theory does not always give the same results as the Dirac theory, it is important to consider the validity of the new equation in the case of other physical problems. One of the early crucial tests of the Dirac theory was its application to the scattering of a photon by a free electron: the so-called Compton scattering problem. In this paper we apply the new theory to the calculation of Compton scattering to order e 2 . It will be shown that in spite of the considerable difference in the structure of the new theory and that of Dirac the cross section is given by the Klein-Nishina formula

Effective field equations for expectation values

International Nuclear Information System (INIS)

Jordan, R.D.

1986-01-01

We discuss functional methods which allow calculation of expectation values, rather than the usual in-out amplitudes, from a path integral. The technique, based on Schwinger's idea of summing over paths which go from the past to the future and then back to the past, provides effective field equations satisfied by the expectation value of the field. These equations are shown to be real and causal for a general theory up to two-loop order, and unitarity is checked to this order. These methods are applied to a simple quantum-mechanical example to illustrate the differences between the new formalism and the standard theory. When applied to the gravitational field, the new effective field equations should be useful for studies of quantum cosmology

B-splines and Faddeev equations

International Nuclear Information System (INIS)

Huizing, A.J.

1990-01-01

Two numerical methods for solving the three-body equations describing relativistic pion deuteron scattering have been investigated. For separable two body interactions these equations form a set of coupled one-dimensional integral equations. They are plagued by singularities which occur in the kernel of the integral equations as well as in the solution. The methods to solve these equations differ in the way they treat the singularities. First the Fuda-Stuivenberg method is discussed. The basic idea of this method is an one time iteration of the set of integral equations to treat the logarithmic singularities. In the second method, the spline method, the unknown solution is approximated by splines. Cubic splines have been used with cubic B-splines as basis. If the solution is approximated by a linear combination of basis functions, an integral equation can be transformed into a set of linear equations for the expansion coefficients. This set of linear equations is solved by standard means. Splines are determined by points called knots. A proper choice of splines to approach the solution stands for a proper choice of the knots. The solution of the three-body scattering equations has a square root behaviour at a certain point. Hence it was investigated how the knots should be chosen to approximate the square root function by cubic B-splines in an optimal way. Before applying this method to solve numerically the three-body equations describing pion-deuteron scattering, an analytically solvable example has been constructed with a singularity structure of both kernel and solution comparable to those of the three-body equations. The accuracy of the numerical solution was determined to a large extent by the accuracy of the approximation of the square root part. The results for a pion laboratory energy of 47.4 MeV agree very well with those from literature. In a complete calculation for 47.7 MeV the spline method turned out to be a factor thousand faster than the Fuda

Accurate heterogeneous dose calculation for lung cancer patients without high‐resolution CT densities

Science.gov (United States)

Li, Jonathan G.; Liu, Chihray; Olivier, Kenneth R.; Dempsey, James F.

2009-01-01

The aim of this study was to investigate the relative accuracy of megavoltage photon‐beam dose calculations employing either five bulk densities or independent voxel densities determined by calibration of the CT Houndsfield number. Full‐resolution CT and bulk density treatment plans were generated for 70 lung or esophageal cancer tumors (66 cases) using a commercial treatment planning system with an adaptive convolution dose calculation algorithm (Pinnacle3, Philips Medicals Systems). Bulk densities were applied to segmented regions. Individual and population average densities were compared to the full‐resolution plan for each case. Monitor units were kept constant and no normalizations were employed. Dose volume histograms (DVH) and dose difference distributions were examined for all cases. The average densities of the segmented air, lung, fat, soft tissue, and bone for the entire set were found to be 0.14, 0.26, 0.89, 1.02, and 1.12 g/cm3, respectively. In all cases, the normal tissue DVH agreed to better than 2% in dose. In 62 of 70 DVHs of the planning target volume (PTV), agreement to better than 3% in dose was observed. Six cases demonstrated emphysema, one with bullous formations and one with a hiatus hernia having a large volume of gas. These required the additional assignment of density to the emphysemic lung and inflammatory changes to the lung, the regions of collapsed lung, the bullous formations, and the hernia gas. Bulk tissue density dose calculation provides an accurate method of heterogeneous dose calculation. However, patients with advanced emphysema may require high‐resolution CT studies for accurate treatment planning. PACS number: 87.53.Tf

Predicting health-related quality of life in cancer patients receiving chemotherapy: a structural equation approach using the self-control model.

Science.gov (United States)

Park, Yu-Ri; Park, Eun-Young; Kim, Jung-Hee

2017-11-09

According to the self-control model, self-control works as a protective factor and a psychological resource. Although an understanding of the effect(s) of peripheral neuropathy on quality of life is important to healthcare professionals, previous studies do not facilitate broad comprehension in this regard. The purpose of this cross-sectional study was to test the multidimensional assumptions of quality of life of patients with cancer, with focus on their self-control. A structural equation model was tested on patients with cancer at the oncology clinic of a university hospital where patients received chemotherapy. A model was tested using structural equation modeling, which allows the researcher to find the empirical evidence by testing a measurement model and a structural model. The model comprised three variables, self-control, health related quality of life, and chemotherapy-induced peripheral neuropathy. Among the variables, self-control was the endogenous and mediating variable. The proposed models showed good fit indices. Self-control partially mediated chemotherapy-induced peripheral neuropathy and quality of life. It was found that the physical symptoms of peripheral neuropathy influenced health-related quality of life both indirectly and directly. Self-control plays a significant role in the protection and promotion of physical and mental health in various stressful situations, and thus, as a psychological resource, it plays a significant role in quality of life. Our results can be used to develop a quality of life model for patients receiving chemotherapy and as a theoretical foundation for the development of appropriate nursing interventions.

Online plasma calculator

Science.gov (United States)

Wisniewski, H.; Gourdain, P.-A.

2017-10-01

APOLLO is an online, Linux based plasma calculator. Users can input variables that correspond to their specific plasma, such as ion and electron densities, temperatures, and external magnetic fields. The system is based on a webserver where a FastCGI protocol computes key plasma parameters including frequencies, lengths, velocities, and dimensionless numbers. FastCGI was chosen to overcome security problems caused by JAVA-based plugins. The FastCGI also speeds up calculations over PHP based systems. APOLLO is built upon the WT library, which turns any web browser into a versatile, fast graphic user interface. All values with units are expressed in SI units except temperature, which is in electron-volts. SI units were chosen over cgs units because of the gradual shift to using SI units within the plasma community. APOLLO is intended to be a fast calculator that also provides the user with the proper equations used to calculate the plasma parameters. This system is intended to be used by undergraduates taking plasma courses as well as graduate students and researchers who need a quick reference calculation.

Crystal structure optimisation using an auxiliary equation of state

Science.gov (United States)

Jackson, Adam J.; Skelton, Jonathan M.; Hendon, Christopher H.; Butler, Keith T.; Walsh, Aron

2015-11-01

Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy-volume curve, fitting an equation of state around the equilibrium cell volume. This is a computationally intensive process, in particular, for low-symmetry crystal structures where each isochoric optimisation involves energy minimisation over many degrees of freedom. Such procedures can be prohibitive for non-local exchange-correlation functionals or other "beyond" density functional theory electronic structure techniques, particularly where analytical gradients are not available. We present a simple approach for efficient optimisation of crystal structures based on a known equation of state. The equilibrium volume can be predicted from one single-point calculation and refined with successive calculations if required. The approach is validated for PbS, PbTe, ZnS, and ZnTe using nine density functionals and applied to the quaternary semiconductor Cu2ZnSnS4 and the magnetic metal-organic framework HKUST-1.

Crystal structure optimisation using an auxiliary equation of state

International Nuclear Information System (INIS)

Jackson, Adam J.; Skelton, Jonathan M.; Hendon, Christopher H.; Butler, Keith T.; 3 Institute and Department of Materials Science and Engineering, Yonsei University, Seoul 120-749 (Korea, Republic of))" data-affiliation=" (Centre for Sustainable Chemical Technologies and Department of Chemistry, University of Bath, Claverton Down, Bath BA2 7AY (United Kingdom); Global E3 Institute and Department of Materials Science and Engineering, Yonsei University, Seoul 120-749 (Korea, Republic of))" >Walsh, Aron

2015-01-01

Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy–volume curve, fitting an equation of state around the equilibrium cell volume. This is a computationally intensive process, in particular, for low-symmetry crystal structures where each isochoric optimisation involves energy minimisation over many degrees of freedom. Such procedures can be prohibitive for non-local exchange-correlation functionals or other “beyond” density functional theory electronic structure techniques, particularly where analytical gradients are not available. We present a simple approach for efficient optimisation of crystal structures based on a known equation of state. The equilibrium volume can be predicted from one single-point calculation and refined with successive calculations if required. The approach is validated for PbS, PbTe, ZnS, and ZnTe using nine density functionals and applied to the quaternary semiconductor Cu 2 ZnSnS 4 and the magnetic metal-organic framework HKUST-1

Crystal structure optimisation using an auxiliary equation of state

Energy Technology Data Exchange (ETDEWEB)

Jackson, Adam J.; Skelton, Jonathan M.; Hendon, Christopher H.; Butler, Keith T. [Centre for Sustainable Chemical Technologies and Department of Chemistry, University of Bath, Claverton Down, Bath BA2 7AY (United Kingdom); Walsh, Aron, E-mail: a.walsh@bath.ac.uk [Centre for Sustainable Chemical Technologies and Department of Chemistry, University of Bath, Claverton Down, Bath BA2 7AY (United Kingdom); Global E" 3 Institute and Department of Materials Science and Engineering, Yonsei University, Seoul 120-749 (Korea, Republic of)

2015-11-14

Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy–volume curve, fitting an equation of state around the equilibrium cell volume. This is a computationally intensive process, in particular, for low-symmetry crystal structures where each isochoric optimisation involves energy minimisation over many degrees of freedom. Such procedures can be prohibitive for non-local exchange-correlation functionals or other “beyond” density functional theory electronic structure techniques, particularly where analytical gradients are not available. We present a simple approach for efficient optimisation of crystal structures based on a known equation of state. The equilibrium volume can be predicted from one single-point calculation and refined with successive calculations if required. The approach is validated for PbS, PbTe, ZnS, and ZnTe using nine density functionals and applied to the quaternary semiconductor Cu{sub 2}ZnSnS{sub 4} and the magnetic metal-organic framework HKUST-1.

Parametric Equations: Push 'Em Back, Push 'Em Back, Way Back!

Science.gov (United States)

Cieply, Joseph F.

1993-01-01

Stresses using the features of graphing calculators to teach parametric equations much earlier in the curriculum than is presently done. Examples using parametric equations to teach slopes and lines in beginning algebra, inverse functions in advanced algebra, the wrapping function, and simulations of physical phenomena are presented. (MAZ)

Estimating order-picking times for return heuristic - equations and simulations

Directory of Open Access Journals (Sweden)

Grzegorz Tarczyński

2015-09-01

Full Text Available Background: A key element of the evaluation of warehouse operation is the average order-picking time. In warehouses where the order-picking process is carried out according to the "picker-to-part" rule the order-picking time is usually proportional to the distance covered by the picker while picking items. This distance can by estimated by simulations or using mathematical equations. In the paper only the best described in the literature one-block rectangular warehouses are considered. Material and methods: For the one-block rectangular warehouses there are well known five routing heuristics. In the paper the author considers the return heuristic in two variants. The paper presents well known Hall's and De Koster's equations for the average distance traveled by the picker while completing items from one pick list. The author presents own proposals for calculating the expected distance. Results: the results calculated by the use of mathematical equations (the formulas of Hall, De Koster and own propositions were compared with the average values obtained using computer simulations. For the most cases the average error does not exceed 1% (except for Hall's equations. To carry out simulation the computer software Warehouse Real-Time Simulator was used. Conclusions: the order-picking time is a function of many variables and its optimization is not easy. It can be done in two stages: firstly using mathematical equations the set of the potentially best variants is established, next the results are verified using simulations. The results calculated by the use of equations are not precise, but possible to achieve immediately. The simulations are more time-consuming, but allow to analyze the order-picking process more accurately.

Integration of differential equations by the pseudo-linear (PL) approximation

International Nuclear Information System (INIS)

Bonalumi, Riccardo A.

1998-01-01

A new method of integrating differential equations was originated with the technique of approximately calculating the integrals called the pseudo-linear (PL) procedure: this method is A-stable. This article contains the following examples: 1st order ordinary differential equations (ODEs), 2nd order linear ODEs, stiff system of ODEs (neutron kinetics), one-dimensional parabolic (diffusion) partial differential equations. In this latter case, this PL method coincides with the Crank-Nicholson method

Wave equation of hydrogen atom

International Nuclear Information System (INIS)

Suwito.

1977-01-01

The calculation of the energy levels of the hydrogen atom using Bohr, Schroedinger and Dirac theories is reviewed. The result is compared with that obtained from infinite component wave equations theory which developed recently. The conclusion can be stated that the latter theory is better to describe the composit system than the former. (author)

The Bethe-Salpeter equation with fermions

International Nuclear Information System (INIS)

Efimov, G.V.

2007-01-01

The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a fermion theory: two fermion fields (constituents) with mass m interacting via an exchange of a scalar field with mass μ. The BS equation can be written in the form of an integral equation in the configuration Euclidean x-space with the symmetric kernel K for which Tr K 2 = ∞ due to the singular character of the fermion propagator. This kernel is represented in the form K = K 0 + K I . The operator K 0 with Tr K 0 2 ∞ is of the 'fall at the center' potential type and describes a continuous spectrum only. Besides the presence of this operator leads to a restriction on the value of the coupling constant. The kernel K I with Tr K I 2 2 c 2 and the variational procedure of calculations of eigenvalues and eigenfunctions can be applied. The quantum pseudoscalar and scalar mesodynamics is considered. The binding energy of the state 1 + (deuteron) as a function of the coupling constant is calculated in the framework of the procedure formulated above. It is shown that this bound state is absent in the pseudoscalar mesodynamics and does exist in the scalar mesodynamics. A comparison with the non-relativistic Schroedinger picture is made. (author)

IMPROVEMENT OF THE REDLICH-KWONG EQUATION OF STATE BY MODIFICATION OF CO-VOLUME PARAMETER

Directory of Open Access Journals (Sweden)

Ratnawati Ratnawati

2012-02-01

Full Text Available Cubic equations of state are widely used in phase-equilibrium calculations because of their simplicity and accuracy. Most equations of states are not accurate enough for predicting density of liquid and dense gas. A modification on the Redlich-Kwong (RK equation of state is developed. Parameter b is modified by introducing a new parameter,b, which is a function of molecular weight and temperature. The modification gives a significant improvement over the original RK equation for predicting density. For 6538 data points of 27 compounds, the proposed equation gives only 2.8% of average absolute deviation (AAD, while the original RK and the Soave-Redlich-Kwong (SRK equations give 11.4% and 11.7%, respectively. The proposed modification improves the performance of the RK equation for predicting vapor pressure as well. For 2829 data points of 94 compounds, the proposed modification lowers the AAD of the RK equation from 1460% down to 30.8%. It is comparable to the famous SRK equation, which give 5.8% of AAD. The advantage of the proposed equation is that it uses only critical pressure and temperature as other equations of states do, and molecular weight, which is easily calculated. Another advantage is that the proposed equation simpler than the SRK equation of state.

Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

Science.gov (United States)

Zhou, L.-Q.; Meleshko, S. V.

2017-07-01

The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

Three-phase Power Flow Calculation of Low Voltage Distribution Network Considering Characteristics of Residents Load

Science.gov (United States)

Wang, Yaping; Lin, Shunjiang; Yang, Zhibin

2017-05-01

In the traditional three-phase power flow calculation of the low voltage distribution network, the load model is described as constant power. Since this model cannot reflect the characteristics of actual loads, the result of the traditional calculation is always different from the actual situation. In this paper, the load model in which dynamic load represented by air conditioners parallel with static load represented by lighting loads is used to describe characteristics of residents load, and the three-phase power flow calculation model is proposed. The power flow calculation model includes the power balance equations of three-phase (A,B,C), the current balance equations of phase 0, and the torque balancing equations of induction motors in air conditioners. And then an alternating iterative algorithm of induction motor torque balance equations with each node balance equations is proposed to solve the three-phase power flow model. This method is applied to an actual low voltage distribution network of residents load, and by the calculation of three different operating states of air conditioners, the result demonstrates the effectiveness of the proposed model and the algorithm.

ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

Science.gov (United States)

Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

2018-04-01

In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

Cash flow in the context of economic equation of continuity

Directory of Open Access Journals (Sweden)

Fernando Gómez Villarraga

2006-07-01

Full Text Available The mathematic scheme, known as economic equation of continuity, is established for the balance of economic resources. In order to apply this equation it is necessary to determine an economic volume of control. The patrimonial equation is also proposed as a speed equationfor this volurne. The integral equation of economic continuity is applied to the «cash» system along with the integral patrimonial equation and so it gets expressions that correspond to model to elaborate cashflow statement with the particularities of the direct and indirect method. This model generales a useful definition for the calculation of this basic financial statement classified by operating, investing and financing activities.

On the solution of the Liouville equation over a rectangle

Directory of Open Access Journals (Sweden)

A. M. Arthurs

1996-01-01

Full Text Available Methods for integral equations are used to derive pointwise bounds for the solution of a boundary value problem for the nonlinear Liouville partial differential equation over a rectangle. Several test calculations are performed and the resulting solutions are more accurate than those obtained previously by other methods.

HLW disposal by fission reactors; calculation of trans-mutation rate and recycle

International Nuclear Information System (INIS)

Mulyanto

1997-01-01

Transmutation of MA (Minor actinide) and LLFPS (long-lived fission products) into stable nuclide or short-lived isotopes by fission reactors seem to become an alternative technology for HLW disposal. in this study, transmutation rate and recycle calculation were developed in order to evaluate transmutation characteristics of MA and LLFPs in the fission reactors. inventory of MA and LLFPs in the transmutation reactors were determined by solving of criticality equation with 1-D cylindrical geometry of multigroup diffusion equations at the beginning of cycle (BOC). transmutation rate and burn-up was determined by solving of depletion equation. inventory of MA and LLFPs was calculated for 40 years recycle. From this study, it was concluded that characteristics of MA and LLFPs in the transmutation reactors can be evaluated by recycle calculation. by calculation of transmutation rate, performance of fission reactor for transmutation of MA or LLFPs can be discussed

Energy master equation

DEFF Research Database (Denmark)

Dyre, Jeppe

1995-01-01

energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk model—the energy master equation...... (EME)—is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...

An analytical solution of the Navier-Stokes equation for internal flows

International Nuclear Information System (INIS)

Lyberg, Mats D; Tryggeson, Henrik

2007-01-01

This paper derives a solution to the Navier-Stokes equation by considering vorticity generated at system boundaries. The result is an explicit expression for the velocity. The Navier-Stokes equation is reformulated as a divergence and integrated, giving a tensor equation that splits into a symmetric and a skew-symmetric part. One equation gives an algebraic system of quadratic equations involving velocity components. A system of nonlinear partial differential equations is reduced to algebra. The velocity is then explicitly calculated and shown to depend on boundary conditions only. This removes the need to solve the Navier-Stokes equation by a 3D numerical computation, replacing it by computation of 2D surface integrals over the boundary. (fast track communication)

Vortex dynamics equation in type-II superconductors in a temperature gradient

International Nuclear Information System (INIS)

Vega Monroy, R.; Sarmiento Castillo, J.; Puerta Torres, D.

2010-01-01

In this work we determined a vortex dynamics equation in a temperature gradient in the frame of the time dependent Ginzburg-Landau equation. In this sense, we derived a local solvability condition, which governs the vortex dynamics. Also, we calculated the explicit form for the force coefficients, which are the keys for the understanding of the balance equation due to vortex interactions with the environment. (author)

Vortex dynamics equation in type-II superconductors in a temperature gradient

Energy Technology Data Exchange (ETDEWEB)

Vega Monroy, R.; Sarmiento Castillo, J. [Universidad del Atlantico, Barranquilla (Colombia). Facultad de Ciencias Basicas; Puerta Torres, D. [Universidad de Cartagena (Colombia). Facultad de Ciencias Exactas

2010-12-15

In this work we determined a vortex dynamics equation in a temperature gradient in the frame of the time dependent Ginzburg-Landau equation. In this sense, we derived a local solvability condition, which governs the vortex dynamics. Also, we calculated the explicit form for the force coefficients, which are the keys for the understanding of the balance equation due to vortex interactions with the environment. (author)

European Randomized Study of Screening for Prostate Cancer Risk Calculator: External Validation, Variability, and Clinical Significance.

Science.gov (United States)

Gómez-Gómez, Enrique; Carrasco-Valiente, Julia; Blanca-Pedregosa, Ana; Barco-Sánchez, Beatriz; Fernandez-Rueda, Jose Luis; Molina-Abril, Helena; Valero-Rosa, Jose; Font-Ugalde, Pilar; Requena-Tapia, Maria José

2017-04-01

To externally validate the European Randomized Study of Screening for Prostate Cancer (ERSPC) risk calculator (RC) and to evaluate its variability between 2 consecutive prostate-specific antigen (PSA) values. We prospectively catalogued 1021 consecutive patients before prostate biopsy for suspicion of prostate cancer (PCa). The risk of PCa and significant PCa (Gleason score ≥7) from 749 patients was calculated according to ERSPC-RC (digital rectal examination-based version 3 of 4) for 2 consecutive PSA tests per patient. The calculators' predictions were analyzed using calibration plots and the area under the receiver operating characteristic curve (area under the curve). Cohen kappa coefficient was used to compare the ability and variability. Of 749 patients, PCa was detected in 251 (33.5%) and significant PCa was detected in 133 (17.8%). Calibration plots showed an acceptable parallelism and similar discrimination ability for both PSA levels with an area under the curve of 0.69 for PCa and 0.74 for significant PCa. The ERSPC showed 226 (30.2%) unnecessary biopsies with the loss of 10 significant PCa. The variability of the RC was 16% for PCa and 20% for significant PCa, and a higher variability was associated with a reduced risk of significant PCa. We can conclude that the performance of the ERSPC-RC in the present cohort shows a high similitude between the 2 PSA levels; however, the RC variability value is associated with a decreased risk of significant PCa. The use of the ERSPC in our cohort detects a high number of unnecessary biopsies. Thus, the incorporation of ERSPC-RC could help the clinical decision to carry out a prostate biopsy. Copyright © 2016 Elsevier Inc. All rights reserved.

Empirical method to calculate Clinch River Breeder Reactor (CRBR) inlet plenum transient temperatures

International Nuclear Information System (INIS)

Howarth, W.L.

1976-01-01

Sodium flow enters the CRBR inlet plenum via three loops or inlets. An empirical equation was developed to calculate transient temperatures in the CRBR inlet plenum from known loop flows and temperatures. The constants in the empirical equation were derived from 1/4 scale Inlet Plenum Model tests using water as the test fluid. The sodium temperature distribution was simulated by an electrolyte. Step electrolyte transients at 100 percent model flow were used to calculate the equation constants. Step electrolyte runs at 50 percent and 10 percent flow confirmed that the constants were independent of flow. Also, a transient was tested which varied simultaneously flow rate and electrolyte. Agreement of the test results with the empirical equation results was good which verifies the empirical equation

Nuclear fission with a Langevin equation

International Nuclear Information System (INIS)

Boilley, D.; Suraud, E.; Abe, Yasuhisa

1992-01-01

A microscopically derived Langevin equation is applied to thermally induced nuclear fission. An important memory effect is pointed out and discussed. A strong friction coefficient, estimated from microscopic quantities, tends to decrease the stationary limit of the fission rate and to increase the transient time. The calculations are performed with a collective mass depending on the collective variable and with a constant mass. Fission rates calculated at different temperatures are shown and compared with previous available results. (author) 23 refs.; 7 figs

The effect of KZK pressure equation on the sonoluminescence in water and fat tissues

International Nuclear Information System (INIS)

Gheshlaghi, M.; Sadighi-Bonabi, R.; Ghadirifar, A.

2015-01-01

The effect of the produced light flashes from sonoluminescence (SL) on the fat tissue and water is studied. By using KZK equation as an essential equation for calculating the thermal source in bio-liquids, the effective bubble parameters in quasi-adiabatic model are calculated and compared in these systems. It is noticed that the temperature and the intensity for fat tissue are about 30% and 38% less than the ones for water respectively. These results are almost in good agreement with the only experimental measurement denoting less SL temperature in bio-liquids which present more suitable condition for using SL in such applications. - Highlights: • Coupling of acoustic pressure and the pressure's KZK equation for using Sonoluminescence equations. • The Sonoluminescence parameters (temperature, pressure and intensity) are calculated and Compared for water and fat tissue. • The high-intensity radiation of Sonoluminescence bubble is used in medical applications

The effect of KZK pressure equation on the sonoluminescence in water and fat tissues

Energy Technology Data Exchange (ETDEWEB)

Gheshlaghi, M. [Payame Noor University, P.O.B. 19395-3697, Tehran (Iran, Islamic Republic of); Sadighi-Bonabi, R., E-mail: Sadighi@sharif.ir [Department of Physics, Sharif University of Technology, 11365-91, Tehran (Iran, Islamic Republic of); Ghadirifar, A. [Islamic Azad University, Faculty of Mechanical Engineering, Mashhad (Iran, Islamic Republic of)

2015-09-25

The effect of the produced light flashes from sonoluminescence (SL) on the fat tissue and water is studied. By using KZK equation as an essential equation for calculating the thermal source in bio-liquids, the effective bubble parameters in quasi-adiabatic model are calculated and compared in these systems. It is noticed that the temperature and the intensity for fat tissue are about 30% and 38% less than the ones for water respectively. These results are almost in good agreement with the only experimental measurement denoting less SL temperature in bio-liquids which present more suitable condition for using SL in such applications. - Highlights: • Coupling of acoustic pressure and the pressure's KZK equation for using Sonoluminescence equations. • The Sonoluminescence parameters (temperature, pressure and intensity) are calculated and Compared for water and fat tissue. • The high-intensity radiation of Sonoluminescence bubble is used in medical applications.

New nonlinear methods for linear transport calculations

International Nuclear Information System (INIS)

Adams, M.L.

1993-01-01

We present a new family of methods for the numerical solution of the linear transport equation. With these methods an iteration consists of an 'S N sweep' followed by an 'S 2 -like' calculation. We show, by analysis as well as numerical results, that iterative convergence is always rapid. We show that this rapid convergence does not depend on a consistent discretization of the S 2 -like equations - they can be discretized independently from the S N equations. We show further that independent discretizations can offer significant advantages over consistent ones. In particular, we find that in a wide range of problems, an accurate discretization of the S 2 -like equation can be combined with a crude discretization of the S N equations to produce an accurate S N answer. We demonstrate this by analysis as well as numerical results. (orig.)

Methodology for calculating power consumption of planetary mixers

Science.gov (United States)

Antsiferov, S. I.; Voronov, V. P.; Evtushenko, E. I.; Yakovlev, E. A.

2018-03-01

The paper presents the methodology and equations for calculating the power consumption necessary to overcome the resistance of a dry mixture caused by the movement of cylindrical rods in the body of a planetary mixer, as well as the calculation of the power consumed by idling mixers of this type. The equations take into account the size and physico-mechanical properties of mixing material, the size and shape of the mixer's working elements and the kinematics of its movement. The dependence of the power consumption on the angle of rotation in the plane perpendicular to the axis of rotation of the working member is presented.

Contribution to the study of the Fokker-planck equation; Contribution a l'etude de l'equation de Fokker-planck

Energy Technology Data Exchange (ETDEWEB)

Blaquiere, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1963-07-01

In the first paragraphs of this report, the Fokker-Planck equation is presented using the presentation method due to S. Chandrasekhar. Certain conventional resolution methods are given, and then a consideration of the physical interpretation of its various terms leads to a new study method based on the use of Campbell's theorems. This gives a solution to the equation in an integral form. The integral kernel of the solution is a normal centred distribution. Finally, the use of the Laplace transformation leads to a simple determination of the parameters of this integral kernel and connects the present theory to the characteristic function method used in particular in the field of nuclear reactors. The method also makes it possible to calculate the moments of the different orders of the probability distribution without the necessity of solving the Fokker-Planck equation. (author) [French] Dans les premiers paragraphes de ce rapport, l'equation de FOKKER-PLANCK est introduite en utilisant le mode d'expose de S. CHANDRASEKHAR. Puis, apres avoir rappele certaines methodes classiques de resolution, l'interpretation physique de ses differents termes nous conduit a une nouvelle methode d'etude qui repose sur l'utilisation des theoremes de CAMPBELL. On est ainsi conduit a la solution de l'equation sous forme integrale. Le noyau integral de la solution est une distribution normale centree. Enfin l'emploi de la transformation de LAPLACE conduit a une determination simple des parametres de ce noyau integral, et relie la theorie actuelle a la methode de la fonction caracteristique associee, utilisee en particulier dans le domaine des reacteurs nucleaires. Finalement cette methode permet le calcul des moments des differents ordres de la distribution de probabilites, sans passer par la resolution souvent laborieuse de l'equation de FOKKER-PLANCK. (auteur)

Calculation of propellant gas pressure by simple extended corresponding state principle

OpenAIRE

Bin Xu; San-jiu Ying; Xin Liao

2016-01-01

The virial equation can well describe gas state at high temperature and pressure, but the difficulties in virial coefficient calculation limit the use of virial equation. Simple extended corresponding state principle (SE-CSP) is introduced in virial equation. Based on a corresponding state equation, including three characteristic parameters, an extended parameter is introduced to describe the second virial coefficient expressions of main products of propellant gas. The modified SE-CSP second ...

Empirical equations for viscosity and specific heat capacity determination of paraffin PCM and fatty acid PCM

Science.gov (United States)

Barreneche, C.; Ferrer, G.; Palacios, A.; Solé, A.; Inés Fernández, A.; Cabeza, L. F.

2017-10-01

Phase change materials (PCM) used in thermal energy storage (TES) systems have been presented, over recent years, as one of the most effective options in energy storage. Paraffin and fatty acids are some of the most used PCM in TES systems, as they have high phase change enthalpy and in addition they do not present subcooling nor hysteresis and have proper cycling stability. The simulations and design of TES systems require the knowledge of the thermophysical properties of PCM. Thermal conductivity, viscosity, specific heat capacity (Cp) can be experimentally determined, but these are material and time consuming tasks. To avoid or to reduce them, and to have reliable data without the need of experimentation, thermal properties can be calculated by empirical equations. In this study, five different equations are given to calculate the viscosity and specific heat capacity of fatty acid PCM and paraffin PCM. Two of these equations concern, respectively, the empirical calculation of the viscosity and liquid Cp of the whole paraffin PCM family, while the other three equations presented are for the corresponding calculation of viscosity, solid Cp, liquid Cp of the whole fatty acid family of PCM. Therefore, this study summarize the work performed to obtain the main empirical equations to measure the above mentioned properties for whole fatty acid PCM family and whole paraffin PCM family. Moreover, empirical equations have been obtained to calculate these properties for other materials of these PCM groups and these empirical equations can be extrapolated for PCM with higher or lower phase change temperatures within a lower relative error 4%.

Equations of motion for train derailment dynamics

Science.gov (United States)

2007-09-11

This paper describes a planar or two-dimensional model to : examine the gross motions of rail cars in a generalized train : derailment. Three coupled, second-order differential equations : are derived from Newton's Laws to calculate rigid-body car : ...

Calculations of mass and moment of inertia for neutron stars

International Nuclear Information System (INIS)

Moelnvik, T.; Oestgaard, E.

1985-01-01

Masses and moments of inertia for slowly-rotating neutron stars are calculated from the Tolman-Oppenheimer-Volkoff equations and various equations of state for neutron-star matter. We have also obtained pressure and density as a function of the distance from the centre of the star. Generally, two different equations of state are applied for particle densities n>0.47 fm -3 and n -3 . The maximum mass is, in our calculations for all equations of state except for the unrealistic non-relativistic ideal Fermi gas, given by 1.50 Msub(sun) 44 gxcm 2 45 gxcm 2 , which also seem to agree very well with 'experimental results'. The radius of the star corresponding to maximum mass and maximum moment of inertia is given by 8.2 km< R<10.0 km, but a smaller central density rhosub(c) will give a larger radius. (orig.)

Detailed performance calculations: Wayne State University and Ford Motor Company, appendix C

Science.gov (United States)

1984-12-01

The laser-generated OH through ozone dissociation is defined in equations. Using these equations, the ozone interference levels corresponding to various humidity and ozone concentrations can be calculated readily.

Magnetic Positioning Equations Theory and Applications

CERN Document Server

Esh, Mordechay

2012-01-01

In the study of Magnetic Positioning Equations, it is possible to calculate and create analytical expressions for the intensity of magnetic fields when the coordinates x, y and z are known; identifying the inverse expressions is more difficult. This book is designed to explore the discovery of how to get the coordinates of analytical expressions x, y and z when the intensity of the magnetic fields are known. The discovery also deals with the problem of how to analyze, define and design any type of transmitter along with its positioning equation(s).Presents new simple mathematical solution expr

Optimal moving grids for time-dependent partial differential equations

Science.gov (United States)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Differential Equations Compatible with KZ Equations

International Nuclear Information System (INIS)

Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

2000-01-01

We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

Study of fission dynamics with the three-dimensional Langevin equations

Energy Technology Data Exchange (ETDEWEB)

Eslamizadeh, H. [Persian Gulf University, Department of Physics, Bushehr (Iran, Islamic Republic of)

2011-11-15

The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei {sup 210}Po and {sup 224}Th formed in the fusion-fission reactions {sup 4}He+{sup 206}Pb, {sup 16}O+{sup 208}Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data. (orig.)

Graphical Calculation of Estimated Energy Expenditure in Burn Patients.

Science.gov (United States)

Egro, Francesco M; Manders, Ernest C; Manders, Ernest K

2018-03-01

Historically, estimated energy expenditure (EEE) has been related to the percent of body surface area burned. Subsequent evaluations of these estimates have indicated that the earlier formulas may overestimate the amount of caloric support necessary for burn-injured patients. Ireton-Jones et al derived 2 equations for determining the EEE required to support burn patients, 1 for ventilator-dependent patients and 1 for spontaneously breathing patients. Evidence has proved their reliability, but they remain challenging to apply in a clinical setting given the difficult and cumbersome mathematics involved. This study aims to introduce a graphical calculation of EEE in burn patients that can be easily used in the clinical setting. The multivariant linear regression analysis from Ireton-Jones et al yielded equations that were rearranged into the form of a simple linear equation of the type y = mx + b. By choosing an energy expenditure and the age of the subject, the weight was calculated. The endpoints were then calculated, and a graph was mapped by means of Adobe FrameMaker. A graphical representation of Ireton-Jones et al's equations was obtained by plotting the weight (kg) on the y axis, the age (years) on the x axis, and a series of parallel lines representing the EEE in burn patients. The EEE has been displayed graphically on a grid to allow rapid determination of the EEE needed for a given patient of a designated weight and age. Two graphs were plotted: 1 for ventilator-dependent patients and 1 for spontaneously breathing patients. Correction factors for sex, the presence of additional trauma, and obesity are indicated on the graphical calculators. We propose a graphical tool to calculate caloric requirements in a fast, easy, and portable manner.

Calculating Relativistic Transition Matrix Elements for Hydrogenic Atoms Using Monte Carlo Methods

Science.gov (United States)

Alexander, Steven; Coldwell, R. L.

2015-03-01

The nonrelativistic transition matrix elements for hydrogen atoms can be computed exactly and these expressions are given in a number of classic textbooks. The relativistic counterparts of these equations can also be computed exactly but these expressions have been described in only a few places in the literature. In part, this is because the relativistic equations lack the elegant simplicity of the nonrelativistic equations. In this poster I will describe how variational Monte Carlo methods can be used to calculate the energy and properties of relativistic hydrogen atoms and how the wavefunctions for these systems can be used to calculate transition matrix elements.

Numerical solution of the point reactor kinetics equations with fuel burn-up and temperature feedback

International Nuclear Information System (INIS)

Tashakor, S.; Jahanfarnia, G.; Hashemi-Tilehnoee, M.

2010-01-01

Point reactor kinetics equations are solved numerically using one group of delayed neutrons and with fuel burn-up and temperature feedback included. To calculate the fraction of one-group delayed neutrons, a group of differential equations are solved by an implicit time method. Using point reactor kinetics equations, changes in mean neutrons density, temperature, and reactivity are calculated in different times during the reactor operation. The variation of reactivity, temperature, and maximum power with time are compared with the predictions by other methods.

Multistate electron transfer dynamics in the condensed phase: Exact calculations from the reduced hierarchy equations of motion approach

International Nuclear Information System (INIS)

Tanaka, Midori; Tanimura, Yoshitaka

2010-01-01

Multiple displaced oscillators coupled to an Ohmic heat bath are used to describe electron transfer (ET) in a dissipative environment. By performing a canonical transformation, the model is reduced to a multilevel system coupled to a heat bath with the Brownian spectral distribution. A reduced hierarchy equations of motion approach is introduced for numerically rigorous simulation of the dynamics of the three-level system with various oscillator configurations, for different nonadiabatic coupling strengths and damping rates, and at different temperatures. The time evolution of the reduced density matrix elements illustrates the interplay of coherences between the electronic and vibrational states. The ET reaction rates, defined as a flux-flux correlation function, are calculated using the linear response of the system to an external perturbation as a function of activation energy. The results exhibit an asymmetric inverted parabolic profile in a small activation regime due to the presence of the intermediate state between the reactant and product states and a slowly decaying profile in a large activation energy regime, which arises from the quantum coherent transitions.

Deriving the bond pricing equation

Directory of Open Access Journals (Sweden)

Kožul Nataša

2014-01-01

Full Text Available Given the recent focus on Eurozone debt crisis and the credit rating downgrade not only of US debt, but that of other countries and many UK major banking institutions, this paper aims to explain the concept of bond yield, its different measures and bond pricing equation. Yields on capital market instruments are rarely quoted on the same basis, which makes direct comparison between different as investment choices impossible. Some debt instruments are quoted on discount basis, whilst coupon-bearing ones accrue interest differently, offer different compounding opportunities, have different coupon payment frequencies, and manage non-business day maturity dates differently. Moreover, rules governing debt vary across countries, markets and currencies, making yield calculation and comparison a rather complex issue. Thus, some fundamental concepts applicable to debt instrument yield measurement, with focus on bond equation, are presented here. In addition, bond equation expressed in annuity form and used to apply Newton-Raphson algorithm to derive true bond yield is also shown.

Finite element calculation of stress induced heating of superconductors

International Nuclear Information System (INIS)

Akin, J.E.; Moazed, A.

1976-01-01

This research is concerned with the calculation of the amount of heat generated due to the development of mechanical stresses in superconducting composites. An emperical equation is used to define the amount of stress-induced heat generation per unit volume. The equation relates the maximum applied stress and the experimental measured hysteresis loop of the composite stress-strain diagram. It is utilized in a finite element program to calculate the total stress-induced heat generation for the superconductor. An example analysis of a solenoid indicates that the stress-induced heating can be of the same order of magnitude as eddy current effects

Equation for the melting curve of solids under high pressure

International Nuclear Information System (INIS)

Boguslavskii, Yu.Ya.

1982-01-01

Simon's equation of the melting curve is obtained using the Clausius-Clapeyron equation in the linear approximation of the pressure dependence of the melting entropy and the volume change at the melting point. The constants in Simon's equation are calculated in this approximation for the alkali metals Li, Na, K, Rb, Cs and also for hydrogen, H 2 , and argon. It is shown that one can obtain the constants of Simon's equation in a pressure range which is wider than the region of the thermodynamical validity of Simon's equation by averaging the values of the constants determined in different points of the melting curves. The constants obtained by this manner agree well with the experimental data. (author)

Revision of the equation Calculated Cetane Index for the characteristics of diesel commercialized in the Parana-Brazil; Revisao da equacao de Calculo do Indice de Cetano para as caracteristicas do diesel comercializado no Parana

Energy Technology Data Exchange (ETDEWEB)

Souza, Tatiana Bittencourt de; Yamamoto, Carlos Itsuo; Cocco, Lilian Cristina [Universidade Federal do Parana (UFPR), Curitiba, PR (Brazil). Lab. de Analise de Combustiveis Automotivos (LACAUTets)

2008-07-01

This work presents the development of models for Calculated Cetane Index (CCI) determination with the purpose of tailor it to the diesel oil sold in Brazil, using optimization techniques. As the diesel is the main fuel on the Brazilian territory, their quality is of great importance. The CCI calculation is important to evaluate the diesel quality. The standard ASTM D 4737 does not take into account the presence of cetane booster additive and biodiesel, which creates the need to recast the equation of the CCI determination. About 300 representative samples were selected of diesel in Parana, during the 2006 to 2007 period, which had their physic-chemical properties determined using the methodology adopted by the ANP - the Brazilian petroleum, natural gas and biofuel agency. The Derived Cetane Number was obtained in the IQT apparatus and several models were proposed, all with better predictive capability than the equation of the standard ASTM D 4737. It is pointed out that biodiesel can act as cetane booster additive depending upon its origin, mostly in concentrations above 5%. The methodology can be expanded to generate a representative equation for the diesel sold in the whole Brazilian territory. (author)

The limiting temperature of hot nuclei from microscopic equation of state

International Nuclear Information System (INIS)

Baldo, M.; Ferreira, L.S.; Nicotra, O.E.

2004-01-01

The limiting temperature T lim of a series of nuclei is calculated employing a set of microscopic nuclear equations of state (EOS's). It is shown that the value of T lim is sensitive to the nuclear matter equation of state used. Comparison with the values extracted in recent phenomenological analysis appears to favor a definite selection of EOS's. On the basis of this phenomenological analysis, it therefore seems possible to check the microscopic calculations of the nuclear EOS at finite temperature, which is hardly accessible through other experimental information

On the calculation of soft phase space integral

International Nuclear Information System (INIS)

Zhu, Hua Xing

2015-01-01

The recent discovery of the Higgs boson at the LHC attracts much attention to the precise calculation of its production cross section in quantum chromodynamics. In this work, we discuss the calculation of soft triple-emission phase space integral, which is an essential ingredient in the recently calculated soft-virtual corrections to Higgs boson production at next-to-next-to-next-to-leading order. The main techniques used this calculation are method of differential equation for Feynman integral, and integration of harmonic polylogarithms.

Carbon Footprint Calculations: An Application of Chemical Principles

Science.gov (United States)

Treptow, Richard S.

2010-01-01

Topics commonly taught in a general chemistry course can be used to calculate the quantity of carbon dioxide emitted into the atmosphere by various human activities. Each calculation begins with the balanced chemical equation for the reaction that produces the CO[subscript 2] gas. Stoichiometry, thermochemistry, the ideal gas law, and dimensional…

On the hierarchy of partially invariant submodels of differential equations

OpenAIRE

Golovin, Sergey V.

2007-01-01

It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ...

Equation of state of liquid Indium under high pressure

Directory of Open Access Journals (Sweden)

Huaming Li

2015-09-01

Full Text Available We apply an equation of state of a power law form to liquid Indium to study its thermodynamic properties under high temperature and high pressure. Molar volume of molten indium is calculated along the isothermal line at 710K within good precision as compared with the experimental data in an externally heated diamond anvil cell. Bulk modulus, thermal expansion and internal pressure are obtained for isothermal compression. Other thermodynamic properties are also calculated along the fitted high pressure melting line. While our results suggest that the power law form may be a better choice for the equation of state of liquids, these detailed predictions are yet to be confirmed by further experiment.

Whole core transport calculation for the VHTR hexagonal core

International Nuclear Information System (INIS)

Cho, J. Y.; Kim, K. S.; Lee, C. C.; Joo, H. G.

2007-01-01

Recently, the DeCART code which performs the whole core calculation by coupling the radial MOC transport kernel with the axial nodal kernel has equipped a kernel to deal with the hexagonal geometry and applied to the VHTR hexagonal core to examine the accuracy and the computational efficiency of the implemented kernel. The implementation includes a modular ray tracing module based on the hexagonal assembly and a multi-group CMFD module to perform an efficient transport calculation. The requirements for the modular ray are: (1) the assembly based path linking and (2) the complete reflection capabilities. The first requirement is met by adjusting the azimuthal angle and the ray spacing for the modular ray to construct a core ray by the path linking. The second requirement is met by expanding the constructed azimuthal angle in the range of [0,30 degree] to the remained range to reflect completely at the core boundaries. The considered reflecting surface angles for the complete reflection are 30n's (n=1,2,1,12). The CMFD module performs the equivalent diffusion calculation to the radial MOC transport calculation based on the homogenized structure units. The structure units include the hexagonal pin cells and gap cells appearing at the assembly boundary. Therefore, the CMFD module is programmed to deal with the unstructured cells such as the gap cells. The CMFD equation consists of the two parts of (1) the conventional FDM and (2) the current corrective parts. Since the second part of the CMFD equation guarantees the reproducibility of the radial MOC transport solutions for the cell averaged reaction rate and the net current at the cell surfaces, how to build the first part of the CMFD equation is not important. Therefore, the first part of the CMFD equation is roughly built by using the normal distance from the gravity center to the surface. The VHTR core uses helium as a coolant which is realized as a void hole in a neutronics calculation. This void hole which

Towards a mulitphase equation of state of Carbon from first principles

Science.gov (United States)

Correa, Alfredo; Benedict, Lorin; Schwegler, Eric

2007-03-01

Ab initio molecular dynamics and electronic structure calculation had become one of the most useful tools to investigate properties of materials. Unfortunately these atomistic detailed results are rarely reused in calculations at a higher level of description, such as fluid dynamics and finite elements calculations. In this talk we present a concrete example showing the way that first principles results can be expressed in a way that is useful for hydrodynamics calculations, in particular we show how to build a analytic equation of state for Carbon that involves solid (diamond and BC8) and liquid phases. Applications of this newly obtained equation of state will be presented. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.

A simplified model for computing equation of state of argon plasma

International Nuclear Information System (INIS)

Wang Caixia; Tian Yangmeng

2006-01-01

The paper present a simplified new model of computing equation of state and ionization degree of Argon plasma, which based on Thomas-Fermi (TF) statistical model: the authors fitted the numerical results of the ionization potential calculated by Thomas-Fermi statistical model and gained the analytical function of the potential versus the degree of ionization, then calculated the ionization potential and the average degree of ionization for Argon versus temperature and density in local thermal equilibrium case at 10-1000 eV. The results calculated of this simplified model are basically in agreement with several sets of theory data and experimental data. This simplified model can be used to calculation of the equation of state of plasmas mixture and is expected to have a more wide use in the field of EML technology involving the strongly ionized plasmas. (authors)

Biases and statistical errors in Monte Carlo burnup calculations: an unbiased stochastic scheme to solve Boltzmann/Bateman coupled equations

International Nuclear Information System (INIS)

Dumonteil, E.; Diop, C.M.

2011-01-01

External linking scripts between Monte Carlo transport codes and burnup codes, and complete integration of burnup capability into Monte Carlo transport codes, have been or are currently being developed. Monte Carlo linked burnup methodologies may serve as an excellent benchmark for new deterministic burnup codes used for advanced systems; however, there are some instances where deterministic methodologies break down (i.e., heavily angularly biased systems containing exotic materials without proper group structure) and Monte Carlo burn up may serve as an actual design tool. Therefore, researchers are also developing these capabilities in order to examine complex, three-dimensional exotic material systems that do not contain benchmark data. Providing a reference scheme implies being able to associate statistical errors to any neutronic value of interest like k(eff), reaction rates, fluxes, etc. Usually in Monte Carlo, standard deviations are associated with a particular value by performing different independent and identical simulations (also referred to as 'cycles', 'batches', or 'replicas'), but this is only valid if the calculation itself is not biased. And, as will be shown in this paper, there is a bias in the methodology that consists of coupling transport and depletion codes because Bateman equations are not linear functions of the fluxes or of the reaction rates (those quantities being always measured with an uncertainty). Therefore, we have to quantify and correct this bias. This will be achieved by deriving an unbiased minimum variance estimator of a matrix exponential function of a normal mean. The result is then used to propose a reference scheme to solve Boltzmann/Bateman coupled equations, thanks to Monte Carlo transport codes. Numerical tests will be performed with an ad hoc Monte Carlo code on a very simple depletion case and will be compared to the theoretical results obtained with the reference scheme. Finally, the statistical error propagation

"Quod Erat Demonstrandum": Understanding and Explaining Equations in Physics Teacher Education

Science.gov (United States)

Karam, Ricardo; Krey, Olaf

2015-01-01

In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this…

Paraxial WKB solution of a scalar wave equation

International Nuclear Information System (INIS)

Pereverzev, G.V.

1993-04-01

An asymptotic method of solving a scalar wave equation in inhomogeneous media is developed. This method is an extension of the WKB method to the multidimensional case. It reduces a general wave equation to a set of ordinary differential equations similar to that of the eikonal approach and includes the latter as a particular case. However, the WKB method makes use of another kind of asymptotic expansion and, unlike the eikonal approach, describes the wave properties, i.e. diffraction and interference. At the same time, the three-dimensional WKB method is more simple for numerical treatment because the number of equations is less than in the eikonal approach. The method developed may be used for a calculation of wave fields in problems of RF heating, current drive and plasma diagnostics with microwave beams. (orig.)

Argosy 4 - A programme for lattice calculations

International Nuclear Information System (INIS)

MacDougall, J.D.

1965-07-01

This report contains a detailed description of the methods of calculation used in the Argosy 4 computer programme, and of the input requirements and printed results produced by the programme. An outline of the physics of the Argosy method is given. Section 2 describes the lattice calculation, including the burn up calculation, section 3 describes the control rod calculation and section 4 the reflector calculation. In these sections the detailed equations solved by the programme are given. In section 5 input requirements are given, and in section 6 the printed output obtained from an Argosy calculation is described. In section 7 are noted the principal differences between Argosy 4 and earlier versions of the Argosy programme

A composite velocity procedure for the compressible Navier-Stokes equations

Science.gov (United States)

Khosla, P. K.; Rubin, S. G.

1982-01-01

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Swarm analysis by using transport equations, 1

International Nuclear Information System (INIS)

Dote, Toshihiko; Shimada, Masatoshi

1980-01-01

By evolving Maxwell-Boltzmann transport equations, various quantities on swarm of charged particles have been analyzed. Although this treatment is properly general, and common transport equations for charged particles ought to be given, in particular, equations only for electrons were presented here. The relation between the random energy and the drift energy was first derived and the general expression of the electron velocity was deduced too. For a simple example, one dimensional steady-state electron swarm in a uniform medium was treated. Electron swarm characteristics numerically calculated in He, Ne or Ar exhibited some interesting properties, which were physically clearly elucidated. These results were also compared with several data already published. Agreements between them were qualitatively rather well in detailed structures. (author)

Algorithm development for Maxwell's equations for computational electromagnetism

Science.gov (United States)

Goorjian, Peter M.

1990-01-01

A new algorithm has been developed for solving Maxwell's equations for the electromagnetic field. It solves the equations in the time domain with central, finite differences. The time advancement is performed implicitly, using an alternating direction implicit procedure. The space discretization is performed with finite volumes, using curvilinear coordinates with electromagnetic components along those directions. Sample calculations are presented of scattering from a metal pin, a square and a circle to demonstrate the capabilities of the new algorithm.

Some properties of matter at very HTGH temperatures and high pressures (equations of state, opacity); Quelques proprietes de la matiere aux tres hautes temperatures et fortes pressions (equation d'etat, opacite)

Energy Technology Data Exchange (ETDEWEB)

Gervat, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1964-06-15

The Thomas-Fermi equations which' are zero-order approximations of the Hartree-Fock equations, make it possible to study some aspects of the behaviour of matter at high pressures. In the first chapter is considered the calculation of 1 values which do not require the Schroedinger equation to be solved. The values of the quantum and exchange corrections give the zone of validity of the theory. For each R and T pair it is possible to calculate the energy and the pressure. For the calculation of the energy 'it has been necessary, in the region close to the nucleus where the corrections diverge, to replace the density given by the Thomas-Fermi theory by that deduced from the wave-functions which, in the small region, are very similar to that of a hydrogen atom of charge z. The calculation of the degree of ionization is particularly simple and does not require the Saha equations to be solved. Besides the distribution of electrons in the r space it is simple to determine the distribution according to the quantum number I, and this for each value of the R, T pair. In the second chapter, the introduction of the, Thomas and Fermi potential into the Schroedinger equation makes it possible to obtain the energy spectrum of a perfect isolated atom supposed to represent an average atom of the hot, compressed matter. The changes in the levels with increasing temperature and pressure can be deduced from this. It is particular easy with this model to interpret the phenomenon of ionization caused by pressure. A knowledge of the wave functions makes it possible to calculate the transition probabilities which, coupled with the occupation probabilities, lead to the opacity coefficients. Only the bound-free and free-free transitions have been considered but these latter include, because of the properties of the model used, a large part of bound-bound or band-band transitions. Finally, the use of the Thomas-Fermi potential for the calculation of bands is particularly suitable for

The polaron problem and the Boltzmann equation

International Nuclear Information System (INIS)

Devreese, J.

1979-01-01

A mobility theory for the Feynman polaron is developed. It is shown that the Boltzmann equation for polarons is valid for weak coupling and not too high electric fields. The analytical results indicate that for E → 0 the relaxation time approximation is valid. A comparison is made of three methods to calculate the mobility in a linear electron transport theory. An approximation to the Kubo formula, a mobility calculation using path integrals by Feynman and a calculation based on the displaced Maxwell distribution function are considered. The three methods lead to equivalent results in the weak scattering and small electric field limit

Membrane Protein Properties Revealed through Data-Rich Electrostatics Calculations.

Science.gov (United States)

Marcoline, Frank V; Bethel, Neville; Guerriero, Christopher J; Brodsky, Jeffrey L; Grabe, Michael

2015-08-04

The electrostatic properties of membrane proteins often reveal many of their key biophysical characteristics, such as ion channel selectivity and the stability of charged membrane-spanning segments. The Poisson-Boltzmann (PB) equation is the gold standard for calculating protein electrostatics, and the software APBSmem enables the solution of the PB equation in the presence of a membrane. Here, we describe significant advances to APBSmem, including full automation of system setup, per-residue energy decomposition, incorporation of PDB2PQR, calculation of membrane-induced pKa shifts, calculation of non-polar energies, and command-line scripting for large-scale calculations. We highlight these new features with calculations carried out on a number of membrane proteins, including the recently solved structure of the ion channel TRPV1 and a large survey of 1,614 membrane proteins of known structure. This survey provides a comprehensive list of residues with large electrostatic penalties for being embedded in the membrane, potentially revealing interesting functional information. Copyright © 2015 Elsevier Ltd. All rights reserved.

Use of the Local Variation Methods for Nuclear Design Calculations

International Nuclear Information System (INIS)

Zhukov, A.I.

2006-01-01

A new problem-solving method for steady-state equations, which describe neutron diffusion, is presented. The method bases on a variation principal for steady-state diffusion equations and direct search the minimum of a corresponding functional. Benchmark problem calculation for power of fuel assemblies show ∼ 2% relative accuracy

APBSmem: a graphical interface for electrostatic calculations at the membrane.

Directory of Open Access Journals (Sweden)

Keith M Callenberg

2010-09-01

Full Text Available Electrostatic forces are one of the primary determinants of molecular interactions. They help guide the folding of proteins, increase the binding of one protein to another and facilitate protein-DNA and protein-ligand binding. A popular method for computing the electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB equation, and there are several easy-to-use software packages available that solve the PB equation for soluble proteins. Here we present a freely available program, called APBSmem, for carrying out these calculations in the presence of a membrane. The Adaptive Poisson-Boltzmann Solver (APBS is used as a back-end for solving the PB equation, and a Java-based graphical user interface (GUI coordinates a set of routines that introduce the influence of the membrane, determine its placement relative to the protein, and set the membrane potential. The software Jmol is embedded in the GUI to visualize the protein inserted in the membrane before the calculation and the electrostatic potential after completing the computation. We expect that the ease with which the GUI allows one to carry out these calculations will make this software a useful resource for experimenters and computational researchers alike. Three examples of membrane protein electrostatic calculations are carried out to illustrate how to use APBSmem and to highlight the different quantities of interest that can be calculated.

Detailed channel thermal-hydraulic calculation of nuclear reactor fuel assemblies

International Nuclear Information System (INIS)

Zhukov, A.V.; Sorokin, A.P.; Ushakov, P.A.; Yur'ev, Yu.S.

1981-01-01

The system of equations of mass balance, quantity of motion and energy used in calculation of nuclear reactor fuel assemblies is obtained. The equation system is obtained on the base of integral equations of hydrodynamics interaction in assemblies of smooth fuel elements and fuel elements with wire packing. The calculation results of coolant heating distributions by the fast reactor assembly channels are presented. The analysis of the results obtained shows that interchannel exchange essentially uniforms the coolant heating distribution in the peripheral range of the assembly but it does not remove non-uniformity caused by power distribution non-uniformity in the cross section. Geometry of the peripheral assembly range plays an essential role in the heating distribution. Change of the calculation gap between the peripheral fuel elements and assembly shells can result either in superheating or in subcooling in the peripheral channels relatively to joint internal channels of the assembly. Heat supply to the coolant passing through interassembly gaps decreases temperature in the assembly periphery and results in the increase of temperature non-uniformity by the perimeter of peripheral fuel elements. It is concluded that the applied method of the channel-by-channel calculation is ef-- fective in thermal-physical calculation of nuclear reactor fuel assemblies and it permits to solve a wide range of problems [ru

Calculation of conventional and prompt lepton fluxes at very high energy

CERN Document Server

Fedynitch, Anatoli; Gaisser, Thomas K; Riehn, Felix; Stanev, Todor

2015-01-01

An efficient method for calculating inclusive conventional and prompt atmospheric leptons fluxes is presented. The coupled cascade equations are solved numerically by formulating them as matrix equation. The presented approach is very flexible and allows the use of different hadronic interaction models, realistic parametrizations of the primary cosmic-ray flux and the Earth's atmosphere, and a detailed treatment of particle interactions and decays. The power of the developed method is illustrated by calculating lepton flux predictions for a number of different scenarios.

The establishment of in-process plutonium mass equation in Rokkasho Reprocessing Plant

International Nuclear Information System (INIS)

Yamaya, Kosuke; Ebata, Takashi; Yamazaki, Yoshihiro; Kawai, Akio; Iwamoto, Tomonori

2008-01-01

At Rokkasho Reprocessing Plant (RRP), Active Test (AT) using actual spent fuels for the final confirmation of the equipment and the system has been performed toward the commercial operation. From the safeguards viewpoint, performance of material accountancy equipment is confirmed and data for evaluating parameters of the inspection equipment is obtained by making use of the AT period. RRP is applied to Near Real Time material Accountancy (NRTA). Under the NRTA scheme, the inventory at a cut-off time during process operation needs to be accounted for. There are some un-measurable inventories of plutonium in the process, which will be calculated from inventory estimation equations. The amount of these plutonium inventories calculated from the equations is so large that it is essential to improve the inventory estimation equations to be quite accurate. Therefore, correctness of the inventory estimation equations is evaluated by using process operation data obtained during AT. This paper describes the results of evaluating the inventory estimation equations by using the process operation data and the NRTA procedure under continuous operating condition as well. (author)

Calculation of normal modes of the closed waveguides in general vector case

Science.gov (United States)

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

2018-04-01

The article is devoted to the calculation of normal modes of the closed waveguides with an arbitrary filling ɛ, μ in the system of computer algebra Sage. Maxwell equations in the cylinder are reduced to the system of two bounded Helmholtz equations, the notion of weak solution of this system is given and then this system is investigated as a system of ordinary differential equations. The normal modes of this system are an eigenvectors of a matrix pencil. We suggest to calculate the matrix elements approximately and to truncate the matrix by usual way but further to solve the truncated eigenvalue problem exactly in the field of algebraic numbers. This approach allows to keep the symmetry of the initial problem and in particular the multiplicity of the eigenvalues. In the work would be presented some results of calculations.

On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations

International Nuclear Information System (INIS)

Valat, J.

1960-12-01

Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [fr

Analytical Approach to Space- and Time-Fractional Burgers Equations

International Nuclear Information System (INIS)

Yıldırım, Ahmet; Mohyud-Din, Syed Tauseef

2010-01-01

A scheme is developed to study numerical solution of the space- and time-fractional Burgers equations under initial conditions by the homotopy analysis method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed

Broyden's method in nuclear structure calculations

International Nuclear Information System (INIS)

Baran, Andrzej; Bulgac, Aurel; Forbes, Michael McNeil; Hagen, Gaute; Nazarewicz, Witold; Schunck, Nicolas; Stoitsov, Mario V.

2008-01-01

Broyden's method, widely used in quantum chemistry electronic-structure calculations for the numerical solution of nonlinear equations in many variables, is applied in the context of the nuclear many-body problem. Examples include the unitary gas problem, the nuclear density functional theory with Skyrme functionals, and the nuclear coupled-cluster theory. The stability of the method, its ease of use, and its rapid convergence rates make Broyden's method a tool of choice for large-scale nuclear structure calculations

Calculation of risk for workers in dust working site

Directory of Open Access Journals (Sweden)

Geldová Erika

2004-03-01

Full Text Available The fibrogeneous dust is considered as a specific harmful substance in the mine working site. Such kind of dust cumulates in lungs and this fact usually results in lungs dusting, so - called pneumoconiosis. Thus, dustiness risk poses a probability of lungs damage by pneumoconiosis. For the calculation of dustiness risk it is needed to know the following data: the value of average dustiness kC in the working site per a definite time period, the dispersivity of dust “D” (it determines a portion of dust particles with a diameter under 5 µm, so - called respirable particles and the percentage content of quartz Qr in the respirable grain size fraction.The contribution presents the calculation of dustiness risk “R” according to the equation (1, where “R” is in percentage, “ša” is the analytically specific harmfulness and “KDc” is the total cumulative dust dose received by worker in time of its dust exposure.The total cumulative dust dose is calculated on the basis of the equation (4, where “kc” is the average dust concentration in the assessed time period, t–time of exposure, V –average amount of air inspired by exposed worker per time unit ( standardized on the value of 1,2 m3h-1,10-6-recalculation from mg to kg for “KDc”.If the values of “Qr”, “D” and “kc” during the worker exposure on a definite workplace are constant, the dustiness risk “R” is calculated according to the equation (1 and (5 respectively. In the case of “n” time intervals in that the values “Qr”, “D” and “kc” are known the dustiness risk “R” is calculated according to the equation (7. The total personal risk of worker is given by the equation (8.Conclusively, the influence of parameters change namely “Qr”, “D” and “kc” on the value of dustiness risk per equal time period is reported.

Monitoring of Renal Allograft Function with Different Equations: What are the Differences?

Directory of Open Access Journals (Sweden)

Bushljetikj Irena Rambabova

2017-06-01

Full Text Available Introduction. Monitoring of graft function by creatinine concentrations in serum and calculated glomerular filtration rate (GFR is recommended after kidney transplantation. KDIGO recommendations on the treatment of transplant patients advocate usage of one of the existing mathematical equations based on serum creatinine. We compared clinical application of three equations based on serum creatinine in monitoring the function of transplanted kidney. Methods. A total number of 55 adult patients who received their first renal allograft from living donors at our transplant center in between 2011-2014 were included into the study. Renal allograft GFR was estimated by the Cockroft-Gault, Nankivell and MDRD formula, and correlated with clinical parameters of donors and recipients. Results. The mean age of recipients was 35.7±9.5 (range 16-58, and the mean age of donors was 55.5±9.0 (34- 77 years. Out of this group of 55 transplant patients, 50(90.91% were on hemodialysis (HD prior to transplantation. HD treatment was shorter than 24 months in 37(74% transplant patients. The calculated GFR with MDRD equation showed the highest mean value at 6 and 12 months (68.46±21.5; 68.39±24.6, respectively and the lowest at 48 months (42.79±12.9. According to the Cockroft&Gault equation GFR was the highest at 12 months (88.91±24.9 and the lowest at 48 months (66.53±18.1 ml/min. The highest mean level (80.53±17.7 of the calculated GFR with the Nankivell equation was obtained at 12 months and the lowest (67.81±16.7 ml/min at 48 months. The values of Pearson’s correlation coefficient between the calculated GFR and the MDRD at 2 years after transplantation according to donor’s age of r=-0.3224, correlation between GFR and the Cockfroft & Gault at 6 and 12 months and donor’s age (r=-0.2735 and r=-0.2818, and correlation between GFR and the Nankivell at 2 years and donor’s age of r=-0.2681, suggested a conclusion that calculated GFR was lower in recipients

Guiding Center Equations in Toroidal Equilibria

International Nuclear Information System (INIS)

White, Roscoe; Zakharov, Leonid

2002-01-01

Guiding center equations for particle motion in a general toroidal magnetic equilibrium configuration are derived using magnetic coordinates. Previous derivations made use of Boozer coordinates, in which the poloidal and toroidal angle variables are chosen so that the Jacobian is inversely proportional to the square of the magnetic field. It is shown that the equations for guiding center motion in any equilibrium possessing nested flux surfaces have exactly the same simple form as those derived in this special case. This allows the use of more spatially uniform coordinates instead of the Boozer coordinates, greatly increasing the accuracy of calculations in large beta and strongly shaped equilibria

On the biophysics of cathodal galvanotaxis in rat prostate cancer cells: Poisson-Nernst-Planck equation approach.

Science.gov (United States)

Borys, Przemysław

2012-06-01

Rat prostate cancer cells have been previously investigated using two cell lines: a highly metastatic one (Mat-Ly-Lu) and a nonmetastatic one (AT-2). It turns out that the highly metastatic Mat-Ly-Lu cells exhibit a phenomenon of cathodal galvanotaxis in an electric field which can be blocked by interrupting the voltage-gated sodium channel (VGSC) activity. The VGSC activity is postulated to be characteristic for metastatic cells and seems to be a reasonable driving force for motile behavior. However, the classical theory of cellular motion depends on calcium ions rather than sodium ions. The current research provides a theoretical connection between cellular sodium inflow and cathodal galvanotaxis of Mat-Ly-Lu cells. Electrical repulsion of intracellular calcium ions by entering sodium ions is proposed after depolarization starting from the cathodal side. The disturbance in the calcium distribution may then drive actin polymerization and myosin contraction. The presented modeling is done within a continuous one-dimensional Poisson-Nernst-Planck equation framework.

BMN correlators by loop equations

International Nuclear Information System (INIS)

Eynard, Bertrand; Kristjansen, Charlotte

2002-01-01

In the BMN approach to N=4 SYM a large class of correlators of interest are expressible in terms of expectation values of traces of words in a zero-dimensional gaussian complex matrix model. We develop a loop-equation based, analytic strategy for evaluating such expectation values to any order in the genus expansion. We reproduce the expectation values which were needed for the calculation of the one-loop, genus one correction to the anomalous dimension of BMN-operators and which were earlier obtained by combinatorial means. Furthermore, we present the expectation values needed for the calculation of the one-loop, genus two correction. (author)

Differential geometry techniques for sets of nonlinear partial differential equations

Science.gov (United States)

Estabrook, Frank B.

1990-01-01

An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.

Approximate solution to neutron transport equation with linear anisotropic scattering

International Nuclear Information System (INIS)

Coppa, G.; Ravetto, P.; Sumini, M.

1983-01-01

A method to obtain an approximate solution to the transport equation, when both sources and collisions show a linearly anisotropic behavior, is outlined and the possible implications for numerical calculations in applied neutronics as well as shielding evaluations are investigated. The form of the differential system of equations taken by the method is quite handy and looks simpler and more manageable than any other today available technique. To go deeper into the efficiency of the method, some typical calculations concerning critical dimension of multiplying systems are then performed and the results are compared with the ones coming from the classical Ssub(N) approximations. The outcome of such calculations leads us to think of interesting developments of the method which could be quite useful in alternative to other today widespread approximate procedures, for any geometry, but especially for curved ones. (author)

Formation for the calculation of reactivity without nuclear power history

International Nuclear Information System (INIS)

Suescun Diaz, Daniel; Senra Martinez, Aquilino; Carvalho Da Silva, Fernando

2007-01-01

This paper presents a new method for the solution of the inverse point kinetics equation. This method is based on the integration by parts of the integral of the inverse point kinetics equation, which results in a power series in terms of the nuclear power in time dependence. With the imposition of conditions to the nuclear power, the reactivity is represented as first and second derivatives of this nuclear power. This new calculation method for reactivity has very special characteristics, amongst which the possibility of using longer sampling period, and the possibility of restarting the calculation, after its interruption, allowing the calculation of reactivity in a non-continuous way. Beside that, the reactivity can be obtained independent of the nuclear power memory. (author)

Novel algorithm of large-scale simultaneous linear equations

International Nuclear Information System (INIS)

Fujiwara, T; Hoshi, T; Yamamoto, S; Sogabe, T; Zhang, S-L

2010-01-01

We review our recently developed methods of solving large-scale simultaneous linear equations and applications to electronic structure calculations both in one-electron theory and many-electron theory. This is the shifted COCG (conjugate orthogonal conjugate gradient) method based on the Krylov subspace, and the most important issue for applications is the shift equation and the seed switching method, which greatly reduce the computational cost. The applications to nano-scale Si crystals and the double orbital extended Hubbard model are presented.

theory and calculation of the design of nuclear reactor

International Nuclear Information System (INIS)

Refaat, R.A.

1994-01-01

For the sake of formation of a complete general code for nuclear power reactor design, this thesis deals with a great part of this code. the code links the solution of the neutron integral transport equation by the multigroup treatment (76 energy groups) for the calculation of the reactor cell parameters by the fuel management program that solves the neutron diffusion equation inside a large number of nuclear fuel assemblies. the lattice cell code is modified to accommodate the calculation of lattice cell parameters for more than one enrichment ( one after the other). it is also modified to calculate the burn up parameters using unequal time steps. these two modifications are complicated but necessary for the link between the cell program and fuel management program. the comparison between the results of the fitted cross sections and that given by the cell calculations shows the necessity of using the cell code cross sections. this is also necessary for the sake of generality for any type of reactors. the comparison for the fuel management calculation depending on fitted data and that depending on cell calculation data insures the necessity for using the cell data i.e. insures the necessity of linking the cell calculation program by the fuel management program

General solution of the aerosol dynamic equation: growth and diffusion processes

International Nuclear Information System (INIS)

Elgarayhi, A.; Elhanbaly, A.

2004-01-01

The dispersion of aerosol particles in a fluid media is studied considering the main mechanism for condensation and diffusion. This has been done when the technique of Lie is used for solving the aerosol dynamic equation. This method is very useful in sense that it reduces the partial differential equation to some ordinary differential equations. So, different classes of similarity solutions have been obtained. The quantity of well-defined physical interest is the mean particle volume has been calculated

Reduced equations for finite beta tearing modes in tokamaks

International Nuclear Information System (INIS)

Izzo, R.; Monticello, D.A.; DeLucia, J.; Park, W.; Ryu, C.M.

1984-10-01

The equations of resistive magnetohydrodynamics (MHD) are recast in a form that is useful for studying the evolution of those toroidal systems where the fast magnetosonic wave plays no important role. The equations are exact and have nabla vector.B vector = O satisfied explicitly. From this set of equations it is a simple matter to derive the equations of reduced MHD to any order in the inverse aspect ratio epsilon of the torus, and for β approx. epsilon or smaller. We demonstrate this by deriving a reduced set of MHD equations that are correct to 5th order in epsilon. These equations contain the exact equilibrium relation and as such can be used to find 3-D stellarator equilibria. In addition, if a subsidiary ordering in eta, the resistivity, is made, the equations of Glasser, Greene, and Johnson are recovered. This set of reduced equations has been coded by extending the initial value code, HILO. Results obtained, for both ideal and resistive linear stability, from the reduced equations are compared with those obtained by solving the full set of MHD equations in a cylinder. The agreement is shown to be excellent for both zero and finite beta calculations. Comparisons are also made with analytic theory illuminating the present limitations of the latter

Deriving Langevin equations in curved spacetime

International Nuclear Information System (INIS)

Ramos, Rudnei O.; Tavares, Romulo F.

2013-01-01

Full text: Warm inflation is an inflationary scenario where the interactions between the inflaton and other degrees of freedom are considered. The effective equation of motion for the inflaton is in general of the form of a Langevin equation, that includes both quantum and thermal effects and where these effects manifest in the form of dissipation and stochastic noise terms, which are related by a generalized fluctuation-dissipation relation. The dissipation term is related to the interactions of the inflaton with other degrees of freedom of the thermal bath that can be obtained from the appropriate Feynman propagators. As the inflaton evolves into an expanding metric, these effects have to be taken into account when calculating the Green functions and consequently the Feynman propagators. In this work we present the considerations that must be made to calculate the Green functions in curved space (expanding metric) and in the presence of radiation in order to proper derive the effective evolution of the inflaton in the warm-inflation scenario. (author)

Oscillation results for certain fractional difference equations

Directory of Open Access Journals (Sweden)

Zhiyun WANG

2017-08-01

Full Text Available Fractional calculus is a theory that studies the properties and application of arbitrary order differentiation and integration. It can describe the physical properties of some systems more accurately, and better adapt to changes in the system, playing an important role in many fields. For example, it can describe the process of tumor growth (growth stimulation and growth inhibition in biomedical science. The oscillation of solutions of two kinds of fractional difference equations is studied, mainly using the proof by contradiction, that is, assuming the equation has a nonstationary solution. For the first kind of equation, the function symbol is firstly determined, and by constructing the Riccati function, the difference is calculated. Then the condition of the function is used to satisfy the contradiction, that is, the assumption is false, which verifies the oscillation of the solution. For the second kind of equation with initial condition, the equivalent fractional sum form of the fractional difference equation are firstly proved. With considering 0<α≤1 and α>1, respectively, by using the properties of Stirling formula and factorial function, the contradictory is got through enhanced processing, namely the assuming is not established, and the sufficient condition for the bounded solutions of the fractional difference equation is obtained. The above results will optimize the relevant conclusions and enrich the relevant results. The results are applied to the specific equations, and the oscillation of the solutions of equations is proved.

Calculation of conventional and prompt lepton fluxes at very high energy

Directory of Open Access Journals (Sweden)

Fedynitch Anatoli

2015-01-01

Full Text Available An efficient method for calculating inclusive conventional and prompt atmospheric leptons fluxes is presented. The coupled cascade equations are solved numerically by formulating them as matrix equation. The presented approach is very flexible and allows the use of different hadronic interaction models, realistic parametrizations of the primary cosmic-ray flux and the Earth's atmosphere, and a detailed treatment of particle interactions and decays. The power of the developed method is illustrated by calculating lepton flux predictions for a number of different scenarios.

Monte Carlo calculations of the elastic moduli and pressure-volume-temperature equation of state for hexahydro-1,3,5-trinitro-1,3,5-triazine

International Nuclear Information System (INIS)

Sewell, Thomas D.; Bennett, Carl M.

2000-01-01

Isothermal-isobaric Monte Carlo calculations were used to obtain predictions of the elastic coefficients and derived engineering moduli and Poisson ratios for crystalline hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX). The elastic coefficients were computed using the strain fluctuation formula due to Rahman and Parrinello [J. Chem. Phys. 76, 2662 (1982)]. Calculations were performed as a function of temperature (218 K≤T≤333 K) and hydrostatic pressure (0 GPa≤p≤4 GPa). The predicted values of the moduli and Poisson ratios under ambient conditions are in accord with general expectations for molecular crystals and with a very recent, unpublished determination for RDX. The moduli exhibit a sensitive pressure dependence whereas the Poisson ratios are relatively independent of pressure. The temperature dependence of the moduli is comparable to the precision of the results. However, the crystal does exhibit thermal softening for most pressures. An additional product of the calculations is information about the pressure-volume-temperature (pVT) equation of state. We obtain near-quantitative agreement with experiment for the case of hydrostatic compression and reasonable, but not quantitative, correspondence for thermal expansion. The results indicate a significant dependence of the thermal expansion coefficients on hydrostatic pressure. (c) 2000 American Institute of Physics

One-dimensional calculation of flow branching using the method of characteristics

International Nuclear Information System (INIS)

Meier, R.W.; Gido, R.G.

1978-05-01

In one-dimensional flow systems, the flow often branches, such as at a tee or manifold. The study develops a formulation for calculating the flow through branch points with one-dimensional method of characteristics equations. The resultant equations were verified by comparison with experimental measurements

Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation

Science.gov (United States)

Poleshkin, Sergey O.; Malkov, Ewgenij A.; Kudryavtsev, Alexey N.; Shershnev, Anton A.; Bondar, Yevgeniy A.; Kohanchik, A. A.

2017-10-01

There are various methods for calculating rarefied gas flows, in particular, statistical methods and deterministic methods based on the finite-difference solutions of the Boltzmann nonlinear kinetic equation and on the solutions of model kinetic equations. There is no universal method; each has its disadvantages in terms of efficiency or accuracy. The choice of the method depends on the problem to be solved and on parameters of calculated flows. Qualitative theoretical arguments help to determine the range of parameters of effectively solved problems for each method; however, it is advisable to perform comparative tests of calculations of the classical problems performed by different methods and with different parameters to have quantitative confirmation of this reasoning. The paper provides the results of the calculations performed by the authors with the help of the Direct Simulation Monte Carlo method and finite-difference methods of solving the Boltzmann equation and model kinetic equations. Based on this comparison, conclusions are made on selecting a particular method for flow simulations in various ranges of flow parameters.

Relativistic quasiparticle random-phase approximation calculation of total muon capture rates

International Nuclear Information System (INIS)

Marketin, T.; Paar, N.; Niksic, T.; Vretenar, D.

2009-01-01

The relativistic proton-neutron quasiparticle random phase approximation (pn-RQRPA) is applied in the calculation of total muon capture rates on a large set of nuclei from 12 C to 244 Pu, for which experimental values are available. The microscopic theoretical framework is based on the relativistic Hartree-Bogoliubov (RHB) model for the nuclear ground state, and transitions to excited states are calculated using the pn-RQRPA. The calculation is fully consistent, i.e., the same interactions are used both in the RHB equations that determine the quasiparticle basis, and in the matrix equations of the pn-RQRPA. The calculated capture rates are sensitive to the in-medium quenching of the axial-vector coupling constant. By reducing this constant from its free-nucleon value g A =1.262 by 10% for all multipole transitions, the calculation reproduces the experimental muon capture rates to better than 10% accuracy.

Newnes circuit calculations pocket book with computer programs

CERN Document Server

Davies, Thomas J

2013-01-01

Newnes Circuit Calculations Pocket Book: With Computer Programs presents equations, examples, and problems in circuit calculations. The text includes 300 computer programs that help solve the problems presented. The book is comprised of 20 chapters that tackle different aspects of circuit calculation. The coverage of the text includes dc voltage, dc circuits, and network theorems. The book also covers oscillators, phasors, and transformers. The text will be useful to electrical engineers and other professionals whose work involves electronic circuitry.

Method of characteristics - Based sensitivity calculations for international PWR benchmark

International Nuclear Information System (INIS)

Suslov, I. R.; Tormyshev, I. V.; Komlev, O. G.

2013-01-01

Method to calculate sensitivity of fractional-linear neutron flux functionals to transport equation coefficients is proposed. Implementation of the method on the basis of MOC code MCCG3D is developed. Sensitivity calculations for fission intensity for international PWR benchmark are performed. (authors)

Calculation and analysis of thermal–hydraulics fluctuations in pressurized water reactors

International Nuclear Information System (INIS)

Malmir, Hessam; Vosoughi, Naser

2015-01-01

Highlights: • Single-phase thermal–hydraulics noise equations are originally derived in the frequency domain. • The fluctuations of all the coolant parameters are calculated, without any simplifying assumptions. • The radial distribution of the temperature fluctuations in the fuel, gap and cladding are taken into account. • The closed-loop calculations are performed by means of the point kinetics noise theory. • Both the space- and frequency-dependence of the thermal–hydraulics fluctuations are analyzed. - Abstract: Analysis of thermal–hydraulics fluctuations in pressurized water reactors (e.g., local and global temperature or density fluctuations, as well as primary and charging pumps fluctuations) has various applications in calculation or measurement of the core dynamical parameters (temperature or density reactivity coefficients) in addition to thermal–hydraulics surveillance and diagnostics. In this paper, the thermal–hydraulics fluctuations in PWRs are investigated. At first, the single-phase thermal–hydraulics noise equations (in the frequency domain) are originally derived, without any simplifying assumptions. The fluctuations of all the coolant parameters, as well as the radial distribution of the temperature fluctuations in the fuel, gap and cladding are taken into account. Then, the derived governing equations are discretized using the finite volume method (FVM). Based on the discretized equations and the proposed algorithm of solving, a single heated channel noise calculation code (SHC-Noise) is developed, by which the steady-state and fluctuating parameters of PWR fuel assemblies can be calculated. The noise sources include the inlet coolant temperature and velocity fluctuations, in addition to the power density noises. The developed SHC-Noise code is benchmarked in different cases and scenarios. Furthermore, to show the effects of the power feedbacks, the closed-loop calculations are performed by means of the point kinetics noise

Multi-Center Electronic Structure Calculations for Plasma Equation of State

Energy Technology Data Exchange (ETDEWEB)

Wilson, B G; Johnson, D D; Alam, A

2010-12-14

We report on an approach for computing electronic structure utilizing solid-state multi-center scattering techniques, but generalized to finite temperatures to model plasmas. This approach has the advantage of handling mixtures at a fundamental level without the imposition of ad hoc continuum lowering models, and incorporates bonding and charge exchange, as well as multi-center effects in the calculation of the continuum density of states.

Dosimetric impact of Acuros XB deterministic radiation transport algorithm for heterogeneous dose calculation in lung cancer

International Nuclear Information System (INIS)

Han Tao; Followill, David; Repchak, Roman; Molineu, Andrea; Howell, Rebecca; Salehpour, Mohammad; Mikell, Justin; Mourtada, Firas

2013-01-01

Purpose: The novel deterministic radiation transport algorithm, Acuros XB (AXB), has shown great potential for accurate heterogeneous dose calculation. However, the clinical impact between AXB and other currently used algorithms still needs to be elucidated for translation between these algorithms. The purpose of this study was to investigate the impact of AXB for heterogeneous dose calculation in lung cancer for intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT). Methods: The thorax phantom from the Radiological Physics Center (RPC) was used for this study. IMRT and VMAT plans were created for the phantom in the Eclipse 11.0 treatment planning system. Each plan was delivered to the phantom three times using a Varian Clinac iX linear accelerator to ensure reproducibility. Thermoluminescent dosimeters (TLDs) and Gafchromic EBT2 film were placed inside the phantom to measure delivered doses. The measurements were compared with dose calculations from AXB 11.0.21 and the anisotropic analytical algorithm (AAA) 11.0.21. Two dose reporting modes of AXB, dose-to-medium in medium (D m,m ) and dose-to-water in medium (D w,m ), were studied. Point doses, dose profiles, and gamma analysis were used to quantify the agreement between measurements and calculations from both AXB and AAA. The computation times for AAA and AXB were also evaluated. Results: For the RPC lung phantom, AAA and AXB dose predictions were found in good agreement to TLD and film measurements for both IMRT and VMAT plans. TLD dose predictions were within 0.4%–4.4% to AXB doses (both D m,m and D w,m ); and within 2.5%–6.4% to AAA doses, respectively. For the film comparisons, the gamma indexes (±3%/3 mm criteria) were 94%, 97%, and 98% for AAA, AXB Dm,m , and AXB Dw,m , respectively. The differences between AXB and AAA in dose–volume histogram mean doses were within 2% in the planning target volume, lung, heart, and within 5% in the spinal cord. However

A modified SOR method for the Poisson equation in unsteady free-surface flow calculations.

NARCIS (Netherlands)

Botta, E.F.F.; Ellenbroek, Marcellinus Hermannus Maria

1985-01-01

Convergence difficulties that sometimes occur if the successive overrelaxation (SOR) method is applied to the Poisson equation on a region with irregular free boundaries are analyzed. It is shown that these difficulties are related to the treatment of the free boundaries and caused by the appearance

Derivation of a new kinetic equation. Application to the determination of viscosity coefficients

International Nuclear Information System (INIS)

Frey, Jean-Jacques

1970-01-01

By introducing a new hypothesis concerning the closure in the B.B.G.K.Y. equation system, an approximate expression for f 12 is obtained. By inserting this expression in the first B.B.G.K.Y. equation, a new kinetic equation results. It is verified that this equation does in fact give the fluid mechanics equations, and new expressions for the shear and expansion viscosity coefficients are obtained. The numerical calculations which have been carried out show that very satisfactory agreement exists with experimental results. (author) [fr

Three-dimensional space-charge calculation method

International Nuclear Information System (INIS)

Lysenko, W.P.; Wadlinger, E.A.

1980-09-01

A method is presented for calculating space-charge forces on individual particles in a particle tracing simulation code. Poisson's equation is solved in three dimensions with boundary conditions specified on an arbitrary surface. When the boundary condition is defined by an impressed radio-frequency field, the external electric fields as well as the space-charge fields are determined. A least squares fitting procedure is used to calculate the coefficients of expansion functions, which need not be orthogonal nor individually satisfy the boundary condition

A method to calculate spatial xenon oscillations in PWR reactors

International Nuclear Information System (INIS)

Ronig, H.

1976-01-01

The new digital computer programme SEXI for the calculation of spatial Xe oscillations is described. A series expansion of the flux density and the particle densities following the geometrical eigenfunctions of a homogeneous block reactor is chosen as an approach to the solution of the system of differential equations describing this feedback process between neutron flux density and Xe particle density. To calculate the neutron flux density, the time-dependent form of the diffusion equation is used instead of the more common stationary form. Integration is carried out using formal time differential quotients of the Fourier coefficients. (orig./RW) [de

Three-dimensional static and dynamic reactor calculations by the nodal expansion method

International Nuclear Information System (INIS)

Christensen, B.

1985-05-01

This report reviews various method for the calculation of the neutron-flux- and power distribution in an nuclear reactor. The nodal expansion method (NEM) is especially described in much detail. The nodal expansion method solves the diffusion equation. In this method the reactor core is divided into nodes, typically 10 to 20 cm in each direction, and the average flux in each node is calculated. To obtain the coupling between the nodes the local flux inside each node is expressed by use of a polynomial expansion. The expansion is one-dimensional, so inside each node such three expansions occur. To calculate the expansion coefficients it is necessary that the polynomial expansion is a solution to the one-dimensional diffusion equation. When the one-dimensional diffusion equation is established a term with the transversal leakage occur, and this term is expanded after the same polynomials. The resulting equation system with the expansion coefficients as the unknowns is solved with weigthed residual technique. The nodal expansion method is built into a computer program (also called NEM), which is divided into two parts, one part for steady-state calculations and one part for dynamic calculations. It is possible to take advantage of symmetry properties of the reactor core. The program is very flexible with regard to the number of energy groups, the node size, the flux expansion order and the transverse leakage expansion order. The boundary of the core is described by albedos. The program and input to it are described. The program is tested on a number of examples extending from small theoretical one up to realistic reactor cores. Many calculations are done on the wellknown IAEA benchmark case. The calculations have tested the accuracy and the computing time for various node sizes and polynomial expansions. In the dynamic examples various strategies for variation of the time step-length have been tested. (author)

Solution of 3-dimensional diffusion equation by finite Fourier transformation

International Nuclear Information System (INIS)

Krishnani, P.D.

1978-01-01

Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)

Parallel processing of neutron transport in fuel assembly calculation

International Nuclear Information System (INIS)

Song, Jae Seung

1992-02-01

Group constants, which are used for reactor analyses by nodal method, are generated by fuel assembly calculations based on the neutron transport theory, since one or a quarter of the fuel assembly corresponds to a unit mesh in the current nodal calculation. The group constant calculation for a fuel assembly is performed through spectrum calculations, a two-dimensional fuel assembly calculation, and depletion calculations. The purpose of this study is to develop a parallel algorithm to be used in a parallel processor for the fuel assembly calculation and the depletion calculations of the group constant generation. A serial program, which solves the neutron integral transport equation using the transmission probability method and the linear depletion equation, was prepared and verified by a benchmark calculation. Small changes from the serial program was enough to parallelize the depletion calculation which has inherent parallel characteristics. In the fuel assembly calculation, however, efficient parallelization is not simple and easy because of the many coupling parameters in the calculation and data communications among CPU's. In this study, the group distribution method is introduced for the parallel processing of the fuel assembly calculation to minimize the data communications. The parallel processing was performed on Quadputer with 4 CPU's operating in NURAD Lab. at KAIST. Efficiencies of 54.3 % and 78.0 % were obtained in the fuel assembly calculation and depletion calculation, respectively, which lead to the overall speedup of about 2.5. As a result, it is concluded that the computing time consumed for the group constant generation can be easily reduced by parallel processing on the parallel computer with small size CPU's

Osmotic potential calculations of inorganic and organic aqueous solutions over wide solute concentration levels and temperatures

Energy Technology Data Exchange (ETDEWEB)

Cochrane, T. T., E-mail: agteca@hotmail.com [AGTECA S.A., 230 Oceanbeach Road, Mount Maunganui, Tauranga 3116 (New Zealand); Cochrane, T. A., E-mail: tom.cochrane@canterbury.ac.nz [Department of Civil and Natural Resources Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140 (New Zealand)

2016-01-15

Purpose: To demonstrate that the authors’ new “aqueous solution vs pure water” equation to calculate osmotic potential may be used to calculate the osmotic potentials of inorganic and organic aqueous solutions over wide ranges of solute concentrations and temperatures. Currently, the osmotic potentials of solutions used for medical purposes are calculated from equations based on the thermodynamics of the gas laws which are only accurate at low temperature and solute concentration levels. Some solutions used in medicine may need their osmotic potentials calculated more accurately to take into account solute concentrations and temperatures. Methods: The authors experimented with their new equation for calculating the osmotic potentials of inorganic and organic aqueous solutions up to and beyond body temperatures by adjusting three of its factors; (a) the volume property of pure water, (b) the number of “free” water molecules per unit volume of solution, “N{sub f},” and (c) the “t” factor expressing the cooperative structural relaxation time of pure water at given temperatures. Adequate information on the volume property of pure water at different temperatures is available in the literature. However, as little information on the relative densities of inorganic and organic solutions, respectively, at varying temperatures needed to calculate N{sub f} was available, provisional equations were formulated to approximate values. Those values together with tentative t values for different temperatures chosen from values calculated by different workers were substituted into the authors’ equation to demonstrate how osmotic potentials could be estimated over temperatures up to and beyond bodily temperatures. Results: The provisional equations formulated to calculate N{sub f}, the number of free water molecules per unit volume of inorganic and organic solute solutions, respectively, over wide concentration ranges compared well with the calculations of N{sub f

Osmotic potential calculations of inorganic and organic aqueous solutions over wide solute concentration levels and temperatures

International Nuclear Information System (INIS)

Cochrane, T. T.; Cochrane, T. A.

2016-01-01

Purpose: To demonstrate that the authors’ new “aqueous solution vs pure water” equation to calculate osmotic potential may be used to calculate the osmotic potentials of inorganic and organic aqueous solutions over wide ranges of solute concentrations and temperatures. Currently, the osmotic potentials of solutions used for medical purposes are calculated from equations based on the thermodynamics of the gas laws which are only accurate at low temperature and solute concentration levels. Some solutions used in medicine may need their osmotic potentials calculated more accurately to take into account solute concentrations and temperatures. Methods: The authors experimented with their new equation for calculating the osmotic potentials of inorganic and organic aqueous solutions up to and beyond body temperatures by adjusting three of its factors; (a) the volume property of pure water, (b) the number of “free” water molecules per unit volume of solution, “N f ,” and (c) the “t” factor expressing the cooperative structural relaxation time of pure water at given temperatures. Adequate information on the volume property of pure water at different temperatures is available in the literature. However, as little information on the relative densities of inorganic and organic solutions, respectively, at varying temperatures needed to calculate N f was available, provisional equations were formulated to approximate values. Those values together with tentative t values for different temperatures chosen from values calculated by different workers were substituted into the authors’ equation to demonstrate how osmotic potentials could be estimated over temperatures up to and beyond bodily temperatures. Results: The provisional equations formulated to calculate N f , the number of free water molecules per unit volume of inorganic and organic solute solutions, respectively, over wide concentration ranges compared well with the calculations of N f using recorded

Tegen - an onedimensional program to calculate a thermoelectric generator

International Nuclear Information System (INIS)

Rosa, M.A.P.; Ferreira, P.A.; Castro Lobo, P.D. de.

1990-01-01

A computer program for the solution of the one-dimensional, steady-state temperature equation in the arms of a thermoelectric generator. The discretized equations obtained through a finite difference scheme are solved by Gaussian Elimination. Due to nonlinearities caused by the temperature dependence of the coefficients of such equations, an iterative procedure is used to obtain the temperature distribution in the arms. Such distributions are used in the calculation of the efficiency, electric power, load voltage and other relevant parameters for the design of a thermoelectric generator. (author)

Precise calculation of the energies of heavy hydrogenlike ions

International Nuclear Information System (INIS)

Driker, M.N.; Ivanova, E.P.; Ivanov, L.N.

1983-01-01

Energies of the 1s, 2s, and 2p states are calculated for hydrogenlike ions with z = 30--170. The calculation is based on Dirac's equation taking into account radiation effects and the finiteness of the nucleus. The hyperfine splitting constants are calculated taking the finiteness of the nucleus into account, and derivatives are taken with respect to the volume of the nucleus for all S-state characteristics

Novel method for solution of coupled radial Schrödinger equations

International Nuclear Information System (INIS)

Ershov, S. N.; Vaagen, J. S.; Zhukov, M. V.

2011-01-01

One of the major problems in numerical solution of coupled differential equations is the maintenance of linear independence for different sets of solution vectors. A novel method for solution of radial Schrödinger equations is suggested. It consists of rearrangement of coupled equations in a way that is appropriate to avoid usual numerical instabilities associated with components of the wave function in their classically forbidden regions. Applications of the new method for nuclear structure calculations within the hyperspherical harmonics approach are given.

A drainage data-based calculation method for coalbed permeability

International Nuclear Information System (INIS)

Lai, Feng-peng; Li, Zhi-ping; Fu, Ying-kun; Yang, Zhi-hao

2013-01-01

This paper establishes a drainage data-based calculation method for coalbed permeability. The method combines material balance and production equations. We use a material balance equation to derive the average pressure of the coalbed in the production process. The dimensionless water production index is introduced into the production equation for the water production stage. In the subsequent stage, which uses both gas and water, the gas and water production ratio is introduced to eliminate the effect of flush-flow radius, skin factor, and other uncertain factors in the calculation of coalbed methane permeability. The relationship between permeability and surface cumulative liquid production can be described as a single-variable cubic equation by derivation. The trend shows that the permeability initially declines and then increases after ten wells in the southern Qinshui coalbed methane field. The results show an exponential relationship between permeability and cumulative water production. The relationship between permeability and cumulative gas production is represented by a linear curve and that between permeability and surface cumulative liquid production is represented by a cubic polynomial curve. The regression result of the permeability and surface cumulative liquid production agrees with the theoretical mathematical relationship. (paper)

Internal Dosimetric Calculations for Occupationally Exposed Workers

International Nuclear Information System (INIS)

Hussein, M.T.; Farag, H.I.

2005-01-01

The Internal radiation dosimetry calculations are very important to estimate the benefit and the risk of radiation in nuclear medicine field for both patient and worker. MIRD scheme and ICRP model have valid methods in this type of calculations. In this work, a new program called WIRDST the Workers Internal Radiation Dosimetry Simulation for Thyroid gland has been built up by using the Monte Carlo (MC) method to simulate the internal exposure of sodium iodide by inhalation for workers. The working conditions have been taken as the same as found in the hot laboratory of nuclear medicine unit in the National Cancer Institute in Cairo University. The point source equivalent model as a parameterization equation has developed newly by using the fitting model of MC method for uniform distribution of radioactive sodium iodide in the thyroid gland. This model is used for the first time in this type of calculation, and then applied on 3 D coordinates of mathematical geometry for the adult phantom of the reference man. The latest parameters (anatomical data and inhalation metabolic data) of ICRP pamphlets and recommendations have been used in this purpose. Moreover, the latest scheme for iodine decay mode and the latest geometry model for thyroid gland are used also. The results showed that the specific effective energy and the effective dose decrease from the thyroid gland to the nearest organs then decrease gradually until terminated in the organs that have large distance from the thyroid. The Annual Limit of Intake (ALI) has been calculated for a wide range of thyroid uptake (5%, 15%, 25%, 35%, 45%, and 55%) in addition to change of the working time order per week in one year. The results showed that the critical point of intake limits are decreased when the thyroid uptake is increased and/or the number of working time in the hot laboratory per week is increased

Calculation of afterbody flows with a composite velocity formulation

Science.gov (United States)

Swanson, R. C.; Rubin, S. G.; Khosla, P. K.

1983-01-01

A recently developed technique for numerical solution of the Navier-Stokes equations for subsonic, laminar flows is investigated. It is extended here to allow for the computation of transonic and turbulent flows. The basic approach involves a multiplicative composite of the appropriate velocity representations for the inviscid and viscous flow regions. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli equation for the pressure, while the continuity equation reduces to the familiar potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary layers. The velocity components are computed with a coupled strongly implicity procedure. For transonic flows the artificial compressibility method is used to treat supersonic regions. Calculations are made for both laminar and turbulent flows over axisymmetric afterbody configurations. Present results compare favorably with other numerical solutions and/or experimental data.

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

Science.gov (United States)

Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

2013-09-01

Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

DRAGON 3.05D, Reactor Cell Calculation System with Burnup

International Nuclear Information System (INIS)

2007-01-01

1 - Description of program or function: The computer code DRAGON contains a collection of models that can simulate the neutron behavior of a unit cell or a fuel assembly in a nuclear reactor. It includes all of the functions that characterize a lattice cell code, namely: the interpolation of microscopic cross sections supplied by means of standard libraries; resonance self-shielding calculations in multidimensional geometries; multigroup and multidimensional neutron flux calculations that can take into account neutron leakage; transport-transport or transport-diffusion equivalence calculations as well as editing of condensed and homogenized nuclear properties for reactor calculations; and finally isotopic depletion calculations. 2 - Methods: The code DRAGON contains a multigroup flux solver conceived that can use a various algorithms to solve the neutron transport equation for the spatial and angular distribution of the flux. Each of these algorithms is presented in the form of a one-group solution procedure where the contributions from other energy groups are considered as sources. The current release of DRAGON contains five such algorithms. The JPM option that solves the integral transport equation using the J+- method, (interface current method applied to homogeneous blocks); the SYBIL option that solves the integral transport equation using the collision probability method for simple one dimensional (1-D) or two dimensional (2-D) geometries and the interface current method for 2-D Cartesian or hexagonal assemblies; the EXCELL/NXT option to solve the integral transport equation using the collision probability method for more general 2-D geometries and for three dimensional (3-D) assemblies; the MOCC option to solve the transport equation using the method of cyclic characteristics in 2-D Cartesian, and finally the MCU option to solve the transport equation using the method of characteristics (non cyclic) for 3-D Cartesian geometries. The execution of DRAGON is

Simulation of lung cancer treatment with equivalent dose calculation and analysis of the dose distribution profile

International Nuclear Information System (INIS)

Thalhofer, J. L.; Marques L, J.; Da Silva, A. X.; Dos Reis J, J. P.; Da Silva J, W. F. R.; Arruda C, S. C.; Monteiro de S, E.; Santos B, D. V.

2017-10-01

Actually, lung cancer is one of the most lethal types, due to the disease in the majority of the cases asymptomatic in the early stages, being the detection of the pathology in advanced stage, with tumor considerable volume. Dosimetry analysis of healthy organs under real conditions is not feasible. Therefore, computational simulations are used to auxiliary in dose verification in organs of patients submitted to radiotherapy. The goal of this study is to calculate the equivalent dose, due to photons, in surrounding in healthy organs of a patient submitted to radiotherapy for lung cancer, through computational modeling. The simulation was performed using the MCNPX code (Version, 2006], Rex and Regina phantom [ICRP 110, 2008], radiotherapy room, Siemens Oncor Expression accelerator operating at 6 MV and treatment protocol adopted at the Inca (National Cancer Institute, Brazil). The results obtained, considering the dose due to photons for both phantom indicate that organs located inside the thoracic cavity received higher dose, being the bronchi, heart and esophagus more affected, due to the anatomical positioning. Clinical data describe the development of bronchiolitis, esophagitis, and cardiomyopathies with decreased cardiopulmonary function as one of the major effects of lung cancer treatment. In the Regina phantom, the second largest dose was in the region of the breasts with 615,73 mSv / Gy, while in the Rex 514,06 mSv / Gy, event related to the difference of anatomical structure of the organ. Through the t mesh command, a qualitative analysis was performed between the dose deposition profile of the planning system and the simulated treatment, with a similar profile of the dose distribution being verified along the patients body. (Author)

An Implementation of Interfacial Transport Equation into the CUPID code

Energy Technology Data Exchange (ETDEWEB)

Park, Ik Kyu; Cho, Heong Kyu; Yoon, Han Young; Jeong, Jae Jun

2009-11-15

A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components for a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted a three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAS, semi-implicit ICE, SIMPLE. The governing equations for a 2-phase flow are composed of mass, momentum, and energy conservation equations for each phase. These equation sets are closed by the interfacial transfer rate of mass, momentum, and energy. The interfacial transfer of mass, momentum, and energy occurs through the interfacial area, and this area plays an important role in the transfer rate. The flow regime based correlations are used for calculating the interracial area in the traditional style 2-phase flow model. This is dependent upon the flow regime and is limited to the fully developed 2-phase flow region. Its application to the multi-dimensional 2-phase flow has some limitation because it adopts the measured results of 2-phase flow in the 1-dimensional tube. The interfacial area concentration transport equation had been suggested in order to calculate the interfacial area without the interfacial area correlations. The source terms to close the interfacial area transport equation should be further developed for a wide ranger usage of it. In this study, the one group interfacial area concentration transport equation has been implemented into the CUPID code. This interfacial area concentration transport equation can be used instead of the interfacial area concentration correlations for the bubbly flow region.

An Implementation of Interfacial Transport Equation into the CUPID code

International Nuclear Information System (INIS)

Park, Ik Kyu; Cho, Heong Kyu; Yoon, Han Young; Jeong, Jae Jun

2009-11-01

A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components for a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted a three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAS, semi-implicit ICE, SIMPLE. The governing equations for a 2-phase flow are composed of mass, momentum, and energy conservation equations for each phase. These equation sets are closed by the interfacial transfer rate of mass, momentum, and energy. The interfacial transfer of mass, momentum, and energy occurs through the interfacial area, and this area plays an important role in the transfer rate. The flow regime based correlations are used for calculating the interracial area in the traditional style 2-phase flow model. This is dependent upon the flow regime and is limited to the fully developed 2-phase flow region. Its application to the multi-dimensional 2-phase flow has some limitation because it adopts the measured results of 2-phase flow in the 1-dimensional tube. The interfacial area concentration transport equation had been suggested in order to calculate the interfacial area without the interfacial area correlations. The source terms to close the interfacial area transport equation should be further developed for a wide ranger usage of it. In this study, the one group interfacial area concentration transport equation has been implemented into the CUPID code. This interfacial area concentration transport equation can be used instead of the interfacial area concentration correlations for the bubbly flow region

KINETIC-J: A computational kernel for solving the linearized Vlasov equation applied to calculations of the kinetic, configuration space plasma current for time harmonic wave electric fields

Science.gov (United States)

Green, David L.; Berry, Lee A.; Simpson, Adam B.; Younkin, Timothy R.

2018-04-01

We present the KINETIC-J code, a computational kernel for evaluating the linearized Vlasov equation with application to calculating the kinetic plasma response (current) to an applied time harmonic wave electric field. This code addresses the need for a configuration space evaluation of the plasma current to enable kinetic full-wave solvers for waves in hot plasmas to move beyond the limitations of the traditional Fourier spectral methods. We benchmark the kernel via comparison with the standard k →-space forms of the hot plasma conductivity tensor.

Calculation of reactivity using a finite impulse response filter

Energy Technology Data Exchange (ETDEWEB)

Suescun Diaz, Daniel [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, CEP 21941-914, RJ (Brazil); Senra Martinez, Aquilino [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, CEP 21941-914, RJ (Brazil)], E-mail: aquilino@lmp.ufrj.br; Carvalho Da Silva, Fernando [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, CEP 21941-914, RJ (Brazil)

2008-03-15

A new formulation is presented in this paper to solve the inverse kinetics equation. This method is based on the Laplace transform of the point kinetics equations, resulting in an expression equivalent to the inverse kinetics equation as a function of the power history. Reactivity can be written in terms of the summation of convolution with response to impulse, characteristic of a linear system. For its digital form the Z-transform is used, which is the discrete version of the Laplace transform. This new method of reactivity calculation has very special features, amongst which it can be pointed out that the linear part is characterized by a filter named finite impulse response (FIR). The FIR filter will always be, stable and non-varying in time, and, apart from this, it can be implemented in the non-recursive form. This type of implementation does not require feedback, allowing the calculation of reactivity in a continuous way.

Summary of transient high-voltage calculations for the FRX-C experiment

International Nuclear Information System (INIS)

Kewish, R.W. Jr.; Rej, D.J.

1982-06-01

Calculations of the electrical circuit equations are performed over a wide range of parameters corresponding to the FRX-C field-reversed THETA-pinch experiment at Los Alamos. Without any plasma or external damping, serious voltage doubling and quadrupling of the main capacitor bank charge voltage are observed. These oscillating high voltages are found to be adequately suppressed by the strategic placement of external snubber circuitry. On the other hand, no doubling of the THETA-pinch preionization bank charge voltage is found. Calculations of the equations for the z-pinch preionization circuit are also performed

The Poisson equation at second order in relativistic cosmology

International Nuclear Information System (INIS)

Hidalgo, J.C.; Christopherson, Adam J.; Malik, Karim A.

2013-01-01

We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field

Fokker-Planck equation resolution for N variables-Application examples

International Nuclear Information System (INIS)

Munoz Roldan, A.; Garcia-Olivares, A.

1994-01-01

A set of problems which are reducible to Fokker-Planck equations are presented. Those problems have been solved by using the CHAPKOL library. This library of programs solves stochastic ''Fokker-Planck'' equations in one or several dimensions by using the Chapman-Kolmogorov integral. This method calculates the probability distribution at a time t+dt from a distribution given at time t through a convolution integral in which the integrant is the product of the distribution function at time t and the Green function of the Fokker-Planck equation. The method have some numerical advantages when compared with finite differences algorithms. The accuracy of the method is analysed in several specific cases

Implementation of an implicit method into heat conduction calculation of TRAC-PF1/MOD2 code

International Nuclear Information System (INIS)

Akimoto, Hajime; Abe, Yutaka; Ohnuki, Akira; Murao, Yoshio

1990-08-01

A two-dimensional unsteady heat conduction equation is solved in the TRAC-PF/MOD2 code to calculate temperature transients in fuel rod. A large CPU time is often required to get stable solution of temperature transients in the TRAC calculation with a small axial node size (less than 1.0 mm), because the heat conduction equation is discretized explicitly. To eliminate the restriction of the maximum time step size by the heat conduction calculation, an implicit method for solving the heat condition equation was developed and implemented into the TRAC code. Several assessment calculations were performed with the original and modified TRAC codes. It is confirmed that the implicit method is reliable and is successfully implemented into the TRAC code through comparison with theoretical solutions and assessment calculation results. It is demonstrated that the implicit method makes the heat conduction calculation practical even for the analyses of temperature transients with the axial node size less than 0.1 mm. (author)

DRAGON, Reactor Cell Calculation System with Burnup

International Nuclear Information System (INIS)

2007-01-01

1 - Description of program or function: DRAGON is a collection of models to simulate the neutronic behavior of a unit cell or a fuel assembly in a nuclear reactor. It includes all of the functions that characterize a lattice cell code, namely: interpolation of microscopic cross sections supplied by means of standard libraries; resonance self-shielding calculations in multidimensional geometries; multigroup and multidimensional neutron flux calculations which can take into account neutron leakage; transport-transport or transport-diffusion equivalence calculations as well as editing of condensed and homogenized nuclear properties for reactor calculations; and finally isotopic depletion calculations. The user must supply cross sections. DRAGON can access directly standard microscopic cross-section libraries in the following formats: DRAGON, MATXS (TRANSX-CTR), WIMSD4, WIMS-AECL, and APOLLO. It has the capability of exchanging macroscopic and microscopic cross-section libraries with a code such as PSR-0206/TRANSX-CTR or PSR-0317/TRANSX-2 by the use of the GOXS and ISOTXS format files. Macroscopic cross sections can also be read in DRAGON via the input data stream. 2 - Method of solution: DRAGON contains a multigroup iterator conceived to control a number of different algorithms for the solution of the neutron transport equation. Each of these algorithms is presented in the form of a one-group solution procedure where the contributions from other energy groups are included in a source term. The current version, DRAGON 9 71124 (Release 3.02), which was released in January 1998, contains three such algorithms. The JPM option solves the integral transport equation using the interface current method applied to homogeneous blocks; the SYBIL option solves the integral transport equation using the collision probability method for simple one-dimensional (1-D) or two-dimensional (2-D) geometries and the interface current method for 2-D Cartesian or hexagonal assemblies; and the

Introduction to the Yang-Baxter Equation with Open Problems

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